/* 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 * powi (x, +/-0) is 1 for any x (even a zero, quiet NaN, or infinity) * powi (+1, y) is 1 for any y (even a quiet NaN) * powi (+/-0, y) is +/-oo and signals the divideByZero exception for y an odd integer < 0 * powi (+/-0, y) is +oo and signals the divideByZero exception for finite y < 0 and not an odd integer * powi (+/-0, y) is +/-0 for finite y > 0 an odd integer * powi (+/-0, y) is +0 for finite y > 0 and not an odd integer powi (-inf, y) = +0 for y<0 and not an odd integer powi (-inf, y) = -inf for y an odd integer > 0 powi (-inf, y) = +inf for y>0 and not an odd integer powi (+/-inf, y) is +/-0 with no exception for y an odd integer < 0 powi (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer powi (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer powi (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer powi (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 #include #include #include #include static __FLT_TYPE do_powi_iter(__FLT_TYPE d, int y) { unsigned int u = (unsigned int) y; __FLT_TYPE rslt = ((u & 1) != 0) ? d : __FLT_CST(1.0); u >>= 1; do { d *= d; if ((u & 1) != 0) rslt *= d; u >>= 1; } while (u > 0); return rslt; } __FLT_TYPE __cdecl __FLT_ABI(__powi) (__FLT_TYPE x, int y); __FLT_TYPE __cdecl __FLT_ABI(__powi) (__FLT_TYPE x, int y) { int x_class = fpclassify (x); int odd_y = y & 1; int recip = 0; __FLT_TYPE d, rslt; if (y == 0 || x == __FLT_CST(1.0)) return __FLT_CST(1.0); else if (x_class == FP_NAN) { rslt = (signbit(x) ? -__FLT_NAN : __FLT_NAN); __FLT_RPT_DOMAIN ("__powi", x, (__FLT_TYPE) y, rslt); return rslt; } else if (x_class == FP_ZERO) { if (y >= 0) { 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 (x_class == FP_INFINITE) { /* pow( -inf, y) = +0 for y<0 and not an odd integer, */ if (signbit(x) && y < 0 && !odd_y) return __FLT_CST(0.0); /* pow( -inf, y) = -inf for y an odd integer > 0. */ if (signbit(x) && y >= 0 && odd_y) return -__FLT_HUGE_VAL; /* pow( -inf, y) = +inf for y>0 and not an odd integer. */ if (signbit(x) && y >= 0 && !odd_y) return __FLT_HUGE_VAL; /* pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0. */ if (y < 0) { /* 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); } d = __FLT_ABI(fabs) (x); if (y < 0) { /* By default, do the reciprocal of the result. */ recip = 1; y = -y; } if (!y) rslt = __FLT_CST(1.0); else if (y == 1) rslt = d; else { rslt = do_powi_iter(d, y); if (recip && fpclassify(rslt) == FP_INFINITE && d > __FLT_CST(1.0)) { /* Uncommon case - we had overflow, but we're going to calculate the reciprocal. If this happened, redo the calculation by doing the reciprocal upfront instead. Instead of trying to calculate whether this will happen, we prefer keeping the default case cheap. */ d = __FLT_CST(1.0) / d; recip = 0; rslt = do_powi_iter(d, y); } } if (recip) rslt = __FLT_CST(1.0) / rslt; if (signbit (x) && odd_y) rslt = -rslt; return rslt; }