svn commit: r238722 - in head/lib/msun: . ld128 ld80 man src
Steve Kargl
kargl at FreeBSD.org
Mon Jul 23 19:13:56 UTC 2012
Author: kargl
Date: Mon Jul 23 19:13:55 2012
New Revision: 238722
URL: http://svn.freebsd.org/changeset/base/238722
Log:
Compute the exponential of x for Intel 80-bit format and IEEE 128-bit
format. These implementations are based on
PTP Tang, "Table-driven implementation of the exponential function
in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 15,
144-157 (1989).
PR: standards/152415
Submitted by: kargl
Reviewed by: bde, das
Approved by: das (mentor)
Added:
head/lib/msun/ld128/s_expl.c (contents, props changed)
head/lib/msun/ld80/s_expl.c (contents, props changed)
Modified:
head/lib/msun/Symbol.map
head/lib/msun/man/exp.3
head/lib/msun/src/e_exp.c
head/lib/msun/src/math.h
head/lib/msun/src/math_private.h
Modified: head/lib/msun/Symbol.map
==============================================================================
--- head/lib/msun/Symbol.map Mon Jul 23 16:36:13 2012 (r238721)
+++ head/lib/msun/Symbol.map Mon Jul 23 19:13:55 2012 (r238722)
@@ -249,4 +249,5 @@ FBSD_1.3 {
ctanf;
ctanh;
ctanhf;
+ expl;
};
Added: head/lib/msun/ld128/s_expl.c
==============================================================================
--- /dev/null 00:00:00 1970 (empty, because file is newly added)
+++ head/lib/msun/ld128/s_expl.c Mon Jul 23 19:13:55 2012 (r238722)
@@ -0,0 +1,260 @@
+/*-
+ * Copyright (c) 2012 Steven G. Kargl
+ * 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 unmodified, 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 ``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 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>
+__FBSDID("$FreeBSD$");
+
+#include <float.h>
+
+#include "math.h"
+#include "math_private.h"
+#include "fpmath.h"
+
+#define BIAS (LDBL_MAX_EXP - 1)
+#define EXPMASK (BIAS + LDBL_MAX_EXP)
+
+static volatile const long double twom10000 = 0x1p-10000L, tiny = 0x1p-10000L;
+
+static const long double
+huge = 0x1p10000L,
+o_threshold = 11356.523406294143949491931077970763428L,
+u_threshold = -11433.462743336297878837243843452621503L,
+L1 = 5.41521234812457272982212595914567508e-03L,
+L2 = -1.02536706388947310094527932552595546e-29L,
+INV_L = 1.84664965233787316142070359168242182e+02L;
+
+static const long double
+P2 = 5.00000000000000000000000000000000000e-1L,
+P3 = 1.66666666666666666666666666666666972e-1L,
+P4 = 4.16666666666666666666666666653708268e-2L,
+P5 = 8.33333333333333333333333315069867254e-3L,
+P6 = 1.38888888888888888888996596213795377e-3L,
+P7 = 1.98412698412698412718821436278644414e-4L,
+P8 = 2.48015873015869681884882576649543128e-5L,
+P9 = 2.75573192240103867817876199544468806e-6L,
+P10 = 2.75573236172670046201884000197885520e-7L,
+P11 = 2.50517544183909126492878226167697856e-8L;
+
+#define NUM 128
+
+static const struct {
+ long double hi;
+ long double lo;
+} s[NUM] = {
+ 0x1p0L, 0x0p0L,
+ 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L,
+ 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L,
+ 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L,
+ 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L,
+ 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L,
+ 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L,
+ 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L,
+ 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L,
+ 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L,
+ 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L,
+ 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L,
+ 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L,
+ 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L,
+ 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L,
+ 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L,
+ 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L,
+ 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L,
+ 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L,
+ 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L,
+ 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L,
+ 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L,
+ 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L,
+ 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L,
+ 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L,
+ 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L,
+ 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L,
+ 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L,
+ 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L,
+ 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L,
+ 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L,
+ 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L,
+ 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L,
+ 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L,
+ 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L,
+ 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L,
+ 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L,
+ 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L,
+ 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L,
+ 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L,
+ 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L,
+ 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L,
+ 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L,
+ 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L,
+ 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L,
+ 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L,
+ 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L,
+ 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L,
+ 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L,
+ 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L,
+ 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L,
+ 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L,
+ 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L,
+ 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L,
+ 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L,
+ 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L,
+ 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L,
+ 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L,
+ 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L,
+ 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L,
