/* Common base code for the decNumber C Library.
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/* Common base code for the decNumber C Library.
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Copyright (C) 2007 Free Software Foundation, Inc.
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Copyright (C) 2007 Free Software Foundation, Inc.
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Contributed by IBM Corporation. Author Mike Cowlishaw.
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Contributed by IBM Corporation. Author Mike Cowlishaw.
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This file is part of GCC.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 2, or (at your option) any later
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Software Foundation; either version 2, or (at your option) any later
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version.
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version.
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In addition to the permissions in the GNU General Public License,
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In addition to the permissions in the GNU General Public License,
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the Free Software Foundation gives you unlimited permission to link
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the Free Software Foundation gives you unlimited permission to link
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the compiled version of this file into combinations with other
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the compiled version of this file into combinations with other
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programs, and to distribute those combinations without any
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programs, and to distribute those combinations without any
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restriction coming from the use of this file. (The General Public
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restriction coming from the use of this file. (The General Public
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License restrictions do apply in other respects; for example, they
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License restrictions do apply in other respects; for example, they
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cover modification of the file, and distribution when not linked
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cover modification of the file, and distribution when not linked
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into a combine executable.)
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into a combine executable.)
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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for more details.
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You should have received a copy of the GNU General Public License
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You should have received a copy of the GNU General Public License
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along with GCC; see the file COPYING. If not, write to the Free
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along with GCC; see the file COPYING. If not, write to the Free
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Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
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Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
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02110-1301, USA. */
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02110-1301, USA. */
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/* ------------------------------------------------------------------ */
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/* ------------------------------------------------------------------ */
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/* decBasic.c -- common base code for Basic decimal types */
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/* decBasic.c -- common base code for Basic decimal types */
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/* ------------------------------------------------------------------ */
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/* ------------------------------------------------------------------ */
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/* This module comprises code that is shared between decDouble and */
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/* This module comprises code that is shared between decDouble and */
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/* decQuad (but not decSingle). The main arithmetic operations are */
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/* decQuad (but not decSingle). The main arithmetic operations are */
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/* here (Add, Subtract, Multiply, FMA, and Division operators). */
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/* here (Add, Subtract, Multiply, FMA, and Division operators). */
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/* */
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/* */
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/* Unlike decNumber, parameterization takes place at compile time */
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/* Unlike decNumber, parameterization takes place at compile time */
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/* rather than at runtime. The parameters are set in the decDouble.c */
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/* rather than at runtime. The parameters are set in the decDouble.c */
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/* (etc.) files, which then include this one to produce the compiled */
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/* (etc.) files, which then include this one to produce the compiled */
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/* code. The functions here, therefore, are code shared between */
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/* code. The functions here, therefore, are code shared between */
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/* multiple formats. */
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/* multiple formats. */
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/* */
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/* */
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/* This must be included after decCommon.c. */
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/* This must be included after decCommon.c. */
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/* ------------------------------------------------------------------ */
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/* ------------------------------------------------------------------ */
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/* Names here refer to decFloat rather than to decDouble, etc., and */
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/* Names here refer to decFloat rather than to decDouble, etc., and */
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/* the functions are in strict alphabetical order. */
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/* the functions are in strict alphabetical order. */
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/* The compile-time flags SINGLE, DOUBLE, and QUAD are set up in */
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/* The compile-time flags SINGLE, DOUBLE, and QUAD are set up in */
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/* decCommon.c */
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/* decCommon.c */
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#if !defined(QUAD)
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#if !defined(QUAD)
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#error decBasic.c must be included after decCommon.c
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#error decBasic.c must be included after decCommon.c
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#endif
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#endif
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#if SINGLE
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#if SINGLE
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#error Routines in decBasic.c are for decDouble and decQuad only
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#error Routines in decBasic.c are for decDouble and decQuad only
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#endif
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#endif
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/* Private constants */
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/* Private constants */
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#define DIVIDE 0x80000000 /* Divide operations [as flags] */
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#define DIVIDE 0x80000000 /* Divide operations [as flags] */
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#define REMAINDER 0x40000000 /* .. */
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#define REMAINDER 0x40000000 /* .. */
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#define DIVIDEINT 0x20000000 /* .. */
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#define DIVIDEINT 0x20000000 /* .. */
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#define REMNEAR 0x10000000 /* .. */
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#define REMNEAR 0x10000000 /* .. */
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/* Private functions (local, used only by routines in this module) */
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/* Private functions (local, used only by routines in this module) */
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static decFloat *decDivide(decFloat *, const decFloat *,
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static decFloat *decDivide(decFloat *, const decFloat *,
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const decFloat *, decContext *, uInt);
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const decFloat *, decContext *, uInt);
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static decFloat *decCanonical(decFloat *, const decFloat *);
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static decFloat *decCanonical(decFloat *, const decFloat *);
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static void decFiniteMultiply(bcdnum *, uByte *, const decFloat *,
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static void decFiniteMultiply(bcdnum *, uByte *, const decFloat *,
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const decFloat *);
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const decFloat *);
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static decFloat *decInfinity(decFloat *, const decFloat *);
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static decFloat *decInfinity(decFloat *, const decFloat *);
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static decFloat *decInvalid(decFloat *, decContext *);
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static decFloat *decInvalid(decFloat *, decContext *);
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static decFloat *decNaNs(decFloat *, const decFloat *, const decFloat *,
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static decFloat *decNaNs(decFloat *, const decFloat *, const decFloat *,
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decContext *);
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decContext *);
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static Int decNumCompare(const decFloat *, const decFloat *, Flag);
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static Int decNumCompare(const decFloat *, const decFloat *, Flag);
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static decFloat *decToIntegral(decFloat *, const decFloat *, decContext *,
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static decFloat *decToIntegral(decFloat *, const decFloat *, decContext *,
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enum rounding, Flag);
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enum rounding, Flag);
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static uInt decToInt32(const decFloat *, decContext *, enum rounding,
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static uInt decToInt32(const decFloat *, decContext *, enum rounding,
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Flag, Flag);
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Flag, Flag);
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/* ------------------------------------------------------------------ */
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/* ------------------------------------------------------------------ */
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/* decCanonical -- copy a decFloat, making canonical */
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/* decCanonical -- copy a decFloat, making canonical */
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/* */
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/* */
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/* result gets the canonicalized df */
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/* result gets the canonicalized df */
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/* df is the decFloat to copy and make canonical */
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/* df is the decFloat to copy and make canonical */
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/* returns result */
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/* returns result */
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/* */
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/* */
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/* This is exposed via decFloatCanonical for Double and Quad only. */
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/* This is exposed via decFloatCanonical for Double and Quad only. */
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/* This works on specials, too; no error or exception is possible. */
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/* This works on specials, too; no error or exception is possible. */
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/* ------------------------------------------------------------------ */
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/* ------------------------------------------------------------------ */
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static decFloat * decCanonical(decFloat *result, const decFloat *df) {
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static decFloat * decCanonical(decFloat *result, const decFloat *df) {
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uInt encode, precode, dpd; /* work */
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uInt encode, precode, dpd; /* work */
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uInt inword, uoff, canon; /* .. */
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uInt inword, uoff, canon; /* .. */
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Int n; /* counter (down) */
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Int n; /* counter (down) */
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if (df!=result) *result=*df; /* effect copy if needed */
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if (df!=result) *result=*df; /* effect copy if needed */
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if (DFISSPECIAL(result)) {
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if (DFISSPECIAL(result)) {
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if (DFISINF(result)) return decInfinity(result, df); /* clean Infinity */
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if (DFISINF(result)) return decInfinity(result, df); /* clean Infinity */
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/* is a NaN */
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/* is a NaN */
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DFWORD(result, 0)&=~ECONNANMASK; /* clear ECON except selector */
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DFWORD(result, 0)&=~ECONNANMASK; /* clear ECON except selector */
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if (DFISCCZERO(df)) return result; /* coefficient continuation is 0 */
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if (DFISCCZERO(df)) return result; /* coefficient continuation is 0 */
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/* drop through to check payload */
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/* drop through to check payload */
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}
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}
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/* return quickly if the coefficient continuation is canonical */
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/* return quickly if the coefficient continuation is canonical */
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{ /* declare block */
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{ /* declare block */
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#if DOUBLE
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#if DOUBLE
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uInt sourhi=DFWORD(df, 0);
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uInt sourhi=DFWORD(df, 0);
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uInt sourlo=DFWORD(df, 1);
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uInt sourlo=DFWORD(df, 1);
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if (CANONDPDOFF(sourhi, 8)
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if (CANONDPDOFF(sourhi, 8)
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&& CANONDPDTWO(sourhi, sourlo, 30)
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&& CANONDPDTWO(sourhi, sourlo, 30)
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&& CANONDPDOFF(sourlo, 20)
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&& CANONDPDOFF(sourlo, 20)
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&& CANONDPDOFF(sourlo, 10)
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&& CANONDPDOFF(sourlo, 10)
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&& CANONDPDOFF(sourlo, 0)) return result;
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&& CANONDPDOFF(sourlo, 0)) return result;
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#elif QUAD
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#elif QUAD
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uInt sourhi=DFWORD(df, 0);
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uInt sourhi=DFWORD(df, 0);
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uInt sourmh=DFWORD(df, 1);
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uInt sourmh=DFWORD(df, 1);
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uInt sourml=DFWORD(df, 2);
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uInt sourml=DFWORD(df, 2);
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uInt sourlo=DFWORD(df, 3);
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uInt sourlo=DFWORD(df, 3);
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if (CANONDPDOFF(sourhi, 4)
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if (CANONDPDOFF(sourhi, 4)
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&& CANONDPDTWO(sourhi, sourmh, 26)
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&& CANONDPDTWO(sourhi, sourmh, 26)
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&& CANONDPDOFF(sourmh, 16)
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&& CANONDPDOFF(sourmh, 16)
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&& CANONDPDOFF(sourmh, 6)
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&& CANONDPDOFF(sourmh, 6)
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&& CANONDPDTWO(sourmh, sourml, 28)
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&& CANONDPDTWO(sourmh, sourml, 28)
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&& CANONDPDOFF(sourml, 18)
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&& CANONDPDOFF(sourml, 18)
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&& CANONDPDOFF(sourml, 8)
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&& CANONDPDOFF(sourml, 8)
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&& CANONDPDTWO(sourml, sourlo, 30)
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&& CANONDPDTWO(sourml, sourlo, 30)
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&& CANONDPDOFF(sourlo, 20)
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&& CANONDPDOFF(sourlo, 20)
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&& CANONDPDOFF(sourlo, 10)
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&& CANONDPDOFF(sourlo, 10)
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&& CANONDPDOFF(sourlo, 0)) return result;
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&& CANONDPDOFF(sourlo, 0)) return result;
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#endif
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#endif
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} /* block */
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} /* block */
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/* Loop to repair a non-canonical coefficent, as needed */
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/* Loop to repair a non-canonical coefficent, as needed */
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inword=DECWORDS-1; /* current input word */
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inword=DECWORDS-1; /* current input word */
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uoff=0; /* bit offset of declet */
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uoff=0; /* bit offset of declet */
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encode=DFWORD(result, inword);
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encode=DFWORD(result, inword);
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for (n=DECLETS-1; n>=0; n--) { /* count down declets of 10 bits */
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for (n=DECLETS-1; n>=0; n--) { /* count down declets of 10 bits */
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dpd=encode>>uoff;
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dpd=encode>>uoff;
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uoff+=10;
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uoff+=10;
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if (uoff>32) { /* crossed uInt boundary */
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if (uoff>32) { /* crossed uInt boundary */
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inword--;
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inword--;
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encode=DFWORD(result, inword);
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encode=DFWORD(result, inword);
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uoff-=32;
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uoff-=32;
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dpd|=encode<<(10-uoff); /* get pending bits */
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dpd|=encode<<(10-uoff); /* get pending bits */
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}
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}
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dpd&=0x3ff; /* clear uninteresting bits */
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dpd&=0x3ff; /* clear uninteresting bits */
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if (dpd<0x16e) continue; /* must be canonical */
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if (dpd<0x16e) continue; /* must be canonical */
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canon=BIN2DPD[DPD2BIN[dpd]]; /* determine canonical declet */
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canon=BIN2DPD[DPD2BIN[dpd]]; /* determine canonical declet */
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if (canon==dpd) continue; /* have canonical declet */
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if (canon==dpd) continue; /* have canonical declet */
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/* need to replace declet */
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/* need to replace declet */
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if (uoff>=10) { /* all within current word */
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if (uoff>=10) { /* all within current word */
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encode&=~(0x3ff<<(uoff-10)); /* clear the 10 bits ready for replace */
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encode&=~(0x3ff<<(uoff-10)); /* clear the 10 bits ready for replace */
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encode|=canon<<(uoff-10); /* insert the canonical form */
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encode|=canon<<(uoff-10); /* insert the canonical form */
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DFWORD(result, inword)=encode; /* .. and save */
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DFWORD(result, inword)=encode; /* .. and save */
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continue;
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continue;
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}
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}
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/* straddled words */
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/* straddled words */
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precode=DFWORD(result, inword+1); /* get previous */
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precode=DFWORD(result, inword+1); /* get previous */
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precode&=0xffffffff>>(10-uoff); /* clear top bits */
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precode&=0xffffffff>>(10-uoff); /* clear top bits */
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DFWORD(result, inword+1)=precode|(canon<<(32-(10-uoff)));
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DFWORD(result, inword+1)=precode|(canon<<(32-(10-uoff)));
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encode&=0xffffffff<<uoff; /* clear bottom bits */
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encode&=0xffffffff<<uoff; /* clear bottom bits */
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encode|=canon>>(10-uoff); /* insert canonical */
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encode|=canon>>(10-uoff); /* insert canonical */
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DFWORD(result, inword)=encode; /* .. and save */
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DFWORD(result, inword)=encode; /* .. and save */
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} /* n */
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} /* n */
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return result;
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return result;
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} /* decCanonical */
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} /* decCanonical */
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/* ------------------------------------------------------------------ */
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/* ------------------------------------------------------------------ */
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/* decDivide -- divide operations */
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/* decDivide -- divide operations */
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/* */
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/* */
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/* result gets the result of dividing dfl by dfr: */
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/* result gets the result of dividing dfl by dfr: */
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/* dfl is the first decFloat (lhs) */
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/* dfl is the first decFloat (lhs) */
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/* dfr is the second decFloat (rhs) */
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/* dfr is the second decFloat (rhs) */
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/* set is the context */
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/* set is the context */
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/* op is the operation selector */
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/* op is the operation selector */
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/* returns result */
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/* returns result */
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/* */
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/* */
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/* op is one of DIVIDE, REMAINDER, DIVIDEINT, or REMNEAR. */
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/* op is one of DIVIDE, REMAINDER, DIVIDEINT, or REMNEAR. */
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/* ------------------------------------------------------------------ */
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/* ------------------------------------------------------------------ */
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#define DIVCOUNT 0 /* 1 to instrument subtractions counter */
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#define DIVCOUNT 0 /* 1 to instrument subtractions counter */
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#define DIVBASE BILLION /* the base used for divide */
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#define DIVBASE BILLION /* the base used for divide */
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#define DIVOPLEN DECPMAX9 /* operand length ('digits' base 10**9) */
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#define DIVOPLEN DECPMAX9 /* operand length ('digits' base 10**9) */
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#define DIVACCLEN (DIVOPLEN*3) /* accumulator length (ditto) */
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#define DIVACCLEN (DIVOPLEN*3) /* accumulator length (ditto) */
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static decFloat * decDivide(decFloat *result, const decFloat *dfl,
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static decFloat * decDivide(decFloat *result, const decFloat *dfl,
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const decFloat *dfr, decContext *set, uInt op) {
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const decFloat *dfr, decContext *set, uInt op) {
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decFloat quotient; /* for remainders */
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decFloat quotient; /* for remainders */
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bcdnum num; /* for final conversion */
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bcdnum num; /* for final conversion */
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uInt acc[DIVACCLEN]; /* coefficent in base-billion .. */
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uInt acc[DIVACCLEN]; /* coefficent in base-billion .. */
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uInt div[DIVOPLEN]; /* divisor in base-billion .. */
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uInt div[DIVOPLEN]; /* divisor in base-billion .. */
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uInt quo[DIVOPLEN+1]; /* quotient in base-billion .. */
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uInt quo[DIVOPLEN+1]; /* quotient in base-billion .. */
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uByte bcdacc[(DIVOPLEN+1)*9+2]; /* for quotient in BCD, +1, +1 */
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uByte bcdacc[(DIVOPLEN+1)*9+2]; /* for quotient in BCD, +1, +1 */
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uInt *msua, *msud, *msuq; /* -> msu of acc, div, and quo */
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uInt *msua, *msud, *msuq; /* -> msu of acc, div, and quo */
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Int divunits, accunits; /* lengths */
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Int divunits, accunits; /* lengths */
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Int quodigits; /* digits in quotient */
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Int quodigits; /* digits in quotient */
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uInt *lsua, *lsuq; /* -> current acc and quo lsus */
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uInt *lsua, *lsuq; /* -> current acc and quo lsus */
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Int length, multiplier; /* work */
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Int length, multiplier; /* work */
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uInt carry, sign; /* .. */
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uInt carry, sign; /* .. */
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uInt *ua, *ud, *uq; /* .. */
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uInt *ua, *ud, *uq; /* .. */
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uByte *ub; /* .. */
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uByte *ub; /* .. */
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uInt divtop; /* top unit of div adjusted for estimating */
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uInt divtop; /* top unit of div adjusted for estimating */
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#if DIVCOUNT
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#if DIVCOUNT
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static uInt maxcount=0; /* worst-seen subtractions count */
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static uInt maxcount=0; /* worst-seen subtractions count */
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uInt divcount=0; /* subtractions count [this divide] */
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uInt divcount=0; /* subtractions count [this divide] */
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#endif
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#endif
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/* calculate sign */
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/* calculate sign */
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num.sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;
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num.sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;
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|
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if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { /* either is special? */
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if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { /* either is special? */
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/* NaNs are handled as usual */
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/* NaNs are handled as usual */
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if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
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if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
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/* one or two infinities */
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/* one or two infinities */
