| |
| /* |
| * Copyright (C) 2008-2009 Advanced Micro Devices, Inc. All Rights Reserved. |
| * |
| * This file is part of libacml_mv. |
| * |
| * libacml_mv is free software; you can redistribute it and/or |
| * modify it under the terms of the GNU Lesser General Public |
| * License as published by the Free Software Foundation; either |
| * version 2.1 of the License, or (at your option) any later version. |
| * |
| * libacml_mv is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public |
| * License along with libacml_mv. If not, see |
| * <http://www.gnu.org/licenses/>. |
| * |
| */ |
| |
| |
| |
| #include "../inc/libm_amd.h" |
| #include "../inc/libm_util_amd.h" |
| |
| #define USE_SPLITEXP |
| #define USE_SCALEDOUBLE_1 |
| #define USE_SCALEDOUBLE_2 |
| #define USE_INFINITY_WITH_FLAGS |
| #define USE_VAL_WITH_FLAGS |
| #define USE_HANDLE_ERROR |
| #include "../inc/libm_inlines_amd.h" |
| #undef USE_HANDLE_ERROR |
| #undef USE_SPLITEXP |
| #undef USE_SCALEDOUBLE_1 |
| #undef USE_SCALEDOUBLE_2 |
| #undef USE_INFINITY_WITH_FLAGS |
| #undef USE_VAL_WITH_FLAGS |
| |
| #include "../inc/libm_errno_amd.h" |
| #ifndef WINDOWS |
| /* Deal with errno for out-of-range result */ |
| static inline double retval_errno_erange(double x) |
| { |
| struct exception exc; |
| exc.arg1 = x; |
| exc.arg2 = x; |
| exc.type = OVERFLOW; |
| exc.name = (char *)"cosh"; |
| if (_LIB_VERSION == _SVID_) |
| { |
| exc.retval = HUGE; |
| } |
| else |
| { |
| exc.retval = infinity_with_flags(AMD_F_OVERFLOW); |
| } |
| if (_LIB_VERSION == _POSIX_) |
| __set_errno(ERANGE); |
| else if (!matherr(&exc)) |
| __set_errno(ERANGE); |
| return exc.retval; |
| } |
| #endif |
| |
| double FN_PROTOTYPE(cosh)(double x) |
| { |
| /* |
| Derived from sinh subroutine |
| |
| After dealing with special cases the computation is split into |
| regions as follows: |
| |
| abs(x) >= max_cosh_arg: |
| cosh(x) = sign(x)*Inf |
| |
| abs(x) >= small_threshold: |
| cosh(x) = sign(x)*exp(abs(x))/2 computed using the |
| splitexp and scaleDouble functions as for exp_amd(). |
| |
| abs(x) < small_threshold: |
| compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0))) |
| cosh(x) is then sign(x)*z. */ |
| |
| static const double |
| max_cosh_arg = 7.10475860073943977113e+02, /* 0x408633ce8fb9f87e */ |
| thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */ |
| log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */ |
| log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */ |
| // small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889; |
| small_threshold = 20.0; |
| /* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */ |
| |
| /* Lead and tail tabulated values of sinh(i) and cosh(i) |
| for i = 0,...,36. The lead part has 26 leading bits. */ |
| |
| static const double sinh_lead[ 37] = { |
| 0.00000000000000000000e+00, /* 0x0000000000000000 */ |
| 1.17520117759704589844e+00, /* 0x3ff2cd9fc0000000 */ |
| 3.62686038017272949219e+00, /* 0x400d03cf60000000 */ |
| 1.00178747177124023438e+01, /* 0x40240926e0000000 */ |
| 2.72899169921875000000e+01, /* 0x403b4a3800000000 */ |
| 7.42032089233398437500e+01, /* 0x40528d0160000000 */ |
| 2.01713153839111328125e+02, /* 0x406936d228000000 */ |
| 5.48316116333007812500e+02, /* 0x4081228768000000 */ |
| 1.49047882080078125000e+03, /* 0x409749ea50000000 */ |
| 4.05154187011718750000e+03, /* 0x40afa71570000000 */ |
| 1.10132326660156250000e+04, /* 0x40c5829dc8000000 */ |
| 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */ |
| 8.13773945312500000000e+04, /* 0x40f3de1650000000 */ |
| 2.21206695312500000000e+05, /* 0x410b00b590000000 */ |
