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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/root.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/root.c | 331 |
1 files changed, 0 insertions, 331 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/root.c b/Build/source/libs/mpfr/mpfr-src/src/root.c deleted file mode 100644 index a8bd7d04eed..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/root.c +++ /dev/null @@ -1,331 +0,0 @@ -/* mpfr_root -- kth root. - -Copyright 2005-2020 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" - - /* The computation of y = x^(1/k) is done as follows, except for large - values of k, for which this would be inefficient or yield internal - integer overflows: - - Let x = sign * m * 2^(k*e) where m is an integer - - with 2^(k*(n-1)) <= m < 2^(k*n) where n = PREC(y) - - and m = s^k + t where 0 <= t and m < (s+1)^k - - we want that s has n bits i.e. s >= 2^(n-1), or m >= 2^(k*(n-1)) - i.e. m must have at least k*(n-1)+1 bits - - then, not taking into account the sign, the result will be - x^(1/k) = s * 2^e or (s+1) * 2^e according to the rounding mode. - */ - -static int -mpfr_root_aux (mpfr_ptr y, mpfr_srcptr x, unsigned long k, - mpfr_rnd_t rnd_mode); - -int -mpfr_rootn_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode) -{ - mpz_t m; - mpfr_exp_t e, r, sh, f; - mpfr_prec_t n, size_m, tmp; - int inexact, negative; - MPFR_SAVE_EXPO_DECL (expo); - - MPFR_LOG_FUNC - (("x[%Pu]=%.*Rg k=%lu rnd=%d", - mpfr_get_prec (x), mpfr_log_prec, x, k, rnd_mode), - ("y[%Pu]=%.*Rg inexact=%d", - mpfr_get_prec (y), mpfr_log_prec, y, inexact)); - - if (MPFR_UNLIKELY (k <= 1)) - { - if (k == 0) - { - /* rootn(x,0) is NaN (IEEE 754-2008). */ - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - else /* y = x^(1/1) = x */ - return mpfr_set (y, x, rnd_mode); - } - - /* Singular values */ - if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) - { - if (MPFR_IS_NAN (x)) - { - MPFR_SET_NAN (y); /* NaN^(1/k) = NaN */ - MPFR_RET_NAN; - } - - if (MPFR_IS_INF (x)) /* (+Inf)^(1/k) = +Inf - (-Inf)^(1/k) = -Inf if k odd - (-Inf)^(1/k) = NaN if k even */ - { - if (MPFR_IS_NEG (x) && (k & 1) == 0) - { - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - MPFR_SET_INF (y); - MPFR_SET_SAME_SIGN (y, x); - } - else /* x is necessarily 0: (+0)^(1/k) = +0 - (-0)^(1/k) = -0 */ - { - MPFR_ASSERTD (MPFR_IS_ZERO (x)); - MPFR_SET_ZERO (y); - if (MPFR_IS_POS (x) || (k & 1) == 0) - MPFR_SET_POS (y); - else - MPFR_SET_NEG (y); - } - MPFR_RET (0); - } - - /* Returns NAN for x < 0 and k even */ - if (MPFR_UNLIKELY (MPFR_IS_NEG (x) && (k & 1) == 0)) - { - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - - /* Special case |x| = 1. Note that if x = -1, then k is odd - (NaN results have already been filtered), so that y = -1. */ - if (mpfr_cmpabs (x, __gmpfr_one) == 0) - return mpfr_set (y, x, rnd_mode); - - /* General case */ - - /* For large k, use exp(log(x)/k). The threshold of 100 seems to be quite - good when the precision goes to infinity. */ - if (k > 100) - return mpfr_root_aux (y, x, k, rnd_mode); - - MPFR_SAVE_EXPO_MARK (expo); - mpz_init (m); - - e = mpfr_get_z_2exp (m, x); /* x = m * 2^e */ - if ((negative = MPFR_IS_NEG(x))) - mpz_neg (m, m); - r = e % (mpfr_exp_t) k; - if (r < 0) - r += k; /* now r = e (mod k) with 0 <= r < k */ - MPFR_ASSERTD (0 <= r && r < k); - /* x = (m*2^r) * 2^(e-r) where e-r is a multiple of k */ - - MPFR_MPZ_SIZEINBASE2 (size_m, m); - /* for rounding to nearest, we want the round bit to be in the root */ - n = MPFR_PREC (y) + (rnd_mode == MPFR_RNDN); - - /* we now multiply m by 2^sh so that root(m,k) will give - exactly n bits: we want k*(n-1)+1 <= size_m + sh <= k*n - i.e. sh = k*f + r with f = max(floor((k*n-size_m-r)/k),0) */ - if ((mpfr_exp_t) size_m + r >= k * (mpfr_exp_t) n) - f = 0; /* we already have too many bits */ - else - f = (k * (mpfr_exp_t) n - (mpfr_exp_t) size_m - r) / k; - sh = k * f + r; - mpz_mul_2exp (m, m, sh); - e = e - sh; - - /* invariant: x = m*2^e, with e divisible by k */ - - /* we reuse the variable m to store the kth root, since it is not needed - any more: we just need to know if the root is exact */ - inexact = mpz_root (m, m, k) == 0; - - MPFR_MPZ_SIZEINBASE2 (tmp, m); - sh = tmp - n; - if (sh > 0) /* we have to flush to 0 the last sh bits from m */ - { - inexact = inexact || (mpz_scan1 (m, 0) < sh); - mpz_fdiv_q_2exp (m, m, sh); - e += k * sh; - } - - if (inexact) - { - if (negative) - rnd_mode = MPFR_INVERT_RND (rnd_mode); - if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA - || (rnd_mode == MPFR_RNDN && mpz_tstbit (m, 0))) - inexact = 1, mpz_add_ui (m, m, 1); - else - inexact = -1; - } - - /* either inexact is not zero, and the conversion is exact, i.e. inexact - is not changed; or inexact=0, and inexact is set only when - rnd_mode=MPFR_RNDN and bit (n+1) from m is 1 */ - inexact += mpfr_set_z (y, m, MPFR_RNDN); - MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / (mpfr_exp_t) k); - - if (negative) - { - MPFR_CHANGE_SIGN (y); - inexact = -inexact; - } - - mpz_clear (m); - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); -} - -/* Compute y <- x^(1/k) using exp(log(x)/k). - Assume all special cases have been eliminated before. - In the extended exponent range, overflows/underflows are not possible. - Assume x > 0, or x < 0 and k odd. - Also assume |x| <> 1 because log(1) = 0, which does not have an exponent - and would yield a failure in the error bound computation. A priori, this - constraint is quite artificial because if |x| is close enough to 1, then - the exponent of log|x| does not need to be used (in the code, err would - be 1 in such a domain). So this constraint |x| <> 1 could be avoided in - the code. However, this is an exact case easy to detect, so that such a - change would be useless. Values very close to 1 are not an issue, since - an underflow is not possible before the MPFR_GET_EXP. -*/ -static int -mpfr_root_aux (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode) -{ - int inexact, exact_root = 0; - mpfr_prec_t w; /* working precision */ - mpfr_t absx, t; - MPFR_GROUP_DECL(group); - MPFR_TMP_DECL(marker); - MPFR_ZIV_DECL(loop); - MPFR_SAVE_EXPO_DECL (expo); - - MPFR_TMP_INIT_ABS (absx, x); - - MPFR_TMP_MARK(marker); - w = MPFR_PREC(y) + 10; - /* Take some guard bits to prepare for the 'expt' lost bits below. - If |x| < 2^k, then log|x| < k, thus taking log2(k) bits should be fine. */ - if (MPFR_GET_EXP(x) > 0) - w += MPFR_INT_CEIL_LOG2 (MPFR_GET_EXP(x)); - MPFR_GROUP_INIT_1(group, w, t); - MPFR_SAVE_EXPO_MARK (expo); - MPFR_ZIV_INIT (loop, w); - for (;;) - { - mpfr_exp_t expt; - unsigned int err; - - mpfr_log (t, absx, MPFR_RNDN); - /* t = log|x| * (1 + theta) with |theta| <= 2^(-w) */ - mpfr_div_ui (t, t, k, MPFR_RNDN); - /* No possible underflow in mpfr_log and mpfr_div_ui. */ - expt = MPFR_GET_EXP (t); /* assumes t <> 0 */ - /* t = log|x|/k * (1 + theta) + eps with |theta| <= 2^(-w) - and |eps| <= 1/2 ulp(t), thus the total error is bounded - by 1.5 * 2^(expt - w) */ - mpfr_exp (t, t, MPFR_RNDN); - /* t = |x|^(1/k) * exp(tau) * (1 + theta1) with - |tau| <= 1.5 * 2^(expt - w) and |theta1| <= 2^(-w). - For |tau| <= 0.5 we have |exp(tau)-1| < 4/3*tau, thus - for w >= expt + 2 we have: - t = |x|^(1/k) * (1 + 2^(expt+2)*theta2) * (1 + theta1) with - |theta1|, |theta2| <= 2^(-w). - If expt+2 > 0, as long as w >= 1, we have: - t = |x|^(1/k) * (1 + 2^(expt+3)*theta3) with |theta3| < 2^(-w). - For expt+2 = 0, we have: - t = |x|^(1/k) * (1 + 2^2*theta3) with |theta3| < 2^(-w). - Finally for expt+2 < 0 we have: - t = |x|^(1/k) * (1 + 2*theta3) with |theta3| < 2^(-w). - */ - err = (expt + 2 > 0) ? expt + 3 - : (expt + 2 == 0) ? 2 : 1; - /* now t = |x|^(1/k) * (1 + 2^(err-w)) thus the error is at most - 2^(EXP(t) - w + err) */ - if (MPFR_LIKELY (MPFR_CAN_ROUND(t, w - err, MPFR_PREC(y), rnd_mode))) - break; - - /* If we fail to round correctly, check for an exact result or a - midpoint result with MPFR_RNDN (regarded as hard-to-round in - all precisions in order to determine the ternary value). */ - { - mpfr_t z, zk; - - mpfr_init2 (z, MPFR_PREC(y) + (rnd_mode == MPFR_RNDN)); - mpfr_init2 (zk, MPFR_PREC(x)); - mpfr_set (z, t, MPFR_RNDN); - inexact = mpfr_pow_ui (zk, z, k, MPFR_RNDN); - exact_root = !inexact && mpfr_equal_p (zk, absx); - if (exact_root) /* z is the exact root, thus round z directly */ - inexact = mpfr_set4 (y, z, rnd_mode, MPFR_SIGN (x)); - mpfr_clear (zk); - mpfr_clear (z); - if (exact_root) - break; - } - - MPFR_ZIV_NEXT (loop, w); - MPFR_GROUP_REPREC_1(group, w, t); - } - MPFR_ZIV_FREE (loop); - - if (!exact_root) - inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (x)); - - MPFR_GROUP_CLEAR(group); - MPFR_TMP_FREE(marker); - MPFR_SAVE_EXPO_FREE (expo); - - return mpfr_check_range (y, inexact, rnd_mode); -} - -int -mpfr_root (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode) -{ - MPFR_LOG_FUNC - (("x[%Pu]=%.*Rg k=%lu rnd=%d", - mpfr_get_prec (x), mpfr_log_prec, x, k, rnd_mode), - ("y[%Pu]=%.*Rg", - mpfr_get_prec (y), mpfr_log_prec, y)); - - /* Like mpfr_rootn_ui... */ - if (MPFR_UNLIKELY (k <= 1)) - { - if (k == 0) - { - /* rootn(x,0) is NaN (IEEE 754-2008). */ - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - else /* y = x^(1/1) = x */ - return mpfr_set (y, x, rnd_mode); - } - - if (MPFR_UNLIKELY (MPFR_IS_ZERO (x))) - { - /* The only case that may differ from mpfr_rootn_ui. */ - MPFR_SET_ZERO (y); - MPFR_SET_SAME_SIGN (y, x); - MPFR_RET (0); - } - else - return mpfr_rootn_ui (y, x, k, rnd_mode); -} |