/* * Copyright (c) 2002 Apple Computer, Inc. All rights reserved. * * @APPLE_LICENSE_HEADER_START@ * * Copyright (c) 1999-2003 Apple Computer, Inc. All Rights Reserved. * * This file contains Original Code and/or Modifications of Original Code * as defined in and that are subject to the Apple Public Source License * Version 2.0 (the 'License'). You may not use this file except in * compliance with the License. Please obtain a copy of the License at * http://www.opensource.apple.com/apsl/ and read it before using this * file. * * The Original Code and all software distributed under the License are * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT. * Please see the License for the specific language governing rights and * limitations under the License. * * @APPLE_LICENSE_HEADER_END@ */ /******************************************************************************** * File: remmod.c * * * * Contains: C source code for implementations of some floating-point * * functions defined in header <fp.h>. In particular, this * * file contains implementations of functions fmod, remainder, * * and remquo. * * * * Copyright © 1992-2001 by Apple Computer, Inc. All rights reserved. * * * * Written by Jon Okada, started on December 7th, 1992. * * Modified by Paul Finlayson (PAF) for MathLib v2. * * Modified by A. Sazegari (ali) for MathLib v3. * * Modified and ported by Robert A. Murley (ram) for Mac OS X. * * * * A MathLib v4 file. * * * * Change History (most recent first): * * * * 08 Nov 01 ram renamed remquo to avoid conflict with CarbonCore. * * 06 Nov 01 ram commented out warning about Intel architectures. * * changed i386 stub to call abort(). * * 02 Nov 01 ram added stub for i386 version of remquo. * * 08 Oct 01 ram removed <CoreServices/CoreServices.h>. * * changed compiler errors to warnings. * * 18 Sep 01 ali added <CoreServices/CoreServices.h> to get <fp.h>. * * 17 Sep 01 ali replaced "fp.h" & "fenv.h" with <fp.h> & <fenv.h>. * * 13 Sep 01 ali replaced double_t by double. * * 10 Sep 01 ali added more comments. * * 09 Sep 01 ali added macros to detect PowerPC and correct compiler. * * 06 Sep 01 ram added #ifdef __ppc__. * * 16 Jul 01 ram Replaced __setflm with FEGETENVD/FESETENVD. * * replaced DblInHex typedef with hexdouble. * * 09 Oct 94 ali made environmental changes to use __setflm * * instead of _feprocentry. * * 05 Oct 93 PAF Fixed rounding sensitivity and flag errors. * * 14 Dec 92 JPO Fixed case where |x| = |y|. * * 11 Dec 92 JPO Fixed bug that created overflow for |x| in * * highest binade. * * 07 Dec 92 JPO First created. * * * * W A R N I N G: * * These routines require a 64-bit double precision IEEE-754 model. * * They are written for PowerPC only and are expecting the compiler * * to generate the correct sequence of multiply-add fused instructions. * * * * These routines are not intended for 32-bit Intel architectures. * * * * A version of gcc higher than 932 is required. * * * * GCC compiler options: * * optimization level 3 (-O3) * * -fschedule-insns -finline-functions -funroll-all-loops * * * ********************************************************************************/ #ifdef __APPLE_CC__ #if __APPLE_CC__ > 930 #include "math.h" #include "fp_private.h" #include "fenv_private.h" #define REM_NAN "9" static const hexdouble Huge = HEXDOUBLE(0x7ff00000, 0x00000000); static const hexdouble HugeHalved = HEXDOUBLE(0x7fe00000, 0x00000000); static const hexsingle HugeF = { 0x7f800000 }; static const hexsingle HugeFHalved = { 0x7f000000 }; #if defined(BUILDING_FOR_CARBONCORE_LEGACY) static long int ___fpclassifyd ( double arg ) { register unsigned long