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, 384 insertions, 0 deletions

diff --git a/src/math/exp2.c b/src/math/exp2.c
new file mode 100644
index 00000000..bf7421ee
--- /dev/null
+++ b/src/math/exp2.c
@@ -0,0 +1,384 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_exp2.c */
+/*-
+ * Copyright (c) 2005 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"
+
+#define TBLBITS 8
+#define TBLSIZE (1 << TBLBITS)
+
+static const double
+huge  = 0x1p1000,
+redux = 0x1.8p52 / TBLSIZE,
+P1    = 0x1.62e42fefa39efp-1,
+P2    = 0x1.ebfbdff82c575p-3,
+P3    = 0x1.c6b08d704a0a6p-5,
+P4    = 0x1.3b2ab88f70400p-7,
+P5    = 0x1.5d88003875c74p-10;
+
+static volatile double twom1000 = 0x1p-1000;
+
+static const double tbl[TBLSIZE * 2] = {
+/*  exp2(z + eps)          eps     */
+  0x1.6a09e667f3d5dp-1,  0x1.9880p-44,
+  0x1.6b052fa751744p-1,  0x1.8000p-50,
+  0x1.6c012750bd9fep-1, -0x1.8780p-45,
+  0x1.6cfdcddd476bfp-1,  0x1.ec00p-46,
+  0x1.6dfb23c651a29p-1, -0x1.8000p-50,
+  0x1.6ef9298593ae3p-1, -0x1.c000p-52,
+  0x1.6ff7df9519386p-1, -0x1.fd80p-45,
+  0x1.70f7466f42da3p-1, -0x1.c880p-45,
+  0x1.71f75e8ec5fc3p-1,  0x1.3c00p-46,
+  0x1.72f8286eacf05p-1, -0x1.8300p-44,
+  0x1.73f9a48a58152p-1, -0x1.0c00p-47,
+  0x1.74fbd35d7ccfcp-1,  0x1.f880p-45,
+  0x1.75feb564267f1p-1,  0x1.3e00p-47,
+  0x1.77024b1ab6d48p-1, -0x1.7d00p-45,
+  0x1.780694fde5d38p-1, -0x1.d000p-50,
+  0x1.790b938ac1d00p-1,  0x1.3000p-49,
+  0x1.7a11473eb0178p-1, -0x1.d000p-49,
+  0x1.7b17b0976d060p-1,  0x1.0400p-45,
+  0x1.7c1ed0130c133p-1,  0x1.0000p-53,
+  0x1.7d26a62ff8636p-1, -0x1.6900p-45,
+  0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47,
+  0x1.7f3878491c3e8p-1, -0x1.4580p-45,
+  0x1.80427543e1b4ep-1,  0x1.3000p-44,
+  0x1.814d2add1071ap-1,  0x1.f000p-47,
+  0x1.82589994ccd7ep-1, -0x1.1c00p-45,
+  0x1.8364c1eb942d0p-1,  0x1.9d00p-45,
+  0x1.8471a4623cab5p-1,  0x1.7100p-43,
+  0x1.857f4179f5bbcp-1,  0x1.2600p-45,
+  0x1.868d99b4491afp-1, -0x1.2c40p-44,
+  0x1.879cad931a395p-1, -0x1.3000p-45,
+  0x1.88ac7d98a65b8p-1, -0x1.a800p-45,
+  0x1.89bd0a4785800p-1, -0x1.d000p-49,
+  0x1.8ace5422aa223p-1,  0x1.3280p-44,
+  0x1.8be05bad619fap-1,  0x1.2b40p-43,
+  0x1.8cf3216b54383p-1, -0x1.ed00p-45,
+  0x1.8e06a5e08664cp-1, -0x1.0500p-45,
