
/*
*  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_NAN_WITH_FLAGS
#define USE_VAL_WITH_FLAGS
#define USE_INFINITY_WITH_FLAGS
#define USE_HANDLE_ERROR
#include "../inc/libm_inlines_amd.h"
#undef USE_NAN_WITH_FLAGS
#undef USE_VAL_WITH_FLAGS
#undef USE_INFINITY_WITH_FLAGS
#undef USE_HANDLE_ERROR

#include "../inc/libm_errno_amd.h"

#ifndef WINDOWS
/* Deal with errno for out-of-range result */
static inline double retval_errno_erange_overflow(double x)
{
  struct exception exc;
  exc.arg1 = x;
  exc.arg2 = x;
  exc.type = SING;
  exc.name = (char *)"log1p";
  if (_LIB_VERSION == _SVID_)
    exc.retval = -HUGE;
  else
    exc.retval = -infinity_with_flags(AMD_F_DIVBYZERO);
  if (_LIB_VERSION == _POSIX_)
    __set_errno(ERANGE);
  else if (!matherr(&exc))
    __set_errno(ERANGE);
  return exc.retval;
}

/* Deal with errno for out-of-range argument */
static inline double retval_errno_edom(double x)
{
  struct exception exc;
  exc.arg1 = x;
  exc.arg2 = x;
  exc.type = DOMAIN;
  exc.name = (char *)"log1p";
  if (_LIB_VERSION == _SVID_)
    exc.retval = -HUGE;
  else
    exc.retval = nan_with_flags(AMD_F_INVALID);
  if (_LIB_VERSION == _POSIX_)
    __set_errno(EDOM);
  else if (!matherr(&exc))
    {
      if(_LIB_VERSION == _SVID_)
        (void)fputs("log1p: DOMAIN error\n", stderr);
    __set_errno(EDOM);
    }
  return exc.retval;
}
#endif

#undef _FUNCNAME
#define _FUNCNAME "log1p"

double FN_PROTOTYPE(log1p)(double x)
{

  int xexp;
  double r, r1, r2, correction, f, f1, f2, q, u, v, z1, z2, poly, m2;
  int index;
  unsigned long long ux, ax;

  /*
    Computes natural log(1+x). Algorithm based on:
    Ping-Tak Peter Tang
    "Table-driven implementation of the logarithm function in IEEE
    floating-point arithmetic"
    ACM Transactions on Mathematical Software (TOMS)
    Volume 16, Issue 4 (December 1990)
    Note that we use a lookup table of size 64 rather than 128,
    and compensate by having extra terms in the minimax polynomial
    for the kernel approximation.
  */

/* Arrays ln_lead_table and ln_tail_table contain
   leading and trailing parts respectively of precomputed
   values of natural log(1+i/64), for i = 0, 1, ..., 64.
   ln_lead_table contains the first 24 bits of precision,
   and ln_tail_table contains a further 53 bits precision. */

