/* Correctly-rounded logarithm of the absolute value of the gamma function for binary16 value.

Copyright (c) 2023-2025 Alexei Sibidanov and Paul Zimmermann

This file is part of the CORE-MATH project
(https://core-math.gitlabpages.inria.fr/).

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation 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,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

/* This code is based on the binary32 code lgammaf.c:
   at input we convert the inputs to _Float16 (exactly),
   we then use the same code than for lgammaf,
   and at output we round to _Float16.
   The changes with respect to lgammaf.c are marked with a comment
   "specific lgammaf16". */

#include <stdint.h>
#ifdef CORE_MATH_SUPPORT_ERRNO
#include <errno.h>
#endif
#include <math.h> // for signgam
#include <limits.h>

// Warning: clang also defines __GNUC__
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC diagnostic ignored "-Wunknown-pragmas"
#endif

typedef union {float f; uint32_t u;} b32u32_u;
typedef union {double f; uint64_t u;} b64u64_u;

static double as_r7(double x, const double *c){
  return (((x-c[0])*(x-c[1]))*((x-c[2])*(x-c[3])))*(((x-c[4])*(x-c[5]))*((x-c[6])));
}

static double as_r8(double x, const double *c){
  return (((x-c[0])*(x-c[1]))*((x-c[2])*(x-c[3])))*(((x-c[4])*(x-c[5]))*((x-c[6])*(x-c[7])));
}

static double as_sinpi(double x){
  static const double c[] =
    {0x1p+2, -0x1.de9e64df22ea4p+1, 0x1.472be122401f8p+0, -0x1.d4fcd82df91bp-3,
     0x1.9f05c97e0aab2p-6, -0x1.f3091c427b611p-10, 0x1.b22c9bfdca547p-14, -0x1.15484325ef569p-18};
  x -= 0.5;
  double x2 = x*x, x4 = x2*x2, x8 = x4*x4;
  return (0.25 - x2)*((c[0] + x2*c[1]) + x4*(c[2] + x2*c[3]) + x8*((c[4] + x2*c[5]) + x4*(c[6] + x2*c[7])));
}

static double as_ln(double x){
  b64u64_u t = {.f = x};
  int e = (t.u >> 52) - 0x3ff;
  static const double c[] =
    {0x1.fffffffffff24p-1, -0x1.ffffffffd1d67p-2, 0x1.55555537802dep-2, -0x1.ffffeca81b866p-3,
     0x1.999611761d772p-3, -0x1.54f3e581b61bfp-3, 0x1.1e642b4cb5143p-3, -0x1.9115a5af1e1edp-4};
  static const double il[] =
    {0x1.59caeec280116p-57, 0x1.f0a30c01162aap-5, 0x1.e27076e2af2ebp-4, 0x1.5ff3070a793d6p-3,
     0x1.c8ff7c79a9a2p-3, 0x1.1675cababa60fp-2, 0x1.4618bc21c5ec2p-2, 0x1.739d7f6bbd007p-2,
     0x1.9f323ecbf984dp-2, 0x1.c8ff7c79a9a21p-2, 0x1.f128f5faf06ecp-2, 0x1.0be72e4252a83p-1,
     0x1.1e85f5e7040d1p-1, 0x1.307d7334f10bep-1, 0x1.41d8fe84672afp-1, 0x1.52a2d265bc5abp-1};
  static const double ix[] =
    {0x1p+0, 0x1.e1e1e1e1e1e1ep-1, 0x1.c71c71c71c71cp-1, 0x1.af286bca1af28p-1,
     0x1.999999999999ap-1, 0x1.8618618618618p-1, 0x1.745d1745d1746p-1, 0x1.642c8590b2164p-1,
     0x1.5555555555555p-1, 0x1.47ae147ae147bp-1, 0x1.3b13b13b13b14p-1, 0x1.2f684bda12f68p-1,
     0x1.2492492492492p-1, 0x1.1a7b9611a7b96p-1, 0x1.1111111111111p-1, 0x1.0842108421084p-1};
  int i = (t.u>>48)&0xf;
  t.u = (t.u&(~(uint64_t)0>>12))|((int64_t)0x3ff<<52);
  double z = ix[i]*t.f - 1, z2 = z*z, z4 = z2*z2;
  return e*0x1.62e42fefa39efp-1 + il[i] + z*((c[0] + z*c[1]) + z2*(c[2] + z*c[3]) + z4*((c[4] + z*c[5]) + z2*(c[6] + z*c[7])));
}

