diff options
| -rw-r--r-- | Makefile.am | 2 | ||||
| -rw-r--r-- | algorithms.tex | 46 | ||||
| -rw-r--r-- | jn.c | 140 | ||||
| -rw-r--r-- | mpfr.h | 4 | ||||
| -rw-r--r-- | mpfr.texi | 11 | ||||
| -rw-r--r-- | tests/Makefile.am | 2 | ||||
| -rw-r--r-- | tests/reuse.c | 4 | ||||
| -rw-r--r-- | tests/tj0.c | 96 | ||||
| -rw-r--r-- | tests/tj1.c | 84 | ||||
| -rw-r--r-- | tests/tjn.c | 136 |
10 files changed, 521 insertions, 4 deletions
diff --git a/Makefile.am b/Makefile.am index 0ed9f3991..e58367370 100644 --- a/Makefile.am +++ b/Makefile.am @@ -7,7 +7,7 @@ include_HEADERS = mpfr.h mpf2mpfr.h lib_LTLIBRARIES = libmpfr.la -libmpfr_la_SOURCES = mpfr.h mpf2mpfr.h mpfr-gmp.h mpfr-impl.h mpfr-longlong.h mpfr-test.h exceptions.c extract.c uceil_exp2.c uceil_log2.c ufloor_log2.c add.c add1.c add_ui.c agm.c clear.c cmp.c cmp_abs.c cmp_si.c cmp_ui.c comparisons.c div_2exp.c div_2si.c div_2ui.c div.c div_ui.c dump.c eq.c exp10.c exp2.c exp3.c exp.c frac.c get_d.c get_exp.c get_str.c init.c inp_str.c isinteger.c isinf.c isnan.c isnum.c const_log2.c log.c mul_2exp.c mul_2si.c mul_2ui.c mul.c mul_ui.c neg.c next.c out_str.c const_pi.c pow.c pow_si.c pow_ui.c print_raw.c print_rnd_mode.c random2.c random.c reldiff.c round_prec.c set.c setmax.c setmin.c set_d.c set_dfl_prec.c set_exp.c set_rnd.c set_f.c set_prc_raw.c set_prec.c set_q.c set_si.c set_str.c set_str_raw.c set_ui.c set_z.c sqrt.c sqrt_ui.c sub.c sub1.c sub_ui.c rint.c ui_div.c ui_sub.c urandomb.c get_z_exp.c swap.c factorial.c cosh.c sinh.c tanh.c acosh.c asinh.c atanh.c atan.c cmp2.c exp_2.c asin.c const_euler.c cos.c sin.c tan.c fma.c hypot.c log1p.c expm1.c log2.c log10.c ui_pow.c ui_pow_ui.c minmax.c dim.c copysign.c gmp_op.c init2.c acos.c sin_cos.c set_nan.c set_inf.c powerof2.c gamma.c set_ld.c get_ld.c cbrt.c volatile.c fits_s.h fits_sshort.c fits_sint.c fits_slong.c fits_u.h fits_ushort.c fits_uint.c fits_ulong.c fits_uintmax.c fits_intmax.c get_si.c get_ui.c zeta.c cmp_d.c erf.c inits.c inits2.c clears.c sgn.c check.c sub1sp.c version.c mpn_exp.c mpfr-gmp.c mp_clz_tab.c sum.c add1sp.c free_cache.c si_op.c cmp_ld.c set_ui_2exp.c set_si_2exp.c set_uj.c set_sj.c get_sj.c get_uj.c get_z.c iszero.c cache.c sqr.c int_ceil_log2.c isqrt.c strtofr.c pow_z.c logging.c mulders.c get_f.c round_p.c erfc.c atan2.c subnormal.c const_catalan.c root.c gen_inverse.h sec.c csc.c cot.c eint.c sech.c csch.c coth.c round_near_x.c constant.c abort_prec_max.c stack_interface.c lngamma.c zeta_ui.c set_d64.c get_d64.c +libmpfr_la_SOURCES = mpfr.h mpf2mpfr.h mpfr-gmp.h mpfr-impl.h mpfr-longlong.h mpfr-test.h exceptions.c extract.c uceil_exp2.c uceil_log2.c ufloor_log2.c add.c add1.c add_ui.c agm.c clear.c cmp.c cmp_abs.c cmp_si.c cmp_ui.c comparisons.c div_2exp.c div_2si.c div_2ui.c div.c div_ui.c dump.c eq.c exp10.c exp2.c exp3.c exp.c frac.c get_d.c get_exp.c get_str.c init.c inp_str.c isinteger.c isinf.c isnan.c isnum.c const_log2.c log.c mul_2exp.c mul_2si.c mul_2ui.c mul.c mul_ui.c neg.c next.c out_str.c const_pi.c pow.c pow_si.c pow_ui.c print_raw.c print_rnd_mode.c random2.c