mingw-w64-crt/math/pow.def.h

/*
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 Copyright (c) 2009, 2010 by the mingw-w64 project

 See the AUTHORS file for the list of contributors to the mingw-w64 project.

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 as GPL compatible by the Free Software Foundation (FSF).

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      notice, this list of conditions, and the following disclaimer.
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      in the documentation and/or other materials provided with the
      distribution.
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      products derived from this software without prior written permission
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      not give you the right to use Servicemarks (sm) or Trademarks (tm) of
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      with the copyright holders.
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*/

/* IEEE 754 - Elementary Functions - Special Cases
 * pow(+/-0, oo) is +0
 * pow(+/-0, -oo) is +oo
 * pow (x, +/-0) is 1 for any x (even a zero, quiet NaN, or infinity)
 * pow (+1, y) is 1 for any y (even a quiet NaN)
 * pow (+/-0, y) is +/-oo and signals the divideByZero exception for y an odd integer < 0
 * pow (+/-0, y) is +oo and signals the divideByZero exception for finite y < 0 and not an odd integer
 * pow (+/-0, y) is +/-0 for finite y > 0 an odd integer
 * pow (+/-0, y) is +0 for finite y > 0 and not an odd integer
 * pow (-1, +/-oo) is 1 with no exception
 pow( -inf, y) = +0 for y<0 and not an odd integer
 pow( -inf, y) = -inf for y an odd integer > 0
 pow( -inf, y) = +inf for y>0 and not an odd integer
 pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0
 pow (+/-inf, -inf) is +0 with no exception
 pow (+/-inf, +inf) is +inf with no exception
 pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer
 pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer
 pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer
 pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y.
 
 For x /= 0: lim y->oo (1/x)^y results as: for |x| < 1 that sgn(x)*0 and for |x| > 0 that sgn(x)*Infinity

*/
#include "../complex/complex_internal.h"
#include <errno.h>
#include <limits.h>
#include <fenv.h>
#include <math.h>
#include <errno.h>
#define FE_ROUNDING_MASK \
  (FE_TONEAREST | FE_DOWNWARD | FE_UPWARD | FE_TOWARDZERO)

static __FLT_TYPE
internal_modf (__FLT_TYPE value, __FLT_TYPE *iptr)
{
  __FLT_TYPE int_part = (__FLT_TYPE) 0.0;
  /* truncate */ 
  /* truncate */
#ifdef _WIN64
  asm ("subq $8, %%rsp\n"
    "fnstcw 4(%%rsp)\n"
    "movzwl 4(%%rsp), %%eax\n"
    "orb $12, %%ah\n"
    "movw %%ax, (%%rsp)\n"
    "fldcw (%%rsp)\n"
    "frndint\n"
    "fldcw 4(%%rsp)\n"
    "addq $8, %%rsp\n" : "=t" (int_part) : "0" (value)); /* round */
#else
  asm ("push %%eax\n\tsubl $8, %%esp\n"
    "fnstcw 4(%%esp)\n"
    "movzwl 4(%%esp), %%eax\n"
    "orb $12, %%ah\n"
    "movw %%ax, (%%esp)\n"
    "fldcw (%%esp)\n"
    "frndint\n"
    "fldcw 4(%%esp)\n"
    "addl $8, %%esp\n\tpop %%eax\n" : "=t" (int_part) : "0" (value)); /* round */
#endif
  if (iptr)
    *iptr = int_part;
  return (isinf (value) ?  (__FLT_TYPE) 0.0 : value - int_part);
}

__FLT_TYPE __cdecl __FLT_ABI(__powi) (__FLT_TYPE x, int n);

__FLT_TYPE __cdecl
__FLT_ABI(pow) (__FLT_TYPE x, __FLT_TYPE y)
{
  int x_class = fpclassify (x);
  int y_class = fpclassify (y);
  long odd_y = 0;
  __FLT_TYPE d, rslt;

  if (y_class == FP_ZERO || x == __FLT_CST(1.0))
    return __FLT_CST(1.0);
  else if (x_class == FP_NAN || y_class == FP_NAN)
    {
      rslt = (signbit(x) ? -__FLT_NAN : __FLT_NAN);
      __FLT_RPT_DOMAIN ("pow", x, y, rslt);
      return rslt;
    }
  else if (x_class == FP_ZERO)
    {
      if (y_class == FP_INFINITE)
	return (signbit(y) ? __FLT_HUGE_VAL : __FLT_CST(0.0));

      if (signbit(x) && internal_modf (y, &d) != 0.0)
	{
	  __FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
	  return -__FLT_NAN;
	}
      odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
      if (!signbit(y))
	{
	  if (!odd_y || !signbit (x))
	    return __FLT_CST (0.0);
	  return -__FLT_CST(0.0);
	}

      if (!odd_y || !signbit (x))
	return __FLT_HUGE_VAL;
      return (signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
    }
  else if (y_class == FP_INFINITE)
    {
      __FLT_TYPE a_x;

      if (x_class == FP_INFINITE)
	return (signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
      a_x = (signbit (x) ? -x : x);
      if (a_x == 1.0)
	return __FLT_CST (1.0);
      if (a_x > 1.0)
	return (signbit (y) == 0 ? __FLT_HUGE_VAL : __FLT_CST (0.0));
      return (!signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
    }
  else if (x_class == FP_INFINITE)
    {
      /* pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y.  */
      if (signbit(x) && internal_modf (y, &d) != 0.0)
	{
	  __FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
	  return -__FLT_NAN;
	}
      odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
      /* pow( -inf, y) = +0 for y<0 and not an odd integer,  */
      if (signbit(x) && signbit(y) && !odd_y)
	return __FLT_CST(0.0);
      /* pow( -inf, y) = -inf for y an odd integer > 0.  */
      if (signbit(x) && !signbit(y) && odd_y)
	return -__FLT_HUGE_VAL;
      /* pow( -inf, y) = +inf for y>0 and not an odd integer.  */
      if (signbit(x) && !signbit(y) && !odd_y)
	return __FLT_HUGE_VAL;
      /* pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0. */
      if (signbit(y))
      {
        /* pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer.  */
	return (odd_y && signbit(x) ? -__FLT_CST(0.0) : __FLT_CST(0.0));
      }
      /* pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer.  */
      /* pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer.  */
      return (odd_y && signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
    }

  if (internal_modf (y, &d) != 0.0)
    {
      if (signbit (x))
	{
	  __FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
	  return -__FLT_NAN;
	}
      if (y == __FLT_CST(0.5))
	{
	  asm ("fsqrt" : "=t" (rslt) : "0" (x));
	  return rslt;
	}
    }
  else if ((d <= (__FLT_TYPE) INT_MAX && d >= (__FLT_TYPE) INT_MIN))
     return __FLT_ABI (__powi) (x, (int) y);
  /* As exp already checks for minlog and maxlog no further checks are necessary.  */
  rslt = (__FLT_TYPE) exp2l ((long double) y * log2l ((long double) __FLT_ABI(fabs) (x)));

  if (signbit (x) && internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0)
    rslt = -rslt;
  return rslt;
}