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, 277 insertions, 0 deletions

diff --git a/src/math/exp2l.c b/src/math/exp2l.c
new file mode 100644
index 00000000..ce085a73
--- /dev/null
+++ b/src/math/exp2l.c
@@ -0,0 +1,277 @@
+/* origin: FreeBSD /usr/src/lib/msun/ld80/s_exp2l.c */
+/*-
+ * Copyright (c) 2005-2008 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 exp2l(long double x)
+{
+	return exp2l(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+
+#define TBLBITS 7
+#define TBLSIZE (1 << TBLBITS)
+
+#define BIAS    (LDBL_MAX_EXP - 1)
+#define EXPMASK (BIAS + LDBL_MAX_EXP)
+
+static const long double huge = 0x1p10000L;
+/* XXX Prevent gcc from erroneously constant folding this. */
+static volatile long double twom10000 = 0x1p-10000L;
+
+static const double
+redux = 0x1.8p63 / TBLSIZE,
+P1    = 0x1.62e42fefa39efp-1,
+P2    = 0x1.ebfbdff82c58fp-3,
+P3    = 0x1.c6b08d7049fap-5,
+P4    = 0x1.3b2ab6fba4da5p-7,
+P5    = 0x1.5d8804780a736p-10,
+P6    = 0x1.430918835e33dp-13;
+
+static const double tbl[TBLSIZE * 2] = {
+	0x1.6a09e667f3bcdp-1,   -0x1.bdd3413b2648p-55,
+	0x1.6c012750bdabfp-1,   -0x1.2895667ff0cp-57,
+	0x1.6dfb23c651a2fp-1,   -0x1.bbe3a683c88p-58,
+	0x1.6ff7df9519484p-1,   -0x1.83c0f25860fp-56,
+	0x1.71f75e8ec5f74p-1,   -0x1.16e4786887bp-56,
+	0x1.73f9a48a58174p-1,   -0x1.0a8d96c65d5p-55,
+	0x1.75feb564267c9p-1,   -0x1.0245957316ep-55,
+	0x1.780694fde5d3fp-1,    0x1.866b80a0216p-55,
+	0x1.7a11473eb0187p-1,   -0x1.41577ee0499p-56,
+	0x1.7c1ed0130c132p-1,    0x1.f124cd1164ep-55,
+	0x1.7e2f336cf4e62p-1,    0x1.05d02ba157ap-57,
+	0x1.80427543e1a12p-1,   -0x1.27c86626d97p-55,
+	0x1.82589994cce13p-1,   -0x1.d4c1dd41533p-55,
+	0x1.8471a4623c7adp-1,   -0x1.8d684a341cep-56,
+	0x1.868d99b4492edp-1,   -0x1.fc6f89bd4f68p-55,
+	0x1.88ac7d98a6699p-1,    0x1.994c2f37cb5p-55,
+	0x1.8ace5422aa0dbp-1,    0x1.6e9f156864bp-55,
+	0x1.8cf3216b5448cp-1,   -0x1.0d55e32e9e4p-57,
+	0x1.8f1ae99157736p-1,    0x1.5cc13a2e397p-56,
+	0x1.9145b0b91ffc6p-1,   -0x1.dd6792e5825p-55,
+	0x1.93737b0cdc5e5p-1,   -0x1.75fc781b58p-58,
+	0x1.95a44cbc8520fp-1,   -0x1.64b7c96a5fp-57,
+	0x1.97d829fde4e5p-1,    -0x1.d185b7c1b86p-55,
+	0x1.9a0f170ca07bap-1,   -0x1.173bd91cee6p-55,
+	0x1.9c49182a3f09p-1,     0x1.c7c46b071f2p-57,
+	0x1.9e86319e32323p-1,    0x1.824ca78e64cp-57,
+	0x1.a0c667b5de565p-1,   -0x1.359495d1cd5p-55,
+	0x1.a309bec4a2d33p-1,    0x1.6305c7ddc368p-55,
+	0x1.a5503b23e255dp-1,   -0x1.d2f6edb8d42p-55,
