summaryrefslogtreecommitdiff
path: root/Build/source/libs/mpfr/mpfr-src/src/jn.c
diff options
context:
space:
mode:
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/jn.c')
-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/jn.c334
1 files changed, 0 insertions, 334 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/jn.c b/Build/source/libs/mpfr/mpfr-src/src/jn.c
deleted file mode 100644
index 9ab7743aa3b..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/jn.c
+++ /dev/null
@@ -1,334 +0,0 @@
-/* mpfr_j0, mpfr_j1, mpfr_jn -- Bessel functions of 1st kind, integer order.
- http://www.opengroup.org/onlinepubs/009695399/functions/j0.html
-
-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"
-
-/* Relations: j(-n,z) = (-1)^n j(n,z)
- j(n,-z) = (-1)^n j(n,z)
-*/
-
-static int mpfr_jn_asympt (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
-
-int
-mpfr_j0 (mpfr_ptr res, mpfr_srcptr z, mpfr_rnd_t r)
-{
- return mpfr_jn (res, 0, z, r);
-}
-
-int
-mpfr_j1 (mpfr_ptr res, mpfr_srcptr z, mpfr_rnd_t r)
-{
- return mpfr_jn (res, 1, z, r);
-}
-
-/* Estimate k1 such that z^2/4 = k1 * (k1 + n)
- i.e., k1 = (sqrt(n^2+z^2)-n)/2 = n/2 * (sqrt(1+(z/n)^2) - 1) if n != 0.
- Return k0 = min(2*k1/log(2), ULONG_MAX).
-*/
-static unsigned long
-mpfr_jn_k0 (unsigned long n, mpfr_srcptr z)
-{
- mpfr_t t, u;
- unsigned long k0;
-
- mpfr_init2 (t, 32);
- mpfr_init2 (u, 32);
- if (n == 0)
- {
- mpfr_abs (t, z, MPFR_RNDN); /* t = 2*k1 */
- }
- else
- {
- mpfr_div_ui (t, z, n, MPFR_RNDN);
- mpfr_sqr (t, t, MPFR_RNDN);
- mpfr_add_ui (t, t, 1, MPFR_RNDN);
- mpfr_sqrt (t, t, MPFR_RNDN);
- mpfr_sub_ui (t, t, 1, MPFR_RNDN);
- mpfr_mul_ui (t, t, n, MPFR_RNDN); /* t = 2*k1 */
- }
- /* the following is a 32-bit approximation to nearest to 1/log(2) */
- mpfr_set_str_binary (u, "1.0111000101010100011101100101001");
- mpfr_mul (t, t, u, MPFR_RNDN);
- if (mpfr_fits_ulong_p (t, MPFR_RNDN))
- k0 = mpfr_get_ui (t, MPFR_RNDN);
- else
- k0 = ULONG_MAX;
- mpfr_clear (t);
- mpfr_clear (u);
- return k0;
-}
-
-int
-mpfr_jn (mpfr_ptr res, long n, mpfr_srcptr z, mpfr_rnd_t r)
-{
- int inex;
- int exception = 0;
- unsigned long absn;
- mpfr_prec_t prec, pbound, err;
- mpfr_uprec_t uprec;
- mpfr_exp_t exps, expT, diffexp;
- mpfr_t y, s, t, absz;
- unsigned long k, zz, k0;
- MPFR_GROUP_DECL(g);
- MPFR_SAVE_EXPO_DECL (expo);
- MPFR_ZIV_DECL (loop);
-
- MPFR_LOG_FUNC
- (("n=%d x[%Pu]=%.*Rg rnd=%d", n, mpfr_get_prec (z), mpfr_log_prec, z, r),
- ("res[%Pu]=%.*Rg inexact=%d",
- mpfr_get_prec (res), mpfr_log_prec, res, inex));
-
- absn = SAFE_ABS (unsigned long, n);
-
- if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (z)))
- {
- if (MPFR_IS_NAN (z))
- {
- MPFR_SET_NAN (res);
- MPFR_RET_NAN;
- }
- /* j(n,z) tends to zero when z goes to +Inf or -Inf, oscillating around
- 0. We choose to return +0 in that case. */
- else if (MPFR_IS_INF (z)) /* FIXME: according to j(-n,z) = (-1)^n j(n,z)
- we might want to give a sign depending on
- z and n */
- return mpfr_set_ui (res, 0, r);
- else /* z=0: j(0,0)=1, j(n odd,+/-0) = +/-0 if n > 0, -/+0 if n < 0,
- j(n even,+/-0) = +0 */
- {
- if (n == 0)
- return mpfr_set_ui (res, 1, r);
- else if (absn & 1) /* n odd */
- return (n > 0) ? mpfr_set (res, z, r) : mpfr_neg (res, z, r);
- else /* n even */
- return mpfr_set_ui (res, 0, r);
- }
- }
-
- MPFR_SAVE_EXPO_MARK (expo);
-
- /* check for tiny input for j0: j0(z) = 1 - z^2/4 + ..., more precisely
- |j0(z) - 1| <= z^2/4 for -1 <= z <= 1. */
- if (n == 0)
- MPFR_FAST_COMPUTE_IF_SMALL_INPUT (res, __gmpfr_one, -2 * MPFR_GET_EXP (z),
- 2, 0, r, inex = _inexact; goto end);
-
- /* idem for j1: j1(z) = z/2 - z^3/16 + ..., more precisely
- |j1(z) - z/2| <= |z^3|/16 for -1 <= z <= 1, with the sign of j1(z) - z/2
- being the opposite of that of z. */
- /* TODO: add a test to trigger an error when
- inex = _inexact; goto end
- is forgotten in MPFR_FAST_COMPUTE_IF_SMALL_INPUT below. */
- if (n == 1)
- {
- /* We first compute 2j1(z) = z - z^3/8 + ..., then divide by 2 using
- the "extra" argument of MPFR_FAST_COMPUTE_IF_SMALL_INPUT. But we
- must also handle the underflow case (an overflow is not possible
- for small inputs). If an underflow occurred in mpfr_round_near_x,
- the rounding was to zero or equivalent, and the result is 0, so
- that the division by 2 will give the wanted result. Otherwise...
