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authorJoel Sherrill <joel.sherrill@OARcorp.com>2011-04-08 17:33:11 +0000
committerJoel Sherrill <joel.sherrill@OARcorp.com>2011-04-08 17:33:11 +0000
commit73f643f3f4a55310b2c8c1a9858906b2dd676e72 (patch)
treeb1df97f18dace4a5702b0bc7aafdfee8a2f25ada /gsl-1.9/specfunc/poch.c
parentee523abdace8337d05ec4a179fcdf5de3fe0f634 (diff)
2011-04-08 Joel Sherrill <joel.sherrill@oarcorp.com>
* AUTHORS, BUGS, COPYING, ChangeLog, INSTALL, Makefile.am, Makefile.in, NEWS, README, SUPPORT, THANKS, TODO, acconfig.h, aclocal.m4, autogen.sh, config.guess, config.h.in, config.sub, configure, configure.ac, gsl-config.in, gsl-histogram.c, gsl-randist.c, gsl.m4, gsl.pc.in, gsl.spec.in, gsl_machine.h, gsl_math.h, gsl_mode.h, gsl_nan.h, gsl_pow_int.h, gsl_precision.h, gsl_types.h, gsl_version.h.in, install-sh, ltmain.sh, mdate-sh, missing, mkinstalldirs, templates_off.h, templates_on.h, test_gsl_histogram.sh, version.c, blas/ChangeLog, blas/Makefile.am, blas/Makefile.in, blas/TODO, blas/blas.c, blas/gsl_blas.h, blas/gsl_blas_types.h, block/ChangeLog, block/Makefile.am, block/Makefile.in, block/block.c, block/block_source.c, block/file.c, block/fprintf_source.c, block/fwrite_source.c, block/gsl_block.h, block/gsl_block_char.h, block/gsl_block_complex_double.h, block/gsl_block_complex_float.h, block/gsl_block_complex_long_double.h, block/gsl_block_double.h, block/gsl_block_float.h, block/gsl_block_int.h, block/gsl_block_long.h, block/gsl_block_long_double.h, block/gsl_block_short.h, block/gsl_block_uchar.h, block/gsl_block_uint.h, block/gsl_block_ulong.h, block/gsl_block_ushort.h, block/gsl_check_range.h, block/init.c, block/init_source.c, block/test.c, block/test_complex_io.c, block/test_complex_source.c, block/test_io.c, block/test_source.c, bspline/ChangeLog, bspline/Makefile.am, bspline/Makefile.in, bspline/TODO, bspline/bspline.c, bspline/gsl_bspline.h, bspline/test.c, cblas/ChangeLog, cblas/Makefile.am, cblas/Makefile.in, cblas/TODO, cblas/caxpy.c, cblas/cblas.h, cblas/ccopy.c, cblas/cdotc_sub.c, cblas/cdotu_sub.c, cblas/cgbmv.c, cblas/cgemm.c, cblas/cgemv.c, cblas/cgerc.c, cblas/cgeru.c, cblas/chbmv.c, cblas/chemm.c, cblas/chemv.c, cblas/cher.c, cblas/cher2.c, cblas/cher2k.c, cblas/cherk.c, cblas/chpmv.c, cblas/chpr.c, cblas/chpr2.c, cblas/cscal.c, cblas/csscal.c, cblas/cswap.c, cblas/csymm.c, cblas/csyr2k.c, cblas/csyrk.c, cblas/ctbmv.c, cblas/ctbsv.c, cblas/ctpmv.c, cblas/ctpsv.c, cblas/ctrmm.c, cblas/ctrmv.c, cblas/ctrsm.c, cblas/ctrsv.c, cblas/dasum.c, cblas/daxpy.c, cblas/dcopy.c, cblas/ddot.c, cblas/dgbmv.c, cblas/dgemm.c, cblas/dgemv.c, cblas/dger.c, cblas/dnrm2.c, cblas/drot.c, cblas/drotg.c, cblas/drotm.c, cblas/drotmg.c, cblas/dsbmv.c, cblas/dscal.c, cblas/dsdot.c, cblas/dspmv.c, cblas/dspr.c, cblas/dspr2.c, cblas/dswap.c, cblas/dsymm.c, cblas/dsymv.c, cblas/dsyr.c, cblas/dsyr2.c, cblas/dsyr2k.c, cblas/dsyrk.c, cblas/dtbmv.c, cblas/dtbsv.c, cblas/dtpmv.c, cblas/dtpsv.c, cblas/dtrmm.c, cblas/dtrmv.c, cblas/dtrsm.c, cblas/dtrsv.c, cblas/dzasum.c, cblas/dznrm2.c, cblas/gsl_cblas.h, cblas/hypot.c, cblas/icamax.c, cblas/idamax.c, cblas/isamax.c, cblas/izamax.c, cblas/sasum.c, cblas/saxpy.c, cblas/scasum.c, cblas/scnrm2.c, cblas/scopy.c, cblas/sdot.c, cblas/sdsdot.c, cblas/sgbmv.c, cblas/sgemm.c, cblas/sgemv.c, cblas/sger.c, cblas/snrm2.c, cblas/source_asum_c.h, cblas/source