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1325 |
phoenix |
/*******************************************************************************
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** File: rndint.c
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**
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** Contains: C source code for implementations of floating-point
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** functions which round to integral value or format, as
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** defined in header <fp.h>. In particular, this file
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** contains implementations of functions rint, nearbyint,
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** rinttol, round, roundtol, trunc, modf and modfl. This file
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** targets PowerPC or Power platforms.
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**
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** Written by: A. Sazegari, Apple AltiVec Group
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** Created originally by Jon Okada, Apple Numerics Group
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**
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** Copyright: © 1992-2001 by Apple Computer, Inc., all rights reserved
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**
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** Change History (most recent first):
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**
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** 13 Jul 01 ram replaced --setflm calls with inline assembly
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** 03 Mar 01 ali first port to os x using gcc, added the crucial __setflm
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** definition.
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** 1. removed double_t, put in double for now.
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** 2. removed iclass from nearbyint.
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** 3. removed wrong comments intrunc.
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** 4.
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** 13 May 97 ali made performance improvements in rint, rinttol, roundtol
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** and trunc by folding some of the taligent ideas into this
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** implementation. nearbyint is faster than the one in taligent,
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** rint is more elegant, but slower by %30 than the taligent one.
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** 09 Apr 97 ali deleted modfl and deferred to AuxiliaryDD.c
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** 15 Sep 94 ali Major overhaul and performance improvements of all functions.
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** 20 Jul 94 PAF New faster version
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** 16 Jul 93 ali Added the modfl function.
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** 18 Feb 93 ali Changed the return value of fenv functions
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** feclearexcept and feraiseexcept to their new
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** NCEG X3J11.1/93-001 definitions.
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** 16 Dec 92 JPO Removed __itrunc implementation to a
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** separate file.
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** 15 Dec 92 JPO Added __itrunc implementation and modified
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** rinttol to include conversion from double
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** to long int format. Modified roundtol to
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** call __itrunc.
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** 10 Dec 92 JPO Added modf (double) implementation.
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** 04 Dec 92 JPO First created.
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**
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*******************************************************************************/
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#include <limits.h>
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#include <math.h>
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#define SET_INVALID 0x01000000UL
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typedef union
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{
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struct {
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#if defined(__BIG_ENDIAN__)
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unsigned long int hi;
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unsigned long int lo;
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#else
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unsigned long int lo;
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unsigned long int hi;
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#endif
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} words;
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double dbl;
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} DblInHex;
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static const unsigned long int signMask = 0x80000000ul;
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static const double twoTo52 = 4503599627370496.0;
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static const double doubleToLong = 4503603922337792.0; // 2^52
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static const DblInHex Huge = {{ 0x7FF00000, 0x00000000 }};
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static const DblInHex TOWARDZERO = {{ 0x00000000, 0x00000001 }};
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/*******************************************************************************
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* *
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* The function nearbyint rounds its double argument to integral value *
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* according to the current rounding direction and returns the result in *
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* double format. This function does not signal inexact. *
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* *
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********************************************************************************
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* *
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* This function calls fabs and copysign. *
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* *
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*******************************************************************************/
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double nearbyint ( double x )
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{
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double y;
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double OldEnvironment;
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y = twoTo52;
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asm ("mffs %0" : "=f" (OldEnvironment)); /* get the environement */
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if ( fabs ( x ) >= y ) /* huge case is exact */
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return x;
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if ( x < 0 ) y = -y; /* negative case */
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y = ( x + y ) - y; /* force rounding */
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if ( y == 0.0 ) /* zero results mirror sign of x */
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y = copysign ( y, x );
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// restore old flags
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment ));
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return ( y );
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}
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/*******************************************************************************
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* *
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* The function rinttol converts its double argument to integral value *
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* according to the current rounding direction and returns the result in *
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* long int format. This conversion signals invalid if the argument is a *
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* NaN or the rounded intermediate result is out of range of the *
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* destination long int format, and it delivers an unspecified result in *
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* this case. This function signals inexact if the rounded result is *
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* within range of the long int format but unequal to the operand. *