// specific lgammaf16: input renamed to xf16
_Float16 cr_lgammaf16 (_Float16 xf16){
  float x = xf16;
  // specific lgammaf16: removed array tb[] of exceptional cases

  float fx = __builtin_floor(x), ax = __builtin_fabsf(x);
  b32u32_u t = {.f = ax};
  if(__builtin_expect(t.u>=(0xffu<<23), 0)){ // NaN or Inf
    if(t.u==(0xffu<<23)){ // +-inf
      signgam = 1;
      return 1.0f/0.0f;
    }
    return x + x; // nan
  }
  if(__builtin_expect(fx==x, 0)){ // x integer
    if(x <= 0.0f) {
#ifdef CORE_MATH_SUPPORT_ERRNO
      errno = ERANGE;
#endif
      t.f = x;
      // gamma(+0) = +Inf, gamma(-0) = -Inf
      if(!(t.u<<1)) signgam = 1 - 2*(t.u >> 31);
      return 1.0f/0.0f;
    }
    if(x==1.0f || x==2.0f) {
      signgam = 1;
      return 0.0f;
    }
  }

  double s = x;
  /* Check the value of fx to avoid a spurious invalid exception.
     Note that for a binary32 |x| >= 2^23, x is necessarily an integer,
     and we already dealed with negative integers, thus now:
     -2^23 < x < +Inf and x is not a negative integer nor 0, 1, 2. */
  if (__builtin_expect (fx >= 0, 1))
    signgam = 1;
  else
    // gamma(x) is negative in (-2n-1,-2n), thus when fx is odd
    signgam = 1 - ((((int)fx)&1)<<1);
  double z = ax, f;
  if(__builtin_expect(ax<0x1.52p-1f, 0)){
    static const double rn[] =
      {-0x1.505bdf4b65acp+4, -0x1.51c80eb47e068p+2, 0x1.0000000007cb8p+0, -0x1.4ac529250a1fcp+1,
       -0x1.a8c99dbe1621ap+0, -0x1.4abdcc74115eap+0, -0x1.1b87fe5a5b923p+0, -0x1.05b8a4d47ff64p+0};
    const double c0 = 0x1.0fc0fad268c4dp+2;
    static const double rd[] =
      {-0x1.4db2cfe9a5265p+5, -0x1.062e99d1c4f27p+3, -0x1.c81bc2ecf25f6p+1, -0x1.108e55c10091bp+1,
       -0x1.7dd25af0b83d4p+0, -0x1.36bf1880125fcp+0, -0x1.1379fc8023d9cp+0, -0x1.03712e41525d2p+0};
    f = (c0*s)*as_r8(s, rn)/as_r8(s, rd) - as_ln(z);
  } else { // |x| >= 0x1.52p-1
    if(ax > 0x1.afc1ap+1f){
      if(__builtin_expect(x >= 0x1.ff4p+12f, 0)){ // specific lgammaf16
        /* for x=0x1.ff4p+12, lgamma(x) ~ 0x1.ffd3p+15, thus there is no
           overflow for rounding towards zero, downwards or to nearest */
#ifndef __clang__
	_Float16 r = (x > 0x1.ff4p+12f) ? 0x1p15f16 * 0x1p15f16
          : 0x1.ffcp+15f16 + 1.0f16;
#else
        /* clang 19 raises a spurious overflow with the above code
           for x=0x1.ff4p+12 and RNDN with -frounding-math: apparently it
           evaluates the ? part even if the conditional is false:
           https://github.com/llvm/llvm-project/issues/157395.
           We thus use a workaround. */
        _Float16 r;
        if (x > 0x1.ff4p+12f)
          r = 0x1p15f16 * 0x1p15f16;
        else
          r = 0x1.ffcp+15f16 + 1.0f16;
#endif
#ifdef CORE_MATH_SUPPORT_ERRNO
	if (x > 0x1.ff4p+12f || (x == 0x1.ff4p+12f && x + 0x1p-12f > x))
          errno = ERANGE; // overflow
#endif
	return r;
      }
      double lz = as_ln(z);
      f = (z - 0.5)*(lz - 1) + 0x1.acfe390c97d69p-2;
      // specific lgammaf16: remove the condition ax < 0x1.0p+20f (always true)
      double iz = 1.0/z, iz2 = iz*iz;
      if(ax > 1198.0f){
        f +=  iz*(1./12.);
      } else if(ax > 0x1.279a7p+6f){
        static const double c[] =
          {0x1.555555547fbadp-4, -0x1.6c0fd270c465p-9};
