diff options
author | neel <neel@FreeBSD.org> | 2012-11-11 03:26:14 +0000 |
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committer | neel <neel@FreeBSD.org> | 2012-11-11 03:26:14 +0000 |
commit | bc4be3dff1bc1b0cdc3ea30df0fd3e83998cf9eb (patch) | |
tree | b6b271fb331d43e30e10d824f2042de2c063f2eb /lib/msun | |
parent | 263c4acf84c3be71025f3484c0378a83cd668e15 (diff) | |
parent | de6ea8b20e870490db809a8d8a965bd784981d81 (diff) | |
download | FreeBSD-src-bc4be3dff1bc1b0cdc3ea30df0fd3e83998cf9eb.zip FreeBSD-src-bc4be3dff1bc1b0cdc3ea30df0fd3e83998cf9eb.tar.gz |
IFC @ r242684
Diffstat (limited to 'lib/msun')
-rw-r--r-- | lib/msun/Makefile | 2 | ||||
-rw-r--r-- | lib/msun/Symbol.map | 1 | ||||
-rw-r--r-- | lib/msun/i387/s_cos.S | 10 | ||||
-rw-r--r-- | lib/msun/i387/s_sin.S | 10 | ||||
-rw-r--r-- | lib/msun/i387/s_tan.S | 12 | ||||
-rw-r--r-- | lib/msun/ld128/s_expl.c | 261 | ||||
-rw-r--r-- | lib/msun/ld80/s_expl.c | 304 | ||||
-rw-r--r-- | lib/msun/man/cexp.3 | 10 | ||||
-rw-r--r-- | lib/msun/man/exp.3 | 14 | ||||
-rw-r--r-- | lib/msun/man/ieee.3 | 67 | ||||
-rw-r--r-- | lib/msun/src/e_exp.c | 4 | ||||
-rw-r--r-- | lib/msun/src/e_rem_pio2.c | 6 | ||||
-rw-r--r-- | lib/msun/src/e_rem_pio2f.c | 8 | ||||
-rw-r--r-- | lib/msun/src/k_cosf.c | 6 | ||||
-rw-r--r-- | lib/msun/src/k_sinf.c | 6 | ||||
-rw-r--r-- | lib/msun/src/k_tanf.c | 6 | ||||
-rw-r--r-- | lib/msun/src/math.h | 2 | ||||
-rw-r--r-- | lib/msun/src/math_private.h | 66 | ||||
-rw-r--r-- | lib/msun/src/s_cbrtl.c | 26 | ||||
-rw-r--r-- | lib/msun/src/s_cosl.c | 9 | ||||
-rw-r--r-- | lib/msun/src/s_sinl.c | 9 | ||||
-rw-r--r-- | lib/msun/src/s_tanl.c | 9 |
22 files changed, 733 insertions, 115 deletions
diff --git a/lib/msun/Makefile b/lib/msun/Makefile index 0646dc0..a1ec6c9 100644 --- a/lib/msun/Makefile +++ b/lib/msun/Makefile @@ -94,7 +94,7 @@ COMMON_SRCS+= e_acosl.c e_asinl.c e_atan2l.c e_fmodl.c \ e_hypotl.c e_remainderl.c e_sqrtl.c \ invtrig.c k_cosl.c k_sinl.c k_tanl.c \ s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \ - s_csqrtl.c s_exp2l.c s_floorl.c s_fmal.c \ + s_csqrtl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \ s_frexpl.c s_logbl.c s_nanl.c s_nextafterl.c s_nexttoward.c \ s_remquol.c s_rintl.c s_scalbnl.c \ s_sinl.c s_tanl.c s_truncl.c w_cabsl.c diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map index f3d3000..76f1bfb 100644 --- a/lib/msun/Symbol.map +++ b/lib/msun/Symbol.map @@ -249,4 +249,5 @@ FBSD_1.3 { ctanf; ctanh; ctanhf; + expl; }; diff --git a/lib/msun/i387/s_cos.S b/lib/msun/i387/s_cos.S index 9c3f2ca..9951ab0 100644 --- a/lib/msun/i387/s_cos.S +++ b/lib/msun/i387/s_cos.S @@ -40,16 +40,16 @@ ENTRY(cos) fldl 4(%esp) fcos fnstsw %ax - andw $0x400,%ax - jnz 1f + sahf + jp 1f ret 1: fldpi fadd %st(0) fxch %st(1) -2: fprem1 +2: fprem fnstsw %ax - andw $0x400,%ax - jnz 2b + sahf + jp 2b fstp %st(1) fcos ret diff --git a/lib/msun/i387/s_sin.S b/lib/msun/i387/s_sin.S index 11c4d63..eb04754 100644 --- a/lib/msun/i387/s_sin.S +++ b/lib/msun/i387/s_sin.S @@ -40,16 +40,16 @@ ENTRY(sin) fldl 4(%esp) fsin fnstsw %ax - andw $0x400,%ax - jnz 1f + sahf + jp 1f ret 1: fldpi fadd %st(0) fxch %st(1) -2: fprem1 +2: fprem fnstsw %ax - andw $0x400,%ax - jnz 2b + sahf + jp 2b fstp %st(1) fsin ret diff --git a/lib/msun/i387/s_tan.S b/lib/msun/i387/s_tan.S index e31ebdf..182b9f7 100644 --- a/lib/msun/i387/s_tan.S +++ b/lib/msun/i387/s_tan.S @@ -40,17 +40,17 @@ ENTRY(tan) fldl 4(%esp) fptan fnstsw %ax - andw $0x400,%ax - jnz 1f + sahf + jp 1f fstp %st(0) ret 1: fldpi fadd %st(0) fxch %st(1) -2: fprem1 - fstsw %ax - andw $0x400,%ax - jnz 2b +2: fprem + fnstsw %ax + sahf + jp 2b fstp %st(1) fptan fstp %st(0) diff --git a/lib/msun/ld128/s_expl.c b/lib/msun/ld128/s_expl.c new file mode 100644 index 0000000..5052c3a --- /dev/null +++ b/lib/msun/ld128/s_expl.c @@ -0,0 +1,261 @@ +/*- + * Copyright (c) 2012 Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +/* + * ld128 version of s_expl.c. See ../ld80/s_expl.c for most comments. + */ + +#include <float.h> + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +#define INTERVALS 128 +#define BIAS (LDBL_MAX_EXP - 1) + +static volatile const long double tiny = 0x1p-10000L; + +static const long double +INV_L = 1.84664965233787316142070359168242182e+02L, +L1 = 5.41521234812457272982212595914567508e-03L, +L2 = -1.02536706388947310094527932552595546e-29L, +huge = 0x1p10000L, +o_threshold = 11356.523406294143949491931077970763428L, +twom10000 = 0x1p-10000L, +u_threshold = -11433.462743336297878837243843452621503L; + +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; + +static const struct { + long double hi; + long double lo; +} s[INTERVALS] = { + 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, 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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 & 0x7fff; + if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */ + if (ix == BIAS + LDBL_MAX_EXP) { + if (hx & 0x8000 && u.xbits.manh == 0 && + u.xbits.manl == 0) + return (0.0L); /* x is -Inf */ + return (x + x); /* x is +Inf or NaN */ + } + if (x > o_threshold) + return (huge * huge); + if (x < u_threshold) + return (tiny * tiny); + } else if (ix < BIAS - 115) { /* |x| < 0x1p-115 */ + if (huge + x > 1.0L) /* trigger inexact iff x != 0 */ + return (1.0L + x); + } + + /* Reduce x to (k*ln2 + midpoint[n2] + r1 + r2). */ + fn = x * INV_L + 0x1.8p112 - 0x1.8p112; + n = (int)fn; + n2 = (unsigned)n % INTERVALS; + k = (n - n2) / INTERVALS; + 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); + } +} diff --git a/lib/msun/ld80/s_expl.c b/lib/msun/ld80/s_expl.c new file mode 100644 index 0000000..af63668 --- /dev/null +++ b/lib/msun/ld80/s_expl.c @@ -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 INTERVALS (see below). + */ + +#include <float.h> + +#ifdef __i386__ +#include <ieeefp.h> +#endif + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +#define INTERVALS 128 +#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, 11356.5234062941439488L), +/* log(2**(-16381-64-1)) rounded towards zero: */ +u_threshold = LD80C(0xb21dfe7f09e2baa9, 13, -11399.4985314888605581L); + +static const double +/* + * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must + * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest + * bits zero so that multiplication of it by n is exact. + */ +INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */ +L1 = 5.4152123484527692e-3, /* 0x162e42ff000000.0p-60 */ +L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */ +/* + * Domain [-0.002708, 0.002708], range ~[-5.7136e-24, 5.7110e-24]: + * |exp(x) - p(x)| < 2**-77.2 + * (0.002708 is ln2/(2*INTERVALS) 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/INTERVALS) for i in [0,INTERVALS] is represented by two values where + * the first 53 bits of the significand are stored in hi and the next 53 + * bits are in lo. Tang's paper states that the trailing 6 bits of hi must + * be zero for his algorithm in both single and double precision, because + * the table is re-used in the implementation of expm1() where a floating + * point addition involving hi must be exact. Here hi is double, so + * converting it to long double gives 11 trailing zero bits. + */ +static const struct { + double hi; + double lo; +/* XXX should rename 's'. */ +} s[INTERVALS] = { + 0x1p+0, 0x0p+0, + 0x1.0163da9fb3335p+0, 0x1.b61299ab8cdb7p-54, + 0x1.02c9a3e778060p+0, 0x1.dcdef95949ef4p-53, + 0x1.04315e86e7f84p+0, 0x1.7ae71f3441b49p-53, + 0x1.059b0d3158574p+0, 0x1.d73e2a475b465p-55, + 0x1.0706b29ddf6ddp+0, 0x1.8db880753b0f6p-53, + 0x1.0874518759bc8p+0, 0x1.186be4bb284ffp-57, + 0x1.09e3ecac6f383p+0, 0x1.1487818316136p-54, + 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc610bp-54, + 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f71p-54, + 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c57b53p-59, + 0x1.0fb66affed31ap+0, 0x1.e464123bb1428p-53, + 0x1.11301d0125b50p+0, 0x1.49d77e35db263p-53, + 0x1.12abdc06c31cbp+0, 0x1.f72575a649ad2p-53, + 0x1.1429aaea92ddfp+0, 0x1.66820328764b1p-53, + 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeab0ap-55, + 0x1.172b83c7d517ap+0, 0x1.b9bef918a1d63p-53, + 0x1.18af9388c8de9p+0, 0x1.777ee1734784ap-53, + 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4968e4p-55, + 0x1.1bbe084045cd3p+0, 0x1.3563ce56884fcp-53, + 0x1.1d4873168b9aap+0, 0x1.e016e00a2643cp-54, + 0x1.1ed5022fcd91cp+0, 0x1.71033fec2243ap-53, + 0x1.2063b88628cd6p+0, 0x1.dc775814a8495p-55, + 0x1.21f49917ddc96p+0, 0x1.2a97e9494a5eep-55, + 0x1.2387a6e756238p+0, 0x1.9b07eb6c70573p-54, + 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f4a4p-55, + 0x1.26b4565e27cddp+0, 0x1.2bd339940e9d9p-55, + 0x1.284dfe1f56380p+0, 0x1.2d9e2b9e07941p-53, + 0x1.29e9df51fdee1p+0, 0x1.612e8afad1255p-55, + 0x1.2b87fd0dad98fp+0, 0x1.fbbd48ca71f95p-53, + 0x1.2d285a6e4030bp+0, 0x1.0024754db41d5p-54, + 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d52383p-56, + 0x1.306fe0a31b715p+0, 0x1.6f46ad23182e4p-55, + 0x1.32170fc4cd831p+0, 0x1.a9ce78e18047cp-55, + 0x1.33c08b26416ffp+0, 0x1.32721843659a6p-54, + 0x1.356c55f929ff0p+0, 0x1.928c468ec6e76p-53, + 0x1.371a7373aa9cap+0, 0x1.4e28aa05e8a8fp-53, + 0x1.38cae6d05d865p+0, 0x1.0b53961b37da2p-53, + 0x1.3a7db34e59ff6p+0, 0x1.d43792533c144p-53, + 0x1.3c32dc313a8e4p+0, 0x1.08003e4516b1ep-53, + 0x1.3dea64c123422p+0, 0x1.ada0911f09ebcp-55, + 0x1.3fa4504ac801bp+0, 0x1.417ee03548306p-53, + 0x1.4160a21f72e29p+0, 0x1.f0864b71e7b6cp-53, + 0x1.431f5d950a896p+0, 0x1.b8e088728219ap-53, + 0x1.44e086061892dp+0, 0x1.89b7a04ef80d0p-59, + 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a76p-54, + 0x1.486a2b5c13cd0p+0, 0x1.3c1a3b69062f0p-56, + 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be56p-54, + 0x1.4bfdad5362a27p+0, 