+  0x1.8f1ae99157807p-1,  0x1.8280p-45,
+  0x1.902fed0282c0ep-1, -0x1.cb00p-46,
+  0x1.9145b0b91ff96p-1, -0x1.5e00p-47,
+  0x1.925c353aa2ff9p-1,  0x1.5400p-48,
+  0x1.93737b0cdc64ap-1,  0x1.7200p-46,
+  0x1.948b82b5f98aep-1, -0x1.9000p-47,
+  0x1.95a44cbc852cbp-1,  0x1.5680p-45,
+  0x1.96bdd9a766f21p-1, -0x1.6d00p-44,
+  0x1.97d829fde4e2ap-1, -0x1.1000p-47,
+  0x1.98f33e47a23a3p-1,  0x1.d000p-45,
+  0x1.9a0f170ca0604p-1, -0x1.8a40p-44,
+  0x1.9b2bb4d53ff89p-1,  0x1.55c0p-44,
+  0x1.9c49182a3f15bp-1,  0x1.6b80p-45,
+  0x1.9d674194bb8c5p-1, -0x1.c000p-49,
+  0x1.9e86319e3238ep-1,  0x1.7d00p-46,
+  0x1.9fa5e8d07f302p-1,  0x1.6400p-46,
+  0x1.a0c667b5de54dp-1, -0x1.5000p-48,
+  0x1.a1e7aed8eb8f6p-1,  0x1.9e00p-47,
+  0x1.a309bec4a2e27p-1,  0x1.ad80p-45,
+  0x1.a42c980460a5dp-1, -0x1.af00p-46,
+  0x1.a5503b23e259bp-1,  0x1.b600p-47,
+  0x1.a674a8af46213p-1,  0x1.8880p-44,
+  0x1.a799e1330b3a7p-1,  0x1.1200p-46,
+  0x1.a8bfe53c12e8dp-1,  0x1.6c00p-47,
+  0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45,
+  0x1.ab0e521356fb8p-1,  0x1.b700p-45,
+  0x1.ac36bbfd3f381p-1,  0x1.9000p-50,
+  0x1.ad5ff3a3c2780p-1,  0x1.4000p-49,
+  0x1.ae89f995ad2a3p-1, -0x1.c900p-45,
+  0x1.afb4ce622f367p-1,  0x1.6500p-46,
+  0x1.b0e07298db790p-1,  0x1.fd40p-45,
+  0x1.b20ce6c9a89a9p-1,  0x1.2700p-46,
+  0x1.b33a2b84f1a4bp-1,  0x1.d470p-43,
+  0x1.b468415b747e7p-1, -0x1.8380p-44,
+  0x1.b59728de5593ap-1,  0x1.8000p-54,
+  0x1.b6c6e29f1c56ap-1,  0x1.ad00p-47,
+  0x1.b7f76f2fb5e50p-1,  0x1.e800p-50,
+  0x1.b928cf22749b2p-1, -0x1.4c00p-47,
+  0x1.ba5b030a10603p-1, -0x1.d700p-47,
+  0x1.bb8e0b79a6f66p-1,  0x1.d900p-47,
+  0x1.bcc1e904bc1ffp-1,  0x1.2a00p-47,
+  0x1.bdf69c3f3a16fp-1, -0x1.f780p-46,
+  0x1.bf2c25bd71db8p-1, -0x1.0a00p-46,
+  0x1.c06286141b2e9p-1, -0x1.1400p-46,
+  0x1.c199bdd8552e0p-1,  0x1.be00p-47,
+  0x1.c2d1cd9fa64eep-1, -0x1.9400p-47,
+  0x1.c40ab5fffd02fp-1, -0x1.ed00p-47,
+  0x1.c544778fafd15p-1,  0x1.9660p-44,
+  0x1.c67f12e57d0cbp-1, -0x1.a100p-46,
+  0x1.c7ba88988c1b6p-1, -0x1.8458p-42,
+  0x1.c8f6d9406e733p-1, -0x1.a480p-46,
+  0x1.ca3405751c4dfp-1,  0x1.b000p-51,
+  0x1.cb720dcef9094p-1,  0x1.1400p-47,
+  0x1.ccb0f2e6d1689p-1,  0x1.0200p-48,
+  0x1.cdf0b555dc412p-1,  0x1.3600p-48,
+  0x1.cf3155b5bab3bp-1, -0x1.6900p-47,