_asum_r.h, cblas/source_axpy_c.h, cblas/source_axpy_r.h, cblas/source_copy_c.h, cblas/source_copy_r.h, cblas/source_dot_c.h, cblas/source_dot_r.h, cblas/source_gbmv_c.h, cblas/source_gbmv_r.h, cblas/source_gemm_c.h, cblas/source_gemm_r.h, cblas/source_gemv_c.h, cblas/source_gemv_r.h, cblas/source_ger.h, cblas/source_gerc.h, cblas/source_geru.h, cblas/source_hbmv.h, cblas/source_hemm.h, cblas/source_hemv.h, cblas/source_her.h, cblas/source_her2.h, cblas/source_her2k.h, cblas/source_herk.h, cblas/source_hpmv.h, cblas/source_hpr.h, cblas/source_hpr2.h, cblas/source_iamax_c.h, cblas/source_iamax_r.h, cblas/source_nrm2_c.h, cblas/source_nrm2_r.h, cblas/source_rot.h, cblas/source_rotg.h, cblas/source_rotm.h, cblas/source_rotmg.h, cblas/source_sbmv.h, cblas/source_scal_c.h, cblas/source_scal_c_s.h, cblas/source_scal_r.h, cblas/source_spmv.h, cblas/source_spr.h, cblas/source_spr2.h, cblas/source_swap_c.h, cblas/source_swap_r.h, cblas/source_symm_c.h, cblas/source_symm_r.h, cblas/source_symv.h, cblas/source_syr.h, cblas/source_syr2.h, cblas/source_syr2k_c.h, cblas/source_syr2k_r.h, cblas/source_syrk_c.h, cblas/source_syrk_r.h, cblas/source_tbmv_c.h, cblas/source_tbmv_r.h, cblas/source_tbsv_c.h, cblas/source_tbsv_r.h, cblas/source_tpmv_c.h, cblas/source_tpmv_r.h, cblas/source_tpsv_c.h, cblas/source_tpsv_r.h, cblas/source_trmm_c.h, cblas/source_trmm_r.h, cblas/source_trmv_c.h, cblas/source_trmv_r.h, cblas/source_trsm_c.h, cblas/source_trsm_r.h, cblas/source_trsv_c.h, cblas/source_trsv_r.h, cblas/srot.c, cblas/srotg.c, cblas/srotm.c, cblas/srotmg.c, cblas/ssbmv.c, cblas/sscal.c, cblas/sspmv.c, cblas/sspr.c, cblas/sspr2.c, cblas/sswap.c, cblas/ssymm.c, cblas/ssymv.c, cblas/ssyr.c, cblas/ssyr2.c, cblas/ssyr2k.c, cblas/ssyrk.c, cblas/stbmv.c, cblas/stbsv.c, cblas/stpmv.c, cblas/stpsv.c, cblas/strmm.c, cblas/strmv.c, cblas/strsm.c, cblas/strsv.c, cblas/test.c, cblas/test_amax.c, cblas/test_asum.c, cblas/test_axpy.c, cblas/test_copy.c, cblas/test_dot.c, cblas/test_gbmv.c, cblas/test_gemm.c, cblas/test_gemv.c, cblas/test_ger.c, cblas/test_hbmv.c, cblas/test_hemm.c, cblas/test_hemv.c, cblas/test_her.c, cblas/test_her2.c, cblas/test_her2k.c, cblas/test_herk.c, cblas/test_hpmv.c, cblas/test_hpr.c, cblas/test_hpr2.c, cblas/test_nrm2.c, cblas/test_rot.c, cblas/test_rotg.c, cblas/test_rotm.c, cblas/test_rotmg.c, cblas/test_sbmv.c, cblas/test_scal.c, cblas/test_spmv.c, cblas/test_spr.c, cblas/test_spr2.c, cblas/test_swap.c, cblas/test_symm.c, cblas/test_symv.c, cblas/test_syr.c, cblas/test_syr2.c, cblas/test_syr2k.c, cblas/test_syrk.c, cblas/test_tbmv.c, cblas/test_tbsv.c, cblas/test_tpmv.c, cblas/test_tpsv.c, cblas/test_trmm.c, cblas/test_trmv.c, cblas/test_trsm.c, cblas/test_trsv.c, cblas/tests.c, cblas/tests.h, cblas/xerbla.c, cblas/zaxpy.c, cblas/zcopy.c, cblas/zdotc_sub.c, cblas/zdotu_sub.c, cblas/zdscal.c, cblas/zgbmv.c, cblas/zgemm.c, cblas/zgemv.c, cblas/zgerc.c, cblas/zgeru.c, cblas/zhbmv.c, cblas/zhemm.c, cblas/zhemv.c, cblas/zher.c, cblas/zher2.c, cblas/zher2k.c, cblas/zherk.c, cblas/zhpmv.c, cblas/zhpr.c, cblas/zhpr2.c, cblas/zscal.c, cblas/zswap.c, cblas/zsymm.c, cblas/zsyr2k.c, cblas/zsyrk.c, cblas/ztbmv.c, cblas/ztbsv.c, cblas/ztpmv.c, cblas/ztpsv.c, cblas/ztrmm.c, cblas/ztrmv.c, cblas/ztrsm.c, cblas/ztrsv.c, cdf/ChangeLog, cdf/Makefile.am, cdf/Makefile.in, cdf/beta.c, cdf/beta_inc.c, cdf/betainv.c, cdf/binomial.c, cdf/cauchy.c, cdf/cauchyinv.c, cdf/chisq.c, cdf/chisqinv.c, cdf/error.h, cdf/exponential.c, cdf/exponentialinv.c, cdf/exppow.c, cdf/fdist.c, cdf/fdistinv.c, cdf/flat.c, cdf/flatinv.c, cdf/gamma.c, cdf/gammainv.c, cdf/gauss.c, cdf/gaussinv.c, cdf/geometric.c, cdf/gsl_cdf.h, cdf/gumbel1.c, cdf/gumbel1inv.c, cdf/gumbel2.c, cdf/gumbel2inv.c, cdf/hypergeometric.c, cdf/laplace.c, cdf/laplaceinv.c, cdf/logistic.c, cdf/logisticinv.c, cdf/lognormal.c, cdf/lognormalinv.c, cdf/nbinomial.c, cdf/pareto.c, cdf/paretoinv.c, cdf/pascal.c, cdf/poisson.c, cdf/rat_eval.h, cdf/rayleigh.c, cdf/rayleighinv.c, cdf/tdist.c, cdf/tdistinv.c, cdf/test.c, cdf/test_auto.c, cdf/weibull.c, cdf/weibullinv.c, cheb/ChangeLog, cheb/Makefile.am, cheb/Makefile.in, cheb/deriv.c, cheb/eval.c, cheb/gsl_chebyshev.h, cheb/init.c, cheb/integ.c, cheb/test.c, combination/ChangeLog, combination/Makefile.am, combination/Makefile.in, combination/combination.c, combination/file.c, combination/gsl_combination.h, combination/init.c, combination/test.c, complex/ChangeLog, complex/Makefile.am, complex/Makefile.in, complex/TODO, complex/gsl_complex.h, complex/gsl_complex_math.h, complex/math.c, complex/results.h, complex/results1.h, complex/results_real.h, complex/test.c, const/ChangeLog, const/Makefile.am, const/Makefile.in, const/TODO, const/gsl_const.h, const/gsl_const_cgs.h, const/gsl_const_cgsm.h, const/gsl_const_mks.h, const/gsl_const_mksa.h, const/gsl_const_num.h, const/test.c, deriv/ChangeLog, deriv/Makefile.am, deriv/Makefile.in, deriv/deriv.c, deriv/gsl_deriv.h, deriv/test.c, dht/ChangeLog, dht/Makefile.am, dht/Makefile.in, dht/dht.c, dht/gsl_dht.h, dht/test.c, diff/ChangeLog, diff/Makefile.am, diff/Makefile.in, diff/diff.c, diff/gsl_diff.h, diff/test.c, doc/12-cities.eps, doc/ChangeLog, doc/Makefile.am, doc/Makefile.in, doc/algorithm.sty, doc/algorithmic.sty, doc/autoconf.texi, doc/blas.texi, doc/bspline.eps, doc/bspline.texi, doc/calc.sty, doc/cblas.texi, doc/cheb.eps, doc/cheb.texi, doc/combination.texi, doc/complex.texi, doc/const.texi, doc/debug.texi, doc/dht.texi, doc/diff.texi, doc/dwt-orig.eps, doc/dwt-samp.eps, doc/dwt.texi, doc/eigen.texi, doc/err.texi, doc/fdl.texi, doc/fft-complex-radix2-f.eps, doc/fft-complex-radix2-t.eps, doc/fft-complex-radix2.eps, doc/fft-real-mixedradix.eps, doc/fft.texi, doc/fftalgorithms.bib, doc/fftalgorithms.tex, doc/final-route.eps, doc/fit-exp.eps, doc/fit-wlinear.eps, doc/fit-wlinear2.eps, doc/fitting.texi, doc/freemanuals.texi, doc/gpl.texi, doc/gsl-config.1, doc/gsl-design.texi, doc/gsl-histogram.1, doc/gsl-randist.1, doc/gsl-ref.info, doc/gsl-ref.info-1, doc/gsl-ref.info-2, doc/gsl-ref.info-3, doc/gsl-ref.info-4, doc/gsl-ref.info-5, doc/gsl-ref.info-6, doc/gsl-ref.texi, doc/gsl.3, doc/histogram.eps, doc/histogram.texi, doc/histogram2d.eps, doc/ieee754.texi, doc/initial-route.eps, doc/integration.texi, doc/interp.texi, doc/interp2.eps, doc/interpp2.eps, doc/intro.texi, doc/landau.dat, doc/linalg.texi, doc/math.texi, doc/mdate-sh, doc/min-interval.eps, doc/min.texi, doc/montecarlo.texi, doc/multifit.texi, doc/multimin.eps, doc/multimin.texi, doc/multiroots.texi, doc/ntuple.eps, doc/ntuple.texi, doc/ode-initval.texi, doc/permutation.texi, doc/poly.texi, doc/qrng.eps, doc/qrng.texi, doc/rand-bernoulli.tex, doc/rand-beta.tex, doc/rand-binomial.tex, doc/rand-bivariate-gaussian.tex, doc/rand-cauchy.tex, doc/rand-chisq.tex, doc/rand-erlang.tex, doc/rand-exponential.tex, doc/rand-exppow.tex, doc/rand-fdist.tex, doc/rand-flat.tex, doc/rand-gamma.tex, doc/rand-gaussian-tail.tex, doc/rand-gaussian.tex, doc/rand-geometric.tex, doc/rand-gumbel.tex, doc/rand-gumbel1.tex, doc/rand-gumbel2.tex, doc/rand-hypergeometric.tex, doc/rand-landau.tex, doc/rand-laplace.tex, doc/rand-levy.tex, doc/rand-levyskew.tex, doc/rand-logarithmic.tex, doc/rand-logistic.tex, doc/rand-lognormal.tex, doc/rand-nbinomial.tex, doc/rand-pareto.tex, doc/rand-pascal.tex, doc/rand-poisson.tex, doc/rand-rayleigh-tail.tex, doc/rand-rayleigh.tex, doc/rand-tdist.tex, doc/rand-weibull.tex, doc/randist.texi, doc/random-walk.tex, doc/randplots.gnp, doc/rng.texi, doc/roots-bisection.eps, doc/roots-false-position.eps, doc/roots-newtons-method.eps, doc/roots-secant-method.eps, doc/roots.texi, doc/siman-energy.eps, doc/siman-test.eps, doc/siman.texi, doc/sort.texi, doc/specfunc-airy.texi, doc/specfunc-bessel.texi, doc/specfunc-clausen.texi, doc/specfunc-coulomb.texi, doc/specfunc-coupling.texi, doc/specfunc-dawson.texi, doc/specfunc-debye.texi, doc/specfunc-dilog.texi, doc/specfunc-elementary.texi, doc/specfunc-ellint.texi, doc/specfunc-elljac.texi, doc/specfunc-erf.texi, doc/specfunc-exp.texi, doc/specfunc-expint.texi, doc/specfunc-fermi-dirac.texi, doc/specfunc-gamma.texi, doc/specfunc-gegenbauer.texi, doc/specfunc-hyperg.texi, doc/specfunc-laguerre.texi, doc/specfunc-lambert.texi, doc/specfunc-legendre.texi, doc/specfunc-log.texi, doc/specfunc-mathieu.texi, doc/specfunc-pow-int.texi, doc/specfunc-psi.texi, doc/specfunc-synchrotron.texi, doc/specfunc-transport.texi, doc/specfunc-trig.texi, doc/specfunc-zeta.texi, doc/specfunc.texi, doc/stamp-vti, doc/statistics.texi, doc/sum.texi, doc/texinfo.tex, doc/usage.texi, doc/vdp.eps, doc/vectors.texi, doc/version-ref.texi, doc/examples/blas.c, doc/examples/blas.out, doc/examples/block.c, doc/examples/block.out, doc/examples/bspline.c, doc/examples/cblas.c, doc/examples/cblas.out, doc/examples/cdf.c, doc/examples/cdf.out, doc/examples/cheb.c, doc/examples/combination.c, doc/examples/combination.out, doc/examples/const.c, doc/examples/const.out, doc/examples/demo_fn.c, doc/examples/demo_fn.h, doc/examples/diff.c, doc/examples/diff.out, doc/examples/dwt.c, doc/examples/dwt.dat, doc/examples/ecg.dat, doc/examples/eigen.c, doc/examples/eigen_nonsymm.c, doc/examples/expfit.c, doc/examples/fft.c, doc/examples/fftmr.c, doc/examples/fftreal.c, doc/examples/fitting.c, doc/examples/fitting2.c, doc/examples/fitting3.c, doc/examples/histogram.c, doc/examples/histogram2d.c, doc/examples/ieee.c, doc/examples/ieeeround.c, doc/examples/integration.c, doc/examples/integration.out, doc/examples/interp.c, doc/examples/interpp.c, doc/examples/intro.c, doc/examples/intro.out, doc/examples/linalglu.c, doc/examples/linalglu.out, doc/examples/matrix.c, doc/examples/matrixw.c, doc/examples/min.c, doc/examples/min.out, doc/examples/monte.c, doc/examples/nlfit.c, doc/examples/ntupler.c, doc/examples/ntuplew.c, doc/examples/ode-initval.c, doc/examples/odefixed.c, doc/examples/permseq.c, doc/examples/permshuffle.c, doc/examples/polyroots.c, doc/examples/polyroots.out, doc/examples/qrng.c, doc/examples/randpoisson.2.out, doc/examples/randpoisson.c, doc/examples/randpoisson.out, doc/examples/randwalk.c, doc/examples/rng.c, doc/examples/rng