summaryrefslogtreecommitdiff
path: root/mpfr/exp3.c
blob: 175ef143d92a70b49d3ddd9dca26866900d07a1f (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
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
/* mpfr_exp -- exponential of a floating-point number

Copyright (C) 1999 Free Software Foundation.

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 <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"

/* #define DEBUG */

int mpfr_exp_rational _PROTO ((mpfr_ptr, mpz_srcptr, int, int));
int mpfr_exp3 _PROTO ((mpfr_ptr, mpfr_srcptr, mp_rnd_t));

int
#if __STDC__
mpfr_exp_rational (mpfr_ptr y, mpz_srcptr p, int r, int m)
#else
mpfr_exp_rational (y, p, r, m)
     mpfr_ptr y;
     mpz_srcptr p;
     int r;
     int m;
#endif
{
  int n,i,k,j,l;
  mpz_t* P,*S;
  mpz_t* ptoj;
  int diff,expo;
  int precy = MPFR_PREC(y);
  int * mult;
  int prec_i_have;
  int *nb_terms;
  int accu;
  TMP_DECL (marker);

  TMP_MARK (marker);
  n = 1 << m;
  P = (mpz_t*) TMP_ALLOC((m+1) * sizeof(mpz_t));
  S = (mpz_t*) TMP_ALLOC((m+1) * sizeof(mpz_t));
  ptoj = (mpz_t*) TMP_ALLOC((m+1) * sizeof(mpz_t)); /* ptoj[i] = mantissa^(2^i) */
  mult = (int*) TMP_ALLOC((m+1) * sizeof(int)); 
  nb_terms = (int*) TMP_ALLOC((m+1) * sizeof(int)); 
  mult[0] = 0;
  for (i=0;i<=m;i++) { mpz_init(P[i]); mpz_init(S[i]); mpz_init(ptoj[i]); }
  mpz_set(ptoj[0], p);
  for (i=1;i<m;i++) mpz_mul(ptoj[i], ptoj[i-1], ptoj[i-1]);
  mpz_set_ui(P[0], 1);
  mpz_set_ui(S[0], 1);
  k = 0;
  nb_terms[0] = 1;
   prec_i_have = 0; 
   for (i=1;(prec_i_have < precy) && (i < n) ;i++) {
    k++;
    nb_terms[k] = 1;
    mpz_set_ui(P[k], i+1);
    mpz_set(S[k], P[k]);;
    j=i+1; l=0; while ((j & 1) == 0) {      
      mpz_mul(S[k], S[k], ptoj[l]);
      mpz_mul(S[k-1], S[k-1], P[k]);
      mpz_mul_2exp(S[k-1], S[k-1], r*(1<<l));
      mpz_add(S[k-1], S[k-1], S[k]);
      mpz_mul(P[k-1], P[k-1], P[k]);
      nb_terms[k-1] = nb_terms[k-1]+ nb_terms[k];
      mult[k] = mult[k-1] + (1 << l)*(r >> 2) + mpz_sizeinbase(P[k],2) - 1;
      prec_i_have = mult[k];
      l++; j>>=1; k--;
    }
  }
   l = 0;
   accu = 0;
   while (k > 0){
     mpz_mul(S[k], S[k], ptoj[_mpfr_ceil_log2((double) nb_terms[k])]);
     mpz_mul(S[k-1], S[k-1], P[k]);
     accu += nb_terms[k];
     mpz_mul_2exp(S[k-1], S[k-1], r* accu);
     mpz_add(S[k-1], S[k-1], S[k]);
     mpz_mul(P[k-1], P[k-1], P[k]);     
     l++; k--;
   }
   
  diff = mpz_sizeinbase(S[0],2) - 2*precy;
  expo = diff;
  if (diff >=0)
    {
      mpz_div_2exp(S[0],S[0],diff);
    } else 
      {
	mpz_mul_2exp(S[0],S[0],-diff);
      }
  diff = mpz_sizeinbase(P[0],2) - precy;
  expo -= diff;
  if (diff >=0)
    {
      mpz_div_2exp(P[0],P[0],diff);
    } else
      {
	mpz_mul_2exp(P[0],P[0],-diff);
	}

  mpz_tdiv_q(S[0], S[0], P[0]);
  mpfr_set_z(y,S[0], GMP_RNDD);
  MPFR_EXP(y) += expo;

  mpfr_div_2exp(y, y, r*(i-1),GMP_RNDN); 
  for (i=0;i<=m;i++) { mpz_clear(P[i]); mpz_clear(S[i]); mpz_clear(ptoj[i]); }
  TMP_FREE (marker);
  return 0;
}