+  0x1.d072d4a0789bcp-1,  0x1.9a00p-47,
+  0x1.d1b532b08c8fap-1, -0x1.5e00p-46,
+  0x1.d2f87080d8a85p-1,  0x1.d280p-46,
+  0x1.d43c8eacaa203p-1,  0x1.1a00p-47,
+  0x1.d5818dcfba491p-1,  0x1.f000p-50,
+  0x1.d6c76e862e6a1p-1, -0x1.3a00p-47,
+  0x1.d80e316c9834ep-1, -0x1.cd80p-47,
+  0x1.d955d71ff6090p-1,  0x1.4c00p-48,
+  0x1.da9e603db32aep-1,  0x1.f900p-48,
+  0x1.dbe7cd63a8325p-1,  0x1.9800p-49,
+  0x1.dd321f301b445p-1, -0x1.5200p-48,
+  0x1.de7d5641c05bfp-1, -0x1.d700p-46,
+  0x1.dfc97337b9aecp-1, -0x1.6140p-46,
+  0x1.e11676b197d5ep-1,  0x1.b480p-47,
+  0x1.e264614f5a3e7p-1,  0x1.0ce0p-43,
+  0x1.e3b333b16ee5cp-1,  0x1.c680p-47,
+  0x1.e502ee78b3fb4p-1, -0x1.9300p-47,
+  0x1.e653924676d68p-1, -0x1.5000p-49,
+  0x1.e7a51fbc74c44p-1, -0x1.7f80p-47,
+  0x1.e8f7977cdb726p-1, -0x1.3700p-48,
+  0x1.ea4afa2a490e8p-1,  0x1.5d00p-49,
+  0x1.eb9f4867ccae4p-1,  0x1.61a0p-46,
+  0x1.ecf482d8e680dp-1,  0x1.5500p-48,
+  0x1.ee4aaa2188514p-1,  0x1.6400p-51,
+  0x1.efa1bee615a13p-1, -0x1.e800p-49,
+  0x1.f0f9c1cb64106p-1, -0x1.a880p-48,
+  0x1.f252b376bb963p-1, -0x1.c900p-45,
+  0x1.f3ac948dd7275p-1,  0x1.a000p-53,
+  0x1.f50765b6e4524p-1, -0x1.4f00p-48,
+  0x1.f6632798844fdp-1,  0x1.a800p-51,
+  0x1.f7bfdad9cbe38p-1,  0x1.abc0p-48,
+  0x1.f91d802243c82p-1, -0x1.4600p-50,
+  0x1.fa7c1819e908ep-1, -0x1.b0c0p-47,
+  0x1.fbdba3692d511p-1, -0x1.0e00p-51,
+  0x1.fd3c22b8f7194p-1, -0x1.0de8p-46,
+  0x1.fe9d96b2a23eep-1,  0x1.e430p-49,
+  0x1.0000000000000p+0,  0x0.0000p+0,
+  0x1.00b1afa5abcbep+0, -0x1.3400p-52,
+  0x1.0163da9fb3303p+0, -0x1.2170p-46,
+  0x1.02168143b0282p+0,  0x1.a400p-52,
+  0x1.02c9a3e77806cp+0,  0x1.f980p-49,
+  0x1.037d42e11bbcap+0, -0x1.7400p-51,
+  0x1.04315e86e7f89p+0,  0x1.8300p-50,
+  0x1.04e5f72f65467p+0, -0x1.a3f0p-46,
+  0x1.059b0d315855ap+0, -0x1.2840p-47,
+  0x1.0650a0e3c1f95p+0,  0x1.1600p-48,
+  0x1.0706b29ddf71ap+0,  0x1.5240p-46,
+  0x1.07bd42b72a82dp+0, -0x1.9a00p-49,
+  0x1.0874518759bd0p+0,  0x1.6400p-49,
+  0x1.092bdf66607c8p+0, -0x1.0780p-47,
+  0x1.09e3ecac6f383p+0, -0x1.8000p-54,
+  0x1.0a9c79b1f3930p+0,  0x1.fa00p-48,
+  0x1.0b5586cf988fcp+0, -0x1.ac80p-48,
+  0x1.0c0f145e46c8ap+0,  0x1.9c00p-50,
+  0x1.0cc922b724816p+0,  0x1.5200p-47,
+  0x1.0d83b23395dd8p+0, -0x1.ad00p-48,
