/* * Copyright (c) 2002 Apple Computer, Inc. All rights reserved. * * @APPLE_LICENSE_HEADER_START@ * * The contents of this file constitute Original Code as defined in and * are subject to the Apple Public Source License Version 1.1 (the * "License"). You may not use this file except in compliance with the * License. Please obtain a copy of the License at * http://www.apple.com/publicsource and read it before using this file. * * This 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 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 * * * ********************************************************************************/ #include "math.h" #include "fp_private.h" #include "fenv_private.h" #define REM_NAN "9" #if defined(BUILDING_FOR_CARBONCORE_LEGACY) static const hexdouble Huge = HEXDOUBLE(0x7ff00000, 0x00000000); static const hexdouble HugeHalved = HEXDOUBLE(0x7fe00000, 0x00000000); static int ___fpclassifyd ( double arg ) { register uint32_t exponent; hexdouble x; x.d = arg; __NOOP; __NOOP; __NOOP; exponent = x.i.hi & 0x7ff00000; if ( exponent == 0x7ff00000 ) { if ( ( ( x.i.hi & 0x000fffff ) | x.i.lo ) == 0 ) return FP_INFINITE; else return ( x.i.hi & dQuietNan ) ? FP_QNAN : FP_SNAN; } else if ( exponent != 0) return FP_NORMAL; else { if ( ( ( x.i.hi & 0x000fffff ) | x.i.lo ) == 0 ) return FP_ZERO; else return FP_SUBNORMAL; } } static const double twoTo52 = 0x1.0p+52; // 4.50359962737049600e15; static const double klTod = 4503601774854144.0; // 0x1.000008p52 static const hexdouble minusInf = HEXDOUBLE(0xfff00000, 0x00000000); static double __logb ( double x ) { hexdouble xInHex; int32_t shiftedExp; xInHex.d = x; __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; if (unlikely( 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 (likely( shiftedExp != 0 )) // normal number shiftedExp -= 1023; // unbias exponent else if ( x == 0.0 ) { // zero hexdouble OldEnvironment; FEGETENVD_GRP( OldEnvironment.d ); // raise zero divide for DOMAIN error OldEnvironment.i.lo |= FE_DIVBYZERO; FESETENVD_GRP( OldEnvironment.d ); return ( minusInf.d ); // return -infinity } else { // subnormal number xInHex.d *= twoTo52; // scale up __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; shiftedExp -= 1075; // unbias exponent } if (unlikely( shiftedExp == 0 )) // zero result return ( 0.0 ); else { // nonzero result xInHex.d = klTod; __NOOP; __NOOP; __NOOP; xInHex.i.lo += shiftedExp; return ( xInHex.d - klTod ); } } static const double twoTo1023 = 0x1.0p+1023; static const double twoToM1022 = 0x1.0p-1022; static double __scalbn ( double x, int n ) { hexdouble xInHex; xInHex.i.lo = 0u; // 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 = ( ( uint32_t ) ( n + 1023 ) ) << 20; __NOOP; __NOOP; __NOOP; return ( x * xInHex.d ); } static int ___signbitd ( double arg ) { hexdouble z; z.d = arg; __NOOP; __NOOP; __NOOP; return (((int32_t)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) { int iclx,icly; /* classify results of x,y */ int32_t iquo; /* low 32 bits of integral quotient */ int32_t iscx, iscy, idiff; /* logb values and difference */ 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 ); __NOOP; __NOOP; OldEnv = OldEnvironment.i.lo; *quo = 0; /* initialize quotient result */ iclx = ___fpclassifyd(x); icly = ___fpclassifyd(y); if (likely((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 = (int32_t) __logb(x1); /* get binary exponents */ iscy = (int32_t) __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 (likely( 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_GRP( OldEnvironment.d ); goto ret; } else /* trivial cases (finite REM infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD_GRP( 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_GRP( OldEnvironment.d ); return rslt; } #else /* !BUILDING_FOR_CARBONCORE_LEGACY */ static const hexsingle HugeF = { 0x7f800000 }; static const hexsingle HugeFHalved = { 0x7f000000 }; float remquof ( float x, float y, int *quo) { int iclx,icly; /* classify results of x,y */ int32_t iquo; /* low 32 bits of integral quotient */ int32_t iscx, iscy, idiff; /* logb values and difference */ 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 ); __NOOP; __NOOP; OldEnv = OldEnvironment.i.lo; *quo = 0; /* initialize quotient result */ iclx = __fpclassifyf(x); icly = __fpclassifyf(y); if (likely((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 = (int32_t) logbf(x1); /* get binary exponents */ iscy = (int32_t) 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 (likely( 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_GRP( OldEnvironment.d ); goto ret; } else /* trivial cases (finite REM infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD_GRP( 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_GRP( 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 ) { int iclx,icly; /* classify results of x,y */ int32_t iscx,iscy,idiff; /* logb values and difference */ 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 ); __NOOP; __NOOP; OldEnv = OldEnvironment.i.lo; iclx = __fpclassifyd(x); icly = __fpclassifyd(y); if (likely((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 = (int32_t) logb(x1); /* get binary exponents of |x| and |y| */ iscy = (int32_t) 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_GRP ( OldEnvironment.d ); goto ret; } else /* trivial cases (finite MOD infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD_GRP (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_GRP (OldEnvironment.d ); return rslt; } float fmodf ( float x, float y ) { int iclx,icly; /* classify results of x,y */ int32_t iscx,iscy,idiff; /* logb values and difference */ 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 ); __NOOP; __NOOP; OldEnv = OldEnvironment.i.lo; iclx = __fpclassifyf(x); icly = __fpclassifyf(y); if (likely((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 = (int32_t) logbf(x1); /* get binary exponents of |x| and |y| */ iscy = (int32_t) 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_GRP ( OldEnvironment.d ); goto ret; } else /* trivial cases (finite MOD infinite */ rslt = x; /* or zero REM nonzero) with *quo = 0 */ ret: FEGETENVD_GRP (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_GRP (OldEnvironment.d ); return rslt; } #endif /* !BUILDING_FOR_CARBONCORE_LEGACY */