int exponent; hexdouble x; x.d = arg; exponent = x.i.hi & 0x7ff00000; if ( exponent == 0x7ff00000 ) { if ( ( ( x.i.hi & 0x000fffff ) | x.i.lo ) == 0 ) return (long int) FP_INFINITE; else return ( x.i.hi & dQuietNan ) ? FP_QNAN : FP_SNAN; } else if ( exponent != 0) return (long int) FP_NORMAL; else { if ( ( ( x.i.hi & 0x000fffff ) | x.i.lo ) == 0 ) return (long int) FP_ZERO; else return (long int) FP_SUBNORMAL; } } static const double twoTo52 = 4.50359962737049600e15; // 0x1p52 static const double klTod = 4503601774854144.0; // 0x1.000008p52 static const hexdouble minusInf = HEXDOUBLE(0xfff00000, 0x00000000); static double __logb ( double x ) { hexdouble xInHex; long int shiftedExp; xInHex.d = x; shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; if ( shiftedExp == 2047 ) { // NaN or INF if ( ( ( xInHex.i.hi & 0x80000000 ) == 0 ) || ( x != x ) ) return x; // NaN or +INF return x else return -x; // -INF returns +INF } if ( shiftedExp != 0 ) // normal number shiftedExp -= 1023; // unbias exponent else if ( x == 0.0 ) { // zero hexdouble OldEnvironment; FEGETENVD( OldEnvironment.d ); // raise zero divide for DOMAIN error OldEnvironment.i.lo |= FE_DIVBYZERO; FESETENVD( OldEnvironment.d ); return ( minusInf.d ); // return -infinity } else { // subnormal number xInHex.d *= twoTo52; // scale up shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; shiftedExp -= 1075; // unbias exponent } if ( shiftedExp == 0 ) // zero result return ( 0.0 ); else { // nonzero result xInHex.d = klTod; xInHex.i.lo += shiftedExp; return ( xInHex.d - klTod ); } } static const double twoTo1023 = 8.988465674311579539e307; // 0x1p1023 static const double twoToM1022 = 2.225073858507201383e-308; // 0x1p-1022 static double __scalbn ( double x, int n ) { hexdouble xInHex; xInHex.i.lo = 0UL; // init. low half of xInHex if ( n > 1023 ) { // large positive scaling if ( n > 2097 ) // huge scaling return ( ( x * twoTo1023 ) * twoTo1023 ) * twoTo1023; while ( n > 1023 ) { // scale reduction loop x *= twoTo1023; // scale x by 2^1023 n -= 1023; // reduce n by 1023 } } else if ( n < -1022 ) { // large negative scaling if ( n < -2098 ) // huge negative scaling return ( ( x * twoToM1022 ) * twoToM1022 ) * twoToM1022; while ( n < -1022 ) { // scale reduction loop x *= twoToM1022; // scale x by 2^( -1022 ) n += 1022; // incr n by 1022 } } /******************************************************************************* * -1022 <= n <= 1023; convert n to double scale factor. * *******************************************************************************/ xInHex.i.hi = ( ( unsigned long ) ( n + 1023 ) ) << 20; return ( x * xInHex.d ); } static long int ___signbitd ( double arg ) { hexdouble z; z.d = arg; return (((signed long int)z.i.hi) < 0); } /*********************************************************************** The function remquo returns the IEEE-mandated floating-point remainder of its floating-point arguments x and y: x REM y. It also calculates the low seven bits of the integral quotient and writes the signed low quotient result to the location pointed to by the int pointer argument, quo: -127 <= iquo <= +127. This function calls: __fpclassifyd, logb, scalbn, __FABS, signbitd. ***********************************************************************/ double remquo ( double x, double y, int *quo) { long int iclx,icly; /* classify results of x,y */ long int iquo; /* low 32 bits of integral quotient */ long int iscx, iscy, idiff; /* logb values and difference */ long int i; /* loop variable */ double absy,x1,y1,z; /* local floating-point variables */ double rslt; fenv_t OldEnv; hexdouble