0x1.d4397afec42e2p-56, + 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a7833p-54, + 0x1.4f9b2769d2ca6p+0, 0x1.5a67b16d3540ep-53, + 0x1.516daa2cf6641p+0, 0x1.8225ea5909b04p-53, + 0x1.5342b569d4f81p+0, 0x1.be1507893b0d5p-53, + 0x1.551a4ca5d920ep+0, 0x1.8a5d8c4048699p-53, + 0x1.56f4736b527dap+0, 0x1.9bb2c011d93adp-54, + 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1de8p-55, + 0x1.5ab07dd485429p+0, 0x1.6324c054647adp-54, + 0x1.5c9268a5946b7p+0, 0x1.c4b1b816986a2p-60, + 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e65ep-54, + 0x1.605e1b976dc08p+0, 0x1.60edeb25490dcp-53, + 0x1.6247eb03a5584p+0, 0x1.63e1f40dfa5b5p-53, + 0x1.6434634ccc31fp+0, 0x1.8edf0e2989db3p-53, + 0x1.6623882552224p+0, 0x1.224fb3c5371e6p-53, + 0x1.68155d44ca973p+0, 0x1.038ae44f73e65p-57, + 0x1.6a09e667f3bccp+0, 0x1.21165f626cdd5p-53, + 0x1.6c012750bdabep+0, 0x1.daed533001e9ep-53, + 0x1.6dfb23c651a2ep+0, 0x1.e441c597c3775p-53, + 0x1.6ff7df9519483p+0, 0x1.9f0fc369e7c42p-53, + 0x1.71f75e8ec5f73p+0, 0x1.ba46e1e5de15ap-53, + 0x1.73f9a48a58173p+0, 0x1.7ab9349cd1562p-53, + 0x1.75feb564267c8p+0, 0x1.7edd354674916p-53, + 0x1.780694fde5d3fp+0, 0x1.866b80a02162dp-54, + 0x1.7a11473eb0186p+0, 0x1.afaa2047ed9b4p-53, + 0x1.7c1ed0130c132p+0, 0x1.f124cd1164dd6p-54, + 0x1.7e2f336cf4e62p+0, 0x1.05d02ba15797ep-56, + 0x1.80427543e1a11p+0, 0x1.6c1bccec9346bp-53, + 0x1.82589994cce12p+0, 0x1.159f115f56694p-53, + 0x1.8471a4623c7acp+0, 0x1.9ca5ed72f8c81p-53, + 0x1.868d99b4492ecp+0, 0x1.01c83b21584a3p-53, + 0x1.88ac7d98a6699p+0, 0x1.994c2f37cb53ap-54, + 0x1.8ace5422aa0dbp+0, 0x1.6e9f156864b27p-54, + 0x1.8cf3216b5448bp+0, 0x1.de55439a2c38bp-53, + 0x1.8f1ae99157736p+0, 0x1.5cc13a2e3976cp-55, + 0x1.9145b0b91ffc5p+0, 0x1.114c368d3ed6ep-53, + 0x1.93737b0cdc5e4p+0, 0x1.e8a0387e4a814p-53, + 0x1.95a44cbc8520ep+0, 0x1.d36906d2b41f9p-53, + 0x1.97d829fde4e4fp+0, 0x1.173d241f23d18p-53, + 0x1.9a0f170ca07b9p+0, 0x1.7462137188ce7p-53, + 0x1.9c49182a3f090p+0, 0x1.c7c46b071f2bep-56, + 0x1.9e86319e32323p+0, 0x1.824ca78e64c6ep-56, + 0x1.a0c667b5de564p+0, 0x1.6535b51719567p-53, + 0x1.a309bec4a2d33p+0, 0x1.6305c7ddc36abp-54, + 0x1.a5503b23e255cp+0, 0x1.1684892395f0fp-53, + 0x1.a799e1330b358p+0, 0x1.bcb7ecac563c7p-54, + 0x1.a9e6b5579fdbfp+0, 0x1.0fac90ef7fd31p-54, + 0x1.ac36bbfd3f379p+0, 0x1.81b72cd4624ccp-53, + 0x1.ae89f995ad3adp+0, 0x1.7a1cd345dcc81p-54, + 0x1.b0e07298db665p+0, 0x1.2108559bf8deep-53, + 0x1.b33a2b84f15fap+0, 0x1.ed7fa1cf7b290p-53, + 0x1.b59728de55939p+0, 0x1.1c7102222c90ep-53, + 0x1.b7f76f2fb5e46p+0, 0x1.d54f610356a79p-53, + 0x1.ba5b030a10649p+0, 0x1.0819678d5eb69p-53, + 0x1.bcc1e904bc1d2p+0, 0x1.23dd07a2d9e84p-55, + 0x1.bf2c25bd71e08p+0, 0x1.0811ae04a31c7p-53, + 0x1.c199bdd85529cp+0, 0x1.11065895048ddp-55, + 0x1.c40ab5fffd07ap+0, 0x1.b4537e083c60ap-54, + 0x1.c67f12e57d14bp+0, 0x1.2884dff483cadp-54, + 0x1.c8f6d9406e7b5p+0, 0x1.1acbc48805c44p-56, + 0x1.cb720dcef9069p+0, 0x1.503cbd1e949dbp-56, + 0x1.cdf0b555dc3f9p+0, 0x1.889f12b1f58a3p-53, + 0x1.d072d4a07897bp+0, 0x1.1a1e45e4342b2p-53, + 0x1.d2f87080d89f1p+0, 0x1.15bc247313d44p-53, + 0x1.d5818dcfba487p+0, 0x1.2ed02d75b3707p-55, + 0x1.d80e316c98397p+0, 0x1.7709f3a09100cp-53, + 0x1.da9e603db3285p+0, 0x1.c2300696db532p-54, + 0x1.dd321f301b460p+0, 0x1.2da5778f018c3p-54, + 0x1.dfc97337b9b5ep+0, 