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if (DFISINF(dfl)) {
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if (DFISINF(dfl)) {
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if (DFISINF(dfr)) return decInvalid(result, set); /* Two infinities bad */
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if (DFISINF(dfr)) return decInvalid(result, set); /* Two infinities bad */
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if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); /* as is rem */
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if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); /* as is rem */
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/* Infinity/x is infinite and quiet, even if x=0 */
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/* Infinity/x is infinite and quiet, even if x=0 */
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DFWORD(result, 0)=num.sign;
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DFWORD(result, 0)=num.sign;
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return decInfinity(result, result);
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return decInfinity(result, result);
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}
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}
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/* must be x/Infinity -- remainders are lhs */
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/* must be x/Infinity -- remainders are lhs */
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if (op&(REMAINDER|REMNEAR)) return decCanonical(result, dfl);
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if (op&(REMAINDER|REMNEAR)) return decCanonical(result, dfl);
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/* divides: return zero with correct sign and exponent depending */
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/* divides: return zero with correct sign and exponent depending */
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/* on op (Etiny for divide, 0 for divideInt) */
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/* on op (Etiny for divide, 0 for divideInt) */
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decFloatZero(result);
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decFloatZero(result);
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if (op==DIVIDEINT) DFWORD(result, 0)|=num.sign; /* add sign */
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if (op==DIVIDEINT) DFWORD(result, 0)|=num.sign; /* add sign */
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else DFWORD(result, 0)=num.sign; /* zeros the exponent, too */
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else DFWORD(result, 0)=num.sign; /* zeros the exponent, too */
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return result;
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return result;
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}
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}
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/* next, handle zero operands (x/0 and 0/x) */
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/* next, handle zero operands (x/0 and 0/x) */
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if (DFISZERO(dfr)) { /* x/0 */
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if (DFISZERO(dfr)) { /* x/0 */
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if (DFISZERO(dfl)) { /* 0/0 is undefined */
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if (DFISZERO(dfl)) { /* 0/0 is undefined */
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decFloatZero(result);
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decFloatZero(result);
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DFWORD(result, 0)=DECFLOAT_qNaN;
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DFWORD(result, 0)=DECFLOAT_qNaN;
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set->status|=DEC_Division_undefined;
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set->status|=DEC_Division_undefined;
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return result;
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return result;
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}
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}
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if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); /* bad rem */
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if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); /* bad rem */
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set->status|=DEC_Division_by_zero;
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set->status|=DEC_Division_by_zero;
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DFWORD(result, 0)=num.sign;
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DFWORD(result, 0)=num.sign;
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return decInfinity(result, result); /* x/0 -> signed Infinity */
|
return decInfinity(result, result); /* x/0 -> signed Infinity */
|
}
|
}
|
num.exponent=GETEXPUN(dfl)-GETEXPUN(dfr); /* ideal exponent */
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num.exponent=GETEXPUN(dfl)-GETEXPUN(dfr); /* ideal exponent */
|
if (DFISZERO(dfl)) { /* 0/x (x!=0) */
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if (DFISZERO(dfl)) { /* 0/x (x!=0) */
|
/* if divide, result is 0 with ideal exponent; divideInt has */
|
/* if divide, result is 0 with ideal exponent; divideInt has */
|
/* exponent=0, remainders give zero with lower exponent */
|
/* exponent=0, remainders give zero with lower exponent */
|
if (op&DIVIDEINT) {
|
if (op&DIVIDEINT) {
|
decFloatZero(result);
|
decFloatZero(result);
|
DFWORD(result, 0)|=num.sign; /* add sign */
|
DFWORD(result, 0)|=num.sign; /* add sign */
|
return result;
|
return result;
|
}
|
}
|
if (!(op&DIVIDE)) { /* a remainder */
|
if (!(op&DIVIDE)) { /* a remainder */
|
/* exponent is the minimum of the operands */
|
/* exponent is the minimum of the operands */
|
num.exponent=MINI(GETEXPUN(dfl), GETEXPUN(dfr));
|
num.exponent=MINI(GETEXPUN(dfl), GETEXPUN(dfr));
|
/* if the result is zero the sign shall be sign of dfl */
|
/* if the result is zero the sign shall be sign of dfl */
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
}
|
}
|
bcdacc[0]=0;
|
bcdacc[0]=0;
|
num.msd=bcdacc; /* -> 0 */
|
num.msd=bcdacc; /* -> 0 */
|
num.lsd=bcdacc; /* .. */
|
num.lsd=bcdacc; /* .. */
|
return decFinalize(result, &num, set); /* [divide may clamp exponent] */
|
return decFinalize(result, &num, set); /* [divide may clamp exponent] */
|
} /* 0/x */
|
} /* 0/x */
|
/* [here, both operands are known to be finite and non-zero] */
|
/* [here, both operands are known to be finite and non-zero] */
|
|
|
/* extract the operand coefficents into 'units' which are */
|
/* extract the operand coefficents into 'units' which are */
|
/* base-billion; the lhs is high-aligned in acc and the msu of both */
|
/* base-billion; the lhs is high-aligned in acc and the msu of both */
|
/* acc and div is at the right-hand end of array (offset length-1); */
|
/* acc and div is at the right-hand end of array (offset length-1); */
|
/* the quotient can need one more unit than the operands as digits */
|
/* the quotient can need one more unit than the operands as digits */
|
/* in it are not necessarily aligned neatly; further, the quotient */
|
/* in it are not necessarily aligned neatly; further, the quotient */
|
/* may not start accumulating until after the end of the initial */
|
/* may not start accumulating until after the end of the initial */
|
/* operand in acc if that is small (e.g., 1) so the accumulator */
|
/* operand in acc if that is small (e.g., 1) so the accumulator */
|
/* must have at least that number of units extra (at the ls end) */
|
/* must have at least that number of units extra (at the ls end) */
|
GETCOEFFBILL(dfl, acc+DIVACCLEN-DIVOPLEN);
|
GETCOEFFBILL(dfl, acc+DIVACCLEN-DIVOPLEN);
|
GETCOEFFBILL(dfr, div);
|
GETCOEFFBILL(dfr, div);
|
/* zero the low uInts of acc */
|
/* zero the low uInts of acc */
|
acc[0]=0;
|
acc[0]=0;
|
acc[1]=0;
|
acc[1]=0;
|
acc[2]=0;
|
acc[2]=0;
|
acc[3]=0;
|
acc[3]=0;
|
#if DOUBLE
|
#if DOUBLE
|
#if DIVOPLEN!=2
|
#if DIVOPLEN!=2
|
#error Unexpected Double DIVOPLEN
|
#error Unexpected Double DIVOPLEN
|
#endif
|
#endif
|
#elif QUAD
|
#elif QUAD
|
acc[4]=0;
|
acc[4]=0;
|
acc[5]=0;
|
acc[5]=0;
|
acc[6]=0;
|
acc[6]=0;
|
acc[7]=0;
|
acc[7]=0;
|
#if DIVOPLEN!=4
|
#if DIVOPLEN!=4
|
#error Unexpected Quad DIVOPLEN
|
#error Unexpected Quad DIVOPLEN
|
#endif
|
#endif
|
#endif
|
#endif
|
|
|
/* set msu and lsu pointers */
|
/* set msu and lsu pointers */
|
msua=acc+DIVACCLEN-1; /* [leading zeros removed below] */
|
msua=acc+DIVACCLEN-1; /* [leading zeros removed below] */
|
msuq=quo+DIVOPLEN;
|
msuq=quo+DIVOPLEN;
|
/*[loop for div will terminate because operands are non-zero] */
|
/*[loop for div will terminate because operands are non-zero] */
|
for (msud=div+DIVOPLEN-1; *msud==0;) msud--;
|
for (msud=div+DIVOPLEN-1; *msud==0;) msud--;
|
/* the initial least-significant unit of acc is set so acc appears */
|
/* the initial least-significant unit of acc is set so acc appears */
|
/* to have the same length as div. */
|
/* to have the same length as div. */
|
/* This moves one position towards the least possible for each */
|
/* This moves one position towards the least possible for each */
|
/* iteration */
|
/* iteration */
|
divunits=(Int)(msud-div+1); /* precalculate */
|
divunits=(Int)(msud-div+1); /* precalculate */
|
lsua=msua-divunits+1; /* initial working lsu of acc */
|
lsua=msua-divunits+1; /* initial working lsu of acc */
|
lsuq=msuq; /* and of quo */
|
lsuq=msuq; /* and of quo */
|
|
|
/* set up the estimator for the multiplier; this is the msu of div, */
|
/* set up the estimator for the multiplier; this is the msu of div, */
|
/* plus two bits from the unit below (if any) rounded up by one if */
|
/* plus two bits from the unit below (if any) rounded up by one if */
|
/* there are any non-zero bits or units below that [the extra two */
|
/* there are any non-zero bits or units below that [the extra two */
|
/* bits makes for a much better estimate when the top unit is small] */
|
/* bits makes for a much better estimate when the top unit is small] */
|
divtop=*msud<<2;
|
divtop=*msud<<2;
|
if (divunits>1) {
|
if (divunits>1) {
|
uInt *um=msud-1;
|
uInt *um=msud-1;
|
uInt d=*um;
|
uInt d=*um;
|
if (d>=750000000) {divtop+=3; d-=750000000;}
|
if (d>=750000000) {divtop+=3; d-=750000000;}
|
else if (d>=500000000) {divtop+=2; d-=500000000;}
|
else if (d>=500000000) {divtop+=2; d-=500000000;}
|
else if (d>=250000000) {divtop++; d-=250000000;}
|
else if (d>=250000000) {divtop++; d-=250000000;}
|
if (d) divtop++;
|
if (d) divtop++;
|
else for (um--; um>=div; um--) if (*um) {
|
else for (um--; um>=div; um--) if (*um) {
|
divtop++;
|
divtop++;
|
break;
|
break;
|
}
|
}
|
} /* >1 unit */
|
} /* >1 unit */
|
|
|
#if DECTRACE
|
#if DECTRACE
|
{Int i;
|
{Int i;
|
printf("----- div=");
|
printf("----- div=");
|
for (i=divunits-1; i>=0; i--) printf("%09ld ", (LI)div[i]);
|
for (i=divunits-1; i>=0; i--) printf("%09ld ", (LI)div[i]);
|
printf("\n");}
|
printf("\n");}
|
#endif
|
#endif
|
|
|
/* now collect up to DECPMAX+1 digits in the quotient (this may */
|
/* now collect up to DECPMAX+1 digits in the quotient (this may */
|
/* need OPLEN+1 uInts if unaligned) */
|
/* need OPLEN+1 uInts if unaligned) */
|
quodigits=0; /* no digits yet */
|
quodigits=0; /* no digits yet */
|
for (;; lsua--) { /* outer loop -- each input position */
|
for (;; lsua--) { /* outer loop -- each input position */
|
#if DECCHECK
|
#if DECCHECK
|
if (lsua<acc) {
|
if (lsua<acc) {
|
printf("Acc underrun...\n");
|
printf("Acc underrun...\n");
|
break;
|
break;
|
}
|
}
|
#endif
|
#endif
|
#if DECTRACE
|
#if DECTRACE
|
printf("Outer: quodigits=%ld acc=", (LI)quodigits);
|
printf("Outer: quodigits=%ld acc=", (LI)quodigits);
|
for (ua=msua; ua>=lsua; ua--) printf("%09ld ", (LI)*ua);
|
for (ua=msua; ua>=lsua; ua--) printf("%09ld ", (LI)*ua);
|
printf("\n");
|
printf("\n");
|
#endif
|
#endif
|
*lsuq=0; /* default unit result is 0 */
|
*lsuq=0; /* default unit result is 0 */
|
for (;;) { /* inner loop -- calculate quotient unit */
|
for (;;) { /* inner loop -- calculate quotient unit */
|
/* strip leading zero units from acc (either there initially or */
|
/* strip leading zero units from acc (either there initially or */
|
/* from subtraction below); this may strip all if exactly 0 */
|
/* from subtraction below); this may strip all if exactly 0 */
|
for (; *msua==0 && msua>=lsua;) msua--;
|
for (; *msua==0 && msua>=lsua;) msua--;
|
accunits=(Int)(msua-lsua+1); /* [maybe 0] */
|
accunits=(Int)(msua-lsua+1); /* [maybe 0] */
|
/* subtraction is only necessary and possible if there are as */
|
/* subtraction is only necessary and possible if there are as */
|
/* least as many units remaining in acc for this iteration as */
|
/* least as many units remaining in acc for this iteration as */
|
/* there are in div */
|
/* there are in div */
|
if (accunits<divunits) {
|
if (accunits<divunits) {
|
if (accunits==0) msua++; /* restore */
|
if (accunits==0) msua++; /* restore */
|
break;
|
break;
|
}
|
}
|
|
|
/* If acc is longer than div then subtraction is definitely */
|
/* If acc is longer than div then subtraction is definitely */
|
/* possible (as msu of both is non-zero), but if they are the */
|
/* possible (as msu of both is non-zero), but if they are the */
|
/* same length a comparison is needed. */
|
/* same length a comparison is needed. */
|
/* If a subtraction is needed then a good estimate of the */
|
/* If a subtraction is needed then a good estimate of the */
|
/* multiplier for the subtraction is also needed in order to */
|
/* multiplier for the subtraction is also needed in order to */
|
/* minimise the iterations of this inner loop because the */
|
/* minimise the iterations of this inner loop because the */
|
/* subtractions needed dominate division performance. */
|
/* subtractions needed dominate division performance. */
|
if (accunits==divunits) {
|
if (accunits==divunits) {
|
/* compare the high divunits of acc and div: */
|
/* compare the high divunits of acc and div: */
|
/* acc<div: this quotient unit is unchanged; subtraction */
|
/* acc<div: this quotient unit is unchanged; subtraction */
|
/* will be possible on the next iteration */
|
/* will be possible on the next iteration */
|
/* acc==div: quotient gains 1, set acc=0 */
|
/* acc==div: quotient gains 1, set acc=0 */
|
/* acc>div: subtraction necessary at this position */
|
/* acc>div: subtraction necessary at this position */
|
for (ud=msud, ua=msua; ud>div; ud--, ua--) if (*ud!=*ua) break;
|
for (ud=msud, ua=msua; ud>div; ud--, ua--) if (*ud!=*ua) break;
|
/* [now at first mismatch or lsu] */
|
/* [now at first mismatch or lsu] */
|
if (*ud>*ua) break; /* next time... */
|
if (*ud>*ua) break; /* next time... */
|
if (*ud==*ua) { /* all compared equal */
|
if (*ud==*ua) { /* all compared equal */
|
*lsuq+=1; /* increment result */
|
*lsuq+=1; /* increment result */
|
msua=lsua; /* collapse acc units */
|
msua=lsua; /* collapse acc units */
|
*msua=0; /* .. to a zero */
|
*msua=0; /* .. to a zero */
|
break;
|
break;
|
}
|
}
|
|
|
/* subtraction necessary; estimate multiplier [see above] */
|
/* subtraction necessary; estimate multiplier [see above] */
|
/* if both *msud and *msua are small it is cost-effective to */
|
/* if both *msud and *msua are small it is cost-effective to */
|
/* bring in part of the following units (if any) to get a */
|
/* bring in part of the following units (if any) to get a */
|
/* better estimate (assume some other non-zero in div) */
|
/* better estimate (assume some other non-zero in div) */
|
#define DIVLO 1000000U
|
#define DIVLO 1000000U
|
#define DIVHI (DIVBASE/DIVLO)
|
#define DIVHI (DIVBASE/DIVLO)
|
#if DECUSE64
|
#if DECUSE64
|
if (divunits>1) {
|
if (divunits>1) {
|
/* there cannot be a *(msud-2) for DECDOUBLE so next is */
|
/* there cannot be a *(msud-2) for DECDOUBLE so next is */
|
/* an exact calculation unless DECQUAD (which needs to */
|
/* an exact calculation unless DECQUAD (which needs to */
|
/* assume bits out there if divunits>2) */
|
/* assume bits out there if divunits>2) */
|
uLong mul=(uLong)*msua * DIVBASE + *(msua-1);
|
uLong mul=(uLong)*msua * DIVBASE + *(msua-1);
|
uLong div=(uLong)*msud * DIVBASE + *(msud-1);
|
uLong div=(uLong)*msud * DIVBASE + *(msud-1);
|
#if QUAD
|
#if QUAD
|
if (divunits>2) div++;
|
if (divunits>2) div++;
|
#endif
|
#endif
|
mul/=div;
|
mul/=div;
|
multiplier=(Int)mul;
|
multiplier=(Int)mul;
|
}
|
}
|
else multiplier=*msua/(*msud);
|
else multiplier=*msua/(*msud);
|
#else
|
#else
|
if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {
|
if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {
|
multiplier=(*msua*DIVHI + *(msua-1)/DIVLO)
|
multiplier=(*msua*DIVHI + *(msua-1)/DIVLO)
|
/(*msud*DIVHI + *(msud-1)/DIVLO +1);
|
/(*msud*DIVHI + *(msud-1)/DIVLO +1);
|
}
|
}
|
else multiplier=(*msua<<2)/divtop;
|
else multiplier=(*msua<<2)/divtop;
|
#endif
|
#endif
|
}
|
}
|
else { /* accunits>divunits */
|
else { /* accunits>divunits */
|
/* msud is one unit 'lower' than msua, so estimate differently */
|
/* msud is one unit 'lower' than msua, so estimate differently */
|
#if DECUSE64
|
#if DECUSE64
|
uLong mul;
|
uLong mul;
|
/* as before, bring in extra digits if possible */
|
/* as before, bring in extra digits if possible */
|
if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {
|
if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {
|
mul=((uLong)*msua * DIVHI * DIVBASE) + *(msua-1) * DIVHI
|
mul=((uLong)*msua * DIVHI * DIVBASE) + *(msua-1) * DIVHI
|
+ *(msua-2)/DIVLO;
|
+ *(msua-2)/DIVLO;
|
mul/=(*msud*DIVHI + *(msud-1)/DIVLO +1);
|
mul/=(*msud*DIVHI + *(msud-1)/DIVLO +1);
|
}
|
}
|
else if (divunits==1) {
|
else if (divunits==1) {
|
mul=(uLong)*msua * DIVBASE + *(msua-1);
|
mul=(uLong)*msua * DIVBASE + *(msua-1);
|
mul/=*msud; /* no more to the right */
|
mul/=*msud; /* no more to the right */
|
}
|
}
|
else {
|
else {
|
mul=(uLong)(*msua) * (uInt)(DIVBASE<<2) + (*(msua-1)<<2);
|
mul=(uLong)(*msua) * (uInt)(DIVBASE<<2) + (*(msua-1)<<2);
|
mul/=divtop; /* [divtop already allows for sticky bits] */
|
mul/=divtop; /* [divtop already allows for sticky bits] */
|
}
|
}
|
multiplier=(Int)mul;
|
multiplier=(Int)mul;
|
#else
|
#else
|
multiplier=*msua * ((DIVBASE<<2)/divtop);
|
multiplier=*msua * ((DIVBASE<<2)/divtop);
|
#endif
|
#endif
|
}
|
}
|
if (multiplier==0) multiplier=1; /* marginal case */
|
if (multiplier==0) multiplier=1; /* marginal case */
|
*lsuq+=multiplier;
|
*lsuq+=multiplier;
|
|
|
#if DIVCOUNT
|
#if DIVCOUNT
|
/* printf("Multiplier: %ld\n", (LI)multiplier); */
|
/* printf("Multiplier: %ld\n", (LI)multiplier); */
|
divcount++;
|
divcount++;
|
#endif
|
#endif
|
|
|
/* Carry out the subtraction acc-(div*multiplier); for each */
|
/* Carry out the subtraction acc-(div*multiplier); for each */
|
/* unit in div, do the multiply, split to units (see */
|
/* unit in div, do the multiply, split to units (see */
|
/* decFloatMultiply for the algorithm), and subtract from acc */
|
/* decFloatMultiply for the algorithm), and subtract from acc */
|
#define DIVMAGIC 2305843009U /* 2**61/10**9 */
|
#define DIVMAGIC 2305843009U /* 2**61/10**9 */
|
#define DIVSHIFTA 29
|
#define DIVSHIFTA 29
|
#define DIVSHIFTB 32
|
#define DIVSHIFTB 32
|
carry=0;
|
carry=0;
|
for (ud=div, ua=lsua; ud<=msud; ud++, ua++) {
|
for (ud=div, ua=lsua; ud<=msud; ud++, ua++) {
|
uInt lo, hop;
|
uInt lo, hop;
|
#if DECUSE64
|
#if DECUSE64
|
uLong sub=(uLong)multiplier*(*ud)+carry;
|
uLong sub=(uLong)multiplier*(*ud)+carry;
|
if (sub<DIVBASE) {
|
if (sub<DIVBASE) {
|
carry=0;
|
carry=0;
|
lo=(uInt)sub;
|
lo=(uInt)sub;
|
}
|
}
|
else {
|
else {
|
hop=(uInt)(sub>>DIVSHIFTA);
|
hop=(uInt)(sub>>DIVSHIFTA);
|
carry=(uInt)(((uLong)hop*DIVMAGIC)>>DIVSHIFTB);
|
carry=(uInt)(((uLong)hop*DIVMAGIC)>>DIVSHIFTB);
|
/* the estimate is now in hi; now calculate sub-hi*10**9 */
|
/* the estimate is now in hi; now calculate sub-hi*10**9 */
|
/* to get the remainder (which will be <DIVBASE)) */
|
/* to get the remainder (which will be <DIVBASE)) */
|
lo=(uInt)sub;
|
lo=(uInt)sub;
|
lo-=carry*DIVBASE; /* low word of result */
|
lo-=carry*DIVBASE; /* low word of result */
|
if (lo>=DIVBASE) {
|
if (lo>=DIVBASE) {
|
lo-=DIVBASE; /* correct by +1 */
|
lo-=DIVBASE; /* correct by +1 */
|
carry++;
|
carry++;
|
}
|
}
|
}
|
}
|
#else /* 32-bit */
|
#else /* 32-bit */
|
uInt hi;
|
uInt hi;
|
/* calculate multiplier*(*ud) into hi and lo */
|
/* calculate multiplier*(*ud) into hi and lo */
|
LONGMUL32HI(hi, *ud, multiplier); /* get the high word */
|
LONGMUL32HI(hi, *ud, multiplier); /* get the high word */
|
lo=multiplier*(*ud); /* .. and the low */
|
lo=multiplier*(*ud); /* .. and the low */
|
lo+=carry; /* add the old hi */
|
lo+=carry; /* add the old hi */
|
carry=hi+(lo<carry); /* .. with any carry */
|
carry=hi+(lo<carry); /* .. with any carry */
|
if (carry || lo>=DIVBASE) { /* split is needed */
|
if (carry || lo>=DIVBASE) { /* split is needed */
|
hop=(carry<<3)+(lo>>DIVSHIFTA); /* hi:lo/2**29 */
|
hop=(carry<<3)+(lo>>DIVSHIFTA); /* hi:lo/2**29 */
|
LONGMUL32HI(carry, hop, DIVMAGIC); /* only need the high word */
|
LONGMUL32HI(carry, hop, DIVMAGIC); /* only need the high word */
|
/* [DIVSHIFTB is 32, so carry can be used directly] */
|
/* [DIVSHIFTB is 32, so carry can be used directly] */
|
/* the estimate is now in carry; now calculate hi:lo-est*10**9; */
|
/* the estimate is now in carry; now calculate hi:lo-est*10**9; */
|
/* happily the top word of the result is irrelevant because it */
|
/* happily the top word of the result is irrelevant because it */
|
/* will always be zero so this needs only one multiplication */
|
/* will always be zero so this needs only one multiplication */
|
lo-=(carry*DIVBASE);
|
lo-=(carry*DIVBASE);
|
/* the correction here will be at most +1; do it */
|
/* the correction here will be at most +1; do it */
|
if (lo>=DIVBASE) {
|
if (lo>=DIVBASE) {
|
lo-=DIVBASE;
|
lo-=DIVBASE;
|
carry++;
|
carry++;
|
}
|
}
|
}
|
}
|
#endif
|
#endif
|
if (lo>*ua) { /* borrow needed */
|
if (lo>*ua) { /* borrow needed */
|
*ua+=DIVBASE;
|
*ua+=DIVBASE;
|
carry++;
|
carry++;
|
}
|
}
|
*ua-=lo;
|
*ua-=lo;
|
} /* ud loop */
|
} /* ud loop */
|
if (carry) *ua-=carry; /* accdigits>divdigits [cannot borrow] */
|
if (carry) *ua-=carry; /* accdigits>divdigits [cannot borrow] */
|
} /* inner loop */
|
} /* inner loop */
|
|
|
/* the outer loop terminates when there is either an exact result */
|
/* the outer loop terminates when there is either an exact result */
|
/* or enough digits; first update the quotient digit count and */
|
/* or enough digits; first update the quotient digit count and */
|
/* pointer (if any significant digits) */
|
/* pointer (if any significant digits) */
|
#if DECTRACE
|
#if DECTRACE
|
if (*lsuq || quodigits) printf("*lsuq=%09ld\n", (LI)*lsuq);
|
if (*lsuq || quodigits) printf("*lsuq=%09ld\n", (LI)*lsuq);
|
#endif
|
#endif
|
if (quodigits) {
|
if (quodigits) {
|
quodigits+=9; /* had leading unit earlier */
|
quodigits+=9; /* had leading unit earlier */
|
lsuq--;
|
lsuq--;
|
if (quodigits>DECPMAX+1) break; /* have enough */
|
if (quodigits>DECPMAX+1) break; /* have enough */
|
}
|
}
|
else if (*lsuq) { /* first quotient digits */
|
else if (*lsuq) { /* first quotient digits */
|
const uInt *pow;
|
const uInt *pow;
|
for (pow=DECPOWERS; *lsuq>=*pow; pow++) quodigits++;
|
for (pow=DECPOWERS; *lsuq>=*pow; pow++) quodigits++;
|
lsuq--;
|
lsuq--;
|
/* [cannot have >DECPMAX+1 on first unit] */
|
/* [cannot have >DECPMAX+1 on first unit] */
|
}
|
}
|
|
|
if (*msua!=0) continue; /* not an exact result */
|
if (*msua!=0) continue; /* not an exact result */
|
/* acc is zero iff used all of original units and zero down to lsua */
|
/* acc is zero iff used all of original units and zero down to lsua */
|
/* (must also continue to original lsu for correct quotient length) */
|
/* (must also continue to original lsu for correct quotient length) */
|
if (lsua>acc+DIVACCLEN-DIVOPLEN) continue;
|
if (lsua>acc+DIVACCLEN-DIVOPLEN) continue;
|
for (; msua>lsua && *msua==0;) msua--;
|
for (; msua>lsua && *msua==0;) msua--;
|
if (*msua==0 && msua==lsua) break;
|
if (*msua==0 && msua==lsua) break;
|
} /* outer loop */
|
} /* outer loop */
|
|
|
/* all of the original operand in acc has been covered at this point */
|
/* all of the original operand in acc has been covered at this point */
|
/* quotient now has at least DECPMAX+2 digits */
|
/* quotient now has at least DECPMAX+2 digits */
|
/* *msua is now non-0 if inexact and sticky bits */
|
/* *msua is now non-0 if inexact and sticky bits */
|
/* lsuq is one below the last uint of the quotient */
|
/* lsuq is one below the last uint of the quotient */
|
lsuq++; /* set -> true lsu of quo */
|
lsuq++; /* set -> true lsu of quo */
|
if (*msua) *lsuq|=1; /* apply sticky bit */
|
if (*msua) *lsuq|=1; /* apply sticky bit */
|
|
|
/* quo now holds the (unrounded) quotient in base-billion; one */
|
/* quo now holds the (unrounded) quotient in base-billion; one */
|
/* base-billion 'digit' per uInt. */
|
/* base-billion 'digit' per uInt. */
|
#if DECTRACE
|
#if DECTRACE
|
printf("DivQuo:");
|
printf("DivQuo:");
|
for (uq=msuq; uq>=lsuq; uq--) printf(" %09ld", (LI)*uq);
|
for (uq=msuq; uq>=lsuq; uq--) printf(" %09ld", (LI)*uq);
|
printf("\n");
|
printf("\n");
|
#endif
|
#endif
|
|
|
/* Now convert to BCD for rounding and cleanup, starting from the */
|
/* Now convert to BCD for rounding and cleanup, starting from the */
|
/* most significant end [offset by one into bcdacc to leave room */
|
/* most significant end [offset by one into bcdacc to leave room */
|
/* for a possible carry digit if rounding for REMNEAR is needed] */
|
/* for a possible carry digit if rounding for REMNEAR is needed] */
|
for (uq=msuq, ub=bcdacc+1; uq>=lsuq; uq--, ub+=9) {
|
for (uq=msuq, ub=bcdacc+1; uq>=lsuq; uq--, ub+=9) {
|
uInt top, mid, rem; /* work */
|
uInt top, mid, rem; /* work */
|
if (*uq==0) { /* no split needed */
|
if (*uq==0) { /* no split needed */
|
UINTAT(ub)=0; /* clear 9 BCD8s */
|
UINTAT(ub)=0; /* clear 9 BCD8s */
|
UINTAT(ub+4)=0; /* .. */
|
UINTAT(ub+4)=0; /* .. */
|
*(ub+8)=0; /* .. */
|
*(ub+8)=0; /* .. */
|
continue;
|
continue;
|
}
|
}
|
/* *uq is non-zero -- split the base-billion digit into */
|
/* *uq is non-zero -- split the base-billion digit into */
|
/* hi, mid, and low three-digits */
|
/* hi, mid, and low three-digits */
|
#define divsplit9 1000000 /* divisor */
|
#define divsplit9 1000000 /* divisor */
|
#define divsplit6 1000 /* divisor */
|
#define divsplit6 1000 /* divisor */
|
/* The splitting is done by simple divides and remainders, */
|
/* The splitting is done by simple divides and remainders, */
|
/* assuming the compiler will optimize these [GCC does] */
|
/* assuming the compiler will optimize these [GCC does] */
|
top=*uq/divsplit9;
|
top=*uq/divsplit9;
|
rem=*uq%divsplit9;
|
rem=*uq%divsplit9;
|
mid=rem/divsplit6;
|
mid=rem/divsplit6;
|
rem=rem%divsplit6;
|
rem=rem%divsplit6;
|
/* lay out the nine BCD digits (plus one unwanted byte) */
|
/* lay out the nine BCD digits (plus one unwanted byte) */
|
UINTAT(ub) =UINTAT(&BIN2BCD8[top*4]);
|
UINTAT(ub) =UINTAT(&BIN2BCD8[top*4]);
|
UINTAT(ub+3)=UINTAT(&BIN2BCD8[mid*4]);
|
UINTAT(ub+3)=UINTAT(&BIN2BCD8[mid*4]);
|
UINTAT(ub+6)=UINTAT(&BIN2BCD8[rem*4]);
|
UINTAT(ub+6)=UINTAT(&BIN2BCD8[rem*4]);
|
} /* BCD conversion loop */
|
} /* BCD conversion loop */
|
ub--; /* -> lsu */
|
ub--; /* -> lsu */
|
|
|
/* complete the bcdnum; quodigits is correct, so the position of */
|
/* complete the bcdnum; quodigits is correct, so the position of */
|
/* the first non-zero is known */
|
/* the first non-zero is known */
|
num.msd=bcdacc+1+(msuq-lsuq+1)*9-quodigits;
|
num.msd=bcdacc+1+(msuq-lsuq+1)*9-quodigits;
|
num.lsd=ub;
|
num.lsd=ub;
|
|
|
/* make exponent adjustments, etc */
|
/* make exponent adjustments, etc */
|
if (lsua<acc+DIVACCLEN-DIVOPLEN) { /* used extra digits */
|
if (lsua<acc+DIVACCLEN-DIVOPLEN) { /* used extra digits */
|
num.exponent-=(Int)((acc+DIVACCLEN-DIVOPLEN-lsua)*9);
|
num.exponent-=(Int)((acc+DIVACCLEN-DIVOPLEN-lsua)*9);
|
/* if the result was exact then there may be up to 8 extra */
|
/* if the result was exact then there may be up to 8 extra */
|
/* trailing zeros in the overflowed quotient final unit */
|
/* trailing zeros in the overflowed quotient final unit */
|
if (*msua==0) {
|
if (*msua==0) {
|
for (; *ub==0;) ub--; /* drop zeros */
|
for (; *ub==0;) ub--; /* drop zeros */
|
num.exponent+=(Int)(num.lsd-ub); /* and adjust exponent */
|
num.exponent+=(Int)(num.lsd-ub); /* and adjust exponent */
|
num.lsd=ub;
|
num.lsd=ub;
|
}
|
}
|
} /* adjustment needed */
|
} /* adjustment needed */
|
|
|
#if DIVCOUNT
|
#if DIVCOUNT
|
if (divcount>maxcount) { /* new high-water nark */
|
if (divcount>maxcount) { /* new high-water nark */
|
maxcount=divcount;
|
maxcount=divcount;
|
printf("DivNewMaxCount: %ld\n", (LI)maxcount);
|
printf("DivNewMaxCount: %ld\n", (LI)maxcount);
|
}
|
}
|
#endif
|
#endif
|
|
|
if (op&DIVIDE) return decFinalize(result, &num, set); /* all done */
|
if (op&DIVIDE) return decFinalize(result, &num, set); /* all done */
|
|
|
/* Is DIVIDEINT or a remainder; there is more to do -- first form */
|
/* Is DIVIDEINT or a remainder; there is more to do -- first form */
|
/* the integer (this is done 'after the fact', unlike as in */
|
/* the integer (this is done 'after the fact', unlike as in */
|
/* decNumber, so as not to tax DIVIDE) */
|
/* decNumber, so as not to tax DIVIDE) */
|
|
|
/* The first non-zero digit will be in the first 9 digits, known */
|
/* The first non-zero digit will be in the first 9 digits, known */
|
/* from quodigits and num.msd, so there is always space for DECPMAX */
|
/* from quodigits and num.msd, so there is always space for DECPMAX */
|
/* digits */
|
/* digits */
|
|
|
length=(Int)(num.lsd-num.msd+1);
|
length=(Int)(num.lsd-num.msd+1);
|
/*printf("Length exp: %ld %ld\n", (LI)length, (LI)num.exponent); */
|
/*printf("Length exp: %ld %ld\n", (LI)length, (LI)num.exponent); */
|
|
|
if (length+num.exponent>DECPMAX) { /* cannot fit */
|
if (length+num.exponent>DECPMAX) { /* cannot fit */
|
decFloatZero(result);
|
decFloatZero(result);
|
DFWORD(result, 0)=DECFLOAT_qNaN;
|
DFWORD(result, 0)=DECFLOAT_qNaN;
|
set->status|=DEC_Division_impossible;
|
set->status|=DEC_Division_impossible;
|
return result;
|
return result;
|
}
|
}
|
|
|
if (num.exponent>=0) { /* already an int, or need pad zeros */
|
if (num.exponent>=0) { /* already an int, or need pad zeros */
|
for (ub=num.lsd+1; ub<=num.lsd+num.exponent; ub++) *ub=0;
|
for (ub=num.lsd+1; ub<=num.lsd+num.exponent; ub++) *ub=0;
|
num.lsd+=num.exponent;
|
num.lsd+=num.exponent;
|
}
|
}
|
else { /* too long: round or truncate needed */
|
else { /* too long: round or truncate needed */
|
Int drop=-num.exponent;
|
Int drop=-num.exponent;
|
if (!(op&REMNEAR)) { /* simple truncate */
|
if (!(op&REMNEAR)) { /* simple truncate */
|
num.lsd-=drop;
|
num.lsd-=drop;
|
if (num.lsd<num.msd) { /* truncated all */
|
if (num.lsd<num.msd) { /* truncated all */
|
num.lsd=num.msd; /* make 0 */
|
num.lsd=num.msd; /* make 0 */
|
*num.lsd=0; /* .. [sign still relevant] */
|
*num.lsd=0; /* .. [sign still relevant] */
|
}
|
}
|
}
|
}
|
else { /* round to nearest even [sigh] */
|
else { /* round to nearest even [sigh] */
|
/* round-to-nearest, in-place; msd is at or to right of bcdacc+1 */
|
/* round-to-nearest, in-place; msd is at or to right of bcdacc+1 */
|
/* (this is a special case of Quantize -- q.v. for commentary) */
|
/* (this is a special case of Quantize -- q.v. for commentary) */
|
uByte *roundat; /* -> re-round digit */
|
uByte *roundat; /* -> re-round digit */
|
uByte reround; /* reround value */
|
uByte reround; /* reround value */
|
*(num.msd-1)=0; /* in case of left carry, or make 0 */
|
*(num.msd-1)=0; /* in case of left carry, or make 0 */
|
if (drop<length) roundat=num.lsd-drop+1;
|
if (drop<length) roundat=num.lsd-drop+1;
|
else if (drop==length) roundat=num.msd;
|
else if (drop==length) roundat=num.msd;
|
else roundat=num.msd-1; /* [-> 0] */
|
else roundat=num.msd-1; /* [-> 0] */
|
reround=*roundat;
|
reround=*roundat;
|
for (ub=roundat+1; ub<=num.lsd; ub++) {
|
for (ub=roundat+1; ub<=num.lsd; ub++) {
|
if (*ub!=0) {
|
if (*ub!=0) {
|
reround=DECSTICKYTAB[reround];
|
reround=DECSTICKYTAB[reround];
|
break;
|
break;
|
}
|
}
|
} /* check stickies */
|
} /* check stickies */
|
if (roundat>num.msd) num.lsd=roundat-1;
|
if (roundat>num.msd) num.lsd=roundat-1;
|
else {
|
else {
|
num.msd--; /* use the 0 .. */
|
num.msd--; /* use the 0 .. */
|
num.lsd=num.msd; /* .. at the new MSD place */
|
num.lsd=num.msd; /* .. at the new MSD place */
|
}
|
}
|
if (reround!=0) { /* discarding non-zero */
|
if (reround!=0) { /* discarding non-zero */
|
uInt bump=0;
|
uInt bump=0;
|
/* rounding is DEC_ROUND_HALF_EVEN always */
|
/* rounding is DEC_ROUND_HALF_EVEN always */
|
if (reround>5) bump=1; /* >0.5 goes up */
|
if (reround>5) bump=1; /* >0.5 goes up */
|
else if (reround==5) /* exactly 0.5000 .. */
|
else if (reround==5) /* exactly 0.5000 .. */
|
bump=*(num.lsd) & 0x01; /* .. up iff [new] lsd is odd */
|
bump=*(num.lsd) & 0x01; /* .. up iff [new] lsd is odd */
|
if (bump!=0) { /* need increment */
|
if (bump!=0) { /* need increment */
|
/* increment the coefficient; this might end up with 1000... */
|
/* increment the coefficient; this might end up with 1000... */
|
ub=num.lsd;
|
ub=num.lsd;
|
for (; UINTAT(ub-3)==0x09090909; ub-=4) UINTAT(ub-3)=0;
|
for (; UINTAT(ub-3)==0x09090909; ub-=4) UINTAT(ub-3)=0;
|
for (; *ub==9; ub--) *ub=0; /* at most 3 more */
|
for (; *ub==9; ub--) *ub=0; /* at most 3 more */
|
*ub+=1;
|
*ub+=1;
|
if (ub<num.msd) num.msd--; /* carried */
|
if (ub<num.msd) num.msd--; /* carried */
|
} /* bump needed */
|
} /* bump needed */
|
} /* reround!=0 */
|
} /* reround!=0 */
|
} /* remnear */
|
} /* remnear */
|
} /* round or truncate needed */
|
} /* round or truncate needed */
|
num.exponent=0; /* all paths */
|
num.exponent=0; /* all paths */
|
/*decShowNum(&num, "int"); */
|
/*decShowNum(&num, "int"); */
|
|
|
if (op&DIVIDEINT) return decFinalize(result, &num, set); /* all done */
|
if (op&DIVIDEINT) return decFinalize(result, &num, set); /* all done */
|
|
|
/* Have a remainder to calculate */
|
/* Have a remainder to calculate */
|
decFinalize("ient, &num, set); /* lay out the integer so far */
|
decFinalize("ient, &num, set); /* lay out the integer so far */
|
DFWORD("ient, 0)^=DECFLOAT_Sign; /* negate it */
|
DFWORD("ient, 0)^=DECFLOAT_Sign; /* negate it */
|
sign=DFWORD(dfl, 0); /* save sign of dfl */
|
sign=DFWORD(dfl, 0); /* save sign of dfl */
|
decFloatFMA(result, "ient, dfr, dfl, set);
|
decFloatFMA(result, "ient, dfr, dfl, set);
|
if (!DFISZERO(result)) return result;
|
if (!DFISZERO(result)) return result;
|
/* if the result is zero the sign shall be sign of dfl */
|
/* if the result is zero the sign shall be sign of dfl */
|
DFWORD("ient, 0)=sign; /* construct decFloat of sign */
|
DFWORD("ient, 0)=sign; /* construct decFloat of sign */
|
return decFloatCopySign(result, result, "ient);
|
return decFloatCopySign(result, result, "ient);
|
} /* decDivide */
|
} /* decDivide */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFiniteMultiply -- multiply two finite decFloats */
|
/* decFiniteMultiply -- multiply two finite decFloats */
|
/* */
|
/* */
|
/* num gets the result of multiplying dfl and dfr */
|
/* num gets the result of multiplying dfl and dfr */
|
/* bcdacc .. with the coefficient in this array */
|
/* bcdacc .. with the coefficient in this array */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* */
|
/* */
|
/* This effects the multiplication of two decFloats, both known to be */
|
/* This effects the multiplication of two decFloats, both known to be */
|
/* finite, leaving the result in a bcdnum ready for decFinalize (for */
|
/* finite, leaving the result in a bcdnum ready for decFinalize (for */
|
/* use in Multiply) or in a following addition (FMA). */
|