OldEnvironment; int newexc; FEGETENVD ( OldEnvironment.d ); FESETENVD ( 0.0 ); OldEnv = OldEnvironment.i.lo; *quo = 0; /* initialize quotient result */ iclx = ___fpclassifyd(x); icly = ___fpclassifyd(y); if ((iclx & icly) >= FP_NORMAL) { /* x,y both nonzero finite case */ x1 = __FABS(x); /* work with absolute values */ absy = __FABS(y); iquo = 0; /* zero local quotient */ iscx = (long int) __logb(x1); /* get binary exponents */ iscy = (long int) __logb(absy); idiff = iscx - iscy; /* exponent difference */ if (idiff >= 0) { /* exponent of x1 >= exponent of y1 */ if (idiff != 0) { /* exponent of x1 > exponent of y1 */ y1 = __scalbn(absy,-iscy); /* scale |y| to unit binade */ x1 = __scalbn(x1,-iscx); /* ditto for |x| */ for (i = idiff; i != 0; i--) { /* begin remainder loop */ if ((z = x1 - y1) >= 0) { /* nonzero remainder step result */ x1 = z; /* update remainder (x1) */ iquo += 1; /* increment quotient */ } iquo += iquo; /* shift quotient left one bit */ x1 += x1; /* shift (double) remainder */ } /* end of remainder loop */ x1 = __scalbn(x1,iscy); /* scale remainder to binade of |y| */ } /* remainder has exponent <= exponent of y */ if (x1 >= absy) { /* last remainder step */ x1 -= absy; iquo +=1; } /* end of last remainder step */ } /* remainder (x1) has smaller exponent than y */ if ( x1 < HugeHalved.d ) z = x1 + x1; /* double remainder, without overflow */ else z = Huge.d; if ((z > absy) || ((z == absy) && ((iquo & 1) != 0))) { x1 -= absy; /* final remainder correction */ iquo += 1; } if (x < 0.0) x1 = -x1; /* remainder if x is negative */ iquo &= 0x0000007f; /* retain low 7 bits of integer quotient */ if ((___signbitd(x) ^ ___signbitd(y)) != 0) /* take care of sign of quotient */ iquo = -iquo; *quo = iquo; /* deliver quotient result */ rslt = x1; goto ret; } /* end of x,y both nonzero finite case */ else if ((iclx <= FP_QNAN) || (icly <= FP_QNAN)) { rslt = x+y; /* at least one NaN operand */ goto ret; } else if ((iclx == FP_INFINITE)||(icly == FP_ZERO)) { /* invalid result */ rslt = nan(REM_NAN); OldEnvironment.i.lo |= SET_INVALID; FESETENVD( OldEnvironment.d ); goto ret; } else /* trivial cases (finite REM infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD( OldEnvironment.d ); newexc = OldEnvironment.i.lo & FE_ALL_EXCEPT; OldEnvironment.i.lo = OldEnv; if ((newexc & FE_INVALID) != 0) OldEnvironment.i.lo |= SET_INVALID; OldEnvironment.i.lo |= newexc & ( FE_INEXACT | FE_DIVBYZERO | FE_UNDERFLOW | FE_OVERFLOW ); FESETENVD( OldEnvironment.d ); return rslt; } #else /* !BUILDING_FOR_CARBONCORE_LEGACY */ float remquof ( float x, float y, int *quo) { long int iclx,icly; /* classify results of x,y */ long int iquo; /* low 32 bits of integral quotient */ long int iscx, iscy, idiff; /* logb values and difference */ long int i; /* loop variable */ float absy,x1,y1,z; /* local floating-point variables */ float rslt; fenv_t OldEnv; hexdouble OldEnvironment; int newexc; FEGETENVD ( OldEnvironment.d ); FESETENVD ( 0.0 ); OldEnv = OldEnvironment.i.lo; *quo = 0; /* initialize quotient result */ iclx = __fpclassifyf(x); icly = __fpclassifyf(y); if ((iclx & icly) >= FP_NORMAL) { /* x,y both nonzero finite case */ x1 = __FABSF(x); /* work with absolute values */ absy = __FABSF(y); iquo = 0; /* zero local quotient */ iscx = (long int) logbf(x1); /* get binary exponents */ iscy = (long int) logbf(absy); idiff = iscx - iscy; /* exponent difference */ if (idiff >= 0) { /* exponent of x1 >= exponent of y1 */ if (idiff != 0) { /* exponent of x1 > exponent of y1 */ y1 = scalbnf(absy,-iscy); /* scale |y| to unit binade */ x1 = scalbnf(x1,-iscx); /* ditto for |x| */ for (i = idiff; i != 