Annotation of OpenXM_contrib/gmp/mpfr/log.c, Revision 1.1.1.1
1.1 maekawa 1: /* mpfr_log -- natural logarithm of a floating-point number
2:
3: Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
4:
5: This file is part of the MPFR Library.
6:
7: The MPFR Library is free software; you can redistribute it and/or modify
8: it under the terms of the GNU Library General Public License as published by
9: the Free Software Foundation; either version 2 of the License, or (at your
10: option) any later version.
11:
12: The MPFR Library is distributed in the hope that it will be useful, but
13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
15: License for more details.
16:
17: You should have received a copy of the GNU Library General Public License
18: along with the MPFR Library; see the file COPYING.LIB. If not, write to
19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
20: MA 02111-1307, USA. */
21:
22: #include <stdio.h>
23: #include <math.h>
24: #include "gmp.h"
25: #include "gmp-impl.h"
26: #include "mpfr.h"
27:
28:
29: /* The computation of log(a) is done using the formula :
30: if we want p bits of the result,
31: pi
32: log(a) ~ ------------ - m log 2
33: 2 AG(1,4/s)
34:
35: where s = x 2^m > 2^(p/2)
36:
37: More precisely, if F(x) = int(1/sqrt(1-(1-x^2)*sin(t)^2), t=0..PI/2),
38: then for s>=1.26 we have log(s) < F(4/s) < log(s)*(1+4/s^2)
39: from which we deduce pi/2/AG(1,4/s)*(1-4/s^2) < log(s) < pi/2/AG(1,4/s)
40: so the relative error 4/s^2 is < 4/2^p i.e. 4 ulps.
41: */
42:
43:
44: #define MON_INIT(xp, x, p, s) xp = (mp_ptr) TMP_ALLOC(s*BYTES_PER_MP_LIMB); x -> _mp_prec = p; x -> _mp_d = xp; x -> _mp_size = s; x -> _mp_exp = 0;
45:
46: /* #define DEBUG */
47:
48: int
49: #if __STDC__
50: mpfr_log(mpfr_ptr r, mpfr_srcptr a, unsigned char rnd_mode)
51: #else
52: mpfr_log(r, a, rnd_mode)
53: mpfr_ptr r;
54: mpfr_srcptr a;
55: unsigned char rnd_mode;
56: #endif
57: {
58: int p, m, q, bool, size, cancel;
59: mpfr_t cst, rapport, agm, tmp1, tmp2, s, mm;
60: mp_limb_t *cstp, *rapportp, *agmp, *tmp1p, *tmp2p, *sp, *mmp;
61: double ref;
62: TMP_DECL(marker);
63:
64: /* If a is NaN or a is negative or null, the result is NaN */
65: if (FLAG_NAN(a) || (SIGN(a)<=0))
66: { SET_NAN(r); return 1; }
67:
68: /* If a is 1, the result is 0 */
69: if (mpfr_cmp_ui_2exp(a,1,0)==0){
70: SET_ZERO(r);
71: return 0; /* only case where the result is exact */
72: }
73:
74: q=PREC(r);
75:
76: ref=mpfr_get_d(a)-1.0;
77: if (ref<0)
78: ref=-ref;
79:
80: p=q+4;
81: /* adjust to entire limb */
82: if (p%BITS_PER_MP_LIMB) p += BITS_PER_MP_LIMB - (p%BITS_PER_MP_LIMB);
83:
84: bool=1;
85:
86: while (bool==1) {
87: #ifdef DEBUG
88: printf("a="); mpfr_print_raw(a); putchar('\n');
89: printf("p=%d\n", p);
90: #endif
91: /* Calculus of m (depends on p) */
92: m=(int) ceil(((double) p)/2.0) -EXP(a)+1;
93:
94: /* All the mpfr_t needed have a precision of p */
95: TMP_MARK(marker);
96: size=(p-1)/BITS_PER_MP_LIMB+1;
97: MON_INIT(cstp, cst, p, size);
98: MON_INIT(rapportp, rapport, p, size);
99: MON_INIT(agmp, agm, p, size);
100: MON_INIT(tmp1p, tmp1, p, size);
101: MON_INIT(tmp2p, tmp2, p, size);
102: MON_INIT(sp, s, p, size);
103: MON_INIT(mmp, mm, p, size);
104:
105: mpfr_set_si(mm,m,GMP_RNDN); /* I have m, supposed exact */
106: mpfr_set_si(tmp1,1,GMP_RNDN); /* I have 1, exact */
107: mpfr_set_si(tmp2,4,GMP_RNDN); /* I have 4, exact */
108: mpfr_mul_2exp(s,a,m,GMP_RNDN); /* I compute s=a*2^m, err <= 1 ulp */
109: mpfr_div(rapport,tmp2,s,GMP_RNDN); /* I compute 4/s, err <= 2 ulps */
110: mpfr_agm(agm,tmp1,rapport,GMP_RNDN); /* AG(1,4/s), err<=3 ulps */
111: mpfr_mul_2exp(tmp1,agm,1,GMP_RNDN); /* 2*AG(1,4/s), still err<=3 ulps */
112: mpfr_pi(cst, GMP_RNDN); /* I compute pi, err<=1ulp */
113: mpfr_div(tmp2,cst,tmp1,GMP_RNDN); /* pi/2*AG(1,4/s), err<=5ulps */
114: mpfr_log2(cst,GMP_RNDN); /* I compute log(2), err<=1ulp */
115: mpfr_mul(tmp1,cst,mm,GMP_RNDN); /* I compute m*log(2), err<=2ulps */
116: cancel = EXP(tmp2);
117: mpfr_sub(cst,tmp2,tmp1,GMP_RNDN); /* log(a), err<=7ulps+cancel */
118: cancel -= EXP(cst);
119: #ifdef DEBUG
120: printf("cancelled bits=%d\n", cancel);
121: printf("approx="); mpfr_print_raw(cst); putchar('\n');
122: #endif
123: if (cancel<0) cancel=0;
124:
125: /* If we can round the result, we set it and go out of the loop */
126:
127: /* we have 7 ulps of error from the above roundings,
128: 4 ulps from the 4/s^2 second order term,
129: plus the cancelled bits */
130: if (mpfr_can_round(cst,p-cancel-4,GMP_RNDN,rnd_mode,q)==1) {
131: mpfr_set(r,cst,rnd_mode);
132: #ifdef DEBUG
133: printf("result="); mpfr_print_raw(r); putchar('\n');
134: #endif
135: bool=0;
136: }
137: /* else we increase the precision */
138: else {
139: p += BITS_PER_MP_LIMB+cancel;
140: TMP_FREE(marker);
141: }
142:
143: /* We clean */
144: TMP_FREE(marker);
145:
146: }
147: return 1; /* result is inexact */
148: }
149:
150:
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