random.c reldiff.c round_prec.c set.c setmax.c setmin.c set_d.c set_dfl_prec.c set_exp.c set_rnd.c set_f.c set_prc_raw.c set_prec.c set_q.c set_si.c set_str.c set_str_raw.c set_ui.c set_z.c sqrt.c sqrt_ui.c sub.c sub1.c sub_ui.c rint.c ui_div.c ui_sub.c urandomb.c get_z_exp.c swap.c factorial.c cosh.c sinh.c tanh.c acosh.c asinh.c atanh.c atan.c cmp2.c exp_2.c asin.c const_euler.c cos.c sin.c tan.c fma.c hypot.c log1p.c expm1.c log2.c log10.c ui_pow.c ui_pow_ui.c minmax.c dim.c copysign.c gmp_op.c init2.c acos.c sin_cos.c set_nan.c set_inf.c powerof2.c gamma.c set_ld.c get_ld.c cbrt.c volatile.c fits_s.h fits_sshort.c fits_sint.c fits_slong.c fits_u.h fits_ushort.c fits_uint.c fits_ulong.c fits_uintmax.c fits_intmax.c get_si.c get_ui.c zeta.c cmp_d.c erf.c inits.c inits2.c clears.c sgn.c check.c sub1sp.c version.c mpn_exp.c mpfr-gmp.c mp_clz_tab.c sum.c add1sp.c free_cache.c si_op.c cmp_ld.c set_ui_2exp.c set_si_2exp.c set_uj.c set_sj.c get_sj.c get_uj.c get_z.c iszero.c cache.c sqr.c int_ceil_log2.c isqrt.c strtofr.c pow_z.c logging.c mulders.c get_f.c round_p.c erfc.c atan2.c subnormal.c const_catalan.c root.c gen_inverse.h sec.c csc.c cot.c eint.c sech.c csch.c coth.c round_near_x.c constant.c abort_prec_max.c stack_interface.c lngamma.c zeta_ui.c set_d64.c get_d64.c jn.c libmpfr_la_LIBADD = @LIBOBJS@ diff --git a/algorithms.tex b/algorithms.tex index f2bf6f90c..e54c0f56c 100644 --- a/algorithms.tex +++ b/algorithms.tex @@ -456,7 +456,7 @@ error is bounded by $2k$ ulps. If the rounding are not away from zero, the following lemma is still useful \cite{Graillat05}: -\begin{lemma} +\begin{lemma} \label{lemma_graillat} Let $\delta_1, \ldots, \delta_n$ be $n$ real values such that $|\delta_i| \leq \epsilon$, for $n \epsilon < 1$. Then we can write $\prod_{i=1}^n (1+\delta_i) @@ -2995,6 +2995,50 @@ this gives a total bound of $(18n+51) 2^{-p} v_{n+1}$, which is less than $(18n+51) \ulp(r)$, or twice this in the improbable case where there is an exponent loss in the final subtraction $r = \circ(v_{n+1}-w)$. +\subsection{The Bessel function} + +The Bessel function $J_n(z)$ of first kind and integer order $n$ +is defined as follows \cite[Eq.~(9.1.10)]{AbSt73}: +\[ J_n(z) = (z/2)^n \sum_{k=0}^{\infty} \frac{(-z^2/4)^k}{k! (k+n)!}. \] +We use the following algorithm, with working precision $w$, and rounding +to nearest: +\begin{quote} +$x \leftarrow \circ(z^n)$ \\ +$y \leftarrow \circ(z^2)/4$ [division by $4$ is exact] \\ +$u \leftarrow \circ(n!)$ \\ +$t \leftarrow \circ(x/u)/2^n$ [division by $2^n$ is exact] \\ +$s \leftarrow t$ \\ +for $k$ from $1$ do \\ +\q $t \leftarrow -\circ(ty)$ \\ +\q $t \leftarrow \circ(t/k)$ \\ +\q $t \leftarrow \circ(t/(k+n))$ \\ +\q $s \leftarrow \circ(s+t)$ \\ +\q if $|t| < \ulp(s)$ and $z^2 \leq 2k(k+n)$ then return $s$. \\ +\end{quote} +The condition $z^2 \leq 2k(k+n)$ ensures that the next term of the +expansion is smaller than $|t|/2$, thus the sum of the remaining terms +is smaller than $|t| < \ulp(s)$. +Using Higham's method, with $\theta$ denoting a random variable of value +$|\theta| \leq 