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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/rem1.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/rem1.c | 276 |
1 files changed, 0 insertions, 276 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/rem1.c b/Build/source/libs/mpfr/mpfr-src/src/rem1.c deleted file mode 100644 index 9e75e428798..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/rem1.c +++ /dev/null @@ -1,276 +0,0 @@ -/* mpfr_rem1 -- internal function - mpfr_fmod -- compute the floating-point remainder of x/y - mpfr_remquo and mpfr_remainder -- argument reduction functions - -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. */ - -#include "mpfr-impl.h" - -/* we return as many bits as we can, keeping just one bit for the sign */ -# define WANTED_BITS (sizeof(long) * CHAR_BIT - 1) - -/* - rem1 works as follows: - The first rounding mode rnd_q indicate if we are actually computing - a fmod (MPFR_RNDZ) or a remainder/remquo (MPFR_RNDN). - - Let q = x/y rounded to an integer in the direction rnd_q. - Put x - q*y in rem, rounded according to rnd. - If quo is not null, the value stored in *quo has the sign of q, - and agrees with q with the 2^n low order bits. - In other words, *quo = q (mod 2^n) and *quo q >= 0. - If rem is zero, then it has the sign of x. - The returned 'int' is the inexact flag giving the place of rem wrt x - q*y. - - If x or y is NaN: *quo is undefined, rem is NaN. - If x is Inf, whatever y: *quo is undefined, rem is NaN. - If y is Inf, x not NaN nor Inf: *quo is 0, rem is x. - If y is 0, whatever x: *quo is undefined, rem is NaN. - If x is 0, whatever y (not NaN nor 0): *quo is 0, rem is x. - - Otherwise if x and y are neither NaN, Inf nor 0, q is always defined, - thus *quo is. - Since |x - q*y| <= y/2, no overflow is possible. - Only an underflow is possible when y is very small. - */ - -static int -mpfr_rem1 (mpfr_ptr rem, long *quo, mpfr_rnd_t rnd_q, - mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd) -{ - mpfr_exp_t ex, ey; - int compare, inex, q_is_odd, sign, signx = MPFR_SIGN (x); - mpz_t mx, my, r; - int tiny = 0; - - MPFR_ASSERTD (rnd_q == MPFR_RNDN || rnd_q == MPFR_RNDZ); - - if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x) || MPFR_IS_SINGULAR (y))) - { - if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y) || MPFR_IS_INF (x) - || MPFR_IS_ZERO (y)) - { - /* for remquo, quo is undefined */ - MPFR_SET_NAN (rem); - MPFR_RET_NAN; - } - else /* either y is Inf and x is 0 or non-special, - or x is 0 and y is non-special, - in both cases the quotient is zero. */ - { - if (quo) - *quo = 0; - return mpfr_set (rem, x, rnd); - } - } - - /* now neither x nor y is NaN, Inf or zero */ - - mpz_init (mx); - mpz_init (my); - mpz_init (r); - - ex = mpfr_get_z_2exp (mx, x); /* x = mx*2^ex */ - ey = mpfr_get_z_2exp (my, y); /* y = my*2^ey */ - - /* to get rid of sign problems, we compute it separately: - quo(-x,-y) = quo(x,y), rem(-x,-y) = -rem(x,y) - quo(-x,y) = -quo(x,y), rem(-x,y) = -rem(x,y) - thus quo = sign(x/y)*quo(|x|,|y|), rem = sign(x)*rem(|x|,|y|) */ - sign = (signx == MPFR_SIGN (y)) ? 1 : -1; - mpz_abs (mx, mx); - mpz_abs (my, my); - q_is_odd = 0; - - /* Divide my by 2^k if possible to make operations mod my easier. - Since my comes from a regular MPFR number, due to the constraints on the - exponent and the precision, there can be no integer overflow below. */ - { - mpfr_exp_t k = mpz_scan1 (my, 0); - ey += k; - mpz_fdiv_q_2exp (my, my, k); - } - - if (ex <= ey) - { - /* q = x/y = mx/(my*2^(ey-ex)) */ - - /* First detect cases where q=0, to avoid creating a huge number - my*2^(ey-ex): if sx = mpz_sizeinbase (mx, 2) and sy = - mpz_sizeinbase (my, 2), we have x < 2^(ex + sx) and - y >= 2^(ey + sy - 1), thus if ex + sx <= ey + sy - 1 - the quotient is 0 */ - if (ex + (mpfr_exp_t) mpz_sizeinbase (mx, 2) < - ey + (mpfr_exp_t) mpz_sizeinbase (my, 2)) - { - tiny = 1; - mpz_set (r, mx); - mpz_set_ui (mx, 0); - } - else - { - mpz_mul_2exp (my, my, ey - ex); /* divide mx by my*2^(ey-ex) */ - - /* since mx > 0 and my > 0, we can use mpz_tdiv_qr in all cases */ - mpz_tdiv_qr (mx, r, mx, my); - /* 0 <= |r| <= |my|, r has the same sign as mx */ - } - - if (rnd_q == MPFR_RNDN) - q_is_odd = mpz_tstbit (mx, 0); - if (quo) /* mx is the quotient */ - { - mpz_tdiv_r_2exp (mx, mx, WANTED_BITS); - *quo = mpz_get_si (mx); - } - } - else /* ex > ey */ - { - if (quo) /* remquo case */ - /* for remquo, to get the low WANTED_BITS more bits of the quotient, - we first compute R = X mod Y*2^WANTED_BITS, where X and Y are - defined below. Then the low WANTED_BITS of the quotient are - floor(R/Y). */ - mpz_mul_2exp (my, my, WANTED_BITS); /* 2^WANTED_BITS*Y */ - - else if (rnd_q == MPFR_RNDN) /* remainder case */ - /* Let X = mx*2^(ex-ey) and Y = my. Then both X and Y are integers. - Assume X = R mod Y, then x = X*2^ey = R*2^ey mod (Y*2^ey=y). - To be able to perform the rounding, we need the least significant - bit of the quotient, i.e., one more bit in the remainder, - which is obtained by dividing by 2Y. */ - mpz_mul_2exp (my, my, 1); /* 2Y */ - - /* Warning: up to GMP 6.2.0, mpz_powm_ui is not optimized when BASE^EXP - has about the same size as MOD, in which case it should first compute - BASE^EXP exactly, then reduce it modulo MOD: - https://gmplib.org/list-archives/gmp-bugs/2020-February/004736.html - Thus when 2^(ex-ey) is less than my^3, we use this algorithm. */ - if (ex - ey > 3 * mpz_sizeinbase (my, 2)) - { - mpz_set_ui (r, 2); - mpz_powm_ui (r, r, ex - ey, my); /* 2^(ex-ey) mod my */ - } - else - mpz_ui_pow_ui (r, 2, ex - ey); - mpz_mul (r, r, mx); - mpz_mod (r, r, my); - - if (quo) /* now 0 <= r < 2^WANTED_BITS*Y */ - { - mpz_fdiv_q_2exp (my, my, WANTED_BITS); /* back to Y */ - mpz_tdiv_qr (mx, r, r, my); - /* oldr = mx*my + newr */ - *quo = mpz_get_si (mx); - q_is_odd = *quo & 1; - } - else if (rnd_q == MPFR_RNDN) /* now 0 <= r < 2Y in the remainder case */ - { - mpz_fdiv_q_2exp (my, my, 1); /* back to Y */ - /* least significant bit of q */ - q_is_odd = mpz_cmpabs (r, my) >= 0; - if (q_is_odd) - mpz_sub (r, r, my); - } - /* now 0 <= |r| < |my|, and if needed, - q_is_odd is the least significant bit of q */ - } - - if (mpz_cmp_ui (r, 0) == 0) - { - inex = mpfr_set_ui (rem, 0, MPFR_RNDN); - /* take into account sign of x */ - if (signx < 0) - mpfr_neg (rem, rem, MPFR_RNDN); - } - else - { - if (rnd_q == MPFR_RNDN) - { - /* FIXME: the comparison 2*r < my could be done more efficiently - at the mpn level */ - mpz_mul_2exp (r, r, 1); - /* if tiny=1, we should compare r with my*2^(ey-ex) */ - if (tiny) - { - if (ex + (mpfr_exp_t) mpz_sizeinbase (r, 2) < - ey + (mpfr_exp_t) mpz_sizeinbase (my, 2)) - compare = 0; /* r*2^ex < my*2^ey */ - else - { - mpz_mul_2exp (my, my, ey - ex); - compare = mpz_cmpabs (r, my); - } - } - else - compare = mpz_cmpabs (r, my); - mpz_fdiv_q_2exp (r, r, 1); - compare = ((compare > 0) || - ((rnd_q == MPFR_RNDN) && (compare == 0) && q_is_odd)); - /* if compare != 0, we need to subtract my to r, and add 1 to quo */ - if (compare) - { - mpz_sub (r, r, my); - if (quo && (rnd_q == MPFR_RNDN)) - *quo += 1; - } - } - /* take into account sign of x */ - if (signx < 0) - mpz_neg (r, r); - inex = mpfr_set_z_2exp (rem, r, ex > ey ? ey : ex, rnd); - } - - if (quo) - *quo *= sign; - - mpz_clear (mx); - mpz_clear (my); - mpz_clear (r); - - return inex; -} - -int -mpfr_remainder (mpfr_ptr rem, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd) -{ - return mpfr_rem1 (rem, (long *) 0, MPFR_RNDN, x, y, rnd); -} - -int -mpfr_remquo (mpfr_ptr rem, long *quo, - mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd) -{ - return mpfr_rem1 (rem, quo, MPFR_RNDN, x, y, rnd); -} - -int -mpfr_fmod (mpfr_ptr rem, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd) -{ - return mpfr_rem1 (rem, (long *) 0, MPFR_RNDZ, x, y, rnd); -} - -int -mpfr_fmodquo (mpfr_ptr rem, long *quo, mpfr_srcptr x, mpfr_srcptr y, - mpfr_rnd_t rnd) -{ - return mpfr_rem1 (rem, quo, MPFR_RNDZ, x, y, rnd); -} |