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#include <stdio.h>
#include <math.h>
#include "gmp.h"
#include "gmp-impl.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 format is 0.xxxxxxxxEyyyy.
The result is rounded wrt 'rnd_mode'.
*/
/* #define DEBUG */
char *mpfr_get_str(char *str, char *expptr, int base, size_t n,
mpfr_srcptr op, unsigned char rnd_mode)
{
double d; long e, f, q, i, neg, p, err, prec, sh; mpfr_t a, b; mpz_t bz;
char *str0; unsigned char rnd1;
#ifdef DEBUG
printf("op="); mpfr_print_raw(op); printf(" rnd_mode=%d\n",rnd_mode);
printf(" =%1.20e\n",mpfr_get_d(op));
#endif
/* first determines the exponent */
e = EXP(op);
EXP(op)=0; d=fabs(mpfr_get_d(op)); EXP(op)=e;
/* 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));
#ifdef DEBUG
printf("exponent = %d\n",f);
#endif
/* 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)/mp_bits_per_limb)*mp_bits_per_limb;
mpfr_init(a); mpfr_init(b);
p = n-f; if ((neg=(p<0))) p=-p;
rnd1 = (neg) ? GMP_RNDU : GMP_RNDZ; /* if neg we divide by base^p */
do {
q += mp_bits_per_limb;
/* compute base^p with q bits and rounding towards zero */
mpfr_set_prec(b, q, GMP_RNDZ);
if (p==0) {
mpfr_set(b, op, GMP_RNDZ);
}
else {
mpfr_set_prec(a, q, rnd1);
mpfr_set_ui(a, base, rnd1);
for (i=0;(1<<i)<=p;i++);
/* now 2^(i-1) <= p < 2^i */
for (i-=2; i>=0; i--) {
mpfr_mul(b, a, a, rnd1);
if (p & (1<<i)) mpfr_mul_ui(a, b, base, rnd1);
else mpfr_set(a, b, rnd1);
}
/* now a is an approximation by default of base^p */
if (neg) mpfr_div(b, op, a, GMP_RNDZ);
else mpfr_mul(b, op, a, GMP_RNDZ);
}
if (SIGN(op)<0) CHANGE_SIGN(b);
} while (mpfr_can_round(b, q-err, GMP_RNDZ, rnd_mode, prec)==0);
if (SIGN(op)<0)
switch (rnd_mode) {
case GMP_RNDU: rnd_mode=GMP_RNDZ; break;
case GMP_RNDD: rnd_mode=GMP_RNDU; break;
}
#ifdef DEBUG
printf("rnd=%d\n",rnd_mode);
printf("b="); mpfr_print_raw(b); putchar('\n');
printf("=%1.20e\n",mpfr_get_d(b));
#endif
prec=EXP(b);
mpfr_round(b, rnd_mode, prec);
prec=EXP(b); /* may have chnaged due to rounding */
#ifdef DEBUG
printf("b="); mpfr_print_raw(b); putchar('\n');
printf("prec=%d q=%d b=",prec,q); mpfr_print_raw(b); putchar('\n');
printf("=%1.20e\n",mpfr_get_d(b));
#endif
/* now the mantissa is the integer part of b */
mpz_init(bz); q=1+(prec-1)/mp_bits_per_limb; _mpz_realloc(bz, q);
sh = prec%mp_bits_per_limb;
if (sh) mpn_rshift(PTR(bz), MANT(b), q, mp_bits_per_limb-sh);
else MPN_COPY(PTR(bz), MANT(b), q);
bz->_mp_size=q;
#ifdef DEBUG
printf("bz="); mpz_out_str(stdout,10,bz); putchar('\n');
printf("b="); mpfr_print_raw(b); putchar('\n');
#endif
/* computes the number of characters needed */
q = ((SIGN(op)<0) ? 1 : 0) + 2 + n + 2 +
+ (int) ceil(log((double)fabs(f))/log(10.0));
if (f<10 || f>-10) q++;
if (str==NULL) str0=str=malloc(q);
if (SIGN(op)<0) *str++='-';
if (n>1) *str++ = '.';
mpz_get_str(str, base, bz); /* n digits of mantissa */
if (strlen(str)==n+1) f++; /* possible due to rounding */
str[n++] = 'e';
f--; /* replaces 0.xxx*b^f by x.xx*b^(f-1) */
str[n++] = (f>=0) ? '+' : '-'; /* is there a rule for f=0 ? */
if (f<10 && f>-10) str[n++]='0';
sprintf(str+n, "%ld", (f<0) ? -f : f);
if (str[-1]=='.') { str[-1]=str[0]; str[0]='.'; }
mpfr_clear(a); mpfr_clear(b); mpz_clear(bz);
return str0;
}
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