#define shift (BITS_PER_MP_LIMB/2)

int
#if __STDC__
mpfr_exp3 (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
#else
mpfr_exp3 (y, x, rnd_mode)
     mpfr_ptr y;
     mpfr_srcptr x; 
     mp_rnd_t rnd_mode;
#endif
{
  mpfr_t t;
  mpfr_t x_copy;
  int i,k;
  mpz_t uk;
  mpfr_t tmp;
  int ttt;
  int twopoweri;
  int Prec;
  int loop;
  int prec_x;
  int shift_x = 0;
  int good = 0;
  int realprec = 0;
  int iter;
  int logn;

  /* commencons par 0 */
  if (MPFR_IS_NAN(x)) { MPFR_SET_NAN(y); return 1; }

  if (MPFR_IS_INF(x)) 
    { 
      if (MPFR_SIGN(x) > 0) 
	{ MPFR_SET_INF(y); if (MPFR_SIGN(y) == -1) { MPFR_CHANGE_SIGN(y); } }
      else 
	{ MPFR_SET_ZERO(y);  if (MPFR_SIGN(y) == -1) { MPFR_CHANGE_SIGN(y); } }
      /* TODO: conflits entre infinis et zeros ? */
    }

  if (!MPFR_NOTZERO(x)) {
    mpfr_set_ui(y, 1, GMP_RNDN); 
    return 0;
  }

  /* Decomposer x */
  /* on commence par ecrire x = 1.xxxxxxxxxxxxx
     ----- k bits -- */
  prec_x = _mpfr_ceil_log2 ((double) (MPFR_PREC(x)) / BITS_PER_MP_LIMB);
  if (prec_x < 0) prec_x = 0;
  logn =  _mpfr_ceil_log2 ((double) prec_x + MPFR_PREC(y));
  if (logn < 2) logn = 2;
  ttt = MPFR_EXP(x);
  mpfr_init2(x_copy,MPFR_PREC(x));
  mpfr_set(x_copy,x,GMP_RNDD);
  /* on fait le shift pour que le nombre soit inferieur a 1 */
  if (ttt > 0) 
    {
      shift_x = ttt;
      mpfr_mul_2exp(x_copy,x,-ttt, GMP_RNDN); 
      ttt = MPFR_EXP(x_copy);
    }
  realprec = MPFR_PREC(y)+logn;
  mpz_init (uk);
  while (!good){      
    Prec = realprec+shift+2+shift_x;
    k = _mpfr_ceil_log2 ((double) Prec / BITS_PER_MP_LIMB);

    /* now we have to extract */
    mpfr_init2(t, Prec);
    mpfr_init2(tmp, Prec);
    mpfr_set_ui(tmp,1,GMP_RNDN);
    twopoweri = BITS_PER_MP_LIMB;
    if (k <= prec_x) iter = k; else iter= prec_x;
    for(i = 0; i <= iter; i++){
      mpfr_extract (uk, x_copy, i);
#ifdef DEBUG
	mpz_out_str(stderr,2, uk);  
	fprintf(stderr, "---\n");
	fprintf(stderr, "---%d\n", twopoweri - ttt);
#endif 
	if (i)
	    mpfr_exp_rational (t, uk, twopoweri - ttt, k  - i + 1);
	else
	  {
	    /* cas particulier : on est oblige de faire les calculs avec x/2^. 
	       puis elever au carre (plus rapide) */    
	      mpfr_exp_rational (t, uk, shift + twopoweri - ttt, k+1);
	    for (loop= 0 ; loop < shift; loop++)
	      mpfr_mul(t,t,t,GMP_RNDD);

	  }
	mpfr_mul(tmp,tmp,t,GMP_RNDD); 
#ifdef DEBUG
	fprintf(stderr, "fin\n");
	mpfr_out_str(stderr, 2, MPFR_PREC(y), t, GMP_RNDD);
	fprintf(stderr, "\n ii --- ii \n");
#endif
	twopoweri <<= 1;
    }
      for (loop= 0 ; loop < shift_x; loop++)
	mpfr_mul(tmp,tmp,tmp,GMP_RNDD);
      mpfr_clear(t);      	    
      if (mpfr_can_round(tmp, realprec, GMP_RNDD, rnd_mode, MPFR_PREC(y))){
	    mpfr_set(y,tmp,rnd_mode);
	    mpfr_clear(tmp);
	    good = 1;
      } else {
	mpfr_clear(tmp);
	realprec += 3*logn;
      }
  }
  mpz_clear (uk);
  mpfr_clear(x_copy);
  return 0;
}