| Message ID | 20250203212546.911043-3-adhemerval.zanella@linaro.org |
|---|---|
| State | New |
| Headers | show |
| Series | Optimize CORE-MATH internal tables | expand |
Am Montag, 3. Februar 2025, 22:24:18 Mitteleuropäische Normalzeit schrieb Adhemerval Zanella: > The libm size improvement built with "--enable-stack-protector=strong > --enable-bind-now=yes --enable-fortify-source=2": > > Before: > > text data bss dec hex filename > 587304 860 12 588176 8f990 aarch64-linux-gnu-master/math/libm.so > 962855 1068 12 963935 eb55f x86_64-linux-gnu-master/math/libm.so > 1191222 5544 368 1197134 12444e powerpc64le-linux-gnu-master/math/libm.so > > After: > > text data bss dec hex filename > 585192 860 12 586064 8f150 aarch64-linux-gnu/math/libm.so > 960775 1068 12 961855 ead3f x86_64-linux-gnu/math/libm.so > 1189174 5544 368 1195086 123c4e powerpc64le-linux-gnu/math/libm.so > > The are small code changes for x86_64 and powerpc64le, which do not > affect performance; but on aarch64 with gcc-14 I see a slight better > code generation due the usage of ldq for floating point constant loading. LGTM Reviewed-by: Andreas K. Huettel <dilfridge@gentoo.org> > --- > math/Makefile | 1 + > sysdeps/ieee754/flt-32/e_acoshf.c | 111 ++------------------ > sysdeps/ieee754/flt-32/s_asincoshf_data.c | 121 ++++++++++++++++++++++ > sysdeps/ieee754/flt-32/s_asincoshf_data.h | 36 +++++++ > sysdeps/ieee754/flt-32/s_asinhf.c | 109 ++----------------- > 5 files changed, 175 insertions(+), 203 deletions(-) > create mode 100644 sysdeps/ieee754/flt-32/s_asincoshf_data.c > create mode 100644 sysdeps/ieee754/flt-32/s_asincoshf_data.h > > diff --git a/math/Makefile b/math/Makefile > index a6da38a135..febeb253f6 100644 > --- a/math/Makefile > +++ b/math/Makefile > @@ -368,6 +368,7 @@ type-float-routines := \ > e_logf_data \ > e_powf_log2_data \ > math_errf \ > + s_asincoshf_data \ > s_sincosf_data \ > # type-float-routines > ok > diff --git a/sysdeps/ieee754/flt-32/e_acoshf.c b/sysdeps/ieee754/flt-32/e_acoshf.c > index a0a0abc2dd..b2a9c6b2f0 100644 > --- a/sysdeps/ieee754/flt-32/e_acoshf.c > +++ b/sysdeps/ieee754/flt-32/e_acoshf.c > @@ -28,6 +28,7 @@ SOFTWARE. > #include <stdint.h> > #include <libm-alias-finite.h> > #include "math_config.h" > +#include "s_asincoshf_data.h" > > static __attribute__ ((noinline)) float > as_special (float x) > @@ -45,90 +46,6 @@ as_special (float x) > float > __ieee754_acoshf (float x) > { > - static const double ix[] = > - { > - 0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1, 0x1.f44659e4ap-1, > - 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1, 0x1.e9131abfp-1, 0x1.e573ac902p-1, > - 0x1.e1e1e1e1ep-1, 0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1, > - 0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1, 0x1.ca4b3055ep-1, > - 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1, 0x1.c0e070382p-1, 0x1.bdd2b8994p-1, > - 0x1.bacf914c2p-1, 0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1, > - 0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1, 0x1.a6d01a6dp-1, > - 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1, 0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, > - 0x1.99999999ap-1, 0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1, > - 0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1, 0x1.886e5f0acp-1, > - 0x1.861861862p-1, 0x1.83c977ab2p-1, 0x1.818181818p-1, 0x1.7f405fd02p-1, > - 0x1.7d05f417ep-1, 0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1, > - 0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1, 0x1.6e1f76b44p-1, > - 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1, 0x1.681681682p-1, 0x1.661ec6a52p-1, > - 0x1.642c8590cp-1, 0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1, > - 0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1, 0x1.571ed3c5p-1, > - 0x1.555555556p-1, 0x1.5390948f4p-1, 0x1.51d07eae2p-1, 0x1.501501502p-1, > - 0x1.4e5e0a73p-1, 0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1, > - 0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1, 0x1.42d6625d6p-1, > - 0x1.414141414p-1, 0x1.3fb013fbp-1, 0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, > - 0x1.3b13b13b2p-1, 0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1, > - 0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1, 0x1.30d19013p-1, > - 0x1.2f684bda2p-1, 0x1.2e025c04cp-1, 0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, > - 0x1.29e4129e4p-1, 0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1, > - 0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1, 0x1.20b470c68p-1, > - 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1, 0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, > - 0x1.1a7b9611ap-1, 0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1, > - 0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1, 0x1.12358e75ep-1, > - 0x1.111111112p-1, 0x1.0fef010fep-1, 0x1.0ecf56be6p-1, 0x1.0db20a89p-1, > - 0x1.0c9714fbcp-1, 0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1, > - 0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1, 0x1.05197f7d8p-1, > - 0x1.041041042p-1, 0x1.03091b52p-1, 0x1.020408102p-1, 0x1.01010101p-1, > - 0x1p-1 > - }; > - > - static const double lix[] = > - { > - 0x0p+0, 0x1.fe02a6b146789p-8, 0x1.fc0a8b0fa03e4p-7, > - 0x1.7b91b07de311bp-6, 0x1.f829b0e7c33p-6, 0x1.39e87b9fd7d6p-5, > - 0x1.77458f63edcfcp-5, 0x1.b42dd7117b1bfp-5, 0x1.f0a30c01362a6p-5, > - 0x1.16536eea7fae1p-4, 0x1.341d7961791d1p-4, 0x1.51b073f07983fp-4, > - 0x1.6f0d28ae3eb4cp-4, 0x1.8c345d6383b21p-4, 0x1.a926d3a475563p-4, > - 0x1.c5e548f63a743p-4, 0x1.e27076e28f2e6p-4, 0x1.fec9131dbaabbp-4, > - 0x1.0d77e7ccf6e59p-3, 0x1.1b72ad52f87ap-3, 0x1.29552f81eb523p-3, > - 0x1.371fc201f7f74p-3, 0x1.44d2b6ccbfd1ep-3, 0x1.526e5e3a41438p-3, > - 0x1.5ff3070a613d4p-3, 0x1.6d60fe717221dp-3, 0x1.7ab890212b909p-3, > - 0x1.87fa065214911p-3, 0x1.9525a9cf296b4p-3, 0x1.a23bc1fe42563p-3, > - 0x1.af3c94e81bff3p-3, 0x1.bc2867430acd6p-3, 0x1.c8ff7c7989a22p-3, > - 0x1.d5c216b535b91p-3, 0x1.e27076e2f92e6p-3, 0x1.ef0adcbe0d936p-3, > - 0x1.fb9186d5ebe2bp-3, 0x1.0402594b51041p-2, 0x1.0a324e27370e3p-2, > - 0x1.1058bf9ad7ad5p-2, 