+ 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L,
+ 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L,
+ 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L,
+ 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L,
+ 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L,
+ 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L,
+ 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L,
+ 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L,
+ 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L,
+ 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L,
+ 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L,
+ 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L,
+ 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L,
+ 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L,
+ 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L,
+ 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L,
+ 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L,
+ 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L,
+ 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L,
+ 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L,
+ 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L,
+ 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L,
+ 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L,
+ 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L,
+ 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L,
+ 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L,
+ 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L,
+ 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L,
+ 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L,
+ 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L,
+ 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L,
+ 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L,
+ 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L,
+ 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L,
+ 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L,
+ 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L,
+ 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L,
+ 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L,
+ 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L,
+ 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L,
+ 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L,
+ 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L,
+ 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L,
+ 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L,
+ 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L,
+ 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L,
+ 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L,
+ 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L,
+ 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L,
+ 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L,
+ 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L,
+ 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L,
+ 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L,
+ 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L,
+ 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L,
+ 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L,
+ 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L,
+ 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L,
+ 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L,
+ 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L,
+ 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L,
+ 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L,
+ 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L,
+ 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L,
+ 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L,
+ 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L,
+ 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L,
+ 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L
+};
+
+long double
+expl(long double x)
+{
+ union IEEEl2bits u, v;
+ long double fn, r, r1, r2, q, t, twopk, twopkp10000;
+ int k, n, n2;
+ uint32_t hx, ix;
+
+ /* Filter out exceptional cases. */
+ u.e = x;
+ hx = u.xbits.expsign;
+ ix = hx & EXPMASK;
+ if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
+ if (ix == BIAS + LDBL_MAX_EXP) {
+ if (u.xbits.manh != 0
+ || u.xbits.manl != 0
+ || (hx & 0x8000) == 0)
+ return (x + x); /* x is NaN or +Inf */
+ else
+ return (0.0); /* x is -Inf */
+ }
+ if (x > o_threshold)
+ return (huge * huge);
+ if (x < u_threshold)
+ return (tiny * tiny);
+ } else if (ix <= BIAS - 115) { /* |x| < 0x1p-33 */
+ /* includes pseudo-denormals */
+ if (huge + x > 1.0L) /* trigger inexact iff x != 0 */
+ return (1.0L + x);
+ }
+
+ fn = x * INV_L + 0x1.8p112 - 0x1.8p112;
+ n = (int)fn;
+ n2 = (unsigned)n % NUM; /* Tang's j. */
+ k = (n - n2) / NUM;
+ r1 = x - fn * L1;
+ r2 = -fn * L2;
+
+ /* Prepare scale factors. */
+ v.xbits.manh = 0;
+ v.xbits.manl = 0;
+ if (k >= LDBL_MIN_EXP) {
+ v.xbits.expsign = BIAS + k;
+ twopk = v.e;
+ } else {
+ v.xbits.expsign = BIAS + k + 10000;
+ twopkp10000 = v.e;
+ }
+
+ r = r1 + r2;
+ q = r * r * (P2 + r * (P3 + r * (P4 + r * (P5 + r * (P6 + r * (P7 +
+ r * (P8 + r * (P9 + r * (P10 + r * P11)))))))));
+ t = s[n2].lo + s[n2].hi;
+ t = s[n2].hi + (s[n2].lo + t * (r2 + q + r1));
+
+ /* Scale by 2**k. */
+ if (k >= LDBL_MIN_EXP) {
+ if (k == LDBL_MAX_EXP)
+ return (t * 2.0L * 0x1p16383L);
+ return (t * twopk);
+ } else {
+ return (t * twopkp10000 * twom10000);
+ }
+}
Added: head/lib/msun/ld80/s_expl.c
==============================================================================
--- /dev/null 00:00:00 1970 (empty, because file is newly added)
+++ head/lib/msun/ld80/s_expl.c Mon Jul 23 19:13:55 2012 (r238722)
@@ -0,0 +1,304 @@
+/*-
+ * Copyright (c) 2009-2012 Steven G. Kargl
+ * 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 unmodified, 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 ``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 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.
+ *
+ * Optimized by Bruce D. Evans.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * Compute the exponential of x for Intel 80-bit format. This is based on:
+ *
+ * PTP Tang, "Table-driven implementation of the exponential function
+ * in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 15,
+ * 144-157 (1989).
