216 lines
8.0 KiB
C
216 lines
8.0 KiB
C
/*
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This Software is provided under the Zope Public License (ZPL) Version 2.1.
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Copyright (c) 2009, 2010 by the mingw-w64 project
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See the AUTHORS file for the list of contributors to the mingw-w64 project.
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This license has been certified as open source. It has also been designated
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as GPL compatible by the Free Software Foundation (FSF).
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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1. Redistributions in source code must retain the accompanying copyright
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notice, this list of conditions, and the following disclaimer.
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2. Redistributions in binary form must reproduce the accompanying
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copyright notice, this list of conditions, and the following disclaimer
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in the documentation and/or other materials provided with the
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distribution.
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3. Names of the copyright holders must not be used to endorse or promote
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products derived from this software without prior written permission
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from the copyright holders.
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4. The right to distribute this software or to use it for any purpose does
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not give you the right to use Servicemarks (sm) or Trademarks (tm) of
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the copyright holders. Use of them is covered by separate agreement
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with the copyright holders.
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5. If any files are modified, you must cause the modified files to carry
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prominent notices stating that you changed the files and the date of
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any change.
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Disclaimer
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY EXPRESSED
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OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
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EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY DIRECT, INDIRECT,
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INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
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OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
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EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/* IEEE 754 - Elementary Functions - Special Cases
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* pow(+/-0, oo) is +0
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* pow(+/-0, -oo) is +oo
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* pow (x, +/-0) is 1 for any x (even a zero, quiet NaN, or infinity)
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* pow (+1, y) is 1 for any y (even a quiet NaN)
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* pow (+/-0, y) is +/-oo and signals the divideByZero exception for y an odd integer < 0
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* pow (+/-0, y) is +oo and signals the divideByZero exception for finite y < 0 and not an odd integer
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* pow (+/-0, y) is +/-0 for finite y > 0 an odd integer
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* pow (+/-0, y) is +0 for finite y > 0 and not an odd integer
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* pow (-1, +/-oo) is 1 with no exception
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pow( -inf, y) = +0 for y<0 and not an odd integer
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pow( -inf, y) = -inf for y an odd integer > 0
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pow( -inf, y) = +inf for y>0 and not an odd integer
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pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0
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pow (+/-inf, -inf) is +0 with no exception
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pow (+/-inf, +inf) is +inf with no exception
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pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer
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pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer
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pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer
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pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y.
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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
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*/
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#include "complex_internal.h"
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#include <errno.h>
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#include <limits.h>
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#include <fenv.h>
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#include <math.h>
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#include <errno.h>
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#define FE_ROUNDING_MASK \
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(FE_TONEAREST | FE_DOWNWARD | FE_UPWARD | FE_TOWARDZERO)
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static __FLT_TYPE
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internal_modf (__FLT_TYPE value, __FLT_TYPE *iptr)
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{
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__FLT_TYPE int_part = (__FLT_TYPE) 0.0;
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/* truncate */
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/* truncate */
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#ifdef __x86_64__
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asm ("pushq %%rax\n\tsubq $8, %%rsp\n"
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"fnstcw 4(%%rsp)\n"
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"movzwl 4(%%rsp), %%eax\n"
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"orb $12, %%ah\n"
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"movw %%ax, (%%rsp)\n"
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"fldcw (%%rsp)\n"
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"frndint\n"
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"fldcw 4(%%rsp)\n"
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"addq $8, %%rsp\npopq %%rax" : "=t" (int_part) : "0" (value)); /* round */
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#else
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asm ("push %%eax\n\tsubl $8, %%esp\n"
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"fnstcw 4(%%esp)\n"
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"movzwl 4(%%esp), %%eax\n"
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"orb $12, %%ah\n"
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"movw %%ax, (%%esp)\n"
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"fldcw (%%esp)\n"
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"frndint\n"
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"fldcw 4(%%esp)\n"
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"addl $8, %%esp\n\tpop %%eax\n" : "=t" (int_part) : "0" (value)); /* round */
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#endif
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if (iptr)
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*iptr = int_part;
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return (isinf (value) ? (__FLT_TYPE) 0.0 : value - int_part);