0; i--) { /* begin remainder loop */ if ((z = x1 - y1) >= 0) { /* nonzero remainder step result */ x1 = z; /* update remainder (x1) */ iquo += 1; /* increment quotient */ } iquo += iquo; /* shift quotient left one bit */ x1 += x1; /* shift (double) remainder */ } /* end of remainder loop */ x1 = scalbnf(x1,iscy); /* scale remainder to binade of |y| */ } /* remainder has exponent <= exponent of y */ if (x1 >= absy) { /* last remainder step */ x1 -= absy; iquo +=1; } /* end of last remainder step */ } /* remainder (x1) has smaller exponent than y */ if ( x1 < HugeFHalved.fval ) z = x1 + x1; /* double remainder, without overflow */ else z = HugeF.fval; if ((z > absy) || ((z == absy) && ((iquo & 1) != 0))) { x1 -= absy; /* final remainder correction */ iquo += 1; } if (x < 0.0) x1 = -x1; /* remainder if x is negative */ iquo &= 0x0000007f; /* retain low 7 bits of integer quotient */ if ((__signbitf(x) ^ __signbitf(y)) != 0) /* take care of sign of quotient */ iquo = -iquo; *quo = iquo; /* deliver quotient result */ rslt = x1; goto ret; } /* end of x,y both nonzero finite case */ else if ((iclx <= FP_QNAN) || (icly <= FP_QNAN)) { rslt = x+y; /* at least one NaN operand */ goto ret; } else if ((iclx == FP_INFINITE)||(icly == FP_ZERO)) { /* invalid result */ rslt = nanf(REM_NAN); OldEnvironment.i.lo |= SET_INVALID; FESETENVD( OldEnvironment.d ); goto ret; } else /* trivial cases (finite REM infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD( OldEnvironment.d ); newexc = OldEnvironment.i.lo & FE_ALL_EXCEPT; OldEnvironment.i.lo = OldEnv; if ((newexc & FE_INVALID) != 0) OldEnvironment.i.lo |= SET_INVALID; OldEnvironment.i.lo |= newexc & ( FE_INEXACT | FE_DIVBYZERO | FE_UNDERFLOW | FE_OVERFLOW ); FESETENVD( OldEnvironment.d ); return rslt; } /*********************************************************************** The function remainder returns the IEEE-mandated floating-point remainder of its floating-point arguments x and y: x REM y. It returns the same result as remquo, but it discards the integral quotient. This function calls: remquo. ***********************************************************************/ double remainder ( double x, double y ) { int quo; return ( remquo( x, y, &quo )); } float remainderf ( float x, float y ) { int quo; return ( remquof( x, y, &quo )); } /*********************************************************************** The function fmod returns the floating-point modulus of its floating- point arguments x and y: x MOD y, such that the return value has the same sign as x. This function calls: --fpclassify, logb, scalbn, --fabs. ***********************************************************************/ double fmod ( double x, double y ) { long int iclx,icly; /* classify results of x,y */ long int iscx,iscy,idiff; /* logb values and difference */ long int i; /* loop variable */ double absy,x1,y1,z; /* local floating-point variables */ double rslt; fenv_t OldEnv; hexdouble OldEnvironment; int newexc; FEGETENVD( OldEnvironment.d ); FESETENVD( 0.0 ); OldEnv = OldEnvironment.i.lo; iclx = __fpclassifyd(x); icly = __fpclassifyd(y); if ((iclx & icly) >= FP_NORMAL) { /* x,y both nonzero finite case */ x1 = __FABS(x); /* work with absolute values */ absy = __FABS(y); if (absy > x1) { rslt = x; /* trivial case */ goto ret; } else { /* nontrivial case requires reduction */ iscx = (long int) logb(x1); /* get binary exponents of |x| and |y| */ iscy = (long int) logb(absy); idiff = iscx - iscy; /* exponent difference */ if (idiff != 0) { /* exponent of x1 > exponent of y1 */ y1 = scalbn(absy,-iscy); /* scale |y| to unit binade */ x1 = scalbn(x1,-iscx); /* ditto