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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/log1p.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/log1p.c | 243 |
1 files changed, 0 insertions, 243 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/log1p.c b/Build/source/libs/mpfr/mpfr-src/src/log1p.c deleted file mode 100644 index 6f5605fdb0e..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/log1p.c +++ /dev/null @@ -1,243 +0,0 @@ -/* mpfr_log1p -- Compute log(1+x) - -Copyright 2001-2020 Free Software Foundation, Inc. -Contributed by the AriC and Caramba projects, INRIA. - -This file is part of the GNU MPFR Library. - -The GNU 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 3 of the License, or (at your -option) any later version. - -The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see -https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., -51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ - -#define MPFR_NEED_LONGLONG_H -#include "mpfr-impl.h" - -/* Put in y an approximation of log(1+x) for x small. - We assume |x| < 1, in which case: - |x/2| <= |log(1+x)| = |x - x^2/2 + x^3/3 - x^4/4 + ...| <= |x|. - Return k such that the error is bounded by 2^k*ulp(y). -*/ -static int -mpfr_log1p_small (mpfr_ptr y, mpfr_srcptr x) -{ - mpfr_prec_t p = MPFR_PREC(y), err; - mpfr_t t, u; - unsigned long i; - int k; - - MPFR_ASSERTD(MPFR_GET_EXP (x) <= 0); /* ensures |x| < 1 */ - - /* in the following, theta represents a value with |theta| <= 2^(1-p) - (might be a different value each time) */ - - mpfr_init2 (t, p); - mpfr_init2 (u, p); - mpfr_set (t, x, MPFR_RNDF); /* t = x * (1 + theta) */ - mpfr_set (y, t, MPFR_RNDF); /* exact */ - for (i = 2; ; i++) - { - mpfr_mul (t, t, x, MPFR_RNDF); /* t = x^i * (1 + theta)^i */ - mpfr_div_ui (u, t, i, MPFR_RNDF); /* u = x^i/i * (1 + theta)^(i+1) */ - if (MPFR_GET_EXP (u) <= MPFR_GET_EXP (y) - p) /* |u| < ulp(y) */ - break; - if (i & 1) - mpfr_add (y, y, u, MPFR_RNDF); /* error <= ulp(y) */ - else - mpfr_sub (y, y, u, MPFR_RNDF); /* error <= ulp(y) */ - } - /* We assume |(1 + theta)^(i+1)| <= 2. - The neglected part is at most |u| + |u|/2 + ... <= 2|u| < 2 ulp(y) - which has to be multiplied by |(1 + theta)^(i+1)| <= 2, thus at most - 4 ulp(y). - The rounding error on y is bounded by: - * for the (i-2) add/sub, each error is bounded by ulp(y), - and since |y| <= |x|, this yields (i-2)*ulp(x) - * from Lemma 3.1 from [Higham02] (see algorithms.tex), - the relative error on u at step i is bounded by: - (i+1)*epsilon/(1-(i+1)*epsilon) where epsilon = 2^(1-p). - If (i+1)*epsilon <= 1/2, then the relative error on u at - step i is bounded by 2*(i+1)*epsilon, and since |u| <= 1/2^(i+1) - at step i, this gives an absolute error bound of; - 2*epsilon*x*(3/2^3 + 4/2^4 + 5/2^5 + ...) <= 2*2^(1-p)*x = - 4*2^(-p)*x <= 4*ulp(x). - - If (i+1)*epsilon <= 1/2, then the relative error on u at step i - is bounded by (i+1)*epsilon/(1-(i+1)*epsilon) <= 1, thus it follows - |(1 + theta)^(i+1)| <= 2. - - Finally the total error is bounded by 4*ulp(y) + (i-2)*ulp(x) + 4*ulp(x) - = 4*ulp(y) + (i+2)*ulp(x). - Since x/2 <= y, we have ulp(x) <= 2*ulp(y), thus the error is bounded by: - (2*i+8)*ulp(y). - */ - err = 2 * i + 8; - k = __gmpfr_int_ceil_log2 (err); - MPFR_ASSERTN(k < p); - /* if k < p, since k = ceil(log2(err)), we have err <= 2^k <= 2^(p-1), - thus i+4 = err/2 <= 2^(p-2), thus (i+4)*epsilon <= 1/2, which implies - our assumption (i+1)*epsilon <= 1/2. */ - mpfr_clear (t); - mpfr_clear (u); - return k; -} - -/* The computation of log1p is done by - log1p(x) = log(1+x) - except