  static const double ln_lead_table[65] = {
    0.00000000000000000000e+00,   /* 0x0000000000000000 */
    1.55041813850402832031e-02,   /* 0x3f8fc0a800000000 */
    3.07716131210327148438e-02,   /* 0x3f9f829800000000 */
    4.58095073699951171875e-02,   /* 0x3fa7745800000000 */
    6.06245994567871093750e-02,   /* 0x3faf0a3000000000 */
    7.52233862876892089844e-02,   /* 0x3fb341d700000000 */
    8.96121263504028320312e-02,   /* 0x3fb6f0d200000000 */
    1.03796780109405517578e-01,   /* 0x3fba926d00000000 */
    1.17783010005950927734e-01,   /* 0x3fbe270700000000 */
    1.31576299667358398438e-01,   /* 0x3fc0d77e00000000 */
    1.45181953907012939453e-01,   /* 0x3fc2955280000000 */
    1.58604979515075683594e-01,   /* 0x3fc44d2b00000000 */
    1.71850204467773437500e-01,   /* 0x3fc5ff3000000000 */
    1.84922337532043457031e-01,   /* 0x3fc7ab8900000000 */
    1.97825729846954345703e-01,   /* 0x3fc9525a80000000 */
    2.10564732551574707031e-01,   /* 0x3fcaf3c900000000 */
    2.23143517971038818359e-01,   /* 0x3fcc8ff780000000 */
    2.35566020011901855469e-01,   /* 0x3fce270700000000 */
    2.47836112976074218750e-01,   /* 0x3fcfb91800000000 */
    2.59957492351531982422e-01,   /* 0x3fd0a324c0000000 */
    2.71933674812316894531e-01,   /* 0x3fd1675c80000000 */
    2.83768117427825927734e-01,   /* 0x3fd22941c0000000 */
    2.95464158058166503906e-01,   /* 0x3fd2e8e280000000 */
    3.07025015354156494141e-01,   /* 0x3fd3a64c40000000 */
    3.18453729152679443359e-01,   /* 0x3fd4618bc0000000 */
    3.29753279685974121094e-01,   /* 0x3fd51aad80000000 */
    3.40926527976989746094e-01,   /* 0x3fd5d1bd80000000 */
    3.51976394653320312500e-01,   /* 0x3fd686c800000000 */
    3.62905442714691162109e-01,   /* 0x3fd739d7c0000000 */
    3.73716354370117187500e-01,   /* 0x3fd7eaf800000000 */
    3.84411692619323730469e-01,   /* 0x3fd89a3380000000 */
    3.94993782043457031250e-01,   /* 0x3fd9479400000000 */
    4.05465066432952880859e-01,   /* 0x3fd9f323c0000000 */
    4.15827870368957519531e-01,   /* 0x3fda9cec80000000 */
    4.26084339618682861328e-01,   /* 0x3fdb44f740000000 */
    4.36236739158630371094e-01,   /* 0x3fdbeb4d80000000 */
    4.46287095546722412109e-01,   /* 0x3fdc8ff7c0000000 */
    4.56237375736236572266e-01,   /* 0x3fdd32fe40000000 */
    4.66089725494384765625e-01,   /* 0x3fddd46a00000000 */
    4.75845873355865478516e-01,   /* 0x3fde744240000000 */
    4.85507786273956298828e-01,   /* 0x3fdf128f40000000 */
    4.95077252388000488281e-01,   /* 0x3fdfaf5880000000 */
    5.04556000232696533203e-01,   /* 0x3fe02552a0000000 */
    5.13945698738098144531e-01,   /* 0x3fe0723e40000000 */
    5.23248136043548583984e-01,   /* 0x3fe0be72e0000000 */
    5.32464742660522460938e-01,   /* 0x3fe109f380000000 */
    5.41597247123718261719e-01,   /* 0x3fe154c3c0000000 */
    5.50647079944610595703e-01,   /* 0x3fe19ee6a0000000 */
    5.59615731239318847656e-01,   /* 0x3fe1e85f40000000 */
    5.68504691123962402344e-01,   /* 0x3fe23130c0000000 */
    5.77315330505371093750e-01,   /* 0x3fe2795e00000000 */
    5.86049020290374755859e-01,   /* 0x3fe2c0e9e0000000 */
    5.94707071781158447266e-01,   /* 0x3fe307d720000000 */
    6.03290796279907226562e-01,   /* 0x3fe34e2880000000 */
    6.11801505088806152344e-01,   /* 0x3fe393e0c0000000 */
    6.20240390300750732422e-01,   /* 0x3fe3d90260000000 */
    6.28608644008636474609e-01,   /* 0x3fe41d8fe0000000 */
    6.36907458305358886719e-01,   /* 0x3fe4618bc0000000 */
    6.45137906074523925781e-01,   /* 0x3fe4a4f840000000 */
    6.53301239013671875000e-01,   /* 0x3fe4e7d800000000 */
    6.61398470401763916016e-01,   /* 0x3fe52a2d20000000 */
    6.69430613517761230469e-01,   /* 0x3fe56bf9c0000000 */
    6.77398800849914550781e-01,   /* 0x3fe5ad4040000000 */
    6.85303986072540283203e-01,   /* 0x3fe5ee02a0000000 */
    6.93147122859954833984e-01};  /* 0x3fe62e42e0000000 */