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* *
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*******************************************************************************/
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long int rinttol ( double x )
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{
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register double y;
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DblInHex argument, OldEnvironment;
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unsigned long int xHead;
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register long int target;
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argument.dbl = x;
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target = ( argument.words.hi < signMask ); // flag positive sign
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xHead = argument.words.hi & 0x7ffffffful; // high 32 bits of x
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if ( target )
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/*******************************************************************************
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* Sign of x is positive. *
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*******************************************************************************/
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{
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if ( xHead < 0x41dffffful )
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{ // x is safely in long range
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y = ( x + twoTo52 ) - twoTo52; // round at binary point
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argument.dbl = y + doubleToLong; // force result into argument.words.lo
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return ( ( long ) argument.words.lo );
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}
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asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
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if ( xHead > 0x41dffffful )
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{ // x is safely out of long range
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OldEnvironment.words.lo |= SET_INVALID;
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
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return ( LONG_MAX );
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}
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/*******************************************************************************
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* x > 0.0 and may or may not be out of range of long. *
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*******************************************************************************/
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y = ( x + twoTo52 ) - twoTo52; // do rounding
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if ( y > ( double ) LONG_MAX )
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{ // out of range of long
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OldEnvironment.words.lo |= SET_INVALID;
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
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return ( LONG_MAX );
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}
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argument.dbl = y + doubleToLong; // in range
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return ( ( long ) argument.words.lo ); // return result & flags
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}
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/*******************************************************************************
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* Sign of x is negative. *
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*******************************************************************************/
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if ( xHead < 0x41e00000ul )
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{ // x is safely in long range
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y = ( x - twoTo52 ) + twoTo52;
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argument.dbl = y + doubleToLong;
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return ( ( long ) argument.words.lo );
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}
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asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
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if ( xHead > 0x41e00000ul )
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{ // x is safely out of long range
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OldEnvironment.words.lo |= SET_INVALID;
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
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return ( LONG_MIN );
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}
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/*******************************************************************************
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* x < 0.0 and may or may not be out of range of long. *
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*******************************************************************************/
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y = ( x - twoTo52 ) + twoTo52; // do rounding
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if ( y < ( double ) LONG_MIN )
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{ // out of range of long
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OldEnvironment.words.lo |= SET_INVALID;
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
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return ( LONG_MIN );
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}
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argument.dbl = y + doubleToLong; // in range
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return ( ( long ) argument.words.lo ); // return result & flags
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}
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/*******************************************************************************
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* *
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* The function round rounds its double argument to integral value *
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* according to the "add half to the magnitude and truncate" rounding of *
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* Pascal's Round function and FORTRAN's ANINT function and returns the *
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* result in double format. This function signals inexact if an ordered *
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* return value is not equal to the operand. *
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* *
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*******************************************************************************/
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double round ( double x )
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{
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DblInHex argument, OldEnvironment;
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register double y, z;
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register unsigned long int xHead;
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register long int target;
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argument.dbl = x;
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xHead = argument.words.hi & 0x7fffffffUL; // xHead <- high half of |x|
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target = ( argument.words.hi < signMask ); // flag positive sign
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if ( xHead < 0x43300000ul )
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/*******************************************************************************
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* Is |x| < 2.0^52? *
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*******************************************************************************/
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{
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if ( xHead < 0x3ff00000ul )
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/*******************************************************************************
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* Is |x| < 1.0? *
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*******************************************************************************/
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{
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asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
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if ( xHead < 0x3fe00000ul )
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/*******************************************************************************
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* Is |x| < 0.5? *
