Index: head/lib/msun/src/e_fmod.c =================================================================== --- head/lib/msun/src/e_fmod.c (revision 336662) +++ head/lib/msun/src/e_fmod.c (revision 336663) @@ -1,138 +1,138 @@ /* @(#)e_fmod.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); /* * __ieee754_fmod(x,y) * Return x mod y in exact arithmetic * Method: shift and subtract */ #include #include "math.h" #include "math_private.h" static const double one = 1.0, Zero[] = {0.0, -0.0,}; double __ieee754_fmod(double x, double y) { int32_t n,hx,hy,hz,ix,iy,sx,i; u_int32_t lx,ly,lz; EXTRACT_WORDS(hx,lx,x); EXTRACT_WORDS(hy,ly,y); sx = hx&0x80000000; /* sign of x */ hx ^=sx; /* |x| */ hy &= 0x7fffffff; /* |y| */ /* purge off exception values */ if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ - return nan_mix(x, y)/nan_mix(x, y); + return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); if(hx<=hy) { if((hx>31]; /* |x|=|y| return x*0*/ } /* determine ix = ilogb(x) */ if(hx<0x00100000) { /* subnormal x */ if(hx==0) { for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; } else { for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; } } else ix = (hx>>20)-1023; /* determine iy = ilogb(y) */ if(hy<0x00100000) { /* subnormal y */ if(hy==0) { for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; } else { for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; } } else iy = (hy>>20)-1023; /* set up {hx,lx}, {hy,ly} and align y to x */ if(ix >= -1022) hx = 0x00100000|(0x000fffff&hx); else { /* subnormal x, shift x to normal */ n = -1022-ix; if(n<=31) { hx = (hx<>(32-n)); lx <<= n; } else { hx = lx<<(n-32); lx = 0; } } if(iy >= -1022) hy = 0x00100000|(0x000fffff&hy); else { /* subnormal y, shift y to normal */ n = -1022-iy; if(n<=31) { hy = (hy<>(32-n)); ly <<= n; } else { hy = ly<<(n-32); ly = 0; } } /* fix point fmod */ n = ix - iy; while(n--) { hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} else { if((hz|lz)==0) /* return sign(x)*0 */ return Zero[(u_int32_t)sx>>31]; hx = hz+hz+(lz>>31); lx = lz+lz; } } hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} /* convert back to floating value and restore the sign */ if((hx|lx)==0) /* return sign(x)*0 */ return Zero[(u_int32_t)sx>>31]; while(hx<0x00100000) { /* normalize x */ hx = hx+hx+(lx>>31); lx = lx+lx; iy -= 1; } if(iy>= -1022) { /* normalize output */ hx = ((hx-0x00100000)|((iy+1023)<<20)); INSERT_WORDS(x,hx|sx,lx); } else { /* subnormal output */ n = -1022 - iy; if(n<=20) { lx = (lx>>n)|((u_int32_t)hx<<(32-n)); hx >>= n; } else if (n<=31) { lx = (hx<<(32-n))|(lx>>n); hx = sx; } else { lx = hx>>(n-32); hx = sx; } INSERT_WORDS(x,hx|sx,lx); x *= one; /* create necessary signal */ } return x; /* exact output */ } #if (LDBL_MANT_DIG == 53) __weak_reference(fmod, fmodl); #endif Index: head/lib/msun/src/e_fmodf.c =================================================================== --- head/lib/msun/src/e_fmodf.c (revision 336662) +++ head/lib/msun/src/e_fmodf.c (revision 336663) @@ -1,104 +1,104 @@ /* e_fmodf.c -- float version of e_fmod.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); /* * __ieee754_fmodf(x,y) * Return x mod y in exact arithmetic * Method: shift and subtract */ #include "math.h" #include "math_private.h" static const float one = 1.0, Zero[] = {0.0, -0.0,}; float __ieee754_fmodf(float x, float y) { int32_t n,hx,hy,hz,ix,iy,sx,i; GET_FLOAT_WORD(hx,x); GET_FLOAT_WORD(hy,y); sx = hx&0x80000000; /* sign of x */ hx ^=sx; /* |x| */ hy &= 0x7fffffff; /* |y| */ /* purge off exception values */ if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */ (hy>0x7f800000)) /* or y is NaN */ - return nan_mix(x, y)/nan_mix(x, y); + return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); if(hx>31]; /* |x|=|y| return x*0*/ /* determine ix = ilogb(x) */ if(hx<0x00800000) { /* subnormal x */ for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; } else ix = (hx>>23)-127; /* determine iy = ilogb(y) */ if(hy<0x00800000) { /* subnormal y */ for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1; } else iy = (hy>>23)-127; /* set up {hx,lx}, {hy,ly} and align y to x */ if(ix >= -126) hx = 0x00800000|(0x007fffff&hx); else { /* subnormal x, shift x to normal */ n = -126-ix; hx = hx<= -126) hy = 0x00800000|(0x007fffff&hy); else { /* subnormal y, shift y to normal */ n = -126-iy; hy = hy<>31]; hx = hz+hz; } } hz=hx-hy; if(hz>=0) {hx=hz;} /* convert back to floating value and restore the sign */ if(hx==0) /* return sign(x)*0 */ return Zero[(u_int32_t)sx>>31]; while(hx<0x00800000) { /* normalize x */ hx = hx+hx; iy -= 1; } if(iy>= -126) { /* normalize output */ hx = ((hx-0x00800000)|((iy+127)<<23)); SET_FLOAT_WORD(x,hx|sx); } else { /* subnormal output */ n = -126 - iy; hx >>= n; SET_FLOAT_WORD(x,hx|sx); x *= one; /* create necessary signal */ } return x; /* exact output */ } Index: head/lib/msun/src/e_fmodl.c =================================================================== --- head/lib/msun/src/e_fmodl.c (revision 336662) +++ head/lib/msun/src/e_fmodl.c (revision 336663) @@ -1,149 +1,149 @@ /* @(#)e_fmod.c 1.3 95/01/18 */ /*- * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); #include #include #include "fpmath.h" #include "math.h" #include "math_private.h" #define BIAS (LDBL_MAX_EXP - 1) #if LDBL_MANL_SIZE > 32 typedef uint64_t manl_t; #else typedef uint32_t manl_t; #endif #if LDBL_MANH_SIZE > 