+ *
+ * where the 32 table entries have been expanded to NUM (see below).
+ */
+
+#include <float.h>
+
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "math.h"
+#define FPSETPREC
+#ifdef NO_FPSETPREC
+#undef FPSETPREC
+#endif
+#include "math_private.h"
+#include "fpmath.h"
+
+#define BIAS (LDBL_MAX_EXP - 1)
+
+static const long double
+huge = 0x1p10000L,
+twom10000 = 0x1p-10000L;
+/* XXX Prevent gcc from erroneously constant folding this: */
+static volatile const long double tiny = 0x1p-10000L;
+
+static const union IEEEl2bits
+/* log(2**16384 - 0.5) rounded towards zero: */
+o_threshold = LD80C(0xb17217f7d1cf79ab, 13, 0, 11356.5234062941439488L),
+/* log(2**(-16381-64-1)) rounded towards zero: */
+u_threshold = LD80C(0xb21dfe7f09e2baa9, 13, 1, -11399.4985314888605581L);
+
+static const double __aligned(64)
+/*
+ * ln2/NUM = L1+L2 (hi+lo decomposition for multiplication). L1 must have
+ * at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(NUM)) lowest bits zero
+ * so that multiplication of it by n is exact.
+ */
+L1 = 5.4152123484527692e-3, /* 0x162e42ff000000.0p-60 */
+L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */
+INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
+/*
+ * Domain [-0.002708, 0.002708], range ~[-5.7136e-24, 5.7110e-24]:
+ * |exp(x) - p(x)| < 2**-77.2
+ * (0.002708 is ln2/(2*NUM) rounded up a little).
+ */
+P2 = 0.5,
+P3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */
+P4 = 4.1666666666665887e-2, /* 0x155555555554e5.0p-57 */
+P5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */
+P6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */
+
+/*
+ * 2^(i/NUM) for i in [0,NUM] is represented by two values where the
+ * first 47 (?!) bits of the significand is stored in hi and the next 53
+ * bits are in lo.
+ */
+#define NUM 128
+
+static const struct {
+ double hi;
+ double lo;
+} s[NUM] __aligned(16) = {
+ 0x1p+0, 0x0p+0,
+ 0x1.0163da9fb330p+0, 0x1.ab6c25335719bp-47,
+ 0x1.02c9a3e77804p+0, 0x1.07737be56527cp-47,
+ 0x1.04315e86e7f8p+0, 0x1.2f5ce3e688369p-50,
+ 0x1.059b0d315854p+0, 0x1.a1d73e2a475b4p-47,
+ 0x1.0706b29ddf6cp+0, 0x1.dc6dc403a9d88p-48,
+ 0x1.0874518759bcp+0, 0x1.01186be4bb285p-49,
+ 0x1.09e3ecac6f38p+0, 0x1.a290f03062c27p-51,
+ 0x1.0b5586cf9890p+0, 0x1.ec5317256e308p-49,
+ 0x1.0cc922b7247cp+0, 0x1.ba03db82dc49fp-47,
+ 0x1.0e3ec32d3d18p+0, 0x1.10103a1727c58p-47,
+ 0x1.0fb66affed30p+0, 0x1.af232091dd8a1p-48,
+ 0x1.11301d0125b4p+0, 0x1.0a4ebbf1aed93p-48,
+ 0x1.12abdc06c31cp+0, 0x1.7f72575a649adp-49,
+ 0x1.1429aaea92dcp+0, 0x1.fb34101943b26p-48,