0x1.1675cabaa660ep-2, 0x1.1c898c16b91fbp-2, > - 0x1.22941fbcfb966p-2, 0x1.2895a13dd2ea3p-2, 0x1.2e8e2bade7d31p-2, > - 0x1.347dd9a9afd55p-2, 0x1.3a64c556b05eap-2, 0x1.40430868877e4p-2, > - 0x1.4618bc219dec2p-2, 0x1.4be5f9579e0a1p-2, 0x1.51aad872c982dp-2, > - 0x1.5767717432a6cp-2, 0x1.5d1bdbf5669cap-2, 0x1.62c82f2b83795p-2, > - 0x1.686c81e9964afp-2, 0x1.6e08eaa2929e4p-2, 0x1.739d7f6b95007p-2, > - 0x1.792a55fdb7fa2p-2, 0x1.7eaf83b82efc3p-2, 0x1.842d1da1ecb17p-2, > - 0x1.89a3386be825bp-2, 0x1.8f11e87347ac7p-2, 0x1.947941c1f26fbp-2, > - 0x1.99d958119208bp-2, 0x1.9f323ecbd984cp-2, 0x1.a484090e5eb0ap-2, > - 0x1.a9cec9a9cf84ap-2, 0x1.af1293245606bp-2, 0x1.b44f77bc98f63p-2, > - 0x1.b9858969218fbp-2, 0x1.beb4d9da96b7cp-2, 0x1.c3dd7a7d0354dp-2, > - 0x1.c8ff7c79ada22p-2, 0x1.ce1af0b855bebp-2, 0x1.d32fe7e039bd5p-2, > - 0x1.d83e72587673ep-2, 0x1.dd46a04c204a1p-2, 0x1.e24881a7cac26p-2, > - 0x1.e744261d8a788p-2, 0x1.ec399d2457ccp-2, 0x1.f128f5fac86edp-2, > - 0x1.f6123fa71c8acp-2, 0x1.faf588f76631fp-2, 0x1.ffd2e08580c98p-2, > - 0x1.02552a5a4f0ffp-1, 0x1.04bdf9da8b6d2p-1, 0x1.0723e5c1b4f4p-1, > - 0x1.0986f4f589521p-1, 0x1.0be72e423ca83p-1, 0x1.0e44985d0f48cp-1, > - 0x1.109f39e2be497p-1, 0x1.12f71959283bcp-1, 0x1.154c3d2f4f5eap-1, > - 0x1.179eabbd9c9a1p-1, 0x1.19ee6b466516fp-1, 0x1.1c3b81f723c25p-1, > - 0x1.1e85f5e6ec0dp-1, 0x1.20cdcd193f76ep-1, 0x1.23130d7beb743p-1, > - 0x1.2555bce9887cbp-1, 0x1.2795e1288211bp-1, 0x1.29d37fec2308bp-1, > - 0x1.2c0e9ed45768cp-1, 0x1.2e47436e5ae68p-1, 0x1.307d7334ff0bep-1, > - 0x1.32b1339134571p-1, 0x1.34e289d9b39d3p-1, 0x1.37117b5481bb6p-1, > - 0x1.393e0d3549a1ap-1, 0x1.3b6844a017823p-1, 0x1.3d9026a70eefbp-1, > - 0x1.3fb5b84cfeb42p-1, 0x1.41d8fe844b2aep-1, 0x1.43f9fe2fb9267p-1, > - 0x1.4618bc21d86c2p-1, 0x1.48353d1e928dfp-1, 0x1.4a4f85db1debbp-1, > - 0x1.4c679afcc323ap-1, 0x1.4e7d811b77bb1p-1, 0x1.50913cbff8c6bp-1, > - 0x1.52a2d265be5abp-1, 0x1.54b2467998498p-1, 0x1.56bf9d5b34b99p-1, > - 0x1.58cadb5cbe989p-1, 0x1.5ad404c33af2dp-1, 0x1.5cdb1dc6ad765p-1, > - 0x1.5ee02a9241e75p-1, 0x1.60e32f447a8d9p-1, 0x1.62e42fefa39efp-1 > - }; > - > uint32_t t = asuint (x); > if (__glibc_unlikely (t <= 0x3f800000u)) > return as_special (x); ok moved below > @@ -160,36 +77,26 @@ __ieee754_acoshf (float x) > int j = (m + (UINT64_C(1) << (52 - 8))) >> (52 - 7); > int e = (tp >> 52) - 0x3ff; > double w = asdouble (m | UINT64_C(0x3ff) << 52); > - double z = w * ix[j] - 1.0; > - static const double c[] = > - { > - 0x1.0000000066947p+0, -0x1.00007f053d8cbp-1, 0x1.555280111d914p-2 > - }; > + double z = w * IX[j] - 1.0; > double z2 = z * z; > - double r = ((lix[128] * e + lix[j]) + z * c[0]) > - + z2 * (c[1] + z * c[2]); > + double r = ((LIX[128] * e + LIX[j]) + z * C[0]) > + + z2 * (C[1] + z * C[2]); > if (__glibc_unlikely (((asuint64 (r) + 259000) & INT64_C(0xfffffff)) > < 260000)) /* accurate path */ ok > { > - static const double cp[] = > - { > - 0x1p+0, -0x1p-1, > - 0x1.55555555030bcp-2, -0x1.ffffffff2b4e5p-3, > - 0x1.999b5076a42f2p-3, -0x1.55570c45a647dp-3 > - }; > z2 = z * z; > - double c0 = cp[0] + z * cp[1]; > - double c2 = cp[2] + z * cp[3]; > - double c4 = cp[4] + z * cp[5]; > + double c0 = CP[0] + z * CP[1]; > + double c2 = CP[2] + z * CP[3]; > + double c4 = CP[4] + z * CP[5]; > c0 += z2 * (c2 + z2 * c4); > const double ln2l = 0x1.7f7d1cf79abcap-20; > const double ln2h = 0x1.62e4p-1; ok > double Lh = ln2h * e; > double Ll = ln2l * e; > - r = fma (z, c0, Ll + lix[j]) + Lh; > + r = fma (z, c0, Ll + LIX[j]) + Lh; > if (__glibc_unlikely ((asuint64 (r) & UINT64_C(0xfffffff)) == 0)) > { > - double h = fma (z, c0, Ll + lix[j]) + (Lh - r); > + double h = fma (z, c0, Ll + LIX[j]) + (Lh - r); > r = r + 64.0 * h; > } > } ok > diff --git a/sysdeps/ieee754/flt-32/s_asincoshf_data.c b/sysdeps/ieee754/flt-32/s_asincoshf_data.c > new file mode 100644 > index 0000000000..e852122c3e > --- /dev/null > +++ b/sysdeps/ieee754/flt-32/s_asincoshf_data.c > @@ -0,0 +1,121 @@ > +/* Common data for asinhf/acoshf implementations. > + > +Copyright (c) 2022-2025 Alexei Sibidanov. > + > +Permission is hereby granted, free of charge, to any person obtaining a copy > +of this software and associated documentation files (the "Software"), to deal > +in the Software without restriction, including without limitation the rights > +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell > +copies of the Software, and to permit persons to whom the Software is > +furnished to do so, subject to the following conditions: > + > +The above copyright notice and this permission notice shall be included in all > +copies or substantial portions of the Software. > + > +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR > +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, > +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE > +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER > +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, > +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE > +SOFTWARE. > +*/ > + > +#include "s_asincoshf_data.h" > + > +const double __asincoshf_ix[] = > + { > + 0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1, 0x1.f44659e4ap-1, > + 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1, 0x1.e9131abfp-1, 0x1.e573ac902p-1, > + 0x1.e1e1e1e1ep-1, 0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1, > + 0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1, 0x1.ca4b3055ep-1, > + 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1, 0x1.c0e070382p-1, 0x1.bdd2b8994p-1, > + 0x1.bacf914c2p-1, 0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1, > + 0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1, 0x1.a6d01a6dp-1, > + 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1, 0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, > + 0x1.99999999ap-1, 0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1, > + 0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1, 0x1.886e5f0acp-1, > + 0x1.861861862p-1, 0x1.83c977ab2p-1, 0x1.818181818p-1, 0x1.7f405fd02p-1, > + 0x1.7d05f417ep-1, 0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1, > + 0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1, 