first commit of the new libm!

thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).

based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.

various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.

1 files changed, 159 insertions, 0 deletions

diff --git a/src/math/fmodl.c b/src/math/fmodl.c
new file mode 100644
index 00000000..2e3eec1f
--- /dev/null
+++ b/src/math/fmodl.c
@@ -0,0 +1,159 @@
+/* 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
+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 one = 1.0, 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;
+
+	/* 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 */
+		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 */
+	}
+
+	/* 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;
+	}
+
+	/* 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;
+	}
+
+	/* 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;
+		} else {
+			if ((hz|lz)==0)   /* return sign(x)*0 */
+				return Zero[sx];
+			hx = hz+hz+(lz>>MANL_SHIFT);
+			lx = lz+lz;
+		}
+	}
+	hz = hx-hy;
+	lz = lx-ly;
+	if (lx < ly)
+		hz -= 1;
+	if (hz >= 0) {
+		hx = hz;
+		lx = lz;
+	}
+
+	/* 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;
+	}
+	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;
+	}
+	x = ux.e * one;   /* create necessary signal */
+	return x;         /* exact output */
+}
+#endif