+  0x1.0e3ec32d3d1f3p+0,  0x1.bac0p-46,
+  0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47,
+  0x1.0fb66affed2f0p+0, -0x1.d300p-47,
+  0x1.1073028d7234bp+0,  0x1.1500p-48,
+  0x1.11301d0125b5bp+0,  0x1.c000p-49,
+  0x1.11edbab5e2af9p+0,  0x1.6bc0p-46,
+  0x1.12abdc06c31d5p+0,  0x1.8400p-49,
+  0x1.136a814f2047dp+0, -0x1.ed00p-47,
+  0x1.1429aaea92de9p+0,  0x1.8e00p-49,
+  0x1.14e95934f3138p+0,  0x1.b400p-49,
+  0x1.15a98c8a58e71p+0,  0x1.5300p-47,
+  0x1.166a45471c3dfp+0,  0x1.3380p-47,
+  0x1.172b83c7d5211p+0,  0x1.8d40p-45,
+  0x1.17ed48695bb9fp+0, -0x1.5d00p-47,
+  0x1.18af9388c8d93p+0, -0x1.c880p-46,
+  0x1.1972658375d66p+0,  0x1.1f00p-46,
+  0x1.1a35beb6fcba7p+0,  0x1.0480p-46,
+  0x1.1af99f81387e3p+0, -0x1.7390p-43,
+  0x1.1bbe084045d54p+0,  0x1.4e40p-45,
+  0x1.1c82f95281c43p+0, -0x1.a200p-47,
+  0x1.1d4873168b9b2p+0,  0x1.3800p-49,
+  0x1.1e0e75eb44031p+0,  0x1.ac00p-49,
+  0x1.1ed5022fcd938p+0,  0x1.1900p-47,
+  0x1.1f9c18438cdf7p+0, -0x1.b780p-46,
+  0x1.2063b88628d8fp+0,  0x1.d940p-45,
+  0x1.212be3578a81ep+0,  0x1.8000p-50,
+  0x1.21f49917ddd41p+0,  0x1.b340p-45,
+  0x1.22bdda2791323p+0,  0x1.9f80p-46,
+  0x1.2387a6e7561e7p+0, -0x1.9c80p-46,
+  0x1.2451ffb821427p+0,  0x1.2300p-47,
+  0x1.251ce4fb2a602p+0, -0x1.3480p-46,
+  0x1.25e85711eceb0p+0,  0x1.2700p-46,
+  0x1.26b4565e27d16p+0,  0x1.1d00p-46,
+  0x1.2780e341de00fp+0,  0x1.1ee0p-44,
+  0x1.284dfe1f5633ep+0, -0x1.4c00p-46,
+  0x1.291ba7591bb30p+0, -0x1.3d80p-46,
+  0x1.29e9df51fdf09p+0,  0x1.8b00p-47,
+  0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45,
+  0x1.2b87fd0dada3ap+0,  0x1.a340p-45,
+  0x1.2c57e39771af9p+0, -0x1.0800p-46,
+  0x1.2d285a6e402d9p+0, -0x1.ed00p-47,
+  0x1.2df961f641579p+0, -0x1.4200p-48,
+  0x1.2ecafa93e2ecfp+0, -0x1.4980p-45,
+  0x1.2f9d24abd8822p+0, -0x1.6300p-46,
+  0x1.306fe0a31b625p+0, -0x1.2360p-44,
+  0x1.31432edeea50bp+0, -0x1.0df8p-40,
+  0x1.32170fc4cd7b8p+0, -0x1.2480p-45,
+  0x1.32eb83ba8e9a2p+0, -0x1.5980p-45,
+  0x1.33c08b2641766p+0,  0x1.ed00p-46,
+  0x1.3496266e3fa27p+0, -0x1.c000p-50,
+  0x1.356c55f929f0fp+0, -0x1.0d80p-44,
+  0x1.36431a2de88b9p+0,  0x1.2c80p-45,
+  0x1.371a7373aaa39p+0,  0x1.0600p-45,
+  0x1.37f26231e74fep+0, -0x1.6600p-46,
+  0x1.38cae6d05d838p+0, -0x1.ae00p-47,
+  0x1.39a401b713ec3p+0, -0x1.4720p-43,
