105436638acc7c010349a69c3395f1a57c642dc62Ying Wang/* Split a double into fraction and mantissa, for hexadecimal printf. 205436638acc7c010349a69c3395f1a57c642dc62Ying Wang Copyright (C) 2007, 2009-2012 Free Software Foundation, Inc. 305436638acc7c010349a69c3395f1a57c642dc62Ying Wang 405436638acc7c010349a69c3395f1a57c642dc62Ying Wang This program is free software: you can redistribute it and/or modify 505436638acc7c010349a69c3395f1a57c642dc62Ying Wang it under the terms of the GNU General Public License as published by 605436638acc7c010349a69c3395f1a57c642dc62Ying Wang the Free Software Foundation; either version 3 of the License, or 705436638acc7c010349a69c3395f1a57c642dc62Ying Wang (at your option) any later version. 805436638acc7c010349a69c3395f1a57c642dc62Ying Wang 905436638acc7c010349a69c3395f1a57c642dc62Ying Wang This program is distributed in the hope that it will be useful, 1005436638acc7c010349a69c3395f1a57c642dc62Ying Wang but WITHOUT ANY WARRANTY; without even the implied warranty of 1105436638acc7c010349a69c3395f1a57c642dc62Ying Wang MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 1205436638acc7c010349a69c3395f1a57c642dc62Ying Wang GNU General Public License for more details. 1305436638acc7c010349a69c3395f1a57c642dc62Ying Wang 1405436638acc7c010349a69c3395f1a57c642dc62Ying Wang You should have received a copy of the GNU General Public License 1505436638acc7c010349a69c3395f1a57c642dc62Ying Wang along with this program. If not, see <http://www.gnu.org/licenses/>. */ 1605436638acc7c010349a69c3395f1a57c642dc62Ying Wang 1705436638acc7c010349a69c3395f1a57c642dc62Ying Wang#if ! defined USE_LONG_DOUBLE 1805436638acc7c010349a69c3395f1a57c642dc62Ying Wang# include <config.h> 1905436638acc7c010349a69c3395f1a57c642dc62Ying Wang#endif 2005436638acc7c010349a69c3395f1a57c642dc62Ying Wang 2105436638acc7c010349a69c3395f1a57c642dc62Ying Wang/* Specification. */ 2205436638acc7c010349a69c3395f1a57c642dc62Ying Wang#ifdef USE_LONG_DOUBLE 2305436638acc7c010349a69c3395f1a57c642dc62Ying Wang# include "printf-frexpl.h" 2405436638acc7c010349a69c3395f1a57c642dc62Ying Wang#else 2505436638acc7c010349a69c3395f1a57c642dc62Ying Wang# include "printf-frexp.h" 2605436638acc7c010349a69c3395f1a57c642dc62Ying Wang#endif 2705436638acc7c010349a69c3395f1a57c642dc62Ying Wang 2805436638acc7c010349a69c3395f1a57c642dc62Ying Wang#include <float.h> 2905436638acc7c010349a69c3395f1a57c642dc62Ying Wang#include <math.h> 3005436638acc7c010349a69c3395f1a57c642dc62Ying Wang#ifdef USE_LONG_DOUBLE 3105436638acc7c010349a69c3395f1a57c642dc62Ying Wang# include "fpucw.h" 3205436638acc7c010349a69c3395f1a57c642dc62Ying Wang#endif 3305436638acc7c010349a69c3395f1a57c642dc62Ying Wang 3405436638acc7c010349a69c3395f1a57c642dc62Ying Wang/* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater 3505436638acc7c010349a69c3395f1a57c642dc62Ying Wang than 2, or not even a power of 2, some rounding errors can occur, so that 3605436638acc7c010349a69c3395f1a57c642dc62Ying Wang then the returned mantissa is only guaranteed to be <= 2.0, not < 2.0. */ 3705436638acc7c010349a69c3395f1a57c642dc62Ying Wang 3805436638acc7c010349a69c3395f1a57c642dc62Ying Wang#ifdef USE_LONG_DOUBLE 3905436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define FUNC printf_frexpl 4005436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define DOUBLE long double 4105436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define MIN_EXP LDBL_MIN_EXP 4205436638acc7c010349a69c3395f1a57c642dc62Ying Wang# if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC 4305436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define USE_FREXP_LDEXP 4405436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define FREXP frexpl 4505436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define LDEXP ldexpl 4605436638acc7c010349a69c3395f1a57c642dc62Ying Wang# endif 4705436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING 4805436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING () 4905436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define END_ROUNDING() END_LONG_DOUBLE_ROUNDING () 5005436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define L_(literal) literal##L 5105436638acc7c010349a69c3395f1a57c642dc62Ying Wang#else 5205436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define FUNC printf_frexp 5305436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define DOUBLE double 5405436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define MIN_EXP DBL_MIN_EXP 5505436638acc7c010349a69c3395f1a57c642dc62Ying Wang# if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC 5605436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define USE_FREXP_LDEXP 5705436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define FREXP frexp 5805436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define