diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/li2.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/li2.c | 631 |
1 files changed, 0 insertions, 631 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/li2.c b/Build/source/libs/mpfr/mpfr-src/src/li2.c deleted file mode 100644 index 7a4113bc25f..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/li2.c +++ /dev/null @@ -1,631 +0,0 @@ -/* mpfr_li2 -- Dilogarithm. - -Copyright 2007-2020 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" - -/* Compute the alternating series - s = S(z) = \sum_{k=0}^infty B_{2k} (z))^{2k+1} / (2k+1)! - with 0 < z <= log(2) to the precision of s rounded in the direction - rnd_mode. - Return the maximum index of the truncature which is useful - for determinating the relative error. -*/ -static int -li2_series (mpfr_t sum, mpfr_srcptr z, mpfr_rnd_t rnd_mode) -{ - int i; - mpfr_t s, u, v, w; - mpfr_prec_t sump, p; - mpfr_exp_t se, err; - MPFR_ZIV_DECL (loop); - - /* The series converges for |z| < 2 pi, but in mpfr_li2 the argument is - reduced so that 0 < z <= log(2). Here is an additional check that z - is (nearly) correct. */ - MPFR_ASSERTD (MPFR_IS_STRICTPOS (z)); - MPFR_ASSERTD (mpfr_cmp_ui_2exp (z, 89, -7) <= 0); /* z <= 0.6953125 */ - - sump = MPFR_PREC (sum); /* target precision */ - p = sump + MPFR_INT_CEIL_LOG2 (sump) + 4; /* the working precision */ - mpfr_init2 (s, p); - mpfr_init2 (u, p); - mpfr_init2 (v, p); - mpfr_init2 (w, p); - - MPFR_ZIV_INIT (loop, p); - for (;;) - { - mpfr_sqr (u, z, MPFR_RNDU); - mpfr_set (v, z, MPFR_RNDU); - mpfr_set (s, z, MPFR_RNDU); - se = MPFR_GET_EXP (s); - err = 0; - - for (i = 1;; i++) - { - mpfr_mul (v, u, v, MPFR_RNDU); - mpfr_div_ui (v, v, 2 * i, MPFR_RNDU); - mpfr_div_ui (v, v, 2 * i, MPFR_RNDU); - mpfr_div_ui (v, v, 2 * i + 1, MPFR_RNDU); - mpfr_div_ui (v, v, 2 * i + 1, MPFR_RNDU); - /* here, v_2i = v_{2i-2} / (2i * (2i+1))^2 */ - - mpfr_mul_z (w, v, mpfr_bernoulli_cache(i), MPFR_RNDN); - /* here, w_2i = v_2i * B_2i * (2i+1)! with - error(w_2i) < 2^(5 * i + 8) ulp(w_2i) (see algorithms.tex) */ - - mpfr_add (s, s, w, MPFR_RNDN); - - err = MAX (err + se, 5 * i + 8 + MPFR_GET_EXP (w)) - - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err); - se = MPFR_GET_EXP (s); - if (MPFR_GET_EXP (w) <= se - (mpfr_exp_t) p) - break; - } - - /* the previous value of err is the rounding error, - the truncation error is less than EXP(z) - 6 * i - 5 - (see algorithms.tex) */ - err = MAX (err, MPFR_GET_EXP (z) - 6 * i - 5) + 1; - if (MPFR_CAN_ROUND (s, (mpfr_exp_t) p - err, sump, rnd_mode)) - break; - - MPFR_ZIV_NEXT (loop, p); - mpfr_set_prec (s, p); - mpfr_set_prec (u, p); - mpfr_set_prec (v, p); - mpfr_set_prec (w, p); - } - MPFR_ZIV_FREE (loop); - mpfr_set (sum, s, rnd_mode); - - mpfr_clears (s, u, v, w, (mpfr_ptr) 0); - - /* Let K be the returned value. - 1. As we compute an alternating series, the truncation error has the same - sign as the next