.out, doc/examples/rngunif.2.out, doc/examples/rngunif.c, doc/examples/rngunif.out, doc/examples/rootnewt.c, doc/examples/roots.c, doc/examples/siman.c, doc/examples/sortsmall.c, doc/examples/sortsmall.out, doc/examples/specfun.c, doc/examples/specfun.out, doc/examples/specfun_e.c, doc/examples/specfun_e.out, doc/examples/stat.c, doc/examples/stat.out, doc/examples/statsort.c, doc/examples/statsort.out, doc/examples/sum.c, doc/examples/sum.out, doc/examples/vector.c, doc/examples/vectorr.c, doc/examples/vectorview.c, doc/examples/vectorview.out, doc/examples/vectorw.c, eigen/ChangeLog, eigen/Makefile.am, eigen/Makefile.in, eigen/TODO, eigen/francis.c, eigen/gsl_eigen.h, eigen/herm.c, eigen/hermv.c, eigen/jacobi.c, eigen/nonsymm.c, eigen/nonsymmv.c, eigen/qrstep.c, eigen/schur.c, eigen/schur.h, eigen/sort.c, eigen/symm.c, eigen/symmv.c, eigen/test.c, err/ChangeLog, 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statistics/wskew_source.c, statistics/wvariance.c, statistics/wvariance_source.c, sum/ChangeLog, sum/Makefile.am, sum/Makefile.in, sum/gsl_sum.h, sum/levin_u.c, sum/levin_utrunc.c, sum/test.c, sum/work_u.c, sum/work_utrunc.c, sys/ChangeLog, sys/Makefile.am, sys/Makefile.in, sys/coerce.c, sys/expm1.c, sys/fcmp.c, sys/fdiv.c, sys/gsl_sys.h, sys/hypot.c, sys/infnan.c, sys/invhyp.c, sys/ldfrexp.c, sys/log1p.c, sys/minmax.c, sys/pow_int.c, sys/prec.c, sys/test.c, test/ChangeLog, test/Makefile.am, test/Makefile.in, test/gsl_test.h, test/results.c, utils/Makefile.am, utils/Makefile.in, utils/README, utils/memcpy.c, utils/memmove.c, utils/placeholder.c, utils/strdup.c, utils/strtol.c, utils/strtoul.c, utils/system.h, vector/ChangeLog, vector/Makefile.am, vector/Makefile.in, vector/TODO, vector/copy.c, vector/copy_source.c, vector/file.c, vector/file_source.c, vector/gsl_vector.h, vector/gsl_vector_char.h, vector/gsl_vector_complex.h, vector/gsl_vector_complex_double.h, vector/gsl_vector_complex_float.h, vector/gsl_vector_complex_long_double.h, vector/gsl_vector_double.h, vector/gsl_vector_float.h, vector/gsl_vector_int.h, vector/gsl_vector_long.h, vector/gsl_vector_long_double.h, vector/gsl_vector_short.h, vector/gsl_vector_uchar.h, vector/gsl_vector_uint.h, vector/gsl_vector_ulong.h, vector/gsl_vector_ushort.h, vector/init.c, vector/init_source.c, vector/minmax.c, vector/minmax_source.c, vector/oper.c, vector/oper_source.c, vector/prop.c, vector/prop_source.c, vector/reim.c, vector/reim_source.c, vector/subvector.c, vector/subvector_source.c, vector/swap.c, vector/swap_source.c, vector/test.c, vector/test_complex_source.c, vector/test_source.c, vector/test_static.c, vector/vector.c, vector/vector_source.c, vector/view.c, vector/view.h, vector/view_source.c, wavelet/ChangeLog, wavelet/Makefile.am, wavelet/Makefile.in, wavelet/TODO, wavelet/bspline.c, wavelet/daubechies.c, wavelet/dwt.c, wavelet/gsl_wavelet.h, wavelet/gsl_wavelet2d.h, wavelet/haar.c, wavelet/test.c, wavelet/wavelet.c: New files.
Diffstat (limited to 'gsl-1.9/specfunc/poch.c')
-rw-r--r--gsl-1.9/specfunc/poch.c435
1 files changed, 435 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/poch.c b/gsl-1.9/specfunc/poch.c
new file mode 100644
index 0000000..782900e
--- /dev/null
+++ b/gsl-1.9/specfunc/poch.c
@@ -0,0 +1,435 @@
+/* specfunc/poch.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or (at
+ * your option) any later version.