32 typedef uint64_t manh_t; #else typedef uint32_t manh_t; #endif /* * These macros add and remove an explicit integer bit in front of the * fractional mantissa, if the architecture doesn't have such a bit by * default already. */ #ifdef LDBL_IMPLICIT_NBIT #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) #define HFRAC_BITS LDBL_MANH_SIZE #else #define SET_NBIT(hx) (hx) #define HFRAC_BITS (LDBL_MANH_SIZE - 1) #endif #define MANL_SHIFT (LDBL_MANL_SIZE - 1) static const long double one = 1.0, Zero[] = {0.0, -0.0,}; /* * fmodl(x,y) * Return x mod y in exact arithmetic * Method: shift and subtract * * Assumptions: * - The low part of the mantissa fits in a manl_t exactly. * - The high part of the mantissa fits in an int64_t with enough room * for an explicit integer bit in front of the fractional bits. */ long double fmodl(long double x, long double y) { union IEEEl2bits ux, uy; int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ manh_t hy; manl_t lx,ly,lz; int ix,iy,n,sx; ux.e = x; uy.e = y; sx = ux.bits.sign; /* purge off exception values */ if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ (uy.bits.exp == BIAS + LDBL_MAX_EXP && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ - return nan_mix(x, y)/nan_mix(x, y); + return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); if(ux.bits.exp<=uy.bits.exp) { if((ux.bits.exp>MANL_SHIFT); lx = lx+lx;} else { if ((hz|lz)==0) /* return sign(x)*0 */ return Zero[sx]; hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; } } hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} /* convert back to floating value and restore the sign */ if((hx|lx)==0) /* return sign(x)*0 */ return Zero[sx]; while(hx<(1ULL<>MANL_SHIFT); lx = lx+lx; iy -= 1; } ux.bits.manh = hx; /* The mantissa is truncated here if needed. */ ux.bits.manl = lx; if (iy < LDBL_MIN_EXP) { ux.bits.exp = iy + (BIAS + 512); ux.e *= 0x1p-512; } else { ux.bits.exp = iy + BIAS; } x = ux.e * one; /* create necessary signal */ return x; /* exact output */ } Index: head/lib/msun/src/e_remainder.c =================================================================== --- head/lib/msun/src/e_remainder.c (revision 336662) +++ head/lib/msun/src/e_remainder.c (revision 336663) @@ -1,79 +1,79 @@ /* @(#)e_remainder.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); /* __ieee754_remainder(x,p) * Return : * returns x REM p = x - [x/p]*p as if in infinite * precise arithmetic, where [x/p] is the (infinite bit) * integer nearest x/p (in half way case choose the even one). * Method : * Based on fmod() return x-[x/p]chopped*p exactlp. */ #include #include "math.h" #include "math_private.h" static const double zero = 0.0; double __ieee754_remainder(double x, double p) { int32_t hx,hp; u_int32_t sx,lx,lp; double p_half; EXTRACT_WORDS(hx,lx,x); EXTRACT_WORDS(hp,lp,p); sx = hx&0x80000000; hp &= 0x7fffffff; hx &= 0x7fffffff; /* purge off exception values */ if(((hp|lp)==0)|| /* p = 0 */ (hx>=0x7ff00000)|| /* x not finite */ ((hp>=0x7ff00000)&& /* p is NaN */ (((hp-0x7ff00000)|lp)!=0))) - return nan_mix(x, p)/nan_mix(x, p); + return nan_mix_op(x, p, *)/nan_mix_op(x, p, *); if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */ if (((hx-hp)|(lx-lp))==0) return zero*x; x = fabs(x); p = fabs(p); if (hp<0x00200000) { if(x+x>p) { x-=p; if(x+x>=p) x -= p; } } else { p_half = 0.5*p; if(x>p_half) { x-=p; if(x>=p_half) x -= p; } } GET_HIGH_WORD(hx,x); if ((hx&0x7fffffff)==0) hx = 0; SET_HIGH_WORD(x,hx^sx); return x; } #if LDBL_MANT_DIG == 53 __weak_reference(remainder, remainderl); #endif Index: head/lib/msun/src/e_remainderf.c =================================================================== --- head/lib/msun/src/e_remainderf.c (revision 336662) +++ head/lib/msun/src/e_remainderf.c (revision 336663) @@ -1,65 +1,65 @@ /* e_remainderf.c -- float version of e_remainder.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" static const float zero = 0.0; float __ieee754_remainderf(float x, float p) { int32_t hx,hp; u_int32_t sx; float p_half; GET_FLOAT_WORD(hx,x); GET_FLOAT_WORD(hp,p); sx = hx&0x80000000; hp &= 0x7fffffff; hx &= 0x7fffffff; /* purge off exception values */ if((hp==0)|| /* p = 0 */ (hx>=0x7f800000)|| /* x not finite */ ((hp>0x7f800000))) /* p is NaN */ - return nan_mix(x, p)/nan_mix(x, p); + return nan_mix_op(x, p, *)/nan_mix_op(x, p, *); if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */ if ((hx-hp)==0) return zero*x; x = fabsf(x); p = fabsf(p); if (hp<0x01000000) { if(x+x>p) { x-=p; if(x+x>=p) x -= p; } } else { p_half = (float)0.5*p; if(x>p_half) { x-=p; if(x>=p_half) x -= p; } } GET_FLOAT_WORD(hx,x); if ((hx&0x7fffffff)==0) hx = 0; SET_FLOAT_WORD(x,hx^sx); return x; } Index: head/lib/msun/src/math_private.h =================================================================== --- head/lib/msun/src/math_private.h (revision 336662) +++ head/lib/msun/src/math_private.h (revision 336663) @@ -1,917 +1,924 @@ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* * from: @(#)fdlibm.h 5.1 93/09/24 * $FreeBSD$ */ #ifndef _MATH_PRIVATE_H_ #define _MATH_PRIVATE_H_ #include #include /* * The original fdlibm code used statements like: * n0 = ((*(int*)&one)>>29)^1; * index of high word * * ix0 = *(n0+(int*)&x); * high word of x * * ix1 = *((1-n0)+(int*)&x); * low word of x * * to dig two 32 bit words out of the 64 bit IEEE floating point * value. That is non-ANSI, and, moreover, the