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/* mpfr_get_str -- output a floating-point number to a string
Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.
The MPFR Library 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 Library General Public
License for more details.
You should have received a copy of the GNU Library General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
/*
Convert op to a string in base 'base' with 'n' digits and writes the
mantissa in 'str', the exponent in 'expptr'.
The result is rounded wrt 'rnd_mode'.
For op = 3.1416 we get str = "31416" and expptr=1.
*/
#if __STDC__
char *mpfr_get_str(char *str, mp_exp_t *expptr, int base, size_t n,
mpfr_srcptr op, unsigned char rnd_mode)
#else
char *mpfr_get_str(str, expptr, base, n, op, rnd_mode)
char *str;
mp_exp_t *expptr;
int base;
size_t n;
mpfr_srcptr op;
unsigned char rnd_mode;
#endif
{
double d; long e, q, div, p, err, prec, sh; mpfr_t a, b; mpz_t bz;
char *str0; unsigned char rnd1; int f, pow2, ok=0, neg;
if (base<2 || 36<base) {
fprintf(stderr, "Error: too small or too large base in mpfr_get_str: %d\n",
base);
exit(1);
}
neg = (SIGN(op)<0) ? 1 : 0;
if (!NOTZERO(op)) {
if (str==NULL) str0=str=(*_mp_allocate_func)(neg + n + 2);
if (SIGN(op)<0) *str++ = '-';
for (f=0;f<n;f++) *str++ = '0';
*expptr = 1;
return str0;
}
count_leading_zeros(pow2, (mp_limb_t)base);
pow2 = BITS_PER_MP_LIMB - pow2 - 1;
if (base != (1<<pow2)) pow2=0;
/* if pow2 <> 0, then base = 2^pow2 */
/* first determines the exponent */
e = EXP(op);
d = fabs(mpfr_get_d2(op, 0));
/* the absolute value of op is between 1/2*2^e and 2^e */
/* the output exponent f is such that base^(f-1) <= |op| < base^f
i.e. f = 1 + floor(log(|op|)/log(base))
= 1 + floor((log(|m|)+e*log(2))/log(base)) */
f = 1 + (int) floor((log(d)+(double)e*log(2.0))/log((double)base));
if (n==0) {
/* performs exact rounding, i.e. returns y such that for rnd_mode=RNDN
for example, we have:
y*base^(f-n) <= x*2^(e-p) < (x+1)*2^(e-p) <= (y+1)*base^(f-n)
which implies 2^(EXP(op)-PREC(op)) <= base^(f-n)
*/
n = f + (int) ceil(((double)PREC(op)-e)*log(2.0)/log((double)base));
}
/* now the first n digits of the mantissa are obtained from
rnd(op*base^(n-f)) */
prec = (long) ceil((double)n*log((double)base)/log(2.0));
err = 5;
q = prec+err;
/* one has to use at least q bits */
q = (((q-1)/BITS_PER_MP_LIMB)+1)*BITS_PER_MP_LIMB;
mpfr_init2(a,q); mpfr_init2(b,q);
do {
p = n-f; if ((div=(p<0))) p=-p;
rnd1 = rnd_mode;
if (div) {
/* if div we divide by base^p so we have to invert the rounding mode */
switch (rnd1) {
case GMP_RNDN: rnd1=GMP_RNDN; break;
case GMP_RNDZ: rnd1=GMP_RNDU; break;
case GMP_RNDU: rnd1=GMP_RNDZ; break;
case GMP_RNDD: rnd1=GMP_RNDZ; break;
}
}
if (pow2) {
if (div) mpfr_div_2exp(b, op, pow2*p, rnd_mode);
else mpfr_mul_2exp(b, op, pow2*p, rnd_mode);
}
else {
/* compute base^p with q bits and rounding towards zero */
mpfr_set_prec(b, q);
if (p==0) { mpfr_set(b, op, rnd_mode); mpfr_set_ui(a, 1, rnd_mode); }
else {
mpfr_set_prec(a, q);
mpfr_ui_pow_ui(a, base, p, rnd1);
if (div) {
mpfr_set_ui(b, 1, rnd_mode);
mpfr_div(a, b, a, rnd_mode);
}
/* now a is an approximation by default of 1/base^(f-n) */
mpfr_mul(b, op, a, rnd_mode);
}
}
if (neg) CHANGE_SIGN(b); /* put b positive */
if (q>2*prec+BITS_PER_MP_LIMB) {
/* happens when just in the middle between two digits */
n--; q-=BITS_PER_MP_LIMB;
if (n==0) {
fprintf(stderr, "cannot determine leading digit\n"); exit(1);
}
}
ok = pow2 || mpfr_can_round(b, q-err, rnd_mode, rnd_mode, prec);
if (ok) {
if (pow2) {
sh = e-PREC(op) + pow2*(n-f); /* error at most 2^e */
ok = mpfr_can_round(b, EXP(b)-sh-1, rnd_mode, rnd_mode, n*pow2);
}
else {
/* check that value is the same at distance 2^(e-PREC(op))/base^(f-n)
in opposite from rounding direction */
if (e>=PREC(op)) mpfr_mul_2exp(a, a, e-PREC(op), rnd_mode);
else mpfr_div_2exp(a, a, PREC(op)-e, rnd_mode);
if (rnd_mode==GMP_RNDN) {
mpfr_div_2exp(a, a, 2, rnd_mode);
mpfr_sub(b, b, a, rnd_mode); /* b - a/2 */
mpfr_mul_2exp(a, a, 2, rnd_mode);
mpfr_add(a, b, a, rnd_mode); /* b + a/2 */
}
else if ((rnd_mode==GMP_RNDU && neg==0) || (rnd_mode==GMP_RNDD && neg))
mpfr_sub(a, b, a, rnd_mode);
else mpfr_add(a, b, a, rnd_mode);
/* check that a and b are rounded similarly */
prec=EXP(b);
if (EXP(a) != prec) ok=0;
else {
mpfr_round(b, rnd_mode, prec);
mpfr_round(a, rnd_mode, prec);
if (mpfr_cmp(a, b)) ok=0;
}
}
if (ok==0) { /* n is too large */
n--;
if (n==0) {
fprintf(stderr, "cannot determine leading digit\n"); exit(1);
}
q -= BITS_PER_MP_LIMB;
}
}
} while (ok==0 && (q+=BITS_PER_MP_LIMB) );
if (neg)
switch (rnd_mode) {
case GMP_RNDU: rnd_mode=GMP_RNDZ; break;
case GMP_RNDD: rnd_mode=GMP_RNDU; break;
}
prec=EXP(b); /* may have changed due to rounding */
/* now the mantissa is the integer part of b */
mpz_init(bz); q=1+(prec-1)/BITS_PER_MP_LIMB;
_mpz_realloc(bz, q);
sh = prec%BITS_PER_MP_LIMB;
e = 1 + (PREC(b)-1)/BITS_PER_MP_LIMB-q;
if (sh) mpn_rshift(PTR(bz), MANT(b)+e, q, BITS_PER_MP_LIMB-sh);
else MPN_COPY(PTR(bz), MANT(b)+e, q);
bz->_mp_size=q;
/* computes the number of characters needed */
q = neg + n + 2; /* n+1 may not be enough for 100000... */
if (str==NULL) str0=str=(*_mp_allocate_func)(q);
if (neg) *str++='-';
mpz_get_str(str, base, bz); /* n digits of mantissa */
if (strlen(str)==n+1) f++; /* possible due to rounding */
*expptr = f;
mpfr_clear(a); mpfr_clear(b); mpz_clear(bz);
return str0;
}
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