summaryrefslogtreecommitdiff
path: root/Build/source/libs/mpfr/mpfr-src/src/cos.c
diff options
context:
space:
mode:
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/cos.c')
-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/cos.c301
1 files changed, 0 insertions, 301 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/cos.c b/Build/source/libs/mpfr/mpfr-src/src/cos.c
deleted file mode 100644
index 61a9de20b08..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/cos.c
+++ /dev/null
@@ -1,301 +0,0 @@
-/* mpfr_cos -- cosine of a floating-point number
-
-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"
-
-static int
-mpfr_cos_fast (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
-{
- int inex;
-
- inex = mpfr_sincos_fast (NULL, y, x, rnd_mode);
- inex = inex >> 2; /* 0: exact, 1: rounded up, 2: rounded down */
- return (inex == 2) ? -1 : inex;
-}
-
-/* f <- 1 - r/2! + r^2/4! + ... + (-1)^l r^l/(2l)! + ...
- Assumes |r| < 1/2, and f, r have the same precision.
- Returns e such that the error on f is bounded by 2^e ulps.
-*/
-static int
-mpfr_cos2_aux (mpfr_ptr f, mpfr_srcptr r)
-{
- mpz_t x, t, s;
- mpfr_exp_t ex, l, m;
- mpfr_prec_t p, q;
- unsigned long i, maxi, imax;
-
- MPFR_ASSERTD(mpfr_get_exp (r) <= -1);
-
- /* compute minimal i such that i*(i+1) does not fit in an unsigned long,
- assuming that there are no padding bits. */
- maxi = 1UL << (sizeof(unsigned long) * CHAR_BIT / 2);
- if (maxi * (maxi / 2) == 0) /* test checked at compile time */
- {
- /* can occur only when there are padding bits. */
- /* maxi * (maxi-1) is representable iff maxi * (maxi / 2) != 0 */
- do
- maxi /= 2;
- while (maxi * (maxi / 2) == 0);
- }
-
- mpz_init (x);
- mpz_init (s);
- mpz_init (t);
- ex = mpfr_get_z_2exp (x, r); /* r = x*2^ex */
-
- /* Remove trailing zeroes.
- Since x comes from a regular MPFR number, due to the constraints on the
- exponent and the precision, there can be no integer overflow below. */
- l = mpz_scan1 (x, 0);
- ex += l;
- mpz_fdiv_q_2exp (x, x, l);
-
- /* since |r| < 1, r = x*2^ex, and x is an integer, necessarily ex < 0 */
-
- p = mpfr_get_prec (f); /* same than r */
- /* bound for number of iterations */
- imax = p / (-mpfr_get_exp (r));
- imax += (imax == 0);
- q = 2 * MPFR_INT_CEIL_LOG2(imax) + 4; /* bound for (3l)^2 */
-
- mpz_set_ui (s, 1); /* initialize sum with 1 */
- mpz_mul_2exp (s, s, p + q); /* scale all values by 2^(p+q) */
- mpz_set (t, s); /* invariant: t is previous term */
- for (i = 1; (m = mpz_sizeinbase (t, 2)) >= q; i += 2)
- {
- /* adjust precision of x to that of t */
- l = mpz_sizeinbase (x, 2);
- if (l > m)
- {
- l -= m;
- mpz_fdiv_q_2exp (x, x, l);
- ex += l;
- }
- /* multiply t by r */
- mpz_mul (t, t, x);
- mpz_fdiv_q_2exp (t, t, -ex);
- /* divide t by i*(i+1) */
- if (i < maxi)
- mpz_fdiv_q_ui (t, t, i * (i + 1));
- else
- {
- mpz_fdiv_q_ui (t, t, i);
- mpz_fdiv_q_ui (t, t, i + 1);
- }
- /* if m is the (current) number of bits of t, we can consider that
- all operations on t so far had precision >= m, so we can prove
- by induction that the relative error on t is of the form
- (1+u)^(3l)-1, where |u| <= 2^(-m), and l=(i+1)/2 is the # of loops.
