/* Implementation of gamma function according to ISO C.

   Copyright (C) 1997-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.

   The GNU C Library 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.

   The GNU C Library 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 the GNU C Library; if not, see

   <http://www.gnu.org/licenses/>.  */

#include <math.h>

#include <math-narrow-eval.h>

#include <math_private.h>

#include <math-underflow.h>

#include <float.h>

/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's

   approximation to gamma function.  */

static const float gamma_coeff[] =

  {

    0x1.555556p-4f,

    -0xb.60b61p-12f,

    0x3.403404p-12f,

  };

#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0]))

/* Return gamma (X), for positive X less than 42, in the form R *

   2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to

   avoid overflow or underflow in intermediate calculations.  */

static float

gammaf_positive (float x, int *exp2_adj)

{

  int local_signgam;

  if (x < 0.5f)

    {

      *exp2_adj = 0;

      return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x;

    }

  else if (x <= 1.5f)

    {

      *exp2_adj = 0;

      return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam));

    }

  else if (x < 2.5f)

    {

      *exp2_adj = 0;

      float x_adj = x - 1;

      return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam))

	      * x_adj);

    }

  else

    {

      float eps = 0;

      float x_eps = 0;

      float x_adj = x;

      float prod = 1;

      if (x < 4.0f)

	{

	  /* Adjust into the range for applying Stirling's

	     approximation.  */

	  float n = __ceilf (4.0f - x);

	  x_adj = math_narrow_eval (x + n);

	  x_eps = (x - (x_adj - n));

	  prod = __gamma_productf (x_adj - n, x_eps, n, &eps);

	}

      /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).

	 Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,

	 starting by computing pow (X_ADJ, X_ADJ) with a power of 2

	 factored out.  */

      float exp_adj = -eps;

      float x_adj_int = __roundf (x_adj);

      float x_adj_frac = x_adj - x_adj_int;

      int x_adj_log2;

      float x_adj_mant = __frexpf (x_adj, &x_adj_log2);

      if (x_adj_mant < (float) M_SQRT1_2)

	{

	  x_adj_log2--;

	  x_adj_mant *= 2.0f;

	}

      *exp2_adj = x_adj_log2 * (int) x_adj_int;

      float ret = (__ieee754_powf (x_adj_mant, x_adj)

		   * __ieee754_exp2f (x_adj_log2 * x_adj_frac)

		   * __ieee754_expf (-x_adj)

		   * sqrtf (2 * (float) M_PI / x_adj)

		   / prod);

      exp_adj += x_eps * __ieee754_logf (x_adj);

      float bsum = gamma_coeff[NCOEFF - 1];

      float x_adj2 = x_adj * x_adj;

      for (size_t i = 1; i <= NCOEFF - 1; i++)

	bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];

      exp_adj += bsum / x_adj;

      return ret + ret * __expm1f (exp_adj);

    }

}

float

__ieee754_gammaf_r (float x, int *signgamp)

{

  int32_t hx;

  float ret;

  GET_FLOAT_WORD (hx, x);

  if (__glibc_unlikely ((hx & 0x7fffffff) == 0))

    {

      /* Return value for x == 0 is Inf with divide by zero exception.  */

      *signgamp = 0;

      return 1.0 / x;

    }

  if (__builtin_expect (hx < 0, 0)

      && (uint32_t) hx < 0xff800000 && __rintf (x) == x)

    {

      /* Return value for integer x < 0 is NaN with invalid exception.  */

      *signgamp = 0;

      return (x - x) / (x - x);

    }

  if (__glibc_unlikely (hx == 0xff800000))

    {

      /* x == -Inf.  According to ISO this is NaN.  */

      *signgamp = 0;

      return x - x;

    }

  if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000))

    {

      /* Positive infinity (return positive infinity) or NaN (return

	 NaN).  */

      *signgamp = 0;

      return x + x;

    }

  if (x >= 36.0f)

    {

      /* Overflow.  */

      *signgamp = 0;

      ret = math_narrow_eval (FLT_MAX * FLT_MAX);

      return ret;

    }

  else

    {

      SET_RESTORE_ROUNDF (FE_TONEAREST);

      if (x > 0.0f)

	{

	  *signgamp = 0;

	  int exp2_adj;

	  float tret = gammaf_positive (x, &exp2_adj);

	  ret = __scalbnf (tret, exp2_adj);

	}

      else if (x >= -FLT_EPSILON / 4.0f)

	{

	  *signgamp = 0;

	  ret = 1.0f / x;

	}

      else

	{

	  float tx = __truncf (x);

	  *signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1;

	  if (x <= -42.0f)

	    /* Underflow.  */

	    ret = FLT_MIN * FLT_MIN;

	  else

	    {

	      float frac = tx - x;

	      if (frac > 0.5f)

		frac = 1.0f - frac;

	      float sinpix = (frac <= 0.25f

			      ? __sinf ((float) M_PI * frac)

			      : __cosf ((float) M_PI * (0.5f - frac)));

	      int exp2_adj;

	      float tret = (float) M_PI / (-x * sinpix

					   * gammaf_positive (-x, &exp2_adj));

	      ret = __scalbnf (tret, -exp2_adj);

	      math_check_force_underflow_nonneg (ret);

	    }

	}

      ret = math_narrow_eval (ret);

    }

  if (isinf (ret) && x != 0)

    {

      if (*signgamp < 0)

	{

	  ret = math_narrow_eval (-__copysignf (FLT_MAX, ret) * FLT_MAX);

	  ret = -ret;

	}

      else

	ret = math_narrow_eval (__copysignf (FLT_MAX, ret) * FLT_MAX);

      return ret;

    }

  else if (ret == 0)

    {

      if (*signgamp < 0)

	{

	  ret = math_narrow_eval (-__copysignf (FLT_MIN, ret) * FLT_MIN);

	  ret = -ret;

	}

      else

	ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN);

      return ret;

    }

  else

    return ret;

}

strong_alias (__ieee754_gammaf_r, __gammaf_r_finite)