1/* mpfr_log1p -- Compute log(1+x) 2 3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. 4Contributed by the AriC and Caramel projects, INRIA. 5 6This file is part of the GNU MPFR Library. 7 8The GNU MPFR Library is free software; you can redistribute it and/or modify 9it under the terms of the GNU Lesser General Public License as published by 10the Free Software Foundation; either version 3 of the License, or (at your 11option) any later version. 12 13The GNU MPFR Library is distributed in the hope that it will be useful, but 14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16License for more details. 17 18You should have received a copy of the GNU Lesser General Public License 19along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23#define MPFR_NEED_LONGLONG_H 24#include "mpfr-impl.h" 25 26 /* The computation of log1p is done by 27 log1p(x)=log(1+x) */ 28 29int 30mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) 31{ 32 int comp, inexact; 33 mpfr_exp_t ex; 34 MPFR_SAVE_EXPO_DECL (expo); 35 36 MPFR_LOG_FUNC 37 (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), 38 ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, 39 inexact)); 40 41 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 42 { 43 if (MPFR_IS_NAN (x)) 44 { 45 MPFR_SET_NAN (y); 46 MPFR_RET_NAN; 47 } 48 /* check for inf or -inf (result is not defined) */ 49 else if (MPFR_IS_INF (x)) 50 { 51 if (MPFR_IS_POS (x)) 52 { 53 MPFR_SET_INF (y); 54 MPFR_SET_POS (y); 55 MPFR_RET (0); 56 } 57 else 58 { 59 MPFR_SET_NAN (y); 60 MPFR_RET_NAN; 61 } 62 } 63 else /* x is zero */ 64 { 65 MPFR_ASSERTD (MPFR_IS_ZERO (x)); 66 MPFR_SET_ZERO (y); /* log1p(+/- 0) = +/- 0 */ 67 MPFR_SET_SAME_SIGN (y, x); 68 MPFR_RET (0); 69 } 70 } 71 72 ex = MPFR_GET_EXP (x); 73 if (ex < 0) /* -0.5 < x < 0.5 */ 74 { 75 /* For x > 0, abs(log(1+x)-x) < x^2/2. 76 For x > -0.5, abs(log(1+x)-x) < x^2. */ 77 if (MPFR_IS_POS (x)) 78 MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex - 1, 0, 0, rnd_mode, {}); 79 else 80 MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {}); 81 } 82 83 comp = mpfr_cmp_si (x, -1); 84 /* log1p(x) is undefined for x < -1 */ 85 if (MPFR_UNLIKELY(comp <= 0)) 86 { 87 if (comp == 0) 88 /* x=0: log1p(-1)=-inf (divide-by-zero exception) */ 89 { 90 MPFR_SET_INF (y); 91 MPFR_SET_NEG (y); 92 mpfr_set_divby0 (); 93 MPFR_RET (0); 94 } 95 MPFR_SET_NAN (y); 96 MPFR_RET_NAN; 97 } 98 99 MPFR_SAVE_EXPO_MARK (expo); 100 101 /* General case */ 102 { 103 /* Declaration of the intermediary variable */ 104 mpfr_t t; 105 /* Declaration of the size variable */ 106 mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */ 107 mpfr_prec_t Nt; /* working precision */ 108 mpfr_exp_t err; /* error */ 109 MPFR_ZIV_DECL (loop); 110 111 /* compute the precision of intermediary variable */ 112 /* the optimal number of bits : see algorithms.tex */ 113 Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6; 114 115 /* if |x| is smaller than 2^(-e), we will loose about e bits 116 in log(1+x) */ 117 if (MPFR_EXP(x) < 0) 118 Nt += -MPFR_EXP(x); 119 120 /* initialise of intermediary variable */ 121 mpfr_init2 (t, Nt); 122 123 /* First computation of log1p */ 124 MPFR_ZIV_INIT (loop, Nt); 125 for (;;) 126 { 127 /* compute log1p */ 128 inexact = mpfr_add_ui (t, x, 1, MPFR_RNDN); /* 1+x */ 129 /* if inexact = 0, then t = x+1, and the result is simply log(t) */ 130 if (inexact == 0) 131 { 132 inexact = mpfr_log (y, t, rnd_mode); 133 goto end; 134 } 135 mpfr_log (t, t, MPFR_RNDN); /* log(1+x) */ 136 137 /* the error is bounded by (1/2+2^(1-EXP(t))*ulp(t) (cf algorithms.tex) 138 if EXP(t)>=2, then error <= ulp(t) 139 if EXP(t)<=1, then error <= 2^(2-EXP(t))*ulp(t) */ 140 err = Nt - MAX (0, 2 - MPFR_GET_EXP (t)); 141 142 if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) 143 break; 144 145 /* increase the precision */ 146 MPFR_ZIV_NEXT (loop, Nt); 147 mpfr_set_prec (t, Nt); 148 } 149 inexact = mpfr_set (y, t, rnd_mode); 150 151 end: 152 MPFR_ZIV_FREE (loop); 153 mpfr_clear (t); 154 } 155 156 MPFR_SAVE_EXPO_FREE (expo); 157 return mpfr_check_range (y, inexact, rnd_mode); 158} 159