/* use in Multiply) or in a following addition (FMA). */
|
/* */
|
/* */
|
/* bcdacc must have space for at least DECPMAX9*18+1 bytes. */
|
/* bcdacc must have space for at least DECPMAX9*18+1 bytes. */
|
/* No error is possible and no status is set. */
|
/* No error is possible and no status is set. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* This routine has two separate implementations of the core */
|
/* This routine has two separate implementations of the core */
|
/* multiplication; both using base-billion. One uses only 32-bit */
|
/* multiplication; both using base-billion. One uses only 32-bit */
|
/* variables (Ints and uInts) or smaller; the other uses uLongs (for */
|
/* variables (Ints and uInts) or smaller; the other uses uLongs (for */
|
/* multiplication and addition only). Both implementations cover */
|
/* multiplication and addition only). Both implementations cover */
|
/* both arithmetic sizes (DOUBLE and QUAD) in order to allow timing */
|
/* both arithmetic sizes (DOUBLE and QUAD) in order to allow timing */
|
/* comparisons. In any one compilation only one implementation for */
|
/* comparisons. In any one compilation only one implementation for */
|
/* each size can be used, and if DECUSE64 is 0 then use of the 32-bit */
|
/* each size can be used, and if DECUSE64 is 0 then use of the 32-bit */
|
/* version is forced. */
|
/* version is forced. */
|
/* */
|
/* */
|
/* Historical note: an earlier version of this code also supported the */
|
/* Historical note: an earlier version of this code also supported the */
|
/* 256-bit format and has been preserved. That is somewhat trickier */
|
/* 256-bit format and has been preserved. That is somewhat trickier */
|
/* during lazy carry splitting because the initial quotient estimate */
|
/* during lazy carry splitting because the initial quotient estimate */
|
/* (est) can exceed 32 bits. */
|
/* (est) can exceed 32 bits. */
|
|
|
#define MULTBASE BILLION /* the base used for multiply */
|
#define MULTBASE BILLION /* the base used for multiply */
|
#define MULOPLEN DECPMAX9 /* operand length ('digits' base 10**9) */
|
#define MULOPLEN DECPMAX9 /* operand length ('digits' base 10**9) */
|
#define MULACCLEN (MULOPLEN*2) /* accumulator length (ditto) */
|
#define MULACCLEN (MULOPLEN*2) /* accumulator length (ditto) */
|
#define LEADZEROS (MULACCLEN*9 - DECPMAX*2) /* leading zeros always */
|
#define LEADZEROS (MULACCLEN*9 - DECPMAX*2) /* leading zeros always */
|
|
|
/* Assertions: exponent not too large and MULACCLEN is a multiple of 4 */
|
/* Assertions: exponent not too large and MULACCLEN is a multiple of 4 */
|
#if DECEMAXD>9
|
#if DECEMAXD>9
|
#error Exponent may overflow when doubled for Multiply
|
#error Exponent may overflow when doubled for Multiply
|
#endif
|
#endif
|
#if MULACCLEN!=(MULACCLEN/4)*4
|
#if MULACCLEN!=(MULACCLEN/4)*4
|
/* This assumption is used below only for initialization */
|
/* This assumption is used below only for initialization */
|
#error MULACCLEN is not a multiple of 4
|
#error MULACCLEN is not a multiple of 4
|
#endif
|
#endif
|
|
|
static void decFiniteMultiply(bcdnum *num, uByte *bcdacc,
|
static void decFiniteMultiply(bcdnum *num, uByte *bcdacc,
|
const decFloat *dfl, const decFloat *dfr) {
|
const decFloat *dfl, const decFloat *dfr) {
|
uInt bufl[MULOPLEN]; /* left coefficient (base-billion) */
|
uInt bufl[MULOPLEN]; /* left coefficient (base-billion) */
|
uInt bufr[MULOPLEN]; /* right coefficient (base-billion) */
|
uInt bufr[MULOPLEN]; /* right coefficient (base-billion) */
|
uInt *ui, *uj; /* work */
|
uInt *ui, *uj; /* work */
|
uByte *ub; /* .. */
|
uByte *ub; /* .. */
|
|
|
#if DECUSE64
|
#if DECUSE64
|
uLong accl[MULACCLEN]; /* lazy accumulator (base-billion+) */
|
uLong accl[MULACCLEN]; /* lazy accumulator (base-billion+) */
|
uLong *pl; /* work -> lazy accumulator */
|
uLong *pl; /* work -> lazy accumulator */
|
uInt acc[MULACCLEN]; /* coefficent in base-billion .. */
|
uInt acc[MULACCLEN]; /* coefficent in base-billion .. */
|
#else
|
#else
|
uInt acc[MULACCLEN*2]; /* accumulator in base-billion .. */
|
uInt acc[MULACCLEN*2]; /* accumulator in base-billion .. */
|
#endif
|
#endif
|
uInt *pa; /* work -> accumulator */
|
uInt *pa; /* work -> accumulator */
|
/*printf("Base10**9: OpLen=%d MulAcclen=%d\n", OPLEN, MULACCLEN); */
|
/*printf("Base10**9: OpLen=%d MulAcclen=%d\n", OPLEN, MULACCLEN); */
|
|
|
/* Calculate sign and exponent */
|
/* Calculate sign and exponent */
|
num->sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;
|
num->sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;
|
num->exponent=GETEXPUN(dfl)+GETEXPUN(dfr); /* [see assertion above] */
|
num->exponent=GETEXPUN(dfl)+GETEXPUN(dfr); /* [see assertion above] */
|
|
|
/* Extract the coefficients and prepare the accumulator */
|
/* Extract the coefficients and prepare the accumulator */
|
/* the coefficients of the operands are decoded into base-billion */
|
/* the coefficients of the operands are decoded into base-billion */
|
/* numbers in uInt arrays (bufl and bufr, LSD at offset 0) of the */
|
/* numbers in uInt arrays (bufl and bufr, LSD at offset 0) of the */
|
/* appropriate size. */
|
/* appropriate size. */
|
GETCOEFFBILL(dfl, bufl);
|
GETCOEFFBILL(dfl, bufl);
|
GETCOEFFBILL(dfr, bufr);
|
GETCOEFFBILL(dfr, bufr);
|
#if DECTRACE && 0
|
#if DECTRACE && 0
|
printf("CoeffbL:");
|
printf("CoeffbL:");
|
for (ui=bufl+MULOPLEN-1; ui>=bufl; ui--) printf(" %08lx", (LI)*ui);
|
for (ui=bufl+MULOPLEN-1; ui>=bufl; ui--) printf(" %08lx", (LI)*ui);
|
printf("\n");
|
printf("\n");
|
printf("CoeffbR:");
|
printf("CoeffbR:");
|
for (uj=bufr+MULOPLEN-1; uj>=bufr; uj--) printf(" %08lx", (LI)*uj);
|
for (uj=bufr+MULOPLEN-1; uj>=bufr; uj--) printf(" %08lx", (LI)*uj);
|
printf("\n");
|
printf("\n");
|
#endif
|
#endif
|
|
|
/* start the 64-bit/32-bit differing paths... */
|
/* start the 64-bit/32-bit differing paths... */
|
#if DECUSE64
|
#if DECUSE64
|
|
|
/* zero the accumulator */
|
/* zero the accumulator */
|
#if MULACCLEN==4
|
#if MULACCLEN==4
|
accl[0]=0; accl[1]=0; accl[2]=0; accl[3]=0;
|
accl[0]=0; accl[1]=0; accl[2]=0; accl[3]=0;
|
#else /* use a loop */
|
#else /* use a loop */
|
/* MULACCLEN is a multiple of four, asserted above */
|
/* MULACCLEN is a multiple of four, asserted above */
|
for (pl=accl; pl<accl+MULACCLEN; pl+=4) {
|
for (pl=accl; pl<accl+MULACCLEN; pl+=4) {
|
*pl=0; *(pl+1)=0; *(pl+2)=0; *(pl+3)=0;/* [reduce overhead] */
|
*pl=0; *(pl+1)=0; *(pl+2)=0; *(pl+3)=0;/* [reduce overhead] */
|
} /* pl */
|
} /* pl */
|
#endif
|
#endif
|
|
|
/* Effect the multiplication */
|
/* Effect the multiplication */
|
/* The multiplcation proceeds using MFC's lazy-carry resolution */
|
/* The multiplcation proceeds using MFC's lazy-carry resolution */
|
/* algorithm from decNumber. First, the multiplication is */
|
/* algorithm from decNumber. First, the multiplication is */
|
/* effected, allowing accumulation of the partial products (which */
|
/* effected, allowing accumulation of the partial products (which */
|
/* are in base-billion at each column position) into 64 bits */
|
/* are in base-billion at each column position) into 64 bits */
|
/* without resolving back to base=billion after each addition. */
|
/* without resolving back to base=billion after each addition. */
|
/* These 64-bit numbers (which may contain up to 19 decimal digits) */
|
/* These 64-bit numbers (which may contain up to 19 decimal digits) */
|
/* are then split using the Clark & Cowlishaw algorithm (see below). */
|
/* are then split using the Clark & Cowlishaw algorithm (see below). */
|
/* [Testing for 0 in the inner loop is not really a 'win'] */
|
/* [Testing for 0 in the inner loop is not really a 'win'] */
|
for (ui=bufr; ui<bufr+MULOPLEN; ui++) { /* over each item in rhs */
|
for (ui=bufr; ui<bufr+MULOPLEN; ui++) { /* over each item in rhs */
|
if (*ui==0) continue; /* product cannot affect result */
|
if (*ui==0) continue; /* product cannot affect result */
|
pl=accl+(ui-bufr); /* where to add the lhs */
|
pl=accl+(ui-bufr); /* where to add the lhs */
|
for (uj=bufl; uj<bufl+MULOPLEN; uj++, pl++) { /* over each item in lhs */
|
for (uj=bufl; uj<bufl+MULOPLEN; uj++, pl++) { /* over each item in lhs */
|
/* if (*uj==0) continue; // product cannot affect result */
|
/* if (*uj==0) continue; // product cannot affect result */
|
*pl+=((uLong)*ui)*(*uj);
|
*pl+=((uLong)*ui)*(*uj);
|
} /* uj */
|
} /* uj */
|
} /* ui */
|
} /* ui */
|
|
|
/* The 64-bit carries must now be resolved; this means that a */
|
/* The 64-bit carries must now be resolved; this means that a */
|
/* quotient/remainder has to be calculated for base-billion (1E+9). */
|
/* quotient/remainder has to be calculated for base-billion (1E+9). */
|
/* For this, Clark & Cowlishaw's quotient estimation approach (also */
|
/* For this, Clark & Cowlishaw's quotient estimation approach (also */
|
/* used in decNumber) is needed, because 64-bit divide is generally */
|
/* used in decNumber) is needed, because 64-bit divide is generally */
|
/* extremely slow on 32-bit machines, and may be slower than this */
|
/* extremely slow on 32-bit machines, and may be slower than this */
|
/* approach even on 64-bit machines. This algorithm splits X */
|
/* approach even on 64-bit machines. This algorithm splits X */
|
/* using: */
|
/* using: */
|
/* */
|
/* */
|
/* magic=2**(A+B)/1E+9; // 'magic number' */
|
/* magic=2**(A+B)/1E+9; // 'magic number' */
|
/* hop=X/2**A; // high order part of X (by shift) */
|
/* hop=X/2**A; // high order part of X (by shift) */
|
/* est=magic*hop/2**B // quotient estimate (may be low by 1) */
|
/* est=magic*hop/2**B // quotient estimate (may be low by 1) */
|
/* */
|
/* */
|
/* A and B are quite constrained; hop and magic must fit in 32 bits, */
|
/* A and B are quite constrained; hop and magic must fit in 32 bits, */
|
/* and 2**(A+B) must be as large as possible (which is 2**61 if */
|
/* and 2**(A+B) must be as large as possible (which is 2**61 if */
|
/* magic is to fit). Further, maxX increases with the length of */
|
/* magic is to fit). Further, maxX increases with the length of */
|
/* the operands (and hence the number of partial products */
|
/* the operands (and hence the number of partial products */
|
/* accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. */
|
/* accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. */
|
/* */
|
/* */
|
/* It can be shown that when OPLEN is 2 then the maximum error in */
|
/* It can be shown that when OPLEN is 2 then the maximum error in */
|
/* the estimated quotient is <1, but for larger maximum x the */
|
/* the estimated quotient is <1, but for larger maximum x the */
|
/* maximum error is above 1 so a correction that is >1 may be */
|
/* maximum error is above 1 so a correction that is >1 may be */
|
/* needed. Values of A and B are chosen to satisfy the constraints */
|
/* needed. Values of A and B are chosen to satisfy the constraints */
|
/* just mentioned while minimizing the maximum error (and hence the */
|
/* just mentioned while minimizing the maximum error (and hence the */
|
/* maximum correction), as shown in the following table: */
|
/* maximum correction), as shown in the following table: */
|
/* */
|
/* */
|
/* Type OPLEN A B maxX maxError maxCorrection */
|
/* Type OPLEN A B maxX maxError maxCorrection */
|
/* --------------------------------------------------------- */
|
/* --------------------------------------------------------- */
|
/* DOUBLE 2 29 32 <2*10**18 0.63 1 */
|
/* DOUBLE 2 29 32 <2*10**18 0.63 1 */
|
/* QUAD 4 30 31 <4*10**18 1.17 2 */
|
/* QUAD 4 30 31 <4*10**18 1.17 2 */
|
/* */
|
/* */
|
/* In the OPLEN==2 case there is most choice, but the value for B */
|
/* In the OPLEN==2 case there is most choice, but the value for B */
|
/* of 32 has a big advantage as then the calculation of the */
|
/* of 32 has a big advantage as then the calculation of the */
|
/* estimate requires no shifting; the compiler can extract the high */
|
/* estimate requires no shifting; the compiler can extract the high */
|
/* word directly after multiplying magic*hop. */
|
/* word directly after multiplying magic*hop. */
|
#define MULMAGIC 2305843009U /* 2**61/10**9 [both cases] */
|
#define MULMAGIC 2305843009U /* 2**61/10**9 [both cases] */
|
#if DOUBLE
|
#if DOUBLE
|
#define MULSHIFTA 29
|
#define MULSHIFTA 29
|
#define MULSHIFTB 32
|
#define MULSHIFTB 32
|
#elif QUAD
|
#elif QUAD
|
#define MULSHIFTA 30
|
#define MULSHIFTA 30
|
#define MULSHIFTB 31
|
#define MULSHIFTB 31
|
#else
|
#else
|
#error Unexpected type
|
#error Unexpected type
|
#endif
|
#endif
|
|
|
#if DECTRACE
|
#if DECTRACE
|
printf("MulAccl:");
|
printf("MulAccl:");
|
for (pl=accl+MULACCLEN-1; pl>=accl; pl--)
|
for (pl=accl+MULACCLEN-1; pl>=accl; pl--)
|
printf(" %08lx:%08lx", (LI)(*pl>>32), (LI)(*pl&0xffffffff));
|
printf(" %08lx:%08lx", (LI)(*pl>>32), (LI)(*pl&0xffffffff));
|
printf("\n");
|
printf("\n");
|
#endif
|
#endif
|
|
|
for (pl=accl, pa=acc; pl<accl+MULACCLEN; pl++, pa++) { /* each column position */
|
for (pl=accl, pa=acc; pl<accl+MULACCLEN; pl++, pa++) { /* each column position */
|
uInt lo, hop; /* work */
|
uInt lo, hop; /* work */
|
uInt est; /* cannot exceed 4E+9 */
|
uInt est; /* cannot exceed 4E+9 */
|
if (*pl>MULTBASE) {
|
if (*pl>MULTBASE) {
|
/* *pl holds a binary number which needs to be split */
|
/* *pl holds a binary number which needs to be split */
|
hop=(uInt)(*pl>>MULSHIFTA);
|
hop=(uInt)(*pl>>MULSHIFTA);
|
est=(uInt)(((uLong)hop*MULMAGIC)>>MULSHIFTB);
|
est=(uInt)(((uLong)hop*MULMAGIC)>>MULSHIFTB);
|
/* the estimate is now in est; now calculate hi:lo-est*10**9; */
|
/* the estimate is now in est; now calculate hi:lo-est*10**9; */
|
/* happily the top word of the result is irrelevant because it */
|
/* happily the top word of the result is irrelevant because it */
|
/* will always be zero so this needs only one multiplication */
|
/* will always be zero so this needs only one multiplication */
|
lo=(uInt)(*pl-((uLong)est*MULTBASE)); /* low word of result */
|
lo=(uInt)(*pl-((uLong)est*MULTBASE)); /* low word of result */
|
/* If QUAD, the correction here could be +2 */
|
/* If QUAD, the correction here could be +2 */
|
if (lo>=MULTBASE) {
|
if (lo>=MULTBASE) {
|
lo-=MULTBASE; /* correct by +1 */
|
lo-=MULTBASE; /* correct by +1 */
|
est++;
|
est++;
|
#if QUAD
|
#if QUAD
|
/* may need to correct by +2 */
|
/* may need to correct by +2 */
|
if (lo>=MULTBASE) {
|
if (lo>=MULTBASE) {
|
lo-=MULTBASE;
|
lo-=MULTBASE;
|
est++;
|
est++;
|
}
|
}
|
#endif
|
#endif
|
}
|
}
|
/* finally place lo as the new coefficient 'digit' and add est to */
|
/* finally place lo as the new coefficient 'digit' and add est to */
|
/* the next place up [this is safe because this path is never */
|
/* the next place up [this is safe because this path is never */
|
/* taken on the final iteration as *pl will fit] */
|
/* taken on the final iteration as *pl will fit] */
|
*pa=lo;
|
*pa=lo;
|
*(pl+1)+=est;
|
*(pl+1)+=est;
|
} /* *pl needed split */
|
} /* *pl needed split */
|
else { /* *pl<MULTBASE */
|
else { /* *pl<MULTBASE */
|
*pa=(uInt)*pl; /* just copy across */
|
*pa=(uInt)*pl; /* just copy across */
|
}
|
}
|
} /* pl loop */
|
} /* pl loop */
|
|
|
#else /* 32-bit */
|
#else /* 32-bit */
|
for (pa=acc;; pa+=4) { /* zero the accumulator */
|
for (pa=acc;; pa+=4) { /* zero the accumulator */
|
*pa=0; *(pa+1)=0; *(pa+2)=0; *(pa+3)=0; /* [reduce overhead] */
|
*pa=0; *(pa+1)=0; *(pa+2)=0; *(pa+3)=0; /* [reduce overhead] */
|
if (pa==acc+MULACCLEN*2-4) break; /* multiple of 4 asserted */
|
if (pa==acc+MULACCLEN*2-4) break; /* multiple of 4 asserted */
|
} /* pa */
|
} /* pa */
|
|
|
/* Effect the multiplication */
|
/* Effect the multiplication */
|
/* uLongs are not available (and in particular, there is no uLong */
|
/* uLongs are not available (and in particular, there is no uLong */
|
/* divide) but it is still possible to use MFC's lazy-carry */
|
/* divide) but it is still possible to use MFC's lazy-carry */
|
/* resolution algorithm from decNumber. First, the multiplication */
|
/* resolution algorithm from decNumber. First, the multiplication */
|
/* is effected, allowing accumulation of the partial products */
|
/* is effected, allowing accumulation of the partial products */
|
/* (which are in base-billion at each column position) into 64 bits */
|
/* (which are in base-billion at each column position) into 64 bits */
|
/* [with the high-order 32 bits in each position being held at */
|
/* [with the high-order 32 bits in each position being held at */
|
/* offset +ACCLEN from the low-order 32 bits in the accumulator]. */
|
/* offset +ACCLEN from the low-order 32 bits in the accumulator]. */
|
/* These 64-bit numbers (which may contain up to 19 decimal digits) */
|
/* These 64-bit numbers (which may contain up to 19 decimal digits) */
|
/* are then split using the Clark & Cowlishaw algorithm (see */
|
/* are then split using the Clark & Cowlishaw algorithm (see */
|
/* below). */
|
/* below). */
|
for (ui=bufr;; ui++) { /* over each item in rhs */
|
for (ui=bufr;; ui++) { /* over each item in rhs */
|
uInt hi, lo; /* words of exact multiply result */
|
uInt hi, lo; /* words of exact multiply result */
|
pa=acc+(ui-bufr); /* where to add the lhs */
|
pa=acc+(ui-bufr); /* where to add the lhs */
|
for (uj=bufl;; uj++, pa++) { /* over each item in lhs */
|
for (uj=bufl;; uj++, pa++) { /* over each item in lhs */
|
LONGMUL32HI(hi, *ui, *uj); /* calculate product of digits */
|
LONGMUL32HI(hi, *ui, *uj); /* calculate product of digits */
|
lo=(*ui)*(*uj); /* .. */
|
lo=(*ui)*(*uj); /* .. */
|
*pa+=lo; /* accumulate low bits and .. */
|
*pa+=lo; /* accumulate low bits and .. */
|
*(pa+MULACCLEN)+=hi+(*pa<lo); /* .. high bits with any carry */
|
*(pa+MULACCLEN)+=hi+(*pa<lo); /* .. high bits with any carry */
|
if (uj==bufl+MULOPLEN-1) break;
|
if (uj==bufl+MULOPLEN-1) break;
|
}
|
}
|
if (ui==bufr+MULOPLEN-1) break;
|
if (ui==bufr+MULOPLEN-1) break;
|
}
|
}
|
|
|
/* The 64-bit carries must now be resolved; this means that a */
|
/* The 64-bit carries must now be resolved; this means that a */
|
/* quotient/remainder has to be calculated for base-billion (1E+9). */
|
/* quotient/remainder has to be calculated for base-billion (1E+9). */
|
/* For this, Clark & Cowlishaw's quotient estimation approach (also */
|
/* For this, Clark & Cowlishaw's quotient estimation approach (also */
|
/* used in decNumber) is needed, because 64-bit divide is generally */
|
/* used in decNumber) is needed, because 64-bit divide is generally */
|
/* extremely slow on 32-bit machines. This algorithm splits X */
|
/* extremely slow on 32-bit machines. This algorithm splits X */
|
/* using: */
|
/* using: */
|
/* */
|
/* */
|
/* magic=2**(A+B)/1E+9; // 'magic number' */
|
/* magic=2**(A+B)/1E+9; // 'magic number' */
|
/* hop=X/2**A; // high order part of X (by shift) */
|
/* hop=X/2**A; // high order part of X (by shift) */
|
/* est=magic*hop/2**B // quotient estimate (may be low by 1) */
|
/* est=magic*hop/2**B // quotient estimate (may be low by 1) */
|
/* */
|
/* */
|
/* A and B are quite constrained; hop and magic must fit in 32 bits, */
|
/* A and B are quite constrained; hop and magic must fit in 32 bits, */
|
/* and 2**(A+B) must be as large as possible (which is 2**61 if */
|
/* and 2**(A+B) must be as large as possible (which is 2**61 if */
|
/* magic is to fit). Further, maxX increases with the length of */
|
/* magic is to fit). Further, maxX increases with the length of */
|
/* the operands (and hence the number of partial products */
|
/* the operands (and hence the number of partial products */
|
/* accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. */
|
/* accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. */
|
/* */
|
/* */
|
/* It can be shown that when OPLEN is 2 then the maximum error in */
|
/* It can be shown that when OPLEN is 2 then the maximum error in */
|
/* the estimated quotient is <1, but for larger maximum x the */
|
/* the estimated quotient is <1, but for larger maximum x the */
|
/* maximum error is above 1 so a correction that is >1 may be */
|
/* maximum error is above 1 so a correction that is >1 may be */
|
/* needed. Values of A and B are chosen to satisfy the constraints */
|
/* needed. Values of A and B are chosen to satisfy the constraints */
|
/* just mentioned while minimizing the maximum error (and hence the */
|
/* just mentioned while minimizing the maximum error (and hence the */
|
/* maximum correction), as shown in the following table: */
|
/* maximum correction), as shown in the following table: */
|
/* */
|
/* */
|
/* Type OPLEN A B maxX maxError maxCorrection */
|
/* Type OPLEN A B maxX maxError maxCorrection */
|
/* --------------------------------------------------------- */
|
/* --------------------------------------------------------- */
|
/* DOUBLE 2 29 32 <2*10**18 0.63 1 */
|
/* DOUBLE 2 29 32 <2*10**18 0.63 1 */
|
/* QUAD 4 30 31 <4*10**18 1.17 2 */
|
/* QUAD 4 30 31 <4*10**18 1.17 2 */
|
/* */
|
/* */
|
/* In the OPLEN==2 case there is most choice, but the value for B */
|
/* In the OPLEN==2 case there is most choice, but the value for B */
|
/* of 32 has a big advantage as then the calculation of the */
|
/* of 32 has a big advantage as then the calculation of the */
|
/* estimate requires no shifting; the high word is simply */
|
/* estimate requires no shifting; the high word is simply */
|
/* calculated from multiplying magic*hop. */
|
/* calculated from multiplying magic*hop. */
|
#define MULMAGIC 2305843009U /* 2**61/10**9 [both cases] */
|
#define MULMAGIC 2305843009U /* 2**61/10**9 [both cases] */
|
#if DOUBLE
|
#if DOUBLE
|
#define MULSHIFTA 29
|
#define MULSHIFTA 29
|
#define MULSHIFTB 32
|
#define MULSHIFTB 32
|
#elif QUAD
|
#elif QUAD
|
#define MULSHIFTA 30
|
#define MULSHIFTA 30
|
#define MULSHIFTB 31
|
#define MULSHIFTB 31
|
#else
|
#else
|
#error Unexpected type
|
#error Unexpected type
|
#endif
|
#endif
|
|
|
#if DECTRACE
|
#if DECTRACE
|
printf("MulHiLo:");
|
printf("MulHiLo:");
|
for (pa=acc+MULACCLEN-1; pa>=acc; pa--)
|
for (pa=acc+MULACCLEN-1; pa>=acc; pa--)
|
printf(" %08lx:%08lx", (LI)*(pa+MULACCLEN), (LI)*pa);
|
printf(" %08lx:%08lx", (LI)*(pa+MULACCLEN), (LI)*pa);
|
printf("\n");
|
printf("\n");
|
#endif
|
#endif
|
|
|
for (pa=acc;; pa++) { /* each low uInt */
|
for (pa=acc;; pa++) { /* each low uInt */
|
uInt hi, lo; /* words of exact multiply result */
|
uInt hi, lo; /* words of exact multiply result */
|
uInt hop, estlo; /* work */
|
uInt hop, estlo; /* work */
|
#if QUAD
|
#if QUAD
|
uInt esthi; /* .. */
|
uInt esthi; /* .. */
|
#endif
|
#endif
|
|
|
lo=*pa;
|
lo=*pa;
|
hi=*(pa+MULACCLEN); /* top 32 bits */
|
hi=*(pa+MULACCLEN); /* top 32 bits */
|
/* hi and lo now hold a binary number which needs to be split */
|
/* hi and lo now hold a binary number which needs to be split */
|
|
|
#if DOUBLE
|
#if DOUBLE
|
hop=(hi<<3)+(lo>>MULSHIFTA); /* hi:lo/2**29 */
|
hop=(hi<<3)+(lo>>MULSHIFTA); /* hi:lo/2**29 */
|
LONGMUL32HI(estlo, hop, MULMAGIC);/* only need the high word */
|
LONGMUL32HI(estlo, hop, MULMAGIC);/* only need the high word */
|
/* [MULSHIFTB is 32, so estlo can be used directly] */
|
/* [MULSHIFTB is 32, so estlo can be used directly] */
|
/* the estimate is now in estlo; now calculate hi:lo-est*10**9; */
|
/* the estimate is now in estlo; now calculate hi:lo-est*10**9; */
|
/* happily the top word of the result is irrelevant because it */
|
/* happily the top word of the result is irrelevant because it */
|
/* will always be zero so this needs only one multiplication */
|
/* will always be zero so this needs only one multiplication */
|
lo-=(estlo*MULTBASE);
|
lo-=(estlo*MULTBASE);
|
/* esthi=0; // high word is ignored below */
|
/* esthi=0; // high word is ignored below */
|
/* the correction here will be at most +1; do it */
|
/* the correction here will be at most +1; do it */
|
if (lo>=MULTBASE) {
|
if (lo>=MULTBASE) {
|
lo-=MULTBASE;
|
lo-=MULTBASE;
|
estlo++;
|
estlo++;
|
}
|
}
|
#elif QUAD
|
#elif QUAD
|
hop=(hi<<2)+(lo>>MULSHIFTA); /* hi:lo/2**30 */
|
hop=(hi<<2)+(lo>>MULSHIFTA); /* hi:lo/2**30 */
|
LONGMUL32HI(esthi, hop, MULMAGIC);/* shift will be 31 .. */
|
LONGMUL32HI(esthi, hop, MULMAGIC);/* shift will be 31 .. */
|
estlo=hop*MULMAGIC; /* .. so low word needed */
|
estlo=hop*MULMAGIC; /* .. so low word needed */
|
estlo=(esthi<<1)+(estlo>>MULSHIFTB); /* [just the top bit] */
|
estlo=(esthi<<1)+(estlo>>MULSHIFTB); /* [just the top bit] */
|
/* esthi=0; // high word is ignored below */
|
/* esthi=0; // high word is ignored below */
|
lo-=(estlo*MULTBASE); /* as above */
|
lo-=(estlo*MULTBASE); /* as above */
|
/* the correction here could be +1 or +2 */
|
/* the correction here could be +1 or +2 */
|
if (lo>=MULTBASE) {
|
if (lo>=MULTBASE) {
|
lo-=MULTBASE;
|
lo-=MULTBASE;
|
estlo++;
|
estlo++;
|
}
|
}
|
if (lo>=MULTBASE) {
|
if (lo>=MULTBASE) {
|
lo-=MULTBASE;
|
lo-=MULTBASE;
|
estlo++;
|
estlo++;
|
}
|
}
|
#else
|
#else
|
#error Unexpected type
|
#error Unexpected type
|
#endif
|
#endif
|
|
|
/* finally place lo as the new accumulator digit and add est to */
|
/* finally place lo as the new accumulator digit and add est to */
|
/* the next place up; this latter add could cause a carry of 1 */
|
/* the next place up; this latter add could cause a carry of 1 */
|
/* to the high word of the next place */
|
/* to the high word of the next place */
|
*pa=lo;
|
*pa=lo;
|
*(pa+1)+=estlo;
|
*(pa+1)+=estlo;
|
/* esthi is always 0 for DOUBLE and QUAD so this is skipped */
|
/* esthi is always 0 for DOUBLE and QUAD so this is skipped */
|
/* *(pa+1+MULACCLEN)+=esthi; */
|
/* *(pa+1+MULACCLEN)+=esthi; */
|
if (*(pa+1)<estlo) *(pa+1+MULACCLEN)+=1; /* carry */
|
if (*(pa+1)<estlo) *(pa+1+MULACCLEN)+=1; /* carry */
|
if (pa==acc+MULACCLEN-2) break; /* [MULACCLEN-1 will never need split] */
|
if (pa==acc+MULACCLEN-2) break; /* [MULACCLEN-1 will never need split] */
|
} /* pa loop */
|
} /* pa loop */
|
#endif
|
#endif
|
|
|
/* At this point, whether using the 64-bit or the 32-bit paths, the */
|
/* At this point, whether using the 64-bit or the 32-bit paths, the */
|
/* accumulator now holds the (unrounded) result in base-billion; */
|
/* accumulator now holds the (unrounded) result in base-billion; */
|
/* one base-billion 'digit' per uInt. */
|
/* one base-billion 'digit' per uInt. */
|
#if DECTRACE
|
#if DECTRACE
|
printf("MultAcc:");
|
printf("MultAcc:");
|
for (pa=acc+MULACCLEN-1; pa>=acc; pa--) printf(" %09ld", (LI)*pa);
|
for (pa=acc+MULACCLEN-1; pa>=acc; pa--) printf(" %09ld", (LI)*pa);
|
printf("\n");
|
printf("\n");
|
#endif
|
#endif
|
|
|
/* Now convert to BCD for rounding and cleanup, starting from the */
|
/* Now convert to BCD for rounding and cleanup, starting from the */
|
/* most significant end */
|
/* most significant end */
|
pa=acc+MULACCLEN-1;
|
pa=acc+MULACCLEN-1;
|
if (*pa!=0) num->msd=bcdacc+LEADZEROS;/* drop known lead zeros */
|
if (*pa!=0) num->msd=bcdacc+LEADZEROS;/* drop known lead zeros */
|
else { /* >=1 word of leading zeros */
|
else { /* >=1 word of leading zeros */
|
num->msd=bcdacc; /* known leading zeros are gone */
|
num->msd=bcdacc; /* known leading zeros are gone */
|
pa--; /* skip first word .. */
|
pa--; /* skip first word .. */
|
for (; *pa==0; pa--) if (pa==acc) break; /* .. and any more leading 0s */
|
for (; *pa==0; pa--) if (pa==acc) break; /* .. and any more leading 0s */
|
}
|
}
|
for (ub=bcdacc;; pa--, ub+=9) {
|
for (ub=bcdacc;; pa--, ub+=9) {
|
if (*pa!=0) { /* split(s) needed */
|
if (*pa!=0) { /* split(s) needed */
|
uInt top, mid, rem; /* work */
|
uInt top, mid, rem; /* work */
|
/* *pa is non-zero -- split the base-billion acc digit into */
|
/* *pa is non-zero -- split the base-billion acc digit into */
|
/* hi, mid, and low three-digits */
|
/* hi, mid, and low three-digits */
|
#define mulsplit9 1000000 /* divisor */
|
#define mulsplit9 1000000 /* divisor */
|
#define mulsplit6 1000 /* divisor */
|
#define mulsplit6 1000 /* divisor */
|
/* The splitting is done by simple divides and remainders, */
|
/* The splitting is done by simple divides and remainders, */
|
/* assuming the compiler will optimize these where useful */
|
/* assuming the compiler will optimize these where useful */
|
/* [GCC does] */
|
/* [GCC does] */
|
top=*pa/mulsplit9;
|
top=*pa/mulsplit9;
|
rem=*pa%mulsplit9;
|
rem=*pa%mulsplit9;
|
mid=rem/mulsplit6;
|
mid=rem/mulsplit6;
|
rem=rem%mulsplit6;
|
rem=rem%mulsplit6;
|
/* lay out the nine BCD digits (plus one unwanted byte) */
|
/* lay out the nine BCD digits (plus one unwanted byte) */
|
UINTAT(ub) =UINTAT(&BIN2BCD8[top*4]);
|
UINTAT(ub) =UINTAT(&BIN2BCD8[top*4]);
|
UINTAT(ub+3)=UINTAT(&BIN2BCD8[mid*4]);
|
UINTAT(ub+3)=UINTAT(&BIN2BCD8[mid*4]);
|
UINTAT(ub+6)=UINTAT(&BIN2BCD8[rem*4]);
|
UINTAT(ub+6)=UINTAT(&BIN2BCD8[rem*4]);
|
}
|
}
|
else { /* *pa==0 */
|
else { /* *pa==0 */
|
UINTAT(ub)=0; /* clear 9 BCD8s */
|
UINTAT(ub)=0; /* clear 9 BCD8s */
|
UINTAT(ub+4)=0; /* .. */
|
UINTAT(ub+4)=0; /* .. */
|
*(ub+8)=0; /* .. */
|
*(ub+8)=0; /* .. */
|
}
|
}
|
if (pa==acc) break;
|
if (pa==acc) break;
|
} /* BCD conversion loop */
|
} /* BCD conversion loop */
|
|
|
num->lsd=ub+8; /* complete the bcdnum .. */
|
num->lsd=ub+8; /* complete the bcdnum .. */
|
|
|
#if DECTRACE
|
#if DECTRACE
|
decShowNum(num, "postmult");
|
decShowNum(num, "postmult");
|
decFloatShow(dfl, "dfl");
|
decFloatShow(dfl, "dfl");
|
decFloatShow(dfr, "dfr");
|
decFloatShow(dfr, "dfr");
|
#endif
|
#endif
|
return;
|
return;
|
} /* decFiniteMultiply */
|
} /* decFiniteMultiply */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatAbs -- absolute value, heeding NaNs, etc. */
|
/* decFloatAbs -- absolute value, heeding NaNs, etc. */
|
/* */
|
/* */
|
/* result gets the canonicalized df with sign 0 */
|
/* result gets the canonicalized df with sign 0 */
|
/* df is the decFloat to abs */
|
/* df is the decFloat to abs */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This has the same effect as decFloatPlus unless df is negative, */
|
/* This has the same effect as decFloatPlus unless df is negative, */
|
/* in which case it has the same effect as decFloatMinus. The */
|
/* in which case it has the same effect as decFloatMinus. The */
|
/* effect is also the same as decFloatCopyAbs except that NaNs are */
|
/* effect is also the same as decFloatCopyAbs except that NaNs are */
|
/* handled normally (the sign of a NaN is not affected, and an sNaN */
|
/* handled normally (the sign of a NaN is not affected, and an sNaN */
|
/* will signal) and the result will be canonical. */
|
/* will signal) and the result will be canonical. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatAbs(decFloat *result, const decFloat *df,
|
decFloat * decFloatAbs(decFloat *result, const decFloat *df,
|
decContext *set) {
|
decContext *set) {
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
decCanonical(result, df); /* copy and check */
|
decCanonical(result, df); /* copy and check */
|
DFBYTE(result, 0)&=~0x80; /* zero sign bit */
|
DFBYTE(result, 0)&=~0x80; /* zero sign bit */
|
return result;
|
return result;
|
} /* decFloatAbs */
|
} /* decFloatAbs */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatAdd -- add two decFloats */
|
/* decFloatAdd -- add two decFloats */
|
/* */
|
/* */
|
/* result gets the result of adding dfl and dfr: */
|
/* result gets the result of adding dfl and dfr: */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatAdd(decFloat *result,
|
decFloat * decFloatAdd(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
bcdnum num; /* for final conversion */
|
bcdnum num; /* for final conversion */
|
Int expl, expr; /* left and right exponents */
|
Int expl, expr; /* left and right exponents */
|
uInt *ui, *uj; /* work */
|
uInt *ui, *uj; /* work */
|
uByte *ub; /* .. */
|
uByte *ub; /* .. */
|
|
|
uInt sourhil, sourhir; /* top words from source decFloats */
|
uInt sourhil, sourhir; /* top words from source decFloats */
|
/* [valid only until specials */
|
/* [valid only until specials */
|
/* handled or exponents decoded] */
|
/* handled or exponents decoded] */
|
uInt diffsign; /* non-zero if signs differ */
|
uInt diffsign; /* non-zero if signs differ */
|
uInt carry; /* carry: 0 or 1 before add loop */
|
uInt carry; /* carry: 0 or 1 before add loop */
|
Int overlap; /* coefficient overlap (if full) */
|
Int overlap; /* coefficient overlap (if full) */
|
/* the following buffers hold coefficients with various alignments */
|
/* the following buffers hold coefficients with various alignments */
|
/* (see commentary and diagrams below) */
|
/* (see commentary and diagrams below) */
|
uByte acc[4+2+DECPMAX*3+8];
|
uByte acc[4+2+DECPMAX*3+8];
|
uByte buf[4+2+DECPMAX*2];
|
uByte buf[4+2+DECPMAX*2];
|
uByte *umsd, *ulsd; /* local MSD and LSD pointers */
|
uByte *umsd, *ulsd; /* local MSD and LSD pointers */
|
|
|
#if DECLITEND
|
#if DECLITEND
|
#define CARRYPAT 0x01000000 /* carry=1 pattern */
|
#define CARRYPAT 0x01000000 /* carry=1 pattern */
|
#else
|
#else
|
#define CARRYPAT 0x00000001 /* carry=1 pattern */
|
#define CARRYPAT 0x00000001 /* carry=1 pattern */
|
#endif
|
#endif
|
|
|
/* Start decoding the arguments */
|
/* Start decoding the arguments */
|
/* the initial exponents are placed into the opposite Ints to */
|
/* the initial exponents are placed into the opposite Ints to */
|
/* that which might be expected; there are two sets of data to */
|
/* that which might be expected; there are two sets of data to */
|
/* keep track of (each decFloat and the corresponding exponent), */
|
/* keep track of (each decFloat and the corresponding exponent), */
|
/* and this scheme means that at the swap point (after comparing */
|
/* and this scheme means that at the swap point (after comparing */
|
/* exponents) only one pair of words needs to be swapped */
|
/* exponents) only one pair of words needs to be swapped */
|
/* whichever path is taken (thereby minimising worst-case path) */
|
/* whichever path is taken (thereby minimising worst-case path) */
|
sourhil=DFWORD(dfl, 0); /* LHS top word */
|
sourhil=DFWORD(dfl, 0); /* LHS top word */
|
expr=DECCOMBEXP[sourhil>>26]; /* get exponent high bits (in place) */
|
expr=DECCOMBEXP[sourhil>>26]; /* get exponent high bits (in place) */
|
sourhir=DFWORD(dfr, 0); /* RHS top word */
|
sourhir=DFWORD(dfr, 0); /* RHS top word */
|
expl=DECCOMBEXP[sourhir>>26];
|
expl=DECCOMBEXP[sourhir>>26];
|
|
|
diffsign=(sourhil^sourhir)&DECFLOAT_Sign;
|
diffsign=(sourhil^sourhir)&DECFLOAT_Sign;
|
|
|
if (EXPISSPECIAL(expl | expr)) { /* either is special? */
|
if (EXPISSPECIAL(expl | expr)) { /* either is special? */
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
/* one or two infinities */
|
/* one or two infinities */
|
/* two infinities with different signs is invalid */
|
/* two infinities with different signs is invalid */
|
if (diffsign && DFISINF(dfl) && DFISINF(dfr))
|
if (diffsign && DFISINF(dfl) && DFISINF(dfr))
|
return decInvalid(result, set);
|
return decInvalid(result, set);
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* LHS is infinite */
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* LHS is infinite */
|
return decInfinity(result, dfr); /* RHS must be Infinite */
|
return decInfinity(result, dfr); /* RHS must be Infinite */
|
}
|
}
|
|
|
/* Here when both arguments are finite */
|
/* Here when both arguments are finite */
|
|
|
/* complete exponent gathering (keeping swapped) */
|
/* complete exponent gathering (keeping swapped) */
|
expr+=GETECON(dfl)-DECBIAS; /* .. + continuation and unbias */
|
expr+=GETECON(dfl)-DECBIAS; /* .. + continuation and unbias */
|
expl+=GETECON(dfr)-DECBIAS;
|
expl+=GETECON(dfr)-DECBIAS;
|
/* here expr has exponent from lhs, and vice versa */
|
/* here expr has exponent from lhs, and vice versa */
|
|
|
/* now swap either exponents or argument pointers */
|
/* now swap either exponents or argument pointers */
|
if (expl<=expr) {
|
if (expl<=expr) {
|
/* original left is bigger */
|
/* original left is bigger */
|
Int expswap=expl;
|
Int expswap=expl;
|
expl=expr;
|
expl=expr;
|
expr=expswap;
|
expr=expswap;
|
/* printf("left bigger\n"); */
|
/* printf("left bigger\n"); */
|
}
|
}
|
else {
|
else {
|
const decFloat *dfswap=dfl;
|
const decFloat *dfswap=dfl;
|
dfl=dfr;
|
dfl=dfr;
|
dfr=dfswap;
|
dfr=dfswap;
|
/* printf("right bigger\n"); */