        f +=  iz*(c[0] + iz2*c[1]);
      } else if(ax > 0x1.555556p+3f){
        static const double c[] =
          {0x1.555555554de0bp-4, -0x1.6c16bdc45944fp-9, 0x1.a0077f300ecb3p-11, -0x1.2e9cfff3b29c2p-11};
        double iz4 = iz2*iz2;
        f +=  iz*((c[0] + iz2*c[1]) + iz4*(c[2] + iz2*c[3]));
      } else {
        static const double c[] =
          {0x1.5555555551286p-4, -0x1.6c16c0e7c4cf4p-9, 0x1.a0193267fe6f2p-11, -0x1.37e87ec19cb45p-11,
           0x1.b40011dfff081p-11, -0x1.c16c8946b19b6p-10, 0x1.e9f47ace150d8p-9, -0x1.4f5843a71a338p-8};
        double iz4 = iz2*iz2, iz8 = iz4*iz4;
        double p = ((c[0] + iz2*c[1]) + iz4*(c[2] + iz2*c[3])) + iz8*((c[4] + iz2*c[5]) + iz4*(c[6] + iz2*c[7]));
        f += iz*p;
      }
      if(x < 0.0f){
	f = 0x1.250d048e7a1bdp+0 - f - lz;
	double lp = as_ln(as_sinpi(x-fx));
	f -= lp;
      }
    } else {
      static const double rn[] =
	{-0x1.667923ff14df7p+5, -0x1.2d35f25ad8f64p+3, -0x1.b8c9eab9d5bd3p+1, -0x1.7a4a97f494127p+0,
	 -0x1.3a6c8295b4445p-1, -0x1.da44e8b810024p-3, -0x1.9061e81c77e4ap-5};
      const double c0 = 0x1.3cc0e6a0106b3p+2;
      static const double rd[] =
	{-0x1.491a899e84c52p+6, -0x1.d202961b9e098p+3, -0x1.4ced68c631ed6p+2, -0x1.2589eedf40738p+1,
	 -0x1.1302e3337271p+0, -0x1.c36b802f26dffp-2, -0x1.3ded448acc39dp-3, -0x1.bffc491078eafp-6};
      f = (z-1)*(z-2)*c0*as_r7(z, rn)/as_r8(z, rd);
      if(x < 0.0f){
	if(__builtin_expect(t.u < 0x40301b93u && t.u > 0x402f95c2u, 0)){
	  double h = (s + 0x1.5fb410a1bd901p+1) - 0x1.a19a96d2e6f85p-54, h2 = h*h, h4 = h2*h2;
	  static const double c[] =
	    {-0x1.ea12da904b18cp+0, 0x1.3267f3c265a54p+3, -0x1.4185ac30cadb3p+4, 0x1.f504accc3f2e4p+5,
	     -0x1.8588444c679b4p+7, 0x1.43740491dc22p+9, -0x1.12400ea23f9e6p+11, 0x1.dac829f365795p+12};
	  f = h*((c[0] + h*c[1]) + h2*(c[2] + h*c[3]) + h4*((c[4] + h*c[5]) + h2*(c[6] + h*c[7])));
	} else if(__builtin_expect(t.u >  0x401ceccbu && t.u < 0x401d95cau, 0)){
	  double h = (s + 0x1.3a7fc9600f86cp+1) + 0x1.55f64f98af8dp-55, h2 = h*h, h4 = h2*h2;
	  static const double c[] =
	    {0x1.83fe966af535fp+0, 0x1.36eebb002f61ap+2, 0x1.694a60589a0b3p+0, 0x1.1718d7aedb0b5p+3,
	     0x1.733a045eca0d3p+2, 0x1.8d4297421205bp+4, 0x1.7feea5fb29965p+4};
	  f = h*((c[0] + h*c[1]) + h2*(c[2] + h*c[3]) + h4*((c[4] + h*c[5]) + h2*(c[6])));
#ifdef CORE_MATH_SUPPORT_ERRNO // specific lgammaf16
          if (x == -0x1.3a8p+1)
            errno = ERANGE; // underflow
#endif
	} else if(__builtin_expect(t.u > 0x40492009u && t.u < 0x404940efu, 0)){
	  double h = (s + 0x1.9260dbc9e59afp+1) + 0x1.f717cd335a7b3p-53, h2 = h*h, h4 = h2*h2;
	  static const double c[] =
	    {0x1.f20a65f2fac55p+2, 0x1.9d4d297715105p+4, 0x1.c1137124d5b21p+6, 0x1.267203d24de38p+9,
	     0x1.99a63399a0b44p+11, 0x1.2941214faaf0cp+14, 0x1.bb912c0c9cdd1p+16};
	  f = h*((c[0] + h*c[1]) + h2*(c[2] + h*c[3]) + h4*((c[4] + h*c[5]) + h2*(c[6])));
	} else {
	  f = 0x1.250d048e7a1bdp+0 - f;
	  double lp = as_ln(as_sinpi(x-fx)*z);
	  f -= lp;
	}
      }
    }
  }

  _Float16 r = f; // specific lgammaf16
  // specific lgammaf16: removed exceptional cases
  return r;
}

// dummy function since GNU libc does not provide it
_Float16 lgammaf16 (_Float16 x) {
  return (_Float16) lgammaf ((float) x);
}