0x1.6e1f76b44p-1, > + 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1, 0x1.681681682p-1, 0x1.661ec6a52p-1, > + 0x1.642c8590cp-1, 0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1, > + 0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1, 0x1.571ed3c5p-1, > + 0x1.555555556p-1, 0x1.5390948f4p-1, 0x1.51d07eae2p-1, 0x1.501501502p-1, > + 0x1.4e5e0a73p-1, 0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1, > + 0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1, 0x1.42d6625d6p-1, > + 0x1.414141414p-1, 0x1.3fb013fbp-1, 0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, > + 0x1.3b13b13b2p-1, 0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1, > + 0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1, 0x1.30d19013p-1, > + 0x1.2f684bda2p-1, 0x1.2e025c04cp-1, 0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, > + 0x1.29e4129e4p-1, 0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1, > + 0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1, 0x1.20b470c68p-1, > + 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1, 0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, > + 0x1.1a7b9611ap-1, 0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1, > + 0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1, 0x1.12358e75ep-1, > + 0x1.111111112p-1, 0x1.0fef010fep-1, 0x1.0ecf56be6p-1, 0x1.0db20a89p-1, > + 0x1.0c9714fbcp-1, 0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1, > + 0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1, 0x1.05197f7d8p-1, > + 0x1.041041042p-1, 0x1.03091b52p-1, 0x1.020408102p-1, 0x1.01010101p-1, > + 0x1p-1 > + }; ok (random sample) > + > +const double __asincoshf_lix[] = > + { > + 0x0p+0, 0x1.fe02a6b146789p-8, 0x1.fc0a8b0fa03e4p-7, > + 0x1.7b91b07de311bp-6, 0x1.f829b0e7c33p-6, 0x1.39e87b9fd7d6p-5, > + 0x1.77458f63edcfcp-5, 0x1.b42dd7117b1bfp-5, 0x1.f0a30c01362a6p-5, > + 0x1.16536eea7fae1p-4, 0x1.341d7961791d1p-4, 0x1.51b073f07983fp-4, > + 0x1.6f0d28ae3eb4cp-4, 0x1.8c345d6383b21p-4, 0x1.a926d3a475563p-4, > + 0x1.c5e548f63a743p-4, 0x1.e27076e28f2e6p-4, 0x1.fec9131dbaabbp-4, > + 0x1.0d77e7ccf6e59p-3, 0x1.1b72ad52f87ap-3, 0x1.29552f81eb523p-3, > + 0x1.371fc201f7f74p-3, 0x1.44d2b6ccbfd1ep-3, 0x1.526e5e3a41438p-3, > + 0x1.5ff3070a613d4p-3, 0x1.6d60fe717221dp-3, 0x1.7ab890212b909p-3, > + 0x1.87fa065214911p-3, 0x1.9525a9cf296b4p-3, 0x1.a23bc1fe42563p-3, > + 0x1.af3c94e81bff3p-3, 0x1.bc2867430acd6p-3, 0x1.c8ff7c7989a22p-3, > + 0x1.d5c216b535b91p-3, 0x1.e27076e2f92e6p-3, 0x1.ef0adcbe0d936p-3, > + 0x1.fb9186d5ebe2bp-3, 0x1.0402594b51041p-2, 0x1.0a324e27370e3p-2, > + 0x1.1058bf9ad7ad5p-2, 0x1.1675cabaa660ep-2, 0x1.1c898c16b91fbp-2, > + 0x1.22941fbcfb966p-2, 0x1.2895a13dd2ea3p-2, 0x1.2e8e2bade7d31p-2, > + 0x1.347dd9a9afd55p-2, 0x1.3a64c556b05eap-2, 0x1.40430868877e4p-2, > + 0x1.4618bc219dec2p-2, 0x1.4be5f9579e0a1p-2, 0x1.51aad872c982dp-2, > + 0x1.5767717432a6cp-2, 0x1.5d1bdbf5669cap-2, 0x1.62c82f2b83795p-2, > + 0x1.686c81e9964afp-2, 0x1.6e08eaa2929e4p-2, 0x1.739d7f6b95007p-2, > + 0x1.792a55fdb7fa2p-2, 0x1.7eaf83b82efc3p-2, 0x1.842d1da1ecb17p-2, > + 0x1.89a3386be825bp-2, 0x1.8f11e87347ac7p-2, 0x1.947941c1f26fbp-2, > + 0x1.99d958119208bp-2, 0x1.9f323ecbd984cp-2, 0x1.a484090e5eb0ap-2, > + 0x1.a9cec9a9cf84ap-2, 0x1.af1293245606bp-2, 0x1.b44f77bc98f63p-2, > + 0x1.b9858969218fbp-2, 0x1.beb4d9da96b7cp-2, 0x1.c3dd7a7d0354dp-2, > + 0x1.c8ff7c79ada22p-2, 0x1.ce1af0b855bebp-2, 0x1.d32fe7e039bd5p-2, > + 0x1.d83e72587673ep-2, 0x1.dd46a04c204a1p-2, 0x1.e24881a7cac26p-2, > + 0x1.e744261d8a788p-2, 0x1.ec399d2457ccp-2, 0x1.f128f5fac86edp-2, > + 0x1.f6123fa71c8acp-2, 0x1.faf588f76631fp-2, 0x1.ffd2e08580c98p-2, > + 0x1.02552a5a4f0ffp-1, 0x1.04bdf9da8b6d2p-1, 0x1.0723e5c1b4f4p-1, > + 0x1.0986f4f589521p-1, 0x1.0be72e423ca83p-1, 0x1.0e44985d0f48cp-1, > + 0x1.109f39e2be497p-1, 0x1.12f71959283bcp-1, 0x1.154c3d2f4f5eap-1, > + 0x1.179eabbd9c9a1p-1, 0x1.19ee6b466516fp-1, 0x1.1c3b81f723c25p-1, > + 0x1.1e85f5e6ec0dp-1, 0x1.20cdcd193f76ep-1, 0x1.23130d7beb743p-1, > + 0x1.2555bce9887cbp-1, 0x1.2795e1288211bp-1, 0x1.29d37fec2308bp-1, > + 0x1.2c0e9ed45768cp-1, 0x1.2e47436e5ae68p-1, 0x1.307d7334ff0bep-1, > + 0x1.32b1339134571p-1, 0x1.34e289d9b39d3p-1, 0x1.37117b5481bb6p-1, > + 0x1.393e0d3549a1ap-1, 0x1.3b6844a017823p-1, 0x1.3d9026a70eefbp-1, > + 0x1.3fb5b84cfeb42p-1, 0x1.41d8fe844b2aep-1, 0x1.43f9fe2fb9267p-1, > + 0x1.4618bc21d86c2p-1, 0x1.48353d1e928dfp-1, 0x1.4a4f85db1debbp-1, > + 0x1.4c679afcc323ap-1, 0x1.4e7d811b77bb1p-1, 0x1.50913cbff8c6bp-1, > + 0x1.52a2d265be5abp-1, 0x1.54b2467998498p-1, 0x1.56bf9d5b34b99p-1, > + 0x1.58cadb5cbe989p-1, 0x1.5ad404c33af2dp-1, 0x1.5cdb1dc6ad765p-1, > + 0x1.5ee02a9241e75p-1, 0x1.60e32f447a8d9p-1, 0x1.62e42fefa39efp-1 > + }; > + ok (random sample) > +const double __asincoshf_c[] = > + { > + 0x1.0000000066947p+0, -0x1.00007f053d8cbp-1, 0x1.555280111d914p-2 > + }; > + ok > + > +const double __asincoshf_cp[] = > + { > + 0x1p+0, -0x1p-1, > + 0x1.55555555030bcp-2, -0x1.ffffffff2b4e5p-3, > + 0x1.999b5076a42f2p-3, -0x1.55570c45a647dp-3 > + }; ok > diff --git a/sysdeps/ieee754/flt-32/s_asincoshf_data.h b/sysdeps/ieee754/flt-32/s_asincoshf_data.h > new file mode 100644 > index 0000000000..2a7947a563 > --- /dev/null > +++ b/sysdeps/ieee754/flt-32/s_asincoshf_data.h > @@ -0,0 +1,36 @@ > +/* Common data for asinpif/acospif implementations. > + > +Copyright (c) 2022-2025 Alexei Sibidanov. > + > +Permission is hereby granted, free of charge, to any person obtaining a copy > +of this software and associated documentation files (the "Software"), to deal > +in the Software without restriction, including without limitation the rights > +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell > +copies of the Software, and to permit persons to whom the Software is > +furnished to do so, subject to the following conditions: > + > +The above copyright notice and this permission notice shall be included in all > +copies or substantial portions of the Software. > + > +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR > +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, > +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE > +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER > +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, > +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE > +SOFTWARE. > +*/ > + > +#ifndef _ASINCOSHF_H > +#define _ASINCOSHF_H > + > +extern const double __asincoshf_ix[] attribute_hidden; > +#define IX __asincoshf_ix > +extern const double __asincoshf_lix[] attribute_hidden; > +#define LIX __asincoshf_lix > +extern const double __asincoshf_c[] attribute_hidden; > +#define C __asincoshf_c > +extern const double __asincoshf_cp[] attribute_hidden; > +#define CP __asincoshf_cp > + > +#endif ok > diff --git a/sysdeps/ieee754/flt-32/s_asinhf.c b/sysdeps/ieee754/flt-32/s_asinhf.c > index 93750f5dae..9353b421d4 100644 > --- a/sysdeps/ieee754/flt-32/s_asinhf.c > +++ b/sysdeps/ieee754/flt-32/s_asinhf.c > @@ -28,94 +28,11 @@ SOFTWARE. > #include <stdint.h> > #include <libm-alias-float.h> > #include "math_config.h" > +#include "s_asincoshf_data.h" > > float > __asinhf (float x) > { > - static const double ix[] = > - { > - 0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1, 0x1.f44659e4ap-1, > - 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1, 0x1.e9131abfp-1, 0x1.e573ac902p-1, > - 0x1.e1e1e1e1ep-1, 0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1, > - 0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1, 0x1.ca4b3055ep-1, > - 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1, 0x1.c0e070382p-1, 0x1.bdd2b8994p-1, > - 0x1.bacf914c2p-1, 0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1, > - 0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1, 0x1.a6d01a6dp-1, > - 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1, 0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, > - 0x1.99999999ap-1, 0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1, > - 0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1, 0x1.886e5f0acp-1, > - 0x1.861861862p-1, 0x1.83c977ab2p-1, 0x1.818181818p-1, 0x1.7f405fd02p-1, > - 0x1.7d05f417ep-1, 0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1, > - 0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1, 0x1.6e1f76b44p-1, > - 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1, 0x1.681681682p-1, 0x1.661ec6a52p-1, > - 0x1.642c8590cp-1, 0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1, > - 0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1, 0x1.571ed3c5p-1, > - 0x1.555555556p-1, 0x1.5390948f4p-1, 0x1.51d07eae2p-1, 0x1.501501502p-1, > - 0x1.4e5e0a73p-1, 0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1, > - 0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1, 0x1.42d6625d6p-1, > - 0x1.414141414p-1, 0x1.3fb013fbp-1, 0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, > - 0x1.3b13b13b2p-1, 0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1, > - 0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1, 0x1.30d19013p-1, > - 0x1.2f684bda2p-1, 0x1.2e025c04cp-1, 0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, > - 0x1.29e4129e4p-1, 0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1, > - 0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1, 0x1.20b470c68p-1, > - 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1, 0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, > - 0x1.1a7b9611ap-1, 0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1, > - 0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1, 0x1.12358e75ep-1, > - 0x1.111111112p-1, 0x1.0fef010fep-1, 0x1.0ecf56be6p-1, 0x1.0db20a89p-1, > - 0x1.0c9714fbcp-1, 0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1, > - 0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1, 0x1.05197f7d8p-1, > - 0x1.041041042p-1, 0x1.03091b52p-1, 0x1.020408102p-1, 0x1.01010101p-1, > - 0x1p-1 > - }; > - ok (spot check) > - static const double lix[] = > - { > - 0x0p+0, 0x1.fe02a6b146789p-8, 0x1.fc0a8b0fa03e4p-7, > - 0x1.7b91b07de311bp-6, 0x1.f829b0e7c33p-6, 0x1.39e87b9fd7d6p-5, > - 0x1.77458f63edcfcp-5, 0x1.b42dd7117b1bfp-5, 0x1.f0a30c01362a6p-5, > - 0x1.16536eea7fae1p-4, 0x1.341d7961791d1p-4, 0x1.51b073f07983fp-4, > - 0x1.6f0d28ae3eb4cp-4, 0x1.8c345d6383b21p-4, 0x1.a926d3a475563p-4, > - 0x1.c5e548f63a743p-4, 0x1.e27076e28f2e6p-4, 0x1.fec9131dbaabbp-4, > - 0x1.0d77e7ccf6e59p-3, 0x1.1b72ad52f87ap-3, 0x1.29552f81eb523p-3, > - 0x1.371fc201f7f74p-3, 0x1.44d2b6ccbfd1ep-3, 0x1.526e5e3a41438p-3, > - 0x1.5ff3070a613d4p-3, 0x1.6d60fe717221dp-3, 0x1.7ab890212b909p-3, > - 0x1.87fa065214911p-3, 0x1.9525a9cf296b4p-3, 0x1.a23bc1fe42563p-3, > - 0x1.af3c94e81bff3p-3, 0x1.bc2867430acd6p-3, 0x1.c8ff7c7989a22p-3, > - 0x1.d5c216b535b91p-3, 0x1.e27076e2f92e6p-3, 0x1.ef0adcbe0d936p-3, > - 0x1.fb9186d5ebe2bp-3, 0x1.0402594b51041p-2, 0x1.0a324e27370e3p-2, > - 0x1.1058bf9ad7ad5p-2, 0x1.1675cabaa660ep-2, 0x1.1c898c16b91fbp-2, > - 0x1.22941fbcfb966p-2, 0x1.2895a13dd2ea3p-2, 0x1.2e8e2bade7d31p-2, > - 0x1.347dd9a9afd55p-2, 0x1.3a64c556b05eap-2, 0x1.40430868877e4p-2, > - 0x1.4618bc219dec2p-2, 0x1.4be5f9579e0a1p-2, 0x1.51aad872c982dp-2, > - 0x1.5767717432a6cp-2, 0x1.5d1bdbf5669cap-2, 0x1.62c82f2b83795p-2, > - 0x1.686c81e9964afp-2, 0x1.6e08eaa2929e4p-2, 0x1.739d7f6b95007p-2, > - 0x1.792a55fdb7fa2p-2, 0x1.7eaf83b82efc3p-2, 0x1.842d1da1ecb17p-2, > - 0x1.89a3386be825bp-2, 0x1.8f11e87347ac7p-2, 0x1.947941c1f26fbp-2, > - 0x1.99d958119208bp-2, 0x1.9f323ecbd984cp-2, 0x1.a484090e5eb0ap-2, > - 0x1.a9cec9a9cf84ap-2, 0x1.af1293245606bp-2, 0x1.b44f77bc98f63p-2, > - 0x1.b9858969218fbp-2, 0x1.beb4d9da96b7cp-2, 0x1.c3dd7a7d0354dp-2, > - 0x1.c8ff7c79ada22p-2, 0x1.ce1af0b855bebp-2, 0x1.d32fe7e039bd5p-2, > - 0x1.d83e72587673ep-2, 0x1.dd46a04c204a1p-2, 0x1.e24881a7cac26p-2, > - 0x1.e744261d8a788p-2, 0x1.ec399d2457ccp-2, 0x1.f128f5fac86edp-2, > - 0x1.f6123fa71c8acp-2, 0x1.faf588f76631fp-2, 0x1.ffd2e08580c98p-2, > - 0x1.02552a5a4f0ffp-1, 0x1.04bdf9da8b6d2p-1, 0x1.0723e5c1b4f4p-1, > - 0x1.0986f4f589521p-1, 0x1.0be72e423ca83p-1, 0x1.0e44985d0f48cp-1, > - 0x1.109f39e2be497p-1, 0x1.12f71959283bcp-1, 0x1.154c3d2f4f5eap-1, > - 0x1.179eabbd9c9a1p-1, 0x1.19ee6b466516fp-1, 0x1.1c3b81f723c25p-1, > - 0x1.1e85f5e6ec0dp-1, 0x1.20cdcd193f76ep-1, 0x1.23130d7beb743p-1, > - 0x1.2555bce9887cbp-1, 0x1.2795e1288211bp-1, 0x1.29d37fec2308bp-1, > - 