+  0x1.3a7db34e5a020p+0,  0x1.8200p-47,
+  0x1.3b57fbfec6e95p+0,  0x1.e800p-44,
+  0x1.3c32dc313a8f2p+0,  0x1.f800p-49,
+  0x1.3d0e544ede122p+0, -0x1.7a00p-46,
+  0x1.3dea64c1234bbp+0,  0x1.6300p-45,
+  0x1.3ec70df1c4eccp+0, -0x1.8a60p-43,
+  0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44,
+  0x1.40822c367a0bbp+0,  0x1.5b80p-45,
+  0x1.4160a21f72e95p+0,  0x1.ec00p-46,
+  0x1.423fb27094646p+0, -0x1.3600p-46,
+  0x1.431f5d950a920p+0,  0x1.3980p-45,
+  0x1.43ffa3f84b9ebp+0,  0x1.a000p-48,
+  0x1.44e0860618919p+0, -0x1.6c00p-48,
+  0x1.45c2042a7d201p+0, -0x1.bc00p-47,
+  0x1.46a41ed1d0016p+0, -0x1.2800p-46,
+  0x1.4786d668b3326p+0,  0x1.0e00p-44,
+  0x1.486a2b5c13c00p+0, -0x1.d400p-45,
+  0x1.494e1e192af04p+0,  0x1.c200p-47,
+  0x1.4a32af0d7d372p+0, -0x1.e500p-46,
+  0x1.4b17dea6db801p+0,  0x1.7800p-47,
+  0x1.4bfdad53629e1p+0, -0x1.3800p-46,
+  0x1.4ce41b817c132p+0,  0x1.0800p-47,
+  0x1.4dcb299fddddbp+0,  0x1.c700p-45,
+  0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46,
+  0x1.4f9b2769d2d02p+0,  0x1.9200p-46,
+  0x1.508417f4531c1p+0, -0x1.8c00p-47,
+  0x1.516daa2cf662ap+0, -0x1.a000p-48,
+  0x1.5257de83f51eap+0,  0x1.a080p-43,
+  0x1.5342b569d4edap+0, -0x1.6d80p-45,
+  0x1.542e2f4f6ac1ap+0, -0x1.2440p-44,
+  0x1.551a4ca5d94dbp+0,  0x1.83c0p-43,
+  0x1.56070dde9116bp+0,  0x1.4b00p-45,
+  0x1.56f4736b529dep+0,  0x1.15a0p-43,
+  0x1.57e27dbe2c40ep+0, -0x1.9e00p-45,
+  0x1.58d12d497c76fp+0, -0x1.3080p-45,
+  0x1.59c0827ff0b4cp+0,  0x1.dec0p-43,
+  0x1.5ab07dd485427p+0, -0x1.4000p-51,
+  0x1.5ba11fba87af4p+0,  0x1.0080p-44,
+  0x1.5c9268a59460bp+0, -0x1.6c80p-45,
+  0x1.5d84590998e3fp+0,  0x1.69a0p-43,
+  0x1.5e76f15ad20e1p+0, -0x1.b400p-46,
+  0x1.5f6a320dcebcap+0,  0x1.7700p-46,
+  0x1.605e1b976dcb8p+0,  0x1.6f80p-45,
+  0x1.6152ae6cdf715p+0,  0x1.1000p-47,
+  0x1.6247eb03a5531p+0, -0x1.5d00p-46,
+  0x1.633dd1d1929b5p+0, -0x1.2d00p-46,
+  0x1.6434634ccc313p+0, -0x1.a800p-49,
+  0x1.652b9febc8efap+0, -0x1.8600p-45,
+  0x1.6623882553397p+0,  0x1.1fe0p-40,
+  0x1.671c1c708328ep+0, -0x1.7200p-44,
+  0x1.68155d44ca97ep+0,  0x1.6800p-49,
+  0x1.690f4b19e9471p+0, -0x1.9780p-45,
+};
+
+/*
+ * exp2(x): compute the base 2 exponential of x
+ *
+ * Accuracy: Peak error < 0.503 ulp for normalized results.
