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, 266 insertions, 0 deletions

diff --git a/src/math/fmal.c b/src/math/fmal.c
new file mode 100644
index 00000000..200bd5a5
--- /dev/null
+++ b/src/math/fmal.c
@@ -0,0 +1,266 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_fmal.c */
+/*-
+ * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "libm.h"
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double fmal(long double x, long double y, long double z)
+{
+	return fma(x, y, z);
+}
+#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#include <fenv.h>
+
+/*
+ * A struct dd represents a floating-point number with twice the precision
+ * of a long double.  We maintain the invariant that "hi" stores the high-order
+ * bits of the result.
+ */
+struct dd {
+	long double hi;
+	long double lo;
+};
+
+/*
+ * Compute a+b exactly, returning the exact result in a struct dd.  We assume
+ * that both a and b are finite, but make no assumptions about their relative
+ * magnitudes.
+ */
+static inline struct dd dd_add(long double a, long double b)
+{
+	struct dd ret;
+	long double s;
+
+	ret.hi = a + b;
+	s = ret.hi - a;
+	ret.lo = (a - (ret.hi - s)) + (b - s);
+	return (ret);
+}
+
+/*
+ * Compute a+b, with a small tweak:  The least significant bit of the
+ * result is adjusted into a sticky bit summarizing all the bits that
+ * were lost to rounding.  This adjustment negates the effects of double
+ * rounding when the result is added to another number with a higher
+ * exponent.  For an explanation of round and sticky bits, see any reference
+ * on FPU design, e.g.,
+ *
+ *     J. Coonen.  An Implementation Guide to a Proposed Standard for
+ *     Floating-Point Arithmetic.  Computer, vol. 13, no. 1, Jan 1980.
+ */
+static inline long double add_adjusted(long double a, long double b)
+{
+	struct dd sum;
+	union IEEEl2bits u;
+
+	sum = dd_add(a, b);
+	if (sum.lo != 0) {
+		u.e = sum.hi;
+		if ((u.bits.manl & 1) == 0)
+			sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
+	}
+	return (sum.hi);
+}
+
+/*
+ * Compute ldexp(a+b, scale) with a single rounding error. It is assumed
+ * that the result will be subnormal, and care is taken to ensure that
+ * double rounding does not occur.
+ */
+static inline long double add_and_denormalize(long double a, long double b, int scale)
+{
+	struct dd sum;
+	int bits_lost;
+	union IEEEl2bits u;
+
+	sum = dd_add(a, b);
+
+	/*
+	 * If we are losing at least two bits of accuracy to denormalization,
+	 * then the first lost bit becomes a round bit, and we adjust the
+	 * lowest bit of sum.hi to make it a sticky bit summarizing all the
+	 * bits in sum.lo. With the sticky bit adjusted, the hardware will
+	 * break any ties in the correct direction.
+	 *
+	 * If we are losing only one bit to denormalization, however, we must
+	 * break the ties manually.
+	 */
+	if (sum.lo != 0) {
+		u.e = sum.hi;
+		bits_lost = -u.bits.exp - scale + 1;
+		if (bits_lost != 1 ^ (int)(u.bits.manl & 1))
+			sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
+	}
+	return (ldexp(sum.hi, scale));
+}
+
+/*
+ * Compute a*b exactly, returning the exact result in a struct dd.  We assume
+ * that both a and b are normalized, so no underflow or overflow will occur.
+ * The current rounding mode must be round-to-nearest.
+ */
+static inline struct dd dd_mul(long double a, long double b)
+{
+#if LDBL_MANT_DIG == 64
+	static const long double split = 0x1p32L + 1.0;
+#elif LDBL_MANT_DIG == 113
+	static const long double split = 0x1p57L + 1.0;
+#endif
+	struct dd ret;
+	long double ha, hb, la, lb, p, q;
+
+	p = a * split;
+	ha = a - p;
+	ha += p;
+	la = a - ha;
+
+	p = b * split;
+	hb = b - p;
+	hb += p;
+	lb = b - hb;
+
+	p = ha * hb;
+	q = ha * lb + la * hb;
+
+	ret.hi = p + q;
+	ret.lo = p - ret.hi + q + la * lb;
+	return (ret);
+}
+
+/*
+ * Fused multiply-add: Compute x * y + z with a single rounding error.