| 6.01302140625000000000e+05, /* 0x412259ac48000000 */ |
| 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */ |
| 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */ |
| 1.20774762500000000000e+07, /* 0x4167093488000000 */ |
| 3.28299845000000000000e+07, /* 0x417f4f2208000000 */ |
| 8.92411500000000000000e+07, /* 0x419546d8f8000000 */ |
| 2.42582596000000000000e+08, /* 0x41aceb0888000000 */ |
| 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */ |
| 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */ |
| 4.87240166400000000000e+09, /* 0x41f226af30000000 */ |
| 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */ |
| 3.60024494080000000000e+10, /* 0x4220c3d390000000 */ |
| 9.78648043520000000000e+10, /* 0x4236c93268000000 */ |
| 2.66024116224000000000e+11, /* 0x424ef822f0000000 */ |
| 7.23128516608000000000e+11, /* 0x42650bba30000000 */ |
| 1.96566712320000000000e+12, /* 0x427c9aae40000000 */ |
| 5.34323724288000000000e+12, /* 0x4293704708000000 */ |
| 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */ |
| 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */ |
| 1.07321789251584000000e+14, /* 0x42d866f348000000 */ |
| 2.91730863685632000000e+14, /* 0x42f0953e28000000 */ |
| 7.93006722514944000000e+14, /* 0x430689e220000000 */ |
| 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */ |
| |
| static const double sinh_tail[ 37] = { |
| 0.00000000000000000000e+00, /* 0x0000000000000000 */ |
| 1.60467555584448807892e-08, /* 0x3e513ae6096a0092 */ |
| 2.76742892754807136947e-08, /* 0x3e5db70cfb79a640 */ |
| 2.09697499555224576530e-07, /* 0x3e8c2526b66dc067 */ |
| 2.04940252448908240062e-07, /* 0x3e8b81b18647f380 */ |
| 1.65444891522700935932e-06, /* 0x3ebbc1cdd1e1eb08 */ |
| 3.53116789999998198721e-06, /* 0x3ecd9f201534fb09 */ |
| 6.94023870987375490695e-06, /* 0x3edd1c064a4e9954 */ |
| 4.98876893611587449271e-06, /* 0x3ed4eca65d06ea74 */ |
| 3.19656024605152215752e-05, /* 0x3f00c259bcc0ecc5 */ |
| 2.08687768377236501204e-04, /* 0x3f2b5a6647cf9016 */ |
| 4.84668088325403796299e-05, /* 0x3f09691adefb0870 */ |
| 1.17517985422733832468e-03, /* 0x3f53410fc29cde38 */ |
| 6.90830086959560562415e-04, /* 0x3f46a31a50b6fb3c */ |
| 1.45697262451506548420e-03, /* 0x3f57defc71805c40 */ |
| 2.99859023684906737806e-02, /* 0x3f9eb49fd80e0bab */ |
| 1.02538800507941396667e-02, /* 0x3f84fffc7bcd5920 */ |
| 1.26787628407699110022e-01, /* 0x3fc03a93b6c63435 */ |
| 6.86652479544033744752e-02, /* 0x3fb1940bb255fd1c */ |
| 4.81593627621056619148e-01, /* 0x3fded26e14260b50 */ |
| 1.70489513795397629181e+00, /* 0x3ffb47401fc9f2a2 */ |
| 1.12416073482258713767e+01, /* 0x40267bb3f55634f1 */ |
| 7.06579578070110514432e+00, /* 0x401c435ff8194ddc */ |
| 5.91244512999659974639e+01, /* 0x404d8fee052ba63a */ |
| 1.68921736147050694399e+02, /* 0x40651d7edccde3f6 */ |
| 2.60692936262073658327e+02, /* 0x40704b1644557d1a */ |
| 3.62419382134885609048e+02, /* 0x4076a6b5ca0a9dc4 */ |
| 4.07689930834187271103e+03, /* 0x40afd9cc72249aba */ |
| 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */ |
| 2.53720210371943067003e+04, /* 0x40d8c70158ac6363 */ |
| 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */ |
| 1.81871712615542812273e+05, /* 0x4106337db36fc718 */ |
| 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */ |
| 6.41374032312148716301e+05, /* 0x412392bc108b37cc */ |
| 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */ |
| 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */ |
| 7.63580561355670914054e+06}; /* 0x415d20d76744835c */ |
| |
| static const double cosh_lead[ 37] = { |
| 1.00000000000000000000e+00, /* 0x3ff0000000000000 */ |