for |x| */ for (i = idiff; i != 0; i--) { /* begin remainder loop */ if ((z = x1 - y1) >= 0) { /* nonzero remainder step result */ x1 = z; /* update remainder (x1) */ } x1 += x1; /* shift (by doubling) remainder */ } /* end of remainder loop */ x1 = scalbn(x1,iscy); /* scale result to binade of |y| */ } /* remainder exponent >= exponent of y */ if (x1 >= absy) { /* last step to obtain modulus */ x1 -= absy; } } /* x1 is |result| */ if (x < 0.0) x1 = -x1; /* modulus if x is negative */ rslt = x1; goto ret; } /* end of x,y both nonzero finite case */ else if ((iclx <= FP_QNAN) || (icly <= FP_QNAN)) { rslt = x+y; /* at least one NaN operand */ goto ret; } else if ((iclx == FP_INFINITE)||(icly == FP_ZERO)) { /* invalid result */ rslt = nan(REM_NAN); OldEnvironment.i.lo |= SET_INVALID; FESETENVD ( OldEnvironment.d ); goto ret; } else /* trivial cases (finite MOD infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD (OldEnvironment.d ); newexc = OldEnvironment.i.lo & FE_ALL_EXCEPT; OldEnvironment.i.lo = OldEnv; if ((newexc & FE_INVALID) != 0) OldEnvironment.i.lo |= SET_INVALID; OldEnvironment.i.lo |= newexc & ( FE_INEXACT | FE_DIVBYZERO | FE_UNDERFLOW | FE_OVERFLOW ); FESETENVD (OldEnvironment.d ); return rslt; } float fmodf ( float x, float y ) { long int iclx,icly; /* classify results of x,y */ long int iscx,iscy,idiff; /* logb values and difference */ long int i; /* loop variable */ float absy,x1,y1,z; /* local floating-point variables */ float rslt; fenv_t OldEnv; hexdouble OldEnvironment; int newexc; FEGETENVD( OldEnvironment.d ); FESETENVD( 0.0 ); OldEnv = OldEnvironment.i.lo; iclx = __fpclassifyf(x); icly = __fpclassifyf(y); if ((iclx & icly) >= FP_NORMAL) { /* x,y both nonzero finite case */ x1 = __FABSF(x); /* work with absolute values */ absy = __FABSF(y); if (absy > x1) { rslt = x; /* trivial case */ goto ret; } else { /* nontrivial case requires reduction */ iscx = (long int) logbf(x1); /* get binary exponents of |x| and |y| */ iscy = (long int) logbf(absy); idiff = iscx - iscy; /* exponent difference */ if (idiff != 0) { /* exponent of x1 > exponent of y1 */ y1 = scalbnf(absy,-iscy); /* scale |y| to unit binade */ x1 = scalbnf(x1,-iscx); /* ditto for |x| */ for (i = idiff; i != 0; i--) { /* begin remainder loop */ if ((z = x1 - y1) >= 0) { /* nonzero remainder step result */ x1 = z; /* update remainder (x1) */ } x1 += x1; /* shift (by doubling) remainder */ } /* end of remainder loop */ x1 = scalbnf(x1,iscy); /* scale result to binade of |y| */ } /* remainder exponent >= exponent of y */ if (x1 >= absy) { /* last step to obtain modulus */ x1 -= absy; } } /* x1 is |result| */ if (x < 0.0) x1 = -x1; /* modulus if x is negative */ rslt = x1; goto ret; } /* end of x,y both nonzero finite case */ else if ((iclx <= FP_QNAN) || (icly <= FP_QNAN)) { rslt = x+y; /* at least one NaN operand */ goto ret; } else if ((iclx == FP_INFINITE)||(icly == FP_ZERO)) { /* invalid result */ rslt = nanf(REM_NAN); OldEnvironment.i.lo |= SET_INVALID; FESETENVD ( OldEnvironment.d ); goto ret; } else /* trivial cases (finite MOD infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD (OldEnvironment.d ); newexc = OldEnvironment.i.lo & FE_ALL_EXCEPT; OldEnvironment.i.lo = OldEnv; if ((newexc & FE_INVALID) != 0) OldEnvironment.i.lo |= SET_INVALID; OldEnvironment.i.lo |= newexc & ( FE_INEXACT | FE_DIVBYZERO | FE_UNDERFLOW | FE_OVERFLOW ); FESETENVD (OldEnvironment.d ); return rslt; } #endif /* !BUILDING_FOR_CARBONCORE_LEGACY */ #else /* __APPLE_CC__ version */ #warning A higher version than gcc-932 is required. #endif /* __APPLE_CC__ version */ #endif /* __APPLE_CC__ */