+ *
+ * We use scaling to avoid overflow/underflow, along with the
+ * canonical precision-doubling technique adapted from:
+ *
+ *      Dekker, T.  A Floating-Point Technique for Extending the
+ *      Available Precision.  Numer. Math. 18, 224-242 (1971).
+ */
+long double fmal(long double x, long double y, long double z)
+{
+	long double xs, ys, zs, adj;
+	struct dd xy, r;
+	int oround;
+	int ex, ey, ez;
+	int spread;
+
+	/*
+	 * Handle special cases. The order of operations and the particular
+	 * return values here are crucial in handling special cases involving
+	 * infinities, NaNs, overflows, and signed zeroes correctly.
+	 */
+	if (x == 0.0 || y == 0.0)
+		return (x * y + z);
+	if (z == 0.0)
+		return (x * y);
+	if (!isfinite(x) || !isfinite(y))
+		return (x * y + z);
+	if (!isfinite(z))
+		return (z);
+
+	xs = frexpl(x, &ex);
+	ys = frexpl(y, &ey);
+	zs = frexpl(z, &ez);
+	oround = fegetround();
+	spread = ex + ey - ez;
+
+	/*
+	 * If x * y and z are many orders of magnitude apart, the scaling
+	 * will overflow, so we handle these cases specially.  Rounding
+	 * modes other than FE_TONEAREST are painful.
+	 */
+	if (spread < -LDBL_MANT_DIG) {
+		feraiseexcept(FE_INEXACT);
+		if (!isnormal(z))
+			feraiseexcept(FE_UNDERFLOW);
+		switch (oround) {
+		case FE_TONEAREST:
+			return (z);
+		case FE_TOWARDZERO:
+			if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
+				return (z);
+			else
+				return (nextafterl(z, 0));
+		case FE_DOWNWARD:
+			if (x > 0.0 ^ y < 0.0)
+				return (z);
+			else
+				return (nextafterl(z, -INFINITY));
+		default:        /* FE_UPWARD */
+			if (x > 0.0 ^ y < 0.0)
+				return (nextafterl(z, INFINITY));
+			else
+				return (z);
+		}
+	}
+	if (spread <= LDBL_MANT_DIG * 2)
+		zs = ldexpl(zs, -spread);
+	else
+		zs = copysignl(LDBL_MIN, zs);
+
+	fesetround(FE_TONEAREST);
+
+	/*
+	 * Basic approach for round-to-nearest:
+	 *
+	 *     (xy.hi, xy.lo) = x * y           (exact)
+	 *     (r.hi, r.lo)   = xy.hi + z       (exact)
+	 *     adj = xy.lo + r.lo               (inexact; low bit is sticky)
+	 *     result = r.hi + adj              (correctly rounded)
+	 */
+	xy = dd_mul(xs, ys);
+	r = dd_add(xy.hi, zs);
+
+	spread = ex + ey;
+
+	if (r.hi == 0.0) {
+		/*
+		 * When the addends cancel to 0, ensure that the result has
+		 * the correct sign.
+		 */
+		fesetround(oround);
+		volatile long double vzs = zs; /* XXX gcc CSE bug workaround */
+		return (xy.hi + vzs + ldexpl(xy.lo, spread));
+	}
+
+	if (oround != FE_TONEAREST) {
+		/*
+		 * There is no need to worry about double rounding in directed
+		 * rounding modes.
+		 */
+		fesetround(oround);
+		adj = r.lo + xy.lo;
+		return (ldexpl(r.hi + adj, spread));
+	}
+
+	adj = add_adjusted(r.lo, xy.lo);
+	if (spread + ilogbl(r.hi) > -16383)
+		return (ldexpl(r.hi + adj, spread));
+	else
+		return (add_and_denormalize(r.hi, adj, spread));
+}
+#endif