2^{-w}$ --- different instances of $\theta$ denoting +different values --- we can write $x = z^n (1+\theta)$, +$y = z^2/4 (1+\theta)$, +and before the for-loop $s = t = (z/2)^n/n! (1+\theta)^3$. +Now write $t = (z/2)^n (-z^2/4)^k / (k! (k+n)!) (1+\theta)^{e_k}$ at the end of +the for-loop with index $k$; each loop involves a factor $(1+\theta)^4$, +thus we have $e_k = 4k+3$. +Now let $T$ be an upper bound on the values of $|t|$ and $|s|$ during the +for-loop, and assume we exit at $k=K$. +The roundoff error in the additions +$\circ(s+t)$, including the error in the series +truncation, is bounded by $(K/2+1) \ulp(T)$. +The error in the value of $t$ at step $k$ is bounded by $\epsilon_k := +T |(1+\theta)^{4k+3} +-1|$; if we assume $(4k+3) 2^{-w} \leq 1/2$, Lemma~\ref{lemma_graillat} +yields $\epsilon_k \leq 2 T (4k+3) 2^{-w}$. Summing from $k=0$ to $K$, +this gives an absolute error bound on $s$ at the end of the for-loop of: +\[ (K/2+1) \ulp(T) + 2 (2K^2+5K+3) 2^{-w} T \leq (4K^2+21/2K+7) \ulp(T), \] +where we used $2^{-w} T \leq \ulp(T)$. + \subsection{Summary} \begin{table} @@ -0,0 +1,140 @@ +/* mpfr_j0, mpfr_j1, mpfr_jn -- Bessel functions of 1st kind and integer order. + http://www.opengroup.org/onlinepubs/009695399/functions/j0.html + +Copyright 2007 Free Software Foundation, Inc. +Contributed by the Arenaire and Cacao projects, INRIA. + +This file is part of the MPFR Library. + +The 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 2.1 of the License, or (at your +option) any later version. + +The 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 MPFR Library; see the file COPYING.LIB. If not, 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) */ + +int +mpfr_j0 (mpfr_ptr res, mpfr_srcptr z, mp_rnd_t r) +{ + return mpfr_jn (res, z, 0, r); +} + +int +mpfr_j1 (mpfr_ptr res, mpfr_srcptr z, mp_rnd_t r) +{ + return mpfr_jn (res, z, 1, r); +} + +int +mpfr_jn (mpfr_ptr res, mpfr_srcptr z, int n, mp_rnd_t r) +{ + int inex, absn; + mp_prec_t prec, err; + mp_exp_t exps, expT; + mpfr_t y, s, t; + unsigned long k, zz; + MPFR_ZIV_DECL (loop); + + MPFR_LOG_FUNC (("x[%#R]=%R n=%d rnd=%d", z, z, n, r), + ("y[%#R]=%R inexact=%d", res, res, inex)); + + absn = (n >= 0) ? n : -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); + } + } + + prec = MPFR_PREC (res) + MPFR_INT_CEIL_LOG2 (MPFR_PREC (res)) + 3; + + mpfr_init2 (y, prec); + mpfr_init2 (s, prec); + mpfr_init2 (t, prec); + + MPFR_ZIV_INIT (loop, prec); + for (;;) + { + mpfr_pow_ui (t, z, absn, GMP_RNDN); + mpfr_mul (y, z, z, GMP_RNDN); + zz = mpfr_get_ui (y, GMP_RNDU); + MPFR_ASSERTN (zz < ULONG_MAX); + mpfr_div_2ui (y, y, 2, GMP_RNDN); + mpfr_fac_ui (s, absn, GMP_RNDN); + mpfr_div (t, t, s, GMP_RNDN); + if (absn > 0) + mpfr_div_2ui (t, t, absn, GMP_RNDN); + mpfr_set (s, t, GMP_RNDN); + exps = MPFR_EXP (s); + expT = exps; + for (k = 1; ; k++) + { + mpfr_mul (t, t, y, GMP_RNDN); + mpfr_neg (t, t, GMP_RNDN); + if (k + absn <= ULONG_MAX / k) + mpfr_div_ui (t, t, k * (k + absn), GMP_RNDN); + else + { + mpfr_div_ui (t, t, k, GMP_RNDN); + mpfr_div_ui (t, t, absn, GMP_RNDN); + } + exps = MPFR_EXP (t); + if (exps > expT) + expT = exps; + mpfr_add (s, s, t, GMP_RNDN); + exps = MPFR_EXP (s); + if (exps > expT) + expT = exps; + if (MPFR_EXP (t) + (mp_exp_t) prec <= MPFR_EXP (s) && + zz / (2 * k) < k + n) + 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) */ + err = 2 * MPFR_INT_CEIL_LOG2(k + 2) + 2 + expT - MPFR_EXP (s); + if (MPFR_LIKELY (MPFR_CAN_ROUND (s, prec - err, MPFR_PREC(res), r))) + break; + MPFR_ZIV_NEXT (loop, prec); + } + MPFR_ZIV_FREE (loop); + + inex = (n >= 0) ? mpfr_set (res, s, r) : mpfr_neg (res, s, r); + + mpfr_clear (y); + mpfr_clear (s); + mpfr_clear (t); + + return inex; +} @@ -513,6 +513,10 @@ __MPFR_DECLSPEC int mpfr_zeta _MPFR_PROTO ((mpfr_ptr,mpfr_srcptr,mpfr_rnd_t)); __MPFR_DECLSPEC int mpfr_zeta_ui _MPFR_PROTO ((mpfr_ptr,unsigned long,mpfr_rnd_t)); __MPFR_DECLSPEC int mpfr_fac_ui _MPFR_PROTO ((mpfr_ptr, unsigned long int, mpfr_rnd_t)); +__MPFR_DECLSPEC int mpfr_j0 _MPFR_PROTO ((mpfr_ptr,mpfr_srcptr,mpfr_rnd_t)); +__MPFR_DECLSPEC int mpfr_j1 _MPFR_PROTO ((mpfr_ptr,mpfr_srcptr,mpfr_rnd_t)); +__MPFR_DECLSPEC int mpfr_jn _MPFR_PROTO ((mpfr_ptr, mpfr_srcptr, int, + mpfr_rnd_t)); __MPFR_DECLSPEC int mpfr_min _MPFR_PROTO ((mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t)); @@ -1482,6 +1482,17 @@ Set @var{rop} to the value of the complementary error function on @var{op}, rounded in the direction @var{rnd}. @end deftypefun +@deftypefun int mpfr_j0 (mpfr_t @var{rop}, mpfr_t @var{op}, mp_rnd_t @var{rnd}) +@deftypefunx int mpfr_j1 (mpfr_t @var{rop}, mpfr_t @var{op}, mp_rnd_t @var{rnd}) +@deftypefunx int mpfr_jn (mpfr_t @var{rop}, mpfr_t @var{op}, int @var{n}, mp_rnd_t @var{rnd}) +Set @var{rop} to the value of the first order Bessel function of order 0, 1 +and @var{n} on @var{op}, rounded in the direction @var{rnd}. When @var{op} is +NaN, @var{rop} is always set to NaN. When @var{op} is plus or minus Infinity, +@var{rop} is set to +0. When @var{op} is zero, and @var{n} is not zero, +@var{rop} is +0 or -0 depending on the parity and sign of @var{n}, and the +sign of @var{op}. +@end deftypefun + @deftypefun int mpfr_fma (mpfr_t @var{rop}, mpfr_t @var{op1}, mpfr_t @var{op2}, mpfr_t @var{op3}, mp_rnd_t @var{rnd}) Set @var{rop} to @math{@var{op1} @GMPtimes{} @var{op2} + @var{op3}}, rounded in the direction @var{rnd}. diff --git a/tests/Makefile.am b/tests/Makefile.am index f75349f0b..179e11e82 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -1,6 +1,6 @@ AUTOMAKE_OPTIONS = 1.6 gnu $(top_builddir)/ansi2knr -check_PROGRAMS = tversion tinternals tinits tsgn tcheck tisnan texceptions tset_exp tset tabs tset_d tset_f tset_q tset_si tset_str tset_z tset_ld tset_sj tswap tcopysign tcmp tcmp2 tcmpabs tcmp_d tcmp_ld tcomparisons teq tadd tsub tmul tdiv tsub1sp tadd1sp tadd_ui tsub_ui tcmp_ui tdiv_ui tmul_ui tsqrt_ui tui_div tui_sub tgmpop tsi_op tmul_2exp tfma tsum tdim tminmax tnext tfits tget_d tget_d_2exp tget_z tget_str tget_sj tout_str tinp_str toutimpl tcan_round tround_prec tsqrt tconst_log2 tconst_pi tconst_euler trandom ttrunc trint tfrac texp