0x1.72d195873da52p-53, + 0x1.e264614f5a128p+0, 0x1.424ec3f42f5b5p-53, + 0x1.e502ee78b3ff6p+0, 0x1.39e8980a9cc8fp-55, + 0x1.e7a51fbc74c83p+0, 0x1.2d522ca0c8de2p-54, + 0x1.ea4afa2a490d9p+0, 0x1.0b1ee7431ebb6p-53, + 0x1.ecf482d8e67f0p+0, 0x1.1b60625f7293ap-53, + 0x1.efa1bee615a27p+0, 0x1.dc7f486a4b6b0p-54, + 0x1.f252b376bba97p+0, 0x1.3a1a5bf0d8e43p-54, + 0x1.f50765b6e4540p+0, 0x1.9d3e12dd8a18bp-54, + 0x1.f7bfdad9cbe13p+0, 0x1.1227697fce57bp-53, + 0x1.fa7c1819e90d8p+0, 0x1.74853f3a5931ep-55, + 0x1.fd3c22b8f71f1p+0, 0x1.2eb74966579e7p-57 +}; + +long double +expl(long double x) +{ + union IEEEl2bits u, v; + long double fn, q, r, r1, r2, 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 - 66) { /* |x| < 0x1p-66 */ + /* 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 % INTERVALS; + k = (n - n2) / INTERVALS; + 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); + } +} diff --git a/lib/msun/man/cexp.3 b/lib/msun/man/cexp.3 index 59bb1cd..97e36c1 100644 --- a/lib/msun/man/cexp.3 +++ b/lib/msun/man/cexp.3 @@ -59,17 +59,17 @@ behaves according to Euler's formula: .Bd -ragged -offset indent .Fn cexp "x + I*y" = -.Ns ( Sy e Ns ** Ns +.Po Sy e Ns ** Ns .Fa x * -.Em cos Ns ( Ns -.Fa y Ns )) + ( Ns +.Em cos Ns Po Ns +.Fa y Ns Pc Pc + Po Ns .Sy I * .Sy e Ns ** Ns .Fa x * -.Em sin Ns ( Ns -.Fa y Ns )) +.Em sin Ns Po Ns +.Fa y Ns Pc Pc .Ed .Pp Generally speaking, infinities, zeroes and \*(Nas are handled as would diff --git a/lib/msun/man/exp.3 b/lib/msun/man/exp.3 index b051e5b..5907337 100644 --- a/lib/msun/man/exp.3 +++ b/lib/msun/man/exp.3 @@ -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 diff --git a/lib/msun/man/ieee.3 b/lib/msun/man/ieee.3 index 57e1fcd..5c1c531 100644 --- a/lib/msun/man/ieee.3 +++ b/lib/msun/man/ieee.3 @@ -156,59 +156,60 @@ Wordsize: 32 bits. .Pp Precision: 24 significant bits, roughly like 7 significant decimals. -.Bd -ragged -offset indent -compact +.Pp If x and x' are consecutive positive single-precision numbers (they differ by 1 .Em ulp ) , then -.Bd -ragged -compact +.Bl -column "XXX" -compact 5.9e\-08 < 0.5**24 < (x'\-x)/x \(<= 0.5**23 < 1.2e\-07. -.Ed -.Ed +.El .Pp .Bl -column "XXX" -compact Range: Overflow threshold = 2.0**128 = 3.4e38 Underflow threshold = 0.5**126 = 1.2e\-38 .El -.Bd -ragged -offset indent -compact +.Pp Underflowed results round to the nearest -integer multiple of 0.5**149 = 1.4e\-45. -.Ed +integer multiple of +.Bl -column "XXX" -compact +0.5**149 = 1.4e\-45. +.El .Ed .Pp Double-precision: .Bd -ragged -offset indent -compact Type name: .Vt double -.Bd -ragged -offset indent -compact -On some architectures, +.Po On some architectures, .Vt long double is the same as -.Vt double . -.Ed +.Vt double +.Pc .Pp Wordsize: 64 bits. .Pp Precision: 53 significant bits, roughly like 16 significant decimals. -.Bd -ragged -offset indent -compact +.Pp If x and x' are consecutive positive double-precision numbers (they differ by 1 .Em ulp ) , then -.Bd -ragged -compact +.Bl -column "XXX" -compact 1.1e\-16 < 0.5**53 < (x'\-x)/x \(<= 0.5**52 < 2.3e\-16. -.Ed -.Ed +.El .Pp .Bl -column "XXX" -compact Range: Overflow threshold = 2.0**1024 = 1.8e308 Underflow threshold = 0.5**1022 = 2.2e\-308 .El -.Bd -ragged -offset indent -compact +.Pp Underflowed