+ 0x1.15a98c8a58e4p+0, 0x1.12480d573dd56p-48,
+ 0x1.172b83c7d514p+0, 0x1.d6e6fbe462876p-47,
+ 0x1.18af9388c8dcp+0, 0x1.4dddfb85cd1e1p-47,
+ 0x1.1a35beb6fcb4p+0, 0x1.a9e5b4c7b4969p-47,
+ 0x1.1bbe084045ccp+0, 0x1.39ab1e72b4428p-48,
+ 0x1.1d4873168b98p+0, 0x1.53c02dc0144c8p-47,
+ 0x1.1ed5022fcd90p+0, 0x1.cb8819ff61122p-48,
+ 0x1.2063b88628ccp+0, 0x1.63b8eeb029509p-48,
+ 0x1.21f49917ddc8p+0, 0x1.62552fd29294cp-48,
+ 0x1.2387a6e75620p+0, 0x1.c3360fd6d8e0bp-47,
+ 0x1.251ce4fb2a60p+0, 0x1.f9ac155bef4f5p-47,
+ 0x1.26b4565e27ccp+0, 0x1.d257a673281d4p-48,
+ 0x1.284dfe1f5638p+0, 0x1.2d9e2b9e07941p-53,
+ 0x1.29e9df51fdecp+0, 0x1.09612e8afad12p-47,
+ 0x1.2b87fd0dad98p+0, 0x1.ffbbd48ca71f9p-49,
+ 0x1.2d285a6e4030p+0, 0x1.680123aa6da0fp-49,
+ 0x1.2ecafa93e2f4p+0, 0x1.611ca0f45d524p-48,
+ 0x1.306fe0a31b70p+0, 0x1.52de8d5a46306p-48,
+ 0x1.32170fc4cd80p+0, 0x1.89a9ce78e1804p-47,
+ 0x1.33c08b26416cp+0, 0x1.fa64e43086cb3p-47,
+ 0x1.356c55f929fcp+0, 0x1.864a311a3b1bap-47,
+ 0x1.371a7373aa9cp+0, 0x1.54e28aa05e8a9p-49,
+ 0x1.38cae6d05d84p+0, 0x1.2c2d4e586cdf7p-47,
+ 0x1.3a7db34e59fcp+0, 0x1.b750de494cf05p-47,
+ 0x1.3c32dc313a8cp+0, 0x1.242000f9145acp-47,
+ 0x1.3dea64c12340p+0, 0x1.11ada0911f09fp-47,
+ 0x1.3fa4504ac800p+0, 0x1.ba0bf701aa418p-48,
+ 0x1.4160a21f72e0p+0, 0x1.4fc2192dc79eep-47,
+ 0x1.431f5d950a88p+0, 0x1.6dc704439410dp-48,
+ 0x1.44e086061890p+0, 0x1.68189b7a04ef8p-47,
+ 0x1.46a41ed1d004p+0, 0x1.772512f45922ap-48,
+ 0x1.486a2b5c13ccp+0, 0x1.013c1a3b69063p-48,
+ 0x1.4a32af0d7d3cp+0, 0x1.e672d8bcf46f9p-48,
+ 0x1.4bfdad5362a0p+0, 0x1.38ea1cbd7f621p-47,
+ 0x1.4dcb299fddd0p+0, 0x1.ac766dde353c2p-49,
+ 0x1.4f9b2769d2c8p+0, 0x1.35699ec5b4d50p-47,
+ 0x1.516daa2cf664p+0, 0x1.c112f52c84d82p-52,
+ 0x1.5342b569d4f8p+0, 0x1.df0a83c49d86ap-52,
+ 0x1.551a4ca5d920p+0, 0x1.d8a5d8c40486ap-49,
+ 0x1.56f4736b527cp+0, 0x1.a66ecb004764fp-48,
+ 0x1.58d12d497c7cp+0, 0x1.e9295e15b9a1ep-47,
+ 0x1.5ab07dd48540p+0, 0x1.4ac64980a8c8fp-47,
+ 0x1.5c9268a59468p+0, 0x1.b80e258dc0b4cp-47,
+ 0x1.5e76f15ad214p+0, 0x1.0dd37c9840733p-49,
+ 0x1.605e1b976dc0p+0, 0x1.160edeb25490ep-49,
+ 0x1.6247eb03a558p+0, 0x1.2c7c3e81bf4b7p-50,
+ 0x1.6434634ccc30p+0, 0x1.fc76f8714c4eep-48,
+ 0x1.662388255220p+0, 0x1.24893ecf14dc8p-47,
+ 0x1.68155d44ca94p+0, 0x1.9840e2b913dd0p-47,
+ 0x1.6a09e667f3bcp+0, 0x1.921165f626cddp-49,
+ 0x1.6c012750bda8p+0, 0x1.f76bb54cc007ap-47,
+ 0x1.6dfb23c651a0p+0, 0x1.779107165f0dep-47,
+ 0x1.6ff7df951948p+0, 0x1.e7c3f0da79f11p-51,
+ 0x1.71f75e8ec5f4p+0, 0x1.9ee91b8797785p-47,
+ 0x1.73f9a48a5814p+0, 0x1.9deae4d273456p-47,
+ 0x1.75feb564267cp+0, 0x1.17edd35467491p-49,
+ 0x1.780694fde5d0p+0, 0x1.fb0cd7014042cp-47,
+ 0x1.7a11473eb018p+0, 0x1.b5f54408fdb37p-50,
+ 0x1.7c1ed0130c10p+0, 0x1.93e2499a22c9cp-47,
+ 0x1.7e2f336cf4e4p+0, 0x1.1082e815d0abdp-47,
+ 0x1.80427543e1a0p+0, 0x1.1b60de67649a3p-48,
+ 0x1.82589994cce0p+0, 0x1.28acf88afab35p-48,
+ 0x1.8471a4623c78p+0, 0x1.667297b5cbe32p-47,
+ 0x1.868d99b4492cp+0, 0x1.640720ec85613p-47,
+ 0x1.88ac7d98a668p+0, 0x1.966530bcdf2d5p-48,
+ 0x1.8ace5422aa0cp+0, 0x1.b5ba7c55a192dp-48,
+ 0x1.8cf3216b5448p+0, 0x1.7de55439a2c39p-49,
+ 0x1.8f1ae9915770p+0, 0x1.b15cc13a2e397p-47,
+ 0x1.9145b0b91ffcp+0, 0x1.622986d1a7daep-50,
+ 0x1.93737b0cdc5cp+0, 0x1.27a280e1f92a0p-47,
+ 0x1.95a44cbc8520p+0, 0x1.dd36906d2b420p-49,
+ 0x1.97d829fde4e4p+0, 0x1.f173d241f23d1p-49,
+ 0x1.9a0f170ca078p+0, 0x1.cdd1884dc6234p-47,
+ 0x1.9c49182a3f08p+0, 0x1.01c7c46b071f3p-48,
+ 0x1.9e86319e3230p+0, 0x1.18c12653c7326p-47,
+ 0x1.a0c667b5de54p+0, 0x1.2594d6d45c656p-47,
+ 0x1.a309bec4a2d0p+0, 0x1.9ac60b8fbb86dp-47,
+ 0x1.a5503b23e254p+0, 0x1.c8b424491caf8p-48,
+ 0x1.a799e1330b34p+0, 0x1.86f2dfb2b158fp-48,
+ 0x1.a9e6b5579fd8p+0, 0x1.fa1f5921deffap-47,
+ 0x1.ac36bbfd3f34p+0, 0x1.ce06dcb351893p-47,
+ 0x1.ae89f995ad38p+0, 0x1.6af439a68bb99p-47,
+ 0x1.b0e07298db64p+0, 0x1.2c8421566fe38p-47,
+ 0x1.b33a2b84f15cp+0, 0x1.d7b5fe873decap-47,
+ 0x1.b59728de5590p+0, 0x1.cc71c40888b24p-47,
+ 0x1.b7f76f2fb5e4p+0, 0x1.baa9ec206ad4fp-50,
+ 0x1.ba5b030a1064p+0, 0x1.30819678d5eb7p-49,
+ 0x1.bcc1e904bc1cp+0, 0x1.2247ba0f45b3dp-48,
+ 0x1.bf2c25bd71e0p+0, 0x1.10811ae04a31cp-49,
+ 0x1.c199bdd85528p+0, 0x1.c2220cb12a092p-48,
+ 0x1.c40ab5fffd04p+0, 0x1.d368a6fc1078cp-47,
+ 0x1.c67f12e57d14p+0, 0x1.694426ffa41e5p-49,
+ 0x1.c8f6d9406e78p+0, 0x1.a88d65e24402ep-47,
+ 0x1.cb720dcef904p+0, 0x1.48a81e5e8f4a5p-47,
+ 0x1.cdf0b555dc3cp+0, 0x1.ce227c4ac7d63p-47,
+ 0x1.d072d4a07894p+0, 0x1.dc68791790d0bp-47,
+ 0x1.d2f87080d89cp+0, 0x1.8c56f091cc4f5p-47,
+ 0x1.d5818dcfba48p+0, 0x1.c976816bad9b8p-50,
+ 0x1.d80e316c9838p+0, 0x1.7bb84f9d04880p-48,
+ 0x1.da9e603db328p+0, 0x1.5c2300696db53p-50,
+ 0x1.dd321f301b44p+0, 0x1.025b4aef1e032p-47,
+ 0x1.dfc97337b9b4p+0, 0x1.eb968cac39ed3p-48,
+ 0x1.e264614f5a10p+0, 0x1.45093b0fd0bd7p-47,
+ 0x1.e502ee78b3fcp+0, 0x1.b139e8980a9cdp-47,
+ 0x1.e7a51fbc74c8p+0, 0x1.a5aa4594191bcp-51,
+ 0x1.ea4afa2a490cp+0, 0x1.9858f73a18f5ep-48,
+ 0x1.ecf482d8e67cp+0, 0x1.846d81897dca5p-47,
+ 0x1.efa1bee615a0p+0, 0x1.3bb8fe90d496dp-47,
+ 0x1.f252b376bba8p+0, 0x1.74e8696fc3639p-48,
+ 0x1.f50765b6e454p+0, 0x1.9d3e12dd8a18bp-54,
+ 0x1.f7bfdad9cbe0p+0, 0x1.38913b4bfe72cp-48,
