/* Split a double into fraction and mantissa. Copyright (C) 2007-2012 Free Software Foundation, Inc. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>. */ /* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and Bruno Haible <bruno@clisp.org>, 2007. */ #if ! defined USE_LONG_DOUBLE # include <config.h> #endif /* Specification. */ #include <math.h> #include <float.h> #ifdef USE_LONG_DOUBLE # include "isnanl-nolibm.h" # include "fpucw.h" #else # include "isnand-nolibm.h" #endif /* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater than 2, or not even a power of 2, some rounding errors can occur, so that then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0. */ #ifdef USE_LONG_DOUBLE # define FUNC frexpl # define DOUBLE long double # define ISNAN isnanl # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING () # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING () # define L_(literal) literal##L #else # define FUNC frexp # define DOUBLE double # define ISNAN isnand # define DECL_ROUNDING # define BEGIN_ROUNDING() # define END_ROUNDING() # define L_(literal) literal #endif DOUBLE FUNC (DOUBLE x, int *expptr) { int sign; int exponent; DECL_ROUNDING /* Test for NaN, infinity, and zero. */ if (ISNAN (x) || x + x == x) { *expptr = 0; return x; } sign = 0; if (x < 0) { x = - x; sign = -1; } BEGIN_ROUNDING (); { /* Since the exponent is an 'int', it fits in 64 bits. Therefore the loops are executed no more than 64 times. */ DOUBLE pow2[64]; /* pow2[i] = 2^2^i */ DOUBLE powh[64]; /* powh[i] = 2^-2^i */ int i; exponent = 0; if (x >= L_(1.0)) { /* A positive exponent. */ DOUBLE pow2_i; /* = pow2[i] */ DOUBLE powh_i; /* = powh[i] */ /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, x * 2^exponent = argument, x >= 1.0. */ for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); ; i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) { if (x >= pow2_i) { exponent += (1 << i); x *= powh_i; } else break; pow2[i] = pow2_i; powh[i] = powh_i; } /* Avoid making x too small, as it could become a denormalized number and thus lose precision. */ while (i > 0 && x < pow2[i - 1]) { i--; powh_i = powh[i]; } exponent += (1 << i); x *= powh_i; /* Here 2^-2^i <= x < 1.0. */ } else { /* A negative or zero exponent. */ DOUBLE pow2_i; /* = pow2[i] */ DOUBLE powh_i; /* = powh[i] */ /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, x * 2^exponent = argument, x < 1.0. */ for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); ; i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) { if (x < powh_i) { exponent -= (1 << i); x *= pow2_i; } else break; pow2[i] = pow2_i; powh[i] = powh_i; } /* Here 2^-2^i <= x < 1.0. */ } /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */ while (i > 0) { i--; if (x < powh[i]) { exponent -= (1 << i); x *= pow2[i]; } } /* Here 0.5 <= x < 1.0. */ } if (sign < 0) x = - x; END_ROUNDING (); *expptr = exponent; return x; }