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

* 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

1 files changed, 51 insertions, 128 deletions

diff --git a/src/math/fmod.c b/src/math/fmod.c
index 84a1b4ac..6849722b 100644
--- a/src/math/fmod.c
+++ b/src/math/fmod.c
@@ -1,145 +1,68 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_fmod.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * fmod(x,y)
- * Return x mod y in exact arithmetic
- * Method: shift and subtract
- */
-
-#include "libm.h"
-
-static const double Zero[] = {0.0, -0.0,};
+#include <math.h>
+#include <stdint.h>
 
 double fmod(double x, double y)
 {
-	int32_t n,hx,hy,hz,ix,iy,sx,i;
-	uint32_t lx,ly,lz;
+	union {double f; uint64_t i;} ux = {x}, uy = {y};
+	int ex = ux.i>>52 & 0x7ff;
+	int ey = uy.i>>52 & 0x7ff;
+	int sx = ux.i>>63;
+	uint64_t i;
 
-	EXTRACT_WORDS(hx, lx, x);
-	EXTRACT_WORDS(hy, ly, y);
-	sx = hx & 0x80000000;  /* sign of x */
-	hx ^= sx;              /* |x| */
-	hy &= 0x7fffffff;      /* |y| */
+	/* in the followings uxi should be ux.i, but then gcc wrongly adds */
+	/* float load/store to inner loops ruining performance and code size */
+	uint64_t uxi = ux.i;
 
-	/* 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 */
+	if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
 		return (x*y)/(x*y);
-	if (hx <= hy) {
-		if (hx < hy || lx < ly)  /* |x| < |y| */
-			return x;
-		if (lx == ly)            /* |x| = |y|, return x*0 */
-			return Zero[(uint32_t)sx>>31];
+	if (uxi<<1 <= uy.i<<1) {
+		if (uxi<<1 == uy.i<<1)
+			return 0*x;
+		return x;
 	}
 
-	/* 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;
-		}
+	/* normalize x and y */
+	if (!ex) {
+		for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1);
+		uxi <<= -ex + 1;
+	} else {
+		uxi &= -1ULL >> 12;
+		uxi |= 1ULL << 52;
 	}
-	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;
-		}
+	if (!ey) {
+		for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1);
+		uy.i <<= -ey + 1;
+	} else {
+		uy.i &= -1ULL >> 12;
+		uy.i |= 1ULL << 52;
 	}
 
-	/* fix point fmod */
-	n = ix - iy;
-	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 {
-			if ((hz|lz) == 0)   /* return sign(x)*0 */
-				return Zero[(uint32_t)sx>>31];
-			hx = hz+hz+(lz>>31);
-			lx = lz+lz;
+	/* x mod y */
+	for (; ex > ey; ex--) {
+		i = uxi - uy.i;
+		if (i >> 63 == 0) {
+			if (i == 0)
+				return 0*x;
+			uxi = i;
 		}
+		uxi <<= 1;
 	}
-	hz = hx-hy;
-	lz = lx-ly;
-	if (lx < ly)
-		hz -= 1;
-	if (hz >= 0) {
-		hx = hz;
-		lx = lz;
+	i = uxi - uy.i;
+	if (i >> 63 == 0) {
+		if (i == 0)
+			return 0*x;
+		uxi = i;
 	}
+	for (; uxi>>52 == 0; uxi <<= 1, ex--);
 
-	/* convert back to floating value and restore the sign */
-	if ((hx|lx) == 0)          /* return sign(x)*0 */
-		return Zero[(uint32_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)|((uint32_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);
+	/* scale result */
+	if (ex > 0) {
+		uxi -= 1ULL << 52;
+		uxi |= (uint64_t)ex << 52;
+	} else {
+		uxi >>= -ex + 1;
 	}
-	return x;  /* exact output */
+	uxi |= (uint64_t)sx << 63;
+	ux.i = uxi;
+	return ux.f;
 }