+	0x1.a799e1330b358p-1,    0x1.bcb7ecac564p-55,
+	0x1.a9e6b5579fdbfp-1,    0x1.0fac90ef7fdp-55,
+	0x1.ac36bbfd3f37ap-1,   -0x1.f9234cae76dp-56,
+	0x1.ae89f995ad3adp-1,    0x1.7a1cd345dcc8p-55,
+	0x1.b0e07298db666p-1,   -0x1.bdef54c80e4p-55,
+	0x1.b33a2b84f15fbp-1,   -0x1.2805e3084d8p-58,
+	0x1.b59728de5593ap-1,   -0x1.c71dfbbba6ep-55,
+	0x1.b7f76f2fb5e47p-1,   -0x1.5584f7e54acp-57,
+	0x1.ba5b030a1064ap-1,   -0x1.efcd30e5429p-55,
+	0x1.bcc1e904bc1d2p-1,    0x1.23dd07a2d9fp-56,
+	0x1.bf2c25bd71e09p-1,   -0x1.efdca3f6b9c8p-55,
+	0x1.c199bdd85529cp-1,    0x1.11065895049p-56,
+	0x1.c40ab5fffd07ap-1,    0x1.b4537e083c6p-55,
+	0x1.c67f12e57d14bp-1,    0x1.2884dff483c8p-55,
+	0x1.c8f6d9406e7b5p-1,    0x1.1acbc48805cp-57,
+	0x1.cb720dcef9069p-1,    0x1.503cbd1e94ap-57,
+	0x1.cdf0b555dc3fap-1,   -0x1.dd83b53829dp-56,
+	0x1.d072d4a07897cp-1,   -0x1.cbc3743797a8p-55,
+	0x1.d2f87080d89f2p-1,   -0x1.d487b719d858p-55,
+	0x1.d5818dcfba487p-1,    0x1.2ed02d75b37p-56,
+	0x1.d80e316c98398p-1,   -0x1.11ec18bedep-55,
+	0x1.da9e603db3285p-1,    0x1.c2300696db5p-55,
+	0x1.dd321f301b46p-1,     0x1.2da5778f019p-55,
+	0x1.dfc97337b9b5fp-1,   -0x1.1a5cd4f184b8p-55,
+	0x1.e264614f5a129p-1,   -0x1.7b627817a148p-55,
+	0x1.e502ee78b3ff6p-1,    0x1.39e8980a9cdp-56,
+	0x1.e7a51fbc74c83p-1,    0x1.2d522ca0c8ep-55,
+	0x1.ea4afa2a490dap-1,   -0x1.e9c23179c288p-55,
+	0x1.ecf482d8e67f1p-1,   -0x1.c93f3b411ad8p-55,
+	0x1.efa1bee615a27p-1,    0x1.dc7f486a4b68p-55,
+	0x1.f252b376bba97p-1,    0x1.3a1a5bf0d8e8p-55,
+	0x1.f50765b6e454p-1,     0x1.9d3e12dd8a18p-55,
+	0x1.f7bfdad9cbe14p-1,   -0x1.dbb12d00635p-55,
+	0x1.fa7c1819e90d8p-1,    0x1.74853f3a593p-56,
+	0x1.fd3c22b8f71f1p-1,    0x1.2eb74966578p-58,
+	0x1p+0,                  0x0p+0,
+	0x1.0163da9fb3335p+0,    0x1.b61299ab8cd8p-54,
+	0x1.02c9a3e778061p+0,   -0x1.19083535b08p-56,
+	0x1.04315e86e7f85p+0,   -0x1.0a31c1977c98p-54,
+	0x1.059b0d3158574p+0,    0x1.d73e2a475b4p-55,
+	0x1.0706b29ddf6dep+0,   -0x1.c91dfe2b13cp-55,
+	0x1.0874518759bc8p+0,    0x1.186be4bb284p-57,
+	0x1.09e3ecac6f383p+0,    0x1.14878183161p-54,
+	0x1.0b5586cf9890fp+0,    0x1.8a62e4adc61p-54,
+	0x1.0cc922b7247f7p+0,    0x1.01edc16e24f8p-54,
+	0x1.0e3ec32d3d1a2p+0,    0x1.03a1727c58p-59,
+	0x1.0fb66affed31bp+0,   -0x1.b9bedc44ebcp-57,
+	0x1.11301d0125b51p+0,   -0x1.6c51039449bp-54,
+	0x1.12abdc06c31ccp+0,   -0x1.1b514b36ca8p-58,
+	0x1.1429aaea92dep+0,    -0x1.32fbf9af1368p-54,
+	0x1.15a98c8a58e51p+0,    0x1.2406ab9eeabp-55,