  static const double ln_tail_table[65] = {
    0.00000000000000000000e+00,   /* 0x0000000000000000 */
    5.15092497094772879206e-09,   /* 0x3e361f807c79f3db */
    4.55457209735272790188e-08,   /* 0x3e6873c1980267c8 */
    2.86612990859791781788e-08,   /* 0x3e5ec65b9f88c69e */
    2.23596477332056055352e-08,   /* 0x3e58022c54cc2f99 */
    3.49498983167142274770e-08,   /* 0x3e62c37a3a125330 */
    3.23392843005887000414e-08,   /* 0x3e615cad69737c93 */
    1.35722380472479366661e-08,   /* 0x3e4d256ab1b285e9 */
    2.56504325268044191098e-08,   /* 0x3e5b8abcb97a7aa2 */
    5.81213608741512136843e-08,   /* 0x3e6f34239659a5dc */
    5.59374849578288093334e-08,   /* 0x3e6e07fd48d30177 */
    5.06615629004996189970e-08,   /* 0x3e6b32df4799f4f6 */
    5.24588857848400955725e-08,   /* 0x3e6c29e4f4f21cf8 */
    9.61968535632653505972e-10,   /* 0x3e1086c848df1b59 */
    1.34829655346594463137e-08,   /* 0x3e4cf456b4764130 */
    3.65557749306383026498e-08,   /* 0x3e63a02ffcb63398 */
    3.33431709374069198903e-08,   /* 0x3e61e6a6886b0976 */
    5.13008650536088382197e-08,   /* 0x3e6b8abcb97a7aa2 */
    5.09285070380306053751e-08,   /* 0x3e6b578f8aa35552 */
    3.20853940845502057341e-08,   /* 0x3e6139c871afb9fc */
    4.06713248643004200446e-08,   /* 0x3e65d5d30701ce64 */
    5.57028186706125221168e-08,   /* 0x3e6de7bcb2d12142 */
    5.48356693724804282546e-08,   /* 0x3e6d708e984e1664 */
    1.99407553679345001938e-08,   /* 0x3e556945e9c72f36 */
    1.96585517245087232086e-09,   /* 0x3e20e2f613e85bda */
    6.68649386072067321503e-09,   /* 0x3e3cb7e0b42724f6 */
    5.89936034642113390002e-08,   /* 0x3e6fac04e52846c7 */
    2.85038578721554472484e-08,   /* 0x3e5e9b14aec442be */
    5.09746772910284482606e-08,   /* 0x3e6b5de8034e7126 */
    5.54234668933210171467e-08,   /* 0x3e6dc157e1b259d3 */
    6.29100830926604004874e-09,   /* 0x3e3b05096ad69c62 */
    2.61974119468563937716e-08,   /* 0x3e5c2116faba4cdd */
    4.16752115011186398935e-08,   /* 0x3e665fcc25f95b47 */
    2.47747534460820790327e-08,   /* 0x3e5a9a08498d4850 */
    5.56922172017964209793e-08,   /* 0x3e6de647b1465f77 */
    2.76162876992552906035e-08,   /* 0x3e5da71b7bf7861d */
    7.08169709942321478061e-09,   /* 0x3e3e6a6886b09760 */
    5.77453510221151779025e-08,   /* 0x3e6f0075eab0ef64 */
    4.43021445893361960146e-09,   /* 0x3e33071282fb989b */
    3.15140984357495864573e-08,   /* 0x3e60eb43c3f1bed2 */
    2.95077445089736670973e-08,   /* 0x3e5faf06ecb35c84 */
    1.44098510263167149349e-08,   /* 0x3e4ef1e63db35f68 */
    1.05196987538551827693e-08,   /* 0x3e469743fb1a71a5 */
    5.23641361722697546261e-08,   /* 0x3e6c1cdf404e5796 */
    7.72099925253243069458e-09,   /* 0x3e4094aa0ada625e */
    5.62089493829364197156e-08,   /* 0x3e6e2d4c96fde3ec */
    3.53090261098577946927e-08,   /* 0x3e62f4d5e9a98f34 */
    3.80080516835568242269e-08,   /* 0x3e6467c96ecc5cbe */
    5.66961038386146408282e-08,   /* 0x3e6e7040d03dec5a */
    4.42287063097349852717e-08,   /* 0x3e67bebf4282de36 */
    3.45294525105681104660e-08,   /* 0x3e6289b11aeb783f */
    2.47132034530447431509e-08,   /* 0x3e5a891d1772f538 */
    3.59655343422487209774e-08,   /* 0x3e634f10be1fb591 */
    5.51581770357780862071e-08,   /* 0x3e6d9ce1d316eb93 */
    3.60171867511861372793e-08,   /* 0x3e63562a19a9c442 */
    1.94511067964296180547e-08,   /* 0x3e54e2adf548084c */
    1.54137376631349347838e-08,   /* 0x3e508ce55cc8c97a */
    3.93171034490174464173e-09,   /* 0x3e30e2f613e85bda */
    5.52990607758839766440e-08,   /* 0x3e6db03ebb0227bf */
    3.29990737637586136511e-08,   /* 0x3e61b75bb09cb098 */
    1.18436010922446096216e-08,   /* 0x3e496f16abb9df22 */
    4.04248680368301346709e-08,   /* 0x3e65b3f399411c62 */
    2.27418915900284316293e-08,   /* 0x3e586b3e59f65355 */
    1.70263791333409206020e-08,   /* 0x3e52482ceae1ac12 */
    5.76999904754328540596e-08};  /* 0x3e6efa39ef35793c */

