/*******************************************************************************
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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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*******************************************************************************/

#include "libm.h"
#include "libm_util.h"

#define USE_SPLITEXP
#define USE_SCALEDOUBLE_1
#define USE_SCALEDOUBLE_2
#define USE_INFINITYF_WITH_FLAGS
#define USE_VALF_WITH_FLAGS
#define USE_HANDLE_ERRORF
#include "libm_inlines.h"
#undef USE_SPLITEXP
#undef USE_SCALEDOUBLE_1
#undef USE_SCALEDOUBLE_2
#undef USE_INFINITYF_WITH_FLAGS
#undef USE_VALF_WITH_FLAGS
#undef USE_HANDLE_ERRORF

#ifdef _MSC_VER
// Disable "C4163: not available as intrinsic function" warning that older
// compilers may issue here.
#pragma warning(disable:4163)
#pragma function(coshf)
#endif

float coshf(float fx)
{
  /*
    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
    /* The max argument of coshf, but stored as a double */
    max_cosh_arg = 8.94159862922329438106e+01, /* 0x40565a9f84f82e63 */
    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) */

  /* Tabulated values of sinh(i) and cosh(i) for i = 0,...,36. */

  static const double sinh_lead[   37] = {
    0.00000000000000000000e+00,  /* 0x0000000000000000 */
    1.17520119364380137839e+00,  /* 0x3ff2cd9fc44eb982 */
    3.62686040784701857476e+00,  /* 0x400d03cf63b6e19f */
    1.00178749274099008204e+01,  /* 0x40240926e70949ad */
    2.72899171971277496596e+01,  /* 0x403b4a3803703630 */
    7.42032105777887522891e+01,  /* 0x40528d0166f07374 */
    2.01713157370279219549e+02,  /* 0x406936d22f67c805 */
    5.48316123273246489589e+02,  /* 0x408122876ba380c9 */
    1.49047882578955000099e+03,  /* 0x409749ea514eca65 */
    4.05154190208278987484e+03,  /* 0x40afa7157430966f */
    1.10132328747033916443e+04,  /* 0x40c5829dced69991 */
    2.99370708492480553105e+04,  /* 0x40dd3c4488cb48d6 */
    8.13773957064298447222e+04,  /* 0x40f3de1654d043f0 */
    2.21206696003330085659e+05,  /* 0x410b00b5916a31a5 */
    6.01302142081972560845e+05,  /* 0x412259ac48bef7e3 */
    1.63450868623590236530e+06,  /* 0x4138f0ccafad27f6 */
    4.44305526025387924165e+06,  /* 0x4150f2ebd0a7ffe3 */
    1.20774763767876271158e+07,  /* 0x416709348c0ea4ed */
    3.28299845686652474105e+07,  /* 0x417f4f22091940bb */
    8.92411504815936237574e+07,  /* 0x419546d8f9ed26e1 */
    2.42582597704895108938e+08,  /* 0x41aceb088b68e803 */
    6.59407867241607308388e+08,  /* 0x41c3a6e1fd9eecfd */
    1.79245642306579566002e+09,  /* 0x41dab5adb9c435ff */
    4.87240172312445068359e+09,  /* 0x41f226af33b1fdc0 */
    1.32445610649217357635e+10,  /* 0x4208ab7fb5475fb7 */
    3.60024496686929321289e+10,  /* 0x4220c3d3920962c8 */
    9.78648047144193725586e+10,  /* 0x4236c932696a6b5c */
    2.66024120300899291992e+11,  /* 0x424ef822f7f6731c */
    7.23128532145737548828e+11,  /* 0x42650bba3796379a */
    1.96566714857202099609e+12,  /* 0x427c9aae4631c056 */
    5.34323729076223046875e+12,  /* 0x429370470aec28ec */
    1.45244248326237109375e+13,  /* 0x42aa6b765d8cdf6c */
    3.94814800913403437500e+13,  /* 0x42c1f43fcc4b662c */
    1.07321789892958031250e+14,  /* 0x42d866f34a725782 */
    2.91730871263727437500e+14,  /* 0x42f0953e2f3a1ef7 */
    7.93006726156715250000e+14,  /* 0x430689e221bc8d5a */
    2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */

  static const double cosh_lead[   37] = {
    1.00000000000000000000e+00,  /* 0x3ff0000000000000 */
    1.54308063481524371241e+00,  /* 0x3ff8b07551d9f550 */
    3.76219569108363138810e+00,  /* 0x400e18fa0df2d9bc */
    1.00676619957777653269e+01,  /* 0x402422a497d6185e */
    2.73082328360164865444e+01,  /* 0x403b4ee858de3e80 */
    7.42099485247878334349e+01,  /* 0x40528d6fcbeff3a9 */
    2.01715636122455890700e+02,  /* 0x406936e67db9b919 */
    5.48317035155212010977e+02,  /* 0x4081228949ba3a8b */
    1.49047916125217807348e+03,  /* 0x409749eaa93f4e76 */
    4.05154202549259389343e+03,  /* 0x40afa715845d8894 */
    1.10132329201033226127e+04,  /* 0x40c5829dd053712d */
    2.99370708659497577173e+04,  /* 0x40dd3c4489115627 */
    8.13773957125740562333e+04,  /* 0x40f3de1654d6b543 */
    2.21206696005590405548e+05,  /* 0x410b00b5916b6105 */
    6.01302142082804115489e+05,  /* 0x412259ac48bf13ca */
    1.63450868623620807193e+06,  /* 0x4138f0ccafad2d17 */
    4.44305526025399193168e+06,  /* 0x4150f2ebd0a8005c */
    1.20774763767876680940e+07,  /* 0x416709348c0ea503 */
    3.28299845686652623117e+07,  /* 0x417f4f22091940bf */
    8.92411504815936237574e+07,  /* 0x419546d8f9ed26e1 */
    2.42582597704895138741e+08,  /* 0x41aceb088b68e804 */
    6.59407867241607308388e+08,  /* 0x41c3a6e1fd9eecfd */
    1.79245642306579566002e+09,  /* 0x41dab5adb9c435ff */
    4.87240172312445068359e+09,  /* 0x41f226af33b1fdc0 */
    1.32445610649217357635e+10,  /* 0x4208ab7fb5475fb7 */
    3.60024496686929321289e+10,  /* 0x4220c3d3920962c8 */
    9.78648047144193725586e+10,  /* 0x4236c932696a6b5c */
    2.66024120300899291992e+11,  /* 0x424ef822f7f6731c */
    7.23128532145737548828e+11,  /* 0x42650bba3796379a */
    1.96566714857202099609e+12,  /* 0x427c9aae4631c056 */
    5.34323729076223046875e+12,  /* 0x429370470aec28ec */
    1.45244248326237109375e+13,  /* 0x42aa6b765d8cdf6c */
    3.94814800913403437500e+13,  /* 0x42c1f43fcc4b662c */
    1.07321789892958031250e+14,  /* 0x42d866f34a725782 */
    2.91730871263727437500e+14,  /* 0x42f0953e2f3a1ef7 */
    7.93006726156715250000e+14,  /* 0x430689e221bc8d5a */
    2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */

  unsigned long long ux, aux, xneg;
  unsigned int uhx;
  double x = fx, y, z, z1, z2;
  int m;

  /* Special cases */

  GET_BITS_DP64(x, ux);
  aux = ux & ~SIGNBIT_DP64;
  if (aux < 0x3f10000000000000) /* |x| small enough that cosh(x) = 1 */
    {
      if (aux == 0) return (float)1.0; /* with no inexact */
      if (LAMBDA_DP64 + x  > 1.0) return valf_with_flags((float)1.0, AMD_F_INEXACT); /* with inexact */
    }
  else if (aux >= PINFBITPATT_DP64) /* |x| is NaN or Inf */
    {
      if (aux > PINFBITPATT_DP64) /* x is NaN */
      {
        GET_BITS_SP32(fx, uhx);
        return _handle_errorf("coshf",OP_COSH,uhx|0x00400000,_DOMAIN, 0,
                        EDOM, fx, 0.0, 1);
      }
      else     /* x is infinity */
        return infinityf_with_flags(0);
    }
  xneg = (aux != ux);

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

  if (y >= max_cosh_arg)
    /* Return +infinity with overflow flag. */
         return _handle_errorf("coshf",OP_COSH,PINFBITPATT_SP32,_OVERFLOW, 
                        AMD_F_INEXACT|AMD_F_OVERFLOW,ERANGE, fx, 0.0, 1);
//    z = infinity_with_flags(AMD_F_OVERFLOW);
  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;

      /* scaleDouble_1 is always safe because the argument x was
         float, rather than double */
      z = scaleDouble_1((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 + 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 = 1 + 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);

      z = cosh_lead[ind]*cdy + sinh_lead[ind]*sdy;
    }

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