xref: /reactos/sdk/lib/crt/math/libm_sse2/sinh.c (revision 9e8ed3f8)

/*******************************************************************************
MIT License
-----------

Copyright (c) 2002-2019 Advanced Micro Devices, Inc.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this Software and associated documentaon 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,
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THE SOFTWARE.
*******************************************************************************/

#include "libm.h"
#include "libm_util.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 "libm_inlines.h"
#undef USE_SPLITEXP
#undef USE_SCALEDOUBLE_1
#undef USE_SCALEDOUBLE_2
#undef USE_INFINITY_WITH_FLAGS
#undef USE_VAL_WITH_FLAGS
#undef USE_HANDLE_ERROR

#include "libm_errno.h"

#ifdef _MSC_VER
#pragma function(sinh)
#endif

double sinh(double x)
{
  /*
    After dealing with special cases the computation is split into
    regions as follows:

    abs(x) >= max_sinh_arg:
    sinh(x) = sign(x)*Inf

    abs(x) >= small_threshold:
    sinh(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)))
    sinh(x) is then sign(x)*z.                             */

  static const double
    max_sinh_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;
  /* (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 sinh(x) = x */
    {
      if (aux == 0)
        /* with no inexact */
        return x;
      else
        return val_with_flags(x, AMD_F_INEXACT);
    }
  else if (aux >= 0x7ff0000000000000) /* |x| is NaN or Inf */
    {
      if (aux > 0x7ff0000000000000)
        /* x is NaN */
        return _handle_error("sinh", OP_SINH, ux|0x0008000000000000, _DOMAIN,
                            0, EDOM, x, 0.0, 1);
      else
      return x + x;
    }


  xneg = (aux != ux);

  y = x;
  if (xneg) y = -x;

  if (y >= max_sinh_arg)
    {
      if (xneg)
        return _handle_error("sinh", OP_SINH, NINFBITPATT_DP64, _OVERFLOW,
                            AMD_F_OVERFLOW, ERANGE, x, 0.0, 1);
      else
        return _handle_error("sinh", OP_SINH, PINFBITPATT_DP64, _OVERFLOW,
                            AMD_F_OVERFLOW, ERANGE, x, 0.0, 1);
    }
  else if (y >= small_threshold)
    {
      /* In this range y is large enough so that
         the negative exponential is negligible,
         so sinh(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)

         where sinh(y0) and cosh(y0) are tabulated above. */

      int ind;
      double dy, dy2, sdy, cdy, sdy1, sdy2;

      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.
	 Shift some significant bits from dy to sdy. */

      GET_BITS_DP64(dy, ux);
      ux &= 0xfffffffff8000000;
      PUT_BITS_DP64(ux, sdy1);
      sdy2 = sdy + (dy - sdy1);

      z = ((((((cosh_tail[ind]*sdy2 + sinh_tail[ind]*cdy)
	       + cosh_tail[ind]*sdy1) + sinh_tail[ind])
	     + cosh_lead[ind]*sdy2) + sinh_lead[ind]*cdy)
	   + cosh_lead[ind]*sdy1) + sinh_lead[ind];
    }

  if (xneg) z = - z;
  return z;
}