0x1.2c0e9ed45768cp-1, 0x1.2e47436e5ae68p-1, 0x1.307d7334ff0bep-1, > - 0x1.32b1339134571p-1, 0x1.34e289d9b39d3p-1, 0x1.37117b5481bb6p-1, > - 0x1.393e0d3549a1ap-1, 0x1.3b6844a017823p-1, 0x1.3d9026a70eefbp-1, > - 0x1.3fb5b84cfeb42p-1, 0x1.41d8fe844b2aep-1, 0x1.43f9fe2fb9267p-1, > - 0x1.4618bc21d86c2p-1, 0x1.48353d1e928dfp-1, 0x1.4a4f85db1debbp-1, > - 0x1.4c679afcc323ap-1, 0x1.4e7d811b77bb1p-1, 0x1.50913cbff8c6bp-1, > - 0x1.52a2d265be5abp-1, 0x1.54b2467998498p-1, 0x1.56bf9d5b34b99p-1, > - 0x1.58cadb5cbe989p-1, 0x1.5ad404c33af2dp-1, 0x1.5cdb1dc6ad765p-1, > - 0x1.5ee02a9241e75p-1, 0x1.60e32f447a8d9p-1, 0x1.62e42fefa39efp-1 > - }; > - ok (spot check) > uint32_t t = asuint (x); > t &= ~0u >> 1; > double xs = x; > @@ -152,35 +69,25 @@ __asinhf (float x) > int j = (m + (UINT64_C(1) << (52 - 8))) >> (52 - 7); > int e = (tp >> 52) - 0x3ff; > double w = asdouble (m | UINT64_C(0x3ff) << 52); > - double z = w * ix[j] - 1.0; > - static const double c[] = > - { > - 0x1.0000000066947p+0, -0x1.00007f053d8cbp-1, 0x1.555280111d914p-2 > - }; > + double z = w * IX[j] - 1.0; > double z2 = z * z; > - double r = ((lix[128] * e + lix[j]) + z * c[0]) + z2 * (c[1] + z * c[2]); > + double r = ((LIX[128] * e + LIX[j]) + z * C[0]) + z2 * (C[1] + z * C[2]); > if (__glibc_unlikely (((asuint64 (r) + 259000) & INT64_C(0xfffffff)) > < 260000)) /* accurate path */ > { > - static const double cp[] = > - { > - 0x1p+0, -0x1p-1, > - 0x1.55555555030bcp-2, -0x1.ffffffff2b4e5p-3, > - 0x1.999b5076a42f2p-3, -0x1.55570c45a647dp-3 > - }; ok > z2 = z * z; > - double c0 = cp[0] + z * cp[1]; > - double c2 = cp[2] + z * cp[3]; > - double c4 = cp[4] + z * cp[5]; > + double c0 = CP[0] + z * CP[1]; > + double c2 = CP[2] + z * CP[3]; > + double c4 = CP[4] + z * CP[5]; > c0 += z2 * (c2 + z2 * c4); > const double ln2l = 0x1.7f7d1cf79abcap-20; > const double ln2h = 0x1.62e4p-1; > double Lh = ln2h * e; > double Ll = ln2l * e; > - r = fma (z, c0, Ll + lix[j]) + Lh; > + r = fma (z, c0, Ll + LIX[j]) + Lh; > if (__glibc_unlikely ((asuint64 (r) & INT64_C(0xfffffff)) == 0)) > { > - double h = fma (z, c0, Ll + lix[j]) + (Lh - r); > + double h = fma (z, c0, Ll + LIX[j]) + (Lh - r); > r = r + 64 * h; > } > } > ok
diff --git a/math/Makefile b/math/Makefile index a6da38a135..febeb253f6 100644 --- a/math/Makefile +++ b/math/Makefile @@ -368,6 +368,7 @@ type-float-routines := \ e_logf_data \ e_powf_log2_data \ math_errf \ + s_asincoshf_data \ s_sincosf_data \ # type-float-routines diff --git a/sysdeps/ieee754/flt-32/e_acoshf.c b/sysdeps/ieee754/flt-32/e_acoshf.c index a0a0abc2dd..b2a9c6b2f0 100644 --- a/sysdeps/ieee754/flt-32/e_acoshf.c +++ b/sysdeps/ieee754/flt-32/e_acoshf.c @@ -28,6 +28,7 @@ SOFTWARE. #include <stdint.h> #include <libm-alias-finite.h> #include "math_config.h" +#include "s_asincoshf_data.h" static __attribute__ ((noinline)) float as_special (float x) @@ -45,90 +46,6 @@ as_special (float x) float __ieee754_acoshf (float x) { - static const double ix[] = - { - 0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1, 0x1.f44659e4ap-1, - 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1, 0x1.e9131abfp-1, 0x1.e573ac902p-1, - 0x1.e1e1e1e1ep-1, 0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1, - 0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1, 0x1.ca4b3055ep-1, - 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1, 0x1.c0e070382p-1, 0x1.bdd2b8994p-1, - 0x1.bacf914c2p-1, 0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1, - 0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1, 0x1.a6d01a6dp-1, - 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1, 0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, - 0x1.99999999ap-1, 0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1, - 0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1, 0x1.886e5f0acp-1, - 0x1.861861862p-1, 0x1.83c977ab2p-1, 0x1.818181818p-1, 0x1.7f405fd02p-1, - 0x1.7d05f417ep-1, 0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1, - 0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1, 0x1.6e1f76b44p-1, - 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1, 0x1.681681682p-1, 0x1.661ec6a52p-1, - 0x1.642c8590cp-1, 0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1, - 0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1, 0x1.571ed3c5p-1, - 0x1.555555556p-1, 0x1.5390948f4p-1, 0x1.51d07eae2p-1, 0x1.501501502p-1, - 0x1.4e5e0a73p-1, 0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1, - 0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1, 0x1.42d6625d6p-1, - 0x1.414141414p-1, 0x1.3fb013fbp-1, 0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, - 0x1.3b13b13b2p-1, 0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1, - 0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1, 0x1.30d19013p-1, - 0x1.2f684bda2p-1, 0x1.2e025c04cp-1, 0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, - 0x1.29e4129e4p-1, 0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1, - 0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1, 0x1.20b470c68p-1, - 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1, 0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, - 0x1.1a7b9611ap-1, 0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1, - 0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1, 0x1.12358e75ep-1, - 0x1.111111112p-1, 0x1.0fef010fep-1, 0x1.0ecf56be6p-1, 0x1.0db20a89p-1, - 0x1.0c9714fbcp-1, 0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1, - 0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1, 0x1.05197f7d8p-1, - 0x1.041041042p-1, 0x1.03091b52p-1, 0x1.020408102p-1, 0x1.01010101p-1, - 0x1p-1 - }; - - static const double lix[] = - { - 0x0p+0, 0x1.fe02a6b146789p-8, 0x1.fc0a8b0fa03e4p-7, - 0x1.7b91b07de311bp-6, 0x1.f829b0e7c33p-6, 0x1.39e87b9fd7d6p-5, - 0x1.77458f63edcfcp-5, 0x1.b42dd7117b1bfp-5, 0x1.f0a30c01362a6p-5, - 0x1.16536eea7fae1p-4, 0x1.341d7961791d1p-4, 0x1.51b073f07983fp-4, - 0x1.6f0d28ae3eb4cp-4, 0x1.8c345d6383b21p-4, 0x1.a926d3a475563p-4, - 0x1.c5e548f63a743p-4, 0x1.e27076e28f2e6p-4, 0x1.fec9131dbaabbp-4, - 0x1.0d77e7ccf6e59p-3, 0x1.1b72ad52f87ap-3, 0x1.29552f81eb523p-3, - 0x1.371fc201f7f74p-3, 0x1.44d2b6ccbfd1ep-3, 