- The rounded result in unbounded exponent range is res/2. If the
- division by 2 doesn't underflow, it is exact, and we can return
- this result. And an underflow in the division is a real underflow.
- In case of directed rounding mode, the result is correct. But in
- case of rounding to nearest, there is a double rounding problem,
- and the result is 0 iff the result before the division is the
- minimum positive number and _inexact has the same sign as z;
- but in rounding to nearest, res/2 will yield 0 iff |res| is the
- minimum positive number, so that we just need to test the result
- of the division and the sign of _inexact. */
- MPFR_CLEAR_FLAGS ();
- MPFR_FAST_COMPUTE_IF_SMALL_INPUT
- (res, z, -2 * MPFR_GET_EXP (z), 3, 0, r, {
- int inex2 = mpfr_div_2ui (res, res, 1, r);
- if (MPFR_UNLIKELY (r == MPFR_RNDN && MPFR_IS_ZERO (res)) &&
- (MPFR_ASSERTN (inex2 != 0), VSIGN (_inexact) != MPFR_SIGN (z)))
- {
- mpfr_nexttoinf (res);
- inex = - inex2;
- }
- else
- inex = inex2 != 0 ? inex2 : _inexact;
- MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
- goto end;
- });
- }
-
- /* we can use the asymptotic expansion as soon as |z| > p log(2)/2,
- but to get some margin we use it for |z| > p/2 */
- pbound = MPFR_PREC (res) / 2 + 3;
- MPFR_ASSERTN (pbound <= ULONG_MAX);
- MPFR_ALIAS (absz, z, 1, MPFR_EXP (z));
- if (mpfr_cmp_ui (absz, pbound) > 0)
- {
- inex = mpfr_jn_asympt (res, n, z, r);
- if (inex != 0)
- goto end;
- }
-
- MPFR_GROUP_INIT_3 (g, 32, y, s, t);
-
- /* check underflow case: |j(n,z)| <= 1/sqrt(2 Pi n) (ze/2n)^n
- (see algorithms.tex) */
- /* FIXME: the code below doesn't detect all the underflow cases. Either
- this should be done, or the generic code should detect underflows. */
- if (absn > 0)
- {
- /* the following is an upper 32-bit approximation to exp(1)/2 */
- mpfr_set_str_binary (y, "1.0101101111110000101010001011001");
- if (MPFR_IS_POS (z))
- mpfr_mul (y, y, z, MPFR_RNDU);
- else
- {
- mpfr_mul (y, y, z, MPFR_RNDD);
- mpfr_neg (y, y, MPFR_RNDU);
- }
- mpfr_div_ui (y, y, absn, MPFR_RNDU);
- /* now y is an upper approximation to |ze/2n|: y < 2^EXP(y),
- thus |j(n,z)| < 1/2*y^n < 2^(n*EXP(y)-1).
- If n*EXP(y) < emin then we have an underflow.
- Note that if emin = MPFR_EMIN_MIN and j = 1, this inequality
- will never be satisfied.