| 1.54308062791824340820e+00, /* 0x3ff8b07550000000 */ |
| 3.76219564676284790039e+00, /* 0x400e18fa08000000 */ |
| 1.00676617622375488281e+01, /* 0x402422a490000000 */ |
| 2.73082327842712402344e+01, /* 0x403b4ee858000000 */ |
| 7.42099475860595703125e+01, /* 0x40528d6fc8000000 */ |
| 2.01715633392333984375e+02, /* 0x406936e678000000 */ |
| 5.48317031860351562500e+02, /* 0x4081228948000000 */ |
| 1.49047915649414062500e+03, /* 0x409749eaa8000000 */ |
| 4.05154199218750000000e+03, /* 0x40afa71580000000 */ |
| 1.10132329101562500000e+04, /* 0x40c5829dd0000000 */ |
| 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */ |
| 8.13773945312500000000e+04, /* 0x40f3de1650000000 */ |
| 2.21206695312500000000e+05, /* 0x410b00b590000000 */ |
| 6.01302140625000000000e+05, /* 0x412259ac48000000 */ |
| 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */ |
| 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */ |
| 1.20774762500000000000e+07, /* 0x4167093488000000 */ |
| 3.28299845000000000000e+07, /* 0x417f4f2208000000 */ |
| 8.92411500000000000000e+07, /* 0x419546d8f8000000 */ |
| 2.42582596000000000000e+08, /* 0x41aceb0888000000 */ |
| 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */ |
| 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */ |
| 4.87240166400000000000e+09, /* 0x41f226af30000000 */ |
| 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */ |
| 3.60024494080000000000e+10, /* 0x4220c3d390000000 */ |
| 9.78648043520000000000e+10, /* 0x4236c93268000000 */ |
| 2.66024116224000000000e+11, /* 0x424ef822f0000000 */ |
| 7.23128516608000000000e+11, /* 0x42650bba30000000 */ |
| 1.96566712320000000000e+12, /* 0x427c9aae40000000 */ |
| 5.34323724288000000000e+12, /* 0x4293704708000000 */ |
| 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */ |
| 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */ |
| 1.07321789251584000000e+14, /* 0x42d866f348000000 */ |
| 2.91730863685632000000e+14, /* 0x42f0953e28000000 */ |
| 7.93006722514944000000e+14, /* 0x430689e220000000 */ |
| 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */ |
| |
| static const double cosh_tail[ 37] = { |
| 0.00000000000000000000e+00, /* 0x0000000000000000 */ |
| 6.89700037027478056904e-09, /* 0x3e3d9f5504c2bd28 */ |
| 4.43207835591715833630e-08, /* 0x3e67cb66f0a4c9fd */ |
| 2.33540217013828929694e-07, /* 0x3e8f58617928e588 */ |
| 5.17452463948269748331e-08, /* 0x3e6bc7d000c38d48 */ |
| 9.38728274131605919153e-07, /* 0x3eaf7f9d4e329998 */ |
| 2.73012191010840495544e-06, /* 0x3ec6e6e464885269 */ |
| 3.29486051438996307950e-06, /* 0x3ecba3a8b946c154 */ |
| 4.75803746362771416375e-06, /* 0x3ed3f4e76110d5a4 */ |
| 3.33050940471947692369e-05, /* 0x3f017622515a3e2b */ |
| 9.94707313972136215365e-06, /* 0x3ee4dc4b528af3d0 */ |
| 6.51685096227860253398e-05, /* 0x3f11156278615e10 */ |
| 1.18132406658066663359e-03, /* 0x3f535ad50ed821f5 */ |
| 6.93090416366541877541e-04, /* 0x3f46b61055f2935c */ |
| 1.45780415323416845386e-03, /* 0x3f57e2794a601240 */ |
| 2.99862082708111758744e-02, /* 0x3f9eb4b45f6aadd3 */ |
| 1.02539925859688602072e-02, /* 0x3f85000b967b3698 */ |
| 1.26787669807076286421e-01, /* 0x3fc03a940fadc092 */ |
| 6.86652631843830962843e-02, /* 0x3fb1940bf3bf874c */ |
| 4.81593633223853068159e-01, /* 0x3fded26e1a2a2110 */ |
| 1.70489514001513020602e+00, /* 0x3ffb4740205796d6 */ |
| 1.12416073489841270572e+01, /* 0x40267bb3f55cb85d */ |
| 7.06579578098005001152e+00, /* 0x401c435ff81e18ac */ |
| 5.91244513000686140458e+01, /* 0x404d8fee052bdea4 */ |
| 1.68921736147088438429e+02, /* 0x40651d7edccde926 */ |
| 2.60692936262087528121e+02, /* 0x40704b1644557e0e */ |
