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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 rint 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 signals inexact if an ordered return *
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* value is not equal to the operand. *
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* *
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********************************************************************************
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* *
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* This function calls: fabs. *
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* *
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*******************************************************************************/
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/*******************************************************************************
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* First, an elegant implementation. *
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********************************************************************************
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*
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*double rint ( double x )
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* {
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* double y;
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*
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* y = twoTo52.fval;
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*
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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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* return ( y );
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* }
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********************************************************************************
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* Now a bit twidling version that is about %30 faster. *
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*******************************************************************************/
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double rint ( double x )
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{
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DblInHex argument;
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register double y;
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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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xHead = argument.words.hi & 0x7fffffffUL; // xHead <- high half of |x|
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target = ( argument.words.hi < signMask ); // flags 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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if ( target )
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y = ( x + twoTo52 ) - twoTo52; // round at binary point
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else
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y = ( x - twoTo52 ) + twoTo52; // round at binary point
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if ( y == 0.0 )
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{ // fix sign of zero result
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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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return y;
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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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if ( target )
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return ( ( x + twoTo52 ) - twoTo52 ); // round at binary pt.
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else
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return ( ( x - twoTo52 ) + twoTo52 );
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}
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/*******************************************************************************
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* |x| >= 2.0^52 or x is a NaN. *
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*******************************************************************************/
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return ( x );
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}
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