| /* |
| This Software is provided under the Zope Public License (ZPL) Version 2.1. |
| |
| Copyright (c) 2009, 2010 by the mingw-w64 project |
| |
| See the AUTHORS file for the list of contributors to the mingw-w64 project. |
| |
| This license has been certified as open source. It has also been designated |
| as GPL compatible by the Free Software Foundation (FSF). |
| |
| Redistribution and use in source and binary forms, with or without |
| modification, are permitted provided that the following conditions are met: |
| |
| 1. Redistributions in source code must retain the accompanying copyright |
| notice, this list of conditions, and the following disclaimer. |
| 2. Redistributions in binary form must reproduce the accompanying |
| copyright notice, this list of conditions, and the following disclaimer |
| in the documentation and/or other materials provided with the |
| distribution. |
| 3. Names of the copyright holders must not be used to endorse or promote |
| products derived from this software without prior written permission |
| from the copyright holders. |
| 4. The right to distribute this software or to use it for any purpose does |
| not give you the right to use Servicemarks (sm) or Trademarks (tm) of |
| the copyright holders. Use of them is covered by separate agreement |
| with the copyright holders. |
| 5. If any files are modified, you must cause the modified files to carry |
| prominent notices stating that you changed the files and the date of |
| any change. |
| |
| Disclaimer |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY EXPRESSED |
| OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
| OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO |
| EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY DIRECT, INDIRECT, |
| INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, |
| OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF |
| LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING |
| NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, |
| EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| */ |
| |
| /* 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 ("pushq %%rax\n\tsubq $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\npopq %%rax" : "=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) |
| { |
| return signbit (y) ? (1.0 / -x) : __FLT_CST (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) |
| { |
| return signbit(y) ? 1.0 / -x : -x; |
| /*__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; |
| } |