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, 80 insertions, 133 deletions

diff --git a/src/math/fmodl.c b/src/math/fmodl.c
index b930c49d..54af6a3f 100644
--- a/src/math/fmodl.c
+++ b/src/math/fmodl.c
@@ -1,15 +1,3 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_fmodl.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.
- * ====================================================
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -18,141 +6,100 @@ long double fmodl(long double x, long double y)
 	return fmod(x, y);
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-
-#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[] = {0.0, -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;
+	union ldshape ux = {x}, uy = {y};
+	int ex = ux.i.se & 0x7fff;
+	int ey = uy.i.se & 0x7fff;
+	int sx = ux.i.se & 0x8000;
 
-	/* 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 */
+	if (y == 0 || isnan(y) || ex == 0x7fff)
 		return (x*y)/(x*y);
-	if (ux.bits.exp <= uy.bits.exp) {
-		if (ux.bits.exp < uy.bits.exp ||
-		    (ux.bits.manh<=uy.bits.manh &&
-		     (ux.bits.manh<uy.bits.manh ||
-		      ux.bits.manl<uy.bits.manl)))  /* |x|<|y| return x or x-y */
-			return x;
-		if (ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl)
-			return Zero[sx];  /* |x| = |y| return x*0 */
+	ux.i.se = ex;
+	uy.i.se = ey;
+	if (ux.f <= uy.f) {
+		if (ux.f == uy.f)
+			return 0*x;
+		return x;
 	}
 
-	/* determine ix = ilogb(x) */
-	if (ux.bits.exp == 0) {  /* subnormal x */
-		ux.e *= 0x1.0p512;
-		ix = ux.bits.exp - (BIAS + 512);
-	} else {
-		ix = ux.bits.exp - BIAS;
+	/* normalize x and y */
+	if (!ex) {
+		ux.f *= 0x1p120f;
+		ex = ux.i.se - 120;
 	}
-
-	/* determine iy = ilogb(y) */
-	if (uy.bits.exp == 0) {  /* subnormal y */
-		uy.e *= 0x1.0p512;
-		iy = uy.bits.exp - (BIAS + 512);
-	} else {
-		iy = uy.bits.exp - BIAS;
+	if (!ey) {
+		uy.f *= 0x1p120f;
+		ey = uy.i.se - 120;
 	}
 
-	/* set up {hx,lx}, {hy,ly} and align y to x */
-	hx = SET_NBIT(ux.bits.manh);
-	hy = SET_NBIT(uy.bits.manh);
-	lx = ux.bits.manl;
-	ly = uy.bits.manl;
-
-	/* 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>>MANL_SHIFT);
-			lx = lx+lx;
+	/* x mod y */
+#if LDBL_MANT_DIG == 64
+	uint64_t i, mx, my;
+	mx = ux.i.m;
+	my = uy.i.m;
+	for (; ex > ey; ex--) {
+		i = mx - my;
+		if (mx >= my) {
+			if (i == 0)
+				return 0*x;
+			mx = 2*i;
+		} else if (2*mx < mx) {
+			mx = 2*mx - my;
 		} else {
-			if ((hz|lz)==0)   /* return sign(x)*0 */
-				return Zero[sx];
-			hx = hz+hz+(lz>>MANL_SHIFT);
-			lx = lz+lz;
+			mx = 2*mx;
 		}
 	}
-	hz = hx-hy;
-	lz = lx-ly;
-	if (lx < ly)
-		hz -= 1;
-	if (hz >= 0) {
-		hx = hz;
-		lx = lz;
+	i = mx - my;
+	if (mx >= my) {
+		if (i == 0)
+			return 0*x;
+		mx = i;
 	}
-
-	/* convert back to floating value and restore the sign */
-	if ((hx|lx) == 0)   /* return sign(x)*0 */
-		return Zero[sx];
-	while (hx < (1ULL<<HFRAC_BITS)) {  /* normalize x */
-		hx = hx+hx+(lx>>MANL_SHIFT);
-		lx = lx+lx;
-		iy -= 1;
+	for (; mx >> 63 == 0; mx *= 2, ex--);
+	ux.i.m = mx;
+#elif LDBL_MANT_DIG == 113
+	uint64_t hi, lo, xhi, xlo, yhi, ylo;
+	xhi = (ux.i2.hi & -1ULL>>16) | 1ULL<<48;
+	yhi = (uy.i2.hi & -1ULL>>16) | 1ULL<<48;
+	xlo = ux.i2.lo;
+	ylo = ux.i2.lo;
+	for (; ex > ey; ex--) {
+		hi = xhi - yhi;
+		lo = xlo - ylo;
+		if (xlo < ylo)
+			hi -= 1;
+		if (hi >> 63 == 0) {
+			if ((hi|lo) == 0)
+				return 0*x;
+			xhi = 2*hi + (lo>>63);
+			xlo = 2*lo;
+		} else {
+			xhi = 2*xhi + (xlo>>63);
+			xlo = 2*xlo;
+		}
 	}
-	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;
+	hi = xhi - yhi;
+	lo = xlo - ylo;
+	if (xlo < ylo)
+		hi -= 1;
+	if (hi >> 63 == 0) {
+		if ((hi|lo) == 0)
+			return 0*x;
+		xhi = hi;
+		xlo = lo;
 	}
-	return ux.e;       /* exact output */
+	for (; xhi >> 48 == 0; xhi = 2*xhi + (xlo>>63), xlo = 2*xlo, ex--);
+	ux.i2.hi = xhi;
+	ux.i2.lo = xlo;
+#endif
+
+	/* scale result */
+	if (ex <= 0) {
+		ux.i.se = (ex+120)|sx;
+		ux.f *= 0x1p-120f;
+	} else
+		ux.i.se = ex|sx;
+	return ux.f;
 }
 #endif