+	0x1.172b83c7d517bp+0,   -0x1.19041b9d78ap-55,
+	0x1.18af9388c8deap+0,   -0x1.11023d1970f8p-54,
+	0x1.1a35beb6fcb75p+0,    0x1.e5b4c7b4969p-55,
+	0x1.1bbe084045cd4p+0,   -0x1.95386352ef6p-54,
+	0x1.1d4873168b9aap+0,    0x1.e016e00a264p-54,
+	0x1.1ed5022fcd91dp+0,   -0x1.1df98027bb78p-54,
+	0x1.2063b88628cd6p+0,    0x1.dc775814a85p-55,
+	0x1.21f49917ddc96p+0,    0x1.2a97e9494a6p-55,
+	0x1.2387a6e756238p+0,    0x1.9b07eb6c7058p-54,
+	0x1.251ce4fb2a63fp+0,    0x1.ac155bef4f5p-55,
+	0x1.26b4565e27cddp+0,    0x1.2bd339940eap-55,
+	0x1.284dfe1f56381p+0,   -0x1.a4c3a8c3f0d8p-54,
+	0x1.29e9df51fdee1p+0,    0x1.612e8afad12p-55,
+	0x1.2b87fd0dad99p+0,    -0x1.10adcd6382p-59,
+	0x1.2d285a6e4030bp+0,    0x1.0024754db42p-54,
+	0x1.2ecafa93e2f56p+0,    0x1.1ca0f45d524p-56,
+	0x1.306fe0a31b715p+0,    0x1.6f46ad23183p-55,
+	0x1.32170fc4cd831p+0,    0x1.a9ce78e1804p-55,
+	0x1.33c08b26416ffp+0,    0x1.327218436598p-54,
+	0x1.356c55f929ff1p+0,   -0x1.b5cee5c4e46p-55,
+	0x1.371a7373aa9cbp+0,   -0x1.63aeabf42ebp-54,
+	0x1.38cae6d05d866p+0,   -0x1.e958d3c99048p-54,
+	0x1.3a7db34e59ff7p+0,   -0x1.5e436d661f6p-56,
+	0x1.3c32dc313a8e5p+0,   -0x1.efff8375d2ap-54,
+	0x1.3dea64c123422p+0,    0x1.ada0911f09fp-55,
+	0x1.3fa4504ac801cp+0,   -0x1.7d023f956fap-54,
+	0x1.4160a21f72e2ap+0,   -0x1.ef3691c309p-58,
+	0x1.431f5d950a897p+0,   -0x1.1c7dde35f7ap-55,
+	0x1.44e086061892dp+0,    0x1.89b7a04ef8p-59,
+	0x1.46a41ed1d0057p+0,    0x1.c944bd1648a8p-54,
+	0x1.486a2b5c13cdp+0,     0x1.3c1a3b69062p-56,
+	0x1.4a32af0d7d3dep+0,    0x1.9cb62f3d1be8p-54,
+	0x1.4bfdad5362a27p+0,    0x1.d4397afec42p-56,
+	0x1.4dcb299fddd0dp+0,    0x1.8ecdbbc6a78p-54,
+	0x1.4f9b2769d2ca7p+0,   -0x1.4b309d25958p-54,
+	0x1.516daa2cf6642p+0,   -0x1.f768569bd94p-55,
+	0x1.5342b569d4f82p+0,   -0x1.07abe1db13dp-55,
+	0x1.551a4ca5d920fp+0,   -0x1.d689cefede6p-55,
+	0x1.56f4736b527dap+0,    0x1.9bb2c011d938p-54,
+	0x1.58d12d497c7fdp+0,    0x1.295e15b9a1ep-55,
+	0x1.5ab07dd485429p+0,    0x1.6324c0546478p-54,
+	0x1.5c9268a5946b7p+0,    0x1.c4b1b81698p-60,
+	0x1.5e76f15ad2148p+0,    0x1.ba6f93080e68p-54,
+	0x1.605e1b976dc09p+0,   -0x1.3e2429b56de8p-54,
+	0x1.6247eb03a5585p+0,   -0x1.383c17e40b48p-54,
+	0x1.6434634ccc32p+0,    -0x1.c483c759d89p-55,
+	0x1.6623882552225p+0,   -0x1.bb60987591cp-54,
+	0x1.68155d44ca973p+0,    0x1.038ae44f74p-57,
+};
+
+/*
+ * exp2l(x): compute the base 2 exponential of x
+ *
+ * Accuracy: Peak error < 0.511 ulp.