texp2 texpm1 tlog tlog2 tlog10 tlog1p tpow tui_pow tpow3 tcosh tsinh ttanh tacosh tasinh tatanh thyperbolic tasin tacos tcos tatan tsin ttan tsin_cos tagm thypot tfactorial tgamma terf tcbrt tzeta mpf_compat mpfr_compat reuse tsqr tstrtofr tpow_z tget_f tconst_catalan troot tsec tcsc tcot teint tcoth tcsch tsech tstckintc tsubnormal tlngamma tzeta_ui tget_ld_2exp tget_set_d64 +check_PROGRAMS = tversion tinternals tinits tsgn tcheck tisnan texceptions tset_exp tset tabs tset_d tset_f tset_q tset_si tset_str tset_z tset_ld tset_sj tswap tcopysign tcmp tcmp2 tcmpabs tcmp_d tcmp_ld tcomparisons teq tadd tsub tmul tdiv tsub1sp tadd1sp tadd_ui tsub_ui tcmp_ui tdiv_ui tmul_ui tsqrt_ui tui_div tui_sub tgmpop tsi_op tmul_2exp tfma tsum tdim tminmax tnext tfits tget_d tget_d_2exp tget_z tget_str tget_sj tout_str tinp_str toutimpl tcan_round tround_prec tsqrt tconst_log2 tconst_pi tconst_euler trandom ttrunc trint tfrac texp texp2 texpm1 tlog tlog2 tlog10 tlog1p tpow tui_pow tpow3 tcosh tsinh ttanh tacosh tasinh tatanh thyperbolic tasin tacos tcos tatan tsin ttan tsin_cos tagm thypot tfactorial tgamma terf tcbrt tzeta mpf_compat mpfr_compat reuse tsqr tstrtofr tpow_z tget_f tconst_catalan troot tsec tcsc tcot teint tcoth tcsch tsech tstckintc tsubnormal tlngamma tzeta_ui tget_ld_2exp tget_set_d64 tj0 tj1 tjn EXTRA_DIST = tgeneric.c tgeneric_ui.c mpf_compat.h inp_str.data diff --git a/tests/reuse.c b/tests/reuse.c index cdd0092fb..1c1fb80dd 100644 --- a/tests/reuse.c +++ b/tests/reuse.c @@ -590,8 +590,10 @@ main (void) test2 (mpfr_csc, "mpfr_csc", p, rnd); test2 (mpfr_cot, "mpfr_cot", p, rnd); - test2 (mpfr_erf, "mpfr_erf", p, rnd); + test2 (mpfr_erf, "mpfr_erf", p, rnd); test2 (mpfr_erfc, "mpfr_erfc", p, rnd); + test2 (mpfr_j0, "mpfr_j0", p, rnd); + test2 (mpfr_j1, "mpfr_j1", p, rnd); test2 (mpfr_zeta, "mpfr_zeta", p, rnd); test2 (mpfr_gamma, "mpfr_gamma", p, rnd); diff --git a/tests/tj0.c b/tests/tj0.c new file mode 100644 index 000000000..2f80eb8fb --- /dev/null +++ b/tests/tj0.c @@ -0,0 +1,96 @@ +/* tj0 -- test file for the Bessel function of first kind (order 0) + +Copyright 2007 Free Software Foundation, Inc. +Contributed by the Arenaire and Cacao projects, INRIA. + +This file is part of the MPFR Library. + +The 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 2.1 of the License, or (at your +option) any later version. + +The 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 MPFR Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, +MA 02110-1301, USA. */ + +#include <stdio.h> +#include <stdlib.h> + +#include "mpfr-test.h" + +#define TEST_FUNCTION mpfr_zeta +#include "tgeneric.c" + +int +main (int argc, char *argv[]) +{ + mpfr_t x, y; + + tests_start_mpfr (); + + mpfr_init (x); + mpfr_init (y); + + /* special values */ + mpfr_set_nan (x); + mpfr_j0 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_nan_p (y)); + + mpfr_set_inf (x, 1); /* +Inf */ + mpfr_j0 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); + + mpfr_set_inf (x, -1); /* -Inf */ + mpfr_j0 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); + + mpfr_set_ui (x, 0, GMP_RNDN); /* +0 */ + mpfr_j0 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(+0)=1 */ + + mpfr_set_ui (x, 0, GMP_RNDN); + mpfr_neg (x, x, GMP_RNDN); /* -0 */ + mpfr_j0 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(-0)=1 */ + + mpfr_set_prec (x, 53); + mpfr_set_prec (y, 53); + + mpfr_set_ui (x, 1, GMP_RNDN); + mpfr_j0 (y, x, GMP_RNDN); + mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_j0 for x=1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + + mpfr_set_si (x, -1, GMP_RNDN); + mpfr_j0 (y, x, GMP_RNDN); + mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_j0 for x=-1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + + mpfr_clear (x); + mpfr_clear (y); + + test_generic (2, 100, 1); + + tests_end_mpfr (); + + return 0; +} diff --git a/tests/tj1.c b/tests/tj1.c new file mode 100644 index 000000000..5151aa5af --- /dev/null +++ b/tests/tj1.c @@ -0,0 +1,84 @@ +/* tj1 -- test file for the Bessel function of first kind (order 1) + +Copyright 2007 Free Software Foundation, Inc. +Contributed by the Arenaire and Cacao projects, INRIA. + +This file is part of the MPFR Library. + +The 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 2.1 of the License, or (at your +option) any later version. + +The 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 MPFR Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, +MA 02110-1301, USA. */ + +#include <stdio.h> +#include <stdlib.h> + +#include "mpfr-test.h" + +#define TEST_FUNCTION mpfr_zeta +#include "tgeneric.c" + +int +main (int argc, char *argv[]) +{ + mpfr_t x, y; + + tests_start_mpfr (); + + mpfr_init (x); + mpfr_init (y); + + /* special values */ + mpfr_set_nan (x); + mpfr_j1 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_nan_p (y)); + + mpfr_set_inf (x, 1); /* +Inf */ + mpfr_j1 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); + + mpfr_set_inf (x, -1); /* -Inf */ + mpfr_j1 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); + + mpfr_set_ui (x, 0, GMP_RNDN); /* +0 */ + mpfr_j1 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j1(+0)=+0 */ + + mpfr_set_ui (x, 0, GMP_RNDN); + mpfr_neg (x, x, GMP_RNDN); /* -0 */ + mpfr_j1 (y, x, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_NEG (y)); /* j1(-0)=-0 */ + + mpfr_set_prec (x, 53); + mpfr_set_prec (y, 53); + + mpfr_set_ui (x, 1, GMP_RNDN); + mpfr_j1 (y, x, GMP_RNDN); + mpfr_set_str_binary (x, "0.0111000010100111001001111011101001011100001100011011"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_j1 for x=1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + mpfr_clear (x); + mpfr_clear (y); + + test_generic (2, 100, 1); + + tests_end_mpfr (); + + return 0; +} diff --git a/tests/tjn.c b/tests/tjn.c new file mode 100644 index 000000000..5d4eb6186 --- /dev/null +++ b/tests/tjn.c @@ -0,0 +1,136 @@ +/* tjn -- test file for the Bessel function of first kind + +Copyright 2007 Free Software Foundation, Inc. +Contributed by the Arenaire and Cacao projects, INRIA. + +This file is part of the MPFR Library. + +The 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 