|
/* printf("right bigger\n"); */
|
}
|
}
|
/* [here dfl and expl refer to the datum with the larger exponent, */
|
/* [here dfl and expl refer to the datum with the larger exponent, */
|
/* of if the exponents are equal then the original LHS argument] */
|
/* of if the exponents are equal then the original LHS argument] */
|
|
|
/* if lhs is zero then result will be the rhs (now known to have */
|
/* if lhs is zero then result will be the rhs (now known to have */
|
/* the smaller exponent), which also may need to be tested for zero */
|
/* the smaller exponent), which also may need to be tested for zero */
|
/* for the weird IEEE 754 sign rules */
|
/* for the weird IEEE 754 sign rules */
|
if (DFISZERO(dfl)) {
|
if (DFISZERO(dfl)) {
|
decCanonical(result, dfr); /* clean copy */
|
decCanonical(result, dfr); /* clean copy */
|
/* "When the sum of two operands with opposite signs is */
|
/* "When the sum of two operands with opposite signs is */
|
/* exactly zero, the sign of that sum shall be '+' in all */
|
/* exactly zero, the sign of that sum shall be '+' in all */
|
/* rounding modes except round toward -Infinity, in which */
|
/* rounding modes except round toward -Infinity, in which */
|
/* mode that sign shall be '-'." */
|
/* mode that sign shall be '-'." */
|
if (diffsign && DFISZERO(result)) {
|
if (diffsign && DFISZERO(result)) {
|
DFWORD(result, 0)&=~DECFLOAT_Sign; /* assume sign 0 */
|
DFWORD(result, 0)&=~DECFLOAT_Sign; /* assume sign 0 */
|
if (set->round==DEC_ROUND_FLOOR) DFWORD(result, 0)|=DECFLOAT_Sign;
|
if (set->round==DEC_ROUND_FLOOR) DFWORD(result, 0)|=DECFLOAT_Sign;
|
}
|
}
|
return result;
|
return result;
|
} /* numfl is zero */
|
} /* numfl is zero */
|
/* [here, LHS is non-zero; code below assumes that] */
|
/* [here, LHS is non-zero; code below assumes that] */
|
|
|
/* Coefficients layout during the calculations to follow: */
|
/* Coefficients layout during the calculations to follow: */
|
/* */
|
/* */
|
/* Overlap case: */
|
/* Overlap case: */
|
/* +------------------------------------------------+ */
|
/* +------------------------------------------------+ */
|
/* acc: |0000| coeffa | tail B | | */
|
/* acc: |0000| coeffa | tail B | | */
|
/* +------------------------------------------------+ */
|
/* +------------------------------------------------+ */
|
/* buf: |0000| pad0s | coeffb | | */
|
/* buf: |0000| pad0s | coeffb | | */
|
/* +------------------------------------------------+ */
|
/* +------------------------------------------------+ */
|
/* */
|
/* */
|
/* Touching coefficients or gap: */
|
/* Touching coefficients or gap: */
|
/* +------------------------------------------------+ */
|
/* +------------------------------------------------+ */
|
/* acc: |0000| coeffa | gap | coeffb | */
|
/* acc: |0000| coeffa | gap | coeffb | */
|
/* +------------------------------------------------+ */
|
/* +------------------------------------------------+ */
|
/* [buf not used or needed; gap clamped to Pmax] */
|
/* [buf not used or needed; gap clamped to Pmax] */
|
|
|
/* lay out lhs coefficient into accumulator; this starts at acc+4 */
|
/* lay out lhs coefficient into accumulator; this starts at acc+4 */
|
/* for decDouble or acc+6 for decQuad so the LSD is word- */
|
/* for decDouble or acc+6 for decQuad so the LSD is word- */
|
/* aligned; the top word gap is there only in case a carry digit */
|
/* aligned; the top word gap is there only in case a carry digit */
|
/* is prefixed after the add -- it does not need to be zeroed */
|
/* is prefixed after the add -- it does not need to be zeroed */
|
#if DOUBLE
|
#if DOUBLE
|
#define COFF 4 /* offset into acc */
|
#define COFF 4 /* offset into acc */
|
#elif QUAD
|
#elif QUAD
|
USHORTAT(acc+4)=0; /* prefix 00 */
|
USHORTAT(acc+4)=0; /* prefix 00 */
|
#define COFF 6 /* offset into acc */
|
#define COFF 6 /* offset into acc */
|
#endif
|
#endif
|
|
|
GETCOEFF(dfl, acc+COFF); /* decode from decFloat */
|
GETCOEFF(dfl, acc+COFF); /* decode from decFloat */
|
ulsd=acc+COFF+DECPMAX-1;
|
ulsd=acc+COFF+DECPMAX-1;
|
umsd=acc+4; /* [having this here avoids */
|
umsd=acc+4; /* [having this here avoids */
|
/* weird GCC optimizer failure] */
|
/* weird GCC optimizer failure] */
|
#if DECTRACE
|
#if DECTRACE
|
{bcdnum tum;
|
{bcdnum tum;
|
tum.msd=umsd;
|
tum.msd=umsd;
|
tum.lsd=ulsd;
|
tum.lsd=ulsd;
|
tum.exponent=expl;
|
tum.exponent=expl;
|
tum.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;
|
tum.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;
|
decShowNum(&tum, "dflx");}
|
decShowNum(&tum, "dflx");}
|
#endif
|
#endif
|
|
|
/* if signs differ, take ten's complement of lhs (here the */
|
/* if signs differ, take ten's complement of lhs (here the */
|
/* coefficient is subtracted from all-nines; the 1 is added during */
|
/* coefficient is subtracted from all-nines; the 1 is added during */
|
/* the later add cycle -- zeros to the right do not matter because */
|
/* the later add cycle -- zeros to the right do not matter because */
|
/* the complement of zero is zero); these are fixed-length inverts */
|
/* the complement of zero is zero); these are fixed-length inverts */
|
/* where the lsd is known to be at a 4-byte boundary (so no borrow */
|
/* where the lsd is known to be at a 4-byte boundary (so no borrow */
|
/* possible) */
|
/* possible) */
|
carry=0; /* assume no carry */
|
carry=0; /* assume no carry */
|
if (diffsign) {
|
if (diffsign) {
|
carry=CARRYPAT; /* for +1 during add */
|
carry=CARRYPAT; /* for +1 during add */
|
UINTAT(acc+ 4)=0x09090909-UINTAT(acc+ 4);
|
UINTAT(acc+ 4)=0x09090909-UINTAT(acc+ 4);
|
UINTAT(acc+ 8)=0x09090909-UINTAT(acc+ 8);
|
UINTAT(acc+ 8)=0x09090909-UINTAT(acc+ 8);
|
UINTAT(acc+12)=0x09090909-UINTAT(acc+12);
|
UINTAT(acc+12)=0x09090909-UINTAT(acc+12);
|
UINTAT(acc+16)=0x09090909-UINTAT(acc+16);
|
UINTAT(acc+16)=0x09090909-UINTAT(acc+16);
|
#if QUAD
|
#if QUAD
|
UINTAT(acc+20)=0x09090909-UINTAT(acc+20);
|
UINTAT(acc+20)=0x09090909-UINTAT(acc+20);
|
UINTAT(acc+24)=0x09090909-UINTAT(acc+24);
|
UINTAT(acc+24)=0x09090909-UINTAT(acc+24);
|
UINTAT(acc+28)=0x09090909-UINTAT(acc+28);
|
UINTAT(acc+28)=0x09090909-UINTAT(acc+28);
|
UINTAT(acc+32)=0x09090909-UINTAT(acc+32);
|
UINTAT(acc+32)=0x09090909-UINTAT(acc+32);
|
UINTAT(acc+36)=0x09090909-UINTAT(acc+36);
|
UINTAT(acc+36)=0x09090909-UINTAT(acc+36);
|
#endif
|
#endif
|
} /* diffsign */
|
} /* diffsign */
|
|
|
/* now process the rhs coefficient; if it cannot overlap lhs then */
|
/* now process the rhs coefficient; if it cannot overlap lhs then */
|
/* it can be put straight into acc (with an appropriate gap, if */
|
/* it can be put straight into acc (with an appropriate gap, if */
|
/* needed) because no actual addition will be needed (except */
|
/* needed) because no actual addition will be needed (except */
|
/* possibly to complete ten's complement) */
|
/* possibly to complete ten's complement) */
|
overlap=DECPMAX-(expl-expr);
|
overlap=DECPMAX-(expl-expr);
|
#if DECTRACE
|
#if DECTRACE
|
printf("exps: %ld %ld\n", (LI)expl, (LI)expr);
|
printf("exps: %ld %ld\n", (LI)expl, (LI)expr);
|
printf("Overlap=%ld carry=%08lx\n", (LI)overlap, (LI)carry);
|
printf("Overlap=%ld carry=%08lx\n", (LI)overlap, (LI)carry);
|
#endif
|
#endif
|
|
|
if (overlap<=0) { /* no overlap possible */
|
if (overlap<=0) { /* no overlap possible */
|
uInt gap; /* local work */
|
uInt gap; /* local work */
|
/* since a full addition is not needed, a ten's complement */
|
/* since a full addition is not needed, a ten's complement */
|
/* calculation started above may need to be completed */
|
/* calculation started above may need to be completed */
|
if (carry) {
|
if (carry) {
|
for (ub=ulsd; *ub==9; ub--) *ub=0;
|
for (ub=ulsd; *ub==9; ub--) *ub=0;
|
*ub+=1;
|
*ub+=1;
|
carry=0; /* taken care of */
|
carry=0; /* taken care of */
|
}
|
}
|
/* up to DECPMAX-1 digits of the final result can extend down */
|
/* up to DECPMAX-1 digits of the final result can extend down */
|
/* below the LSD of the lhs, so if the gap is >DECPMAX then the */
|
/* below the LSD of the lhs, so if the gap is >DECPMAX then the */
|
/* rhs will be simply sticky bits. In this case the gap is */
|
/* rhs will be simply sticky bits. In this case the gap is */
|
/* clamped to DECPMAX and the exponent adjusted to suit [this is */
|
/* clamped to DECPMAX and the exponent adjusted to suit [this is */
|
/* safe because the lhs is non-zero]. */
|
/* safe because the lhs is non-zero]. */
|
gap=-overlap;
|
gap=-overlap;
|
if (gap>DECPMAX) {
|
if (gap>DECPMAX) {
|
expr+=gap-1;
|
expr+=gap-1;
|
gap=DECPMAX;
|
gap=DECPMAX;
|
}
|
}
|
ub=ulsd+gap+1; /* where MSD will go */
|
ub=ulsd+gap+1; /* where MSD will go */
|
/* Fill the gap with 0s; note that there is no addition to do */
|
/* Fill the gap with 0s; note that there is no addition to do */
|
ui=&UINTAT(acc+COFF+DECPMAX); /* start of gap */
|
ui=&UINTAT(acc+COFF+DECPMAX); /* start of gap */
|
for (; ui<&UINTAT(ub); ui++) *ui=0; /* mind the gap */
|
for (; ui<&UINTAT(ub); ui++) *ui=0; /* mind the gap */
|
if (overlap<-DECPMAX) { /* gap was > DECPMAX */
|
if (overlap<-DECPMAX) { /* gap was > DECPMAX */
|
*ub=(uByte)(!DFISZERO(dfr)); /* make sticky digit */
|
*ub=(uByte)(!DFISZERO(dfr)); /* make sticky digit */
|
}
|
}
|
else { /* need full coefficient */
|
else { /* need full coefficient */
|
GETCOEFF(dfr, ub); /* decode from decFloat */
|
GETCOEFF(dfr, ub); /* decode from decFloat */
|
ub+=DECPMAX-1; /* new LSD... */
|
ub+=DECPMAX-1; /* new LSD... */
|
}
|
}
|
ulsd=ub; /* save new LSD */
|
ulsd=ub; /* save new LSD */
|
} /* no overlap possible */
|
} /* no overlap possible */
|
|
|
else { /* overlap>0 */
|
else { /* overlap>0 */
|
/* coefficients overlap (perhaps completely, although also */
|
/* coefficients overlap (perhaps completely, although also */
|
/* perhaps only where zeros) */
|
/* perhaps only where zeros) */
|
ub=buf+COFF+DECPMAX-overlap; /* where MSD will go */
|
ub=buf+COFF+DECPMAX-overlap; /* where MSD will go */
|
/* Fill the prefix gap with 0s; 8 will cover most common */
|
/* Fill the prefix gap with 0s; 8 will cover most common */
|
/* unalignments, so start with direct assignments (a loop is */
|
/* unalignments, so start with direct assignments (a loop is */
|
/* then used for any remaining -- the loop (and the one in a */
|
/* then used for any remaining -- the loop (and the one in a */
|
/* moment) is not then on the critical path because the number */
|
/* moment) is not then on the critical path because the number */
|
/* of additions is reduced by (at least) two in this case) */
|
/* of additions is reduced by (at least) two in this case) */
|
UINTAT(buf+4)=0; /* [clears decQuad 00 too] */
|
UINTAT(buf+4)=0; /* [clears decQuad 00 too] */
|
UINTAT(buf+8)=0;
|
UINTAT(buf+8)=0;
|
if (ub>buf+12) {
|
if (ub>buf+12) {
|
ui=&UINTAT(buf+12); /* start of any remaining */
|
ui=&UINTAT(buf+12); /* start of any remaining */
|
for (; ui<&UINTAT(ub); ui++) *ui=0; /* fill them */
|
for (; ui<&UINTAT(ub); ui++) *ui=0; /* fill them */
|
}
|
}
|
GETCOEFF(dfr, ub); /* decode from decFloat */
|
GETCOEFF(dfr, ub); /* decode from decFloat */
|
|
|
/* now move tail of rhs across to main acc; again use direct */
|
/* now move tail of rhs across to main acc; again use direct */
|
/* assignment for 8 digits-worth */
|
/* assignment for 8 digits-worth */
|
UINTAT(acc+COFF+DECPMAX)=UINTAT(buf+COFF+DECPMAX);
|
UINTAT(acc+COFF+DECPMAX)=UINTAT(buf+COFF+DECPMAX);
|
UINTAT(acc+COFF+DECPMAX+4)=UINTAT(buf+COFF+DECPMAX+4);
|
UINTAT(acc+COFF+DECPMAX+4)=UINTAT(buf+COFF+DECPMAX+4);
|
if (buf+COFF+DECPMAX+8<ub+DECPMAX) {
|
if (buf+COFF+DECPMAX+8<ub+DECPMAX) {
|
uj=&UINTAT(buf+COFF+DECPMAX+8); /* source */
|
uj=&UINTAT(buf+COFF+DECPMAX+8); /* source */
|
ui=&UINTAT(acc+COFF+DECPMAX+8); /* target */
|
ui=&UINTAT(acc+COFF+DECPMAX+8); /* target */
|
for (; uj<&UINTAT(ub+DECPMAX); ui++, uj++) *ui=*uj;
|
for (; uj<&UINTAT(ub+DECPMAX); ui++, uj++) *ui=*uj;
|
}
|
}
|
|
|
ulsd=acc+(ub-buf+DECPMAX-1); /* update LSD pointer */
|
ulsd=acc+(ub-buf+DECPMAX-1); /* update LSD pointer */
|
|
|
/* now do the add of the non-tail; this is all nicely aligned, */
|
/* now do the add of the non-tail; this is all nicely aligned, */
|
/* and is over a multiple of four digits (because for Quad two */
|
/* and is over a multiple of four digits (because for Quad two */
|
/* two 0 digits were added on the left); words in both acc and */
|
/* two 0 digits were added on the left); words in both acc and */
|
/* buf (buf especially) will often be zero */
|
/* buf (buf especially) will often be zero */
|
/* [byte-by-byte add, here, is about 15% slower than the by-fours] */
|
/* [byte-by-byte add, here, is about 15% slower than the by-fours] */
|
|
|
/* Now effect the add; this is harder on a little-endian */
|
/* Now effect the add; this is harder on a little-endian */
|
/* machine as the inter-digit carry cannot use the usual BCD */
|
/* machine as the inter-digit carry cannot use the usual BCD */
|
/* addition trick because the bytes are loaded in the wrong order */
|
/* addition trick because the bytes are loaded in the wrong order */
|
/* [this loop could be unrolled, but probably scarcely worth it] */
|
/* [this loop could be unrolled, but probably scarcely worth it] */
|
|
|
ui=&UINTAT(acc+COFF+DECPMAX-4); /* target LSW (acc) */
|
ui=&UINTAT(acc+COFF+DECPMAX-4); /* target LSW (acc) */
|
uj=&UINTAT(buf+COFF+DECPMAX-4); /* source LSW (buf, to add to acc) */
|
uj=&UINTAT(buf+COFF+DECPMAX-4); /* source LSW (buf, to add to acc) */
|
|
|
#if !DECLITEND
|
#if !DECLITEND
|
for (; ui>=&UINTAT(acc+4); ui--, uj--) {
|
for (; ui>=&UINTAT(acc+4); ui--, uj--) {
|
/* bcd8 add */
|
/* bcd8 add */
|
carry+=*uj; /* rhs + carry */
|
carry+=*uj; /* rhs + carry */
|
if (carry==0) continue; /* no-op */
|
if (carry==0) continue; /* no-op */
|
carry+=*ui; /* lhs */
|
carry+=*ui; /* lhs */
|
/* Big-endian BCD adjust (uses internal carry) */
|
/* Big-endian BCD adjust (uses internal carry) */
|
carry+=0x76f6f6f6; /* note top nibble not all bits */
|
carry+=0x76f6f6f6; /* note top nibble not all bits */
|
*ui=(carry & 0x0f0f0f0f) - ((carry & 0x60606060)>>4); /* BCD adjust */
|
*ui=(carry & 0x0f0f0f0f) - ((carry & 0x60606060)>>4); /* BCD adjust */
|
carry>>=31; /* true carry was at far left */
|
carry>>=31; /* true carry was at far left */
|
} /* add loop */
|
} /* add loop */
|
#else
|
#else
|
for (; ui>=&UINTAT(acc+4); ui--, uj--) {
|
for (; ui>=&UINTAT(acc+4); ui--, uj--) {
|
/* bcd8 add */
|
/* bcd8 add */
|
carry+=*uj; /* rhs + carry */
|
carry+=*uj; /* rhs + carry */
|
if (carry==0) continue; /* no-op [common if unaligned] */
|
if (carry==0) continue; /* no-op [common if unaligned] */
|
carry+=*ui; /* lhs */
|
carry+=*ui; /* lhs */
|
/* Little-endian BCD adjust; inter-digit carry must be manual */
|
/* Little-endian BCD adjust; inter-digit carry must be manual */
|
/* because the lsb from the array will be in the most-significant */
|
/* because the lsb from the array will be in the most-significant */
|
/* byte of carry */
|
/* byte of carry */
|
carry+=0x76767676; /* note no inter-byte carries */
|
carry+=0x76767676; /* note no inter-byte carries */
|
carry+=(carry & 0x80000000)>>15;
|
carry+=(carry & 0x80000000)>>15;
|
carry+=(carry & 0x00800000)>>15;
|
carry+=(carry & 0x00800000)>>15;
|
carry+=(carry & 0x00008000)>>15;
|
carry+=(carry & 0x00008000)>>15;
|
carry-=(carry & 0x60606060)>>4; /* BCD adjust back */
|
carry-=(carry & 0x60606060)>>4; /* BCD adjust back */
|
*ui=carry & 0x0f0f0f0f; /* clear debris and save */
|
*ui=carry & 0x0f0f0f0f; /* clear debris and save */
|
/* here, final carry-out bit is at 0x00000080; move it ready */
|
/* here, final carry-out bit is at 0x00000080; move it ready */
|
/* for next word-add (i.e., to 0x01000000) */
|
/* for next word-add (i.e., to 0x01000000) */
|
carry=(carry & 0x00000080)<<17;
|
carry=(carry & 0x00000080)<<17;
|
} /* add loop */
|
} /* add loop */
|
#endif
|
#endif
|
#if DECTRACE
|
#if DECTRACE
|
{bcdnum tum;
|
{bcdnum tum;
|
printf("Add done, carry=%08lx, diffsign=%ld\n", (LI)carry, (LI)diffsign);
|
printf("Add done, carry=%08lx, diffsign=%ld\n", (LI)carry, (LI)diffsign);
|
tum.msd=umsd; /* acc+4; */
|
tum.msd=umsd; /* acc+4; */
|
tum.lsd=ulsd;
|
tum.lsd=ulsd;
|
tum.exponent=0;
|
tum.exponent=0;
|
tum.sign=0;
|
tum.sign=0;
|
decShowNum(&tum, "dfadd");}
|
decShowNum(&tum, "dfadd");}
|
#endif
|
#endif
|
} /* overlap possible */
|
} /* overlap possible */
|
|
|
/* ordering here is a little strange in order to have slowest path */
|
/* ordering here is a little strange in order to have slowest path */
|
/* first in GCC asm listing */
|
/* first in GCC asm listing */
|
if (diffsign) { /* subtraction */
|
if (diffsign) { /* subtraction */
|
if (!carry) { /* no carry out means RHS<LHS */
|
if (!carry) { /* no carry out means RHS<LHS */
|
/* borrowed -- take ten's complement */
|
/* borrowed -- take ten's complement */
|
/* sign is lhs sign */
|
/* sign is lhs sign */
|
num.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;
|
num.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;
|
|
|
/* invert the coefficient first by fours, then add one; space */
|
/* invert the coefficient first by fours, then add one; space */
|
/* at the end of the buffer ensures the by-fours is always */
|
/* at the end of the buffer ensures the by-fours is always */
|
/* safe, but lsd+1 must be cleared to prevent a borrow */
|
/* safe, but lsd+1 must be cleared to prevent a borrow */
|
/* if big-endian */
|
/* if big-endian */
|
#if !DECLITEND
|
#if !DECLITEND
|
*(ulsd+1)=0;
|
*(ulsd+1)=0;
|
#endif
|
#endif
|
/* there are always at least four coefficient words */
|
/* there are always at least four coefficient words */
|
UINTAT(umsd) =0x09090909-UINTAT(umsd);
|
UINTAT(umsd) =0x09090909-UINTAT(umsd);
|
UINTAT(umsd+4) =0x09090909-UINTAT(umsd+4);
|
UINTAT(umsd+4) =0x09090909-UINTAT(umsd+4);
|
UINTAT(umsd+8) =0x09090909-UINTAT(umsd+8);
|
UINTAT(umsd+8) =0x09090909-UINTAT(umsd+8);
|
UINTAT(umsd+12)=0x09090909-UINTAT(umsd+12);
|
UINTAT(umsd+12)=0x09090909-UINTAT(umsd+12);
|
#if DOUBLE
|
#if DOUBLE
|
#define BNEXT 16
|
#define BNEXT 16
|
#elif QUAD
|
#elif QUAD
|
UINTAT(umsd+16)=0x09090909-UINTAT(umsd+16);
|
UINTAT(umsd+16)=0x09090909-UINTAT(umsd+16);
|
UINTAT(umsd+20)=0x09090909-UINTAT(umsd+20);
|
UINTAT(umsd+20)=0x09090909-UINTAT(umsd+20);
|
UINTAT(umsd+24)=0x09090909-UINTAT(umsd+24);
|
UINTAT(umsd+24)=0x09090909-UINTAT(umsd+24);
|
UINTAT(umsd+28)=0x09090909-UINTAT(umsd+28);
|
UINTAT(umsd+28)=0x09090909-UINTAT(umsd+28);
|
UINTAT(umsd+32)=0x09090909-UINTAT(umsd+32);
|
UINTAT(umsd+32)=0x09090909-UINTAT(umsd+32);
|
#define BNEXT 36
|
#define BNEXT 36
|
#endif
|
#endif
|
if (ulsd>=umsd+BNEXT) { /* unaligned */
|
if (ulsd>=umsd+BNEXT) { /* unaligned */
|
/* eight will handle most unaligments for Double; 16 for Quad */
|
/* eight will handle most unaligments for Double; 16 for Quad */
|
UINTAT(umsd+BNEXT)=0x09090909-UINTAT(umsd+BNEXT);
|
UINTAT(umsd+BNEXT)=0x09090909-UINTAT(umsd+BNEXT);
|
UINTAT(umsd+BNEXT+4)=0x09090909-UINTAT(umsd+BNEXT+4);
|
UINTAT(umsd+BNEXT+4)=0x09090909-UINTAT(umsd+BNEXT+4);
|
#if DOUBLE
|
#if DOUBLE
|
#define BNEXTY (BNEXT+8)
|
#define BNEXTY (BNEXT+8)
|
#elif QUAD
|
#elif QUAD
|
UINTAT(umsd+BNEXT+8)=0x09090909-UINTAT(umsd+BNEXT+8);
|
UINTAT(umsd+BNEXT+8)=0x09090909-UINTAT(umsd+BNEXT+8);
|
UINTAT(umsd+BNEXT+12)=0x09090909-UINTAT(umsd+BNEXT+12);
|
UINTAT(umsd+BNEXT+12)=0x09090909-UINTAT(umsd+BNEXT+12);
|
#define BNEXTY (BNEXT+16)
|
#define BNEXTY (BNEXT+16)
|
#endif
|
#endif
|
if (ulsd>=umsd+BNEXTY) { /* very unaligned */
|
if (ulsd>=umsd+BNEXTY) { /* very unaligned */
|
ui=&UINTAT(umsd+BNEXTY); /* -> continue */
|
ui=&UINTAT(umsd+BNEXTY); /* -> continue */
|
for (;;ui++) {
|
for (;;ui++) {
|
*ui=0x09090909-*ui; /* invert four digits */
|
*ui=0x09090909-*ui; /* invert four digits */
|
if (ui>=&UINTAT(ulsd-3)) break; /* all done */
|
if (ui>=&UINTAT(ulsd-3)) break; /* all done */
|
}
|
}
|
}
|
}
|
}
|
}
|
/* complete the ten's complement by adding 1 */
|
/* complete the ten's complement by adding 1 */
|
for (ub=ulsd; *ub==9; ub--) *ub=0;
|
for (ub=ulsd; *ub==9; ub--) *ub=0;
|
*ub+=1;
|
*ub+=1;
|
} /* borrowed */
|
} /* borrowed */
|
|
|
else { /* carry out means RHS>=LHS */
|
else { /* carry out means RHS>=LHS */
|
num.sign=DFWORD(dfr, 0) & DECFLOAT_Sign;
|
num.sign=DFWORD(dfr, 0) & DECFLOAT_Sign;
|
/* all done except for the special IEEE 754 exact-zero-result */
|
/* all done except for the special IEEE 754 exact-zero-result */
|
/* rule (see above); while testing for zero, strip leading */
|
/* rule (see above); while testing for zero, strip leading */
|
/* zeros (which will save decFinalize doing it) (this is in */
|
/* zeros (which will save decFinalize doing it) (this is in */
|
/* diffsign path, so carry impossible and true umsd is */
|
/* diffsign path, so carry impossible and true umsd is */
|
/* acc+COFF) */
|
/* acc+COFF) */
|
|
|
/* Check the initial coefficient area using the fast macro; */
|
/* Check the initial coefficient area using the fast macro; */
|
/* this will often be all that needs to be done (as on the */
|
/* this will often be all that needs to be done (as on the */
|
/* worst-case path when the subtraction was aligned and */
|
/* worst-case path when the subtraction was aligned and */
|
/* full-length) */
|
/* full-length) */
|
if (ISCOEFFZERO(acc+COFF)) {
|
if (ISCOEFFZERO(acc+COFF)) {
|
umsd=acc+COFF+DECPMAX-1; /* so far, so zero */
|
umsd=acc+COFF+DECPMAX-1; /* so far, so zero */
|
if (ulsd>umsd) { /* more to check */
|
if (ulsd>umsd) { /* more to check */
|
umsd++; /* to align after checked area */
|
umsd++; /* to align after checked area */
|
for (; UINTAT(umsd)==0 && umsd+3<ulsd;) umsd+=4;
|
for (; UINTAT(umsd)==0 && umsd+3<ulsd;) umsd+=4;
|
for (; *umsd==0 && umsd<ulsd;) umsd++;
|
for (; *umsd==0 && umsd<ulsd;) umsd++;
|
}
|
}
|
if (*umsd==0) { /* must be true zero (and diffsign) */
|
if (*umsd==0) { /* must be true zero (and diffsign) */
|
num.sign=0; /* assume + */
|
num.sign=0; /* assume + */
|
if (set->round==DEC_ROUND_FLOOR) num.sign=DECFLOAT_Sign;
|
if (set->round==DEC_ROUND_FLOOR) num.sign=DECFLOAT_Sign;
|
}
|
}
|
}
|
}
|
/* [else was not zero, might still have leading zeros] */
|
/* [else was not zero, might still have leading zeros] */
|
} /* subtraction gave positive result */
|
} /* subtraction gave positive result */
|
} /* diffsign */
|
} /* diffsign */
|
|
|
else { /* same-sign addition */
|
else { /* same-sign addition */
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
#if DOUBLE
|
#if DOUBLE
|
if (carry) { /* only possible with decDouble */
|
if (carry) { /* only possible with decDouble */
|
*(acc+3)=1; /* [Quad has leading 00] */
|
*(acc+3)=1; /* [Quad has leading 00] */
|
umsd=acc+3;
|
umsd=acc+3;
|
}
|
}
|
#endif
|
#endif
|
} /* same sign */
|
} /* same sign */
|
|
|
num.msd=umsd; /* set MSD .. */
|
num.msd=umsd; /* set MSD .. */
|
num.lsd=ulsd; /* .. and LSD */
|
num.lsd=ulsd; /* .. and LSD */
|
num.exponent=expr; /* set exponent to smaller */
|
num.exponent=expr; /* set exponent to smaller */
|
|
|
#if DECTRACE
|
#if DECTRACE
|
decFloatShow(dfl, "dfl");
|
decFloatShow(dfl, "dfl");
|
decFloatShow(dfr, "dfr");
|
decFloatShow(dfr, "dfr");
|
decShowNum(&num, "postadd");
|
decShowNum(&num, "postadd");
|
#endif
|
#endif
|
return decFinalize(result, &num, set); /* round, check, and lay out */
|
return decFinalize(result, &num, set); /* round, check, and lay out */
|
} /* decFloatAdd */
|
} /* decFloatAdd */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatAnd -- logical digitwise AND of two decFloats */
|
/* decFloatAnd -- logical digitwise AND of two decFloats */
|
/* */
|
/* */
|
/* result gets the result of ANDing dfl and dfr */
|
/* result gets the result of ANDing dfl and dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result, which will be canonical with sign=0 */
|
/* returns result, which will be canonical with sign=0 */
|
/* */
|
/* */
|
/* The operands must be positive, finite with exponent q=0, and */
|
/* The operands must be positive, finite with exponent q=0, and */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatAnd(decFloat *result,
|
decFloat * decFloatAnd(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
|
if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
|
|| !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);
|
|| !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);
|
/* the operands are positive finite integers (q=0) with just 0s and 1s */
|
/* the operands are positive finite integers (q=0) with just 0s and 1s */
|
#if DOUBLE
|
#if DOUBLE
|
DFWORD(result, 0)=ZEROWORD
|
DFWORD(result, 0)=ZEROWORD
|
|((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04009124);
|
|((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04009124);
|
DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x49124491;
|
DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x49124491;
|
#elif QUAD
|
#elif QUAD
|
DFWORD(result, 0)=ZEROWORD
|
DFWORD(result, 0)=ZEROWORD
|
|((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04000912);
|
|((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04000912);
|
DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x44912449;
|
DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x44912449;
|
DFWORD(result, 2)=(DFWORD(dfl, 2) & DFWORD(dfr, 2))&0x12449124;
|
DFWORD(result, 2)=(DFWORD(dfl, 2) & DFWORD(dfr, 2))&0x12449124;
|
DFWORD(result, 3)=(DFWORD(dfl, 3) & DFWORD(dfr, 3))&0x49124491;
|
DFWORD(result, 3)=(DFWORD(dfl, 3) & DFWORD(dfr, 3))&0x49124491;
|
#endif
|
#endif
|
return result;
|
return result;
|
} /* decFloatAnd */
|
} /* decFloatAnd */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCanonical -- copy a decFloat, making canonical */
|
/* decFloatCanonical -- copy a decFloat, making canonical */
|
/* */
|
/* */
|
/* result gets the canonicalized df */
|
/* result gets the canonicalized df */
|
/* df is the decFloat to copy and make canonical */
|
/* df is the decFloat to copy and make canonical */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This works on specials, too; no error or exception is possible. */
|
/* This works on specials, too; no error or exception is possible. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCanonical(decFloat *result, const decFloat *df) {
|
decFloat * decFloatCanonical(decFloat *result, const decFloat *df) {
|
return decCanonical(result, df);
|
return decCanonical(result, df);
|
} /* decFloatCanonical */
|
} /* decFloatCanonical */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatClass -- return the class of a decFloat */
|
/* decFloatClass -- return the class of a decFloat */
|
/* */
|
/* */
|
/* df is the decFloat to test */
|
/* df is the decFloat to test */
|
/* returns the decClass that df falls into */
|
/* returns the decClass that df falls into */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
enum decClass decFloatClass(const decFloat *df) {
|
enum decClass decFloatClass(const decFloat *df) {
|
Int exp; /* exponent */
|
Int exp; /* exponent */
|
if (DFISSPECIAL(df)) {
|
if (DFISSPECIAL(df)) {
|
if (DFISQNAN(df)) return DEC_CLASS_QNAN;
|
if (DFISQNAN(df)) return DEC_CLASS_QNAN;
|
if (DFISSNAN(df)) return DEC_CLASS_SNAN;
|
if (DFISSNAN(df)) return DEC_CLASS_SNAN;
|
/* must be an infinity */
|
/* must be an infinity */
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_INF;
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_INF;
|
return DEC_CLASS_POS_INF;
|
return DEC_CLASS_POS_INF;
|
}
|
}
|
if (DFISZERO(df)) { /* quite common */
|
if (DFISZERO(df)) { /* quite common */
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_ZERO;
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_ZERO;
|
return DEC_CLASS_POS_ZERO;
|
return DEC_CLASS_POS_ZERO;
|
}
|
}
|
/* is finite and non-zero; similar code to decFloatIsNormal, here */
|
/* is finite and non-zero; similar code to decFloatIsNormal, here */
|
/* [this could be speeded up slightly by in-lining decFloatDigits] */
|
/* [this could be speeded up slightly by in-lining decFloatDigits] */
|
exp=GETEXPUN(df) /* get unbiased exponent .. */
|
exp=GETEXPUN(df) /* get unbiased exponent .. */
|
+decFloatDigits(df)-1; /* .. and make adjusted exponent */
|
+decFloatDigits(df)-1; /* .. and make adjusted exponent */
|
if (exp>=DECEMIN) { /* is normal */
|
if (exp>=DECEMIN) { /* is normal */
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_NORMAL;
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_NORMAL;
|
return DEC_CLASS_POS_NORMAL;
|
return DEC_CLASS_POS_NORMAL;
|
}
|
}
|
/* is subnormal */
|
/* is subnormal */
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_SUBNORMAL;
|
if (DFISSIGNED(df)) return DEC_CLASS_NEG_SUBNORMAL;
|
return DEC_CLASS_POS_SUBNORMAL;
|
return DEC_CLASS_POS_SUBNORMAL;
|
} /* decFloatClass */
|
} /* decFloatClass */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatClassString -- return the class of a decFloat as a string */
|
/* decFloatClassString -- return the class of a decFloat as a string */
|
/* */
|
/* */
|
/* df is the decFloat to test */
|
/* df is the decFloat to test */
|
/* returns a constant string describing the class df falls into */
|
/* returns a constant string describing the class df falls into */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
const char *decFloatClassString(const decFloat *df) {
|
const char *decFloatClassString(const decFloat *df) {
|
enum decClass eclass=decFloatClass(df);
|
enum decClass eclass=decFloatClass(df);
|
if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
|
if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
|
if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
|
if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
|
if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
|
if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
|
if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
|
if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
|
if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
|
if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
|
if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
|
if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
|
if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
|
if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
|
if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
|
if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
|
if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
|
if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
|
if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
|
if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
|
return DEC_ClassString_UN; /* Unknown */
|
return DEC_ClassString_UN; /* Unknown */
|
} /* decFloatClassString */
|
} /* decFloatClassString */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCompare -- compare two decFloats; quiet NaNs allowed */
|
/* decFloatCompare -- compare two decFloats; quiet NaNs allowed */
|
/* */
|
/* */
|
/* result gets the result of comparing dfl and dfr */
|
/* result gets the result of comparing dfl and dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result, which may be -1, 0, 1, or NaN (Unordered) */
|
/* returns result, which may be -1, 0, 1, or NaN (Unordered) */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCompare(decFloat *result,
|
decFloat * decFloatCompare(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int comp; /* work */
|
Int comp; /* work */
|
/* NaNs are handled as usual */
|
/* NaNs are handled as usual */
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
/* numeric comparison needed */
|
/* numeric comparison needed */
|
comp=decNumCompare(dfl, dfr, 0);
|
comp=decNumCompare(dfl, dfr, 0);
|
decFloatZero(result);
|
decFloatZero(result);
|
if (comp==0) return result;
|
if (comp==0) return result;
|
DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */
|
DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */
|
if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */
|
if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */
|
return result;
|
return result;
|
} /* decFloatCompare */
|
} /* decFloatCompare */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCompareSignal -- compare two decFloats; all NaNs signal */
|
/* decFloatCompareSignal -- compare two decFloats; all NaNs signal */
|
/* */
|
/* */
|
/* result gets the result of comparing dfl and dfr */
|
/* result gets the result of comparing dfl and dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result, which may be -1, 0, 1, or NaN (Unordered) */
|
/* returns result, which may be -1, 0, 1, or NaN (Unordered) */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCompareSignal(decFloat *result,
|
decFloat * decFloatCompareSignal(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int comp; /* work */
|
Int comp; /* work */
|
/* NaNs are handled as usual, except that all NaNs signal */
|
/* NaNs are handled as usual, except that all NaNs signal */
|
if (DFISNAN(dfl) || DFISNAN(dfr)) {
|
if (DFISNAN(dfl) || DFISNAN(dfr)) {
|
set->status|=DEC_Invalid_operation;
|
set->status|=DEC_Invalid_operation;
|
return decNaNs(result, dfl, dfr, set);
|
return decNaNs(result, dfl, dfr, set);
|
}
|
}
|
/* numeric comparison needed */
|
/* numeric comparison needed */
|
comp=decNumCompare(dfl, dfr, 0);
|
comp=decNumCompare(dfl, dfr, 0);
|
decFloatZero(result);
|
decFloatZero(result);
|
if (comp==0) return result;
|
if (comp==0) return result;
|
DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */
|
DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */
|
if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */
|
if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */
|
return result;
|
return result;
|
} /* decFloatCompareSignal */
|
} /* decFloatCompareSignal */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCompareTotal -- compare two decFloats with total ordering */
|
/* decFloatCompareTotal -- compare two decFloats with total ordering */
|
/* */
|
/* */
|
/* result gets the result of comparing dfl and dfr */
|
/* result gets the result of comparing dfl and dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* returns result, which may be -1, 0, or 1 */
|
/* returns result, which may be -1, 0, or 1 */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCompareTotal(decFloat *result,
|
decFloat * decFloatCompareTotal(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr) {
|
const decFloat *dfl, const decFloat *dfr) {
|
Int comp; /* work */
|
Int comp; /* work */
|
if (DFISNAN(dfl) || DFISNAN(dfr)) {
|
if (DFISNAN(dfl) || DFISNAN(dfr)) {
|
Int nanl, nanr; /* work */
|
Int nanl, nanr; /* work */
|
/* morph NaNs to +/- 1 or 2, leave numbers as 0 */
|
/* morph NaNs to +/- 1 or 2, leave numbers as 0 */
|
nanl=DFISSNAN(dfl)+DFISQNAN(dfl)*2; /* quiet > signalling */
|
nanl=DFISSNAN(dfl)+DFISQNAN(dfl)*2; /* quiet > signalling */
|
if (DFISSIGNED(dfl)) nanl=-nanl;
|
if (DFISSIGNED(dfl)) nanl=-nanl;
|
nanr=DFISSNAN(dfr)+DFISQNAN(dfr)*2;
|
nanr=DFISSNAN(dfr)+DFISQNAN(dfr)*2;
|
if (DFISSIGNED(dfr)) nanr=-nanr;
|
if (DFISSIGNED(dfr)) nanr=-nanr;
|
if (nanl>nanr) comp=+1;
|
if (nanl>nanr) comp=+1;
|
else if (nanl<nanr) comp=-1;
|
else if (nanl<nanr) comp=-1;
|
else { /* NaNs are the same type and sign .. must compare payload */
|
else { /* NaNs are the same type and sign .. must compare payload */
|
/* buffers need +2 for QUAD */
|
/* buffers need +2 for QUAD */
|
uByte bufl[DECPMAX+4]; /* for LHS coefficient + foot */
|
uByte bufl[DECPMAX+4]; /* for LHS coefficient + foot */
|
uByte bufr[DECPMAX+4]; /* for RHS coefficient + foot */
|
uByte bufr[DECPMAX+4]; /* for RHS coefficient + foot */
|
uByte *ub, *uc; /* work */
|
uByte *ub, *uc; /* work */
|
Int sigl; /* signum of LHS */
|
Int sigl; /* signum of LHS */
|
sigl=(DFISSIGNED(dfl) ? -1 : +1);
|
sigl=(DFISSIGNED(dfl) ? -1 : +1);
|
|
|
/* decode the coefficients */
|
/* decode the coefficients */
|
/* (shift both right two if Quad to make a multiple of four) */
|
/* (shift both right two if Quad to make a multiple of four) */
|
#if QUAD
|
#if QUAD
|
USHORTAT(bufl)=0;
|
USHORTAT(bufl)=0;
|
USHORTAT(bufr)=0;
|
USHORTAT(bufr)=0;
|
#endif
|
#endif
|
GETCOEFF(dfl, bufl+QUAD*2); /* decode from decFloat */
|
GETCOEFF(dfl, bufl+QUAD*2); /* decode from decFloat */
|
GETCOEFF(dfr, bufr+QUAD*2); /* .. */
|
GETCOEFF(dfr, bufr+QUAD*2); /* .. */