results round to the nearest -integer multiple of 0.5**1074 = 4.9e\-324. -.Ed +integer multiple of +.Bl -column "XXX" -compact +0.5**1074 = 4.9e\-324. +.El .Ed .Pp Extended-precision: @@ -221,24 +222,25 @@ Wordsize: 96 bits. .Pp Precision: 64 significant bits, roughly like 19 significant decimals. -.Bd -ragged -offset indent -compact +.Pp If x and x' are consecutive positive extended-precision numbers (they differ by 1 .Em ulp ) , then -.Bd -ragged -compact +.Bl -column "XXX" -compact 1.0e\-19 < 0.5**63 < (x'\-x)/x \(<= 0.5**62 < 2.2e\-19. -.Ed -.Ed +.El .Pp .Bl -column "XXX" -compact Range: Overflow threshold = 2.0**16384 = 1.2e4932 Underflow threshold = 0.5**16382 = 3.4e\-4932 .El -.Bd -ragged -offset indent -compact +.Pp Underflowed results round to the nearest -integer multiple of 0.5**16445 = 5.7e\-4953. -.Ed +integer multiple of +.Bl -column "XXX" -compact +0.5**16445 = 5.7e\-4953. +.El .Ed .Pp Quad-extended-precision: @@ -251,24 +253,25 @@ Wordsize: 128 bits. .Pp Precision: 113 significant bits, roughly like 34 significant decimals. -.Bd -ragged -offset indent -compact +.Pp If x and x' are consecutive positive quad-extended-precision numbers (they differ by 1 .Em ulp ) , then -.Bd -ragged -compact +.Bl -column "XXX" -compact 9.6e\-35 < 0.5**113 < (x'\-x)/x \(<= 0.5**112 < 2.0e\-34. -.Ed -.Ed +.El .Pp .Bl -column "XXX" -compact Range: Overflow threshold = 2.0**16384 = 1.2e4932 Underflow threshold = 0.5**16382 = 3.4e\-4932 .El -.Bd -ragged -offset indent -compact +.Pp Underflowed results round to the nearest -integer multiple of 0.5**16494 = 6.5e\-4966. -.Ed +integer multiple of +.Bl -column "XXX" -compact +0.5**16494 = 6.5e\-4966. +.El .Ed .Ss Additional Information Regarding Exceptions For each kind of floating-point exception, IEEE 754 diff --git a/lib/msun/src/e_exp.c b/lib/msun/src/e_exp.c index b47aef5..e432bc8 100644 --- a/lib/msun/src/e_exp.c +++ b/lib/msun/src/e_exp.c @@ -158,3 +158,7 @@ __ieee754_exp(double x) /* default IEEE double exp */ return y*twopk*twom1000; } } + +#if (LDBL_MANT_DIG == 53) +__weak_reference(exp, expl); +#endif diff --git a/lib/msun/src/e_rem_pio2.c b/lib/msun/src/e_rem_pio2.c index fde9660..be2630b 100644 --- a/lib/msun/src/e_rem_pio2.c +++ b/lib/msun/src/e_rem_pio2.c @@ -48,10 +48,10 @@ pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ -#ifndef INLINE_REM_PIO2 -extern +#ifdef INLINE_REM_PIO2 +static __inline __always_inline #endif -__inline int +int __ieee754_rem_pio2(double x, double *y) { double z,w,t,r,fn; diff --git a/lib/msun/src/e_rem_pio2f.c b/lib/msun/src/e_rem_pio2f.c index fb608d1..f1ee7a0 100644 --- a/lib/msun/src/e_rem_pio2f.c +++ b/lib/msun/src/e_rem_pio2f.c @@ -31,7 +31,7 @@ __FBSDID("$FreeBSD$"); /* * invpio2: 53 bits of 2/pi - * pio2_1: first 33 bit of pi/2 + * pio2_1: first 25 bits of pi/2 * pio2_1t: pi/2 - pio2_1 */ @@ -40,10 +40,10 @@ invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ -#ifndef INLINE_REM_PIO2F -extern +#ifdef INLINE_REM_PIO2F +static __inline __always_inline #endif -__inline int +int __ieee754_rem_pio2f(float x, double *y) { double w,r,fn; diff --git a/lib/msun/src/k_cosf.c b/lib/msun/src/k_cosf.c index 92bce48..f7a2c0a 100644 --- a/lib/msun/src/k_cosf.c +++ b/lib/msun/src/k_cosf.c @@ -30,10 +30,10 @@ C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */ C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */ C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */ -#ifndef INLINE_KERNEL_COSDF -extern +#ifdef INLINE_KERNEL_COSDF +static __inline #endif -__inline float +float __kernel_cosdf(double x) { double r, w, z; diff --git a/lib/msun/src/k_sinf.c b/lib/msun/src/k_sinf.c index aa4f268..0841759 100644 --- a/lib/msun/src/k_sinf.c +++ b/lib/msun/src/k_sinf.c @@ -29,10 +29,10 @@ S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */ S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */ S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */ -#ifndef INLINE_KERNEL_SINDF -extern +#ifdef INLINE_KERNEL_SINDF +static __inline #endif -__inline float +float __kernel_sindf(double x) { double r, s, w, z; diff --git a/lib/msun/src/k_tanf.c b/lib/msun/src/k_tanf.c index 6b073da..52f1aaa 100644 --- a/lib/msun/src/k_tanf.c +++ b/lib/msun/src/k_tanf.c @@ -32,10 +32,10 @@ T[] = { 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ }; -#ifndef INLINE_KERNEL_TANDF -extern +#ifdef INLINE_KERNEL_TANDF +static __inline #endif -__inline float +float __kernel_tandf(double x, int iy) { double z,r,w,s,t,u; diff --git a/lib/msun/src/math.h b/lib/msun/src/math.h index cf34583..c6cee13 100644 --- a/lib/msun/src/math.h +++ b/lib/msun/src/math.h @@ -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); diff --git a/lib/msun/src/math_private.h b/lib/msun/src/math_private.h index 79280e3..5662df0 100644 --- a/lib/msun/src/math_private.h +++ b/lib/msun/src/math_private.h @@ -207,6 +207,17 @@ do { \ (d) = se_u.e; \ } while (0) +#ifdef __i386__ +/* Long double constants are broken on i386. */ +#define LD80C(m, ex, v) { \ + .xbits.man = __CONCAT(m, ULL), \ + .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \ +} +#else +/* The above works on non-i386 too, but we use this to check v. */ +#define LD80C(m, ex, v) { .e = (v), } +#endif + #ifdef FLT_EVAL_METHOD /* * Attempt to get strict C99 semantics for assignment with non-C99 compilers. @@ -217,7 +228,7 @@ do { \ #define STRICT_ASSIGN(type, lval, rval) do { \ volatile type __lval; \ \ - if (sizeof(type) >= sizeof(double)) \ + if (sizeof(type) >= sizeof(long double)) \ (lval) = (rval); \ else { \ __lval = (rval); \ @@ -225,8 +236,30 @@ 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 +356,18 @@ 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 */ /* @@ -390,10 +435,9 @@ irint(double x) int __kernel_rem_pio2(double*,double*,int,int,int); /* double precision kernel functions */ -#ifdef INLINE_REM_PIO2 -__inline -#endif +#ifndef INLINE_REM_PIO2 int __ieee754_rem_pio2(double,double*); +#endif double __kernel_sin(double,double,int); double __kernel_cos(double,double); double __kernel_tan(double,double,int); @@ -403,22 +447,18 @@ double complex __ldexp_cexp(double complex,int); #endif /* float precision kernel functions */ -#ifdef INLINE_REM_PIO2F -__inline -#endif +#ifndef INLINE_REM_PIO2F int __ieee754_rem_pio2f(float,double*); -#ifdef INLINE_KERNEL_SINDF -__inline #endif +#ifndef INLINE_KERNEL_SINDF float __kernel_sindf(double); -#ifdef INLINE_KERNEL_COSDF -__inline #endif +#ifndef INLINE_KERNEL_COSDF float __kernel_cosdf(double); -#ifdef