when x is very small, in which case log1p(x) = x + tiny error, - or when x is small, where we use directly the Taylor expansion. -*/ - -int -mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) -{ - int comp, inexact; - mpfr_exp_t ex; - MPFR_SAVE_EXPO_DECL (expo); - - MPFR_LOG_FUNC - (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), - ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, - inexact)); - - if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) - { - if (MPFR_IS_NAN (x)) - { - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - /* check for inf or -inf (result is not defined) */ - else if (MPFR_IS_INF (x)) - { - if (MPFR_IS_POS (x)) - { - MPFR_SET_INF (y); - MPFR_SET_POS (y); - MPFR_RET (0); - } - else - { - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - } - else /* x is zero */ - { - MPFR_ASSERTD (MPFR_IS_ZERO (x)); - MPFR_SET_ZERO (y); /* log1p(+/- 0) = +/- 0 */ - MPFR_SET_SAME_SIGN (y, x); - MPFR_RET (0); - } - } - - ex = MPFR_GET_EXP (x); - if (ex < 0) /* -0.5 < x < 0.5 */ - { - /* For x > 0, abs(log(1+x)-x) < x^2/2. - For x > -0.5, abs(log(1+x)-x) < x^2. */ - if (MPFR_IS_POS (x)) - MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex - 1, 0, 0, rnd_mode, {}); - else - MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {}); - } - - comp = mpfr_cmp_si (x, -1); - /* log1p(x) is undefined for x < -1 */ - if (MPFR_UNLIKELY(comp <= 0)) - { - if (comp == 0) - /* x=0: log1p(-1)=-inf (divide-by-zero exception) */ - { - MPFR_SET_INF (y); - MPFR_SET_NEG (y); - MPFR_SET_DIVBY0 (); - MPFR_RET (0); - } - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - - MPFR_SAVE_EXPO_MARK (expo); - - /* General case */ - { - /* Declaration of the intermediary variable */ - mpfr_t t; - /* Declaration of the size variable */ - mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */ - mpfr_prec_t Nt; /* working precision */ - mpfr_exp_t err; /* error */ - MPFR_ZIV_DECL (loop); - - /* compute the precision of intermediary variable */ - /* the optimal number of bits : see algorithms.tex */ - Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6; - - /* if |x| is smaller than 2^(-e), we will loose about e bits - in log(1+x) */ - if (MPFR_EXP(x) < 0) - Nt += -MPFR_EXP(x); - - /* initialize of intermediary variable */ - mpfr_init2 (t, Nt); - - /* First computation of log1p */ - MPFR_ZIV_INIT (loop, Nt); - for (;;) - { - int k; - /* small case: assuming the AGM algorithm used by mpfr_log uses - log2(p) steps for a precision of p bits, we try the special - variant whenever EXP(x) <= -p/log2(p). */ - k = 1 + __gmpfr_int_ceil_log2 (Ny); /* the +1 avoids a division by 0 - when Ny=1 */ - if (MPFR_GET_EXP (x) <= - (mpfr_exp_t) (Ny / k)) - /* this implies EXP(x) <= 0 thus x < 1 */ - err = Nt - mpfr_log1p_small (t, x); - else - { - /* compute log1p */ - inexact = mpfr_add_ui (t, x, 1, MPFR_RNDN); /* 1+x */ - /* if inexact = 0, then t = x+1, and the result is simply log(t) */ - if (inexact == 0) - { - inexact = mpfr_log (y, t, rnd_mode); - goto end; - } - mpfr_log (t, t, MPFR_RNDN); /* log(1+x) */ - - /* the error is bounded by (1/2+2^(1-EXP(t))*ulp(t) - (cf algorithms.tex) - if EXP(t)>=2, then error <= ulp(t) - if EXP(t)<=1, then error <= 2^(2-EXP(t))*ulp(t) */ - err = Nt - MAX (0, 2 - MPFR_GET_EXP (t)); - } - - if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) - break; - - /* increase the precision */ - MPFR_ZIV_NEXT (loop, Nt); - mpfr_set_prec (t, Nt); - } - inexact = mpfr_set (y, t, rnd_mode); - - end: - MPFR_ZIV_FREE (loop); - mpfr_clear (t); - } - - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); -} |