gcc instruction * scheduler gets it wrong. We instead use the following macros. * Unlike the original code, we determine the endianness at compile * time, not at run time; I don't see much benefit to selecting * endianness at run time. */ /* * A union which permits us to convert between a double and two 32 bit * ints. */ #ifdef __arm__ #if defined(__VFP_FP__) || defined(__ARM_EABI__) #define IEEE_WORD_ORDER BYTE_ORDER #else #define IEEE_WORD_ORDER BIG_ENDIAN #endif #else /* __arm__ */ #define IEEE_WORD_ORDER BYTE_ORDER #endif /* A union which permits us to convert between a long double and four 32 bit ints. */ #if IEEE_WORD_ORDER == BIG_ENDIAN typedef union { long double value; struct { u_int32_t mswhi; u_int32_t mswlo; u_int32_t lswhi; u_int32_t lswlo; } parts32; struct { u_int64_t msw; u_int64_t lsw; } parts64; } ieee_quad_shape_type; #endif #if IEEE_WORD_ORDER == LITTLE_ENDIAN typedef union { long double value; struct { u_int32_t lswlo; u_int32_t lswhi; u_int32_t mswlo; u_int32_t mswhi; } parts32; struct { u_int64_t lsw; u_int64_t msw; } parts64; } ieee_quad_shape_type; #endif #if IEEE_WORD_ORDER == BIG_ENDIAN typedef union { double value; struct { u_int32_t msw; u_int32_t lsw; } parts; struct { u_int64_t w; } xparts; } ieee_double_shape_type; #endif #if IEEE_WORD_ORDER == LITTLE_ENDIAN typedef union { double value; struct { u_int32_t lsw; u_int32_t msw; } parts; struct { u_int64_t w; } xparts; } ieee_double_shape_type; #endif /* Get two 32 bit ints from a double. */ #define EXTRACT_WORDS(ix0,ix1,d) \ do { \ ieee_double_shape_type ew_u; \ ew_u.value = (d); \ (ix0) = ew_u.parts.msw; \ (ix1) = ew_u.parts.lsw; \ } while (0) /* Get a 64-bit int from a double. */ #define EXTRACT_WORD64(ix,d) \ do { \ ieee_double_shape_type ew_u; \ ew_u.value = (d); \ (ix) = ew_u.xparts.w; \ } while (0) /* Get the more significant 32 bit int from a double. */ #define GET_HIGH_WORD(i,d) \ do { \ ieee_double_shape_type gh_u; \ gh_u.value = (d); \ (i) = gh_u.parts.msw; \ } while (0) /* Get the less significant 32 bit int from a double. */ #define GET_LOW_WORD(i,d) \ do { \ ieee_double_shape_type gl_u; \ gl_u.value = (d); \ (i) = gl_u.parts.lsw; \ } while (0) /* Set a double from two 32 bit ints. */ #define INSERT_WORDS(d,ix0,ix1) \ do { \ ieee_double_shape_type iw_u; \ iw_u.parts.msw = (ix0); \ iw_u.parts.lsw = (ix1); \ (d) = iw_u.value; \ } while (0) /* Set a double from a 64-bit int. */ #define INSERT_WORD64(d,ix) \ do { \ ieee_double_shape_type iw_u; \ iw_u.xparts.w = (ix); \ (d) = iw_u.value; \ } while (0) /* Set the more significant 32 bits of a double from an int. */ #define SET_HIGH_WORD(d,v) \ do { \ ieee_double_shape_type sh_u; \ sh_u.value = (d); \ sh_u.parts.msw = (v); \ (d) = sh_u.value; \ } while (0) /* Set the less significant 32 bits of a double from an int. */ #define SET_LOW_WORD(d,v) \ do { \ ieee_double_shape_type sl_u; \ sl_u.value = (d); \ sl_u.parts.lsw = (v); \ (d) = sl_u.value; \ } while (0) /* * A union which permits us to convert between a float and a 32 bit * int. */ typedef union { float value; /* FIXME: Assumes 32 bit int. */ unsigned int word; } ieee_float_shape_type; /* Get a 32 bit int from a float. */ #define GET_FLOAT_WORD(i,d) \ do { \ ieee_float_shape_type gf_u; \ gf_u.value = (d); \ (i) = gf_u.word; \ } while (0) /* Set a float from a 32 bit int. */ #define SET_FLOAT_WORD(d,i) \ do { \ ieee_float_shape_type sf_u; \ sf_u.word = (i); \ (d) = sf_u.value; \ } while (0) /* * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long * double. */ #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \ do { \ union IEEEl2bits ew_u; \ ew_u.e = (d); \ (ix0) = ew_u.xbits.expsign; \ (ix1) = ew_u.xbits.man; \ } while (0) /* * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit * long double. */ #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \ do { \ union IEEEl2bits ew_u; \ ew_u.e = (d); \ (ix0) = ew_u.xbits.expsign; \ (ix1) = ew_u.xbits.manh; \ (ix2) = ew_u.xbits.manl; \ } while (0) /* Get expsign as a 16 bit int from a long double. */ #define GET_LDBL_EXPSIGN(i,d) \ do { \ union IEEEl2bits ge_u; \ ge_u.e = (d); \ (i) = ge_u.xbits.expsign; \ } while (0) /* * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int * mantissa. */ #define INSERT_LDBL80_WORDS(d,ix0,ix1) \ do { \ union IEEEl2bits iw_u; \ iw_u.xbits.expsign = (ix0); \ iw_u.xbits.man = (ix1); \ (d) = iw_u.e; \ } while (0) /* * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints * comprising the mantissa. */ #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \ do { \ union IEEEl2bits iw_u; \ iw_u.xbits.expsign = (ix0); \ iw_u.xbits.manh = (ix1); \ iw_u.xbits.manl = (ix2); \ (d) = iw_u.e; \ } while (0) /* Set expsign of a long double from a 16 bit int. */ #define SET_LDBL_EXPSIGN(d,v) \ do { \ union IEEEl2bits se_u; \ se_u.e = (d); \ se_u.xbits.expsign = (v); \ (d) = se_u.e; \ } while (0) #ifdef __i386__ /* Long double constants are broken on i386. */ #define LD80C(m, ex, v) { \ .xbits.man = __CONCAT(m, ULL), \ .