2.1 of the License, or (at your +option) any later version. + +The 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 MPFR Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, +MA 02110-1301, USA. */ + +#include <stdio.h> +#include <stdlib.h> + +#include "mpfr-test.h" + +int +main (int argc, char *argv[]) +{ + mpfr_t x, y; + + tests_start_mpfr (); + + mpfr_init (x); + mpfr_init (y); + + /* special values */ + mpfr_set_nan (x); + mpfr_jn (y, x, 17, GMP_RNDN); + MPFR_ASSERTN(mpfr_nan_p (y)); + + mpfr_set_inf (x, 1); /* +Inf */ + mpfr_jn (y, x, 17, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); + + mpfr_set_inf (x, -1); /* -Inf */ + mpfr_jn (y, x, 17, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); + + mpfr_set_ui (x, 0, GMP_RNDN); /* +0 */ + mpfr_jn (y, x, 0, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(+0)=1 */ + mpfr_jn (y, x, 17, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j17(+0)=+0 */ + mpfr_jn (y, x, -17, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_NEG (y)); /* j-17(+0)=-0 */ + mpfr_jn (y, x, 42, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j42(+0)=+0 */ + + mpfr_set_ui (x, 0, GMP_RNDN); + mpfr_neg (x, x, GMP_RNDN); /* -0 */ + mpfr_jn (y, x, 0, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0); /* j0(-0)=1 */ + mpfr_jn (y, x, 17, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_NEG (y)); /* j17(-0)=-0 */ + mpfr_jn (y, x, -17, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j-17(-0)=+0 */ + mpfr_jn (y, x, 42, GMP_RNDN); + MPFR_ASSERTN(mpfr_cmp_ui (y, 0) == 0 && MPFR_IS_POS (y)); /* j42(-0)=+0 */ + + mpfr_set_prec (x, 53); + mpfr_set_prec (y, 53); + + mpfr_set_ui (x, 1, GMP_RNDN); + mpfr_jn (y, x, 0, GMP_RNDN); + mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_jn for n=0, x=1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + + mpfr_set_si (x, -1, GMP_RNDN); + mpfr_jn (y, x, 0, GMP_RNDN); + mpfr_set_str_binary (x, "0.1100001111100011111111101101111010111101110001111"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_jn for n=0, x=-1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + + mpfr_set_ui (x, 1, GMP_RNDN); + mpfr_jn (y, x, 1, GMP_RNDN); + mpfr_set_str_binary (x, "0.0111000010100111001001111011101001011100001100011011"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_jn for n=1, x=1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + + mpfr_set_ui (x, 1, GMP_RNDN); + mpfr_jn (y, x, 17, GMP_RNDN); + mpfr_set_str_binary (x, "0.1100011111001010101001001001000110110000010001011E-65"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_jn for n=17, x=1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + + mpfr_set_ui (x, 1, GMP_RNDN); + mpfr_jn (y, x, 42, GMP_RNDN); + mpfr_set_str_binary (x, "0.10000111100011010100111011100111101101000100000001001E-211"); + if (mpfr_cmp (x, y)) + { + printf ("Error in mpfr_jn for n=42, x=1, rnd=GMP_RNDN\n"); + printf ("Expected "); mpfr_dump (x); + printf ("Got "); mpfr_dump (y); + exit (1); + } + + mpfr_clear (x); + mpfr_clear (y); + + tests_end_mpfr (); + + return 0; +} |