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*******************************************************************************/
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{
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if ( ( xHead | argument.words.lo ) != 0ul )
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OldEnvironment.words.lo |= 0x02000000ul;
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
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if ( target )
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return ( 0.0 );
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else
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return ( -0.0 );
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}
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/*******************************************************************************
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* Is 0.5 ² |x| < 1.0? *
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*******************************************************************************/
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OldEnvironment.words.lo |= 0x02000000ul;
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
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if ( target )
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return ( 1.0 );
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else
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return ( -1.0 );
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}
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/*******************************************************************************
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* Is 1.0 < |x| < 2.0^52? *
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*******************************************************************************/
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256 |
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if ( target )
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{ // positive x
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y = ( x + twoTo52 ) - twoTo52; // round at binary point
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if ( y == x ) // exact case
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return ( x );
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z = x + 0.5; // inexact case
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y = ( z + twoTo52 ) - twoTo52; // round at binary point
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if ( y > z )
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return ( y - 1.0 );
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else
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return ( y );
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}
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/*******************************************************************************
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270 |
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* Is x < 0? *
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271 |
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*******************************************************************************/
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else
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{
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274 |
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y = ( x - twoTo52 ) + twoTo52; // round at binary point
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if ( y == x )
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return ( x );
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z = x - 0.5;
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y = ( z - twoTo52 ) + twoTo52; // round at binary point
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279 |
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if ( y < z )
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280 |
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return ( y + 1.0 );
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281 |
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else
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282 |
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return ( y );
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283 |
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}
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284 |
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}
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285 |
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/*******************************************************************************
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286 |
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* |x| >= 2.0^52 or x is a NaN. *
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287 |
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*******************************************************************************/
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288 |
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return ( x );
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289 |
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}
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290 |
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291 |
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/*******************************************************************************
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292 |
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* *
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293 |
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* The function roundtol converts its double argument to integral format *
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294 |
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* according to the "add half to the magnitude and chop" rounding mode of *
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295 |
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* Pascal's Round function and FORTRAN's NINT function. This conversion *
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296 |
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* signals invalid if the argument is a NaN or the rounded intermediate *
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297 |
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* result is out of range of the destination long int format, and it *
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298 |
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* delivers an unspecified result in this case. This function signals *
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299 |
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* inexact if the rounded result is within range of the long int format but *
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300 |
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* unequal to the operand. *
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301 |
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* *
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302 |
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*******************************************************************************/
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303 |
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304 |
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long int roundtol ( double x )
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305 |
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{
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306 |
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register double y, z;
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307 |
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DblInHex argument, OldEnvironment;
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308 |
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register unsigned long int xhi;
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309 |
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register long int target;
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310 |
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const DblInHex kTZ = {{ 0x0, 0x1 }};
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311 |
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const DblInHex kUP = {{ 0x0, 0x2 }};
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312 |
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313 |
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argument.dbl = x;
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314 |
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xhi = argument.words.hi & 0x7ffffffful; // high 32 bits of x
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315 |
|
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target = ( argument.words.hi < signMask ); // flag positive sign
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316 |
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317 |
