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252 lines
10 KiB
C
252 lines
10 KiB
C
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/*******************************************************************************
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MIT License
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-----------
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Copyright (c) 2002-2019 Advanced Micro Devices, Inc.
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this Software and associated documentaon files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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THE SOFTWARE.
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*******************************************************************************/
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#include "libm.h"
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#include "libm_util.h"
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#define USE_SPLITEXP
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#define USE_SCALEDOUBLE_1
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#define USE_SCALEDOUBLE_2
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#define USE_INFINITYF_WITH_FLAGS
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#define USE_VALF_WITH_FLAGS
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#define USE_HANDLE_ERRORF
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#include "libm_inlines.h"
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#undef USE_SPLITEXP
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#undef USE_SCALEDOUBLE_1
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#undef USE_SCALEDOUBLE_2
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#undef USE_INFINITYF_WITH_FLAGS
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#undef USE_VALF_WITH_FLAGS
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#undef USE_HANDLE_ERRORF
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#ifdef _MSC_VER
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// Disable "C4163: not available as intrinsic function" warning that older
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// compilers may issue here.
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#pragma warning(disable:4163)
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#pragma function(coshf)
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#endif
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float coshf(float fx)
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{
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/*
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After dealing with special cases the computation is split into
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regions as follows:
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abs(x) >= max_cosh_arg:
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cosh(x) = sign(x)*Inf
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abs(x) >= small_threshold:
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cosh(x) = sign(x)*exp(abs(x))/2 computed using the
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splitexp and scaleDouble functions as for exp_amd().
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abs(x) < small_threshold:
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compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
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cosh(x) is then sign(x)*z. */
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static const double
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/* The max argument of coshf, but stored as a double */
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max_cosh_arg = 8.94159862922329438106e+01, /* 0x40565a9f84f82e63 */
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thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */
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log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */
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log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */
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small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889;
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// small_threshold = 20.0;
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/* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */
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/* Tabulated values of sinh(i) and cosh(i) for i = 0,...,36. */
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static const double sinh_lead[ 37] = {
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0.00000000000000000000e+00, /* 0x0000000000000000 */
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1.17520119364380137839e+00, /* 0x3ff2cd9fc44eb982 */
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3.62686040784701857476e+00, /* 0x400d03cf63b6e19f */
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1.00178749274099008204e+01, /* 0x40240926e70949ad */
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2.72899171971277496596e+01, /* 0x403b4a3803703630 */
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7.42032105777887522891e+01, /* 0x40528d0166f07374 */
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2.01713157370279219549e+02, /* 0x406936d22f67c805 */
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5.48316123273246489589e+02, /* 0x408122876ba380c9 */
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1.49047882578955000099e+03, /* 0x409749ea514eca65 */
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4.05154190208278987484e+03, /* 0x40afa7157430966f */
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1.10132328747033916443e+04, /* 0x40c5829dced69991 */
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2.99370708492480553105e+04, /* 0x40dd3c4488cb48d6 */
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8.13773957064298447222e+04, /* 0x40f3de1654d043f0 */
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2.21206696003330085659e+05, /* 0x410b00b5916a31a5 */
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6.01302142081972560845e+05, /* 0x412259ac48bef7e3 */
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1.63450868623590236530e+06, /* 0x4138f0ccafad27f6 */
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4.44305526025387924165e+06, /* 0x4150f2ebd0a7ffe3 */
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1.20774763767876271158e+07, /* 0x416709348c0ea4ed */
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3.28299845686652474105e+07, /* 0x417f4f22091940bb */
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8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */
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2.42582597704895108938e+08, /* 0x41aceb088b68e803 */
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6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */
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1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */
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4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */
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1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */
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3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */
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9.78648047144193725586e+10, /* 0x4236c932696a6b5c */
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2.66024120300899291992e+11, /* 0x424ef822f7f6731c */
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7.23128532145737548828e+11, /* 0x42650bba3796379a */
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1.96566714857202099609e+12, /* 0x427c9aae4631c056 */
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5.34323729076223046875e+12, /* 0x429370470aec28ec */
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1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */
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3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */
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1.07321789892958031250e+14, /* 0x42d866f34a725782 */
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2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */
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7.93006726156715250000e+14, /* 0x430689e221bc8d5a */
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2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */
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static const double cosh_lead[ 37] = {
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1.00000000000000000000e+00, /* 0x3ff0000000000000 */
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1.54308063481524371241e+00, /* 0x3ff8b07551d9f550 */
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3.76219569108363138810e+00, /* 0x400e18fa0df2d9bc */
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1.00676619957777653269e+01, /* 0x402422a497d6185e */
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2.73082328360164865444e+01, /* 0x403b4ee858de3e80 */
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7.42099485247878334349e+01, /* 0x40528d6fcbeff3a9 */
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2.01715636122455890700e+02, /* 0x406936e67db9b919 */
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5.48317035155212010977e+02, /* 0x4081228949ba3a8b */