+ *
+ * Method: (accurate tables)
+ *
+ *   Reduce x:
+ *     x = 2**k + y, for integer k and |y| <= 1/2.
+ *     Thus we have exp2(x) = 2**k * exp2(y).
+ *
+ *   Reduce y:
+ *     y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE.
+ *     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]),
+ *     with |z - eps[i]| <= 2**-9 + 2**-39 for the table used.
+ *
+ *   We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via
+ *   a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61.
+ *   The values in exp2t[] and eps[] are chosen such that
+ *   exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such
+ *   that exp2t[i] is accurate to 2**-64.
+ *
+ *   Note that the range of i is +-TBLSIZE/2, so we actually index the tables
+ *   by i0 = i + TBLSIZE/2.  For cache efficiency, exp2t[] and eps[] are
+ *   virtual tables, interleaved in the real table tbl[].
+ *
+ *   This method is due to Gal, with many details due to Gal and Bachelis:
+ *
+ *      Gal, S. and Bachelis, B.  An Accurate Elementary Mathematical Library
+ *      for the IEEE Floating Point Standard.  TOMS 17(1), 26-46 (1991).
+ */
+double exp2(double x)
+{
+	double r, t, twopk, twopkp1000, z;
+	uint32_t hx, ix, lx, i0;
+	int k;
+
+	/* Filter out exceptional cases. */
+	GET_HIGH_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+	if (ix >= 0x40900000) {        /* |x| >= 1024 */
+		if (ix >= 0x7ff00000) {
+			GET_LOW_WORD(lx, x);
+			if (((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0)
+				return x + x; /* x is NaN or +Inf */
+			else
+				return 0.0;   /* x is -Inf */
+		}
+		if (x >= 0x1.0p10)
+			return huge * huge; /* overflow */
+		if (x <= -0x1.0ccp10)
+			return twom1000 * twom1000; /* underflow */
+	} else if (ix < 0x3c900000) {  /* |x| < 0x1p-54 */
+		return 1.0 + x;
+	}
+
+	/* Reduce x, computing z, i0, and k. */
+	STRICT_ASSIGN(double, t, x + redux);
+	GET_LOW_WORD(i0, t);
+	i0 += TBLSIZE / 2;
+	k = (i0 >> TBLBITS) << 20;
+	i0 = (i0 & (TBLSIZE - 1)) << 1;
+	t -= redux;
+	z = x - t;
+
+	/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
+	t = tbl[i0];       /* exp2t[i0] */
+	z -= tbl[i0 + 1];  /* eps[i0]   */
+	if (k >= -1021 << 20)
+		INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
+	else
+		INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0);
+	r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
+
+	/* Scale by 2**(k>>20). */
+	if (k < -1021 << 20)
+		return r * twopkp1000 * twom1000;
+	if (k == 1024 << 20)
+		return r * 2.0 * 0x1p1023;
+	return r * twopk;
+}