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author | das <das@FreeBSD.org> | 2005-03-25 04:40:44 +0000 |
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committer | das <das@FreeBSD.org> | 2005-03-25 04:40:44 +0000 |
commit | da9b203aafc8ae8081f508c8c207f9711a8ca52c (patch) | |
tree | 3aa300f40f81faa485d0a27d5ad9fc8f018810b6 /lib/msun/src | |
parent | 947b14c9bfec56419ec1b06f736b6ef62efc37ad (diff) | |
download | FreeBSD-src-da9b203aafc8ae8081f508c8c207f9711a8ca52c.zip FreeBSD-src-da9b203aafc8ae8081f508c8c207f9711a8ca52c.tar.gz |
Implement and document remquo() and remquof().
Diffstat (limited to 'lib/msun/src')
-rw-r--r-- | lib/msun/src/math.h | 2 | ||||
-rw-r--r-- | lib/msun/src/s_remquo.c | 152 | ||||
-rw-r--r-- | lib/msun/src/s_remquof.c | 121 |
3 files changed, 275 insertions, 0 deletions
diff --git a/lib/msun/src/math.h b/lib/msun/src/math.h index 9b8f73c..b29ace2 100644 --- a/lib/msun/src/math.h +++ b/lib/msun/src/math.h @@ -239,6 +239,7 @@ long lrint(double); long lround(double); double nextafter(double, double); double remainder(double, double); +double remquo(double, double, int *); double rint(double); #endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */ @@ -341,6 +342,7 @@ long lroundf(float); float nearbyintf(float); float nextafterf(float, float); float remainderf(float, float); +float remquof(float, float, int *); float rintf(float); float scalblnf(float, long); float scalbnf(float, int); diff --git a/lib/msun/src/s_remquo.c b/lib/msun/src/s_remquo.c new file mode 100644 index 0000000..8756c2a --- /dev/null +++ b/lib/msun/src/s_remquo.c @@ -0,0 +1,152 @@ +/* @(#)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 <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +#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 (x*y)/(x*y); + if(hx<=hy) { + if((hx<hy)||(lx<ly)) { + q = 0; + goto fixup; /* |x|<|y| return x or x-y */ + } + if(lx==ly) { + *quo = 1; + return Zero[(u_int32_t)sx>>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<<n)|(lx>>(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<<n)|(ly>>(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<ly) hz -= 1; + if(hz<0){hx = hx+hx+(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<ly) hz -= 1; + if(hz>=0) {hx=hz;lx=lz;q++;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) { /* return sign(x)*0 */ + *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 = sx; + } else { + lx = hx>>(n-32); hx = sx; + } + } +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; +} diff --git a/lib/msun/src/s_remquof.c b/lib/msun/src/s_remquof.c new file mode 100644 index 0000000..3141642 --- /dev/null +++ b/lib/msun/src/s_remquof.c @@ -0,0 +1,121 @@ +/* @(#)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 <sys/cdefs.h> +__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 (x*y)/(x*y); + if(hx<hy) { + q = 0; + goto fixup; /* |x|<|y| return x or x-y */ + } else if(hx==hy) { + *quo = 1; + return Zero[(u_int32_t)sx>>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 */ + *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; +} |