LDEXP ldexp 5905436638acc7c010349a69c3395f1a57c642dc62Ying Wang# endif 6005436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define DECL_ROUNDING 6105436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define BEGIN_ROUNDING() 6205436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define END_ROUNDING() 6305436638acc7c010349a69c3395f1a57c642dc62Ying Wang# define L_(literal) literal 6405436638acc7c010349a69c3395f1a57c642dc62Ying Wang#endif 6505436638acc7c010349a69c3395f1a57c642dc62Ying Wang 6605436638acc7c010349a69c3395f1a57c642dc62Ying WangDOUBLE 6705436638acc7c010349a69c3395f1a57c642dc62Ying WangFUNC (DOUBLE x, int *expptr) 6805436638acc7c010349a69c3395f1a57c642dc62Ying Wang{ 6905436638acc7c010349a69c3395f1a57c642dc62Ying Wang int exponent; 7005436638acc7c010349a69c3395f1a57c642dc62Ying Wang DECL_ROUNDING 7105436638acc7c010349a69c3395f1a57c642dc62Ying Wang 7205436638acc7c010349a69c3395f1a57c642dc62Ying Wang BEGIN_ROUNDING (); 7305436638acc7c010349a69c3395f1a57c642dc62Ying Wang 7405436638acc7c010349a69c3395f1a57c642dc62Ying Wang#ifdef USE_FREXP_LDEXP 7505436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* frexp and ldexp are usually faster than the loop below. */ 7605436638acc7c010349a69c3395f1a57c642dc62Ying Wang x = FREXP (x, &exponent); 7705436638acc7c010349a69c3395f1a57c642dc62Ying Wang 7805436638acc7c010349a69c3395f1a57c642dc62Ying Wang x = x + x; 7905436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent -= 1; 8005436638acc7c010349a69c3395f1a57c642dc62Ying Wang 8105436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (exponent < MIN_EXP - 1) 8205436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 8305436638acc7c010349a69c3395f1a57c642dc62Ying Wang x = LDEXP (x, exponent - (MIN_EXP - 1)); 8405436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent = MIN_EXP - 1; 8505436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 8605436638acc7c010349a69c3395f1a57c642dc62Ying Wang#else 8705436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 8805436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Since the exponent is an 'int', it fits in 64 bits. Therefore the 8905436638acc7c010349a69c3395f1a57c642dc62Ying Wang loops are executed no more than 64 times. */ 9005436638acc7c010349a69c3395f1a57c642dc62Ying Wang DOUBLE pow2[64]; /* pow2[i] = 2^2^i */ 9105436638acc7c010349a69c3395f1a57c642dc62Ying Wang DOUBLE powh[64]; /* powh[i] = 2^-2^i */ 9205436638acc7c010349a69c3395f1a57c642dc62Ying Wang int i; 9305436638acc7c010349a69c3395f1a57c642dc62Ying Wang 9405436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent = 0; 9505436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (x >= L_(1.0)) 9605436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 9705436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* A nonnegative exponent. */ 9805436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 9905436638acc7c010349a69c3395f1a57c642dc62Ying Wang DOUBLE pow2_i; /* = pow2[i] */ 10005436638acc7c010349a69c3395f1a57c642dc62Ying Wang DOUBLE powh_i; /* = powh[i] */ 10105436638acc7c010349a69c3395f1a57c642dc62Ying Wang 10205436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 10305436638acc7c010349a69c3395f1a57c642dc62Ying Wang x * 2^exponent = argument, x >= 1.0. */ 10405436638acc7c010349a69c3395f1a57c642dc62Ying Wang for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 10505436638acc7c010349a69c3395f1a57c642dc62Ying Wang ; 10605436638acc7c010349a69c3395f1a57c642dc62Ying Wang i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 10705436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 10805436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (x >= pow2_i) 10905436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 11005436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent += (1 << i); 11105436638acc7c010349a69c3395f1a57c642dc62Ying Wang x *= powh_i; 11205436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 11305436638acc7c010349a69c3395f1a57c642dc62Ying Wang else 11405436638acc7c010349a69c3395f1a57c642dc62Ying Wang break; 11505436638acc7c010349a69c3395f1a57c642dc62Ying Wang 11605436638acc7c010349a69c3395f1a57c642dc62Ying Wang pow2[i] = pow2_i; 11705436638acc7c010349a69c3395f1a57c642dc62Ying Wang powh[i] = powh_i; 11805436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 11905436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 12005436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Here 1.0 <= x < 2^2^i. */ 12105436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 12205436638acc7c010349a69c3395f1a57c642dc62Ying Wang else 12305436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 12405436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* A negative exponent. */ 12505436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 