+ *
+ * This program 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
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* Author: G. Jungman */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_sf_exp.h>
+#include <gsl/gsl_sf_log.h>
+#include <gsl/gsl_sf_pow_int.h>
+#include <gsl/gsl_sf_psi.h>
+#include <gsl/gsl_sf_gamma.h>
+
+#include "error.h"
+
+static const double bern[21] = {
+ 0.0 /* no element 0 */,
+ +0.833333333333333333333333333333333e-01,
+ -0.138888888888888888888888888888888e-02,
+ +0.330687830687830687830687830687830e-04,
+ -0.826719576719576719576719576719576e-06,
+ +0.208767569878680989792100903212014e-07,
+ -0.528419013868749318484768220217955e-09,
+ +0.133825365306846788328269809751291e-10,
+ -0.338968029632258286683019539124944e-12,
+ +0.858606205627784456413590545042562e-14,
+ -0.217486869855806187304151642386591e-15,
+ +0.550900282836022951520265260890225e-17,
+ -0.139544646858125233407076862640635e-18,
+ +0.353470703962946747169322997780379e-20,
+ -0.895351742703754685040261131811274e-22,
+ +0.226795245233768306031095073886816e-23,
+ -0.574472439520264523834847971943400e-24,
+ +0.145517247561486490186626486727132e-26,
+ -0.368599494066531017818178247990866e-28,
+ +0.933673425709504467203255515278562e-30,
+ -0.236502241570062993455963519636983e-31
+};
+
+
+/* ((a)_x - 1)/x in the "small x" region where
+ * cancellation must be controlled.
+ *
+ * Based on SLATEC DPOCH1().
+ */
+/*
+C When ABS(X) is so small that substantial cancellation will occur if
+C the straightforward formula is used, we use an expansion due
+C to Fields and discussed by Y. L. Luke, The Special Functions and Their
+C Approximations, Vol. 1, Academic Press, 1969, page 34.
+C
+C The ratio POCH(A,X) = GAMMA(A+X)/GAMMA(A) is written by Luke as
+C (A+(X-1)/2)**X * polynomial in (A+(X-1)/2)**(-2) .
+C In order to maintain significance in POCH1, we write for positive a
+C (A+(X-1)/2)**X = EXP(X*LOG(A+(X-1)/2)) = EXP(Q)
+C = 1.0 + Q*EXPREL(Q) .
+C Likewise the polynomial is written
+C POLY = 1.0 + X*POLY1(A,X) .
+C Thus,
+C POCH1(A,X) = (POCH(A,X) - 1) / X
+C = EXPREL(Q)*(Q/X + Q*POLY1(A,X)) + POLY1(A,X)
+C
+*/
+static
+int
+pochrel_smallx(const double a, const double x, gsl_sf_result * result)
+{
+ /*
+ SQTBIG = 1.0D0/SQRT(24.0D0*D1MACH(1))
+ ALNEPS = LOG(D1MACH(3))
+ */
+ const double SQTBIG = 1.0/(2.0*M_SQRT2*M_SQRT3*GSL_SQRT_DBL_MIN);
+ const double ALNEPS = GSL_LOG_DBL_EPSILON - M_LN2;
+
+ if(x == 0.0) {
+ return gsl_sf_psi_e(a, result);
+ }
+ else {
+ const double bp = ( (a < -0.5) ? 1.0-a-x : a );
+ const int incr = ( (bp < 10.0) ? 11.0-bp : 0 );
+ const double b = bp + incr;
+ double dpoch1;
+ gsl_sf_result dexprl;
+ int stat_dexprl;
+ int i;
+
+ double var = b + 0.5*(x-1.0);
+ double alnvar = log(var);
+ double q = x*alnvar;
+
+ double poly1 = 0.0;
+
+ if(var < SQTBIG) {
+ const int nterms = (int)(-0.5*ALNEPS/alnvar + 1.0);
+ const double var2 = (1.0/var)/var;
+ const double rho = 0.5 * (x + 1.0);
+ double term = var2;
+ double gbern[24];
+ int k, j;
+
+ gbern[1] = 1.0;
+ gbern[2] = -rho/12.0;
+ poly1 = gbern[2] * term;
+
+ if(nterms > 20) {
+ /* NTERMS IS TOO BIG, MAYBE D1MACH(3) IS BAD */
+ /* nterms = 20; */
+ result->val = 0.0;
+ result->err = 0.0;
+ GSL_ERROR ("error", GSL_ESANITY);
+ }
+
+ for(k=2; k<=nterms; k++) {
+ double gbk = 0.0;
+ for(j=1; j<=k; j++) {
+ gbk += bern[k-j+1]*gbern[j];
+ }
+ gbern[k+1] = -rho*gbk/k;
+
+ term *= (2*k-2-x)*(2*k-1-x)*var2;
+ poly1 += gbern[k+1]*term;
+ }
+ }
+
+ stat_dexprl = gsl_sf_expm1_e(q, &dexprl);
+ if(stat_dexprl != GSL_SUCCESS) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return stat_dexprl;
+ }
+ dexprl.val = dexprl.val/q;
+ poly1 *= (x - 1.0);
+ dpoch1 = dexprl.val * (alnvar + q * poly1) + poly1;
+
+ for(i=incr-1; i >= 0; i--) {
+ /*
+ C WE HAVE DPOCH1(B,X), BUT BP IS SMALL, SO WE USE BACKWARDS RECURSION
+ C TO OBTAIN DPOCH1(BP,X).
+ */
+ double binv = 1.0/(bp+i);
+ dpoch1 = (dpoch1 - binv) / (1.0 + x*binv);
+ }
+
+ if(bp == a) {
+ result->val = dpoch1;
+ result->err = 2.0 * GSL_DBL_EPSILON * (fabs(incr) + 1.0) * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ /*
+ C WE HAVE DPOCH1(BP,X), BUT A IS LT -0.5. WE THEREFORE USE A
+ C REFLECTION FORMULA TO OBTAIN DPOCH1(A,X).