- Since |(1+x^2)^(1/x) - 1| <= 4x/3 for |x| <= 1/2,
- for |u| <= 1/(3l)^2, the absolute error is bounded by
- 4/3*(3l)*2^(-m)*t <= 4*l since |t| < 2^m.
- Therefore the error on s is bounded by 2*l*(l+1). */
- /* add or subtract to s */
- if (i % 4 == 1)
- mpz_sub (s, s, t);
- else
- mpz_add (s, s, t);
- }
-
- mpfr_set_z (f, s, MPFR_RNDN);
- mpfr_div_2ui (f, f, p + q, MPFR_RNDN);
-
- mpz_clear (x);
- mpz_clear (s);
- mpz_clear (t);
-
- l = (i - 1) / 2; /* number of iterations */
- return 2 * MPFR_INT_CEIL_LOG2 (l + 1) + 1; /* bound is 2l(l+1) */
-}
-
-int
-mpfr_cos (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
-{
- mpfr_prec_t K0, K, precy, m, k, l;
- int inexact, reduce = 0;
- mpfr_t r, s, xr, c;
- mpfr_exp_t exps, cancel = 0, expx;
- MPFR_ZIV_DECL (loop);
- MPFR_SAVE_EXPO_DECL (expo);
- MPFR_GROUP_DECL (group);
-
- 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_IS_INF (x))
- {
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- else
- {
- MPFR_ASSERTD (MPFR_IS_ZERO (x));
- return mpfr_set_ui (y, 1, rnd_mode);
- }
- }
-
- MPFR_SAVE_EXPO_MARK (expo);
-
- /* cos(x) = 1-x^2/2 + ..., so error < 2^(2*EXP(x)-1) */
- expx = MPFR_GET_EXP (x);
- MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, __gmpfr_one, -2 * expx,
- 1, 0, rnd_mode, expo, {});
-
- /* Compute initial precision */
- precy = MPFR_PREC (y);
-
- if (precy >= MPFR_SINCOS_THRESHOLD)
- {
- inexact = mpfr_cos_fast (y, x, rnd_mode);
- goto end;
- }
-
- K0 = __gmpfr_isqrt (precy / 3);
- m = precy + 2 * MPFR_INT_CEIL_LOG2 (precy) + 2 * K0 + 4;
-
- if (expx >= 3)
- {
- reduce = 1;
- /* As expx + m - 1 will silently be converted into mpfr_prec_t
- in the mpfr_init2 call, the assert below may be useful to
- avoid undefined behavior. */
- MPFR_ASSERTN (expx + m - 1 <= MPFR_PREC_MAX);
- mpfr_init2 (c, expx + m - 1);
- mpfr_init2 (xr, m);
- }
-
- MPFR_GROUP_INIT_2 (group, m, r, s);
- MPFR_ZIV_INIT (loop, m);
- for (;;)
- {
- /* If |x| >= 4, first reduce x cmod (2*Pi) into xr, using mpfr_remainder:
- let e = EXP(x) >= 3, and m the target precision:
- (1) c <- 2*Pi [precision e+m-1, nearest]
- (2) xr <- remainder (x, c) [precision m, nearest]
- We have |c - 2*Pi| <= 1/2ulp(c) = 2^(3-e-m)
- |xr - x - k c| <= 1/2ulp(xr) <= 2^(1-m)
- |k| <= |x|/(2*Pi) <= 2^(e-2)
- Thus |xr - x - 2kPi| <= |k| |c - 2Pi| + 2^(1-m) <= 2^(2-m).