  /* log2_lead and log2_tail sum to an extra-precise version
     of log(2) */
  static const double
    log2_lead = 6.93147122859954833984e-01,  /* 0x3fe62e42e0000000 */
    log2_tail = 5.76999904754328540596e-08;  /* 0x3e6efa39ef35793c */

  static const double
  /* Approximating polynomial coefficients for x near 0.0 */
    ca_1 = 8.33333333333317923934e-02,  /* 0x3fb55555555554e6 */
    ca_2 = 1.25000000037717509602e-02,  /* 0x3f89999999bac6d4 */
    ca_3 = 2.23213998791944806202e-03,  /* 0x3f62492307f1519f */
    ca_4 = 4.34887777707614552256e-04,  /* 0x3f3c8034c85dfff0 */

  /* Approximating polynomial coefficients for other x */
    cb_1 = 8.33333333333333593622e-02,  /* 0x3fb5555555555557 */
    cb_2 = 1.24999999978138668903e-02,  /* 0x3f89999999865ede */
    cb_3 = 2.23219810758559851206e-03;  /* 0x3f6249423bd94741 */

  /* The values exp(-1/16)-1 and exp(1/16)-1 */
  static const double
    log1p_thresh1 = -6.05869371865242201114e-02, /* 0xbfaf0540438fd5c4 */
    log1p_thresh2 = 6.44944589178594318568e-02;  /* 0x3fb082b577d34ed8 */


  GET_BITS_DP64(x, ux);
  ax = ux & ~SIGNBIT_DP64;

  if ((ux & EXPBITS_DP64) == EXPBITS_DP64)
    {
      /* x is either NaN or infinity */
      if (ux & MANTBITS_DP64)
        {
          /* x is NaN */
#ifdef WINDOWS
          return handle_error(_FUNCNAME, ux|0x0008000000000000, _DOMAIN,
                              0, EDOM, x, 0.0);
#else
          return x + x; /* Raise invalid if it is a signalling NaN */
#endif
        }
      else
        {
          /* x is infinity */
          if (ux & SIGNBIT_DP64)
            /* x is negative infinity. Return a NaN. */
#ifdef WINDOWS
            return handle_error(_FUNCNAME, INDEFBITPATT_DP64, _DOMAIN,
                                AMD_F_INVALID, EDOM, x, 0.0);
#else
            return retval_errno_edom(x);
#endif
          else
            return x;
        }
    }
  else if (ux >= 0xbff0000000000000)
    {
      /* x <= -1.0 */
      if (ux > 0xbff0000000000000)
        {
          /* x is less than -1.0. Return a NaN. */
#ifdef WINDOWS
          return handle_error(_FUNCNAME, INDEFBITPATT_DP64, _DOMAIN,
                              AMD_F_INVALID, EDOM, x, 0.0);
#else
          return retval_errno_edom(x);
#endif
        }
      else
        {
          /* x is exactly -1.0. Return -infinity with div-by-zero flag. */
#ifdef WINDOWS
          return handle_error(_FUNCNAME, NINFBITPATT_DP64, _SING,
                              AMD_F_DIVBYZERO, ERANGE, x, 0.0);
#else
          return retval_errno_erange_overflow(x);
#endif
        }
    }
  else if (ax < 0x3ca0000000000000)
    {
      if (ax == 0x0000000000000000)
        {
          /* x is +/-zero. Return the same zero. */
          return x;
        }
      else
        /* abs(x) is less than epsilon. Return x with inexact. */
        return val_with_flags(x, AMD_F_INEXACT);
    }


  if (x < log1p_thresh1 || x > log1p_thresh2)
    {
      /* x is outside the range [exp(-1/16)-1, exp(1/16)-1] */
      /*
        First, we decompose the argument x to the form
        1 + x  =  2**M  *  (F1  +  F2),
        where  1 <= F1+F2 < 2, M has the value of an integer,
        F1 = 1 + j/64, j ranges from 0 to 64, and |F2| <= 1/128.

        Second, we approximate log( 1 + F2/F1 ) by an odd polynomial
        in U, where U  =  2 F2 / (2 F1 + F2).
        Note that log( 1 + F2/F1 ) = log( 1 + U/2 ) - log( 1 - U/2 ).
        The core approximation calculates
        Poly = [log( 1 + U/2 ) - log( 1 - U/2 )]/U   -   1.
        Note that  log(1 + U/2) - log(1 - U/2) = 2 arctanh ( U/2 ),
        thus, Poly =  2 arctanh( U/2 ) / U  -  1.