term w_{K+2} which is positive iff K%4 == 0. - 2. Assume that error(z) <= (1+t) z', where z' is the actual value, then - error(s) <= 2 * (K+1) * t (see algorithms.tex). - */ - return 2 * i; -} - -/* try asymptotic expansion when x is large and positive: - Li2(x) = -log(x)^2/2 + Pi^2/3 - 1/x + O(1/x^2). - More precisely for x >= 2 we have for g(x) = -log(x)^2/2 + Pi^2/3: - -2 <= x * (Li2(x) - g(x)) <= -1 - thus |Li2(x) - g(x)| <= 2/x. - Assumes x >= 38, which ensures log(x)^2/2 >= 2*Pi^2/3, and g(x) <= -3.3. - Return 0 if asymptotic expansion failed (unable to round), otherwise - returns 1 for RNDF, and correct ternary value otherwise. -*/ -static int -mpfr_li2_asympt_pos (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) -{ - mpfr_t g, h; - mpfr_prec_t w = MPFR_PREC (y) + 20; - int inex = 0; - - MPFR_ASSERTN (mpfr_cmp_ui (x, 38) >= 0); - - mpfr_init2 (g, w); - mpfr_init2 (h, w); - mpfr_log (g, x, MPFR_RNDN); /* rel. error <= |(1 + theta) - 1| */ - mpfr_sqr (g, g, MPFR_RNDN); /* rel. error <= |(1 + theta)^3 - 1| <= 2^(2-w) */ - mpfr_div_2ui (g, g, 1, MPFR_RNDN); /* rel. error <= 2^(2-w) */ - mpfr_const_pi (h, MPFR_RNDN); /* error <= 2^(1-w) */ - mpfr_sqr (h, h, MPFR_RNDN); /* rel. error <= 2^(2-w) */ - mpfr_div_ui (h, h, 3, MPFR_RNDN); /* rel. error <= |(1 + theta)^4 - 1| - <= 5 * 2^(-w) */ - /* since x is chosen such that log(x)^2/2 >= 2 * (Pi^2/3), we should have - g >= 2*h, thus |g-h| >= |h|, and the relative error on g is at most - multiplied by 2 in the difference, and that by h is unchanged. */ - MPFR_ASSERTN (MPFR_EXP (g) > MPFR_EXP (h)); - mpfr_sub (g, h, g, MPFR_RNDN); /* err <= ulp(g)/2 + g*2^(3-w) + g*5*2^(-w) - <= ulp(g) * (1/2 + 8 + 5) < 14 ulp(g). - - If in addition 2/x <= 2 ulp(g), i.e., - 1/x <= ulp(g), then the total error is - bounded by 16 ulp(g). */ - if ((MPFR_EXP (x) >= (mpfr_exp_t) w - MPFR_EXP (g)) && - MPFR_CAN_ROUND (g, w - 4, MPFR_PREC (y), rnd_mode)) - { - inex = mpfr_set (y, g, rnd_mode); - if (rnd_mode == MPFR_RNDF) - inex = 1; - } - - mpfr_clear (g); - mpfr_clear (h); - - return inex; -} - -/* try asymptotic expansion when x is large and negative: - Li2(x) = -log(-x)^2/2 - Pi^2/6 - 1/x + O(1/x^2). - More precisely for x <= -2 we have for g(x) = -log(-x)^2/2 - Pi^2/6: - |Li2(x) - g(x)| <= 1/|x|. - Assumes x <= -7, which ensures |log(-x)^2/2| >= Pi^2/6, and g(x) <= -3.5. - Return 0 if asymptotic expansion failed (unable to round), otherwise - returns 1 for RNDF, and correct ternary value otherwise. -*/ -static int -mpfr_li2_asympt_neg (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) -{ - mpfr_t g, h; - mpfr_prec_t w = MPFR_PREC (y) + 20; - int inex = 0; - - MPFR_ASSERTN (mpfr_cmp_si (x, -7) <= 0); - - mpfr_init2 (g, w); - mpfr_init2 (h, w); - mpfr_neg (g, x, MPFR_RNDN); - mpfr_log (g, g, MPFR_RNDN); /* rel. error <= |(1 + theta) - 1| */ - mpfr_sqr (g, g, MPFR_RNDN); /* rel. error <= |(1 + theta)^3 - 1| <= 2^(2-w) */ - mpfr_div_2ui (g, g, 