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Up to [cvs.NetBSD.org] / src / lib / libm / src

Change 'i0' to be signed so that the sign bit is preserved on 'k'
  and the code at the bottom splits the multiply.
Fixes denormal results.
This might have been introduced when I deferred shifting 'k' left.

/*-
 * 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 <sys/cdefs.h>
__RCSID("$NetBSD: s_exp2.c,v 1.5 2014/03/18 21:52:19 dsl Exp $");
#ifdef __FBSDID
__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2.c,v 1.7 2008/02/22 02:27:34 das Exp $");
#endif

#include <float.h>

#include "math.h"
#include "math_private.h"

#define	TBLBITS	8
#define	TBLSIZE	(1 << TBLBITS)

static const double
    redux    = 0x1.8p52 / TBLSIZE,
    P1	     = 0x1.62e42fefa39efp-1,
    P2	     = 0x1.ebfbdff82c575p-3,
    P3	     = 0x1.c6b08d704a0a6p-5,
    P4	     = 0x1.3b2ab88f70400p-7,
    P5	     = 0x1.5d88003875c74p-10;

#ifdef __i386__
/* The return value is in %st(0) - we need a 'long double' error. */
static volatile long double huge = 0x1p+16000L;
static volatile long double tiny = 0x1p-16000L;
#else
static volatile double huge = 0x1p+1000;
static volatile double tiny = 0x1p-1000;
#endif

static const struct {
    double exp2;	/* exp2(z + eps) */
    double eps;		/* eps */
} tbl[TBLSIZE] = {
/*	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.
 *
 *   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)
{
	volatile ieee_double_shape_type x_p_redux;
	double r, t, twopk, z;
	uint32_t hx, ix, lx;
	int32_t i0;
	int k;

	/* Filter out exceptional cases. */
	GET_HIGH_WORD(hx,x);
	ix = hx & 0x7fffffff;		/* high word of |x| */
	if(ix >= 0x40900000) {			/* |x| >= 1024 */
		if(ix >= 0x7ff00000) {
			/* x is infinity or NaN */
			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 (tiny * tiny); /* underflow */
	} else if (ix < 0x3c900000) {		/* |x| < 0x1p-54 */
		return (1.0 + x);
	}

	/* Reduce x, computing z, i0, and k. */
	x_p_redux.value = x + redux;
	i0 = x_p_redux.parts.lsw;

	i0 += TBLSIZE / 2;
	k = i0 >> TBLBITS;
	i0 &= TBLSIZE - 1;
	z = x - (x_p_redux.value - redux);

	/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
	t = tbl[i0].exp2;
	z -= tbl[i0].eps;
	r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));

	/*
	 * Scale by 2**k.
	 * For 'normal' values of 'k' we just multply be the correct value,
	 * but at the extremes this doesn't work and the multiply must
	 * be split.
	 */
	if (k >= -1021) {
		if (k == 1024)
			/* Overflow */
			return (r * 2.0 * 0x1p1023);
	} else {
		/* result might be subnormal */
		r *= 0x1p-1000;
		k += 1000;
	}
	INSERT_WORDS(twopk, 0x3ff00000 + (k << 20), 0);
	return (r * twopk);
}

#ifdef notyet
#if (LDBL_MANT_DIG == 53)
__weak_reference(exp2, exp2l);
#endif
#endif