+ 0x1.fa7c1819e90cp+0, 0x1.82e90a7e74b26p-48,
+ 0x1.fd3c22b8f71cp+0, 0x1.884badd25995ep-47
+};
+
+long double
+expl(long double x)
+{
+ union IEEEl2bits u, v;
+ long double fn, r, r1, r2, q, t, t23, t45, twopk, twopkp10000, z;
+ int k, n, n2;
+ uint16_t hx, ix;
+
+ /* Filter out exceptional cases. */
+ u.e = x;
+ hx = u.xbits.expsign;
+ ix = hx & 0x7fff;
+ if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
+ if (ix == BIAS + LDBL_MAX_EXP) {
+ if (hx & 0x8000 && u.xbits.man == 1ULL << 63)
+ return (0.0L); /* x is -Inf */
+ return (x + x); /* x is +Inf, NaN or unsupported */
+ }
+ if (x > o_threshold.e)
+ return (huge * huge);
+ if (x < u_threshold.e)
+ return (tiny * tiny);
+ } else if (ix <= BIAS - 34) { /* |x| < 0x1p-33 */
+ /* includes pseudo-denormals */
+ if (huge + x > 1.0L) /* trigger inexact iff x != 0 */
+ return (1.0L + x);
+ }
+
+ ENTERI();
+
+ /* Reduce x to (k*ln2 + midpoint[n2] + r1 + r2). */
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ fn = x * INV_L + 0x1.8p63 - 0x1.8p63;
+ r = x - fn * L1 - fn * L2; /* r = r1 + r2 done independently. */
+#if defined(HAVE_EFFICIENT_IRINTL)
+ n = irintl(fn);
+#elif defined(HAVE_EFFICIENT_IRINT)
+ n = irint(fn);
+#else
+ n = (int)fn;
+#endif
+ n2 = (unsigned)n % NUM; /* Tang's j. */
+ k = (n - n2) / NUM;
+ r1 = x - fn * L1;
+ r2 = -fn * L2;
+
+ /* Prepare scale factors. */
+ v.xbits.man = 1ULL << 63;
+ if (k >= LDBL_MIN_EXP) {
+ v.xbits.expsign = BIAS + k;
+ twopk = v.e;
+ } else {
+ v.xbits.expsign = BIAS + k + 10000;
+ twopkp10000 = v.e;
+ }
+
+ /* Evaluate expl(midpoint[n2] + r1 + r2) = s[n2] * expl(r1 + r2). */
+ /* Here q = q(r), not q(r1), since r1 is lopped like L1. */
+ t45 = r * P5 + P4;
+ z = r * r;
+ t23 = r * P3 + P2;
+ q = r2 + z * t23 + z * z * t45 + z * z * z * P6;
+ t = (long double)s[n2].lo + s[n2].hi;
+ t = s[n2].lo + t * (q + r1) + s[n2].hi;
+
+ /* Scale by 2**k. */
+ if (k >= LDBL_MIN_EXP) {
+ if (k == LDBL_MAX_EXP)
+ RETURNI(t * 2.0L * 0x1p16383L);
+ RETURNI(t * twopk);
+ } else {
+ RETURNI(t * twopkp10000 * twom10000);
+ }
+}
Modified: head/lib/msun/man/exp.3
==============================================================================
--- head/lib/msun/man/exp.3 Mon Jul 23 16:36:13 2012 (r238721)
+++ head/lib/msun/man/exp.3 Mon Jul 23 19:13:55 2012 (r238722)
@@ -28,13 +28,14 @@
.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
.\" $FreeBSD$
.\"
-.Dd January 17, 2008
+.Dd July 10, 2012
.Dt EXP 3
.Os
.Sh NAME
.Nm exp ,
.Nm expf ,
-.\" The sorting error is intentional. exp and expf should be adjacent.