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if ( xhi > 0x41e00000ul )
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318 |
|
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/*******************************************************************************
|
319 |
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* Is x is out of long range or NaN? *
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320 |
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*******************************************************************************/
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321 |
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{
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322 |
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asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment
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323 |
|
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OldEnvironment.words.lo |= SET_INVALID;
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324 |
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
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325 |
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if ( target ) // pin result
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326 |
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return ( LONG_MAX );
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327 |
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else
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328 |
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return ( LONG_MIN );
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329 |
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}
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330 |
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|
331 |
|
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if ( target )
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332 |
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/*******************************************************************************
|
333 |
|
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* Is sign of x is "+"? *
|
334 |
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*******************************************************************************/
|
335 |
|
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{
|
336 |
|
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if ( x < 2147483647.5 )
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337 |
|
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/*******************************************************************************
|
338 |
|
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* x is in the range of a long. *
|
339 |
|
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*******************************************************************************/
|
340 |
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{
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341 |
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y = ( x + doubleToLong ) - doubleToLong; // round at binary point
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342 |
|
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if ( y != x )
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343 |
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{ // inexact case
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344 |
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asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment
|
345 |
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kTZ.dbl )); // truncate rounding
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346 |
|
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z = x + 0.5; // truncate x + 0.5
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347 |
|
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argument.dbl = z + doubleToLong;
|
348 |
|
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asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
|
349 |
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return ( ( long ) argument.words.lo );
|
350 |
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}
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351 |
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352 |
|
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argument.dbl = y + doubleToLong; // force result into argument.words.lo
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353 |
|
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return ( ( long ) argument.words.lo ); // return long result
|
354 |
|
|
}
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355 |
|
|
/*******************************************************************************
|
356 |
|
|
* Rounded positive x is out of the range of a long. *
|
357 |
|
|
*******************************************************************************/
|
358 |
|
|
asm ("mffs %0" : "=f" (OldEnvironment.dbl));
|
359 |
|
|
OldEnvironment.words.lo |= SET_INVALID;
|
360 |
|
|
asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
|
361 |
|
|
return ( LONG_MAX ); // return pinned result
|
362 |
|
|
}
|
363 |
|
|
/*******************************************************************************
|
364 |
|
|
* x < 0.0 and may or may not be out of the range of a long. *
|
365 |
|
|
*******************************************************************************/
|
366 |
|
|
if ( x > -2147483648.5 )
|
367 |
|
|
/*******************************************************************************
|
368 |
|
|
* x is in the range of a long. *
|
369 |
|
|
*******************************************************************************/
|
370 |
|
|
{
|
371 |
|
|
y = ( x + doubleToLong ) - doubleToLong; // round at binary point
|
372 |
|
|
if ( y != x )
|
373 |
|
|
{ // inexact case
|
374 |
|
|
asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment
|
375 |
|
|
asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kUP.dbl )); // round up
|
376 |
|
|
z = x - 0.5; // truncate x - 0.5
|
377 |
|
|
argument.dbl = z + doubleToLong;
|
378 |
|
|
asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
|
379 |
|
|
return ( ( long ) argument.words.lo );
|
380 |
|
|
}
|
381 |
|
|
|
382 |
|
|
argument.dbl = y + doubleToLong;
|
383 |
|
|
return ( ( long ) argument.words.lo ); // return long result
|
384 |
|
|
}
|
385 |
|
|
/*******************************************************************************
|
386 |
|
|
* Rounded negative x is out of the range of a long. *
|
387 |
|
|
*******************************************************************************/
|
388 |
|
|
asm ("mffs %0" : "=f" (OldEnvironment.dbl));
|
389 |
|
|
OldEnvironment.words.lo |= SET_INVALID;
|
390 |
|
|
asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
|
391 |
|
|
return ( LONG_MIN ); // return pinned result
|
392 |
|
|
}
|
393 |
|
|
|
394 |
|
|
/*******************************************************************************
|
395 |
|
|
* *
|
396 |
|
|
* The function trunc truncates its double argument to integral value *
|
397 |
|
|
* and returns the result in double format. This function signals *
|
398 |
|
|
* inexact if an ordered return value is not equal to the operand. *
|
399 |
|
|
* *
|
400 |
|
|
*******************************************************************************/
|
401 |
|
|
|
402 |
|
|
double trunc ( double x )
|
403 |
|
|
{
|
404 |
|
|
DblInHex argument,OldEnvironment;
|
405 |
|
|
register double y;
|
406 |
|
|
register unsigned long int xhi;
|
407 |
|
|
register long int target;
|
408 |
|
|
|
409 |
|
|
argument.dbl = x;
|
410 |
|
|
xhi = argument.words.hi & 0x7fffffffUL; // xhi <- high half of |x|
|
411 |
|
|
target = ( argument.words.hi < signMask ); // flag positive sign
|
412 |
|
|
|
413 |
|
|
if ( xhi < 0x43300000ul )
|
414 |
|
|
/*******************************************************************************
|
415 |
|
|
* Is |x| < 2.0^53? *
|
416 |
|
|
*******************************************************************************/
|
417 |
|
|
{
|
418 |
|
|
if ( xhi < 0x3ff00000ul )
|
419 |
|
|
/*******************************************************************************
|
420 |
|
|
* Is |x| < 1.0? *
|
421 |
|
|
*******************************************************************************/
|
422 |
|
|
{
|
423 |
|
|
if ( ( xhi | argument.words.lo ) != 0ul )
|
424 |
|
|
{ // raise deserved INEXACT
|
425 |
|
|
asm ("mffs %0" : "=f" (OldEnvironment.dbl));
|
426 |
|
|
OldEnvironment.words.lo |= 0x02000000ul;
|
427 |
|
|
asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
|
428 |
|
|
}
|
429 |
|
|
if ( target ) // return properly signed zero
|
430 |
|
|
return ( 0.0 );
|
431 |
|
|
else
|
432 |
|
|
return ( -0.0 );
|
433 |
|
|
}
|
434 |
|
|
/*******************************************************************************
|
435 |
|
|
* Is 1.0 < |x| < 2.0^52? *
|
436 |
|
|
*******************************************************************************/
|
437 |
|
|
if ( target )
|
438 |
|
|
{
|
439 |
|
|
y = ( x + twoTo52 ) - twoTo52; // round at binary point
|
440 |
|
|
if ( y > x )
|
441 |
|
|
return ( y - 1.0 );
|
442 |
|
|
else
|
443 |
|
|
return ( y );
|
444 |
|
|
}
|
445 |
|
|
|
446 |
|
|
else
|
447 |
|
|
{
|
448 |
|
|
y = ( x - twoTo52 ) + twoTo52; // round at binary point.