+ *
+ * Method: (equally-spaced tables)
+ *
+ *   Reduce x:
+ *     x = 2**k + y, for integer k and |y| <= 1/2.
+ *     Thus we have exp2l(x) = 2**k * exp2(y).
+ *
+ *   Reduce y:
+ *     y = i/TBLSIZE + z for integer i near y * TBLSIZE.
+ *     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
+ *     with |z| <= 2**-(TBLBITS+1).
+ *
+ *   We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
+ *   degree-6 minimax polynomial with maximum error under 2**-69.
+ *   The table entries each have 104 bits of accuracy, encoded as
+ *   a pair of double precision values.
+ */
+long double exp2l(long double x)
+{
+	union IEEEl2bits u, v;
+	long double r, twopk, twopkp10000, z;
+	uint32_t hx, ix, i0;
+	int k;
+
+	/* Filter out exceptional cases. */
+	u.e = x;
+	hx = u.xbits.expsign;
+	ix = hx & EXPMASK;
+	if (ix >= BIAS + 14) {  /* |x| >= 16384 or x is NaN */
+		if (ix == BIAS + LDBL_MAX_EXP) {
+			if (u.xbits.man != 1ULL << 63 || (hx & 0x8000) == 0)
+				return x + x;  /* x is +Inf or NaN */
+			return 0.0;  /* x is -Inf */
+		}
+		if (x >= 16384)
+			return huge * huge;  /* overflow */
+		if (x <= -16446)
+			return twom10000 * twom10000;  /* underflow */
+	} else if (ix <= BIAS - 66) {  /* |x| < 0x1p-66 */
+		return 1.0 + x;
+	}
+
+	/*
+	 * Reduce x, computing z, i0, and k. The low bits of x + redux
+	 * contain the 16-bit integer part of the exponent (k) followed by
+	 * TBLBITS fractional bits (i0). We use bit tricks to extract these
+	 * as integers, then set z to the remainder.
+	 *
+	 * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8.
+	 * Then the low-order word of x + redux is 0x000abc12,
+	 * We split this into k = 0xabc and i0 = 0x12 (adjusted to
+	 * index into the table), then we compute z = 0x0.003456p0.
+	 *
+	 * XXX If the exponent is negative, the computation of k depends on
+	 *     '>>' doing sign extension.
+	 */
+	u.e = x + redux;
+	i0 = u.bits.manl + TBLSIZE / 2;
+	k = (int)i0 >> TBLBITS;
+	i0 = (i0 & (TBLSIZE - 1)) << 1;
+	u.e -= redux;
+	z = x - u.e;
+	v.xbits.man = 1ULL << 63;
+	if (k >= LDBL_MIN_EXP) {
+		v.xbits.expsign = LDBL_MAX_EXP - 1 + k;
+		twopk = v.e;
+	} else {
+		v.xbits.expsign = LDBL_MAX_EXP - 1 + k + 10000;
+		twopkp10000 = v.e;
+	}
+
+	/* Compute r = exp2l(y) = exp2lt[i0] * p(z). */
+	long double t_hi = tbl[i0];
+	long double t_lo = tbl[i0 + 1];
+	/* XXX This gives > 1 ulp errors outside of FE_TONEAREST mode */
+	r = t_lo + (t_hi + t_lo) * z * (P1 + z * (P2 + z * (P3 + z * (P4
+	     + z * (P5 + z * P6))))) + t_hi;
+
+	/* Scale by 2**k. */
+	if (k >= LDBL_MIN_EXP) {
+		if (k == LDBL_MAX_EXP)
+			return r * 2.0 * 0x1p16383L;
+		return r * twopk;
+	}
+	return r * twopkp10000 * twom10000;
+}
+#endif