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, 50 insertions, 89 deletions

diff --git a/src/math/fmodf.c b/src/math/fmodf.c
index 837e9371..ff58f933 100644
--- a/src/math/fmodf.c
+++ b/src/math/fmodf.c
@@ -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;
+	/* 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 (iy >= -126)
-		hy = 0x00800000|(0x007fffff&hy);
-	else {          /* subnormal y, shift y to normal */
-		n = -126-iy;
-		hy = hy<<n;
+	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;
 	}
 
-	/* 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;
+	/* 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;
-
-	/* 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;
+	i = uxi - uy.i;
+	if (i >> 31 == 0) {
+		if (i == 0)
+			return 0*x;
+		uxi = i;
 	}
-	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);
+	for (; uxi>>23 == 0; uxi <<= 1, ex--);
+
+	/* scale result up */
+	if (ex > 0) {
+		uxi -= 1U << 23;
+		uxi |= (uint32_t)ex << 23;
+	} else {
+		uxi >>= -ex + 1;
 	}
-	return x;  /* exact output */
+	uxi |= sx;
+	ux.i = uxi;
+	return ux.f;
 }