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}
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__FLT_TYPE __cdecl __FLT_ABI(__powi) (__FLT_TYPE x, int n);
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__FLT_TYPE __cdecl
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__FLT_ABI(pow) (__FLT_TYPE x, __FLT_TYPE y)
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{
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int x_class = fpclassify (x);
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int y_class = fpclassify (y);
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long odd_y = 0;
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__FLT_TYPE d, rslt;
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if (y_class == FP_ZERO || x == __FLT_CST(1.0))
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return __FLT_CST(1.0);
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else if (x_class == FP_NAN || y_class == FP_NAN)
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{
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rslt = (signbit(x) ? -__FLT_NAN : __FLT_NAN);
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__FLT_RPT_DOMAIN ("pow", x, y, rslt);
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return rslt;
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}
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else if (x_class == FP_ZERO)
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{
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if (y_class == FP_INFINITE)
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return (signbit(y) ? __FLT_HUGE_VAL : __FLT_CST(0.0));
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if (signbit(x) && internal_modf (y, &d) != 0.0)
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{
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return signbit (y) ? (1.0 / -x) : __FLT_CST (0.0);
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/*__FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
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return -__FLT_NAN; */
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}
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odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
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if (!signbit(y))
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{
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if (!odd_y || !signbit (x))
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return __FLT_CST (0.0);
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return -__FLT_CST(0.0);
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}
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if (!odd_y || !signbit (x))
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return __FLT_HUGE_VAL;
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return (signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
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}
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else if (y_class == FP_INFINITE)
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{
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__FLT_TYPE a_x;
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if (x_class == FP_INFINITE)
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return (signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
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a_x = (signbit (x) ? -x : x);
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if (a_x == 1.0)
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return __FLT_CST (1.0);
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if (a_x > 1.0)
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return (signbit (y) == 0 ? __FLT_HUGE_VAL : __FLT_CST (0.0));
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return (!signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
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}
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else if (x_class == FP_INFINITE)
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{
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/* pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y. */
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if (signbit(x) && internal_modf (y, &d) != 0.0)
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{
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return signbit(y) ? 1.0 / -x : -x;
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/*__FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
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return -__FLT_NAN;*/
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}
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odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
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/* pow( -inf, y) = +0 for y<0 and not an odd integer, */
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if (signbit(x) && signbit(y) && !odd_y)
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return __FLT_CST(0.0);
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/* pow( -inf, y) = -inf for y an odd integer > 0. */
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if (signbit(x) && !signbit(y) && odd_y)
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return -__FLT_HUGE_VAL;
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/* pow( -inf, y) = +inf for y>0 and not an odd integer. */
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if (signbit(x) && !signbit(y) && !odd_y)
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return __FLT_HUGE_VAL;
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/* pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0. */
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if (signbit(y))
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{
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/* pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer. */
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return (odd_y && signbit(x) ? -__FLT_CST(0.0) : __FLT_CST(0.0));
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}
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/* pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer. */
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/* pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer. */
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return (odd_y && signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
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}
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if (internal_modf (y, &d) != 0.0)
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{
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if (signbit (x))
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{
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__FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
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return -__FLT_NAN;
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}
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if (y == __FLT_CST(0.5))
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{
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asm ("fsqrt" : "=t" (rslt) : "0" (x));
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return rslt;
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}
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}
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else if ((d <= (__FLT_TYPE) INT_MAX && d >= (__FLT_TYPE) INT_MIN))
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return __FLT_ABI (__powi) (x, (int) y);
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/* As exp already checks for minlog and maxlog no further checks are necessary. */
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rslt = (__FLT_TYPE) exp2l ((long double) y * log2l ((long double) __FLT_ABI(fabs) (x)));
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if (signbit (x) && internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0)
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rslt = -rslt;
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return rslt;
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}
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