+ */
+ double sinpxx = sin(M_PI*x)/x;
+ double sinpx2 = sin(0.5*M_PI*x);
+ double t1 = sinpxx/tan(M_PI*b);
+ double t2 = 2.0*sinpx2*(sinpx2/x);
+ double trig = t1 - t2;
+ result->val = dpoch1 * (1.0 + x*trig) + trig;
+ result->err = (fabs(dpoch1*x) + 1.0) * GSL_DBL_EPSILON * (fabs(t1) + fabs(t2));
+ result->err += 2.0 * GSL_DBL_EPSILON * (fabs(incr) + 1.0) * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ }
+}
+
+
+/* Assumes a>0 and a+x>0.
+ */
+static
+int
+lnpoch_pos(const double a, const double x, gsl_sf_result * result)
+{
+ double absx = fabs(x);
+
+ if(absx > 0.1*a || absx*log(GSL_MAX_DBL(a,2.0)) > 0.1) {
+ if(a < GSL_SF_GAMMA_XMAX && a+x < GSL_SF_GAMMA_XMAX) {
+ /* If we can do it by calculating the gamma functions
+ * directly, then that will be more accurate than
+ * doing the subtraction of the logs.
+ */
+ gsl_sf_result g1;
+ gsl_sf_result g2;
+ gsl_sf_gammainv_e(a, &g1);
+ gsl_sf_gammainv_e(a+x, &g2);
+ result->val = -log(g2.val/g1.val);
+ result->err = g1.err/fabs(g1.val) + g2.err/fabs(g2.val);
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ /* Otherwise we must do the subtraction.
+ */
+ gsl_sf_result lg1;
+ gsl_sf_result lg2;
+ int stat_1 = gsl_sf_lngamma_e(a, &lg1);
+ int stat_2 = gsl_sf_lngamma_e(a+x, &lg2);
+ result->val = lg2.val - lg1.val;
+ result->err = lg2.err + lg1.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_ERROR_SELECT_2(stat_1, stat_2);
+ }
+ }
+ else if(absx < 0.1*a && a > 15.0) {
+ /* Be careful about the implied subtraction.
+ * Note that both a+x and and a must be
+ * large here since a is not small
+ * and x is not relatively large.
+ * So we calculate using Stirling for Log[Gamma(z)].
+ *
+ * Log[Gamma(a+x)/Gamma(a)] = x(Log[a]-1) + (x+a-1/2)Log[1+x/a]
+ * + (1/(1+eps) - 1) / (12 a)
+ * - (1/(1+eps)^3 - 1) / (360 a^3)
+ * + (1/(1+eps)^5 - 1) / (1260 a^5)
+ * - (1/(1+eps)^7 - 1) / (1680 a^7)
+ * + ...
+ */
+ const double eps = x/a;
+ const double den = 1.0 + eps;
+ const double d3 = den*den*den;
+ const double d5 = d3*den*den;
+ const double d7 = d5*den*den;
+ const double c1 = -eps/den;
+ const double c3 = -eps*(3.0+eps*(3.0+eps))/d3;
+ const double c5 = -eps*(5.0+eps*(10.0+eps*(10.0+eps*(5.0+eps))))/d5;
+ const double c7 = -eps*(7.0+eps*(21.0+eps*(35.0+eps*(35.0+eps*(21.0+eps*(7.0+eps))))))/d7;
+ const double p8 = gsl_sf_pow_int(1.0+eps,8);
+ const double c8 = 1.0/p8 - 1.0; /* these need not */
+ const double c9 = 1.0/(p8*(1.0+eps)) - 1.0; /* be very accurate */
+ const double a4 = a*a*a*a;
+ const double a6 = a4*a*a;
+ const double ser_1 = c1 + c3/(30.0*a*a) + c5/(105.0*a4) + c7/(140.0*a6);
+ const double ser_2 = c8/(99.0*a6*a*a) - 691.0/360360.0 * c9/(a6*a4);
+ const double ser = (ser_1 + ser_2)/ (12.0*a);
+
+ double term1 = x * log(a/M_E);
+ double term2;
+ gsl_sf_result ln_1peps;
+ gsl_sf_log_1plusx_e(eps, &ln_1peps); /* log(1 + x/a) */
+ term2 = (x + a - 0.5) * ln_1peps.val;
+
+ result->val = term1 + term2 + ser;
+ result->err = GSL_DBL_EPSILON*fabs(term1);
+ result->err += fabs((x + a - 0.5)*ln_1peps.err);
+ result->err += fabs(ln_1peps.val) * GSL_DBL_EPSILON * (fabs(x) + fabs(a) + 0.5);
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ gsl_sf_result poch_rel;
+ int stat_p = pochrel_smallx(a, x, &poch_rel);
+ double eps = x*poch_rel.val;
+ int stat_e = gsl_sf_log_1plusx_e(eps, result);
+ result->err = 2.0 * fabs(x * poch_rel.err / (1.0 + eps));
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_ERROR_SELECT_2(stat_e, stat_p);
+ }
+}
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
+
+int
+gsl_sf_lnpoch_e(const double a, const double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(a <= 0.0 || a+x <= 0.0) {
+ DOMAIN_ERROR(result);
+ }
+ else if(x == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else {
+ return lnpoch_pos(a, x, result);
+ }
+}
+
+
+int
+gsl_sf_lnpoch_sgn_e(const double a, const double x,
+ gsl_sf_result * result, double * sgn)
+{
+ if(a == 0.0 || a+x == 0.0) {
+ *sgn = 0.0;
+ DOMAIN_ERROR(result);
+ }
+ else if(x == 0.0) {
+ *sgn = 1.0;
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(a > 0.0 && a+x > 0.0) {
+ *sgn = 1.0;
+ return lnpoch_pos(a, x, result);
+ }
+ else if(a < 0.0 && a+x < 0.0) {
+ /* Reduce to positive case using reflection.