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \ } #else /* The above works on non-i386 too, but we use this to check v. */ #define LD80C(m, ex, v) { .e = (v), } #endif #ifdef FLT_EVAL_METHOD /* * Attempt to get strict C99 semantics for assignment with non-C99 compilers. */ #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) #else #define STRICT_ASSIGN(type, lval, rval) do { \ volatile type __lval; \ \ if (sizeof(type) >= sizeof(long double)) \ (lval) = (rval); \ else { \ __lval = (rval); \ (lval) = __lval; \ } \ } while (0) #endif #endif /* FLT_EVAL_METHOD */ /* Support switching the mode to FP_PE if necessary. */ #if defined(__i386__) && !defined(NO_FPSETPREC) #define ENTERI() ENTERIT(long double) #define ENTERIT(returntype) \ returntype __retval; \ fp_prec_t __oprec; \ \ if ((__oprec = fpgetprec()) != FP_PE) \ fpsetprec(FP_PE) #define RETURNI(x) do { \ __retval = (x); \ if (__oprec != FP_PE) \ fpsetprec(__oprec); \ RETURNF(__retval); \ } while (0) #define ENTERV() \ fp_prec_t __oprec; \ \ if ((__oprec = fpgetprec()) != FP_PE) \ fpsetprec(FP_PE) #define RETURNV() do { \ if (__oprec != FP_PE) \ fpsetprec(__oprec); \ return; \ } while (0) #else #define ENTERI() #define ENTERIT(x) #define RETURNI(x) RETURNF(x) #define ENTERV() #define RETURNV() return #endif /* Default return statement if hack*_t() is not used. */ #define RETURNF(v) return (v) /* * 2sum gives the same result as 2sumF without requiring |a| >= |b| or * a == 0, but is slower. */ #define _2sum(a, b) do { \ __typeof(a) __s, __w; \ \ __w = (a) + (b); \ __s = __w - (a); \ (b) = ((a) - (__w - __s)) + ((b) - __s); \ (a) = __w; \ } while (0) /* * 2sumF algorithm. * * "Normalize" the terms in the infinite-precision expression a + b for * the sum of 2 floating point values so that b is as small as possible * relative to 'a'. (The resulting 'a' is the value of the expression in * the same precision as 'a' and the resulting b is the rounding error.) * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and * exponent overflow or underflow must not occur. This uses a Theorem of * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum" * is apparently due to Skewchuk (1997). * * For this to always work, assignment of a + b to 'a' must not retain any * extra precision in a + b. This is required by C standards but broken * in many compilers. The brokenness cannot be worked around using * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this * algorithm would be destroyed by non-null strict assignments. (The * compilers are correct to be broken -- the efficiency of all floating * point code calculations would be destroyed similarly if they forced the * conversions.) * * Fortunately, a case that works well can usually be arranged by building * any extra precision into the type of 'a' -- 'a' should have type float_t, * double_t or long double. b's type should be no larger than 'a's type. * Callers should use these types with scopes as large as possible, to * reduce their own extra-precision and efficiciency problems. In * particular, they shouldn't convert back and forth just to call here. */ #ifdef DEBUG #define _2sumF(a, b) do { \ __typeof(a) __w; \ volatile __typeof(a) __ia, __ib, __r, __vw; \ \ __ia = (a); \ __ib = (b); \ assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \ \ __w = (a) + (b); \ (b) = ((a) - __w) + (b); \ (a) = __w; \ \ /* The next 2 assertions are weak if (a) is already long double. */ \ assert((long double)__ia + __ib == (long double)(a) + (b)); \ __vw = __ia + __ib; \ __r = __ia - __vw; \ __r += __ib; \ assert(__vw == (a) && __r == (b)); \ } while (0) #else /* !DEBUG */ #define _2sumF(a, b) do { \ __typeof(a) __w; \ \ __w = (a) + (b); \ (b) = ((a) - __w) + (b); \ (a) = __w; \ } while (0) #endif /* DEBUG */ /* * Set x += c, where x is represented in extra precision as a + b. * x must be sufficiently normalized and sufficiently larger than c, * and the result is then sufficiently normalized. * * The details of ordering are that |a| must be >= |c| (so that (a, c) * can be normalized without extra work to swap 'a' with c). The details of * the normalization are that b must be small relative to the normalized 'a'. * Normalization of (a, c) makes the normalized c tiny relative to the * normalized a, so b remains small relative to 'a' in the result. However, * b need not ever be tiny relative to 'a'. For example, b might be about * 2**20 times smaller than 'a' to give about 20 extra bits of precision. * That is usually enough, and adding c (which by normalization is about * 2**53 times smaller than a) cannot change b significantly. However, * cancellation of 'a' with c in normalization of (a, c) may reduce 'a' * significantly relative to b. The caller must ensure that significant * cancellation doesn't occur, either by having c of the same sign as 'a', * or by having |c| a few percent smaller than |a|. Pre-normalization of * (a, b) may help. * * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2 * exercise 19). We gain considerable efficiency by requiring the terms to * be sufficiently normalized and sufficiently increasing. */ #define _3sumF(a, b, c) do { \ __typeof(a) __tmp; \ \ __tmp = (c); \ _2sumF(__tmp, (a)); \ (b) += (a); \ (a) = __tmp; \ } while (0) /* * Common routine to process the arguments to nan(), nanf(), and nanl(). */ void _scan_nan(uint32_t *__words, int __num_words, const char *__s); /* - * Mix 1 or 2 NaNs. First add 0 to each arg. This normally just turns + * Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns * signaling NaNs into quiet NaNs by setting a quiet bit. We do this * because we want to never return a signaling NaN, and also because we * don't want the quiet bit to affect the result. Then mix the converted - * args using addition. The result is typically