summaryrefslogtreecommitdiff
path: root/get_str.c
blob: 93af194b044d6dc6701e0030dee87ba3610d69a9 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
/* mpfr_get_str -- output a floating-point number to a string

Copyright (C) 1999, 2001 Free Software Foundation, Inc.

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 Lesser General Public License as published by
the Free Software Foundation; either version 2.1 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser 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 <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.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.
 */
char*
mpfr_get_str (char *str, mp_exp_t *expptr, int base, size_t n,
		  mpfr_srcptr op, mp_rnd_t rnd_mode)
{
  double d;
  long e, q, div, p, err, prec, sh;
  mpfr_t a, b;
  mpz_t bz;
  char *str0=NULL;
  mp_rnd_t rnd1;
  int f, pow2, ok=0, neg, str_is_null=(str==NULL);

  if (base<2 || 36<base) {
    fprintf(stderr, "Error: too small or too large base in mpfr_get_str: %d\n",
	    base);
    exit(1);
  }
  
  neg = MPFR_SIGN(op) < 0;

  if (MPFR_IS_INF(op)) { 
    if (str == NULL)
      str = (*__gmp_allocate_func)(neg + 4);
    str0 = str;
    if (neg) { *str++ = '-'; }
    *str++ = 'I'; *str++ = 'n'; *str++ = 'f'; *str='\0';
    return str0; /* strlen(str0) = neg + 3 */
  }

  if (!MPFR_NOTZERO(op)) {
    if (str == NULL)
      str = (*__gmp_allocate_func)(neg + n + 1);
    str0 = str;
    if (neg) *str++ = '-';
    for (f=0;f<n;f++) *str++ = '0';
    *str++ = '\0';
    *expptr = 1;
    return str0; /* strlen(str0) = neg + n */
  }

  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 = MPFR_EXP(op); 
  d = ABS(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)/LOG2+(double)e)*LOG2/log((double)base)); */
  /* when base = 2^pow2, then |op| < 2^(pow2*f)
     i.e. e <= pow2*f and f = ceil(e/pow2) */
  if (pow2)
      f = ((e < 0) ? e : (e + pow2 - 1)) / pow2;
  else
    {
      d = ((double) e + (double) _mpfr_floor_log2(d))
                      * __mp_bases[base].chars_per_bit_exactly;
      /* warning: (int) d rounds towards 0 */
      f = (int) d; /* f equals floor(d) if d >= 0 and ceil(d) if d < 0 */
      if (f <= d) f++;
    }
  if (n==0) {
    /* performs exact rounding, i.e. returns y such that for GMP_RNDU
       for example, we have:       x*2^(e-p) <= y*base^(f-n)
     */
    n = (int) (__mp_bases[base].chars_per_bit_exactly * MPFR_PREC(op));
    if (n==0) n=1;
  }
  /* now the first n digits of the mantissa are obtained from
     rnd(op*base^(n-f)) */
  if (pow2) prec = n*pow2;
  else
    prec = 1 + (long) ((double) n / __mp_bases[base].chars_per_bit_exactly);
  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) MPFR_CHANGE_SIGN(b); /* put b positive */
    if (q>2*prec+BITS_PER_MP_LIMB) {
      /* if the intermediate precision exceeds twice that of the input,
	 a worst-case for the division cannot occur */
      ok=1;
      rnd_mode=GMP_RNDN;
    }
    else ok = pow2 || mpfr_can_round(b, q-err, rnd_mode, rnd_mode, prec);

  } 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;
  }

  if (ok)
    mpfr_round (b, rnd_mode, MPFR_EXP(b));

  prec=MPFR_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 + (MPFR_PREC(b)-1)/BITS_PER_MP_LIMB-q;
  if (sh) mpn_rshift(PTR(bz), MPFR_MANT(b)+e, q, BITS_PER_MP_LIMB-sh);
  else MPN_COPY(PTR(bz), MPFR_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 = (*__gmp_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 */
    str[n]='\0'; /* ensures we get only n digits of output */
  }
  else if (strlen(str)==n-1) {
    f--;
    str[n-1]='0';
    str[n]='\0';
  }
  *expptr = f;
  mpfr_clear(a); mpfr_clear(b); mpz_clear(bz);

  /* if the given string was null, ensure we return a block which is exactly
     strlen(str)+1 bytes long (useful for __gmp_free_func and the C++ wrapper)
  */
  if (str_is_null && ((strlen(str0) + 1) != q))
    str0 = (char*) (*__gmp_reallocate_func) (str0, q, strlen(str0) + 1);

  return str0;
}