|
449 |
|
|
if ( y < x )
|
450 |
|
|
return ( y + 1.0 );
|
451 |
|
|
else
|
452 |
|
|
return ( y );
|
453 |
|
|
}
|
454 |
|
|
}
|
455 |
|
|
/*******************************************************************************
|
456 |
|
|
* Is |x| >= 2.0^52 or x is a NaN. *
|
457 |
|
|
*******************************************************************************/
|
458 |
|
|
return ( x );
|
459 |
|
|
}
|
460 |
|
|
|
461 |
|
|
/*******************************************************************************
|
462 |
|
|
* The modf family of functions separate a floating-point number into its *
|
463 |
|
|
* fractional and integral parts, returning the fractional part and writing *
|
464 |
|
|
* the integral part in floating-point format to the object pointed to by a *
|
465 |
|
|
* pointer argument. If the input argument is integral or infinite in *
|
466 |
|
|
* value, the return value is a zero with the sign of the input argument. *
|
467 |
|
|
* The modf family of functions raises no floating-point exceptions. older *
|
468 |
|
|
* implemenation set the INVALID flag due to signaling NaN input. *
|
469 |
|
|
* *
|
470 |
|
|
*******************************************************************************/
|
471 |
|
|
|
472 |
|
|
/*******************************************************************************
|
473 |
|
|
* modf is the double implementation. *
|
474 |
|
|
*******************************************************************************/
|
475 |
|
|
|
476 |
|
|
double modf ( double x, double *iptr )
|
477 |
|
|
{
|
478 |
|
|
register double OldEnvironment, xtrunc;
|
479 |
|
|
register unsigned long int xHead, signBit;
|
480 |
|
|
DblInHex argument;
|
481 |
|
|
|
482 |
|
|
argument.dbl = x;
|
483 |
|
|
xHead = argument.words.hi & 0x7ffffffful; // |x| high bit pattern
|
484 |
|
|
signBit = ( argument.words.hi & 0x80000000ul ); // isolate sign bit
|
485 |
|
|
if (xHead == 0x7ff81fe0)
|
486 |
|
|
signBit = signBit | 0;
|
487 |
|
|
|
488 |
|
|
if ( xHead < 0x43300000ul )
|
489 |
|
|
/*******************************************************************************
|
490 |
|
|
* Is |x| < 2.0^53? *
|
491 |
|
|
*******************************************************************************/
|
492 |
|
|
{
|
493 |
|
|
if ( xHead < 0x3ff00000ul )
|
494 |
|
|
/*******************************************************************************
|
495 |
|
|
* Is |x| < 1.0? *
|
496 |
|
|
*******************************************************************************/
|
497 |
|
|
{
|
498 |
|
|
argument.words.hi = signBit; // truncate to zero
|
499 |
|
|
argument.words.lo = 0ul;
|
500 |
|
|
*iptr = argument.dbl;
|
501 |
|
|
return ( x );
|
502 |
|
|
}
|
503 |
|
|
/*******************************************************************************
|
504 |
|
|
* Is 1.0 < |x| < 2.0^52? *
|
505 |
|
|
*******************************************************************************/
|
506 |
|
|
asm ("mffs %0" : "=f" (OldEnvironment)); // save environment
|
507 |
|
|
// round toward zero
|
508 |
|
|
asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( TOWARDZERO.dbl ));
|
509 |
|
|
if ( signBit == 0ul ) // truncate to integer
|
510 |
|
|
xtrunc = ( x + twoTo52 ) - twoTo52;
|
511 |
|
|
else
|
512 |
|
|
xtrunc = ( x - twoTo52 ) + twoTo52;
|
513 |
|
|
// restore caller's env
|
514 |
|
|
asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment ));
|
515 |
|
|
*iptr = xtrunc; // store integral part
|
516 |
|
|
if ( x != xtrunc ) // nonzero fraction
|
517 |
|
|
return ( x - xtrunc );
|
518 |
|
|
else
|
519 |
|
|
{ // zero with x's sign
|
520 |
|
|
argument.words.hi = signBit;
|
521 |
|
|
argument.words.lo = 0ul;
|
522 |
|
|
return ( argument.dbl );
|
523 |
|
|
}
|
524 |
|
|
}
|
525 |
|
|
|
526 |
|
|
*iptr = x; // x is integral or NaN
|
527 |
|
|
if ( x != x ) // NaN is returned
|
528 |
|
|
return x;
|
529 |
|
|
else
|
530 |
|
|
{ // zero with x's sign
|
531 |
|
|
argument.words.hi = signBit;
|
532 |
|
|
argument.words.lo = 0ul;
|
533 |
|
|
return ( argument.dbl );
|
534 |
|
|
}
|
535 |
|
|
}
|