+ */
+ double sin_1 = sin(M_PI * (1.0 - a));
+ double sin_2 = sin(M_PI * (1.0 - a - x));
+ if(sin_1 == 0.0 || sin_2 == 0.0) {
+ *sgn = 0.0;
+ DOMAIN_ERROR(result);
+ }
+ else {
+ gsl_sf_result lnp_pos;
+ int stat_pp = lnpoch_pos(1.0-a, -x, &lnp_pos);
+ double lnterm = log(fabs(sin_1/sin_2));
+ result->val = lnterm - lnp_pos.val;
+ result->err = lnp_pos.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * (fabs(1.0-a) + fabs(1.0-a-x)) * fabs(lnterm);
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ *sgn = GSL_SIGN(sin_1*sin_2);
+ return stat_pp;
+ }
+ }
+ else {
+ /* Evaluate gamma ratio directly.
+ */
+ gsl_sf_result lg_apn;
+ gsl_sf_result lg_a;
+ double s_apn, s_a;
+ int stat_apn = gsl_sf_lngamma_sgn_e(a+x, &lg_apn, &s_apn);
+ int stat_a = gsl_sf_lngamma_sgn_e(a, &lg_a, &s_a);
+ if(stat_apn == GSL_SUCCESS && stat_a == GSL_SUCCESS) {
+ result->val = lg_apn.val - lg_a.val;
+ result->err = lg_apn.err + lg_a.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ *sgn = s_a * s_apn;
+ return GSL_SUCCESS;
+ }
+ else if(stat_apn == GSL_EDOM || stat_a == GSL_EDOM){
+ *sgn = 0.0;
+ DOMAIN_ERROR(result);
+ }
+ else {
+ result->val = 0.0;
+ result->err = 0.0;
+ *sgn = 0.0;
+ return GSL_FAILURE;
+ }
+ }
+}
+
+
+int
+gsl_sf_poch_e(const double a, const double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(x == 0.0) {
+ result->val = 1.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else {
+ gsl_sf_result lnpoch;
+ double sgn;
+ int stat_lnpoch = gsl_sf_lnpoch_sgn_e(a, x, &lnpoch, &sgn);
+ int stat_exp = gsl_sf_exp_err_e(lnpoch.val, lnpoch.err, result);
+ result->val *= sgn;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_ERROR_SELECT_2(stat_exp, stat_lnpoch);
+ }
+}
+
+
+int
+gsl_sf_pochrel_e(const double a, const double x, gsl_sf_result * result)
+{
+ const double absx = fabs(x);
+ const double absa = fabs(a);
+
+ /* CHECK_POINTER(result) */
+
+ if(absx > 0.1*absa || absx*log(GSL_MAX(absa,2.0)) > 0.1) {
+ gsl_sf_result lnpoch;
+ double sgn;
+ int stat_poch = gsl_sf_lnpoch_sgn_e(a, x, &lnpoch, &sgn);
+ if(lnpoch.val > GSL_LOG_DBL_MAX) {
+ OVERFLOW_ERROR(result);
+ }
+ else {
+ const double el = exp(lnpoch.val);
+ result->val = (sgn*el - 1.0)/x;
+ result->err = fabs(result->val) * (lnpoch.err + 2.0 * GSL_DBL_EPSILON);
+ result->err += 2.0 * GSL_DBL_EPSILON * (fabs(sgn*el) + 1.0) / fabs(x);
+ return stat_poch;
+ }
+ }
+ else {
+ return pochrel_smallx(a, x, result);
+ }
+}
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"
+
+double gsl_sf_lnpoch(const double a, const double x)
+{
+ EVAL_RESULT(gsl_sf_lnpoch_e(a, x, &result));
+}
+
+double gsl_sf_poch(const double a, const double x)
+{
+ EVAL_RESULT(gsl_sf_poch_e(a, x, &result));
+}
+
+double gsl_sf_pochrel(const double a, const double x)
+{
+ EVAL_RESULT(gsl_sf_pochrel_e(a, x, &result));
+}