|
/* all multiples of four, here */
|
/* all multiples of four, here */
|
comp=0; /* assume equal */
|
comp=0; /* assume equal */
|
for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {
|
for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {
|
if (UINTAT(ub)==UINTAT(uc)) continue; /* so far so same */
|
if (UINTAT(ub)==UINTAT(uc)) continue; /* so far so same */
|
/* about to find a winner; go by bytes in case little-endian */
|
/* about to find a winner; go by bytes in case little-endian */
|
for (;; ub++, uc++) {
|
for (;; ub++, uc++) {
|
if (*ub==*uc) continue;
|
if (*ub==*uc) continue;
|
if (*ub>*uc) comp=sigl; /* difference found */
|
if (*ub>*uc) comp=sigl; /* difference found */
|
else comp=-sigl; /* .. */
|
else comp=-sigl; /* .. */
|
break;
|
break;
|
}
|
}
|
}
|
}
|
} /* same NaN type and sign */
|
} /* same NaN type and sign */
|
}
|
}
|
else {
|
else {
|
/* numeric comparison needed */
|
/* numeric comparison needed */
|
comp=decNumCompare(dfl, dfr, 1); /* total ordering */
|
comp=decNumCompare(dfl, dfr, 1); /* total ordering */
|
}
|
}
|
decFloatZero(result);
|
decFloatZero(result);
|
if (comp==0) return result;
|
if (comp==0) return result;
|
DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */
|
DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */
|
if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */
|
if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */
|
return result;
|
return result;
|
} /* decFloatCompareTotal */
|
} /* decFloatCompareTotal */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCompareTotalMag -- compare magnitudes with total ordering */
|
/* decFloatCompareTotalMag -- compare magnitudes with total ordering */
|
/* */
|
/* */
|
/* result gets the result of comparing abs(dfl) and abs(dfr) */
|
/* result gets the result of comparing abs(dfl) and abs(dfr) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* returns result, which may be -1, 0, or 1 */
|
/* returns result, which may be -1, 0, or 1 */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCompareTotalMag(decFloat *result,
|
decFloat * decFloatCompareTotalMag(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr) {
|
const decFloat *dfl, const decFloat *dfr) {
|
decFloat a, b; /* for copy if needed */
|
decFloat a, b; /* for copy if needed */
|
/* copy and redirect signed operand(s) */
|
/* copy and redirect signed operand(s) */
|
if (DFISSIGNED(dfl)) {
|
if (DFISSIGNED(dfl)) {
|
decFloatCopyAbs(&a, dfl);
|
decFloatCopyAbs(&a, dfl);
|
dfl=&a;
|
dfl=&a;
|
}
|
}
|
if (DFISSIGNED(dfr)) {
|
if (DFISSIGNED(dfr)) {
|
decFloatCopyAbs(&b, dfr);
|
decFloatCopyAbs(&b, dfr);
|
dfr=&b;
|
dfr=&b;
|
}
|
}
|
return decFloatCompareTotal(result, dfl, dfr);
|
return decFloatCompareTotal(result, dfl, dfr);
|
} /* decFloatCompareTotalMag */
|
} /* decFloatCompareTotalMag */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCopy -- copy a decFloat as-is */
|
/* decFloatCopy -- copy a decFloat as-is */
|
/* */
|
/* */
|
/* result gets the copy of dfl */
|
/* result gets the copy of dfl */
|
/* dfl is the decFloat to copy */
|
/* dfl is the decFloat to copy */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCopy(decFloat *result, const decFloat *dfl) {
|
decFloat * decFloatCopy(decFloat *result, const decFloat *dfl) {
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
return result;
|
return result;
|
} /* decFloatCopy */
|
} /* decFloatCopy */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCopyAbs -- copy a decFloat as-is and set sign bit to 0 */
|
/* decFloatCopyAbs -- copy a decFloat as-is and set sign bit to 0 */
|
/* */
|
/* */
|
/* result gets the copy of dfl with sign bit 0 */
|
/* result gets the copy of dfl with sign bit 0 */
|
/* dfl is the decFloat to copy */
|
/* dfl is the decFloat to copy */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCopyAbs(decFloat *result, const decFloat *dfl) {
|
decFloat * decFloatCopyAbs(decFloat *result, const decFloat *dfl) {
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
DFBYTE(result, 0)&=~0x80; /* zero sign bit */
|
DFBYTE(result, 0)&=~0x80; /* zero sign bit */
|
return result;
|
return result;
|
} /* decFloatCopyAbs */
|
} /* decFloatCopyAbs */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCopyNegate -- copy a decFloat as-is with inverted sign bit */
|
/* decFloatCopyNegate -- copy a decFloat as-is with inverted sign bit */
|
/* */
|
/* */
|
/* result gets the copy of dfl with sign bit inverted */
|
/* result gets the copy of dfl with sign bit inverted */
|
/* dfl is the decFloat to copy */
|
/* dfl is the decFloat to copy */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCopyNegate(decFloat *result, const decFloat *dfl) {
|
decFloat * decFloatCopyNegate(decFloat *result, const decFloat *dfl) {
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
DFBYTE(result, 0)^=0x80; /* invert sign bit */
|
DFBYTE(result, 0)^=0x80; /* invert sign bit */
|
return result;
|
return result;
|
} /* decFloatCopyNegate */
|
} /* decFloatCopyNegate */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatCopySign -- copy a decFloat with the sign of another */
|
/* decFloatCopySign -- copy a decFloat with the sign of another */
|
/* */
|
/* */
|
/* result gets the result of copying dfl with the sign of dfr */
|
/* result gets the result of copying dfl with the sign of dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* This is a bitwise operation; no errors or exceptions are possible. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatCopySign(decFloat *result,
|
decFloat * decFloatCopySign(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr) {
|
const decFloat *dfl, const decFloat *dfr) {
|
uByte sign=(uByte)(DFBYTE(dfr, 0)&0x80); /* save sign bit */
|
uByte sign=(uByte)(DFBYTE(dfr, 0)&0x80); /* save sign bit */
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
if (dfl!=result) *result=*dfl; /* copy needed */
|
DFBYTE(result, 0)&=~0x80; /* clear sign .. */
|
DFBYTE(result, 0)&=~0x80; /* clear sign .. */
|
DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); /* .. and set saved */
|
DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); /* .. and set saved */
|
return result;
|
return result;
|
} /* decFloatCopySign */
|
} /* decFloatCopySign */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatDigits -- return the number of digits in a decFloat */
|
/* decFloatDigits -- return the number of digits in a decFloat */
|
/* */
|
/* */
|
/* df is the decFloat to investigate */
|
/* df is the decFloat to investigate */
|
/* returns the number of significant digits in the decFloat; a */
|
/* returns the number of significant digits in the decFloat; a */
|
/* zero coefficient returns 1 as does an infinity (a NaN returns */
|
/* zero coefficient returns 1 as does an infinity (a NaN returns */
|
/* the number of digits in the payload) */
|
/* the number of digits in the payload) */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* private macro to extract a declet according to provided formula */
|
/* private macro to extract a declet according to provided formula */
|
/* (form), and if it is non-zero then return the calculated digits */
|
/* (form), and if it is non-zero then return the calculated digits */
|
/* depending on the declet number (n), where n=0 for the most */
|
/* depending on the declet number (n), where n=0 for the most */
|
/* significant declet; uses uInt dpd for work */
|
/* significant declet; uses uInt dpd for work */
|
#define dpdlenchk(n, form) {dpd=(form)&0x3ff; \
|
#define dpdlenchk(n, form) {dpd=(form)&0x3ff; \
|
if (dpd) return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]);}
|
if (dpd) return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]);}
|
/* next one is used when it is known that the declet must be */
|
/* next one is used when it is known that the declet must be */
|
/* non-zero, or is the final zero declet */
|
/* non-zero, or is the final zero declet */
|
#define dpdlendun(n, form) {dpd=(form)&0x3ff; \
|
#define dpdlendun(n, form) {dpd=(form)&0x3ff; \
|
if (dpd==0) return 1; \
|
if (dpd==0) return 1; \
|
return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]);}
|
return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]);}
|
|
|
uInt decFloatDigits(const decFloat *df) {
|
uInt decFloatDigits(const decFloat *df) {
|
uInt dpd; /* work */
|
uInt dpd; /* work */
|
uInt sourhi=DFWORD(df, 0); /* top word from source decFloat */
|
uInt sourhi=DFWORD(df, 0); /* top word from source decFloat */
|
#if QUAD
|
#if QUAD
|
uInt sourmh, sourml;
|
uInt sourmh, sourml;
|
#endif
|
#endif
|
uInt sourlo;
|
uInt sourlo;
|
|
|
if (DFISINF(df)) return 1;
|
if (DFISINF(df)) return 1;
|
/* A NaN effectively has an MSD of 0; otherwise if non-zero MSD */
|
/* A NaN effectively has an MSD of 0; otherwise if non-zero MSD */
|
/* then the coefficient is full-length */
|
/* then the coefficient is full-length */
|
if (!DFISNAN(df) && DECCOMBMSD[sourhi>>26]) return DECPMAX;
|
if (!DFISNAN(df) && DECCOMBMSD[sourhi>>26]) return DECPMAX;
|
|
|
#if DOUBLE
|
#if DOUBLE
|
if (sourhi&0x0003ffff) { /* ends in first */
|
if (sourhi&0x0003ffff) { /* ends in first */
|
dpdlenchk(0, sourhi>>8);
|
dpdlenchk(0, sourhi>>8);
|
sourlo=DFWORD(df, 1);
|
sourlo=DFWORD(df, 1);
|
dpdlendun(1, (sourhi<<2) | (sourlo>>30));
|
dpdlendun(1, (sourhi<<2) | (sourlo>>30));
|
} /* [cannot drop through] */
|
} /* [cannot drop through] */
|
sourlo=DFWORD(df, 1); /* sourhi not involved now */
|
sourlo=DFWORD(df, 1); /* sourhi not involved now */
|
if (sourlo&0xfff00000) { /* in one of first two */
|
if (sourlo&0xfff00000) { /* in one of first two */
|
dpdlenchk(1, sourlo>>30); /* very rare */
|
dpdlenchk(1, sourlo>>30); /* very rare */
|
dpdlendun(2, sourlo>>20);
|
dpdlendun(2, sourlo>>20);
|
} /* [cannot drop through] */
|
} /* [cannot drop through] */
|
dpdlenchk(3, sourlo>>10);
|
dpdlenchk(3, sourlo>>10);
|
dpdlendun(4, sourlo);
|
dpdlendun(4, sourlo);
|
/* [cannot drop through] */
|
/* [cannot drop through] */
|
|
|
#elif QUAD
|
#elif QUAD
|
if (sourhi&0x00003fff) { /* ends in first */
|
if (sourhi&0x00003fff) { /* ends in first */
|
dpdlenchk(0, sourhi>>4);
|
dpdlenchk(0, sourhi>>4);
|
sourmh=DFWORD(df, 1);
|
sourmh=DFWORD(df, 1);
|
dpdlendun(1, ((sourhi)<<6) | (sourmh>>26));
|
dpdlendun(1, ((sourhi)<<6) | (sourmh>>26));
|
} /* [cannot drop through] */
|
} /* [cannot drop through] */
|
sourmh=DFWORD(df, 1);
|
sourmh=DFWORD(df, 1);
|
if (sourmh) {
|
if (sourmh) {
|
dpdlenchk(1, sourmh>>26);
|
dpdlenchk(1, sourmh>>26);
|
dpdlenchk(2, sourmh>>16);
|
dpdlenchk(2, sourmh>>16);
|
dpdlenchk(3, sourmh>>6);
|
dpdlenchk(3, sourmh>>6);
|
sourml=DFWORD(df, 2);
|
sourml=DFWORD(df, 2);
|
dpdlendun(4, ((sourmh)<<4) | (sourml>>28));
|
dpdlendun(4, ((sourmh)<<4) | (sourml>>28));
|
} /* [cannot drop through] */
|
} /* [cannot drop through] */
|
sourml=DFWORD(df, 2);
|
sourml=DFWORD(df, 2);
|
if (sourml) {
|
if (sourml) {
|
dpdlenchk(4, sourml>>28);
|
dpdlenchk(4, sourml>>28);
|
dpdlenchk(5, sourml>>18);
|
dpdlenchk(5, sourml>>18);
|
dpdlenchk(6, sourml>>8);
|
dpdlenchk(6, sourml>>8);
|
sourlo=DFWORD(df, 3);
|
sourlo=DFWORD(df, 3);
|
dpdlendun(7, ((sourml)<<2) | (sourlo>>30));
|
dpdlendun(7, ((sourml)<<2) | (sourlo>>30));
|
} /* [cannot drop through] */
|
} /* [cannot drop through] */
|
sourlo=DFWORD(df, 3);
|
sourlo=DFWORD(df, 3);
|
if (sourlo&0xfff00000) { /* in one of first two */
|
if (sourlo&0xfff00000) { /* in one of first two */
|
dpdlenchk(7, sourlo>>30); /* very rare */
|
dpdlenchk(7, sourlo>>30); /* very rare */
|
dpdlendun(8, sourlo>>20);
|
dpdlendun(8, sourlo>>20);
|
} /* [cannot drop through] */
|
} /* [cannot drop through] */
|
dpdlenchk(9, sourlo>>10);
|
dpdlenchk(9, sourlo>>10);
|
dpdlendun(10, sourlo);
|
dpdlendun(10, sourlo);
|
/* [cannot drop through] */
|
/* [cannot drop through] */
|
#endif
|
#endif
|
} /* decFloatDigits */
|
} /* decFloatDigits */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatDivide -- divide a decFloat by another */
|
/* decFloatDivide -- divide a decFloat by another */
|
/* */
|
/* */
|
/* result gets the result of dividing dfl by dfr: */
|
/* result gets the result of dividing dfl by dfr: */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* This is just a wrapper. */
|
/* This is just a wrapper. */
|
decFloat * decFloatDivide(decFloat *result,
|
decFloat * decFloatDivide(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
return decDivide(result, dfl, dfr, set, DIVIDE);
|
return decDivide(result, dfl, dfr, set, DIVIDE);
|
} /* decFloatDivide */
|
} /* decFloatDivide */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatDivideInteger -- integer divide a decFloat by another */
|
/* decFloatDivideInteger -- integer divide a decFloat by another */
|
/* */
|
/* */
|
/* result gets the result of dividing dfl by dfr: */
|
/* result gets the result of dividing dfl by dfr: */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatDivideInteger(decFloat *result,
|
decFloat * decFloatDivideInteger(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
return decDivide(result, dfl, dfr, set, DIVIDEINT);
|
return decDivide(result, dfl, dfr, set, DIVIDEINT);
|
} /* decFloatDivideInteger */
|
} /* decFloatDivideInteger */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatFMA -- multiply and add three decFloats, fused */
|
/* decFloatFMA -- multiply and add three decFloats, fused */
|
/* */
|
/* */
|
/* result gets the result of (dfl*dfr)+dff with a single rounding */
|
/* result gets the result of (dfl*dfr)+dff with a single rounding */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dff is the final decFloat (fhs) */
|
/* dff is the final decFloat (fhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatFMA(decFloat *result, const decFloat *dfl,
|
decFloat * decFloatFMA(decFloat *result, const decFloat *dfl,
|
const decFloat *dfr, const decFloat *dff,
|
const decFloat *dfr, const decFloat *dff,
|
decContext *set) {
|
decContext *set) {
|
/* The accumulator has the bytes needed for FiniteMultiply, plus */
|
/* The accumulator has the bytes needed for FiniteMultiply, plus */
|
/* one byte to the left in case of carry, plus DECPMAX+2 to the */
|
/* one byte to the left in case of carry, plus DECPMAX+2 to the */
|
/* right for the final addition (up to full fhs + round & sticky) */
|
/* right for the final addition (up to full fhs + round & sticky) */
|
#define FMALEN (1+ (DECPMAX9*18) +DECPMAX+2)
|
#define FMALEN (1+ (DECPMAX9*18) +DECPMAX+2)
|
uByte acc[FMALEN]; /* for multiplied coefficient in BCD */
|
uByte acc[FMALEN]; /* for multiplied coefficient in BCD */
|
/* .. and for final result */
|
/* .. and for final result */
|
bcdnum mul; /* for multiplication result */
|
bcdnum mul; /* for multiplication result */
|
bcdnum fin; /* for final operand, expanded */
|
bcdnum fin; /* for final operand, expanded */
|
uByte coe[DECPMAX]; /* dff coefficient in BCD */
|
uByte coe[DECPMAX]; /* dff coefficient in BCD */
|
bcdnum *hi, *lo; /* bcdnum with higher/lower exponent */
|
bcdnum *hi, *lo; /* bcdnum with higher/lower exponent */
|
uInt diffsign; /* non-zero if signs differ */
|
uInt diffsign; /* non-zero if signs differ */
|
uInt hipad; /* pad digit for hi if needed */
|
uInt hipad; /* pad digit for hi if needed */
|
Int padding; /* excess exponent */
|
Int padding; /* excess exponent */
|
uInt carry; /* +1 for ten's complement and during add */
|
uInt carry; /* +1 for ten's complement and during add */
|
uByte *ub, *uh, *ul; /* work */
|
uByte *ub, *uh, *ul; /* work */
|
|
|
/* handle all the special values [any special operand leads to a */
|
/* handle all the special values [any special operand leads to a */
|
/* special result] */
|
/* special result] */
|
if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr) || DFISSPECIAL(dff)) {
|
if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr) || DFISSPECIAL(dff)) {
|
decFloat proxy; /* multiplication result proxy */
|
decFloat proxy; /* multiplication result proxy */
|
/* NaNs are handled as usual, giving priority to sNaNs */
|
/* NaNs are handled as usual, giving priority to sNaNs */
|
if (DFISSNAN(dfl) || DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISSNAN(dfl) || DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISSNAN(dff)) return decNaNs(result, dff, NULL, set);
|
if (DFISSNAN(dff)) return decNaNs(result, dff, NULL, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dff)) return decNaNs(result, dff, NULL, set);
|
if (DFISNAN(dff)) return decNaNs(result, dff, NULL, set);
|
/* One or more of the three is infinite */
|
/* One or more of the three is infinite */
|
/* infinity times zero is bad */
|
/* infinity times zero is bad */
|
decFloatZero(&proxy);
|
decFloatZero(&proxy);
|
if (DFISINF(dfl)) {
|
if (DFISINF(dfl)) {
|
if (DFISZERO(dfr)) return decInvalid(result, set);
|
if (DFISZERO(dfr)) return decInvalid(result, set);
|
decInfinity(&proxy, &proxy);
|
decInfinity(&proxy, &proxy);
|
}
|
}
|
else if (DFISINF(dfr)) {
|
else if (DFISINF(dfr)) {
|
if (DFISZERO(dfl)) return decInvalid(result, set);
|
if (DFISZERO(dfl)) return decInvalid(result, set);
|
decInfinity(&proxy, &proxy);
|
decInfinity(&proxy, &proxy);
|
}
|
}
|
/* compute sign of multiplication and place in proxy */
|
/* compute sign of multiplication and place in proxy */
|
DFWORD(&proxy, 0)|=(DFWORD(dfl, 0)^DFWORD(dfr, 0))&DECFLOAT_Sign;
|
DFWORD(&proxy, 0)|=(DFWORD(dfl, 0)^DFWORD(dfr, 0))&DECFLOAT_Sign;
|
if (!DFISINF(dff)) return decFloatCopy(result, &proxy);
|
if (!DFISINF(dff)) return decFloatCopy(result, &proxy);
|
/* dff is Infinite */
|
/* dff is Infinite */
|
if (!DFISINF(&proxy)) return decInfinity(result, dff);
|
if (!DFISINF(&proxy)) return decInfinity(result, dff);
|
/* both sides of addition are infinite; different sign is bad */
|
/* both sides of addition are infinite; different sign is bad */
|
if ((DFWORD(dff, 0)&DECFLOAT_Sign)!=(DFWORD(&proxy, 0)&DECFLOAT_Sign))
|
if ((DFWORD(dff, 0)&DECFLOAT_Sign)!=(DFWORD(&proxy, 0)&DECFLOAT_Sign))
|
return decInvalid(result, set);
|
return decInvalid(result, set);
|
return decFloatCopy(result, &proxy);
|
return decFloatCopy(result, &proxy);
|
}
|
}
|
|
|
/* Here when all operands are finite */
|
/* Here when all operands are finite */
|
|
|
/* First multiply dfl*dfr */
|
/* First multiply dfl*dfr */
|
decFiniteMultiply(&mul, acc+1, dfl, dfr);
|
decFiniteMultiply(&mul, acc+1, dfl, dfr);
|
/* The multiply is complete, exact and unbounded, and described in */
|
/* The multiply is complete, exact and unbounded, and described in */
|
/* mul with the coefficient held in acc[1...] */
|
/* mul with the coefficient held in acc[1...] */
|
|
|
/* now add in dff; the algorithm is essentially the same as */
|
/* now add in dff; the algorithm is essentially the same as */
|
/* decFloatAdd, but the code is different because the code there */
|
/* decFloatAdd, but the code is different because the code there */
|
/* is highly optimized for adding two numbers of the same size */
|
/* is highly optimized for adding two numbers of the same size */
|
fin.exponent=GETEXPUN(dff); /* get dff exponent and sign */
|
fin.exponent=GETEXPUN(dff); /* get dff exponent and sign */
|
fin.sign=DFWORD(dff, 0)&DECFLOAT_Sign;
|
fin.sign=DFWORD(dff, 0)&DECFLOAT_Sign;
|
diffsign=mul.sign^fin.sign; /* note if signs differ */
|
diffsign=mul.sign^fin.sign; /* note if signs differ */
|
fin.msd=coe;
|
fin.msd=coe;
|
fin.lsd=coe+DECPMAX-1;
|
fin.lsd=coe+DECPMAX-1;
|
GETCOEFF(dff, coe); /* extract the coefficient */
|
GETCOEFF(dff, coe); /* extract the coefficient */
|
|
|
/* now set hi and lo so that hi points to whichever of mul and fin */
|
/* now set hi and lo so that hi points to whichever of mul and fin */
|
/* has the higher exponent and lo point to the other [don't care if */
|
/* has the higher exponent and lo point to the other [don't care if */
|
/* the same] */
|
/* the same] */
|
if (mul.exponent>=fin.exponent) {
|
if (mul.exponent>=fin.exponent) {
|
hi=&mul;
|
hi=&mul;
|
lo=&fin;
|
lo=&fin;
|
}
|
}
|
else {
|
else {
|
hi=&fin;
|
hi=&fin;
|
lo=&mul;
|
lo=&mul;
|
}
|
}
|
|
|
/* remove leading zeros on both operands; this will save time later */
|
/* remove leading zeros on both operands; this will save time later */
|
/* and make testing for zero trivial */
|
/* and make testing for zero trivial */
|
for (; UINTAT(hi->msd)==0 && hi->msd+3<hi->lsd;) hi->msd+=4;
|
for (; UINTAT(hi->msd)==0 && hi->msd+3<hi->lsd;) hi->msd+=4;
|
for (; *hi->msd==0 && hi->msd<hi->lsd;) hi->msd++;
|
for (; *hi->msd==0 && hi->msd<hi->lsd;) hi->msd++;
|
for (; UINTAT(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;
|
for (; UINTAT(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;
|
for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;
|
for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;
|
|
|
/* if hi is zero then result will be lo (which has the smaller */
|
/* if hi is zero then result will be lo (which has the smaller */
|
/* exponent), which also may need to be tested for zero for the */
|
/* exponent), which also may need to be tested for zero for the */
|
/* weird IEEE 754 sign rules */
|
/* weird IEEE 754 sign rules */
|
if (*hi->msd==0 && hi->msd==hi->lsd) { /* hi is zero */
|
if (*hi->msd==0 && hi->msd==hi->lsd) { /* hi is zero */
|
/* "When the sum of two operands with opposite signs is */
|
/* "When the sum of two operands with opposite signs is */
|
/* exactly zero, the sign of that sum shall be '+' in all */
|
/* exactly zero, the sign of that sum shall be '+' in all */
|
/* rounding modes except round toward -Infinity, in which */
|
/* rounding modes except round toward -Infinity, in which */
|
/* mode that sign shall be '-'." */
|
/* mode that sign shall be '-'." */
|
if (diffsign) {
|
if (diffsign) {
|
if (*lo->msd==0 && lo->msd==lo->lsd) { /* lo is zero */
|
if (*lo->msd==0 && lo->msd==lo->lsd) { /* lo is zero */
|
lo->sign=0;
|
lo->sign=0;
|
if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;
|
if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;
|
} /* diffsign && lo=0 */
|
} /* diffsign && lo=0 */
|
} /* diffsign */
|
} /* diffsign */
|
return decFinalize(result, lo, set); /* may need clamping */
|
return decFinalize(result, lo, set); /* may need clamping */
|
} /* numfl is zero */
|
} /* numfl is zero */
|
/* [here, both are minimal length and hi is non-zero] */
|
/* [here, both are minimal length and hi is non-zero] */
|
|
|
/* if signs differ, take the ten's complement of hi (zeros to the */
|
/* if signs differ, take the ten's complement of hi (zeros to the */
|
/* right do not matter because the complement of zero is zero); */
|
/* right do not matter because the complement of zero is zero); */
|
/* the +1 is done later, as part of the addition, inserted at the */
|
/* the +1 is done later, as part of the addition, inserted at the */
|
/* correct digit */
|
/* correct digit */
|
hipad=0;
|
hipad=0;
|
carry=0;
|
carry=0;
|
if (diffsign) {
|
if (diffsign) {
|
hipad=9;
|
hipad=9;
|
carry=1;
|
carry=1;
|
/* exactly the correct number of digits must be inverted */
|
/* exactly the correct number of digits must be inverted */
|
for (uh=hi->msd; uh<hi->lsd-3; uh+=4) UINTAT(uh)=0x09090909-UINTAT(uh);
|
for (uh=hi->msd; uh<hi->lsd-3; uh+=4) UINTAT(uh)=0x09090909-UINTAT(uh);
|
for (; uh<=hi->lsd; uh++) *uh=(uByte)(0x09-*uh);
|
for (; uh<=hi->lsd; uh++) *uh=(uByte)(0x09-*uh);
|
}
|
}
|
|
|
/* ready to add; note that hi has no leading zeros so gap */
|
/* ready to add; note that hi has no leading zeros so gap */
|
/* calculation does not have to be as pessimistic as in decFloatAdd */
|
/* calculation does not have to be as pessimistic as in decFloatAdd */
|
/* (this is much more like the arbitrary-precision algorithm in */
|
/* (this is much more like the arbitrary-precision algorithm in */
|
/* Rexx and decNumber) */
|
/* Rexx and decNumber) */
|
|
|
/* padding is the number of zeros that would need to be added to hi */
|
/* padding is the number of zeros that would need to be added to hi */
|
/* for its lsd to be aligned with the lsd of lo */
|
/* for its lsd to be aligned with the lsd of lo */
|
padding=hi->exponent-lo->exponent;
|
padding=hi->exponent-lo->exponent;
|
/* printf("FMA pad %ld\n", (LI)padding); */
|
/* printf("FMA pad %ld\n", (LI)padding); */
|
|
|
/* the result of the addition will be built into the accumulator, */
|
/* the result of the addition will be built into the accumulator, */
|
/* starting from the far right; this could be either hi or lo */
|
/* starting from the far right; this could be either hi or lo */
|
ub=acc+FMALEN-1; /* where lsd of result will go */
|
ub=acc+FMALEN-1; /* where lsd of result will go */
|
ul=lo->lsd; /* lsd of rhs */
|
ul=lo->lsd; /* lsd of rhs */
|
|
|
if (padding!=0) { /* unaligned */
|
if (padding!=0) { /* unaligned */
|
/* if the msd of lo is more than DECPMAX+2 digits to the right of */
|
/* if the msd of lo is more than DECPMAX+2 digits to the right of */
|
/* the original msd of hi then it can be reduced to a single */
|
/* the original msd of hi then it can be reduced to a single */
|
/* digit at the right place, as it stays clear of hi digits */
|
/* digit at the right place, as it stays clear of hi digits */
|
/* [it must be DECPMAX+2 because during a subtraction the msd */
|
/* [it must be DECPMAX+2 because during a subtraction the msd */
|
/* could become 0 after a borrow from 1.000 to 0.9999...] */
|
/* could become 0 after a borrow from 1.000 to 0.9999...] */
|
Int hilen=(Int)(hi->lsd-hi->msd+1); /* lengths */
|
Int hilen=(Int)(hi->lsd-hi->msd+1); /* lengths */
|
Int lolen=(Int)(lo->lsd-lo->msd+1); /* .. */
|
Int lolen=(Int)(lo->lsd-lo->msd+1); /* .. */
|
Int newexp=MINI(hi->exponent, hi->exponent+hilen-DECPMAX)-3;
|
Int newexp=MINI(hi->exponent, hi->exponent+hilen-DECPMAX)-3;
|
Int reduce=newexp-lo->exponent;
|
Int reduce=newexp-lo->exponent;
|
if (reduce>0) { /* [= case gives reduce=0 nop] */
|
if (reduce>0) { /* [= case gives reduce=0 nop] */
|
/* printf("FMA reduce: %ld\n", (LI)reduce); */
|
/* printf("FMA reduce: %ld\n", (LI)reduce); */
|
if (reduce>=lolen) { /* eating all */
|
if (reduce>=lolen) { /* eating all */
|
lo->lsd=lo->msd; /* reduce to single digit */
|
lo->lsd=lo->msd; /* reduce to single digit */
|
lo->exponent=newexp; /* [known to be non-zero] */
|
lo->exponent=newexp; /* [known to be non-zero] */
|
}
|
}
|
else { /* < */
|
else { /* < */
|
uByte *up=lo->lsd;
|
uByte *up=lo->lsd;
|
lo->lsd=lo->lsd-reduce;
|
lo->lsd=lo->lsd-reduce;
|
if (*lo->lsd==0) /* could need sticky bit */
|
if (*lo->lsd==0) /* could need sticky bit */
|
for (; up>lo->lsd; up--) { /* search discarded digits */
|
for (; up>lo->lsd; up--) { /* search discarded digits */
|
if (*up!=0) { /* found one... */
|
if (*up!=0) { /* found one... */
|
*lo->lsd=1; /* set sticky bit */
|
*lo->lsd=1; /* set sticky bit */
|
break;
|
break;
|
}
|
}
|
}
|
}
|
lo->exponent+=reduce;
|
lo->exponent+=reduce;
|
}
|
}
|
padding=hi->exponent-lo->exponent; /* recalculate */
|
padding=hi->exponent-lo->exponent; /* recalculate */
|
ul=lo->lsd; /* .. */
|
ul=lo->lsd; /* .. */
|
} /* maybe reduce */
|
} /* maybe reduce */
|
/* padding is now <= DECPMAX+2 but still > 0; tricky DOUBLE case */
|
/* padding is now <= DECPMAX+2 but still > 0; tricky DOUBLE case */
|
/* is when hi is a 1 that will become a 0.9999... by subtraction: */
|
/* is when hi is a 1 that will become a 0.9999... by subtraction: */
|
/* hi: 1 E+16 */
|
/* hi: 1 E+16 */
|
/* lo: .................1000000000000000 E-16 */
|
/* lo: .................1000000000000000 E-16 */
|
/* which for the addition pads and reduces to: */
|
/* which for the addition pads and reduces to: */
|
/* hi: 1000000000000000000 E-2 */
|
/* hi: 1000000000000000000 E-2 */
|
/* lo: .................1 E-2 */
|
/* lo: .................1 E-2 */
|
#if DECCHECK
|
#if DECCHECK
|
if (padding>DECPMAX+2) printf("FMA excess padding: %ld\n", (LI)padding);
|
if (padding>DECPMAX+2) printf("FMA excess padding: %ld\n", (LI)padding);
|
if (padding<=0) printf("FMA low padding: %ld\n", (LI)padding);
|
if (padding<=0) printf("FMA low padding: %ld\n", (LI)padding);
|
/* printf("FMA padding: %ld\n", (LI)padding); */
|
/* printf("FMA padding: %ld\n", (LI)padding); */
|
#endif
|
#endif
|
/* padding digits can now be set in the result; one or more of */
|
/* padding digits can now be set in the result; one or more of */
|
/* these will come from lo; others will be zeros in the gap */
|
/* these will come from lo; others will be zeros in the gap */
|
for (; ul>=lo->msd && padding>0; padding--, ul--, ub--) *ub=*ul;
|
for (; ul>=lo->msd && padding>0; padding--, ul--, ub--) *ub=*ul;
|
for (;padding>0; padding--, ub--) *ub=0; /* mind the gap */
|
for (;padding>0; padding--, ub--) *ub=0; /* mind the gap */
|
}
|
}
|
|
|
/* addition now complete to the right of the rightmost digit of hi */
|
/* addition now complete to the right of the rightmost digit of hi */
|
uh=hi->lsd;
|
uh=hi->lsd;
|
|
|
/* carry was set up depending on ten's complement above; do the add... */
|
/* carry was set up depending on ten's complement above; do the add... */
|
for (;; ub--) {
|
for (;; ub--) {
|
uInt hid, lod;
|
uInt hid, lod;
|
if (uh<hi->msd) {
|
if (uh<hi->msd) {
|
if (ul<lo->msd) break;
|
if (ul<lo->msd) break;
|
hid=hipad;
|
hid=hipad;
|
}
|
}
|
else hid=*uh--;
|
else hid=*uh--;
|
if (ul<lo->msd) lod=0;
|
if (ul<lo->msd) lod=0;
|
else lod=*ul--;
|
else lod=*ul--;
|
*ub=(uByte)(carry+hid+lod);
|
*ub=(uByte)(carry+hid+lod);
|
if (*ub<10) carry=0;
|
if (*ub<10) carry=0;
|
else {
|
else {
|
*ub-=10;
|
*ub-=10;
|
carry=1;
|
carry=1;
|
}
|
}
|
} /* addition loop */
|
} /* addition loop */
|
|
|
/* addition complete -- now handle carry, borrow, etc. */
|
/* addition complete -- now handle carry, borrow, etc. */
|
/* use lo to set up the num (its exponent is already correct, and */
|
/* use lo to set up the num (its exponent is already correct, and */
|
/* sign usually is) */
|
/* sign usually is) */
|
lo->msd=ub+1;
|
lo->msd=ub+1;
|
lo->lsd=acc+FMALEN-1;
|
lo->lsd=acc+FMALEN-1;
|
/* decShowNum(lo, "lo"); */
|
/* decShowNum(lo, "lo"); */
|
if (!diffsign) { /* same-sign addition */
|
if (!diffsign) { /* same-sign addition */
|
if (carry) { /* carry out */
|
if (carry) { /* carry out */
|
*ub=1; /* place the 1 .. */
|
*ub=1; /* place the 1 .. */
|
lo->msd--; /* .. and update */
|
lo->msd--; /* .. and update */
|
}
|
}
|
} /* same sign */
|
} /* same sign */
|
else { /* signs differed (subtraction) */
|
else { /* signs differed (subtraction) */
|
if (!carry) { /* no carry out means hi<lo */
|
if (!carry) { /* no carry out means hi<lo */
|
/* borrowed -- take ten's complement of the right digits */
|
/* borrowed -- take ten's complement of the right digits */
|
lo->sign=hi->sign; /* sign is lhs sign */
|
lo->sign=hi->sign; /* sign is lhs sign */
|
for (ul=lo->msd; ul<lo->lsd-3; ul+=4) UINTAT(ul)=0x09090909-UINTAT(ul);
|
for (ul=lo->msd; ul<lo->lsd-3; ul+=4) UINTAT(ul)=0x09090909-UINTAT(ul);
|
for (; ul<=lo->lsd; ul++) *ul=(uByte)(0x09-*ul); /* [leaves ul at lsd+1] */
|
for (; ul<=lo->lsd; ul++) *ul=(uByte)(0x09-*ul); /* [leaves ul at lsd+1] */
|
/* complete the ten's complement by adding 1 [cannot overrun] */
|
/* complete the ten's complement by adding 1 [cannot overrun] */
|
for (ul--; *ul==9; ul--) *ul=0;
|
for (ul--; *ul==9; ul--) *ul=0;
|
*ul+=1;
|
*ul+=1;
|
} /* borrowed */
|
} /* borrowed */
|
else { /* carry out means hi>=lo */
|
else { /* carry out means hi>=lo */
|
/* sign to use is lo->sign */
|
/* sign to use is lo->sign */
|
/* all done except for the special IEEE 754 exact-zero-result */
|
/* all done except for the special IEEE 754 exact-zero-result */
|
/* rule (see above); while testing for zero, strip leading */
|
/* rule (see above); while testing for zero, strip leading */
|
/* zeros (which will save decFinalize doing it) */
|
/* zeros (which will save decFinalize doing it) */
|
for (; UINTAT(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;
|
for (; UINTAT(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;
|
for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;
|
for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;
|
if (*lo->msd==0) { /* must be true zero (and diffsign) */
|
if (*lo->msd==0) { /* must be true zero (and diffsign) */
|
lo->sign=0; /* assume + */
|
lo->sign=0; /* assume + */
|
if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;
|
if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;
|
}
|
}
|
/* [else was not zero, might still have leading zeros] */
|
/* [else was not zero, might still have leading zeros] */
|
} /* subtraction gave positive result */
|
} /* subtraction gave positive result */
|
} /* diffsign */
|
} /* diffsign */
|
|
|
return decFinalize(result, lo, set); /* round, check, and lay out */
|
return decFinalize(result, lo, set); /* round, check, and lay out */
|
} /* decFloatFMA */
|
} /* decFloatFMA */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatFromInt -- initialise a decFloat from an Int */
|
/* decFloatFromInt -- initialise a decFloat from an Int */
|
/* */
|
/* */
|
/* result gets the converted Int */
|
/* result gets the converted Int */
|
/* n is the Int to convert */
|
/* n is the Int to convert */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* The result is Exact; no errors or exceptions are possible. */
|
/* The result is Exact; no errors or exceptions are possible. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatFromInt32(decFloat *result, Int n) {
|
decFloat * decFloatFromInt32(decFloat *result, Int n) {
|
uInt u=(uInt)n; /* copy as bits */
|
uInt u=(uInt)n; /* copy as bits */
|
uInt encode; /* work */
|
uInt encode; /* work */
|
DFWORD(result, 0)=ZEROWORD; /* always */
|
DFWORD(result, 0)=ZEROWORD; /* always */
|
#if QUAD
|
#if QUAD
|
DFWORD(result, 1)=0;
|
DFWORD(result, 1)=0;
|
DFWORD(result, 2)=0;
|
DFWORD(result, 2)=0;
|
#endif
|
#endif
|
if (n<0) { /* handle -n with care */
|
if (n<0) { /* handle -n with care */
|
/* [This can be done without the test, but is then slightly slower] */
|
/* [This can be done without the test, but is then slightly slower] */
|
u=(~u)+1;
|
u=(~u)+1;
|
DFWORD(result, 0)|=DECFLOAT_Sign;
|
DFWORD(result, 0)|=DECFLOAT_Sign;
|
}
|
}
|
/* Since the maximum value of u now is 2**31, only the low word of */
|
/* Since the maximum value of u now is 2**31, only the low word of */
|
/* result is affected */
|
/* result is affected */
|
encode=BIN2DPD[u%1000];
|
encode=BIN2DPD[u%1000];
|
u/=1000;
|
u/=1000;
|
encode|=BIN2DPD[u%1000]<<10;
|
encode|=BIN2DPD[u%1000]<<10;
|
u/=1000;
|
u/=1000;
|
encode|=BIN2DPD[u%1000]<<20;
|
encode|=BIN2DPD[u%1000]<<20;
|
u/=1000; /* now 0, 1, or 2 */
|
u/=1000; /* now 0, 1, or 2 */
|
encode|=u<<30;
|
encode|=u<<30;
|
DFWORD(result, DECWORDS-1)=encode;
|
DFWORD(result, DECWORDS-1)=encode;
|
return result;
|
return result;
|
} /* decFloatFromInt32 */
|
} /* decFloatFromInt32 */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatFromUInt -- initialise a decFloat from a uInt */
|
/* decFloatFromUInt -- initialise a decFloat from a uInt */
|
/* */
|
/* */
|
/* result gets the converted uInt */
|
/* result gets the converted uInt */
|
/* n is the uInt to convert */
|
/* n is the uInt to convert */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* The result is Exact; no errors or exceptions are possible. */
|
/* The result is Exact; no errors or exceptions are possible. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatFromUInt32(decFloat *result, uInt u) {
|
decFloat * decFloatFromUInt32(decFloat *result, uInt u) {
|
uInt encode; /* work */
|
uInt encode; /* work */
|
DFWORD(result, 0)=ZEROWORD; /* always */
|
DFWORD(result, 0)=ZEROWORD; /* always */
|
#if QUAD
|
#if QUAD
|
DFWORD(result, 1)=0;
|
DFWORD(result, 1)=0;
|
DFWORD(result, 2)=0;
|
DFWORD(result, 2)=0;
|
#endif
|
#endif
|
encode=BIN2DPD[u%1000];
|
encode=BIN2DPD[u%1000];
|
u/=1000;
|
u/=1000;
|
encode|=BIN2DPD[u%1000]<<10;
|
encode|=BIN2DPD[u%1000]<<10;
|
u/=1000;
|
u/=1000;
|
encode|=BIN2DPD[u%1000]<<20;
|
encode|=BIN2DPD[u%1000]<<20;
|
u/=1000; /* now 0 -> 4 */
|
u/=1000; /* now 0 -> 4 */
|
encode|=u<<30;
|
encode|=u<<30;
|
DFWORD(result, DECWORDS-1)=encode;
|
DFWORD(result, DECWORDS-1)=encode;
|
DFWORD(result, DECWORDS-2)|=u>>2; /* rarely non-zero */
|
DFWORD(result, DECWORDS-2)|=u>>2; /* rarely non-zero */
|
return result;
|
return result;
|
} /* decFloatFromUInt32 */
|