0x1.526e5e3a41438p-3, - 0x1.5ff3070a613d4p-3, 0x1.6d60fe717221dp-3, 0x1.7ab890212b909p-3, - 0x1.87fa065214911p-3, 0x1.9525a9cf296b4p-3, 0x1.a23bc1fe42563p-3, - 0x1.af3c94e81bff3p-3, 0x1.bc2867430acd6p-3, 0x1.c8ff7c7989a22p-3, - 0x1.d5c216b535b91p-3, 0x1.e27076e2f92e6p-3, 0x1.ef0adcbe0d936p-3, - 0x1.fb9186d5ebe2bp-3, 0x1.0402594b51041p-2, 0x1.0a324e27370e3p-2, - 0x1.1058bf9ad7ad5p-2, 0x1.1675cabaa660ep-2, 0x1.1c898c16b91fbp-2, - 0x1.22941fbcfb966p-2, 0x1.2895a13dd2ea3p-2, 0x1.2e8e2bade7d31p-2, - 0x1.347dd9a9afd55p-2, 0x1.3a64c556b05eap-2, 0x1.40430868877e4p-2, - 0x1.4618bc219dec2p-2, 0x1.4be5f9579e0a1p-2, 0x1.51aad872c982dp-2, - 0x1.5767717432a6cp-2, 0x1.5d1bdbf5669cap-2, 0x1.62c82f2b83795p-2, - 0x1.686c81e9964afp-2, 0x1.6e08eaa2929e4p-2, 0x1.739d7f6b95007p-2, - 0x1.792a55fdb7fa2p-2, 0x1.7eaf83b82efc3p-2, 0x1.842d1da1ecb17p-2, - 0x1.89a3386be825bp-2, 0x1.8f11e87347ac7p-2, 0x1.947941c1f26fbp-2, - 0x1.99d958119208bp-2, 0x1.9f323ecbd984cp-2, 0x1.a484090e5eb0ap-2, - 0x1.a9cec9a9cf84ap-2, 0x1.af1293245606bp-2, 0x1.b44f77bc98f63p-2, - 0x1.b9858969218fbp-2, 0x1.beb4d9da96b7cp-2, 0x1.c3dd7a7d0354dp-2, - 0x1.c8ff7c79ada22p-2, 0x1.ce1af0b855bebp-2, 0x1.d32fe7e039bd5p-2, - 0x1.d83e72587673ep-2, 0x1.dd46a04c204a1p-2, 0x1.e24881a7cac26p-2, - 0x1.e744261d8a788p-2, 0x1.ec399d2457ccp-2, 0x1.f128f5fac86edp-2, - 0x1.f6123fa71c8acp-2, 0x1.faf588f76631fp-2, 0x1.ffd2e08580c98p-2, - 0x1.02552a5a4f0ffp-1, 0x1.04bdf9da8b6d2p-1, 0x1.0723e5c1b4f4p-1, - 0x1.0986f4f589521p-1, 0x1.0be72e423ca83p-1, 0x1.0e44985d0f48cp-1, - 0x1.109f39e2be497p-1, 0x1.12f71959283bcp-1, 0x1.154c3d2f4f5eap-1, - 0x1.179eabbd9c9a1p-1, 0x1.19ee6b466516fp-1, 0x1.1c3b81f723c25p-1, - 0x1.1e85f5e6ec0dp-1, 0x1.20cdcd193f76ep-1, 0x1.23130d7beb743p-1, - 0x1.2555bce9887cbp-1, 0x1.2795e1288211bp-1, 0x1.29d37fec2308bp-1, - 0x1.2c0e9ed45768cp-1, 0x1.2e47436e5ae68p-1, 0x1.307d7334ff0bep-1, - 0x1.32b1339134571p-1, 0x1.34e289d9b39d3p-1, 0x1.37117b5481bb6p-1, - 0x1.393e0d3549a1ap-1, 0x1.3b6844a017823p-1, 0x1.3d9026a70eefbp-1, - 0x1.3fb5b84cfeb42p-1, 0x1.41d8fe844b2aep-1, 0x1.43f9fe2fb9267p-1, - 0x1.4618bc21d86c2p-1, 0x1.48353d1e928dfp-1, 0x1.4a4f85db1debbp-1, - 0x1.4c679afcc323ap-1, 0x1.4e7d811b77bb1p-1, 0x1.50913cbff8c6bp-1, - 0x1.52a2d265be5abp-1, 0x1.54b2467998498p-1, 0x1.56bf9d5b34b99p-1, - 0x1.58cadb5cbe989p-1, 0x1.5ad404c33af2dp-1, 0x1.5cdb1dc6ad765p-1, - 0x1.5ee02a9241e75p-1, 0x1.60e32f447a8d9p-1, 0x1.62e42fefa39efp-1 - }; - uint32_t t = asuint (x); if (__glibc_unlikely (t <= 0x3f800000u)) return as_special (x); @@ -160,36 +77,26 @@ __ieee754_acoshf (float x) int j = (m + (UINT64_C(1) << (52 - 8))) >> (52 - 7); int e = (tp >> 52) - 0x3ff; double w = asdouble (m | UINT64_C(0x3ff) << 52); - double z = w * ix[j] - 1.0; - static const double c[] = - { - 0x1.0000000066947p+0, -0x1.00007f053d8cbp-1, 0x1.555280111d914p-2 - }; + double z = w * IX[j] - 1.0; double z2 = z * z; - double r = ((lix[128] * e + lix[j]) + z * c[0]) - + z2 * (c[1] + z * c[2]); + double r = ((LIX[128] * e + LIX[j]) + z * C[0]) + + z2 * (C[1] + z * C[2]); if (__glibc_unlikely (((asuint64 (r) + 259000) & INT64_C(0xfffffff)) < 260000)) /* accurate path */ { - static const double cp[] = - { - 0x1p+0, -0x1p-1, - 0x1.55555555030bcp-2, -0x1.ffffffff2b4e5p-3, - 0x1.999b5076a42f2p-3, -0x1.55570c45a647dp-3 - }; z2 = z * z; - double c0 = cp[0] + z * cp[1]; - double c2 = cp[2] + z * cp[3]; - double c4 = cp[4] + z * cp[5]; + double c0 = CP[0] + z * CP[1]; + double c2 = CP[2] + z * CP[3]; + double c4 = CP[4] + z * CP[5]; c0 += z2 * (c2 + z2 * c4); const double ln2l = 0x1.7f7d1cf79abcap-20; const double ln2h = 0x1.62e4p-1; double Lh = ln2h * e; double Ll = ln2l * e; - r = fma (z, c0, Ll + lix[j]) + Lh; + r = fma (z, c0, Ll + LIX[j]) + Lh; if (__glibc_unlikely ((asuint64 (r) & UINT64_C(0xfffffff)) == 0)) { - double h = fma (z, c0, Ll + lix[j]) + (Lh - r); + double h = fma (z, c0, Ll + LIX[j]) + (Lh - r); r = r + 64.0 * h; } } diff --git a/sysdeps/ieee754/flt-32/s_asincoshf_data.c b/sysdeps/ieee754/flt-32/s_asincoshf_data.c new file mode 100644 index 0000000000..e852122c3e --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_asincoshf_data.c @@ -0,0 +1,121 @@ +/* Common data for asinhf/acoshf implementations. + +Copyright (c) 2022-2025 Alexei Sibidanov. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +*/ + +#include "s_asincoshf_data.h" + +const double __asincoshf_ix[] = + { + 0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1, 0x1.f44659e4ap-1, + 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1, 0x1.e9131abfp-1, 0x1.e573ac902p-1, + 0x1.e1e1e1e1ep-1, 0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1, + 0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1, 0x1.ca4b3055ep-1, + 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1, 0x1.c0e070382p-1, 0x1.bdd2b8994p-1, + 0x1.bacf914c2p-1, 0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1, + 0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1, 0x1.a6d01a6dp-1, + 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1, 0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, + 0x1.99999999ap-1, 0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1, + 0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1, 0x1.886e5f0acp-1, + 0x1.861861862p-1, 0x1.83c977ab2p-1, 0x1.818181818p-1, 0x1.7f405fd02p-1, + 0x1.7d05f417ep-1, 0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1, + 0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1, 0x1.6e1f76b44p-1, + 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1, 0x1.681681682p-1, 0x1.661ec6a52p-1, + 0x1.642c8590cp-1, 0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1, + 0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1, 0x1.571ed3c5p-1, + 0x1.555555556p-1, 0x1.5390948f4p-1, 0x1.51d07eae2p-1, 0x1.501501502p-1, + 0x1.4e5e0a73p-1, 0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1, + 0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1, 0x1.42d6625d6p-1, + 0x1.414141414p-1, 0x1.3fb013fbp-1, 0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, + 0x1.3b13b13b2p-1, 0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1, + 0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1, 