- Warning: absn is an unsigned long. */
- if ((MPFR_GET_EXP (y) < 0 && absn > - expo.saved_emin)
- || (absn <= - MPFR_EMIN_MIN &&
- MPFR_GET_EXP (y) < expo.saved_emin / (mpfr_exp_t) absn))
- {
- MPFR_GROUP_CLEAR (g);
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_underflow (res, (r == MPFR_RNDN) ? MPFR_RNDZ : r,
- (n % 2) ? ((n > 0) ? MPFR_SIGN(z) : -MPFR_SIGN(z))
- : MPFR_SIGN_POS);
- }
- }
-
- /* the logarithm of the ratio between the largest term in the series
- and the first one is roughly bounded by k0, which we add to the
- working precision to take into account this cancellation */
- /* The following operations avoid integer overflow and ensure that
- prec <= MPFR_PREC_MAX (prec = MPFR_PREC_MAX won't prevent an abort,
- but the failure should be handled cleanly). */
- k0 = mpfr_jn_k0 (absn, z);
- MPFR_LOG_MSG (("k0 = %lu\n", k0));
- uprec = MPFR_PREC_MAX - 2 * MPFR_INT_CEIL_LOG2 (MPFR_PREC_MAX) - 3;
- if (k0 < uprec)
- uprec = k0;
- uprec += MPFR_PREC (res) + 2 * MPFR_INT_CEIL_LOG2 (MPFR_PREC (res)) + 3;
- prec = uprec < MPFR_PREC_MAX ? (mpfr_prec_t) uprec : MPFR_PREC_MAX;
-
- MPFR_ZIV_INIT (loop, prec);
- for (;;)
- {
- MPFR_BLOCK_DECL (flags);
-
- MPFR_GROUP_REPREC_3 (g, prec, y, s, t);
- MPFR_BLOCK (flags, {
- mpfr_pow_ui (t, z, absn, MPFR_RNDN); /* z^|n| */
- mpfr_sqr (y, z, MPFR_RNDN); /* z^2 */
- MPFR_CLEAR_ERANGEFLAG ();
- zz = mpfr_get_ui (y, MPFR_RNDU);
- /* FIXME: The error analysis is incorrect in case of range error. */
- MPFR_ASSERTN (! mpfr_erangeflag_p ()); /* since MPFR_CLEAR_ERANGEFLAG */
- mpfr_div_2ui (y, y, 2, MPFR_RNDN); /* z^2/4 */
- mpfr_fac_ui (s, absn, MPFR_RNDN); /* |n|! */
- mpfr_div (t, t, s, MPFR_RNDN);
- if (absn > 0)
- mpfr_div_2ui (t, t, absn, MPFR_RNDN);
- mpfr_set (s, t, MPFR_RNDN);
- /* note: we assume here that the maximal error bound is proportional to
- 2^exps, which is true also in the case where s=0 */
- exps = MPFR_IS_ZERO (s) ? MPFR_EMIN_MIN : MPFR_GET_EXP (s);
- expT = exps;
- for (k = 1; ; k++)
- {
- MPFR_LOG_MSG (("loop on k, k = %lu\n", k));
- mpfr_mul (t, t, y, MPFR_RNDN);
- mpfr_neg (t, t, MPFR_RNDN);
- /* Mathematically: absn <= LONG_MAX + 1 <= (ULONG_MAX + 1) / 2,
- and in practice, k is not very large, so that one should have
- k + absn <= ULONG_MAX. */
- MPFR_ASSERTN (absn <= ULONG_MAX - k);
- if (k + absn <= ULONG_MAX / k)
- mpfr_div_ui (t, t, k * (k + absn), MPFR_RNDN);
- else
- {
- mpfr_div_ui (t, t, k, MPFR_RNDN);
- mpfr_div_ui (t, t, k + absn, MPFR_RNDN);
- }
- /* see above note */
- exps = MPFR_IS_ZERO (s) ? MPFR_EMIN_MIN : MPFR_GET_EXP (t);
- if (exps > expT)
- expT = exps;
- mpfr_add (s, s, t, MPFR_RNDN);
- exps = MPFR_IS_ZERO (s) ? MPFR_EMIN_MIN : MPFR_GET_EXP (s);
- if (exps > expT)
- expT = exps;
- /* Above it has been checked that k + absn <= ULONG_MAX. */
- if (MPFR_GET_EXP (t) + (mpfr_exp_t) prec <= exps &&
- zz / (2 * k) < k + absn)
- break;
- }
- });
- /* the error is bounded by (4k^2+21/2k+7) ulp(s)*2^(expT-exps)
- <= (k+2)^2 ulp(s)*2^(2+expT-exps) */
- diffexp = expT - exps;
- err = 2 * MPFR_INT_CEIL_LOG2(k + 2) + 2;
- /* FIXME: Can an overflow occur in the following sum? */
- MPFR_ASSERTN (diffexp >= 0 && err >= 0 &&
- diffexp <= MPFR_PREC_MAX - err);
- err += diffexp;
- if (MPFR_LIKELY (MPFR_CAN_ROUND (s, prec - err, MPFR_PREC(res), r)))
- {
- if (MPFR_LIKELY (! (MPFR_UNDERFLOW (flags) ||
- MPFR_OVERFLOW (flags))))
- break;
- /* The error analysis is incorrect in case of exception.
- If an underflow or overflow occurred, try once more in
- a larger precision, and if this happens a second time,
- then abort to avoid a probable infinite loop. This is
- a problem that must be fixed! */
- MPFR_ASSERTN (! exception);
- exception = 1;
- }
- /* the expected number of lost bits is k0, if err is larger than k0
- most probably there is a cancellation in the series, thus we add
- err - k0 bits to prec */
- if (err > k0)
- MPFR_INC_PREC (prec, err - k0);
- MPFR_ZIV_NEXT (loop, prec);
- }
- MPFR_ZIV_FREE (loop);
-
- inex = ((n >= 0) || ((n & 1) == 0)) ? mpfr_set (res, s, r)
- : mpfr_neg (res, s, r);
-
- MPFR_GROUP_CLEAR (g);
-
- end:
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (res, inex, r);
-}
-
-#define MPFR_JN
-#include "jyn_asympt.c"