} /* decFloatFromUInt32 */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatInvert -- logical digitwise INVERT of a decFloat */
|
/* decFloatInvert -- logical digitwise INVERT of a decFloat */
|
/* */
|
/* */
|
/* result gets the result of INVERTing df */
|
/* result gets the result of INVERTing df */
|
/* df is the decFloat to invert */
|
/* df is the decFloat to invert */
|
/* set is the context */
|
/* set is the context */
|
/* returns result, which will be canonical with sign=0 */
|
/* returns result, which will be canonical with sign=0 */
|
/* */
|
/* */
|
/* The operand must be positive, finite with exponent q=0, and */
|
/* The operand must be positive, finite with exponent q=0, and */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatInvert(decFloat *result, const decFloat *df,
|
decFloat * decFloatInvert(decFloat *result, const decFloat *df,
|
decContext *set) {
|
decContext *set) {
|
uInt sourhi=DFWORD(df, 0); /* top word of dfs */
|
uInt sourhi=DFWORD(df, 0); /* top word of dfs */
|
|
|
if (!DFISUINT01(df) || !DFISCC01(df)) return decInvalid(result, set);
|
if (!DFISUINT01(df) || !DFISCC01(df)) return decInvalid(result, set);
|
/* the operand is a finite integer (q=0) */
|
/* the operand is a finite integer (q=0) */
|
#if DOUBLE
|
#if DOUBLE
|
DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04009124);
|
DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04009124);
|
DFWORD(result, 1)=(~DFWORD(df, 1)) &0x49124491;
|
DFWORD(result, 1)=(~DFWORD(df, 1)) &0x49124491;
|
#elif QUAD
|
#elif QUAD
|
DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04000912);
|
DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04000912);
|
DFWORD(result, 1)=(~DFWORD(df, 1)) &0x44912449;
|
DFWORD(result, 1)=(~DFWORD(df, 1)) &0x44912449;
|
DFWORD(result, 2)=(~DFWORD(df, 2)) &0x12449124;
|
DFWORD(result, 2)=(~DFWORD(df, 2)) &0x12449124;
|
DFWORD(result, 3)=(~DFWORD(df, 3)) &0x49124491;
|
DFWORD(result, 3)=(~DFWORD(df, 3)) &0x49124491;
|
#endif
|
#endif
|
return result;
|
return result;
|
} /* decFloatInvert */
|
} /* decFloatInvert */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatIs -- decFloat tests (IsSigned, etc.) */
|
/* decFloatIs -- decFloat tests (IsSigned, etc.) */
|
/* */
|
/* */
|
/* df is the decFloat to test */
|
/* df is the decFloat to test */
|
/* returns 0 or 1 in an int32_t */
|
/* returns 0 or 1 in an int32_t */
|
/* */
|
/* */
|
/* Many of these could be macros, but having them as real functions */
|
/* Many of these could be macros, but having them as real functions */
|
/* is a bit cleaner (and they can be referred to here by the generic */
|
/* is a bit cleaner (and they can be referred to here by the generic */
|
/* names) */
|
/* names) */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
uInt decFloatIsCanonical(const decFloat *df) {
|
uInt decFloatIsCanonical(const decFloat *df) {
|
if (DFISSPECIAL(df)) {
|
if (DFISSPECIAL(df)) {
|
if (DFISINF(df)) {
|
if (DFISINF(df)) {
|
if (DFWORD(df, 0)&ECONMASK) return 0; /* exponent continuation */
|
if (DFWORD(df, 0)&ECONMASK) return 0; /* exponent continuation */
|
if (!DFISCCZERO(df)) return 0; /* coefficient continuation */
|
if (!DFISCCZERO(df)) return 0; /* coefficient continuation */
|
return 1;
|
return 1;
|
}
|
}
|
/* is a NaN */
|
/* is a NaN */
|
if (DFWORD(df, 0)&ECONNANMASK) return 0; /* exponent continuation */
|
if (DFWORD(df, 0)&ECONNANMASK) return 0; /* exponent continuation */
|
if (DFISCCZERO(df)) return 1; /* coefficient continuation */
|
if (DFISCCZERO(df)) return 1; /* coefficient continuation */
|
/* drop through to check payload */
|
/* drop through to check payload */
|
}
|
}
|
{ /* declare block */
|
{ /* declare block */
|
#if DOUBLE
|
#if DOUBLE
|
uInt sourhi=DFWORD(df, 0);
|
uInt sourhi=DFWORD(df, 0);
|
uInt sourlo=DFWORD(df, 1);
|
uInt sourlo=DFWORD(df, 1);
|
if (CANONDPDOFF(sourhi, 8)
|
if (CANONDPDOFF(sourhi, 8)
|
&& CANONDPDTWO(sourhi, sourlo, 30)
|
&& CANONDPDTWO(sourhi, sourlo, 30)
|
&& CANONDPDOFF(sourlo, 20)
|
&& CANONDPDOFF(sourlo, 20)
|
&& CANONDPDOFF(sourlo, 10)
|
&& CANONDPDOFF(sourlo, 10)
|
&& CANONDPDOFF(sourlo, 0)) return 1;
|
&& CANONDPDOFF(sourlo, 0)) return 1;
|
#elif QUAD
|
#elif QUAD
|
uInt sourhi=DFWORD(df, 0);
|
uInt sourhi=DFWORD(df, 0);
|
uInt sourmh=DFWORD(df, 1);
|
uInt sourmh=DFWORD(df, 1);
|
uInt sourml=DFWORD(df, 2);
|
uInt sourml=DFWORD(df, 2);
|
uInt sourlo=DFWORD(df, 3);
|
uInt sourlo=DFWORD(df, 3);
|
if (CANONDPDOFF(sourhi, 4)
|
if (CANONDPDOFF(sourhi, 4)
|
&& CANONDPDTWO(sourhi, sourmh, 26)
|
&& CANONDPDTWO(sourhi, sourmh, 26)
|
&& CANONDPDOFF(sourmh, 16)
|
&& CANONDPDOFF(sourmh, 16)
|
&& CANONDPDOFF(sourmh, 6)
|
&& CANONDPDOFF(sourmh, 6)
|
&& CANONDPDTWO(sourmh, sourml, 28)
|
&& CANONDPDTWO(sourmh, sourml, 28)
|
&& CANONDPDOFF(sourml, 18)
|
&& CANONDPDOFF(sourml, 18)
|
&& CANONDPDOFF(sourml, 8)
|
&& CANONDPDOFF(sourml, 8)
|
&& CANONDPDTWO(sourml, sourlo, 30)
|
&& CANONDPDTWO(sourml, sourlo, 30)
|
&& CANONDPDOFF(sourlo, 20)
|
&& CANONDPDOFF(sourlo, 20)
|
&& CANONDPDOFF(sourlo, 10)
|
&& CANONDPDOFF(sourlo, 10)
|
&& CANONDPDOFF(sourlo, 0)) return 1;
|
&& CANONDPDOFF(sourlo, 0)) return 1;
|
#endif
|
#endif
|
} /* block */
|
} /* block */
|
return 0; /* a declet is non-canonical */
|
return 0; /* a declet is non-canonical */
|
}
|
}
|
|
|
uInt decFloatIsFinite(const decFloat *df) {
|
uInt decFloatIsFinite(const decFloat *df) {
|
return !DFISSPECIAL(df);
|
return !DFISSPECIAL(df);
|
}
|
}
|
uInt decFloatIsInfinite(const decFloat *df) {
|
uInt decFloatIsInfinite(const decFloat *df) {
|
return DFISINF(df);
|
return DFISINF(df);
|
}
|
}
|
uInt decFloatIsInteger(const decFloat *df) {
|
uInt decFloatIsInteger(const decFloat *df) {
|
return DFISINT(df);
|
return DFISINT(df);
|
}
|
}
|
uInt decFloatIsNaN(const decFloat *df) {
|
uInt decFloatIsNaN(const decFloat *df) {
|
return DFISNAN(df);
|
return DFISNAN(df);
|
}
|
}
|
uInt decFloatIsNormal(const decFloat *df) {
|
uInt decFloatIsNormal(const decFloat *df) {
|
Int exp; /* exponent */
|
Int exp; /* exponent */
|
if (DFISSPECIAL(df)) return 0;
|
if (DFISSPECIAL(df)) return 0;
|
if (DFISZERO(df)) return 0;
|
if (DFISZERO(df)) return 0;
|
/* is finite and non-zero */
|
/* is finite and non-zero */
|
exp=GETEXPUN(df) /* get unbiased exponent .. */
|
exp=GETEXPUN(df) /* get unbiased exponent .. */
|
+decFloatDigits(df)-1; /* .. and make adjusted exponent */
|
+decFloatDigits(df)-1; /* .. and make adjusted exponent */
|
return (exp>=DECEMIN); /* < DECEMIN is subnormal */
|
return (exp>=DECEMIN); /* < DECEMIN is subnormal */
|
}
|
}
|
uInt decFloatIsSignaling(const decFloat *df) {
|
uInt decFloatIsSignaling(const decFloat *df) {
|
return DFISSNAN(df);
|
return DFISSNAN(df);
|
}
|
}
|
uInt decFloatIsSignalling(const decFloat *df) {
|
uInt decFloatIsSignalling(const decFloat *df) {
|
return DFISSNAN(df);
|
return DFISSNAN(df);
|
}
|
}
|
uInt decFloatIsSigned(const decFloat *df) {
|
uInt decFloatIsSigned(const decFloat *df) {
|
return DFISSIGNED(df);
|
return DFISSIGNED(df);
|
}
|
}
|
uInt decFloatIsSubnormal(const decFloat *df) {
|
uInt decFloatIsSubnormal(const decFloat *df) {
|
if (DFISSPECIAL(df)) return 0;
|
if (DFISSPECIAL(df)) return 0;
|
/* is finite */
|
/* is finite */
|
if (decFloatIsNormal(df)) return 0;
|
if (decFloatIsNormal(df)) return 0;
|
/* it is <Nmin, but could be zero */
|
/* it is <Nmin, but could be zero */
|
if (DFISZERO(df)) return 0;
|
if (DFISZERO(df)) return 0;
|
return 1; /* is subnormal */
|
return 1; /* is subnormal */
|
}
|
}
|
uInt decFloatIsZero(const decFloat *df) {
|
uInt decFloatIsZero(const decFloat *df) {
|
return DFISZERO(df);
|
return DFISZERO(df);
|
} /* decFloatIs... */
|
} /* decFloatIs... */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatLogB -- return adjusted exponent, by 754r rules */
|
/* decFloatLogB -- return adjusted exponent, by 754r rules */
|
/* */
|
/* */
|
/* result gets the adjusted exponent as an integer, or a NaN etc. */
|
/* result gets the adjusted exponent as an integer, or a NaN etc. */
|
/* df is the decFloat to be examined */
|
/* df is the decFloat to be examined */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* Notable cases: */
|
/* Notable cases: */
|
/* A<0 -> Use |A| */
|
/* A<0 -> Use |A| */
|
/* A=0 -> -Infinity (Division by zero) */
|
/* A=0 -> -Infinity (Division by zero) */
|
/* A=Infinite -> +Infinity (Exact) */
|
/* A=Infinite -> +Infinity (Exact) */
|
/* A=1 exactly -> 0 (Exact) */
|
/* A=1 exactly -> 0 (Exact) */
|
/* NaNs are propagated as usual */
|
/* NaNs are propagated as usual */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatLogB(decFloat *result, const decFloat *df,
|
decFloat * decFloatLogB(decFloat *result, const decFloat *df,
|
decContext *set) {
|
decContext *set) {
|
Int ae; /* adjusted exponent */
|
Int ae; /* adjusted exponent */
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
if (DFISINF(df)) {
|
if (DFISINF(df)) {
|
DFWORD(result, 0)=0; /* need +ve */
|
DFWORD(result, 0)=0; /* need +ve */
|
return decInfinity(result, result); /* canonical +Infinity */
|
return decInfinity(result, result); /* canonical +Infinity */
|
}
|
}
|
if (DFISZERO(df)) {
|
if (DFISZERO(df)) {
|
set->status|=DEC_Division_by_zero; /* as per 754r */
|
set->status|=DEC_Division_by_zero; /* as per 754r */
|
DFWORD(result, 0)=DECFLOAT_Sign; /* make negative */
|
DFWORD(result, 0)=DECFLOAT_Sign; /* make negative */
|
return decInfinity(result, result); /* canonical -Infinity */
|
return decInfinity(result, result); /* canonical -Infinity */
|
}
|
}
|
ae=GETEXPUN(df) /* get unbiased exponent .. */
|
ae=GETEXPUN(df) /* get unbiased exponent .. */
|
+decFloatDigits(df)-1; /* .. and make adjusted exponent */
|
+decFloatDigits(df)-1; /* .. and make adjusted exponent */
|
/* ae has limited range (3 digits for DOUBLE and 4 for QUAD), so */
|
/* ae has limited range (3 digits for DOUBLE and 4 for QUAD), so */
|
/* it is worth using a special case of decFloatFromInt32 */
|
/* it is worth using a special case of decFloatFromInt32 */
|
DFWORD(result, 0)=ZEROWORD; /* always */
|
DFWORD(result, 0)=ZEROWORD; /* always */
|
if (ae<0) {
|
if (ae<0) {
|
DFWORD(result, 0)|=DECFLOAT_Sign; /* -0 so far */
|
DFWORD(result, 0)|=DECFLOAT_Sign; /* -0 so far */
|
ae=-ae;
|
ae=-ae;
|
}
|
}
|
#if DOUBLE
|
#if DOUBLE
|
DFWORD(result, 1)=BIN2DPD[ae]; /* a single declet */
|
DFWORD(result, 1)=BIN2DPD[ae]; /* a single declet */
|
#elif QUAD
|
#elif QUAD
|
DFWORD(result, 1)=0;
|
DFWORD(result, 1)=0;
|
DFWORD(result, 2)=0;
|
DFWORD(result, 2)=0;
|
DFWORD(result, 3)=(ae/1000)<<10; /* is <10, so need no DPD encode */
|
DFWORD(result, 3)=(ae/1000)<<10; /* is <10, so need no DPD encode */
|
DFWORD(result, 3)|=BIN2DPD[ae%1000];
|
DFWORD(result, 3)|=BIN2DPD[ae%1000];
|
#endif
|
#endif
|
return result;
|
return result;
|
} /* decFloatLogB */
|
} /* decFloatLogB */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatMax -- return maxnum of two operands */
|
/* decFloatMax -- return maxnum of two operands */
|
/* */
|
/* */
|
/* result gets the chosen decFloat */
|
/* result gets the chosen decFloat */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* If just one operand is a quiet NaN it is ignored. */
|
/* If just one operand is a quiet NaN it is ignored. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatMax(decFloat *result,
|
decFloat * decFloatMax(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int comp;
|
Int comp;
|
if (DFISNAN(dfl)) {
|
if (DFISNAN(dfl)) {
|
/* sNaN or both NaNs leads to normal NaN processing */
|
/* sNaN or both NaNs leads to normal NaN processing */
|
if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);
|
return decCanonical(result, dfr); /* RHS is numeric */
|
return decCanonical(result, dfr); /* RHS is numeric */
|
}
|
}
|
if (DFISNAN(dfr)) {
|
if (DFISNAN(dfr)) {
|
/* sNaN leads to normal NaN processing (both NaN handled above) */
|
/* sNaN leads to normal NaN processing (both NaN handled above) */
|
if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
return decCanonical(result, dfl); /* LHS is numeric */
|
return decCanonical(result, dfl); /* LHS is numeric */
|
}
|
}
|
/* Both operands are numeric; numeric comparison needed -- use */
|
/* Both operands are numeric; numeric comparison needed -- use */
|
/* total order for a well-defined choice (and +0 > -0) */
|
/* total order for a well-defined choice (and +0 > -0) */
|
comp=decNumCompare(dfl, dfr, 1);
|
comp=decNumCompare(dfl, dfr, 1);
|
if (comp>=0) return decCanonical(result, dfl);
|
if (comp>=0) return decCanonical(result, dfl);
|
return decCanonical(result, dfr);
|
return decCanonical(result, dfr);
|
} /* decFloatMax */
|
} /* decFloatMax */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatMaxMag -- return maxnummag of two operands */
|
/* decFloatMaxMag -- return maxnummag of two operands */
|
/* */
|
/* */
|
/* result gets the chosen decFloat */
|
/* result gets the chosen decFloat */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* Returns according to the magnitude comparisons if both numeric and */
|
/* Returns according to the magnitude comparisons if both numeric and */
|
/* unequal, otherwise returns maxnum */
|
/* unequal, otherwise returns maxnum */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatMaxMag(decFloat *result,
|
decFloat * decFloatMaxMag(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int comp;
|
Int comp;
|
decFloat absl, absr;
|
decFloat absl, absr;
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMax(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMax(result, dfl, dfr, set);
|
|
|
decFloatCopyAbs(&absl, dfl);
|
decFloatCopyAbs(&absl, dfl);
|
decFloatCopyAbs(&absr, dfr);
|
decFloatCopyAbs(&absr, dfr);
|
comp=decNumCompare(&absl, &absr, 0);
|
comp=decNumCompare(&absl, &absr, 0);
|
if (comp>0) return decCanonical(result, dfl);
|
if (comp>0) return decCanonical(result, dfl);
|
if (comp<0) return decCanonical(result, dfr);
|
if (comp<0) return decCanonical(result, dfr);
|
return decFloatMax(result, dfl, dfr, set);
|
return decFloatMax(result, dfl, dfr, set);
|
} /* decFloatMaxMag */
|
} /* decFloatMaxMag */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatMin -- return minnum of two operands */
|
/* decFloatMin -- return minnum of two operands */
|
/* */
|
/* */
|
/* result gets the chosen decFloat */
|
/* result gets the chosen decFloat */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* If just one operand is a quiet NaN it is ignored. */
|
/* If just one operand is a quiet NaN it is ignored. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatMin(decFloat *result,
|
decFloat * decFloatMin(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int comp;
|
Int comp;
|
if (DFISNAN(dfl)) {
|
if (DFISNAN(dfl)) {
|
/* sNaN or both NaNs leads to normal NaN processing */
|
/* sNaN or both NaNs leads to normal NaN processing */
|
if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);
|
return decCanonical(result, dfr); /* RHS is numeric */
|
return decCanonical(result, dfr); /* RHS is numeric */
|
}
|
}
|
if (DFISNAN(dfr)) {
|
if (DFISNAN(dfr)) {
|
/* sNaN leads to normal NaN processing (both NaN handled above) */
|
/* sNaN leads to normal NaN processing (both NaN handled above) */
|
if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
return decCanonical(result, dfl); /* LHS is numeric */
|
return decCanonical(result, dfl); /* LHS is numeric */
|
}
|
}
|
/* Both operands are numeric; numeric comparison needed -- use */
|
/* Both operands are numeric; numeric comparison needed -- use */
|
/* total order for a well-defined choice (and +0 > -0) */
|
/* total order for a well-defined choice (and +0 > -0) */
|
comp=decNumCompare(dfl, dfr, 1);
|
comp=decNumCompare(dfl, dfr, 1);
|
if (comp<=0) return decCanonical(result, dfl);
|
if (comp<=0) return decCanonical(result, dfl);
|
return decCanonical(result, dfr);
|
return decCanonical(result, dfr);
|
} /* decFloatMin */
|
} /* decFloatMin */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatMinMag -- return minnummag of two operands */
|
/* decFloatMinMag -- return minnummag of two operands */
|
/* */
|
/* */
|
/* result gets the chosen decFloat */
|
/* result gets the chosen decFloat */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* Returns according to the magnitude comparisons if both numeric and */
|
/* Returns according to the magnitude comparisons if both numeric and */
|
/* unequal, otherwise returns minnum */
|
/* unequal, otherwise returns minnum */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatMinMag(decFloat *result,
|
decFloat * decFloatMinMag(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int comp;
|
Int comp;
|
decFloat absl, absr;
|
decFloat absl, absr;
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMin(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMin(result, dfl, dfr, set);
|
|
|
decFloatCopyAbs(&absl, dfl);
|
decFloatCopyAbs(&absl, dfl);
|
decFloatCopyAbs(&absr, dfr);
|
decFloatCopyAbs(&absr, dfr);
|
comp=decNumCompare(&absl, &absr, 0);
|
comp=decNumCompare(&absl, &absr, 0);
|
if (comp<0) return decCanonical(result, dfl);
|
if (comp<0) return decCanonical(result, dfl);
|
if (comp>0) return decCanonical(result, dfr);
|
if (comp>0) return decCanonical(result, dfr);
|
return decFloatMin(result, dfl, dfr, set);
|
return decFloatMin(result, dfl, dfr, set);
|
} /* decFloatMinMag */
|
} /* decFloatMinMag */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatMinus -- negate value, heeding NaNs, etc. */
|
/* decFloatMinus -- negate value, heeding NaNs, etc. */
|
/* */
|
/* */
|
/* result gets the canonicalized 0-df */
|
/* result gets the canonicalized 0-df */
|
/* df is the decFloat to minus */
|
/* df is the decFloat to minus */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This has the same effect as 0-df where the exponent of the zero is */
|
/* This has the same effect as 0-df where the exponent of the zero is */
|
/* the same as that of df (if df is finite). */
|
/* the same as that of df (if df is finite). */
|
/* The effect is also the same as decFloatCopyNegate except that NaNs */
|
/* The effect is also the same as decFloatCopyNegate except that NaNs */
|
/* are handled normally (the sign of a NaN is not affected, and an */
|
/* are handled normally (the sign of a NaN is not affected, and an */
|
/* sNaN will signal), the result is canonical, and zero gets sign 0. */
|
/* sNaN will signal), the result is canonical, and zero gets sign 0. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatMinus(decFloat *result, const decFloat *df,
|
decFloat * decFloatMinus(decFloat *result, const decFloat *df,
|
decContext *set) {
|
decContext *set) {
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
decCanonical(result, df); /* copy and check */
|
decCanonical(result, df); /* copy and check */
|
if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; /* turn off sign bit */
|
if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; /* turn off sign bit */
|
else DFBYTE(result, 0)^=0x80; /* flip sign bit */
|
else DFBYTE(result, 0)^=0x80; /* flip sign bit */
|
return result;
|
return result;
|
} /* decFloatMinus */
|
} /* decFloatMinus */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatMultiply -- multiply two decFloats */
|
/* decFloatMultiply -- multiply two decFloats */
|
/* */
|
/* */
|
/* result gets the result of multiplying dfl and dfr: */
|
/* result gets the result of multiplying dfl and dfr: */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatMultiply(decFloat *result,
|
decFloat * decFloatMultiply(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
bcdnum num; /* for final conversion */
|
bcdnum num; /* for final conversion */
|
uByte bcdacc[DECPMAX9*18+1]; /* for coefficent in BCD */
|
uByte bcdacc[DECPMAX9*18+1]; /* for coefficent in BCD */
|
|
|
if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { /* either is special? */
|
if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { /* either is special? */
|
/* NaNs are handled as usual */
|
/* NaNs are handled as usual */
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
/* infinity times zero is bad */
|
/* infinity times zero is bad */
|
if (DFISINF(dfl) && DFISZERO(dfr)) return decInvalid(result, set);
|
if (DFISINF(dfl) && DFISZERO(dfr)) return decInvalid(result, set);
|
if (DFISINF(dfr) && DFISZERO(dfl)) return decInvalid(result, set);
|
if (DFISINF(dfr) && DFISZERO(dfl)) return decInvalid(result, set);
|
/* both infinite; return canonical infinity with computed sign */
|
/* both infinite; return canonical infinity with computed sign */
|
DFWORD(result, 0)=DFWORD(dfl, 0)^DFWORD(dfr, 0); /* compute sign */
|
DFWORD(result, 0)=DFWORD(dfl, 0)^DFWORD(dfr, 0); /* compute sign */
|
return decInfinity(result, result);
|
return decInfinity(result, result);
|
}
|
}
|
|
|
/* Here when both operands are finite */
|
/* Here when both operands are finite */
|
decFiniteMultiply(&num, bcdacc, dfl, dfr);
|
decFiniteMultiply(&num, bcdacc, dfl, dfr);
|
return decFinalize(result, &num, set); /* round, check, and lay out */
|
return decFinalize(result, &num, set); /* round, check, and lay out */
|
} /* decFloatMultiply */
|
} /* decFloatMultiply */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatNextMinus -- next towards -Infinity */
|
/* decFloatNextMinus -- next towards -Infinity */
|
/* */
|
/* */
|
/* result gets the next lesser decFloat */
|
/* result gets the next lesser decFloat */
|
/* dfl is the decFloat to start with */
|
/* dfl is the decFloat to start with */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is 754r nextdown; Invalid is the only status possible (from */
|
/* This is 754r nextdown; Invalid is the only status possible (from */
|
/* an sNaN). */
|
/* an sNaN). */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatNextMinus(decFloat *result, const decFloat *dfl,
|
decFloat * decFloatNextMinus(decFloat *result, const decFloat *dfl,
|
decContext *set) {
|
decContext *set) {
|
decFloat delta; /* tiny increment */
|
decFloat delta; /* tiny increment */
|
uInt savestat; /* saves status */
|
uInt savestat; /* saves status */
|
enum rounding saveround; /* .. and mode */
|
enum rounding saveround; /* .. and mode */
|
|
|
/* +Infinity is the special case */
|
/* +Infinity is the special case */
|
if (DFISINF(dfl) && !DFISSIGNED(dfl)) {
|
if (DFISINF(dfl) && !DFISSIGNED(dfl)) {
|
DFSETNMAX(result);
|
DFSETNMAX(result);
|
return result; /* [no status to set] */
|
return result; /* [no status to set] */
|
}
|
}
|
/* other cases are effected by sutracting a tiny delta -- this */
|
/* other cases are effected by sutracting a tiny delta -- this */
|
/* should be done in a wider format as the delta is unrepresentable */
|
/* should be done in a wider format as the delta is unrepresentable */
|
/* here (but can be done with normal add if the sign of zero is */
|
/* here (but can be done with normal add if the sign of zero is */
|
/* treated carefully, because no Inexactitude is interesting); */
|
/* treated carefully, because no Inexactitude is interesting); */
|
/* rounding to -Infinity then pushes the result to next below */
|
/* rounding to -Infinity then pushes the result to next below */
|
decFloatZero(&delta); /* set up tiny delta */
|
decFloatZero(&delta); /* set up tiny delta */
|
DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */
|
DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */
|
DFWORD(&delta, 0)=DECFLOAT_Sign; /* Sign=1 + biased exponent=0 */
|
DFWORD(&delta, 0)=DECFLOAT_Sign; /* Sign=1 + biased exponent=0 */
|
/* set up for the directional round */
|
/* set up for the directional round */
|
saveround=set->round; /* save mode */
|
saveround=set->round; /* save mode */
|
set->round=DEC_ROUND_FLOOR; /* .. round towards -Infinity */
|
set->round=DEC_ROUND_FLOOR; /* .. round towards -Infinity */
|
savestat=set->status; /* save status */
|
savestat=set->status; /* save status */
|
decFloatAdd(result, dfl, &delta, set);
|
decFloatAdd(result, dfl, &delta, set);
|
/* Add rules mess up the sign when going from +Ntiny to 0 */
|
/* Add rules mess up the sign when going from +Ntiny to 0 */
|
if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; /* correct */
|
if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; /* correct */
|
set->status&=DEC_Invalid_operation; /* preserve only sNaN status */
|
set->status&=DEC_Invalid_operation; /* preserve only sNaN status */
|
set->status|=savestat; /* restore pending flags */
|
set->status|=savestat; /* restore pending flags */
|
set->round=saveround; /* .. and mode */
|
set->round=saveround; /* .. and mode */
|
return result;
|
return result;
|
} /* decFloatNextMinus */
|
} /* decFloatNextMinus */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatNextPlus -- next towards +Infinity */
|
/* decFloatNextPlus -- next towards +Infinity */
|
/* */
|
/* */
|
/* result gets the next larger decFloat */
|
/* result gets the next larger decFloat */
|
/* dfl is the decFloat to start with */
|
/* dfl is the decFloat to start with */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is 754r nextup; Invalid is the only status possible (from */
|
/* This is 754r nextup; Invalid is the only status possible (from */
|
/* an sNaN). */
|
/* an sNaN). */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatNextPlus(decFloat *result, const decFloat *dfl,
|
decFloat * decFloatNextPlus(decFloat *result, const decFloat *dfl,
|
decContext *set) {
|
decContext *set) {
|
uInt savestat; /* saves status */
|
uInt savestat; /* saves status */
|
enum rounding saveround; /* .. and mode */
|
enum rounding saveround; /* .. and mode */
|
decFloat delta; /* tiny increment */
|
decFloat delta; /* tiny increment */
|
|
|
/* -Infinity is the special case */
|
/* -Infinity is the special case */
|
if (DFISINF(dfl) && DFISSIGNED(dfl)) {
|
if (DFISINF(dfl) && DFISSIGNED(dfl)) {
|
DFSETNMAX(result);
|
DFSETNMAX(result);
|
DFWORD(result, 0)|=DECFLOAT_Sign; /* make negative */
|
DFWORD(result, 0)|=DECFLOAT_Sign; /* make negative */
|
return result; /* [no status to set] */
|
return result; /* [no status to set] */
|
}
|
}
|
/* other cases are effected by sutracting a tiny delta -- this */
|
/* other cases are effected by sutracting a tiny delta -- this */
|
/* should be done in a wider format as the delta is unrepresentable */
|
/* should be done in a wider format as the delta is unrepresentable */
|
/* here (but can be done with normal add if the sign of zero is */
|
/* here (but can be done with normal add if the sign of zero is */
|
/* treated carefully, because no Inexactitude is interesting); */
|
/* treated carefully, because no Inexactitude is interesting); */
|
/* rounding to +Infinity then pushes the result to next above */
|
/* rounding to +Infinity then pushes the result to next above */
|
decFloatZero(&delta); /* set up tiny delta */
|
decFloatZero(&delta); /* set up tiny delta */
|
DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */
|
DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */
|
DFWORD(&delta, 0)=0; /* Sign=0 + biased exponent=0 */
|
DFWORD(&delta, 0)=0; /* Sign=0 + biased exponent=0 */
|
/* set up for the directional round */
|
/* set up for the directional round */
|
saveround=set->round; /* save mode */
|
saveround=set->round; /* save mode */
|
set->round=DEC_ROUND_CEILING; /* .. round towards +Infinity */
|
set->round=DEC_ROUND_CEILING; /* .. round towards +Infinity */
|
savestat=set->status; /* save status */
|
savestat=set->status; /* save status */
|
decFloatAdd(result, dfl, &delta, set);
|
decFloatAdd(result, dfl, &delta, set);
|
/* Add rules mess up the sign when going from -Ntiny to -0 */
|
/* Add rules mess up the sign when going from -Ntiny to -0 */
|
if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; /* correct */
|
if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; /* correct */
|
set->status&=DEC_Invalid_operation; /* preserve only sNaN status */
|
set->status&=DEC_Invalid_operation; /* preserve only sNaN status */
|
set->status|=savestat; /* restore pending flags */
|
set->status|=savestat; /* restore pending flags */
|
set->round=saveround; /* .. and mode */
|
set->round=saveround; /* .. and mode */
|
return result;
|
return result;
|
} /* decFloatNextPlus */
|
} /* decFloatNextPlus */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatNextToward -- next towards a decFloat */
|
/* decFloatNextToward -- next towards a decFloat */
|
/* */
|
/* */
|
/* result gets the next decFloat */
|
/* result gets the next decFloat */
|
/* dfl is the decFloat to start with */
|
/* dfl is the decFloat to start with */
|
/* dfr is the decFloat to move toward */
|
/* dfr is the decFloat to move toward */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is 754r nextafter; status may be set unless the result is a */
|
/* This is 754r nextafter; status may be set unless the result is a */
|
/* normal number. */
|
/* normal number. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatNextToward(decFloat *result,
|
decFloat * decFloatNextToward(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
decFloat delta; /* tiny increment or decrement */
|
decFloat delta; /* tiny increment or decrement */
|
decFloat pointone; /* 1e-1 */
|
decFloat pointone; /* 1e-1 */
|
uInt savestat; /* saves status */
|
uInt savestat; /* saves status */
|
enum rounding saveround; /* .. and mode */
|
enum rounding saveround; /* .. and mode */
|
uInt deltatop; /* top word for delta */
|
uInt deltatop; /* top word for delta */
|
Int comp; /* work */
|
Int comp; /* work */
|
|
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
/* Both are numeric, so Invalid no longer a possibility */
|
/* Both are numeric, so Invalid no longer a possibility */
|
comp=decNumCompare(dfl, dfr, 0);
|
comp=decNumCompare(dfl, dfr, 0);
|
if (comp==0) return decFloatCopySign(result, dfl, dfr); /* equal */
|
if (comp==0) return decFloatCopySign(result, dfl, dfr); /* equal */
|
/* unequal; do NextPlus or NextMinus but with different status rules */
|
/* unequal; do NextPlus or NextMinus but with different status rules */
|
|
|
if (comp<0) { /* lhs<rhs, do NextPlus, see above for commentary */
|
if (comp<0) { /* lhs<rhs, do NextPlus, see above for commentary */
|
if (DFISINF(dfl) && DFISSIGNED(dfl)) { /* -Infinity special case */
|
if (DFISINF(dfl) && DFISSIGNED(dfl)) { /* -Infinity special case */
|
DFSETNMAX(result);
|
DFSETNMAX(result);
|
DFWORD(result, 0)|=DECFLOAT_Sign;
|
DFWORD(result, 0)|=DECFLOAT_Sign;
|
return result;
|
return result;
|
}
|
}
|
saveround=set->round; /* save mode */
|
saveround=set->round; /* save mode */
|
set->round=DEC_ROUND_CEILING; /* .. round towards +Infinity */
|
set->round=DEC_ROUND_CEILING; /* .. round towards +Infinity */
|
deltatop=0; /* positive delta */
|
deltatop=0; /* positive delta */
|
}
|
}
|
else { /* lhs>rhs, do NextMinus, see above for commentary */
|
else { /* lhs>rhs, do NextMinus, see above for commentary */
|
if (DFISINF(dfl) && !DFISSIGNED(dfl)) { /* +Infinity special case */
|
if (DFISINF(dfl) && !DFISSIGNED(dfl)) { /* +Infinity special case */
|
DFSETNMAX(result);
|
DFSETNMAX(result);
|
return result;
|
return result;
|
}
|
}
|
saveround=set->round; /* save mode */
|
saveround=set->round; /* save mode */
|
set->round=DEC_ROUND_FLOOR; /* .. round towards -Infinity */
|
set->round=DEC_ROUND_FLOOR; /* .. round towards -Infinity */
|
deltatop=DECFLOAT_Sign; /* negative delta */
|
deltatop=DECFLOAT_Sign; /* negative delta */
|
}
|
}
|
savestat=set->status; /* save status */
|
savestat=set->status; /* save status */
|
/* Here, Inexact is needed where appropriate (and hence Underflow, */
|
/* Here, Inexact is needed where appropriate (and hence Underflow, */
|
/* etc.). Therefore the tiny delta which is otherwise */
|
/* etc.). Therefore the tiny delta which is otherwise */
|
/* unrepresentable (see NextPlus and NextMinus) is constructed */
|
/* unrepresentable (see NextPlus and NextMinus) is constructed */
|
/* using the multiplication of FMA. */
|
/* using the multiplication of FMA. */
|
decFloatZero(&delta); /* set up tiny delta */
|
decFloatZero(&delta); /* set up tiny delta */
|
DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */
|
DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */
|
DFWORD(&delta, 0)=deltatop; /* Sign + biased exponent=0 */
|
DFWORD(&delta, 0)=deltatop; /* Sign + biased exponent=0 */
|
decFloatFromString(&pointone, "1E-1", set); /* set up multiplier */
|
decFloatFromString(&pointone, "1E-1", set); /* set up multiplier */
|
decFloatFMA(result, &delta, &pointone, dfl, set);
|
decFloatFMA(result, &delta, &pointone, dfl, set);
|
/* [Delta is truly tiny, so no need to correct sign of zero] */
|
/* [Delta is truly tiny, so no need to correct sign of zero] */
|
/* use new status unless the result is normal */
|
/* use new status unless the result is normal */
|
if (decFloatIsNormal(result)) set->status=savestat; /* else goes forward */
|
if (decFloatIsNormal(result)) set->status=savestat; /* else goes forward */
|
set->round=saveround; /* restore mode */
|
set->round=saveround; /* restore mode */
|
return result;
|
return result;
|
} /* decFloatNextToward */
|
} /* decFloatNextToward */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatOr -- logical digitwise OR of two decFloats */
|
/* decFloatOr -- logical digitwise OR of two decFloats */
|
/* */
|
/* */
|
/* result gets the result of ORing dfl and dfr */
|
/* result gets the result of ORing dfl and dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result, which will be canonical with sign=0 */
|
/* returns result, which will be canonical with sign=0 */
|
/* */
|
/* */
|
/* The operands must be positive, finite with exponent q=0, and */
|
/* The operands must be positive, finite with exponent q=0, and */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatOr(decFloat *result,
|
decFloat * decFloatOr(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
|
if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
|
|| !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);
|
|| !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);
|
/* the operands are positive finite integers (q=0) with just 0s and 1s */
|
/* the operands are positive finite integers (q=0) with just 0s and 1s */
|
#if DOUBLE
|
#if DOUBLE
|
DFWORD(result, 0)=ZEROWORD
|
DFWORD(result, 0)=ZEROWORD
|
|((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04009124);
|
|((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04009124);
|
DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x49124491;
|
DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x49124491;
|
#elif QUAD
|
#elif QUAD
|
DFWORD(result, 0)=ZEROWORD
|
DFWORD(result, 0)=ZEROWORD
|
|((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04000912);
|
|((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04000912);
|
DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x44912449;
|
DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x44912449;
|
DFWORD(result, 2)=(DFWORD(dfl, 2) | DFWORD(dfr, 2))&0x12449124;
|
DFWORD(result, 2)=(DFWORD(dfl, 2) | DFWORD(dfr, 2))&0x12449124;
|
DFWORD(result, 3)=(DFWORD(dfl, 3) | DFWORD(dfr, 3))&0x49124491;
|
DFWORD(result, 3)=(DFWORD(dfl, 3) | DFWORD(dfr, 3))&0x49124491;
|
#endif
|
#endif
|
return result;
|
return result;
|
} /* decFloatOr */
|
} /* decFloatOr */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatPlus -- add value to 0, heeding NaNs, etc. */
|
/* decFloatPlus -- add value to 0, heeding NaNs, etc. */
|
/* */
|
/* */
|
/* result gets the canonicalized 0+df */
|
/* result gets the canonicalized 0+df */
|
/* df is the decFloat to plus */
|
/* df is the decFloat to plus */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This has the same effect as 0+df where the exponent of the zero is */
|
/* This has the same effect as 0+df where the exponent of the zero is */
|
/* the same as that of df (if df is finite). */
|
/* the same as that of df (if df is finite). */
|
/* The effect is also the same as decFloatCopy except that NaNs */
|
/* The effect is also the same as decFloatCopy except that NaNs */
|
/* are handled normally (the sign of a NaN is not affected, and an */
|
/* are handled normally (the sign of a NaN is not affected, and an */
|
/* sNaN will signal), the result is canonical, and zero gets sign 0. */
|
/* sNaN will signal), the result is canonical, and zero gets sign 0. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatPlus(decFloat *result, const decFloat *df,