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1.49047916125217807348e+03, /* 0x409749eaa93f4e76 */
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4.05154202549259389343e+03, /* 0x40afa715845d8894 */
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1.10132329201033226127e+04, /* 0x40c5829dd053712d */
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2.99370708659497577173e+04, /* 0x40dd3c4489115627 */
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8.13773957125740562333e+04, /* 0x40f3de1654d6b543 */
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2.21206696005590405548e+05, /* 0x410b00b5916b6105 */
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6.01302142082804115489e+05, /* 0x412259ac48bf13ca */
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1.63450868623620807193e+06, /* 0x4138f0ccafad2d17 */
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4.44305526025399193168e+06, /* 0x4150f2ebd0a8005c */
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1.20774763767876680940e+07, /* 0x416709348c0ea503 */
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3.28299845686652623117e+07, /* 0x417f4f22091940bf */
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8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */
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2.42582597704895138741e+08, /* 0x41aceb088b68e804 */
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6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */
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1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */
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4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */
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1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */
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3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */
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9.78648047144193725586e+10, /* 0x4236c932696a6b5c */
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2.66024120300899291992e+11, /* 0x424ef822f7f6731c */
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7.23128532145737548828e+11, /* 0x42650bba3796379a */
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1.96566714857202099609e+12, /* 0x427c9aae4631c056 */
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5.34323729076223046875e+12, /* 0x429370470aec28ec */
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1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */
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3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */
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1.07321789892958031250e+14, /* 0x42d866f34a725782 */
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2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */
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7.93006726156715250000e+14, /* 0x430689e221bc8d5a */
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2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */
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unsigned long long ux, aux, xneg;
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unsigned int uhx;
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double x = fx, y, z, z1, z2;
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int m;
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/* Special cases */
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GET_BITS_DP64(x, ux);
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aux = ux & ~SIGNBIT_DP64;
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if (aux < 0x3f10000000000000) /* |x| small enough that cosh(x) = 1 */
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{
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if (aux == 0) return (float)1.0; /* with no inexact */
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if (LAMBDA_DP64 + x > 1.0) return valf_with_flags((float)1.0, AMD_F_INEXACT); /* with inexact */
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}
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else if (aux >= PINFBITPATT_DP64) /* |x| is NaN or Inf */
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{
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if (aux > PINFBITPATT_DP64) /* x is NaN */
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{
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GET_BITS_SP32(fx, uhx);
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return _handle_errorf("coshf",OP_COSH,uhx|0x00400000,_DOMAIN, 0,
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EDOM, fx, 0.0, 1);
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}
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else /* x is infinity */
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return infinityf_with_flags(0);
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}
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xneg = (aux != ux);
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y = x;
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if (xneg) y = -x;
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if (y >= max_cosh_arg)
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/* Return +infinity with overflow flag. */
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return _handle_errorf("coshf",OP_COSH,PINFBITPATT_SP32,_OVERFLOW,
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AMD_F_INEXACT|AMD_F_OVERFLOW,ERANGE, fx, 0.0, 1);
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// z = infinity_with_flags(AMD_F_OVERFLOW);
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else if (y >= small_threshold)
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{
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/* In this range y is large enough so that
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the negative exponential is negligible,
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so cosh(y) is approximated by sign(x)*exp(y)/2. The
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code below is an inlined version of that from
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exp() with two changes (it operates on
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y instead of x, and the division by 2 is
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done by reducing m by 1). */
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splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead,
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log2_by_32_tail, &m, &z1, &z2);
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m -= 1;
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/* scaleDouble_1 is always safe because the argument x was
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float, rather than double */
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z = scaleDouble_1((z1+z2),m);
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}
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else
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{
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/* In this range we find the integer part y0 of y
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and the increment dy = y - y0. We then compute
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z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
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z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy)
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where sinh(y0) and cosh(y0) are tabulated above. */
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int ind;
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double dy, dy2, sdy, cdy;
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ind = (int)y;
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dy = y - ind;
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dy2 = dy*dy;
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sdy = dy + dy*dy2*(0.166666666666666667013899e0 +
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(0.833333333333329931873097e-2 +
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(0.198412698413242405162014e-3 +
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(0.275573191913636406057211e-5 +
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(0.250521176994133472333666e-7 +
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(0.160576793121939886190847e-9 +
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0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
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cdy = 1 + dy2*(0.500000000000000005911074e0 +
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(0.416666666666660876512776e-1 +
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(0.138888888889814854814536e-2 +
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(0.248015872460622433115785e-4 +
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(0.275573350756016588011357e-6 +
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(0.208744349831471353536305e-8 +
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0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
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z = cosh_lead[ind]*cdy + sinh_lead[ind]*sdy;
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}
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// if (xneg) z = - z;
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return (float)z;
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}
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