/* Split a double into fraction and mantissa, for hexadecimal printf. Copyright (C) 2007, 2009-2012 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/>. */ #if ! defined USE_LONG_DOUBLE # include <config.h> #endif /* Specification. */ #ifdef USE_LONG_DOUBLE # include "printf-frexpl.h" #else # include "printf-frexp.h" #endif #include <float.h> #include <math.h> #ifdef USE_LONG_DOUBLE # include "fpucw.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 <= 2.0, not < 2.0. */ #ifdef USE_LONG_DOUBLE # define FUNC printf_frexpl # define DOUBLE long double # define MIN_EXP LDBL_MIN_EXP # if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC # define USE_FREXP_LDEXP # define FREXP frexpl # define LDEXP ldexpl # endif # 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 printf_frexp # define DOUBLE double # define MIN_EXP DBL_MIN_EXP # if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC # define USE_FREXP_LDEXP # define FREXP frexp # define LDEXP ldexp # endif # define DECL_ROUNDING # define BEGIN_ROUNDING() # define END_ROUNDING() # define L_(literal) literal #endif DOUBLE FUNC (DOUBLE x, int *expptr) { int exponent; DECL_ROUNDING BEGIN_ROUNDING (); #ifdef USE_FREXP_LDEXP /* frexp and ldexp are usually faster than the loop below. */ x = FREXP (x, &exponent); x = x + x; exponent -= 1; if (exponent < MIN_EXP - 1) { x = LDEXP (x, exponent - (MIN_EXP - 1)); exponent = MIN_EXP - 1; } #else { /* 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 nonnegative 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; } } /* Here 1.0 <= x < 2^2^i. */ } else { /* A negative 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, exponent >= MIN_EXP - 1. */ 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 (exponent - (1 << i) < MIN_EXP - 1) break; exponent -= (1 << i); x *= pow2_i; if (x >= L_(1.0)) break; pow2[i] = pow2_i; powh[i] = powh_i; } } /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent, or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ if (x < L_(1.0)) /* Invariants: x * 2^exponent = argument, x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent. */ while (i > 0) { i--; if (exponent - (1 << i) >= MIN_EXP - 1) { exponent -= (1 << i); x *= pow2[i]; if (x >= L_(1.0)) break; } } /* Here either x < 1.0 and exponent = MIN_EXP - 1, or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ } /* Invariants: x * 2^exponent = argument, and either x < 1.0 and exponent = MIN_EXP - 1, or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ while (i > 0) { i--; if (x >= pow2[i]) { exponent += (1 << i); x *= powh[i]; } } /* Here either x < 1.0 and exponent = MIN_EXP - 1, or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1. */ } #endif END_ROUNDING (); *expptr = exponent; return x; }