|
decFloat * decFloatPlus(decFloat *result, const decFloat *df,
|
decContext *set) {
|
decContext *set) {
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
decCanonical(result, df); /* copy and check */
|
decCanonical(result, df); /* copy and check */
|
if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; /* turn off sign bit */
|
if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; /* turn off sign bit */
|
return result;
|
return result;
|
} /* decFloatPlus */
|
} /* decFloatPlus */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatQuantize -- quantize a decFloat */
|
/* decFloatQuantize -- quantize a decFloat */
|
/* */
|
/* */
|
/* result gets the result of quantizing dfl to match dfr */
|
/* result gets the result of quantizing dfl to match dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs), which sets the exponent */
|
/* dfr is the second decFloat (rhs), which sets the exponent */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* Unless there is an error or the result is infinite, the exponent */
|
/* Unless there is an error or the result is infinite, the exponent */
|
/* of result is guaranteed to be the same as that of dfr. */
|
/* of result is guaranteed to be the same as that of dfr. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatQuantize(decFloat *result,
|
decFloat * decFloatQuantize(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int explb, exprb; /* left and right biased exponents */
|
Int explb, exprb; /* left and right biased exponents */
|
uByte *ulsd; /* local LSD pointer */
|
uByte *ulsd; /* local LSD pointer */
|
uInt *ui; /* work */
|
uInt *ui; /* work */
|
uByte *ub; /* .. */
|
uByte *ub; /* .. */
|
Int drop; /* .. */
|
Int drop; /* .. */
|
uInt dpd; /* .. */
|
uInt dpd; /* .. */
|
uInt encode; /* encoding accumulator */
|
uInt encode; /* encoding accumulator */
|
uInt sourhil, sourhir; /* top words from source decFloats */
|
uInt sourhil, sourhir; /* top words from source decFloats */
|
/* the following buffer holds the coefficient for manipulation */
|
/* the following buffer holds the coefficient for manipulation */
|
uByte buf[4+DECPMAX*3]; /* + space for zeros to left or right */
|
uByte buf[4+DECPMAX*3]; /* + space for zeros to left or right */
|
#if DECTRACE
|
#if DECTRACE
|
bcdnum num; /* for trace displays */
|
bcdnum num; /* for trace displays */
|
#endif
|
#endif
|
|
|
/* Start decoding the arguments */
|
/* Start decoding the arguments */
|
sourhil=DFWORD(dfl, 0); /* LHS top word */
|
sourhil=DFWORD(dfl, 0); /* LHS top word */
|
explb=DECCOMBEXP[sourhil>>26]; /* get exponent high bits (in place) */
|
explb=DECCOMBEXP[sourhil>>26]; /* get exponent high bits (in place) */
|
sourhir=DFWORD(dfr, 0); /* RHS top word */
|
sourhir=DFWORD(dfr, 0); /* RHS top word */
|
exprb=DECCOMBEXP[sourhir>>26];
|
exprb=DECCOMBEXP[sourhir>>26];
|
|
|
if (EXPISSPECIAL(explb | exprb)) { /* either is special? */
|
if (EXPISSPECIAL(explb | exprb)) { /* either is special? */
|
/* NaNs are handled as usual */
|
/* NaNs are handled as usual */
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
/* one infinity but not both is bad */
|
/* one infinity but not both is bad */
|
if (DFISINF(dfl)!=DFISINF(dfr)) return decInvalid(result, set);
|
if (DFISINF(dfl)!=DFISINF(dfr)) return decInvalid(result, set);
|
/* both infinite; return canonical infinity with sign of LHS */
|
/* both infinite; return canonical infinity with sign of LHS */
|
return decInfinity(result, dfl);
|
return decInfinity(result, dfl);
|
}
|
}
|
|
|
/* Here when both arguments are finite */
|
/* Here when both arguments are finite */
|
/* complete extraction of the exponents [no need to unbias] */
|
/* complete extraction of the exponents [no need to unbias] */
|
explb+=GETECON(dfl); /* + continuation */
|
explb+=GETECON(dfl); /* + continuation */
|
exprb+=GETECON(dfr); /* .. */
|
exprb+=GETECON(dfr); /* .. */
|
|
|
/* calculate the number of digits to drop from the coefficient */
|
/* calculate the number of digits to drop from the coefficient */
|
drop=exprb-explb; /* 0 if nothing to do */
|
drop=exprb-explb; /* 0 if nothing to do */
|
if (drop==0) return decCanonical(result, dfl); /* return canonical */
|
if (drop==0) return decCanonical(result, dfl); /* return canonical */
|
|
|
/* the coefficient is needed; lay it out into buf, offset so zeros */
|
/* the coefficient is needed; lay it out into buf, offset so zeros */
|
/* can be added before or after as needed -- an extra heading is */
|
/* can be added before or after as needed -- an extra heading is */
|
/* added so can safely pad Quad DECPMAX-1 zeros to the left by */
|
/* added so can safely pad Quad DECPMAX-1 zeros to the left by */
|
/* fours */
|
/* fours */
|
#define BUFOFF (buf+4+DECPMAX)
|
#define BUFOFF (buf+4+DECPMAX)
|
GETCOEFF(dfl, BUFOFF); /* decode from decFloat */
|
GETCOEFF(dfl, BUFOFF); /* decode from decFloat */
|
/* [now the msd is at BUFOFF and the lsd is at BUFOFF+DECPMAX-1] */
|
/* [now the msd is at BUFOFF and the lsd is at BUFOFF+DECPMAX-1] */
|
|
|
#if DECTRACE
|
#if DECTRACE
|
num.msd=BUFOFF;
|
num.msd=BUFOFF;
|
num.lsd=BUFOFF+DECPMAX-1;
|
num.lsd=BUFOFF+DECPMAX-1;
|
num.exponent=explb-DECBIAS;
|
num.exponent=explb-DECBIAS;
|
num.sign=sourhil & DECFLOAT_Sign;
|
num.sign=sourhil & DECFLOAT_Sign;
|
decShowNum(&num, "dfl");
|
decShowNum(&num, "dfl");
|
#endif
|
#endif
|
|
|
if (drop>0) { /* [most common case] */
|
if (drop>0) { /* [most common case] */
|
/* (this code is very similar to that in decFloatFinalize, but */
|
/* (this code is very similar to that in decFloatFinalize, but */
|
/* has many differences so is duplicated here -- so any changes */
|
/* has many differences so is duplicated here -- so any changes */
|
/* may need to be made there, too) */
|
/* may need to be made there, too) */
|
uByte *roundat; /* -> re-round digit */
|
uByte *roundat; /* -> re-round digit */
|
uByte reround; /* reround value */
|
uByte reround; /* reround value */
|
/* printf("Rounding; drop=%ld\n", (LI)drop); */
|
/* printf("Rounding; drop=%ld\n", (LI)drop); */
|
|
|
/* there is at least one zero needed to the left, in all but one */
|
/* there is at least one zero needed to the left, in all but one */
|
/* exceptional (all-nines) case, so place four zeros now; this is */
|
/* exceptional (all-nines) case, so place four zeros now; this is */
|
/* needed almost always and makes rounding all-nines by fours safe */
|
/* needed almost always and makes rounding all-nines by fours safe */
|
UINTAT(BUFOFF-4)=0;
|
UINTAT(BUFOFF-4)=0;
|
|
|
/* Three cases here: */
|
/* Three cases here: */
|
/* 1. new LSD is in coefficient (almost always) */
|
/* 1. new LSD is in coefficient (almost always) */
|
/* 2. new LSD is digit to left of coefficient (so MSD is */
|
/* 2. new LSD is digit to left of coefficient (so MSD is */
|
/* round-for-reround digit) */
|
/* round-for-reround digit) */
|
/* 3. new LSD is to left of case 2 (whole coefficient is sticky) */
|
/* 3. new LSD is to left of case 2 (whole coefficient is sticky) */
|
/* Note that leading zeros can safely be treated as useful digits */
|
/* Note that leading zeros can safely be treated as useful digits */
|
|
|
/* [duplicate check-stickies code to save a test] */
|
/* [duplicate check-stickies code to save a test] */
|
/* [by-digit check for stickies as runs of zeros are rare] */
|
/* [by-digit check for stickies as runs of zeros are rare] */
|
if (drop<DECPMAX) { /* NB lengths not addresses */
|
if (drop<DECPMAX) { /* NB lengths not addresses */
|
roundat=BUFOFF+DECPMAX-drop;
|
roundat=BUFOFF+DECPMAX-drop;
|
reround=*roundat;
|
reround=*roundat;
|
for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {
|
for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {
|
if (*ub!=0) { /* non-zero to be discarded */
|
if (*ub!=0) { /* non-zero to be discarded */
|
reround=DECSTICKYTAB[reround]; /* apply sticky bit */
|
reround=DECSTICKYTAB[reround]; /* apply sticky bit */
|
break; /* [remainder don't-care] */
|
break; /* [remainder don't-care] */
|
}
|
}
|
} /* check stickies */
|
} /* check stickies */
|
ulsd=roundat-1; /* set LSD */
|
ulsd=roundat-1; /* set LSD */
|
}
|
}
|
else { /* edge case */
|
else { /* edge case */
|
if (drop==DECPMAX) {
|
if (drop==DECPMAX) {
|
roundat=BUFOFF;
|
roundat=BUFOFF;
|
reround=*roundat;
|
reround=*roundat;
|
}
|
}
|
else {
|
else {
|
roundat=BUFOFF-1;
|
roundat=BUFOFF-1;
|
reround=0;
|
reround=0;
|
}
|
}
|
for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {
|
for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {
|
if (*ub!=0) { /* non-zero to be discarded */
|
if (*ub!=0) { /* non-zero to be discarded */
|
reround=DECSTICKYTAB[reround]; /* apply sticky bit */
|
reround=DECSTICKYTAB[reround]; /* apply sticky bit */
|
break; /* [remainder don't-care] */
|
break; /* [remainder don't-care] */
|
}
|
}
|
} /* check stickies */
|
} /* check stickies */
|
*BUFOFF=0; /* make a coefficient of 0 */
|
*BUFOFF=0; /* make a coefficient of 0 */
|
ulsd=BUFOFF; /* .. at the MSD place */
|
ulsd=BUFOFF; /* .. at the MSD place */
|
}
|
}
|
|
|
if (reround!=0) { /* discarding non-zero */
|
if (reround!=0) { /* discarding non-zero */
|
uInt bump=0;
|
uInt bump=0;
|
set->status|=DEC_Inexact;
|
set->status|=DEC_Inexact;
|
|
|
/* next decide whether to increment the coefficient */
|
/* next decide whether to increment the coefficient */
|
if (set->round==DEC_ROUND_HALF_EVEN) { /* fastpath slowest case */
|
if (set->round==DEC_ROUND_HALF_EVEN) { /* fastpath slowest case */
|
if (reround>5) bump=1; /* >0.5 goes up */
|
if (reround>5) bump=1; /* >0.5 goes up */
|
else if (reround==5) /* exactly 0.5000 .. */
|
else if (reround==5) /* exactly 0.5000 .. */
|
bump=*ulsd & 0x01; /* .. up iff [new] lsd is odd */
|
bump=*ulsd & 0x01; /* .. up iff [new] lsd is odd */
|
} /* r-h-e */
|
} /* r-h-e */
|
else switch (set->round) {
|
else switch (set->round) {
|
case DEC_ROUND_DOWN: {
|
case DEC_ROUND_DOWN: {
|
/* no change */
|
/* no change */
|
break;} /* r-d */
|
break;} /* r-d */
|
case DEC_ROUND_HALF_DOWN: {
|
case DEC_ROUND_HALF_DOWN: {
|
if (reround>5) bump=1;
|
if (reround>5) bump=1;
|
break;} /* r-h-d */
|
break;} /* r-h-d */
|
case DEC_ROUND_HALF_UP: {
|
case DEC_ROUND_HALF_UP: {
|
if (reround>=5) bump=1;
|
if (reround>=5) bump=1;
|
break;} /* r-h-u */
|
break;} /* r-h-u */
|
case DEC_ROUND_UP: {
|
case DEC_ROUND_UP: {
|
if (reround>0) bump=1;
|
if (reround>0) bump=1;
|
break;} /* r-u */
|
break;} /* r-u */
|
case DEC_ROUND_CEILING: {
|
case DEC_ROUND_CEILING: {
|
/* same as _UP for positive numbers, and as _DOWN for negatives */
|
/* same as _UP for positive numbers, and as _DOWN for negatives */
|
if (!(sourhil&DECFLOAT_Sign) && reround>0) bump=1;
|
if (!(sourhil&DECFLOAT_Sign) && reround>0) bump=1;
|
break;} /* r-c */
|
break;} /* r-c */
|
case DEC_ROUND_FLOOR: {
|
case DEC_ROUND_FLOOR: {
|
/* same as _UP for negative numbers, and as _DOWN for positive */
|
/* same as _UP for negative numbers, and as _DOWN for positive */
|
/* [negative reround cannot occur on 0] */
|
/* [negative reround cannot occur on 0] */
|
if (sourhil&DECFLOAT_Sign && reround>0) bump=1;
|
if (sourhil&DECFLOAT_Sign && reround>0) bump=1;
|
break;} /* r-f */
|
break;} /* r-f */
|
case DEC_ROUND_05UP: {
|
case DEC_ROUND_05UP: {
|
if (reround>0) { /* anything out there is 'sticky' */
|
if (reround>0) { /* anything out there is 'sticky' */
|
/* bump iff lsd=0 or 5; this cannot carry so it could be */
|
/* bump iff lsd=0 or 5; this cannot carry so it could be */
|
/* effected immediately with no bump -- but the code */
|
/* effected immediately with no bump -- but the code */
|
/* is clearer if this is done the same way as the others */
|
/* is clearer if this is done the same way as the others */
|
if (*ulsd==0 || *ulsd==5) bump=1;
|
if (*ulsd==0 || *ulsd==5) bump=1;
|
}
|
}
|
break;} /* r-r */
|
break;} /* r-r */
|
default: { /* e.g., DEC_ROUND_MAX */
|
default: { /* e.g., DEC_ROUND_MAX */
|
set->status|=DEC_Invalid_context;
|
set->status|=DEC_Invalid_context;
|
#if DECCHECK
|
#if DECCHECK
|
printf("Unknown rounding mode: %ld\n", (LI)set->round);
|
printf("Unknown rounding mode: %ld\n", (LI)set->round);
|
#endif
|
#endif
|
break;}
|
break;}
|
} /* switch (not r-h-e) */
|
} /* switch (not r-h-e) */
|
/* printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump); */
|
/* printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump); */
|
|
|
if (bump!=0) { /* need increment */
|
if (bump!=0) { /* need increment */
|
/* increment the coefficient; this could give 1000... (after */
|
/* increment the coefficient; this could give 1000... (after */
|
/* the all nines case) */
|
/* the all nines case) */
|
ub=ulsd;
|
ub=ulsd;
|
for (; UINTAT(ub-3)==0x09090909; ub-=4) UINTAT(ub-3)=0;
|
for (; UINTAT(ub-3)==0x09090909; ub-=4) UINTAT(ub-3)=0;
|
/* now at most 3 digits left to non-9 (usually just the one) */
|
/* now at most 3 digits left to non-9 (usually just the one) */
|
for (; *ub==9; ub--) *ub=0;
|
for (; *ub==9; ub--) *ub=0;
|
*ub+=1;
|
*ub+=1;
|
/* [the all-nines case will have carried one digit to the */
|
/* [the all-nines case will have carried one digit to the */
|
/* left of the original MSD -- just where it is needed] */
|
/* left of the original MSD -- just where it is needed] */
|
} /* bump needed */
|
} /* bump needed */
|
} /* inexact rounding */
|
} /* inexact rounding */
|
|
|
/* now clear zeros to the left so exactly DECPMAX digits will be */
|
/* now clear zeros to the left so exactly DECPMAX digits will be */
|
/* available in the coefficent -- the first word to the left was */
|
/* available in the coefficent -- the first word to the left was */
|
/* cleared earlier for safe carry; now add any more needed */
|
/* cleared earlier for safe carry; now add any more needed */
|
if (drop>4) {
|
if (drop>4) {
|
UINTAT(BUFOFF-8)=0; /* must be at least 5 */
|
UINTAT(BUFOFF-8)=0; /* must be at least 5 */
|
for (ui=&UINTAT(BUFOFF-12); ui>&UINTAT(ulsd-DECPMAX-3); ui--) *ui=0;
|
for (ui=&UINTAT(BUFOFF-12); ui>&UINTAT(ulsd-DECPMAX-3); ui--) *ui=0;
|
}
|
}
|
} /* need round (drop>0) */
|
} /* need round (drop>0) */
|
|
|
else { /* drop<0; padding with -drop digits is needed */
|
else { /* drop<0; padding with -drop digits is needed */
|
/* This is the case where an error can occur if the padded */
|
/* This is the case where an error can occur if the padded */
|
/* coefficient will not fit; checking for this can be done in the */
|
/* coefficient will not fit; checking for this can be done in the */
|
/* same loop as padding for zeros if the no-hope and zero cases */
|
/* same loop as padding for zeros if the no-hope and zero cases */
|
/* are checked first */
|
/* are checked first */
|
if (-drop>DECPMAX-1) { /* cannot fit unless 0 */
|
if (-drop>DECPMAX-1) { /* cannot fit unless 0 */
|
if (!ISCOEFFZERO(BUFOFF)) return decInvalid(result, set);
|
if (!ISCOEFFZERO(BUFOFF)) return decInvalid(result, set);
|
/* a zero can have any exponent; just drop through and use it */
|
/* a zero can have any exponent; just drop through and use it */
|
ulsd=BUFOFF+DECPMAX-1;
|
ulsd=BUFOFF+DECPMAX-1;
|
}
|
}
|
else { /* padding will fit (but may still be too long) */
|
else { /* padding will fit (but may still be too long) */
|
/* final-word mask depends on endianess */
|
/* final-word mask depends on endianess */
|
#if DECLITEND
|
#if DECLITEND
|
static const uInt dmask[]={0, 0x000000ff, 0x0000ffff, 0x00ffffff};
|
static const uInt dmask[]={0, 0x000000ff, 0x0000ffff, 0x00ffffff};
|
#else
|
#else
|
static const uInt dmask[]={0, 0xff000000, 0xffff0000, 0xffffff00};
|
static const uInt dmask[]={0, 0xff000000, 0xffff0000, 0xffffff00};
|
#endif
|
#endif
|
for (ui=&UINTAT(BUFOFF+DECPMAX);; ui++) {
|
for (ui=&UINTAT(BUFOFF+DECPMAX);; ui++) {
|
*ui=0;
|
*ui=0;
|
if (UINTAT(&UBYTEAT(ui)-DECPMAX)!=0) { /* could be bad */
|
if (UINTAT(&UBYTEAT(ui)-DECPMAX)!=0) { /* could be bad */
|
/* if all four digits should be zero, definitely bad */
|
/* if all four digits should be zero, definitely bad */
|
if (ui<=&UINTAT(BUFOFF+DECPMAX+(-drop)-4))
|
if (ui<=&UINTAT(BUFOFF+DECPMAX+(-drop)-4))
|
return decInvalid(result, set);
|
return decInvalid(result, set);
|
/* must be a 1- to 3-digit sequence; check more carefully */
|
/* must be a 1- to 3-digit sequence; check more carefully */
|
if ((UINTAT(&UBYTEAT(ui)-DECPMAX)&dmask[(-drop)%4])!=0)
|
if ((UINTAT(&UBYTEAT(ui)-DECPMAX)&dmask[(-drop)%4])!=0)
|
return decInvalid(result, set);
|
return decInvalid(result, set);
|
break; /* no need for loop end test */
|
break; /* no need for loop end test */
|
}
|
}
|
if (ui>=&UINTAT(BUFOFF+DECPMAX+(-drop)-4)) break; /* done */
|
if (ui>=&UINTAT(BUFOFF+DECPMAX+(-drop)-4)) break; /* done */
|
}
|
}
|
ulsd=BUFOFF+DECPMAX+(-drop)-1;
|
ulsd=BUFOFF+DECPMAX+(-drop)-1;
|
} /* pad and check leading zeros */
|
} /* pad and check leading zeros */
|
} /* drop<0 */
|
} /* drop<0 */
|
|
|
#if DECTRACE
|
#if DECTRACE
|
num.msd=ulsd-DECPMAX+1;
|
num.msd=ulsd-DECPMAX+1;
|
num.lsd=ulsd;
|
num.lsd=ulsd;
|
num.exponent=explb-DECBIAS;
|
num.exponent=explb-DECBIAS;
|
num.sign=sourhil & DECFLOAT_Sign;
|
num.sign=sourhil & DECFLOAT_Sign;
|
decShowNum(&num, "res");
|
decShowNum(&num, "res");
|
#endif
|
#endif
|
|
|
/*------------------------------------------------------------------*/
|
/*------------------------------------------------------------------*/
|
/* At this point the result is DECPMAX digits, ending at ulsd, so */
|
/* At this point the result is DECPMAX digits, ending at ulsd, so */
|
/* fits the encoding exactly; there is no possibility of error */
|
/* fits the encoding exactly; there is no possibility of error */
|
/*------------------------------------------------------------------*/
|
/*------------------------------------------------------------------*/
|
encode=((exprb>>DECECONL)<<4) + *(ulsd-DECPMAX+1); /* make index */
|
encode=((exprb>>DECECONL)<<4) + *(ulsd-DECPMAX+1); /* make index */
|
encode=DECCOMBFROM[encode]; /* indexed by (0-2)*16+msd */
|
encode=DECCOMBFROM[encode]; /* indexed by (0-2)*16+msd */
|
/* the exponent continuation can be extracted from the original RHS */
|
/* the exponent continuation can be extracted from the original RHS */
|
encode|=sourhir & ECONMASK;
|
encode|=sourhir & ECONMASK;
|
encode|=sourhil&DECFLOAT_Sign; /* add the sign from LHS */
|
encode|=sourhil&DECFLOAT_Sign; /* add the sign from LHS */
|
|
|
/* finally encode the coefficient */
|
/* finally encode the coefficient */
|
/* private macro to encode a declet; this version can be used */
|
/* private macro to encode a declet; this version can be used */
|
/* because all coefficient digits exist */
|
/* because all coefficient digits exist */
|
#define getDPD3q(dpd, n) ub=ulsd-(3*(n))-2; \
|
#define getDPD3q(dpd, n) ub=ulsd-(3*(n))-2; \
|
dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];
|
dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];
|
|
|
#if DOUBLE
|
#if DOUBLE
|
getDPD3q(dpd, 4); encode|=dpd<<8;
|
getDPD3q(dpd, 4); encode|=dpd<<8;
|
getDPD3q(dpd, 3); encode|=dpd>>2;
|
getDPD3q(dpd, 3); encode|=dpd>>2;
|
DFWORD(result, 0)=encode;
|
DFWORD(result, 0)=encode;
|
encode=dpd<<30;
|
encode=dpd<<30;
|
getDPD3q(dpd, 2); encode|=dpd<<20;
|
getDPD3q(dpd, 2); encode|=dpd<<20;
|
getDPD3q(dpd, 1); encode|=dpd<<10;
|
getDPD3q(dpd, 1); encode|=dpd<<10;
|
getDPD3q(dpd, 0); encode|=dpd;
|
getDPD3q(dpd, 0); encode|=dpd;
|
DFWORD(result, 1)=encode;
|
DFWORD(result, 1)=encode;
|
|
|
#elif QUAD
|
#elif QUAD
|
getDPD3q(dpd,10); encode|=dpd<<4;
|
getDPD3q(dpd,10); encode|=dpd<<4;
|
getDPD3q(dpd, 9); encode|=dpd>>6;
|
getDPD3q(dpd, 9); encode|=dpd>>6;
|
DFWORD(result, 0)=encode;
|
DFWORD(result, 0)=encode;
|
encode=dpd<<26;
|
encode=dpd<<26;
|
getDPD3q(dpd, 8); encode|=dpd<<16;
|
getDPD3q(dpd, 8); encode|=dpd<<16;
|
getDPD3q(dpd, 7); encode|=dpd<<6;
|
getDPD3q(dpd, 7); encode|=dpd<<6;
|
getDPD3q(dpd, 6); encode|=dpd>>4;
|
getDPD3q(dpd, 6); encode|=dpd>>4;
|
DFWORD(result, 1)=encode;
|
DFWORD(result, 1)=encode;
|
encode=dpd<<28;
|
encode=dpd<<28;
|
getDPD3q(dpd, 5); encode|=dpd<<18;
|
getDPD3q(dpd, 5); encode|=dpd<<18;
|
getDPD3q(dpd, 4); encode|=dpd<<8;
|
getDPD3q(dpd, 4); encode|=dpd<<8;
|
getDPD3q(dpd, 3); encode|=dpd>>2;
|
getDPD3q(dpd, 3); encode|=dpd>>2;
|
DFWORD(result, 2)=encode;
|
DFWORD(result, 2)=encode;
|
encode=dpd<<30;
|
encode=dpd<<30;
|
getDPD3q(dpd, 2); encode|=dpd<<20;
|
getDPD3q(dpd, 2); encode|=dpd<<20;
|
getDPD3q(dpd, 1); encode|=dpd<<10;
|
getDPD3q(dpd, 1); encode|=dpd<<10;
|
getDPD3q(dpd, 0); encode|=dpd;
|
getDPD3q(dpd, 0); encode|=dpd;
|
DFWORD(result, 3)=encode;
|
DFWORD(result, 3)=encode;
|
#endif
|
#endif
|
return result;
|
return result;
|
} /* decFloatQuantize */
|
} /* decFloatQuantize */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatReduce -- reduce finite coefficient to minimum length */
|
/* decFloatReduce -- reduce finite coefficient to minimum length */
|
/* */
|
/* */
|
/* result gets the reduced decFloat */
|
/* result gets the reduced decFloat */
|
/* df is the source decFloat */
|
/* df is the source decFloat */
|
/* set is the context */
|
/* set is the context */
|
/* returns result, which will be canonical */
|
/* returns result, which will be canonical */
|
/* */
|
/* */
|
/* This removes all possible trailing zeros from the coefficient; */
|
/* This removes all possible trailing zeros from the coefficient; */
|
/* some may remain when the number is very close to Nmax. */
|
/* some may remain when the number is very close to Nmax. */
|
/* Special values are unchanged and no status is set unless df=sNaN. */
|
/* Special values are unchanged and no status is set unless df=sNaN. */
|
/* Reduced zero has an exponent q=0. */
|
/* Reduced zero has an exponent q=0. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatReduce(decFloat *result, const decFloat *df,
|
decFloat * decFloatReduce(decFloat *result, const decFloat *df,
|
decContext *set) {
|
decContext *set) {
|
bcdnum num; /* work */
|
bcdnum num; /* work */
|
uByte buf[DECPMAX], *ub; /* coefficient and pointer */
|
uByte buf[DECPMAX], *ub; /* coefficient and pointer */
|
if (df!=result) *result=*df; /* copy, if needed */
|
if (df!=result) *result=*df; /* copy, if needed */
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set); /* sNaN */
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set); /* sNaN */
|
/* zeros and infinites propagate too */
|
/* zeros and infinites propagate too */
|
if (DFISINF(df)) return decInfinity(result, df); /* canonical */
|
if (DFISINF(df)) return decInfinity(result, df); /* canonical */
|
if (DFISZERO(df)) {
|
if (DFISZERO(df)) {
|
uInt sign=DFWORD(df, 0)&DECFLOAT_Sign;
|
uInt sign=DFWORD(df, 0)&DECFLOAT_Sign;
|
decFloatZero(result);
|
decFloatZero(result);
|
DFWORD(result, 0)|=sign;
|
DFWORD(result, 0)|=sign;
|
return result; /* exponent dropped, sign OK */
|
return result; /* exponent dropped, sign OK */
|
}
|
}
|
/* non-zero finite */
|
/* non-zero finite */
|
GETCOEFF(df, buf);
|
GETCOEFF(df, buf);
|
ub=buf+DECPMAX-1; /* -> lsd */
|
ub=buf+DECPMAX-1; /* -> lsd */
|
if (*ub) return result; /* no trailing zeros */
|
if (*ub) return result; /* no trailing zeros */
|
for (ub--; *ub==0;) ub--; /* terminates because non-zero */
|
for (ub--; *ub==0;) ub--; /* terminates because non-zero */
|
/* *ub is the first non-zero from the right */
|
/* *ub is the first non-zero from the right */
|
num.sign=DFWORD(df, 0)&DECFLOAT_Sign; /* set up number... */
|
num.sign=DFWORD(df, 0)&DECFLOAT_Sign; /* set up number... */
|
num.exponent=GETEXPUN(df)+(Int)(buf+DECPMAX-1-ub); /* adjusted exponent */
|
num.exponent=GETEXPUN(df)+(Int)(buf+DECPMAX-1-ub); /* adjusted exponent */
|
num.msd=buf;
|
num.msd=buf;
|
num.lsd=ub;
|
num.lsd=ub;
|
return decFinalize(result, &num, set);
|
return decFinalize(result, &num, set);
|
} /* decFloatReduce */
|
} /* decFloatReduce */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatRemainder -- integer divide and return remainder */
|
/* decFloatRemainder -- integer divide and return remainder */
|
/* */
|
/* */
|
/* result gets the remainder of dividing dfl by dfr: */
|
/* result gets the remainder of dividing dfl by dfr: */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatRemainder(decFloat *result,
|
decFloat * decFloatRemainder(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
return decDivide(result, dfl, dfr, set, REMAINDER);
|
return decDivide(result, dfl, dfr, set, REMAINDER);
|
} /* decFloatRemainder */
|
} /* decFloatRemainder */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatRemainderNear -- integer divide to nearest and remainder */
|
/* decFloatRemainderNear -- integer divide to nearest and remainder */
|
/* */
|
/* */
|
/* result gets the remainder of dividing dfl by dfr: */
|
/* result gets the remainder of dividing dfl by dfr: */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This is the IEEE remainder, where the nearest integer is used. */
|
/* This is the IEEE remainder, where the nearest integer is used. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatRemainderNear(decFloat *result,
|
decFloat * decFloatRemainderNear(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
return decDivide(result, dfl, dfr, set, REMNEAR);
|
return decDivide(result, dfl, dfr, set, REMNEAR);
|
} /* decFloatRemainderNear */
|
} /* decFloatRemainderNear */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatRotate -- rotate the coefficient of a decFloat left/right */
|
/* decFloatRotate -- rotate the coefficient of a decFloat left/right */
|
/* */
|
/* */
|
/* result gets the result of rotating dfl */
|
/* result gets the result of rotating dfl */
|
/* dfl is the source decFloat to rotate */
|
/* dfl is the source decFloat to rotate */
|
/* dfr is the count of digits to rotate, an integer (with q=0) */
|
/* dfr is the count of digits to rotate, an integer (with q=0) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* The digits of the coefficient of dfl are rotated to the left (if */
|
/* The digits of the coefficient of dfl are rotated to the left (if */
|
/* dfr is positive) or to the right (if dfr is negative) without */
|
/* dfr is positive) or to the right (if dfr is negative) without */
|
/* adjusting the exponent or the sign of dfl. */
|
/* adjusting the exponent or the sign of dfl. */
|
/* */
|
/* */
|
/* dfr must be in the range -DECPMAX through +DECPMAX. */
|
/* dfr must be in the range -DECPMAX through +DECPMAX. */
|
/* NaNs are propagated as usual. An infinite dfl is unaffected (but */
|
/* NaNs are propagated as usual. An infinite dfl is unaffected (but */
|
/* dfr must be valid). No status is set unless dfr is invalid or an */
|
/* dfr must be valid). No status is set unless dfr is invalid or an */
|
/* operand is an sNaN. The result is canonical. */
|
/* operand is an sNaN. The result is canonical. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
#define PHALF (ROUNDUP(DECPMAX/2, 4)) /* half length, rounded up */
|
#define PHALF (ROUNDUP(DECPMAX/2, 4)) /* half length, rounded up */
|
decFloat * decFloatRotate(decFloat *result,
|
decFloat * decFloatRotate(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int rotate; /* dfr as an Int */
|
Int rotate; /* dfr as an Int */
|
uByte buf[DECPMAX+PHALF]; /* coefficient + half */
|
uByte buf[DECPMAX+PHALF]; /* coefficient + half */
|
uInt digits, savestat; /* work */
|
uInt digits, savestat; /* work */
|
bcdnum num; /* .. */
|
bcdnum num; /* .. */
|
uByte *ub; /* .. */
|
uByte *ub; /* .. */
|
|
|
if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (!DFISINT(dfr)) return decInvalid(result, set);
|
if (!DFISINT(dfr)) return decInvalid(result, set);
|
digits=decFloatDigits(dfr); /* calculate digits */
|
digits=decFloatDigits(dfr); /* calculate digits */
|
if (digits>2) return decInvalid(result, set); /* definitely out of range */
|
if (digits>2) return decInvalid(result, set); /* definitely out of range */
|
rotate=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; /* is in bottom declet */
|
rotate=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; /* is in bottom declet */
|
if (rotate>DECPMAX) return decInvalid(result, set); /* too big */
|
if (rotate>DECPMAX) return decInvalid(result, set); /* too big */
|
/* [from here on no error or status change is possible] */
|
/* [from here on no error or status change is possible] */
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */
|
/* handle no-rotate cases */
|
/* handle no-rotate cases */
|
if (rotate==0 || rotate==DECPMAX) return decCanonical(result, dfl);
|
if (rotate==0 || rotate==DECPMAX) return decCanonical(result, dfl);
|
/* a real rotate is needed: 0 < rotate < DECPMAX */
|
/* a real rotate is needed: 0 < rotate < DECPMAX */
|
/* reduce the rotation to no more than half to reduce copying later */
|
/* reduce the rotation to no more than half to reduce copying later */
|
/* (for QUAD in fact half + 2 digits) */
|
/* (for QUAD in fact half + 2 digits) */
|
if (DFISSIGNED(dfr)) rotate=-rotate;
|
if (DFISSIGNED(dfr)) rotate=-rotate;
|
if (abs(rotate)>PHALF) {
|
if (abs(rotate)>PHALF) {
|
if (rotate<0) rotate=DECPMAX+rotate;
|
if (rotate<0) rotate=DECPMAX+rotate;
|
else rotate=rotate-DECPMAX;
|
else rotate=rotate-DECPMAX;
|
}
|
}
|
/* now lay out the coefficient, leaving room to the right or the */
|
/* now lay out the coefficient, leaving room to the right or the */
|
/* left depending on the direction of rotation */
|
/* left depending on the direction of rotation */
|
ub=buf;
|
ub=buf;
|
if (rotate<0) ub+=PHALF; /* rotate right, so space to left */
|
if (rotate<0) ub+=PHALF; /* rotate right, so space to left */
|
GETCOEFF(dfl, ub);
|
GETCOEFF(dfl, ub);
|
/* copy half the digits to left or right, and set num.msd */
|
/* copy half the digits to left or right, and set num.msd */
|
if (rotate<0) {
|
if (rotate<0) {
|
memcpy(buf, buf+DECPMAX, PHALF);
|
memcpy(buf, buf+DECPMAX, PHALF);
|
num.msd=buf+PHALF+rotate;
|
num.msd=buf+PHALF+rotate;
|
}
|
}
|
else {
|
else {
|
memcpy(buf+DECPMAX, buf, PHALF);
|
memcpy(buf+DECPMAX, buf, PHALF);
|
num.msd=buf+rotate;
|
num.msd=buf+rotate;
|
}
|
}
|
/* fill in rest of num */
|
/* fill in rest of num */
|
num.lsd=num.msd+DECPMAX-1;
|
num.lsd=num.msd+DECPMAX-1;
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
num.exponent=GETEXPUN(dfl);
|
num.exponent=GETEXPUN(dfl);
|
savestat=set->status; /* record */
|
savestat=set->status; /* record */
|
decFinalize(result, &num, set);
|
decFinalize(result, &num, set);
|
set->status=savestat; /* restore */
|
set->status=savestat; /* restore */
|
return result;
|
return result;
|
} /* decFloatRotate */
|
} /* decFloatRotate */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatSameQuantum -- test decFloats for same quantum */
|
/* decFloatSameQuantum -- test decFloats for same quantum */
|
/* */
|
/* */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* returns 1 if the operands have the same quantum, 0 otherwise */
|
/* returns 1 if the operands have the same quantum, 0 otherwise */
|
/* */
|
/* */
|
/* No error is possible and no status results. */
|
/* No error is possible and no status results. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
uInt decFloatSameQuantum(const decFloat *dfl, const decFloat *dfr) {
|
uInt decFloatSameQuantum(const decFloat *dfl, const decFloat *dfr) {
|
if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) {
|
if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) {
|
if (DFISNAN(dfl) && DFISNAN(dfr)) return 1;
|
if (DFISNAN(dfl) && DFISNAN(dfr)) return 1;
|
if (DFISINF(dfl) && DFISINF(dfr)) return 1;
|
if (DFISINF(dfl) && DFISINF(dfr)) return 1;
|
return 0; /* any other special mixture gives false */
|
return 0; /* any other special mixture gives false */
|
}
|
}
|
if (GETEXP(dfl)==GETEXP(dfr)) return 1; /* biased exponents match */
|
if (GETEXP(dfl)==GETEXP(dfr)) return 1; /* biased exponents match */
|
return 0;
|
return 0;
|
} /* decFloatSameQuantum */
|
} /* decFloatSameQuantum */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatScaleB -- multiply by a power of 10, as per 754r */
|
/* decFloatScaleB -- multiply by a power of 10, as per 754r */
|
/* */
|
/* */
|
/* result gets the result of the operation */
|
/* result gets the result of the operation */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs), am integer (with q=0) */
|
/* dfr is the second decFloat (rhs), am integer (with q=0) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* This computes result=dfl x 10**dfr where dfr is an integer in the */
|
/* This computes result=dfl x 10**dfr where dfr is an integer in the */
|
/* range +/-2*(emax+pmax), typically resulting from LogB. */
|
/* range +/-2*(emax+pmax), typically resulting from LogB. */
|
/* Underflow and Overflow (with Inexact) may occur. NaNs propagate */
|
/* Underflow and Overflow (with Inexact) may occur. NaNs propagate */
|
/* as usual. */
|
/* as usual. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
#define SCALEBMAX 2*(DECEMAX+DECPMAX) /* D=800, Q=12356 */
|
#define SCALEBMAX 2*(DECEMAX+DECPMAX) /* D=800, Q=12356 */
|
decFloat * decFloatScaleB(decFloat *result,
|
decFloat * decFloatScaleB(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
uInt digits; /* work */
|
uInt digits; /* work */
|
Int expr; /* dfr as an Int */
|
Int expr; /* dfr as an Int */
|
|
|
if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (!DFISINT(dfr)) return decInvalid(result, set);
|
if (!DFISINT(dfr)) return decInvalid(result, set);
|
digits=decFloatDigits(dfr); /* calculate digits */
|
digits=decFloatDigits(dfr); /* calculate digits */
|
|
|
#if DOUBLE
|
#if DOUBLE
|
if (digits>3) return decInvalid(result, set); /* definitely out of range */
|
if (digits>3) return decInvalid(result, set); /* definitely out of range */
|
expr=DPD2BIN[DFWORD(dfr, 1)&0x3ff]; /* must be in bottom declet */
|
expr=DPD2BIN[DFWORD(dfr, 1)&0x3ff]; /* must be in bottom declet */
|
#elif QUAD
|
#elif QUAD
|
if (digits>5) return decInvalid(result, set); /* definitely out of range */
|
if (digits>5) return decInvalid(result, set); /* definitely out of range */
|
expr=DPD2BIN[DFWORD(dfr, 3)&0x3ff] /* in bottom 2 declets .. */
|
expr=DPD2BIN[DFWORD(dfr, 3)&0x3ff] /* in bottom 2 declets .. */
|
+DPD2BIN[(DFWORD(dfr, 3)>>10)&0x3ff]*1000; /* .. */
|
+DPD2BIN[(DFWORD(dfr, 3)>>10)&0x3ff]*1000; /* .. */
|
#endif
|
#endif
|
if (expr>SCALEBMAX) return decInvalid(result, set); /* oops */
|
if (expr>SCALEBMAX) return decInvalid(result, set); /* oops */
|
/* [from now on no error possible] */
|
/* [from now on no error possible] */
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */
|
if (DFISSIGNED(dfr)) expr=-expr;
|
if (DFISSIGNED(dfr)) expr=-expr;
|
/* dfl is finite and expr is valid */
|
/* dfl is finite and expr is valid */
|
*result=*dfl; /* copy to target */
|
*result=*dfl; /* copy to target */
|
return decFloatSetExponent(result, set, GETEXPUN(result)+expr);
|
return decFloatSetExponent(result, set, GETEXPUN(result)+expr);
|
} /* decFloatScaleB */
|
} /* decFloatScaleB */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatShift -- shift the coefficient of a decFloat left or right */
|
/* decFloatShift -- shift the coefficient of a decFloat left or right */
|
/* */
|
/* */
|
/* result gets the result of shifting dfl */
|
/* result gets the result of shifting dfl */
|
/* dfl is the source decFloat to shift */
|
/* dfl is the source decFloat to shift */
|
/* dfr is the count of digits to shift, an integer (with q=0) */
|
/* dfr is the count of digits to shift, an integer (with q=0) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* The digits of the coefficient of dfl are shifted to the left (if */
|
/* The digits of the coefficient of dfl are shifted to the left (if */
|
/* dfr is positive) or to the right (if dfr is negative) without */
|
/* dfr is positive) or to the right (if dfr is negative) without */
|
/* adjusting the exponent or the sign of dfl. */
|
/* adjusting the exponent or the sign of dfl. */
|
/* */
|
/* */
|
/* dfr must be in the range -DECPMAX through +DECPMAX. */
|
/* dfr must be in the range -DECPMAX through +DECPMAX. */
|
/* NaNs are propagated as usual. An infinite dfl is unaffected (but */
|
/* NaNs are propagated as usual. An infinite dfl is unaffected (but */
|
/* dfr must be valid). No status is set unless dfr is invalid or an */
|
/* dfr must be valid). No status is set unless dfr is invalid or an */
|