the arg whose mantissa - * bits (considered as in integer) are largest. + * args using the specified operation. * - * Technical complications: the result in bits might depend on the precision - * and/or on compiler optimizations, especially when different register sets - * are used for different precisions. Try to make the result not depend on - * at least the precision by always doing the main mixing step in long double + * When one arg is NaN, the result is typically that arg quieted. When both + * args are NaNs, the result is typically the quietening of the arg whose + * mantissa is largest after quietening. When neither arg is NaN, the + * result may be NaN because it is indeterminate, or finite for subsequent + * construction of a NaN as the indeterminate 0.0L/0.0L. + * + * Technical complications: the result in bits after rounding to the final + * precision might depend on the runtime precision and/or on compiler + * optimizations, especially when different register sets are used for + * different precisions. Try to make the result not depend on at least the + * runtime precision by always doing the main mixing step in long double * precision. Try to reduce dependencies on optimizations by adding the * the 0's in different precisions (unless everything is in long double * precision). */ -#define nan_mix(x, y) (((x) + 0.0L) + ((y) + 0)) +#define nan_mix(x, y) (nan_mix_op((x), (y), +)) +#define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0)) #ifdef _COMPLEX_H /* * C99 specifies that complex numbers have the same representation as * an array of two elements, where the first element is the real part * and the second element is the imaginary part. */ typedef union { float complex f; float a[2]; } float_complex; typedef union { double complex f; double a[2]; } double_complex; typedef union { long double complex f; long double a[2]; } long_double_complex; #define REALPART(z) ((z).a[0]) #define IMAGPART(z) ((z).a[1]) /* * Inline functions that can be used to construct complex values. * * The C99 standard intends x+I*y to be used for this, but x+I*y is * currently unusable in general since gcc introduces many overflow, * underflow, sign and efficiency bugs by rewriting I*y as * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted * to -0.0+I*0.0. * * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL() * to construct complex values. Compilers that conform to the C99 * standard require the following functions to avoid the above issues. */ #ifndef CMPLXF static __inline float complex CMPLXF(float x, float y) { float_complex z; REALPART(z) = x; IMAGPART(z) = y; return (z.f); } #endif #ifndef CMPLX static __inline double complex CMPLX(double x, double y) { double_complex z; REALPART(z) = x; IMAGPART(z) = y; return (z.f); } #endif #ifndef CMPLXL static __inline long double complex CMPLXL(long double x, long double y) { long_double_complex z; REALPART(z) = x; IMAGPART(z) = y; return (z.f); } #endif #endif /* _COMPLEX_H */ /* * The rnint() family rounds to the nearest integer for a restricted range * range of args (up to about 2**MANT_DIG). We assume that the current * rounding mode is FE_TONEAREST so that this can be done efficiently. * Extra precision causes more problems in practice, and we only centralize * this here to reduce those problems, and have not solved the efficiency * problems. The exp2() family uses a more delicate version of this that * requires extracting bits from the intermediate value, so it is not * centralized here and should copy any solution of the efficiency problems. */ static inline double rnint(__double_t x) { /* * This casts to double to kill any extra precision. This depends * on the cast being applied to a double_t to avoid compiler bugs * (this is a cleaner version of STRICT_ASSIGN()). This is * inefficient if there actually is extra precision, but is hard * to improve on. We use double_t in the API to minimise conversions * for just calling here. Note that we cannot easily change the * magic number to the one that works directly with double_t, since * the rounding precision is variable at runtime on x86 so the * magic number would need to be variable. Assuming that the * rounding precision is always the default is too fragile. This * and many other complications will move when the default is * changed to FP_PE. */ return ((double)(x + 0x1.8p52) - 0x1.8p52); } static inline float rnintf(__float_t x) { /* * As for rnint(), except we could just call that to handle the * extra precision case, usually without losing efficiency. */ return ((float)(x + 0x1.8p23F) - 0x1.8p23F); } #ifdef LDBL_MANT_DIG /* * The complications for extra precision are smaller for rnintl() since it * can safely assume that the rounding precision has been increased from * its default to FP_PE on x86. We don't exploit that here to get small * optimizations from limiting the rangle to double. We just need it for * the magic number to work with long doubles. ld128 callers should use * rnint() instead of this if possible. ld80 callers should prefer * rnintl() since for amd64 this avoids swapping the register set, while * for i386 it makes no difference (assuming FP_PE), and for other arches * it makes little difference. */ static inline long double rnintl(long double x) { return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 - __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2); } #endif /* LDBL_MANT_DIG */ /* * irint() and i64rint() give the same result as casting to their integer * return type provided their arg is a floating point integer. They can * sometimes be more efficient because no rounding is required. */ #if (defined(amd64) || defined(__i386__)) && defined(__GNUCLIKE_ASM) #define irint(x) \ (sizeof(x) == sizeof(float) && \ sizeof(__float_t) == sizeof(long double) ? irintf(x) : \ sizeof(x) == sizeof(double) && \ sizeof(__double_t) == sizeof(long double) ? irintd(x) : \ sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x)) #else #define irint(x) ((int)(x)) #endif #define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */ #if defined(__i386__) && defined(__GNUCLIKE_ASM) static __inline int irintf(float x) { int n; __asm("fistl %0" : "=m" (n) : "t" (x)); return (n); } static __inline int irintd(double x) { int n; __asm("fistl %0" : "=m" (n) : "t" (x)); return (n); } #endif #if (defined(__amd64__) || defined(__i386__)) && defined(__GNUCLIKE_ASM) static __inline int irintl(long double x) { int n; __asm("fistl %0" : "=m" (n) : "t" (x)); return (n); } #endif #ifdef DEBUG #if defined(__amd64__) || defined(__i386__) #define breakpoint() asm("int $3") #else #include #define breakpoint() raise(SIGTRAP) #endif #endif /* Write a pari script to test things externally. */ #ifdef DOPRINT #include #ifndef DOPRINT_SWIZZLE #define DOPRINT_SWIZZLE 0 #endif #ifdef DOPRINT_LD80 #define DOPRINT_START(xp) do { \ uint64_t __lx; \ uint16_t __hx; \ \ /* Hack to give more-problematic args. */ \ EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \ __lx ^= DOPRINT_SWIZZLE; \ INSERT_LDBL80_WORDS(*xp, __hx, __lx); \ printf("x = %.21Lg; ", (long double)*xp); \ } while (0) #define DOPRINT_END1(v) \ printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) #define DOPRINT_END2(hi, lo) \ printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ (long double)(hi), (long double)(lo)) #elif defined(DOPRINT_D64) #define DOPRINT_START(xp) do { \ uint32_t __hx, __lx; \ \ EXTRACT_WORDS(__hx, __lx, *xp); \ __lx ^= DOPRINT_SWIZZLE; \ INSERT_WORDS(*xp, __hx, __lx); \ printf("x = %.21Lg; ", (long double)*xp); \ } while (0) #define DOPRINT_END1(v) \ printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) #define DOPRINT_END2(hi, lo) \ printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ (long double)(hi), (long double)(lo)) #elif defined(DOPRINT_F32) #define DOPRINT_START(xp) do { \ uint32_t __hx; \ \ GET_FLOAT_WORD(__hx, *xp); \ __hx ^= DOPRINT_SWIZZLE; \ SET_FLOAT_WORD(*xp, __hx); \ printf("x = %.21Lg; ", (long double)*xp); \ } while (0) #define DOPRINT_END1(v) \ printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) #define DOPRINT_END2(hi, lo) \ printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ (long double)(hi), (long double)(lo)) #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */ #ifndef DOPRINT_SWIZZLE_HIGH #define DOPRINT_SWIZZLE_HIGH 0 #endif #define DOPRINT_START(xp) do { \ uint64_t __lx, __llx; \ uint16_t __hx; \ \ EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \ __llx ^= DOPRINT_SWIZZLE; \ __lx ^= DOPRINT_SWIZZLE_HIGH; \ INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \ printf("x = %.36Lg; ", (long double)*xp); \ } while (0) #define DOPRINT_END1(v) \ printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v)) #define DOPRINT_END2(hi, lo) \ printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \ (long double)(hi), (long double)(lo)) #endif /* DOPRINT_LD80 */ #else /* !DOPRINT */ #define DOPRINT_START(xp) #define DOPRINT_END1(v) #define DOPRINT_END2(hi, lo) #endif /* DOPRINT */ #define RETURNP(x) do { \ DOPRINT_END1(x); \ RETURNF(x); \ } while (0) #define RETURNPI(x) do { \ DOPRINT_END1(x); \ RETURNI(x); \ } while (0) #define RETURN2P(x, y) do { \ DOPRINT_END2((x), (y)); \ RETURNF((x) + (y)); \ } while (0) #define RETURN2PI(x, y) do { \ DOPRINT_END2((x), (y)); \ RETURNI((x) + (y)); \ } while (0) #ifdef STRUCT_RETURN #define RETURNSP(rp) do { \ if (!(rp)->lo_set) \ RETURNP((rp)->hi); \ RETURN2P((rp)->hi, (rp)->lo); \ } while (0) #define RETURNSPI(rp) do { \ if (!(rp)->lo_set) \ RETURNPI((rp)->hi); \ RETURN2PI((rp)->hi, (rp)->lo); \ } while (0) #endif #define SUM2P(x, y) ({ \ const __typeof (x) __x = (x); \ const __typeof (y) __y = (y); \ \ DOPRINT_END2(__x, __y); \ __x + __y; \ }) /* * ieee style elementary functions * * We rename functions here to improve other sources' diffability * against fdlibm. */ #define __ieee754_sqrt sqrt #define __ieee754_acos acos #define __ieee754_acosh acosh #define __ieee754_log log #define __ieee754_log2 log2 #define __ieee754_atanh atanh #define __ieee754_asin asin #define __ieee754_atan2 atan2 #define __ieee754_exp exp #define __ieee754_cosh cosh #define __ieee754_fmod fmod #define __ieee754_pow pow #define __ieee754_lgamma lgamma #define __ieee754_gamma gamma #define __ieee754_lgamma_r lgamma_r #define __ieee754_gamma_r gamma_r #define __ieee754_log10 log10 #define __ieee754_sinh sinh #define __ieee754_hypot hypot #define __ieee754_j0 j0 #define __ieee754_j1 j1 #define __ieee754_y0 y0 #define __ieee754_y1 y1 #define __ieee754_jn jn #define __ieee754_yn yn #define __ieee754_remainder remainder #define __ieee754_scalb scalb #define __ieee754_sqrtf sqrtf #define __ieee754_acosf acosf #define __ieee754_acoshf acoshf #define __ieee754_logf logf #define __ieee754_atanhf atanhf #define __ieee754_asinf asinf #define __ieee754_atan2f atan2f #define __ieee754_expf expf #define __ieee754_coshf coshf #define __ieee754_fmodf fmodf #define __ieee754_powf powf #define __ieee754_lgammaf lgammaf #define __ieee754_gammaf gammaf #define __ieee754_lgammaf_r lgammaf_r #define __ieee754_gammaf_r gammaf_r #define __ieee754_log10f log10f #define __ieee754_log2f log2f #define __ieee754_sinhf sinhf #define __ieee754_hypotf hypotf #define __ieee754_j0f j0f #define __ieee754_j1f j1f #define __ieee754_y0f y0f #define __ieee754_y1f y1f #define __ieee754_jnf jnf #define __ieee754_ynf ynf #define __ieee754_remainderf remainderf #define __ieee754_scalbf scalbf /* fdlibm kernel function */ int __kernel_rem_pio2(double*,double*,int,int,int); /* double precision kernel functions */ #ifndef INLINE_REM_PIO2 int __ieee754_rem_pio2(double,double*); #endif double __kernel_sin(double,double,int); double __kernel_cos(double,double); double __kernel_tan(double,double,int); double __ldexp_exp(double,int); #ifdef _COMPLEX_H double complex __ldexp_cexp(double complex,int); #endif /* float precision kernel functions */ #ifndef INLINE_REM_PIO2F int __ieee754_rem_pio2f(float,double*); #endif #ifndef INLINE_KERNEL_SINDF float __kernel_sindf(double); #endif #ifndef INLINE_KERNEL_COSDF float __kernel_cosdf(double); #endif #ifndef INLINE_KERNEL_TANDF float __kernel_tandf(double,int); #endif float __ldexp_expf(float,int); #ifdef _COMPLEX_H float complex __ldexp_cexpf(float complex,int); #endif /* long double precision kernel functions */ long double __kernel_sinl(long double, long double, int); long double __kernel_cosl(long double, long double); long double __kernel_tanl(long double, long double, int); #endif /* !_MATH_PRIVATE_H_ */ Index: head/lib/msun/src/s_remquo.c =================================================================== --- head/lib/msun/src/s_remquo.c (revision 336662) +++ head/lib/msun/src/s_remquo.c (revision 336663) @@ -1,159 +1,159 @@ /* @(#)e_fmod.c 1.3 95/01/18 */ /*- * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); #include #include "math.h" #include "math_private.h" static const double Zero[] = {0.0, -0.0,}; /* * Return the IEEE remainder and set *quo to the last n bits of the * quotient, rounded to the nearest integer. We choose n=31 because * we wind up computing all the integer bits of the quotient anyway as * a side-effect of computing the remainder by the shift and subtract * method. In practice, this is far more bits than are needed to use * remquo in reduction algorithms. */ double remquo(double x, double y, int *quo) { int32_t n,hx,hy,hz,ix,iy,sx,i; u_int32_t lx,ly,lz,q,sxy; EXTRACT_WORDS(hx,lx,x); EXTRACT_WORDS(hy,ly,y); sxy = (hx ^ hy) & 0x80000000; sx = hx&0x80000000; /* sign of x */ hx ^=sx; /* |x| */ hy &= 0x7fffffff; /* |y| */ /* purge off exception values */ if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ - return nan_mix(x, y)/nan_mix(x, y); + return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); if(hx<=hy) { if((hx>31]; /* |x|=|y| return x*0*/ } } /* determine ix = ilogb(x) */ if(hx<0x00100000) { /* subnormal x */ if(hx==0) { for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; } else { for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; } } else ix = (hx>>20)-1023; /* determine iy = ilogb(y) */ if(hy<0x00100000) { /* subnormal y */ if(hy==0) { for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; } else { for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; } } else iy = (hy>>20)-1023; /* set up {hx,lx}, {hy,ly} and align y to x */ if(ix >= -1022) hx = 0x00100000|(0x000fffff&hx); else { /* subnormal x, shift x to normal */ n = -1022-ix; if(n<=31) { hx = (hx<>(32-n)); lx <<= n; } else { hx = lx<<(n-32); lx = 0; } } if(iy >= -1022) hy = 0x00100000|(0x000fffff&hy); else { /* subnormal y, shift y to normal */ n = -1022-iy; if(n<=31) { hy = (hy<>(32-n)); ly <<= n; } else { hy = ly<<(n-32); ly = 0; } } /* fix point fmod */ n = ix - iy; q = 0; while(n--) { hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} q <<= 1; } hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;q++;} /* convert back to floating value and restore the sign */ if((hx|lx)==0) { /* return sign(x)*0 */ q &= 0x7fffffff; *quo = (sxy ? -q : q); return Zero[(u_int32_t)sx>>31]; } while(hx<0x00100000) { /* normalize x */ hx = hx+hx+(lx>>31); lx = lx+lx; iy -= 1; } if(iy>= -1022) { /* normalize output */ hx = ((hx-0x00100000)|((iy+1023)<<20)); } else { /* subnormal output */ n = -1022 - iy; if(n<=20) { lx = (lx>>n)|((u_int32_t)hx<<(32-n)); hx >>= n; } else if (n<=31) { lx = (hx<<(32-n))|(lx>>n); hx = 0; } else { lx = hx>>(n-32); hx = 0; } } fixup: INSERT_WORDS(x,hx,lx); y = fabs(y); if (y < 0x1p-1021) { if (x+x>y || (x+x==y && (q & 1))) { q++; x-=y; } } else if (x>0.5*y || (x==0.5*y && (q & 1))) { q++; x-=y; } GET_HIGH_WORD(hx,x); SET_HIGH_WORD(x,hx^sx); q &= 0x7fffffff; *quo = (sxy ? -q : q); return x; } #if LDBL_MANT_DIG == 53 __weak_reference(remquo, remquol); #endif Index: head/lib/msun/src/s_remquof.c =================================================================== --- head/lib/msun/src/s_remquof.c (revision 336662) +++ head/lib/msun/src/s_remquof.c (revision 336663) @@ -1,122 +1,122 @@ /* @(#)e_fmod.c 1.3 95/01/18 */ /*- * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" static const float Zero[] = {0.0, -0.0,}; /* * Return the IEEE remainder