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math: rewrite remainder functions (remainder, remquo, fmod, modf)

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* results are exact
* modfl follows truncl (raises inexact flag spuriously now)
* modf and modff only had cosmetic cleanup
* remainder is just a wrapper around remquo now
* using iterative shift+subtract for remquo and fmod
* ld80 and ld128 are supported as well
This commit is contained in:
Szabolcs Nagy
2013-09-03 04:09:12 +00:00
parent d1a2ead878
commit ee2ee92d62
11 changed files with 481 additions and 1019 deletions
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143
src/math/fmodf.c
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@ -1,104 +1,65 @@
/* origin: FreeBSD /usr/src/lib/msun/src/e_fmodf.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.
* ====================================================
*/
/*
* fmodf(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include "libm.h"
static const float Zero[] = {0.0, -0.0,};
#include <math.h>
#include <stdint.h>
float fmodf(float x, float y)
{
int32_t n,hx,hy,hz,ix,iy,sx,i;
union {float f; uint32_t i;} ux = {x}, uy = {y};
int ex = ux.i>>23 & 0xff;
int ey = uy.i>>23 & 0xff;
uint32_t sx = ux.i & 0x80000000;
uint32_t i;
uint32_t uxi = ux.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 */
if (uy.i<<1 == 0 || isnan(y) || ex == 0xff)
return (x*y)/(x*y);
if (hx < hy) /* |x| < |y| */
if (uxi<<1 <= uy.i<<1) {
if (uxi<<1 == uy.i<<1)
return 0*x;
return x;
if (hx == hy) /* |x| = |y|, return x*0 */
return Zero[(uint32_t)sx>>31];
/* 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<<n;
}
if (iy >= -126)
hy = 0x00800000|(0x007fffff&hy);
else { /* subnormal y, shift y to normal */
n = -126-iy;
hy = hy<<n;
}
/* fix point fmod */
n = ix - iy;
while (n--) {
hz = hx-hy;
if (hz<0)
hx = hx+hx;
else {
if(hz == 0) /* return sign(x)*0 */
return Zero[(uint32_t)sx>>31];
hx = hz+hz;
/* normalize x and y */
if (!ex) {
for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1);
uxi <<= -ex + 1;
} else {
uxi &= -1U >> 9;
uxi |= 1U << 23;
}
if (!ey) {
for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1);
uy.i <<= -ey + 1;
} else {
uy.i &= -1U >> 9;
uy.i |= 1U << 23;
}
/* x mod y */
for (; ex > ey; ex--) {
i = uxi - uy.i;
if (i >> 31 == 0) {
if (i == 0)
return 0*x;
uxi = i;
}
uxi <<= 1;
}
hz = hx-hy;
if (hz >= 0)
hx = hz;
i = uxi - uy.i;
if (i >> 31 == 0) {
if (i == 0)
return 0*x;
uxi = i;
}
for (; uxi>>23 == 0; uxi <<= 1, ex--);
/* convert back to floating value and restore the sign */
if (hx == 0) /* return sign(x)*0 */
return Zero[(uint32_t)sx>>31];
while (hx < 0x00800000) { /* normalize x */
hx = hx+hx;
iy -= 1;
/* scale result up */
if (ex > 0) {
uxi -= 1U << 23;
uxi |= (uint32_t)ex << 23;
} else {
uxi >>= -ex + 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);
}
return x; /* exact output */
uxi |= sx;
ux.i = uxi;
return ux.f;
}