0x1.30d19013p-1, + 0x1.2f684bda2p-1, 0x1.2e025c04cp-1, 0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, + 0x1.29e4129e4p-1, 0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1, + 0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1, 0x1.20b470c68p-1, + 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1, 0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, + 0x1.1a7b9611ap-1, 0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1, + 0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1, 0x1.12358e75ep-1, + 0x1.111111112p-1, 0x1.0fef010fep-1, 0x1.0ecf56be6p-1, 0x1.0db20a89p-1, + 0x1.0c9714fbcp-1, 0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1, + 0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1, 0x1.05197f7d8p-1, + 0x1.041041042p-1, 0x1.03091b52p-1, 0x1.020408102p-1, 0x1.01010101p-1, + 0x1p-1 + }; + +const double __asincoshf_lix[] = + { + 0x0p+0, 0x1.fe02a6b146789p-8, 0x1.fc0a8b0fa03e4p-7, + 0x1.7b91b07de311bp-6, 0x1.f829b0e7c33p-6, 0x1.39e87b9fd7d6p-5, + 0x1.77458f63edcfcp-5, 0x1.b42dd7117b1bfp-5, 0x1.f0a30c01362a6p-5, + 0x1.16536eea7fae1p-4, 0x1.341d7961791d1p-4, 0x1.51b073f07983fp-4, + 0x1.6f0d28ae3eb4cp-4, 0x1.8c345d6383b21p-4, 0x1.a926d3a475563p-4, + 0x1.c5e548f63a743p-4, 0x1.e27076e28f2e6p-4, 0x1.fec9131dbaabbp-4, + 0x1.0d77e7ccf6e59p-3, 0x1.1b72ad52f87ap-3, 0x1.29552f81eb523p-3, + 0x1.371fc201f7f74p-3, 0x1.44d2b6ccbfd1ep-3, 0x1.526e5e3a41438p-3, + 0x1.5ff3070a613d4p-3, 0x1.6d60fe717221dp-3, 0x1.7ab890212b909p-3, + 0x1.87fa065214911p-3, 0x1.9525a9cf296b4p-3, 0x1.a23bc1fe42563p-3, + 0x1.af3c94e81bff3p-3, 0x1.bc2867430acd6p-3, 0x1.c8ff7c7989a22p-3, + 0x1.d5c216b535b91p-3, 0x1.e27076e2f92e6p-3, 0x1.ef0adcbe0d936p-3, + 0x1.fb9186d5ebe2bp-3, 0x1.0402594b51041p-2, 0x1.0a324e27370e3p-2, + 0x1.1058bf9ad7ad5p-2, 0x1.1675cabaa660ep-2, 0x1.1c898c16b91fbp-2, + 0x1.22941fbcfb966p-2, 0x1.2895a13dd2ea3p-2, 0x1.2e8e2bade7d31p-2, + 0x1.347dd9a9afd55p-2, 0x1.3a64c556b05eap-2, 0x1.40430868877e4p-2, + 0x1.4618bc219dec2p-2, 0x1.4be5f9579e0a1p-2, 0x1.51aad872c982dp-2, + 0x1.5767717432a6cp-2, 0x1.5d1bdbf5669cap-2, 0x1.62c82f2b83795p-2, + 0x1.686c81e9964afp-2, 0x1.6e08eaa2929e4p-2, 0x1.739d7f6b95007p-2, + 0x1.792a55fdb7fa2p-2, 0x1.7eaf83b82efc3p-2, 0x1.842d1da1ecb17p-2, + 0x1.89a3386be825bp-2, 0x1.8f11e87347ac7p-2, 0x1.947941c1f26fbp-2, + 0x1.99d958119208bp-2, 0x1.9f323ecbd984cp-2, 0x1.a484090e5eb0ap-2, + 0x1.a9cec9a9cf84ap-2, 0x1.af1293245606bp-2, 0x1.b44f77bc98f63p-2, + 0x1.b9858969218fbp-2, 0x1.beb4d9da96b7cp-2, 0x1.c3dd7a7d0354dp-2, + 0x1.c8ff7c79ada22p-2, 0x1.ce1af0b855bebp-2, 0x1.d32fe7e039bd5p-2, + 0x1.d83e72587673ep-2, 0x1.dd46a04c204a1p-2, 0x1.e24881a7cac26p-2, + 0x1.e744261d8a788p-2, 0x1.ec399d2457ccp-2, 0x1.f128f5fac86edp-2, + 0x1.f6123fa71c8acp-2, 0x1.faf588f76631fp-2, 0x1.ffd2e08580c98p-2, + 0x1.02552a5a4f0ffp-1, 0x1.04bdf9da8b6d2p-1, 0x1.0723e5c1b4f4p-1, + 0x1.0986f4f589521p-1, 0x1.0be72e423ca83p-1, 0x1.0e44985d0f48cp-1, + 0x1.109f39e2be497p-1, 0x1.12f71959283bcp-1, 0x1.154c3d2f4f5eap-1, + 0x1.179eabbd9c9a1p-1, 0x1.19ee6b466516fp-1, 0x1.1c3b81f723c25p-1, + 0x1.1e85f5e6ec0dp-1, 0x1.20cdcd193f76ep-1, 0x1.23130d7beb743p-1, + 0x1.2555bce9887cbp-1, 0x1.2795e1288211bp-1, 0x1.29d37fec2308bp-1, + 0x1.2c0e9ed45768cp-1, 0x1.2e47436e5ae68p-1, 0x1.307d7334ff0bep-1, + 0x1.32b1339134571p-1, 0x1.34e289d9b39d3p-1, 0x1.37117b5481bb6p-1, + 0x1.393e0d3549a1ap-1, 0x1.3b6844a017823p-1, 0x1.3d9026a70eefbp-1, + 0x1.3fb5b84cfeb42p-1, 0x1.41d8fe844b2aep-1, 0x1.43f9fe2fb9267p-1, + 0x1.4618bc21d86c2p-1, 0x1.48353d1e928dfp-1, 0x1.4a4f85db1debbp-1, + 0x1.4c679afcc323ap-1, 0x1.4e7d811b77bb1p-1, 0x1.50913cbff8c6bp-1, + 0x1.52a2d265be5abp-1, 0x1.54b2467998498p-1, 0x1.56bf9d5b34b99p-1, + 0x1.58cadb5cbe989p-1, 0x1.5ad404c33af2dp-1, 0x1.5cdb1dc6ad765p-1, + 0x1.5ee02a9241e75p-1, 0x1.60e32f447a8d9p-1, 0x1.62e42fefa39efp-1 + }; + +const double __asincoshf_c[] = + { + 0x1.0000000066947p+0, -0x1.00007f053d8cbp-1, 0x1.555280111d914p-2 + }; + + +const double __asincoshf_cp[] = + { + 0x1p+0, -0x1p-1, + 0x1.55555555030bcp-2, -0x1.ffffffff2b4e5p-3, + 0x1.999b5076a42f2p-3, -0x1.55570c45a647dp-3 + }; diff --git a/sysdeps/ieee754/flt-32/s_asincoshf_data.h b/sysdeps/ieee754/flt-32/s_asincoshf_data.h new file mode 100644 index 0000000000..2a7947a563 --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_asincoshf_data.h @@ -0,0 +1,36 @@ +/* Common data for asinpif/acospif implementations. + +Copyright (c) 2022-2025 Alexei Sibidanov. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +*/ + +#ifndef _ASINCOSHF_H +#define _ASINCOSHF_H + +extern const double __asincoshf_ix[] attribute_hidden; +#define IX __asincoshf_ix +extern const double __asincoshf_lix[] attribute_hidden; +#define LIX __asincoshf_lix +extern const double __asincoshf_c[] attribute_hidden; +#define C __asincoshf_c +extern const double __asincoshf_cp[] attribute_hidden; +#define CP __asincoshf_cp + +#endif diff --git a/sysdeps/ieee754/flt-32/s_asinhf.c b/sysdeps/ieee754/flt-32/s_asinhf.c index 93750f5dae..9353b421d4 100644 --- a/sysdeps/ieee754/flt-32/s_asinhf.c +++ b/sysdeps/ieee754/flt-32/s_asinhf.c @@ -28,94 +28,11 @@ SOFTWARE. #include <stdint.h> #include <libm-alias-float.h> #include "math_config.h" +#include "s_asincoshf_data.h" float __asinhf (float x) { - static const double ix[] = - { - 0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1, 0x1.f44659e4ap-1, - 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1, 0x1.e9131abfp-1, 0x1.e573ac902p-1, - 0x1.e1e1e1e1ep-1, 0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1, - 0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1, 0x1.ca4b3055ep-1, - 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1, 0x1.c0e070382p-1, 0x1.bdd2b8994p-1, - 0x1.bacf914c2p-1, 0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1, - 0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1, 0x1.a6d01a6dp-1, - 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1, 0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, - 0x1.99999999ap-1, 0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1, - 0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1, 0x1.886e5f0acp-1, - 0x1.861861862p-1, 0x1.83c977ab2p-1, 