| 3.62419382134890611269e+02, /* 0x4076a6b5ca0a9e1c */ |
| 4.07689930834187453002e+03, /* 0x40afd9cc72249abe */ |
| 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */ |
| 2.53720210371943103382e+04, /* 0x40d8c70158ac6364 */ |
| 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */ |
| 1.81871712615542812273e+05, /* 0x4106337db36fc718 */ |
| 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */ |
| 6.41374032312148716301e+05, /* 0x412392bc108b37cc */ |
| 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */ |
| 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */ |
| 7.63580561355670914054e+06}; /* 0x415d20d76744835c */ |
| |
| unsigned long long ux, aux, xneg; |
| double y, z, z1, z2; |
| int m; |
| |
| /* Special cases */ |
| |
| GET_BITS_DP64(x, ux); |
| aux = ux & ~SIGNBIT_DP64; |
| if (aux < 0x3e30000000000000) /* |x| small enough that cosh(x) = 1 */ |
| { |
| if (aux == 0) |
| /* with no inexact */ |
| return 1.0; |
| else |
| return val_with_flags(1.0, AMD_F_INEXACT); |
| } |
| else if (aux >= PINFBITPATT_DP64) /* |x| is NaN or Inf */ |
| { |
| if (aux > PINFBITPATT_DP64) /* |x| is a NaN? */ |
| return x + x; |
| else /* x is infinity */ |
| return infinity_with_flags(0); |
| } |
| |
| xneg = (aux != ux); |
| |
| y = x; |
| if (xneg) y = -x; |
| |
| if (y >= max_cosh_arg) |
| { |
| /* Return +/-infinity with overflow flag */ |
| #ifdef WINDOWS |
| return handle_error("cosh", PINFBITPATT_DP64, _OVERFLOW, |
| AMD_F_OVERFLOW, EDOM, x, 0.0F); |
| #else |
| return retval_errno_erange(x); |
| #endif |
| |
| |
| } |
| else if (y >= small_threshold) |
| { |
| /* In this range y is large enough so that |
| the negative exponential is negligible, |
| so cosh(y) is approximated by sign(x)*exp(y)/2. The |
| code below is an inlined version of that from |
| exp() with two changes (it operates on |
| y instead of x, and the division by 2 is |
| done by reducing m by 1). */ |
| |
| splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead, |
| log2_by_32_tail, &m, &z1, &z2); |
| m -= 1; |
| |
| if (m >= EMIN_DP64 && m <= EMAX_DP64) |
| z = scaleDouble_1((z1+z2),m); |
| else |
| z = scaleDouble_2((z1+z2),m); |
| } |
| else |
| { |
| /* In this range we find the integer part y0 of y |
| and the increment dy = y - y0. We then compute |
| |
| z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy) |
| z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy) |
| |
| where sinh(y0) and cosh(y0) are tabulated above. */ |
| |
| int ind; |
| double dy, dy2, sdy, cdy; |
| |
| ind = (int)y; |
| dy = y - ind; |
| |
| dy2 = dy*dy; |
| sdy = dy*dy2*(0.166666666666666667013899e0 + |
| (0.833333333333329931873097e-2 + |
| (0.198412698413242405162014e-3 + |
| (0.275573191913636406057211e-5 + |
| (0.250521176994133472333666e-7 + |
| (0.160576793121939886190847e-9 + |
| 0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2); |
| |
| cdy = dy2*(0.500000000000000005911074e0 + |
| (0.416666666666660876512776e-1 + |
| (0.138888888889814854814536e-2 + |
| (0.248015872460622433115785e-4 + |
| (0.275573350756016588011357e-6 + |
| (0.208744349831471353536305e-8 + |
| 0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2); |
| |
| /* At this point sinh(dy) is approximated by dy + sdy, and cosh(dy) is approximated by 1 + cdy. |
| Shift some significant bits from dy to cdy. */ |
| z = ((((((cosh_tail[ind]*cdy + sinh_tail[ind]*sdy) |
| + sinh_tail[ind]*dy) + cosh_tail[ind]) |
| + cosh_lead[ind]*cdy) + sinh_lead[ind]*sdy) |
| + sinh_lead[ind]*dy) + cosh_lead[ind]; |
| } |
| |
| return z; |
| } |
| |
| weak_alias (__cosh, cosh) |