- It follows |cos(xr) - cos(x)| <= 2^(2-m). */
- if (reduce)
- {
- mpfr_const_pi (c, MPFR_RNDN);
- mpfr_mul_2ui (c, c, 1, MPFR_RNDN); /* 2Pi */
- mpfr_remainder (xr, x, c, MPFR_RNDN);
- if (MPFR_IS_ZERO(xr))
- goto ziv_next;
- /* now |xr| <= 4, thus r <= 16 below */
- mpfr_sqr (r, xr, MPFR_RNDU); /* err <= 1 ulp */
- }
- else
- mpfr_sqr (r, x, MPFR_RNDU); /* err <= 1 ulp */
-
- /* now |x| < 4 (or xr if reduce = 1), thus |r| <= 16 */
-
- /* we need |r| < 1/2 for mpfr_cos2_aux, i.e., EXP(r) - 2K <= -1 */
- K = K0 + 1 + MAX(0, MPFR_GET_EXP(r)) / 2;
- /* since K0 >= 0, if EXP(r) < 0, then K >= 1, thus EXP(r) - 2K <= -3;
- otherwise if EXP(r) >= 0, then K >= 1/2 + EXP(r)/2, thus
- EXP(r) - 2K <= -1 */
-
- MPFR_SET_EXP (r, MPFR_GET_EXP (r) - 2 * K); /* Can't overflow! */
-
- /* s <- 1 - r/2! + ... + (-1)^l r^l/(2l)! */
- l = mpfr_cos2_aux (s, r);
- /* l is the error bound in ulps on s */
- MPFR_SET_ONE (r);
- for (k = 0; k < K; k++)
- {
- mpfr_sqr (s, s, MPFR_RNDU); /* err <= 2*olderr */
- MPFR_SET_EXP (s, MPFR_GET_EXP (s) + 1); /* Can't overflow */
- mpfr_sub (s, s, r, MPFR_RNDN); /* err <= 4*olderr */
- if (MPFR_IS_ZERO(s))
- goto ziv_next;
- MPFR_ASSERTD (MPFR_GET_EXP (s) <= 1);
- }
-
- /* The absolute error on s is bounded by (2l+1/3)*2^(2K-m)
- 2l+1/3 <= 2l+1.
- If |x| >= 4, we need to add 2^(2-m) for the argument reduction
- by 2Pi: if K = 0, this amounts to add 4 to 2l+1/3, i.e., to add
- 2 to l; if K >= 1, this amounts to add 1 to 2*l+1/3. */
- l = 2 * l + 1;
- if (reduce)
- l += (K == 0) ? 4 : 1;
- k = MPFR_INT_CEIL_LOG2 (l) + 2 * K;
- /* now the error is bounded by 2^(k-m) = 2^(EXP(s)-err) */
-
- exps = MPFR_GET_EXP (s);
- if (MPFR_LIKELY (MPFR_CAN_ROUND (s, exps + m - k, precy, rnd_mode)))
- break;
-
- if (MPFR_UNLIKELY (exps == 1))
- /* s = 1 or -1, and except x=0 which was already checked above,
- cos(x) cannot be 1 or -1, so we can round if the error is less
- than 2^(-precy) for directed rounding, or 2^(-precy-1) for rounding
- to nearest. */
- {
- if (m > k && (m - k >= precy + (rnd_mode == MPFR_RNDN)))
- {
- /* If round to nearest or away, result is s = 1 or -1,
- otherwise it is round(nexttoward (s, 0)). However in order to
- have the inexact flag correctly set below, we set |s| to
- 1 - 2^(-m) in all cases. */
- mpfr_nexttozero (s);
- break;
- }
- }
-
- if (exps < cancel)
- {
- m += cancel - exps;
- cancel = exps;
- }
-
- ziv_next:
- MPFR_ZIV_NEXT (loop, m);
- MPFR_GROUP_REPREC_2 (group, m, r, s);
- if (reduce)
- {
- mpfr_set_prec (xr, m);
- mpfr_set_prec (c, expx + m - 1);
- }
- }
- MPFR_ZIV_FREE (loop);
- inexact = mpfr_set (y, s, rnd_mode);
- MPFR_GROUP_CLEAR (group);
- if (reduce)
- {
- mpfr_clear (xr);
- mpfr_clear (c);
- }
-
- end:
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (y, inexact, rnd_mode);
-}