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138 lines
4.3 KiB
C
138 lines
4.3 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_HANDLE_ERROR
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#define USE_SPLITEXP
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#define USE_SCALEDOUBLE_2
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#define USE_VAL_WITH_FLAGS
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#include "libm_inlines.h"
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#undef USE_SPLITEXP
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#undef USE_SCALEDOUBLE_2
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#undef USE_VAL_WITH_FLAGS
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#undef USE_HANDLE_ERROR
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#include "libm_errno.h"
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#pragma function(tanh)
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double tanh(double x)
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{
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/*
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The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
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to the following three formulae:
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1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
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2. (1 - (2/(exp(2*x) + 1 )))
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3. (exp(2*x) - 1)/(exp(2*x) + 1)
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but computationally, some formulae are better on some ranges.
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*/
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static const double
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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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large_threshold = 20.0; /* 0x4034000000000000 */
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unsigned long ux, aux, xneg;
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double y, z, p, 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 < 0x3e30000000000000) /* |x| small enough that tanh(x) = x */
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{
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if (aux == 0)
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return x; /* with no inexact */
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else
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return val_with_flags(x, AMD_F_INEXACT);
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}
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else if (aux > 0x7ff0000000000000) /* |x| is NaN */
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return _handle_error("tanh", OP_TANH, ux|0x0008000000000000, _DOMAIN,
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0, EDOM, x, 0.0, 1);
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// return x + x;
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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 > large_threshold)
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{
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/* If x is large then exp(-x) is negligible and
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formula 1 reduces to plus or minus 1.0 */
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z = 1.0;
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}
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else if (y <= 1.0)
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{
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double y2;
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y2 = y*y;
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if (y < 0.9)
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{
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/* Use a [3,3] Remez approximation on [0,0.9]. */
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z = y + y*y2*
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(-0.274030424656179760118928e0 +
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(-0.176016349003044679402273e-1 +
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(-0.200047621071909498730453e-3 -
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0.142077926378834722618091e-7*y2)*y2)*y2)/
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(0.822091273968539282568011e0 +
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(0.381641414288328849317962e0 +
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(0.201562166026937652780575e-1 +
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0.2091140262529164482568557e-3*y2)*y2)*y2);
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}
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else
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{
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/* Use a [3,3] Remez approximation on [0.9,1]. */
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z = y + y*y2*
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(-0.227793870659088295252442e0 +
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(-0.146173047288731678404066e-1 +
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(-0.165597043903549960486816e-3 -
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0.115475878996143396378318e-7*y2)*y2)*y2)/
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(0.683381611977295894959554e0 +
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(0.317204558977294374244770e0 +
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(0.167358775461896562588695e-1 +
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0.173076050126225961768710e-3*y2)*y2)*y2);
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}
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}
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else
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{
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/* Compute p = exp(2*y) + 1. The code is basically inlined
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from exp_amd. */
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splitexp(2*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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p = scaleDouble_2(z1 + z2, m) + 1.0;
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/* Now reconstruct tanh from p. */
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z = (1.0 - 2.0/p);
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}
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if (xneg) z = - z;
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return z;
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}
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