        It is not hard to see that
          log(x) = M*log(2) + log(F1) + log( 1 + F2/F1 ).
        Hence, we return Z1 = log(F1), and  Z2 = log( 1 + F2/F1).
        The values of log(F1) are calculated beforehand and stored
        in the program.
      */

      f = 1.0 + x;
      GET_BITS_DP64(f, ux);

      /* Store the exponent of x in xexp and put
         f into the range [1.0,2.0) */
      xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64;
      PUT_BITS_DP64((ux & MANTBITS_DP64) | ONEEXPBITS_DP64, f);

      /* Now  (1+x) = 2**(xexp)  * f,  1 <= f < 2. */

      /* Set index to be the nearest integer to 64*f */
      /* 64 <= index <= 128 */
      /*
        r = 64.0 * f;
        index = (int)(r + 0.5);
      */
      /* This code instead of the above can save several cycles.
         It only works because 64 <= r < 128, so
         the nearest integer is always contained in exactly
         7 bits, and the right shift is always the same. */
      index = (int)((((ux & 0x000fc00000000000) | 0x0010000000000000) >> 46)
                    + ((ux & 0x0000200000000000) >> 45));

      f1 = index * 0.015625; /* 0.015625 = 1/64 */
      index -= 64;

      /* Now take great care to compute f2 such that f1 + f2 = f */
      if (xexp <= -2 || xexp >= MANTLENGTH_DP64 + 8)
        {
          f2 = f - f1;
        }
      else
        {
          /* Create the number m2 = 2.0^(-xexp) */
          ux = (unsigned long long)(0x3ff - xexp) << EXPSHIFTBITS_DP64;
          PUT_BITS_DP64(ux,m2);
          if (xexp <= MANTLENGTH_DP64 - 1)
            {
              f2 = (m2 - f1) + m2*x;
            }
          else
            {
              f2 = (m2*x - f1) + m2;
            }
        }

      /* At this point, x = 2**xexp * ( f1  +  f2 ) where
         f1 = j/64, j = 1, 2, ..., 64 and |f2| <= 1/128. */

      z1 = ln_lead_table[index];
      q = ln_tail_table[index];

      /* Calculate u = 2 f2 / ( 2 f1 + f2 ) = f2 / ( f1 + 0.5*f2 ) */
      u = f2 / (f1 + 0.5 * f2);

      /* Here, |u| <= 2(exp(1/16)-1) / (exp(1/16)+1).
         The core approximation calculates
         poly = [log(1 + u/2) - log(1 - u/2)]/u  -  1  */
      v = u * u;
      poly = (v * (cb_1 + v * (cb_2 + v * cb_3)));
      z2 = q + (u + u * poly);

      /* Now z1,z2 is an extra-precise approximation of log(f). */

      /* Add xexp * log(2) to z1,z2 to get the result log(1+x).
         The computed r1 is not subject to rounding error because
         xexp has at most 10 significant bits, log(2) has 24 significant
         bits, and z1 has up to 24 bits; and the exponents of z1
         and z2 differ by at most 6. */
      r1 = (xexp * log2_lead + z1);
      r2 = (xexp * log2_tail + z2);
      /* Natural log(1+x) */
      return r1 + r2;
    }
  else
    {
      /* Arguments close to 0.0 are handled separately to maintain
         accuracy.

         The approximation in this region exploits the identity
             log( 1 + r ) = log( 1 + u/2 )  -  log( 1 - u/2 ), where
             u  = 2r / (2+r).
         Note that the right hand side has an odd Taylor series expansion
         which converges much faster than the Taylor series expansion of
         log( 1 + r ) in r. Thus, we approximate log( 1 + r ) by
             u + A1 * u^3 + A2 * u^5 + ... + An * u^(2n+1).

         One subtlety is that since u cannot be calculated from
         r exactly, the rounding error in the first u should be
         avoided if possible. To accomplish this, we observe that
                       u  =  r  -  r*r/(2+r).
         Since x (=r) is the input argument, and thus presumed exact,
         the formula above approximates u accurately because
                       u  =  r  -  correction,
         and the magnitude of "correction" (of the order of r*r)
         is small.
         With these observations, we will approximate log( 1 + r ) by
            r + (  (A1*u^3 + ... + An*u^(2n+1)) - correction ).

         We approximate log(1+r) by an odd polynomial in u, where
                  u = 2r/(2+r) = r - r*r/(2+r).
      */
      r = x;
      u = r / (2.0 + r);
      correction = r * u;
      u          = u + u;
      v          = u * u;
      r1 = r;
      r2 = (u * v * (ca_1 + v * (ca_2 + v * (ca_3 + v * ca_4))) - correction);
      return r1 + r2;
    }
}

weak_alias (__log1p, log1p)