+.Nm expl ,
+.\" The sorting error is intentional. exp, expf, and expl should be adjacent.
.Nm exp2 ,
.Nm exp2f ,
.Nm exp2l ,
@@ -51,6 +52,8 @@
.Fn exp "double x"
.Ft float
.Fn expf "float x"
+.Ft long double
+.Fn expl "long double x"
.Ft double
.Fn exp2 "double x"
.Ft float
@@ -67,9 +70,10 @@
.Fn powf "float x" "float y"
.Sh DESCRIPTION
The
-.Fn exp
-and the
-.Fn expf
+.Fn exp ,
+.Fn expf ,
+and
+.Fn expl
functions compute the base
.Ms e
exponential value of the given argument
Modified: head/lib/msun/src/e_exp.c
==============================================================================
--- head/lib/msun/src/e_exp.c Mon Jul 23 16:36:13 2012 (r238721)
+++ head/lib/msun/src/e_exp.c Mon Jul 23 19:13:55 2012 (r238722)
@@ -158,3 +158,7 @@ __ieee754_exp(double x) /* default IEEE
return y*twopk*twom1000;
}
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(exp, expl);
+#endif
Modified: head/lib/msun/src/math.h
==============================================================================
--- head/lib/msun/src/math.h Mon Jul 23 16:36:13 2012 (r238721)
+++ head/lib/msun/src/math.h Mon Jul 23 19:13:55 2012 (r238722)
@@ -404,6 +404,7 @@ long double ceill(long double);
long double copysignl(long double, long double) __pure2;
long double cosl(long double);
long double exp2l(long double);
+long double expl(long double);
long double fabsl(long double) __pure2;
long double fdiml(long double, long double);
long double floorl(long double);
@@ -461,7 +462,6 @@ long double atanhl(long double);
long double coshl(long double);
long double erfcl(long double);
long double erfl(long double);
-long double expl(long double);
long double expm1l(long double);
long double lgammal(long double);
long double log10l(long double);
Modified: head/lib/msun/src/math_private.h
==============================================================================
--- head/lib/msun/src/math_private.h Mon Jul 23 16:36:13 2012 (r238721)
+++ head/lib/msun/src/math_private.h Mon Jul 23 19:13:55 2012 (r238722)
@@ -207,6 +207,13 @@ do { \
(d) = se_u.e; \
} while (0)
+/* Long double constants are broken on i386. This workaround is OK always. */
+#define LD80C(m, ex, s, v) { \
+ /* .e = v, */ /* overwritten */ \
+ .xbits.man = __CONCAT(m, ULL), \
+ .xbits.expsign = (0x3fff + (ex)) | ((s) ? 0x8000 : 0), \
+}
+
#ifdef FLT_EVAL_METHOD
/*
* Attempt to get strict C99 semantics for assignment with non-C99 compilers.
@@ -225,8 +232,30 @@ do { \
} \
} while (0)
#endif
+#endif /* FLT_EVAL_METHOD */
+
+/* Support switching the mode to FP_PE if necessary. */
+#if defined(__i386__) && !defined(NO_FPSETPREC)
+#define ENTERI() \
+ long double __retval; \
+ fp_prec_t __oprec; \
+ \
+ if ((__oprec = fpgetprec()) != FP_PE) \
+ fpsetprec(FP_PE);
+#define RETURNI(x) do { \
+ __retval = (x); \
+ if (__oprec != FP_PE) \
+ fpsetprec(__oprec); \
+ RETURNF(__retval); \
+} while (0)
+#else
+#define ENTERI(x)
+#define RETURNI(x) RETURNF(x)
#endif
+/* Default return statement if hack*_t() is not used. */
+#define RETURNF(v) return (v)
+
/*
* Common routine to process the arguments to nan(), nanf(), and nanl().
*/
@@ -323,6 +352,18 @@ irint(double x)
#define HAVE_EFFICIENT_IRINT
#endif
+#if defined(__amd64__) || defined(__i386__)
+static __inline int
+irintl(long double x)
+{
+ int n;
+
+ asm("fistl %0" : "=m" (n) : "t" (x));
+ return (n);
+}
+#define HAVE_EFFICIENT_IRINTL
+#endif
+
#endif /* __GNUCLIKE_ASM */
/*
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