/* operand is an sNaN. The result is canonical. */
|
/* operand is an sNaN. The result is canonical. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatShift(decFloat *result,
|
decFloat * decFloatShift(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
Int shift; /* dfr as an Int */
|
Int shift; /* dfr as an Int */
|
uByte buf[DECPMAX*2]; /* coefficient + padding */
|
uByte buf[DECPMAX*2]; /* coefficient + padding */
|
uInt digits, savestat; /* work */
|
uInt digits, savestat; /* work */
|
bcdnum num; /* .. */
|
bcdnum num; /* .. */
|
|
|
if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);
|
if (!DFISINT(dfr)) return decInvalid(result, set);
|
if (!DFISINT(dfr)) return decInvalid(result, set);
|
digits=decFloatDigits(dfr); /* calculate digits */
|
digits=decFloatDigits(dfr); /* calculate digits */
|
if (digits>2) return decInvalid(result, set); /* definitely out of range */
|
if (digits>2) return decInvalid(result, set); /* definitely out of range */
|
shift=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; /* is in bottom declet */
|
shift=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; /* is in bottom declet */
|
if (shift>DECPMAX) return decInvalid(result, set); /* too big */
|
if (shift>DECPMAX) return decInvalid(result, set); /* too big */
|
/* [from here on no error or status change is possible] */
|
/* [from here on no error or status change is possible] */
|
|
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */
|
if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */
|
/* handle no-shift and all-shift (clear to zero) cases */
|
/* handle no-shift and all-shift (clear to zero) cases */
|
if (shift==0) return decCanonical(result, dfl);
|
if (shift==0) return decCanonical(result, dfl);
|
if (shift==DECPMAX) { /* zero with sign */
|
if (shift==DECPMAX) { /* zero with sign */
|
uByte sign=(uByte)(DFBYTE(dfl, 0)&0x80); /* save sign bit */
|
uByte sign=(uByte)(DFBYTE(dfl, 0)&0x80); /* save sign bit */
|
decFloatZero(result); /* make +0 */
|
decFloatZero(result); /* make +0 */
|
DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); /* and set sign */
|
DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); /* and set sign */
|
/* [cannot safely use CopySign] */
|
/* [cannot safely use CopySign] */
|
return result;
|
return result;
|
}
|
}
|
/* a real shift is needed: 0 < shift < DECPMAX */
|
/* a real shift is needed: 0 < shift < DECPMAX */
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;
|
num.exponent=GETEXPUN(dfl);
|
num.exponent=GETEXPUN(dfl);
|
num.msd=buf;
|
num.msd=buf;
|
GETCOEFF(dfl, buf);
|
GETCOEFF(dfl, buf);
|
if (DFISSIGNED(dfr)) { /* shift right */
|
if (DFISSIGNED(dfr)) { /* shift right */
|
/* edge cases are taken care of, so this is easy */
|
/* edge cases are taken care of, so this is easy */
|
num.lsd=buf+DECPMAX-shift-1;
|
num.lsd=buf+DECPMAX-shift-1;
|
}
|
}
|
else { /* shift left -- zero padding needed to right */
|
else { /* shift left -- zero padding needed to right */
|
UINTAT(buf+DECPMAX)=0; /* 8 will handle most cases */
|
UINTAT(buf+DECPMAX)=0; /* 8 will handle most cases */
|
UINTAT(buf+DECPMAX+4)=0; /* .. */
|
UINTAT(buf+DECPMAX+4)=0; /* .. */
|
if (shift>8) memset(buf+DECPMAX+8, 0, 8+QUAD*18); /* all other cases */
|
if (shift>8) memset(buf+DECPMAX+8, 0, 8+QUAD*18); /* all other cases */
|
num.msd+=shift;
|
num.msd+=shift;
|
num.lsd=num.msd+DECPMAX-1;
|
num.lsd=num.msd+DECPMAX-1;
|
}
|
}
|
savestat=set->status; /* record */
|
savestat=set->status; /* record */
|
decFinalize(result, &num, set);
|
decFinalize(result, &num, set);
|
set->status=savestat; /* restore */
|
set->status=savestat; /* restore */
|
return result;
|
return result;
|
} /* decFloatShift */
|
} /* decFloatShift */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatSubtract -- subtract a decFloat from another */
|
/* decFloatSubtract -- subtract a decFloat from another */
|
/* */
|
/* */
|
/* result gets the result of subtracting dfr from dfl: */
|
/* result gets the result of subtracting dfr from dfl: */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatSubtract(decFloat *result,
|
decFloat * decFloatSubtract(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
decFloat temp;
|
decFloat temp;
|
/* NaNs must propagate without sign change */
|
/* NaNs must propagate without sign change */
|
if (DFISNAN(dfr)) return decFloatAdd(result, dfl, dfr, set);
|
if (DFISNAN(dfr)) return decFloatAdd(result, dfl, dfr, set);
|
temp=*dfr; /* make a copy */
|
temp=*dfr; /* make a copy */
|
DFBYTE(&temp, 0)^=0x80; /* flip sign */
|
DFBYTE(&temp, 0)^=0x80; /* flip sign */
|
return decFloatAdd(result, dfl, &temp, set); /* and add to the lhs */
|
return decFloatAdd(result, dfl, &temp, set); /* and add to the lhs */
|
} /* decFloatSubtract */
|
} /* decFloatSubtract */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatToInt -- round to 32-bit binary integer (4 flavours) */
|
/* decFloatToInt -- round to 32-bit binary integer (4 flavours) */
|
/* */
|
/* */
|
/* df is the decFloat to round */
|
/* df is the decFloat to round */
|
/* set is the context */
|
/* set is the context */
|
/* round is the rounding mode to use */
|
/* round is the rounding mode to use */
|
/* returns a uInt or an Int, rounded according to the name */
|
/* returns a uInt or an Int, rounded according to the name */
|
/* */
|
/* */
|
/* Invalid will always be signaled if df is a NaN, is Infinite, or is */
|
/* Invalid will always be signaled if df is a NaN, is Infinite, or is */
|
/* outside the range of the target; Inexact will not be signaled for */
|
/* outside the range of the target; Inexact will not be signaled for */
|
/* simple rounding unless 'Exact' appears in the name. */
|
/* simple rounding unless 'Exact' appears in the name. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
uInt decFloatToUInt32(const decFloat *df, decContext *set,
|
uInt decFloatToUInt32(const decFloat *df, decContext *set,
|
enum rounding round) {
|
enum rounding round) {
|
return decToInt32(df, set, round, 0, 1);}
|
return decToInt32(df, set, round, 0, 1);}
|
|
|
uInt decFloatToUInt32Exact(const decFloat *df, decContext *set,
|
uInt decFloatToUInt32Exact(const decFloat *df, decContext *set,
|
enum rounding round) {
|
enum rounding round) {
|
return decToInt32(df, set, round, 1, 1);}
|
return decToInt32(df, set, round, 1, 1);}
|
|
|
Int decFloatToInt32(const decFloat *df, decContext *set,
|
Int decFloatToInt32(const decFloat *df, decContext *set,
|
enum rounding round) {
|
enum rounding round) {
|
return (Int)decToInt32(df, set, round, 0, 0);}
|
return (Int)decToInt32(df, set, round, 0, 0);}
|
|
|
Int decFloatToInt32Exact(const decFloat *df, decContext *set,
|
Int decFloatToInt32Exact(const decFloat *df, decContext *set,
|
enum rounding round) {
|
enum rounding round) {
|
return (Int)decToInt32(df, set, round, 1, 0);}
|
return (Int)decToInt32(df, set, round, 1, 0);}
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatToIntegral -- round to integral value (two flavours) */
|
/* decFloatToIntegral -- round to integral value (two flavours) */
|
/* */
|
/* */
|
/* result gets the result */
|
/* result gets the result */
|
/* df is the decFloat to round */
|
/* df is the decFloat to round */
|
/* set is the context */
|
/* set is the context */
|
/* round is the rounding mode to use */
|
/* round is the rounding mode to use */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* No exceptions, even Inexact, are raised except for sNaN input, or */
|
/* No exceptions, even Inexact, are raised except for sNaN input, or */
|
/* if 'Exact' appears in the name. */
|
/* if 'Exact' appears in the name. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatToIntegralValue(decFloat *result, const decFloat *df,
|
decFloat * decFloatToIntegralValue(decFloat *result, const decFloat *df,
|
decContext *set, enum rounding round) {
|
decContext *set, enum rounding round) {
|
return decToIntegral(result, df, set, round, 0);}
|
return decToIntegral(result, df, set, round, 0);}
|
|
|
decFloat * decFloatToIntegralExact(decFloat *result, const decFloat *df,
|
decFloat * decFloatToIntegralExact(decFloat *result, const decFloat *df,
|
decContext *set) {
|
decContext *set) {
|
return decToIntegral(result, df, set, set->round, 1);}
|
return decToIntegral(result, df, set, set->round, 1);}
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decFloatXor -- logical digitwise XOR of two decFloats */
|
/* decFloatXor -- logical digitwise XOR of two decFloats */
|
/* */
|
/* */
|
/* result gets the result of XORing dfl and dfr */
|
/* result gets the result of XORing dfl and dfr */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* dfr is the second decFloat (rhs) */
|
/* set is the context */
|
/* set is the context */
|
/* returns result, which will be canonical with sign=0 */
|
/* returns result, which will be canonical with sign=0 */
|
/* */
|
/* */
|
/* The operands must be positive, finite with exponent q=0, and */
|
/* The operands must be positive, finite with exponent q=0, and */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* comprise just zeros and ones; if not, Invalid operation results. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
decFloat * decFloatXor(decFloat *result,
|
decFloat * decFloatXor(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
|
if (!DFISUINT01(dfl) || !DFISUINT01(dfr)
|
|| !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);
|
|| !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);
|
/* the operands are positive finite integers (q=0) with just 0s and 1s */
|
/* the operands are positive finite integers (q=0) with just 0s and 1s */
|
#if DOUBLE
|
#if DOUBLE
|
DFWORD(result, 0)=ZEROWORD
|
DFWORD(result, 0)=ZEROWORD
|
|((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04009124);
|
|((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04009124);
|
DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x49124491;
|
DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x49124491;
|
#elif QUAD
|
#elif QUAD
|
DFWORD(result, 0)=ZEROWORD
|
DFWORD(result, 0)=ZEROWORD
|
|((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04000912);
|
|((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04000912);
|
DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x44912449;
|
DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x44912449;
|
DFWORD(result, 2)=(DFWORD(dfl, 2) ^ DFWORD(dfr, 2))&0x12449124;
|
DFWORD(result, 2)=(DFWORD(dfl, 2) ^ DFWORD(dfr, 2))&0x12449124;
|
DFWORD(result, 3)=(DFWORD(dfl, 3) ^ DFWORD(dfr, 3))&0x49124491;
|
DFWORD(result, 3)=(DFWORD(dfl, 3) ^ DFWORD(dfr, 3))&0x49124491;
|
#endif
|
#endif
|
return result;
|
return result;
|
} /* decFloatXor */
|
} /* decFloatXor */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decInvalid -- set Invalid_operation result */
|
/* decInvalid -- set Invalid_operation result */
|
/* */
|
/* */
|
/* result gets a canonical NaN */
|
/* result gets a canonical NaN */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* status has Invalid_operation added */
|
/* status has Invalid_operation added */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
static decFloat *decInvalid(decFloat *result, decContext *set) {
|
static decFloat *decInvalid(decFloat *result, decContext *set) {
|
decFloatZero(result);
|
decFloatZero(result);
|
DFWORD(result, 0)=DECFLOAT_qNaN;
|
DFWORD(result, 0)=DECFLOAT_qNaN;
|
set->status|=DEC_Invalid_operation;
|
set->status|=DEC_Invalid_operation;
|
return result;
|
return result;
|
} /* decInvalid */
|
} /* decInvalid */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decInfinity -- set canonical Infinity with sign from a decFloat */
|
/* decInfinity -- set canonical Infinity with sign from a decFloat */
|
/* */
|
/* */
|
/* result gets a canonical Infinity */
|
/* result gets a canonical Infinity */
|
/* df is source decFloat (only the sign is used) */
|
/* df is source decFloat (only the sign is used) */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* df may be the same as result */
|
/* df may be the same as result */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
static decFloat *decInfinity(decFloat *result, const decFloat *df) {
|
static decFloat *decInfinity(decFloat *result, const decFloat *df) {
|
uInt sign=DFWORD(df, 0); /* save source signword */
|
uInt sign=DFWORD(df, 0); /* save source signword */
|
decFloatZero(result); /* clear everything */
|
decFloatZero(result); /* clear everything */
|
DFWORD(result, 0)=DECFLOAT_Inf | (sign & DECFLOAT_Sign);
|
DFWORD(result, 0)=DECFLOAT_Inf | (sign & DECFLOAT_Sign);
|
return result;
|
return result;
|
} /* decInfinity */
|
} /* decInfinity */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decNaNs -- handle NaN argument(s) */
|
/* decNaNs -- handle NaN argument(s) */
|
/* */
|
/* */
|
/* result gets the result of handling dfl and dfr, one or both of */
|
/* result gets the result of handling dfl and dfr, one or both of */
|
/* which is a NaN */
|
/* which is a NaN */
|
/* dfl is the first decFloat (lhs) */
|
/* dfl is the first decFloat (lhs) */
|
/* dfr is the second decFloat (rhs) -- may be NULL for a single- */
|
/* dfr is the second decFloat (rhs) -- may be NULL for a single- */
|
/* operand operation */
|
/* operand operation */
|
/* set is the context */
|
/* set is the context */
|
/* returns result */
|
/* returns result */
|
/* */
|
/* */
|
/* Called when one or both operands is a NaN, and propagates the */
|
/* Called when one or both operands is a NaN, and propagates the */
|
/* appropriate result to res. When an sNaN is found, it is changed */
|
/* appropriate result to res. When an sNaN is found, it is changed */
|
/* to a qNaN and Invalid operation is set. */
|
/* to a qNaN and Invalid operation is set. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
static decFloat *decNaNs(decFloat *result,
|
static decFloat *decNaNs(decFloat *result,
|
const decFloat *dfl, const decFloat *dfr,
|
const decFloat *dfl, const decFloat *dfr,
|
decContext *set) {
|
decContext *set) {
|
/* handle sNaNs first */
|
/* handle sNaNs first */
|
if (dfr!=NULL && DFISSNAN(dfr) && !DFISSNAN(dfl)) dfl=dfr; /* use RHS */
|
if (dfr!=NULL && DFISSNAN(dfr) && !DFISSNAN(dfl)) dfl=dfr; /* use RHS */
|
if (DFISSNAN(dfl)) {
|
if (DFISSNAN(dfl)) {
|
decCanonical(result, dfl); /* propagate canonical sNaN */
|
decCanonical(result, dfl); /* propagate canonical sNaN */
|
DFWORD(result, 0)&=~(DECFLOAT_qNaN ^ DECFLOAT_sNaN); /* quiet */
|
DFWORD(result, 0)&=~(DECFLOAT_qNaN ^ DECFLOAT_sNaN); /* quiet */
|
set->status|=DEC_Invalid_operation;
|
set->status|=DEC_Invalid_operation;
|
return result;
|
return result;
|
}
|
}
|
/* one or both is a quiet NaN */
|
/* one or both is a quiet NaN */
|
if (!DFISNAN(dfl)) dfl=dfr; /* RHS must be NaN, use it */
|
if (!DFISNAN(dfl)) dfl=dfr; /* RHS must be NaN, use it */
|
return decCanonical(result, dfl); /* propagate canonical qNaN */
|
return decCanonical(result, dfl); /* propagate canonical qNaN */
|
} /* decNaNs */
|
} /* decNaNs */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decNumCompare -- numeric comparison of two decFloats */
|
/* decNumCompare -- numeric comparison of two decFloats */
|
/* */
|
/* */
|
/* dfl is the left-hand decFloat, which is not a NaN */
|
/* dfl is the left-hand decFloat, which is not a NaN */
|
/* dfr is the right-hand decFloat, which is not a NaN */
|
/* dfr is the right-hand decFloat, which is not a NaN */
|
/* tot is 1 for total order compare, 0 for simple numeric */
|
/* tot is 1 for total order compare, 0 for simple numeric */
|
/* returns -1, 0, or +1 for dfl<dfr, dfl=dfr, dfl>dfr */
|
/* returns -1, 0, or +1 for dfl<dfr, dfl=dfr, dfl>dfr */
|
/* */
|
/* */
|
/* No error is possible; status and mode are unchanged. */
|
/* No error is possible; status and mode are unchanged. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
static Int decNumCompare(const decFloat *dfl, const decFloat *dfr, Flag tot) {
|
static Int decNumCompare(const decFloat *dfl, const decFloat *dfr, Flag tot) {
|
Int sigl, sigr; /* LHS and RHS non-0 signums */
|
Int sigl, sigr; /* LHS and RHS non-0 signums */
|
Int shift; /* shift needed to align operands */
|
Int shift; /* shift needed to align operands */
|
uByte *ub, *uc; /* work */
|
uByte *ub, *uc; /* work */
|
/* buffers +2 if Quad (36 digits), need double plus 4 for safe padding */
|
/* buffers +2 if Quad (36 digits), need double plus 4 for safe padding */
|
uByte bufl[DECPMAX*2+QUAD*2+4]; /* for LHS coefficient + padding */
|
uByte bufl[DECPMAX*2+QUAD*2+4]; /* for LHS coefficient + padding */
|
uByte bufr[DECPMAX*2+QUAD*2+4]; /* for RHS coefficient + padding */
|
uByte bufr[DECPMAX*2+QUAD*2+4]; /* for RHS coefficient + padding */
|
|
|
sigl=1;
|
sigl=1;
|
if (DFISSIGNED(dfl)) {
|
if (DFISSIGNED(dfl)) {
|
if (!DFISSIGNED(dfr)) { /* -LHS +RHS */
|
if (!DFISSIGNED(dfr)) { /* -LHS +RHS */
|
if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;
|
if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;
|
return -1; /* RHS wins */
|
return -1; /* RHS wins */
|
}
|
}
|
sigl=-1;
|
sigl=-1;
|
}
|
}
|
if (DFISSIGNED(dfr)) {
|
if (DFISSIGNED(dfr)) {
|
if (!DFISSIGNED(dfl)) { /* +LHS -RHS */
|
if (!DFISSIGNED(dfl)) { /* +LHS -RHS */
|
if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;
|
if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;
|
return +1; /* LHS wins */
|
return +1; /* LHS wins */
|
}
|
}
|
}
|
}
|
|
|
/* signs are the same; operand(s) could be zero */
|
/* signs are the same; operand(s) could be zero */
|
sigr=-sigl; /* sign to return if abs(RHS) wins */
|
sigr=-sigl; /* sign to return if abs(RHS) wins */
|
|
|
if (DFISINF(dfl)) {
|
if (DFISINF(dfl)) {
|
if (DFISINF(dfr)) return 0; /* both infinite & same sign */
|
if (DFISINF(dfr)) return 0; /* both infinite & same sign */
|
return sigl; /* inf > n */
|
return sigl; /* inf > n */
|
}
|
}
|
if (DFISINF(dfr)) return sigr; /* n < inf [dfl is finite] */
|
if (DFISINF(dfr)) return sigr; /* n < inf [dfl is finite] */
|
|
|
/* here, both are same sign and finite; calculate their offset */
|
/* here, both are same sign and finite; calculate their offset */
|
shift=GETEXP(dfl)-GETEXP(dfr); /* [0 means aligned] */
|
shift=GETEXP(dfl)-GETEXP(dfr); /* [0 means aligned] */
|
/* [bias can be ignored -- the absolute exponent is not relevant] */
|
/* [bias can be ignored -- the absolute exponent is not relevant] */
|
|
|
if (DFISZERO(dfl)) {
|
if (DFISZERO(dfl)) {
|
if (!DFISZERO(dfr)) return sigr; /* LHS=0, RHS!=0 */
|
if (!DFISZERO(dfr)) return sigr; /* LHS=0, RHS!=0 */
|
/* both are zero, return 0 if both same exponent or numeric compare */
|
/* both are zero, return 0 if both same exponent or numeric compare */
|
if (shift==0 || !tot) return 0;
|
if (shift==0 || !tot) return 0;
|
if (shift>0) return sigl;
|
if (shift>0) return sigl;
|
return sigr; /* [shift<0] */
|
return sigr; /* [shift<0] */
|
}
|
}
|
else { /* LHS!=0 */
|
else { /* LHS!=0 */
|
if (DFISZERO(dfr)) return sigl; /* LHS!=0, RHS=0 */
|
if (DFISZERO(dfr)) return sigl; /* LHS!=0, RHS=0 */
|
}
|
}
|
/* both are known to be non-zero at this point */
|
/* both are known to be non-zero at this point */
|
|
|
/* if the exponents are so different that the coefficients do not */
|
/* if the exponents are so different that the coefficients do not */
|
/* overlap (by even one digit) then a full comparison is not needed */
|
/* overlap (by even one digit) then a full comparison is not needed */
|
if (abs(shift)>=DECPMAX) { /* no overlap */
|
if (abs(shift)>=DECPMAX) { /* no overlap */
|
/* coefficients are known to be non-zero */
|
/* coefficients are known to be non-zero */
|
if (shift>0) return sigl;
|
if (shift>0) return sigl;
|
return sigr; /* [shift<0] */
|
return sigr; /* [shift<0] */
|
}
|
}
|
|
|
/* decode the coefficients */
|
/* decode the coefficients */
|
/* (shift both right two if Quad to make a multiple of four) */
|
/* (shift both right two if Quad to make a multiple of four) */
|
#if QUAD
|
#if QUAD
|
UINTAT(bufl)=0;
|
UINTAT(bufl)=0;
|
UINTAT(bufr)=0;
|
UINTAT(bufr)=0;
|
#endif
|
#endif
|
GETCOEFF(dfl, bufl+QUAD*2); /* decode from decFloat */
|
GETCOEFF(dfl, bufl+QUAD*2); /* decode from decFloat */
|
GETCOEFF(dfr, bufr+QUAD*2); /* .. */
|
GETCOEFF(dfr, bufr+QUAD*2); /* .. */
|
if (shift==0) { /* aligned; common and easy */
|
if (shift==0) { /* aligned; common and easy */
|
/* all multiples of four, here */
|
/* all multiples of four, here */
|
for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {
|
for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {
|
if (UINTAT(ub)==UINTAT(uc)) continue; /* so far so same */
|
if (UINTAT(ub)==UINTAT(uc)) continue; /* so far so same */
|
/* about to find a winner; go by bytes in case little-endian */
|
/* about to find a winner; go by bytes in case little-endian */
|
for (;; ub++, uc++) {
|
for (;; ub++, uc++) {
|
if (*ub>*uc) return sigl; /* difference found */
|
if (*ub>*uc) return sigl; /* difference found */
|
if (*ub<*uc) return sigr; /* .. */
|
if (*ub<*uc) return sigr; /* .. */
|
}
|
}
|
}
|
}
|
} /* aligned */
|
} /* aligned */
|
else if (shift>0) { /* lhs to left */
|
else if (shift>0) { /* lhs to left */
|
ub=bufl; /* RHS pointer */
|
ub=bufl; /* RHS pointer */
|
/* pad bufl so right-aligned; most shifts will fit in 8 */
|
/* pad bufl so right-aligned; most shifts will fit in 8 */
|
UINTAT(bufl+DECPMAX+QUAD*2)=0; /* add eight zeros */
|
UINTAT(bufl+DECPMAX+QUAD*2)=0; /* add eight zeros */
|
UINTAT(bufl+DECPMAX+QUAD*2+4)=0; /* .. */
|
UINTAT(bufl+DECPMAX+QUAD*2+4)=0; /* .. */
|
if (shift>8) {
|
if (shift>8) {
|
/* more than eight; fill the rest, and also worth doing the */
|
/* more than eight; fill the rest, and also worth doing the */
|
/* lead-in by fours */
|
/* lead-in by fours */
|
uByte *up; /* work */
|
uByte *up; /* work */
|
uByte *upend=bufl+DECPMAX+QUAD*2+shift;
|
uByte *upend=bufl+DECPMAX+QUAD*2+shift;
|
for (up=bufl+DECPMAX+QUAD*2+8; up<upend; up+=4) UINTAT(up)=0;
|
for (up=bufl+DECPMAX+QUAD*2+8; up<upend; up+=4) UINTAT(up)=0;
|
/* [pads up to 36 in all for Quad] */
|
/* [pads up to 36 in all for Quad] */
|
for (;; ub+=4) {
|
for (;; ub+=4) {
|
if (UINTAT(ub)!=0) return sigl;
|
if (UINTAT(ub)!=0) return sigl;
|
if (ub+4>bufl+shift-4) break;
|
if (ub+4>bufl+shift-4) break;
|
}
|
}
|
}
|
}
|
/* check remaining leading digits */
|
/* check remaining leading digits */
|
for (; ub<bufl+shift; ub++) if (*ub!=0) return sigl;
|
for (; ub<bufl+shift; ub++) if (*ub!=0) return sigl;
|
/* now start the overlapped part; bufl has been padded, so the */
|
/* now start the overlapped part; bufl has been padded, so the */
|
/* comparison can go for the full length of bufr, which is a */
|
/* comparison can go for the full length of bufr, which is a */
|
/* multiple of 4 bytes */
|
/* multiple of 4 bytes */
|
for (uc=bufr; ; uc+=4, ub+=4) {
|
for (uc=bufr; ; uc+=4, ub+=4) {
|
if (UINTAT(uc)!=UINTAT(ub)) { /* mismatch found */
|
if (UINTAT(uc)!=UINTAT(ub)) { /* mismatch found */
|
for (;; uc++, ub++) { /* check from left [little-endian?] */
|
for (;; uc++, ub++) { /* check from left [little-endian?] */
|
if (*ub>*uc) return sigl; /* difference found */
|
if (*ub>*uc) return sigl; /* difference found */
|
if (*ub<*uc) return sigr; /* .. */
|
if (*ub<*uc) return sigr; /* .. */
|
}
|
}
|
} /* mismatch */
|
} /* mismatch */
|
if (uc==bufr+QUAD*2+DECPMAX-4) break; /* all checked */
|
if (uc==bufr+QUAD*2+DECPMAX-4) break; /* all checked */
|
}
|
}
|
} /* shift>0 */
|
} /* shift>0 */
|
|
|
else { /* shift<0) .. RHS is to left of LHS; mirror shift>0 */
|
else { /* shift<0) .. RHS is to left of LHS; mirror shift>0 */
|
uc=bufr; /* RHS pointer */
|
uc=bufr; /* RHS pointer */
|
/* pad bufr so right-aligned; most shifts will fit in 8 */
|
/* pad bufr so right-aligned; most shifts will fit in 8 */
|
UINTAT(bufr+DECPMAX+QUAD*2)=0; /* add eight zeros */
|
UINTAT(bufr+DECPMAX+QUAD*2)=0; /* add eight zeros */
|
UINTAT(bufr+DECPMAX+QUAD*2+4)=0; /* .. */
|
UINTAT(bufr+DECPMAX+QUAD*2+4)=0; /* .. */
|
if (shift<-8) {
|
if (shift<-8) {
|
/* more than eight; fill the rest, and also worth doing the */
|
/* more than eight; fill the rest, and also worth doing the */
|
/* lead-in by fours */
|
/* lead-in by fours */
|
uByte *up; /* work */
|
uByte *up; /* work */
|
uByte *upend=bufr+DECPMAX+QUAD*2-shift;
|
uByte *upend=bufr+DECPMAX+QUAD*2-shift;
|
for (up=bufr+DECPMAX+QUAD*2+8; up<upend; up+=4) UINTAT(up)=0;
|
for (up=bufr+DECPMAX+QUAD*2+8; up<upend; up+=4) UINTAT(up)=0;
|
/* [pads up to 36 in all for Quad] */
|
/* [pads up to 36 in all for Quad] */
|
for (;; uc+=4) {
|
for (;; uc+=4) {
|
if (UINTAT(uc)!=0) return sigr;
|
if (UINTAT(uc)!=0) return sigr;
|
if (uc+4>bufr-shift-4) break;
|
if (uc+4>bufr-shift-4) break;
|
}
|
}
|
}
|
}
|
/* check remaining leading digits */
|
/* check remaining leading digits */
|
for (; uc<bufr-shift; uc++) if (*uc!=0) return sigr;
|
for (; uc<bufr-shift; uc++) if (*uc!=0) return sigr;
|
/* now start the overlapped part; bufr has been padded, so the */
|
/* now start the overlapped part; bufr has been padded, so the */
|
/* comparison can go for the full length of bufl, which is a */
|
/* comparison can go for the full length of bufl, which is a */
|
/* multiple of 4 bytes */
|
/* multiple of 4 bytes */
|
for (ub=bufl; ; ub+=4, uc+=4) {
|
for (ub=bufl; ; ub+=4, uc+=4) {
|
if (UINTAT(ub)!=UINTAT(uc)) { /* mismatch found */
|
if (UINTAT(ub)!=UINTAT(uc)) { /* mismatch found */
|
for (;; ub++, uc++) { /* check from left [little-endian?] */
|
for (;; ub++, uc++) { /* check from left [little-endian?] */
|
if (*ub>*uc) return sigl; /* difference found */
|
if (*ub>*uc) return sigl; /* difference found */
|
if (*ub<*uc) return sigr; /* .. */
|
if (*ub<*uc) return sigr; /* .. */
|
}
|
}
|
} /* mismatch */
|
} /* mismatch */
|
if (ub==bufl+QUAD*2+DECPMAX-4) break; /* all checked */
|
if (ub==bufl+QUAD*2+DECPMAX-4) break; /* all checked */
|
}
|
}
|
} /* shift<0 */
|
} /* shift<0 */
|
|
|
/* Here when compare equal */
|
/* Here when compare equal */
|
if (!tot) return 0; /* numerically equal */
|
if (!tot) return 0; /* numerically equal */
|
/* total ordering .. exponent matters */
|
/* total ordering .. exponent matters */
|
if (shift>0) return sigl; /* total order by exponent */
|
if (shift>0) return sigl; /* total order by exponent */
|
if (shift<0) return sigr; /* .. */
|
if (shift<0) return sigr; /* .. */
|
return 0;
|
return 0;
|
} /* decNumCompare */
|
} /* decNumCompare */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decToInt32 -- local routine to effect ToInteger conversions */
|
/* decToInt32 -- local routine to effect ToInteger conversions */
|
/* */
|
/* */
|
/* df is the decFloat to convert */
|
/* df is the decFloat to convert */
|
/* set is the context */
|
/* set is the context */
|
/* rmode is the rounding mode to use */
|
/* rmode is the rounding mode to use */
|
/* exact is 1 if Inexact should be signalled */
|
/* exact is 1 if Inexact should be signalled */
|
/* unsign is 1 if the result a uInt, 0 if an Int (cast to uInt) */
|
/* unsign is 1 if the result a uInt, 0 if an Int (cast to uInt) */
|
/* returns 32-bit result as a uInt */
|
/* returns 32-bit result as a uInt */
|
/* */
|
/* */
|
/* Invalid is set is df is a NaN, is infinite, or is out-of-range; in */
|
/* Invalid is set is df is a NaN, is infinite, or is out-of-range; in */
|
/* these cases 0 is returned. */
|
/* these cases 0 is returned. */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
static uInt decToInt32(const decFloat *df, decContext *set,
|
static uInt decToInt32(const decFloat *df, decContext *set,
|
enum rounding rmode, Flag exact, Flag unsign) {
|
enum rounding rmode, Flag exact, Flag unsign) {
|
Int exp; /* exponent */
|
Int exp; /* exponent */
|
uInt sourhi, sourpen, sourlo; /* top word from source decFloat .. */
|
uInt sourhi, sourpen, sourlo; /* top word from source decFloat .. */
|
uInt hi, lo; /* .. penultimate, least, etc. */
|
uInt hi, lo; /* .. penultimate, least, etc. */
|
decFloat zero, result; /* work */
|
decFloat zero, result; /* work */
|
Int i; /* .. */
|
Int i; /* .. */
|
|
|
/* Start decoding the argument */
|
/* Start decoding the argument */
|
sourhi=DFWORD(df, 0); /* top word */
|
sourhi=DFWORD(df, 0); /* top word */
|
exp=DECCOMBEXP[sourhi>>26]; /* get exponent high bits (in place) */
|
exp=DECCOMBEXP[sourhi>>26]; /* get exponent high bits (in place) */
|
if (EXPISSPECIAL(exp)) { /* is special? */
|
if (EXPISSPECIAL(exp)) { /* is special? */
|
set->status|=DEC_Invalid_operation; /* signal */
|
set->status|=DEC_Invalid_operation; /* signal */
|
return 0;
|
return 0;
|
}
|
}
|
|
|
/* Here when the argument is finite */
|
/* Here when the argument is finite */
|
if (GETEXPUN(df)==0) result=*df; /* already a true integer */
|
if (GETEXPUN(df)==0) result=*df; /* already a true integer */
|
else { /* need to round to integer */
|
else { /* need to round to integer */
|
enum rounding saveround; /* saver */
|
enum rounding saveround; /* saver */
|
uInt savestatus; /* .. */
|
uInt savestatus; /* .. */
|
saveround=set->round; /* save rounding mode .. */
|
saveround=set->round; /* save rounding mode .. */
|
savestatus=set->status; /* .. and status */
|
savestatus=set->status; /* .. and status */
|
set->round=rmode; /* set mode */
|
set->round=rmode; /* set mode */
|
decFloatZero(&zero); /* make 0E+0 */
|
decFloatZero(&zero); /* make 0E+0 */
|
set->status=0; /* clear */
|
set->status=0; /* clear */
|
decFloatQuantize(&result, df, &zero, set); /* [this may fail] */
|
decFloatQuantize(&result, df, &zero, set); /* [this may fail] */
|
set->round=saveround; /* restore rounding mode .. */
|
set->round=saveround; /* restore rounding mode .. */
|
if (exact) set->status|=savestatus; /* include Inexact */
|
if (exact) set->status|=savestatus; /* include Inexact */
|
else set->status=savestatus; /* .. or just original status */
|
else set->status=savestatus; /* .. or just original status */
|
}
|
}
|
|
|
/* only the last four declets of the coefficient can contain */
|
/* only the last four declets of the coefficient can contain */
|
/* non-zero; check for others (and also NaN or Infinity from the */
|
/* non-zero; check for others (and also NaN or Infinity from the */
|
/* Quantize) first (see DFISZERO for explanation): */
|
/* Quantize) first (see DFISZERO for explanation): */
|
/* decFloatShow(&result, "sofar"); */
|
/* decFloatShow(&result, "sofar"); */
|
#if DOUBLE
|
#if DOUBLE
|
if ((DFWORD(&result, 0)&0x1c03ff00)!=0
|
if ((DFWORD(&result, 0)&0x1c03ff00)!=0
|
|| (DFWORD(&result, 0)&0x60000000)==0x60000000) {
|
|| (DFWORD(&result, 0)&0x60000000)==0x60000000) {
|
#elif QUAD
|
#elif QUAD
|
if ((DFWORD(&result, 2)&0xffffff00)!=0
|
if ((DFWORD(&result, 2)&0xffffff00)!=0
|
|| DFWORD(&result, 1)!=0
|
|| DFWORD(&result, 1)!=0
|
|| (DFWORD(&result, 0)&0x1c003fff)!=0
|
|| (DFWORD(&result, 0)&0x1c003fff)!=0
|
|| (DFWORD(&result, 0)&0x60000000)==0x60000000) {
|
|| (DFWORD(&result, 0)&0x60000000)==0x60000000) {
|
#endif
|
#endif
|
set->status|=DEC_Invalid_operation; /* Invalid or out of range */
|
set->status|=DEC_Invalid_operation; /* Invalid or out of range */
|
return 0;
|
return 0;
|
}
|
}
|
/* get last twelve digits of the coefficent into hi & ho, base */
|
/* get last twelve digits of the coefficent into hi & ho, base */
|
/* 10**9 (see GETCOEFFBILL): */
|
/* 10**9 (see GETCOEFFBILL): */
|
sourlo=DFWORD(&result, DECWORDS-1);
|
sourlo=DFWORD(&result, DECWORDS-1);
|
lo=DPD2BIN0[sourlo&0x3ff]
|
lo=DPD2BIN0[sourlo&0x3ff]
|
+DPD2BINK[(sourlo>>10)&0x3ff]
|
+DPD2BINK[(sourlo>>10)&0x3ff]
|
+DPD2BINM[(sourlo>>20)&0x3ff];
|
+DPD2BINM[(sourlo>>20)&0x3ff];
|
sourpen=DFWORD(&result, DECWORDS-2);
|
sourpen=DFWORD(&result, DECWORDS-2);
|
hi=DPD2BIN0[((sourpen<<2) | (sourlo>>30))&0x3ff];
|
hi=DPD2BIN0[((sourpen<<2) | (sourlo>>30))&0x3ff];
|
|
|
/* according to request, check range carefully */
|
/* according to request, check range carefully */
|
if (unsign) {
|
if (unsign) {
|
if (hi>4 || (hi==4 && lo>294967295) || (hi+lo!=0 && DFISSIGNED(&result))) {
|
if (hi>4 || (hi==4 && lo>294967295) || (hi+lo!=0 && DFISSIGNED(&result))) {
|
set->status|=DEC_Invalid_operation; /* out of range */
|
set->status|=DEC_Invalid_operation; /* out of range */
|
return 0;
|
return 0;
|
}
|
}
|
return hi*BILLION+lo;
|
return hi*BILLION+lo;
|
}
|
}
|
/* signed */
|
/* signed */
|
if (hi>2 || (hi==2 && lo>147483647)) {
|
if (hi>2 || (hi==2 && lo>147483647)) {
|
/* handle the usual edge case */
|
/* handle the usual edge case */
|
if (lo==147483648 && hi==2 && DFISSIGNED(&result)) return 0x80000000;
|
if (lo==147483648 && hi==2 && DFISSIGNED(&result)) return 0x80000000;
|
set->status|=DEC_Invalid_operation; /* truly out of range */
|
set->status|=DEC_Invalid_operation; /* truly out of range */
|
return 0;
|
return 0;
|
}
|
}
|
i=hi*BILLION+lo;
|
i=hi*BILLION+lo;
|
if (DFISSIGNED(&result)) i=-i;
|
if (DFISSIGNED(&result)) i=-i;
|
return (uInt)i;
|
return (uInt)i;
|
} /* decToInt32 */
|
} /* decToInt32 */
|
|
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
/* decToIntegral -- local routine to effect ToIntegral value */
|
/* decToIntegral -- local routine to effect ToIntegral value */
|
/* */
|
/* */
|
/* result gets the result */
|
/* result gets the result */
|
/* df is the decFloat to round */
|
/* df is the decFloat to round */
|
/* set is the context */
|
/* set is the context */
|
/* rmode is the rounding mode to use */
|
/* rmode is the rounding mode to use */
|
/* exact is 1 if Inexact should be signalled */
|
/* exact is 1 if Inexact should be signalled */
|
/* returns result */
|
/* returns result */
|
/* ------------------------------------------------------------------ */
|
/* ------------------------------------------------------------------ */
|
static decFloat * decToIntegral(decFloat *result, const decFloat *df,
|
static decFloat * decToIntegral(decFloat *result, const decFloat *df,
|
decContext *set, enum rounding rmode,
|
decContext *set, enum rounding rmode,
|
Flag exact) {
|
Flag exact) {
|
Int exp; /* exponent */
|
Int exp; /* exponent */
|
uInt sourhi; /* top word from source decFloat */
|
uInt sourhi; /* top word from source decFloat */
|
enum rounding saveround; /* saver */
|
enum rounding saveround; /* saver */
|
uInt savestatus; /* .. */
|
uInt savestatus; /* .. */
|
decFloat zero; /* work */
|
decFloat zero; /* work */
|
|
|
/* Start decoding the argument */
|
/* Start decoding the argument */
|
sourhi=DFWORD(df, 0); /* top word */
|
sourhi=DFWORD(df, 0); /* top word */
|
exp=DECCOMBEXP[sourhi>>26]; /* get exponent high bits (in place) */
|
exp=DECCOMBEXP[sourhi>>26]; /* get exponent high bits (in place) */
|
|
|
if (EXPISSPECIAL(exp)) { /* is special? */
|
if (EXPISSPECIAL(exp)) { /* is special? */
|
/* NaNs are handled as usual */
|
/* NaNs are handled as usual */
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
if (DFISNAN(df)) return decNaNs(result, df, NULL, set);
|
/* must be infinite; return canonical infinity with sign of df */
|
/* must be infinite; return canonical infinity with sign of df */
|
return decInfinity(result, df);
|
return decInfinity(result, df);
|
}
|
}
|
|
|
/* Here when the argument is finite */
|
/* Here when the argument is finite */
|
/* complete extraction of the exponent */
|
/* complete extraction of the exponent */
|
exp+=GETECON(df)-DECBIAS; /* .. + continuation and unbias */
|
exp+=GETECON(df)-DECBIAS; /* .. + continuation and unbias */
|
|
|
if (exp>=0) return decCanonical(result, df); /* already integral */
|
if (exp>=0) return decCanonical(result, df); /* already integral */
|
|
|
saveround=set->round; /* save rounding mode .. */
|
saveround=set->round; /* save rounding mode .. */
|
savestatus=set->status; /* .. and status */
|
savestatus=set->status; /* .. and status */
|
set->round=rmode; /* set mode */
|
set->round=rmode; /* set mode */
|
decFloatZero(&zero); /* make 0E+0 */
|
decFloatZero(&zero); /* make 0E+0 */
|
decFloatQuantize(result, df, &zero, set); /* 'integrate'; cannot fail */
|
decFloatQuantize(result, df, &zero, set); /* 'integrate'; cannot fail */
|
set->round=saveround; /* restore rounding mode .. */
|
set->round=saveround; /* restore rounding mode .. */
|
if (!exact) set->status=savestatus; /* .. and status, unless exact */
|
if (!exact) set->status=savestatus; /* .. and status, unless exact */
|
return result;
|
return result;
|
} /* decToIntegral */
|
} /* decToIntegral */
|
|
|
