/******************************************************************************* ** File: rndint.c ** ** Contains: C source code for implementations of floating-point ** functions which round to integral value or format, as ** defined in header . In particular, this file ** contains implementations of functions rint, nearbyint, ** rinttol, round, roundtol, trunc, modf and modfl. This file ** targets PowerPC or Power platforms. ** ** Written by: A. Sazegari, Apple AltiVec Group ** Created originally by Jon Okada, Apple Numerics Group ** ** Copyright: © 1992-2001 by Apple Computer, Inc., all rights reserved ** ** Change History (most recent first): ** ** 13 Jul 01 ram replaced --setflm calls with inline assembly ** 03 Mar 01 ali first port to os x using gcc, added the crucial __setflm ** definition. ** 1. removed double_t, put in double for now. ** 2. removed iclass from nearbyint. ** 3. removed wrong comments intrunc. ** 4. ** 13 May 97 ali made performance improvements in rint, rinttol, roundtol ** and trunc by folding some of the taligent ideas into this ** implementation. nearbyint is faster than the one in taligent, ** rint is more elegant, but slower by %30 than the taligent one. ** 09 Apr 97 ali deleted modfl and deferred to AuxiliaryDD.c ** 15 Sep 94 ali Major overhaul and performance improvements of all functions. ** 20 Jul 94 PAF New faster version ** 16 Jul 93 ali Added the modfl function. ** 18 Feb 93 ali Changed the return value of fenv functions ** feclearexcept and feraiseexcept to their new ** NCEG X3J11.1/93-001 definitions. ** 16 Dec 92 JPO Removed __itrunc implementation to a ** separate file. ** 15 Dec 92 JPO Added __itrunc implementation and modified ** rinttol to include conversion from double ** to long int format. Modified roundtol to ** call __itrunc. ** 10 Dec 92 JPO Added modf (double) implementation. ** 04 Dec 92 JPO First created. ** *******************************************************************************/ #include #include #define SET_INVALID 0x01000000UL typedef union { struct { #if defined(__BIG_ENDIAN__) unsigned long int hi; unsigned long int lo; #else unsigned long int lo; unsigned long int hi; #endif } words; double dbl; } DblInHex; static const unsigned long int signMask = 0x80000000ul; static const double twoTo52 = 4503599627370496.0; static const double doubleToLong = 4503603922337792.0; // 2^52 static const DblInHex Huge = {{ 0x7FF00000, 0x00000000 }}; static const DblInHex TOWARDZERO = {{ 0x00000000, 0x00000001 }}; /******************************************************************************* * * * The function nearbyint rounds its double argument to integral value * * according to the current rounding direction and returns the result in * * double format. This function does not signal inexact. * * * ******************************************************************************** * * * This function calls fabs and copysign. * * * *******************************************************************************/ double nearbyint ( double x ) { double y; double OldEnvironment; y = twoTo52; asm ("mffs %0" : "=f" (OldEnvironment)); /* get the environement */ if ( fabs ( x ) >= y ) /* huge case is exact */ return x; if ( x < 0 ) y = -y; /* negative case */ y = ( x + y ) - y; /* force rounding */ if ( y == 0.0 ) /* zero results mirror sign of x */ y = copysign ( y, x ); // restore old flags asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment )); return ( y ); } /******************************************************************************* * * * The function rinttol converts its double argument to integral value * * according to the current rounding direction and returns the result in * * long int format. This conversion signals invalid if the argument is a * * NaN or the rounded intermediate result is out of range of the * * destination long int format, and it delivers an unspecified result in * * this case. This function signals inexact if the rounded result is * * within range of the long int format but unequal to the operand. * * * *******************************************************************************/ long int rinttol ( double x ) { register double y; DblInHex argument, OldEnvironment; unsigned long int xHead; register long int target; argument.dbl = x; target = ( argument.words.hi < signMask ); // flag positive sign xHead = argument.words.hi & 0x7ffffffful; // high 32 bits of x if ( target ) /******************************************************************************* * Sign of x is positive. * *******************************************************************************/ { if ( xHead < 0x41dffffful ) { // x is safely in long range y = ( x + twoTo52 ) - twoTo52; // round at binary point argument.dbl = y + doubleToLong; // force result into argument.words.lo return ( ( long ) argument.words.lo ); } asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment if ( xHead > 0x41dffffful ) { // x is safely out of long range OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MAX ); } /******************************************************************************* * x > 0.0 and may or may not be out of range of long. * *******************************************************************************/ y = ( x + twoTo52 ) - twoTo52; // do rounding if ( y > ( double ) LONG_MAX ) { // out of range of long OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MAX ); } argument.dbl = y + doubleToLong; // in range return ( ( long ) argument.words.lo ); // return result & flags } /******************************************************************************* * Sign of x is negative. * *******************************************************************************/ if ( xHead < 0x41e00000ul ) { // x is safely in long range y = ( x - twoTo52 ) + twoTo52; argument.dbl = y + doubleToLong; return ( ( long ) argument.words.lo ); } asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment if ( xHead > 0x41e00000ul ) { // x is safely out of long range OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MIN ); } /******************************************************************************* * x < 0.0 and may or may not be out of range of long. * *******************************************************************************/ y = ( x - twoTo52 ) + twoTo52; // do rounding if ( y < ( double ) LONG_MIN ) { // out of range of long OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MIN ); } argument.dbl = y + doubleToLong; // in range return ( ( long ) argument.words.lo ); // return result & flags } /******************************************************************************* * * * The function round rounds its double argument to integral value * * according to the "add half to the magnitude and truncate" rounding of * * Pascal's Round function and FORTRAN's ANINT function and returns the * * result in double format. This function signals inexact if an ordered * * return value is not equal to the operand. * * * *******************************************************************************/ double round ( double x ) { DblInHex argument, OldEnvironment; register double y, z; register unsigned long int xHead; register long int target; argument.dbl = x; xHead = argument.words.hi & 0x7fffffffUL; // xHead <- high half of |x| target = ( argument.words.hi < signMask ); // flag positive sign if ( xHead < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^52? * *******************************************************************************/ { if ( xHead < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ { asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment if ( xHead < 0x3fe00000ul ) /******************************************************************************* * Is |x| < 0.5? * *******************************************************************************/ { if ( ( xHead | argument.words.lo ) != 0ul ) OldEnvironment.words.lo |= 0x02000000ul; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); if ( target ) return ( 0.0 ); else return ( -0.0 ); } /******************************************************************************* * Is 0.5 ² |x| < 1.0? * *******************************************************************************/ OldEnvironment.words.lo |= 0x02000000ul; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); if ( target ) return ( 1.0 ); else return ( -1.0 ); } /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ if ( target ) { // positive x y = ( x + twoTo52 ) - twoTo52; // round at binary point if ( y == x ) // exact case return ( x ); z = x + 0.5; // inexact case y = ( z + twoTo52 ) - twoTo52; // round at binary point if ( y > z ) return ( y - 1.0 ); else return ( y ); } /******************************************************************************* * Is x < 0? * *******************************************************************************/ else { y = ( x - twoTo52 ) + twoTo52; // round at binary point if ( y == x ) return ( x ); z = x - 0.5; y = ( z - twoTo52 ) + twoTo52; // round at binary point if ( y < z ) return ( y + 1.0 ); else return ( y ); } } /******************************************************************************* * |x| >= 2.0^52 or x is a NaN. * *******************************************************************************/ return ( x ); } /******************************************************************************* * * * The function roundtol converts its double argument to integral format * * according to the "add half to the magnitude and chop" rounding mode of * * Pascal's Round function and FORTRAN's NINT function. This conversion * * signals invalid if the argument is a NaN or the rounded intermediate * * result is out of range of the destination long int format, and it * * delivers an unspecified result in this case. This function signals * * inexact if the rounded result is within range of the long int format but * * unequal to the operand. * * * *******************************************************************************/ long int roundtol ( double x ) { register double y, z; DblInHex argument, OldEnvironment; register unsigned long int xhi; register long int target; const DblInHex kTZ = {{ 0x0, 0x1 }}; const DblInHex kUP = {{ 0x0, 0x2 }}; argument.dbl = x; xhi = argument.words.hi & 0x7ffffffful; // high 32 bits of x target = ( argument.words.hi < signMask ); // flag positive sign if ( xhi > 0x41e00000ul ) /******************************************************************************* * Is x is out of long range or NaN? * *******************************************************************************/ { asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); if ( target ) // pin result return ( LONG_MAX ); else return ( LONG_MIN ); } if ( target ) /******************************************************************************* * Is sign of x is "+"? * *******************************************************************************/ { if ( x < 2147483647.5 ) /******************************************************************************* * x is in the range of a long. * *******************************************************************************/ { y = ( x + doubleToLong ) - doubleToLong; // round at binary point if ( y != x ) { // inexact case asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kTZ.dbl )); // truncate rounding z = x + 0.5; // truncate x + 0.5 argument.dbl = z + doubleToLong; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( ( long ) argument.words.lo ); } argument.dbl = y + doubleToLong; // force result into argument.words.lo return ( ( long ) argument.words.lo ); // return long result } /******************************************************************************* * Rounded positive x is out of the range of a long. * *******************************************************************************/ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MAX ); // return pinned result } /******************************************************************************* * x < 0.0 and may or may not be out of the range of a long. * *******************************************************************************/ if ( x > -2147483648.5 ) /******************************************************************************* * x is in the range of a long. * *******************************************************************************/ { y = ( x + doubleToLong ) - doubleToLong; // round at binary point if ( y != x ) { // inexact case asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kUP.dbl )); // round up z = x - 0.5; // truncate x - 0.5 argument.dbl = z + doubleToLong; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( ( long ) argument.words.lo ); } argument.dbl = y + doubleToLong; return ( ( long ) argument.words.lo ); // return long result } /******************************************************************************* * Rounded negative x is out of the range of a long. * *******************************************************************************/ asm ("mffs %0" : "=f" (OldEnvironment.dbl)); OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MIN ); // return pinned result } /******************************************************************************* * * * The function trunc truncates its double argument to integral value * * and returns the result in double format. This function signals * * inexact if an ordered return value is not equal to the operand. * * * *******************************************************************************/ double trunc ( double x ) { DblInHex argument,OldEnvironment; register double y; register unsigned long int xhi; register long int target; argument.dbl = x; xhi = argument.words.hi & 0x7fffffffUL; // xhi <- high half of |x| target = ( argument.words.hi < signMask ); // flag positive sign if ( xhi < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^53? * *******************************************************************************/ { if ( xhi < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ { if ( ( xhi | argument.words.lo ) != 0ul ) { // raise deserved INEXACT asm ("mffs %0" : "=f" (OldEnvironment.dbl)); OldEnvironment.words.lo |= 0x02000000ul; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); } if ( target ) // return properly signed zero return ( 0.0 ); else return ( -0.0 ); } /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ if ( target ) { y = ( x + twoTo52 ) - twoTo52; // round at binary point if ( y > x ) return ( y - 1.0 ); else return ( y ); } else { y = ( x - twoTo52 ) + twoTo52; // round at binary point. if ( y < x ) return ( y + 1.0 ); else return ( y ); } } /******************************************************************************* * Is |x| >= 2.0^52 or x is a NaN. * *******************************************************************************/ return ( x ); } /******************************************************************************* * The modf family of functions separate a floating-point number into its * * fractional and integral parts, returning the fractional part and writing * * the integral part in floating-point format to the object pointed to by a * * pointer argument. If the input argument is integral or infinite in * * value, the return value is a zero with the sign of the input argument. * * The modf family of functions raises no floating-point exceptions. older * * implemenation set the INVALID flag due to signaling NaN input. * * * *******************************************************************************/ /******************************************************************************* * modf is the double implementation. * *******************************************************************************/ double modf ( double x, double *iptr ) { register double OldEnvironment, xtrunc; register unsigned long int xHead, signBit; DblInHex argument; argument.dbl = x; xHead = argument.words.hi & 0x7ffffffful; // |x| high bit pattern signBit = ( argument.words.hi & 0x80000000ul ); // isolate sign bit if (xHead == 0x7ff81fe0) signBit = signBit | 0; if ( xHead < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^53? * *******************************************************************************/ { if ( xHead < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ { argument.words.hi = signBit; // truncate to zero argument.words.lo = 0ul; *iptr = argument.dbl; return ( x ); } /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ asm ("mffs %0" : "=f" (OldEnvironment)); // save environment // round toward zero asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( TOWARDZERO.dbl )); if ( signBit == 0ul ) // truncate to integer xtrunc = ( x + twoTo52 ) - twoTo52; else xtrunc = ( x - twoTo52 ) + twoTo52; // restore caller's env asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment )); *iptr = xtrunc; // store integral part if ( x != xtrunc ) // nonzero fraction return ( x - xtrunc ); else { // zero with x's sign argument.words.hi = signBit; argument.words.lo = 0ul; return ( argument.dbl ); } } *iptr = x; // x is integral or NaN if ( x != x ) // NaN is returned return x; else { // zero with x's sign argument.words.hi = signBit; argument.words.lo = 0ul; return ( argument.dbl ); } }