1, MPFR_RNDN); /* rel. error <= 2^(2-w) */ - mpfr_const_pi (h, MPFR_RNDN); /* error <= 2^(1-w) */ - mpfr_sqr (h, h, MPFR_RNDN); /* rel. error <= 2^(2-w) */ - mpfr_div_ui (h, h, 6, MPFR_RNDN); /* rel. error <= |(1 + theta)^4 - 1| - <= 5 * 2^(-w) */ - MPFR_ASSERTN (MPFR_EXP (g) >= MPFR_EXP (h)); - mpfr_add (g, g, h, MPFR_RNDN); /* err <= ulp(g)/2 + g*2^(2-w) + g*5*2^(-w) - <= ulp(g) * (1/2 + 4 + 5) < 10 ulp(g). - - If in addition |1/x| <= 4 ulp(g), then the - total error is bounded by 16 ulp(g). */ - if ((MPFR_EXP (x) >= (mpfr_exp_t) (w - 2) - MPFR_EXP (g)) && - MPFR_CAN_ROUND (g, w - 4, MPFR_PREC (y), rnd_mode)) - { - inex = mpfr_neg (y, g, rnd_mode); - if (rnd_mode == MPFR_RNDF) - inex = 1; - } - - mpfr_clear (g); - mpfr_clear (h); - - return inex; -} - -/* Compute the real part of the dilogarithm defined by - Li2(x) = -\Int_{t=0}^x log(1-t)/t dt */ -int -mpfr_li2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) -{ - int inexact; - mpfr_exp_t err; - mpfr_prec_t yp, m; - MPFR_ZIV_DECL (loop); - 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; - } - else if (MPFR_IS_INF (x)) - { - MPFR_SET_NEG (y); - MPFR_SET_INF (y); - MPFR_RET (0); - } - else /* x is zero */ - { - MPFR_ASSERTD (MPFR_IS_ZERO (x)); - MPFR_SET_SAME_SIGN (y, x); - MPFR_SET_ZERO (y); - MPFR_RET (0); - } - } - - /* Li2(x) = x + x^2/4 + x^3/9 + ..., more precisely for 0 < x <= 1/2 - we have |Li2(x) - x| < x^2/2 <= 2^(2EXP(x)-1) and for -1/2 <= x < 0 - we have |Li2(x) - x| < x^2/4 <= 2^(2EXP(x)-2) */ - if (MPFR_IS_POS (x)) - MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -MPFR_GET_EXP (x), 1, 1, rnd_mode, - {}); - else - MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -MPFR_GET_EXP (x), 2, 0, rnd_mode, - {}); - - MPFR_SAVE_EXPO_MARK (expo); - yp = MPFR_PREC (y); - m = yp + MPFR_INT_CEIL_LOG2 (yp) + 13; - - if (MPFR_LIKELY ((mpfr_cmp_ui (x, 0) > 0) && (mpfr_cmp_ui_2exp (x, 1, -1) <= 0))) - /* 0 < x <= 1/2: Li2(x) = S(-log(1-x))-log^2(1-x)/4 */ - { - mpfr_t s, u; - mpfr_exp_t expo_l; - int k; - - mpfr_init2 (u, m); - mpfr_init2 (s, m); - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - mpfr_ui_sub (u, 1, x, MPFR_RNDN); - mpfr_log (u, u, MPFR_RNDU); - if (MPFR_IS_ZERO(u)) - goto next_m; - mpfr_neg (u, u, MPFR_RNDN); /* u = -log(1-x) */ - expo_l = MPFR_GET_EXP (u); - k = li2_series (s, u, MPFR_RNDU); - err = 1 + MPFR_INT_CEIL_LOG2 (k + 1); - - mpfr_sqr (u, u, MPFR_RNDU); - mpfr_div_2ui (u, u, 2, MPFR_RNDU); /* u = log^2(1-x) / 4 */ - mpfr_sub (s, s, u, MPFR_RNDN); - - /* error(s) <= (0.5 + 2^(d-EXP(s)) - + 2^(3 + MAX(1, - expo_l) - EXP(s))) ulp(s) */ - err = MAX (err, MAX (1, - expo_l) - 1) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err); - if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode)) - break; - - next_m: - MPFR_ZIV_NEXT (loop, m); - mpfr_set_prec (u, m); - mpfr_set_prec (s, m); - } - MPFR_ZIV_FREE (loop); - inexact = mpfr_set (y, s, rnd_mode); - - mpfr_clear (u); - mpfr_clear (s); - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); - } - else if (!mpfr_cmp_ui (x, 1)) - /* Li2(1)= pi^2 / 6 */ - { - mpfr_t u; - mpfr_init2 (u, m); - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - mpfr_const_pi (u, MPFR_RNDU); - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_ui (u, u, 6, MPFR_RNDN); - - err = m - 4; /* error(u) <= 19/2 ulp(u) */ - if (MPFR_CAN_ROUND (u, err, yp, rnd_mode)) - break; - - MPFR_ZIV_NEXT (loop, m); - mpfr_set_prec (u, m); - } - MPFR_ZIV_FREE (loop); - inexact = mpfr_set (y, u, rnd_mode); - - mpfr_clear (u); - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); - } - else if (mpfr_cmp_ui (x, 2) >= 0) - /* x >= 2: Li2(x) = -S(-log(1-1/x))-log^2(x)/2+log^2(1-1/x)/4+pi^2/3 */ - { - int k; - mpfr_exp_t expo_l; - mpfr_t s, u, xx; - - if (mpfr_cmp_ui (x, 38) >= 0) - { - inexact = mpfr_li2_asympt_pos (y, x, rnd_mode); - if (inexact != 0) - goto end_of_case_gt2; - } - - mpfr_init2 (u, m); - mpfr_init2 (s, m); - mpfr_init2 (xx, m); - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - mpfr_ui_div (xx, 1, x, MPFR_RNDN); - mpfr_neg (xx, xx, MPFR_RNDN); - mpfr_log1p (u, xx, MPFR_RNDD); - mpfr_neg (u, u, MPFR_RNDU); /* u = -log(1-1/x) */ - expo_l = MPFR_GET_EXP (u); - k = li2_series (s, u, MPFR_RNDN); - mpfr_neg (s, s, MPFR_RNDN); - err = MPFR_INT_CEIL_LOG2 (k + 1) + 1; /* error(s) <= 2^err ulp(s) */ - - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_2ui (u, u, 2, MPFR_RNDN); /* u= log^2(1-1/x)/4 */ - mpfr_add (s, s, u, MPFR_RNDN); - err = - MAX (err, - 3 + MAX (1, -expo_l) + MPFR_GET_EXP (u)) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err); /* error(s) <= 2^err ulp(s) */ - err += MPFR_GET_EXP (s); - - mpfr_log (u, x, MPFR_RNDU); - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_2ui (u, u, 1, MPFR_RNDN); /* u = log^2(x)/2 */ - mpfr_sub (s, s, u, MPFR_RNDN); - err = MAX (err, 3 + MPFR_GET_EXP (u)) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err); /* error(s) <= 2^err ulp(s) */ - err += MPFR_GET_EXP (s); - - mpfr_const_pi (u, MPFR_RNDU); - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_ui (u, u, 3, MPFR_RNDN); /* u = pi^2/3 */ - mpfr_add (s, s, u, MPFR_RNDN); - err = MAX (err, 2) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err); /* error(s) <= 2^err ulp(s) */ - if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode)) - break; - - MPFR_ZIV_NEXT (loop, m); - mpfr_set_prec (u, m); - mpfr_set_prec (s, m); - mpfr_set_prec (xx, m); - } - MPFR_ZIV_FREE (loop); - inexact = mpfr_set (y, s, rnd_mode); - mpfr_clears (s, u, xx, (mpfr_ptr) 0); - - end_of_case_gt2: - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); - } - else if (mpfr_cmp_ui (x, 1) > 0) - /* 2 > x > 1: Li2(x) = S(log(x))+log^2(x)/4-log(x)log(x-1)+pi^2/6 */ - { - int k; - mpfr_exp_t e1, e2; - mpfr_t s, u, v, xx; - mpfr_init2 (s, m); - mpfr_init2 (u, m); - mpfr_init2 (v, m); - mpfr_init2 (xx, m); - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - mpfr_log (v, x, MPFR_RNDU); - k = li2_series (s, v, MPFR_RNDN); - e1 = MPFR_GET_EXP (s); - - mpfr_sqr (u, v, MPFR_RNDN); - mpfr_div_2ui (u, u, 2, MPFR_RNDN); /* u = log^2(x)/4 */ - mpfr_add (s, s, u, MPFR_RNDN); - - mpfr_sub_ui (xx, x, 1, MPFR_RNDN); - mpfr_log (u, xx, MPFR_RNDU); - e2 = MPFR_GET_EXP (u); - mpfr_mul (u, v, u, MPFR_RNDN); /* u = log(x) * log(x-1) */ - mpfr_sub (s, s, u, MPFR_RNDN); - - mpfr_const_pi (u, MPFR_RNDU); - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_ui (u, u, 6, MPFR_RNDN); /* u = pi^2/6 */ - mpfr_add (s, s, u, MPFR_RNDN); - /* error(s) <= (31 + (k+1) * 2^(1-e1) + 2^(1-e2)) ulp(s) - see algorithms.tex */ - err = MAX (MPFR_INT_CEIL_LOG2 (k + 1) + 1 - e1, 1 - e2); - err = 2 + MAX (5, err); - if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode)) - break; - - MPFR_ZIV_NEXT (loop, m); - mpfr_set_prec (s, m); - mpfr_set_prec (u, m); - mpfr_set_prec (v, m); - mpfr_set_prec (xx, m); - } - MPFR_ZIV_FREE (loop); - inexact = mpfr_set (y, s, rnd_mode); - - mpfr_clears (s, u, v, xx, (mpfr_ptr) 0); - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); - } - else if (mpfr_cmp_ui_2exp (x, 1, -1) > 0) /* 1/2 < x < 1 */ - /* 1 > x > 1/2: Li2(x) = -S(-log(x))+log^2(x)/4-log(x)log(1-x)+pi^2/6 */ - { - int k; - mpfr_t s, u, v, xx; - mpfr_init2 (s, m); - mpfr_init2 (u, m); - mpfr_init2 (v, m); - mpfr_init2 (xx, m); - - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - mpfr_log (u, x, MPFR_RNDD); - mpfr_neg (u, u, MPFR_RNDN); - k = li2_series (s, u, MPFR_RNDN); - mpfr_neg (s, s, MPFR_RNDN); - err = 1 + MPFR_INT_CEIL_LOG2 (k + 1) - MPFR_GET_EXP (s); - - mpfr_ui_sub (xx, 1, x, MPFR_RNDN); - mpfr_log (v, xx, MPFR_RNDU); - mpfr_mul (v, v, u, MPFR_RNDN); /* v = - log(x) * log(1-x) */ - mpfr_add (s, s, v, MPFR_RNDN); - err = MAX (err, 1 - MPFR_GET_EXP (v)); - err = 2 + MAX (3, err) - MPFR_GET_EXP (s); - - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_2ui (u, u, 2, MPFR_RNDN); /* u = log^2(x)/4 */ - mpfr_add (s, s, u, MPFR_RNDN); - err = MAX (err, 2 + MPFR_GET_EXP (u)) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err) + MPFR_GET_EXP (s); - - mpfr_const_pi (u, MPFR_RNDU); - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_ui (u, u, 6, MPFR_RNDN); /* u = pi^2/6 */ - mpfr_add (s, s, u, MPFR_RNDN); - err = MAX (err, 3) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err); - - if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode)) - break; - - MPFR_ZIV_NEXT (loop, m); - mpfr_set_prec (s, m); - mpfr_set_prec (u, m); - mpfr_set_prec (v, m); - mpfr_set_prec (xx, m); - } - MPFR_ZIV_FREE (loop); - inexact = mpfr_set (y, s, rnd_mode); - - mpfr_clears (s, u, v, xx, (mpfr_ptr) 0); - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); - } - else if (mpfr_cmp_si (x, -1) >= 0) - /* 0 > x >= -1: Li2(x) = -S(log(1-x))-log^2(1-x)/4 */ - { - int k; - mpfr_exp_t expo_l; - mpfr_t s, u, xx; - mpfr_init2 (s, m); - mpfr_init2 (u, m); - mpfr_init2 (xx, m); - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - mpfr_neg (xx, x, MPFR_RNDN); - mpfr_log1p (u, xx, MPFR_RNDN); - k = li2_series (s, u, MPFR_RNDN); - mpfr_neg (s, s, MPFR_RNDN); - expo_l = MPFR_GET_EXP (u); - err = 1 + MPFR_INT_CEIL_LOG2 (k + 1) - MPFR_GET_EXP (s); - - mpfr_sqr (u, u, MPFR_RNDN); - mpfr_div_2ui (u, u, 2, MPFR_RNDN); /* u = log^2(1-x)/4 */ - mpfr_sub (s, s, u, MPFR_RNDN); - err = MAX (err, - expo_l); - err = 2 + MAX (err, 3); - if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode)) - break; - - MPFR_ZIV_NEXT (loop, m); - mpfr_set_prec (s, m); - mpfr_set_prec (u, m); - mpfr_set_prec (xx, m); - } - MPFR_ZIV_FREE (loop); - inexact = mpfr_set (y, s, rnd_mode); - - mpfr_clears (s, u, xx, (mpfr_ptr) 0); - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); - } - else - /* x < -1: Li2(x) - = S(log(1-1/x))-log^2(-x)/4-log(1-x)log(-x)/2+log^2(1-x)/4-pi^2/6 */ - { - int k; - mpfr_t s, u, v, w, xx; - - if (mpfr_cmp_si (x, -7) <= 0) - { - inexact = mpfr_li2_asympt_neg (y, x, rnd_mode); - if (inexact != 0) - goto end_of_case_ltm1; - } - - mpfr_init2 (s, m); - mpfr_init2 (u, m); - mpfr_init2 (v, m); - mpfr_init2 (w, m); - mpfr_init2 (xx, m); - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - mpfr_ui_div (xx, 1, x, MPFR_RNDN); - mpfr_neg (xx, xx, MPFR_RNDN); - mpfr_log1p (u, xx, MPFR_RNDN); - k = li2_series (s, u, MPFR_RNDN); - - mpfr_ui_sub (xx, 1, x, MPFR_RNDN); - mpfr_log (u, xx, MPFR_RNDU); - mpfr_neg (xx, x, MPFR_RNDN); - mpfr_log (v, xx, MPFR_RNDU); - mpfr_mul (w, v, u, MPFR_RNDN); - mpfr_div_2ui (w, w, 1, MPFR_RNDN); /* w = log(-x) * log(1-x) / 2 */ - mpfr_sub (s, s, w, MPFR_RNDN); - err = 1 + MAX (3, MPFR_INT_CEIL_LOG2 (k+1) + 1 - MPFR_GET_EXP (s)) - + MPFR_GET_EXP (s); - - mpfr_sqr (w, v, MPFR_RNDN); - mpfr_div_2ui (w, w, 2, MPFR_RNDN); /* w = log^2(-x) / 4 */ - mpfr_sub (s, s, w, MPFR_RNDN); - err = MAX (err, 3 + MPFR_GET_EXP(w)) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err) + MPFR_GET_EXP (s); - - mpfr_sqr (w, u, MPFR_RNDN); - mpfr_div_2ui (w, w, 2, MPFR_RNDN); /* w = log^2(1-x) / 4 */ - mpfr_add (s, s, w, MPFR_RNDN); - err = MAX (err, 3 + MPFR_GET_EXP (w)) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err) + MPFR_GET_EXP (s); - - mpfr_const_pi (w, MPFR_RNDU); - mpfr_sqr (w, w, MPFR_RNDN); - mpfr_div_ui (w, w, 6, MPFR_RNDN); /* w = pi^2 / 6 */ - mpfr_sub (s, s, w, MPFR_RNDN); - err = MAX (err, 3) - MPFR_GET_EXP (s); - err = 2 + MAX (-1, err) + MPFR_GET_EXP (s); - - if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode)) - break; - - MPFR_ZIV_NEXT (loop, m); - mpfr_set_prec (s, m); - mpfr_set_prec (u, m); - mpfr_set_prec (v, m); - mpfr_set_prec (w, m); - mpfr_set_prec (xx, m); - } - MPFR_ZIV_FREE (loop); - inexact = mpfr_set (y, s, rnd_mode); - mpfr_clears (s, u, v, w, xx, (mpfr_ptr) 0); - - end_of_case_ltm1: - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); - } - - MPFR_RET_NEVER_GO_HERE (); -} |