INLINE_KERNEL_TANDF -__inline #endif +#ifndef INLINE_KERNEL_TANDF float __kernel_tandf(double,int); +#endif float __ldexp_expf(float,int); #ifdef _COMPLEX_H float complex __ldexp_cexpf(float complex,int); diff --git a/lib/msun/src/s_cbrtl.c b/lib/msun/src/s_cbrtl.c index 23c9184..2236c0f 100644 --- a/lib/msun/src/s_cbrtl.c +++ b/lib/msun/src/s_cbrtl.c @@ -18,7 +18,9 @@ __FBSDID("$FreeBSD$"); #include <float.h> +#ifdef __i386__ #include <ieeefp.h> +#endif #include "fpmath.h" #include "math.h" @@ -51,23 +53,11 @@ cbrtl(long double x) if (k == BIAS + LDBL_MAX_EXP) return (x + x); -#ifdef __i386__ - fp_prec_t oprec; - - oprec = fpgetprec(); - if (oprec != FP_PE) - fpsetprec(FP_PE); -#endif - + ENTERI(); if (k == 0) { /* If x = +-0, then cbrt(x) = +-0. */ - if ((u.bits.manh | u.bits.manl) == 0) { -#ifdef __i386__ - if (oprec != FP_PE) - fpsetprec(oprec); -#endif - return (x); - } + if ((u.bits.manh | u.bits.manl) == 0) + RETURNI(x); /* Adjust subnormal numbers. */ u.e *= 0x1.0p514; k = u.bits.exp; @@ -149,9 +139,5 @@ cbrtl(long double x) t=t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */ t *= v.e; -#ifdef __i386__ - if (oprec != FP_PE) - fpsetprec(oprec); -#endif - return (t); + RETURNI(t); } diff --git a/lib/msun/src/s_cosl.c b/lib/msun/src/s_cosl.c index 8d43626..22e74cf 100644 --- a/lib/msun/src/s_cosl.c +++ b/lib/msun/src/s_cosl.c @@ -33,6 +33,9 @@ __FBSDID("$FreeBSD$"); */ #include <float.h> +#ifdef __i386__ +#include <ieeefp.h> +#endif #include "math.h" #include "math_private.h" @@ -63,9 +66,11 @@ cosl(long double x) if (z.bits.exp == 32767) return ((x - x) / (x - x)); + ENTERI(); + /* Optimize the case where x is already within range. */ if (z.e < M_PI_4) - return (__kernel_cosl(z.e, 0)); + RETURNI(__kernel_cosl(z.e, 0)); e0 = __ieee754_rem_pio2l(x, y); hi = y[0]; @@ -86,5 +91,5 @@ cosl(long double x) break; } - return (hi); + RETURNI(hi); } diff --git a/lib/msun/src/s_sinl.c b/lib/msun/src/s_sinl.c index 919deb9..f454f8f 100644 --- a/lib/msun/src/s_sinl.c +++ b/lib/msun/src/s_sinl.c @@ -28,6 +28,9 @@ __FBSDID("$FreeBSD$"); #include <float.h> +#ifdef __i386__ +#include <ieeefp.h> +#endif #include "math.h" #include "math_private.h" @@ -59,10 +62,12 @@ sinl(long double x) if (z.bits.exp == 32767) return ((x - x) / (x - x)); + ENTERI(); + /* Optimize the case where x is already within range. */ if (z.e < M_PI_4) { hi = __kernel_sinl(z.e, 0, 0); - return (s ? -hi : hi); + RETURNI(s ? -hi : hi); } e0 = __ieee754_rem_pio2l(x, y); @@ -84,5 +89,5 @@ sinl(long double x) break; } - return (hi); + RETURNI(hi); } diff --git a/lib/msun/src/s_tanl.c b/lib/msun/src/s_tanl.c index 9562cf8..eadc837 100644 --- a/lib/msun/src/s_tanl.c +++ b/lib/msun/src/s_tanl.c @@ -34,6 +34,9 @@ __FBSDID("$FreeBSD$"); */ #include <float.h> +#ifdef __i386__ +#include <ieeefp.h> +#endif #include "math.h" #include "math_private.h" @@ -65,10 +68,12 @@ tanl(long double x) if (z.bits.exp == 32767) return ((x - x) / (x - x)); + ENTERI(); + /* Optimize the case where x is already within range. */ if (z.e < M_PI_4) { hi = __kernel_tanl(z.e, 0, 0); - return (s ? -hi : hi); + RETURNI(s ? -hi : hi); } e0 = __ieee754_rem_pio2l(x, y); @@ -86,5 +91,5 @@ tanl(long double x) break; } - return (hi); + RETURNI(hi); } |