This module is also for the 'a' and 'A' conversion of printf: Splitting a
'double' into mantissa and exponent, without requiring libm.
This module assumes that the radix of floating-point numbers is 2. A safe
assumption, I hope, 18 years after IEEE 754.
2007-02-25 Bruno Haible <[EMAIL PROTECTED]>
* modules/printf-frexp: New file.
* lib/printf-frexp.h: New file.
* lib/printf-frexp.c: New file.
* m4/printf-frexp.m4: New file.
============================== modules/printf-frexp ==========================
Description:
printf_frexp() function: split a double into fraction and mantissa, for
hexadecimal printf, without requiring libm.
Files:
lib/printf-frexp.h
lib/printf-frexp.c
m4/printf-frexp.m4
Depends-on:
verify
configure.ac:
gl_FUNC_PRINTF_FREXP
Makefile.am:
lib_SOURCES += printf-frexp.c
Include:
#include "printf-frexp.h"
License:
LGPL
Maintainer:
Bruno Haible
=============================== lib/printf-frexp.h ===========================
/* Split a double into fraction and mantissa, for hexadecimal printf.
Copyright (C) 2007 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 2, 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, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
/* Write a finite, positive number x as
x = mantissa * 2^exp
where exp >= DBL_MIN_EXP - 1,
mantissa < 2.0,
if x is not a denormalized number then mantissa >= 1.0.
Store exp and return mantissa. */
extern double printf_frexp (double x, int *exp);
=============================== lib/printf-frexp.c ===========================
/* Split a double into fraction and mantissa, for hexadecimal printf.
Copyright (C) 2007 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 2, 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, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
#include <config.h>
#if !(defined USE_LONG_DOUBLE && !HAVE_LONG_DOUBLE)
/* Specification. */
# ifdef USE_LONG_DOUBLE
# include "printf-frexpl.h"
# else
# include "printf-frexp.h"
# endif
# include <float.h>
# include <math.h>
# include "verify.h"
/* This file assumes FLT_RADIX is 2. */
verify (FLT_RADIX == 2);
# 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 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 L_(literal) literal
# endif
DOUBLE
FUNC (DOUBLE x, int *exp)
{
int exponent;
# 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
*exp = exponent;
return x;
}
#else
/* This declaration is solely to ensure that after preprocessing
this file is never empty. */
typedef int dummy;
#endif
=============================== m4/printf-frexp.m4 ===========================
# printf-frexp.m4 serial 1
dnl Copyright (C) 2007 Free Software Foundation, Inc.
dnl This file is free software; the Free Software Foundation
dnl gives unlimited permission to copy and/or distribute it,
dnl with or without modifications, as long as this notice is preserved.
dnl Check how to define printf_frexp() without linking with libm.
AC_DEFUN([gl_FUNC_PRINTF_FREXP],
[
AC_CACHE_CHECK([whether frexp can be used without linking with libm],
[gl_cv_func_frexp_no_libm],
[
AC_TRY_LINK([#include <math.h>
double x;
int y;],
[return frexp (x, &y) < 1;],
[gl_cv_func_frexp_no_libm=yes],
[gl_cv_func_frexp_no_libm=no])
])
if test $gl_cv_func_frexp_no_libm = yes; then
AC_DEFINE([HAVE_FREXP_IN_LIBC], 1,
[Define if the frexp function is available in libc.])
fi
AC_CACHE_CHECK([whether ldexp can be used without linking with libm],
[gl_cv_func_ldexp_no_libm],
[
AC_TRY_LINK([#include <math.h>
double x;
int y;],
[return ldexp (x, y) < 1;],
[gl_cv_func_ldexp_no_libm=yes],
[gl_cv_func_ldexp_no_libm=no])
])
if test $gl_cv_func_ldexp_no_libm = yes; then
AC_DEFINE([HAVE_LDEXP_IN_LIBC], 1,
[Define if the ldexp function is available in libc.])
fi
])