12605436638acc7c010349a69c3395f1a57c642dc62Ying Wang DOUBLE pow2_i; /* = pow2[i] */ 12705436638acc7c010349a69c3395f1a57c642dc62Ying Wang DOUBLE powh_i; /* = powh[i] */ 12805436638acc7c010349a69c3395f1a57c642dc62Ying Wang 12905436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 13005436638acc7c010349a69c3395f1a57c642dc62Ying Wang x * 2^exponent = argument, x < 1.0, exponent >= MIN_EXP - 1. */ 13105436638acc7c010349a69c3395f1a57c642dc62Ying Wang for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 13205436638acc7c010349a69c3395f1a57c642dc62Ying Wang ; 13305436638acc7c010349a69c3395f1a57c642dc62Ying Wang i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 13405436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 13505436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (exponent - (1 << i) < MIN_EXP - 1) 13605436638acc7c010349a69c3395f1a57c642dc62Ying Wang break; 13705436638acc7c010349a69c3395f1a57c642dc62Ying Wang 13805436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent -= (1 << i); 13905436638acc7c010349a69c3395f1a57c642dc62Ying Wang x *= pow2_i; 14005436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (x >= L_(1.0)) 14105436638acc7c010349a69c3395f1a57c642dc62Ying Wang break; 14205436638acc7c010349a69c3395f1a57c642dc62Ying Wang 14305436638acc7c010349a69c3395f1a57c642dc62Ying Wang pow2[i] = pow2_i; 14405436638acc7c010349a69c3395f1a57c642dc62Ying Wang powh[i] = powh_i; 14505436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 14605436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 14705436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent, 14805436638acc7c010349a69c3395f1a57c642dc62Ying Wang or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 14905436638acc7c010349a69c3395f1a57c642dc62Ying Wang 15005436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (x < L_(1.0)) 15105436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Invariants: x * 2^exponent = argument, x < 1.0 and 15205436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent - 2^i < MIN_EXP - 1 <= exponent. */ 15305436638acc7c010349a69c3395f1a57c642dc62Ying Wang while (i > 0) 15405436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 15505436638acc7c010349a69c3395f1a57c642dc62Ying Wang i--; 15605436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (exponent - (1 << i) >= MIN_EXP - 1) 15705436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 15805436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent -= (1 << i); 15905436638acc7c010349a69c3395f1a57c642dc62Ying Wang x *= pow2[i]; 16005436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (x >= L_(1.0)) 16105436638acc7c010349a69c3395f1a57c642dc62Ying Wang break; 16205436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 16305436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 16405436638acc7c010349a69c3395f1a57c642dc62Ying Wang 16505436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Here either x < 1.0 and exponent = MIN_EXP - 1, 16605436638acc7c010349a69c3395f1a57c642dc62Ying Wang or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 16705436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 16805436638acc7c010349a69c3395f1a57c642dc62Ying Wang 16905436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Invariants: x * 2^exponent = argument, and 17005436638acc7c010349a69c3395f1a57c642dc62Ying Wang either x < 1.0 and exponent = MIN_EXP - 1, 17105436638acc7c010349a69c3395f1a57c642dc62Ying Wang or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 17205436638acc7c010349a69c3395f1a57c642dc62Ying Wang while (i > 0) 17305436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 17405436638acc7c010349a69c3395f1a57c642dc62Ying Wang i--; 17505436638acc7c010349a69c3395f1a57c642dc62Ying Wang if (x >= pow2[i]) 17605436638acc7c010349a69c3395f1a57c642dc62Ying Wang { 17705436638acc7c010349a69c3395f1a57c642dc62Ying Wang exponent += (1 << i); 17805436638acc7c010349a69c3395f1a57c642dc62Ying Wang x *= powh[i]; 17905436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 18005436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 18105436638acc7c010349a69c3395f1a57c642dc62Ying Wang /* Here either x < 1.0 and exponent = MIN_EXP - 1, 18205436638acc7c010349a69c3395f1a57c642dc62Ying Wang or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1. */ 18305436638acc7c010349a69c3395f1a57c642dc62Ying Wang } 18405436638acc7c010349a69c3395f1a57c642dc62Ying Wang#endif 18505436638acc7c010349a69c3395f1a57c642dc62Ying Wang 18605436638acc7c010349a69c3395f1a57c642dc62Ying Wang END_ROUNDING (); 18705436638acc7c010349a69c3395f1a57c642dc62Ying Wang 18805436638acc7c010349a69c3395f1a57c642dc62Ying Wang *expptr = exponent; 18905436638acc7c010349a69c3395f1a57c642dc62Ying Wang return x; 19005436638acc7c010349a69c3395f1a57c642dc62Ying Wang} 191