and set *quo to the last n bits of the * quotient, rounded to the nearest integer. We choose n=31 because * we wind up computing all the integer bits of the quotient anyway as * a side-effect of computing the remainder by the shift and subtract * method. In practice, this is far more bits than are needed to use * remquo in reduction algorithms. */ float remquof(float x, float y, int *quo) { int32_t n,hx,hy,hz,ix,iy,sx,i; u_int32_t q,sxy; GET_FLOAT_WORD(hx,x); GET_FLOAT_WORD(hy,y); sxy = (hx ^ hy) & 0x80000000; sx = hx&0x80000000; /* sign of x */ hx ^=sx; /* |x| */ hy &= 0x7fffffff; /* |y| */ /* purge off exception values */ if(hy==0||hx>=0x7f800000||hy>0x7f800000) /* y=0,NaN;or x not finite */ - return nan_mix(x, y)/nan_mix(x, y); + return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); if(hx>31]; /* |x|=|y| return x*0*/ } /* determine ix = ilogb(x) */ if(hx<0x00800000) { /* subnormal x */ for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; } else ix = (hx>>23)-127; /* determine iy = ilogb(y) */ if(hy<0x00800000) { /* subnormal y */ for (iy = -126,i=(hy<<8); i>0; i<<=1) iy -=1; } else iy = (hy>>23)-127; /* set up {hx,lx}, {hy,ly} and align y to x */ if(ix >= -126) hx = 0x00800000|(0x007fffff&hx); else { /* subnormal x, shift x to normal */ n = -126-ix; hx <<= n; } if(iy >= -126) hy = 0x00800000|(0x007fffff&hy); else { /* subnormal y, shift y to normal */ n = -126-iy; hy <<= n; } /* fix point fmod */ n = ix - iy; q = 0; while(n--) { hz=hx-hy; if(hz<0) hx = hx << 1; else {hx = hz << 1; q++;} q <<= 1; } hz=hx-hy; if(hz>=0) {hx=hz;q++;} /* convert back to floating value and restore the sign */ if(hx==0) { /* return sign(x)*0 */ q &= 0x7fffffff; *quo = (sxy ? -q : q); return Zero[(u_int32_t)sx>>31]; } while(hx<0x00800000) { /* normalize x */ hx <<= 1; iy -= 1; } if(iy>= -126) { /* normalize output */ hx = ((hx-0x00800000)|((iy+127)<<23)); } else { /* subnormal output */ n = -126 - iy; hx >>= n; } fixup: SET_FLOAT_WORD(x,hx); y = fabsf(y); if (y < 0x1p-125f) { if (x+x>y || (x+x==y && (q & 1))) { q++; x-=y; } } else if (x>0.5f*y || (x==0.5f*y && (q & 1))) { q++; x-=y; } GET_FLOAT_WORD(hx,x); SET_FLOAT_WORD(x,hx^sx); q &= 0x7fffffff; *quo = (sxy ? -q : q); return x; } Index: head/lib/msun/src/s_remquol.c =================================================================== --- head/lib/msun/src/s_remquol.c (revision 336662) +++ head/lib/msun/src/s_remquol.c (revision 336663) @@ -1,178 +1,178 @@ /* @(#)e_fmod.c 1.3 95/01/18 */ /*- * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include __FBSDID("$FreeBSD$"); #include #include #include "fpmath.h" #include "math.h" #include "math_private.h" #define BIAS (LDBL_MAX_EXP - 1) #if LDBL_MANL_SIZE > 32 typedef uint64_t manl_t; #else typedef uint32_t manl_t; #endif #if LDBL_MANH_SIZE > 32 typedef uint64_t manh_t; #else typedef uint32_t manh_t; #endif /* * These macros add and remove an explicit integer bit in front of the * fractional mantissa, if the architecture doesn't have such a bit by * default already. */ #ifdef LDBL_IMPLICIT_NBIT #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) #define HFRAC_BITS LDBL_MANH_SIZE #else #define SET_NBIT(hx) (hx) #define HFRAC_BITS (LDBL_MANH_SIZE - 1) #endif #define MANL_SHIFT (LDBL_MANL_SIZE - 1) static const long double Zero[] = {0.0L, -0.0L}; /* * Return the IEEE remainder and set *quo to the last n bits of the * quotient, rounded to the nearest integer. We choose n=31 because * we wind up computing all the integer bits of the quotient anyway as * a side-effect of computing the remainder by the shift and subtract * method. In practice, this is far more bits than are needed to use * remquo in reduction algorithms. * * Assumptions: * - The low part of the mantissa fits in a manl_t exactly. * - The high part of the mantissa fits in an int64_t with enough room * for an explicit integer bit in front of the fractional bits. */ long double remquol(long double x, long double y, int *quo) { union IEEEl2bits ux, uy; int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ manh_t hy; manl_t lx,ly,lz; int ix,iy,n,q,sx,sxy; ux.e = x; uy.e = y; sx = ux.bits.sign; sxy = sx ^ uy.bits.sign; ux.bits.sign = 0; /* |x| */ uy.bits.sign = 0; /* |y| */ x = ux.e; /* purge off exception values */ if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ (uy.bits.exp == BIAS + LDBL_MAX_EXP && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ - return nan_mix(x, y)/nan_mix(x, y); + return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); if(ux.bits.exp<=uy.bits.exp) { if((ux.bits.exp>MANL_SHIFT); lx = lx+lx;} else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} q <<= 1; } hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;q++;} /* convert back to floating value and restore the sign */ if((hx|lx)==0) { /* return sign(x)*0 */ q &= 0x7fffffff; *quo = (sxy ? -q : q); return Zero[sx]; } while(hx<(1ULL<>MANL_SHIFT); lx = lx+lx; iy -= 1; } ux.bits.manh = hx; /* The integer bit is truncated here if needed. */ ux.bits.manl = lx; if (iy < LDBL_MIN_EXP) { ux.bits.exp = iy + (BIAS + 512); ux.e *= 0x1p-512; } else { ux.bits.exp = iy + BIAS; } ux.bits.sign = 0; x = ux.e; fixup: y = fabsl(y); if (y < LDBL_MIN * 2) { if (x+x>y || (x+x==y && (q & 1))) { q++; x-=y; } } else if (x>0.5*y || (x==0.5*y && (q & 1))) { q++; x-=y; } ux.e = x; ux.bits.sign ^= sx; x = ux.e; q &= 0x7fffffff; *quo = (sxy ? -q : q); return x; }