0x1.818181818p-1, 0x1.7f405fd02p-1, - 0x1.7d05f417ep-1, 0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1, - 0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1, 0x1.6e1f76b44p-1, - 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1, 0x1.681681682p-1, 0x1.661ec6a52p-1, - 0x1.642c8590cp-1, 0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1, - 0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1, 0x1.571ed3c5p-1, - 0x1.555555556p-1, 0x1.5390948f4p-1, 0x1.51d07eae2p-1, 0x1.501501502p-1, - 0x1.4e5e0a73p-1, 0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1, - 0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1, 0x1.42d6625d6p-1, - 0x1.414141414p-1, 0x1.3fb013fbp-1, 0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, - 0x1.3b13b13b2p-1, 0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1, - 0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1, 0x1.30d19013p-1, - 0x1.2f684bda2p-1, 0x1.2e025c04cp-1, 0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, - 0x1.29e4129e4p-1, 0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1, - 0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1, 0x1.20b470c68p-1, - 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1, 0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, - 0x1.1a7b9611ap-1, 0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1, - 0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1, 0x1.12358e75ep-1, - 0x1.111111112p-1, 0x1.0fef010fep-1, 0x1.0ecf56be6p-1, 0x1.0db20a89p-1, - 0x1.0c9714fbcp-1, 0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1, - 0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1, 0x1.05197f7d8p-1, - 0x1.041041042p-1, 0x1.03091b52p-1, 0x1.020408102p-1, 0x1.01010101p-1, - 0x1p-1 - }; - - static const double lix[] = - { - 0x0p+0, 0x1.fe02a6b146789p-8, 0x1.fc0a8b0fa03e4p-7, - 0x1.7b91b07de311bp-6, 0x1.f829b0e7c33p-6, 0x1.39e87b9fd7d6p-5, - 0x1.77458f63edcfcp-5, 0x1.b42dd7117b1bfp-5, 0x1.f0a30c01362a6p-5, - 0x1.16536eea7fae1p-4, 0x1.341d7961791d1p-4, 0x1.51b073f07983fp-4, - 0x1.6f0d28ae3eb4cp-4, 0x1.8c345d6383b21p-4, 0x1.a926d3a475563p-4, - 0x1.c5e548f63a743p-4, 0x1.e27076e28f2e6p-4, 0x1.fec9131dbaabbp-4, - 0x1.0d77e7ccf6e59p-3, 0x1.1b72ad52f87ap-3, 0x1.29552f81eb523p-3, - 0x1.371fc201f7f74p-3, 0x1.44d2b6ccbfd1ep-3, 0x1.526e5e3a41438p-3, - 0x1.5ff3070a613d4p-3, 0x1.6d60fe717221dp-3, 0x1.7ab890212b909p-3, - 0x1.87fa065214911p-3, 0x1.9525a9cf296b4p-3, 0x1.a23bc1fe42563p-3, - 0x1.af3c94e81bff3p-3, 0x1.bc2867430acd6p-3, 0x1.c8ff7c7989a22p-3, - 0x1.d5c216b535b91p-3, 0x1.e27076e2f92e6p-3, 0x1.ef0adcbe0d936p-3, - 0x1.fb9186d5ebe2bp-3, 0x1.0402594b51041p-2, 0x1.0a324e27370e3p-2, - 0x1.1058bf9ad7ad5p-2, 0x1.1675cabaa660ep-2, 0x1.1c898c16b91fbp-2, - 0x1.22941fbcfb966p-2, 0x1.2895a13dd2ea3p-2, 0x1.2e8e2bade7d31p-2, - 0x1.347dd9a9afd55p-2, 0x1.3a64c556b05eap-2, 0x1.40430868877e4p-2, - 0x1.4618bc219dec2p-2, 0x1.4be5f9579e0a1p-2, 0x1.51aad872c982dp-2, - 0x1.5767717432a6cp-2, 0x1.5d1bdbf5669cap-2, 0x1.62c82f2b83795p-2, - 0x1.686c81e9964afp-2, 0x1.6e08eaa2929e4p-2, 0x1.739d7f6b95007p-2, - 0x1.792a55fdb7fa2p-2, 0x1.7eaf83b82efc3p-2, 0x1.842d1da1ecb17p-2, - 0x1.89a3386be825bp-2, 0x1.8f11e87347ac7p-2, 0x1.947941c1f26fbp-2, - 0x1.99d958119208bp-2, 0x1.9f323ecbd984cp-2, 0x1.a484090e5eb0ap-2, - 0x1.a9cec9a9cf84ap-2, 0x1.af1293245606bp-2, 0x1.b44f77bc98f63p-2, - 0x1.b9858969218fbp-2, 0x1.beb4d9da96b7cp-2, 0x1.c3dd7a7d0354dp-2, - 0x1.c8ff7c79ada22p-2, 0x1.ce1af0b855bebp-2, 0x1.d32fe7e039bd5p-2, - 0x1.d83e72587673ep-2, 0x1.dd46a04c204a1p-2, 0x1.e24881a7cac26p-2, - 0x1.e744261d8a788p-2, 0x1.ec399d2457ccp-2, 0x1.f128f5fac86edp-2, - 0x1.f6123fa71c8acp-2, 0x1.faf588f76631fp-2, 0x1.ffd2e08580c98p-2, - 0x1.02552a5a4f0ffp-1, 0x1.04bdf9da8b6d2p-1, 0x1.0723e5c1b4f4p-1, - 0x1.0986f4f589521p-1, 0x1.0be72e423ca83p-1, 0x1.0e44985d0f48cp-1, - 0x1.109f39e2be497p-1, 0x1.12f71959283bcp-1, 0x1.154c3d2f4f5eap-1, - 0x1.179eabbd9c9a1p-1, 0x1.19ee6b466516fp-1, 0x1.1c3b81f723c25p-1, - 0x1.1e85f5e6ec0dp-1, 0x1.20cdcd193f76ep-1, 0x1.23130d7beb743p-1, - 0x1.2555bce9887cbp-1, 0x1.2795e1288211bp-1, 0x1.29d37fec2308bp-1, - 0x1.2c0e9ed45768cp-1, 0x1.2e47436e5ae68p-1, 0x1.307d7334ff0bep-1, - 0x1.32b1339134571p-1, 0x1.34e289d9b39d3p-1, 0x1.37117b5481bb6p-1, - 0x1.393e0d3549a1ap-1, 0x1.3b6844a017823p-1, 0x1.3d9026a70eefbp-1, - 0x1.3fb5b84cfeb42p-1, 0x1.41d8fe844b2aep-1, 0x1.43f9fe2fb9267p-1, - 0x1.4618bc21d86c2p-1, 0x1.48353d1e928dfp-1, 0x1.4a4f85db1debbp-1, - 0x1.4c679afcc323ap-1, 0x1.4e7d811b77bb1p-1, 0x1.50913cbff8c6bp-1, - 0x1.52a2d265be5abp-1, 0x1.54b2467998498p-1, 0x1.56bf9d5b34b99p-1, - 0x1.58cadb5cbe989p-1, 0x1.5ad404c33af2dp-1, 0x1.5cdb1dc6ad765p-1, - 0x1.5ee02a9241e75p-1, 0x1.60e32f447a8d9p-1, 0x1.62e42fefa39efp-1 - }; - uint32_t t = asuint (x); t &= ~0u >> 1; double xs = x; @@ -152,35 +69,25 @@ __asinhf (float x) int j = (m + (UINT64_C(1) << (52 - 8))) >> (52 - 7); int e = (tp >> 52) - 0x3ff; double w = asdouble (m | UINT64_C(0x3ff) << 52); - double z = w * ix[j] - 1.0; - static const double c[] = - { - 0x1.0000000066947p+0, -0x1.00007f053d8cbp-1, 0x1.555280111d914p-2 - }; + double z = w * IX[j] - 1.0; double z2 = z * z; - double r = ((lix[128] * e + lix[j]) + z * c[0]) + z2 * (c[1] + z * c[2]); + double r = ((LIX[128] * e + LIX[j]) + z * C[0]) + z2 * (C[1] + z * C[2]); if (__glibc_unlikely (((asuint64 (r) + 259000) & INT64_C(0xfffffff)) < 260000)) /* accurate path */ { - static const double cp[] = - { - 0x1p+0, -0x1p-1, - 0x1.55555555030bcp-2, -0x1.ffffffff2b4e5p-3, - 0x1.999b5076a42f2p-3, -0x1.55570c45a647dp-3 - }; z2 = z * z; - double c0 = cp[0] + z * cp[1]; - double c2 = cp[2] + z * cp[3]; - double c4 = cp[4] + z * cp[5]; + double c0 = CP[0] + z * CP[1]; + double c2 = CP[2] + z * CP[3]; + double c4 = CP[4] + z * CP[5]; c0 += z2 * (c2 + z2 * c4); const double ln2l = 0x1.7f7d1cf79abcap-20; const double ln2h = 0x1.62e4p-1; double Lh = ln2h * e; double Ll = ln2l * e; - r = fma (z, c0, Ll + lix[j]) + Lh; + r = fma (z, c0, Ll + LIX[j]) + Lh; if (__glibc_unlikely ((asuint64 (r) & INT64_C(0xfffffff)) == 0)) { - double h = fma (z, c0, Ll + lix[j]) + (Lh - r); + double h = fma (z, c0, Ll + LIX[j]) + (Lh - r); r = r + 64 * h; } }