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, err/Makefile.am, err/Makefile.in, err/TODO, err/error.c, err/gsl_errno.h, err/gsl_message.h, err/message.c, err/stream.c, err/strerror.c, err/test.c, fft/ChangeLog, fft/Makefile.am, fft/Makefile.in, fft/TODO, fft/bitreverse.c, fft/bitreverse.h, fft/c_init.c, fft/c_main.c, fft/c_pass.h, fft/c_pass_2.c, fft/c_pass_3.c, fft/c_pass_4.c, fft/c_pass_5.c, fft/c_pass_6.c, fft/c_pass_7.c, fft/c_pass_n.c, fft/c_radix2.c, fft/compare.h, fft/compare_source.c, fft/complex_internal.h, fft/dft.c, fft/dft_source.c, fft/factorize.c, fft/factorize.h, fft/fft.c, fft/gsl_dft_complex.h, fft/gsl_dft_complex_float.h, fft/gsl_fft.h, fft/gsl_fft_complex.h, fft/gsl_fft_complex_float.h, fft/gsl_fft_halfcomplex.h, fft/gsl_fft_halfcomplex_float.h, fft/gsl_fft_real.h, fft/gsl_fft_real_float.h, fft/hc_init.c, fft/hc_main.c, fft/hc_pass.h, fft/hc_pass_2.c, fft/hc_pass_3.c, fft/hc_pass_4.c, fft/hc_pass_5.c, fft/hc_pass_n.c, fft/hc_radix2.c, fft/hc_unpack.c, fft/real_init.c, fft/real_main.c, fft/real_pass.h, fft/real_pass_2.c, fft/real_pass_3.c, fft/real_pass_4.c, fft/real_pass_5.c, fft/real_pass_n.c, fft/real_radix2.c, fft/real_unpack.c, fft/signals.c, fft/signals.h, fft/signals_source.c, fft/test.c, fft/test_complex_source.c, fft/test_real_source.c, fft/test_trap_source.c, fft/urand.c, fit/ChangeLog, fit/Makefile.am, fit/Makefile.in, fit/gsl_fit.h, fit/linear.c, fit/test.c, gsl/Makefile.am, gsl/Makefile.in, histogram/ChangeLog, histogram/Makefile.am, histogram/Makefile.in, histogram/TODO, histogram/add.c, histogram/add2d.c, histogram/calloc_range.c, histogram/calloc_range2d.c, histogram/copy.c, histogram/copy2d.c, histogram/file.c, histogram/file2d.c, histogram/find.c, histogram/find2d.c, histogram/get.c, histogram/get2d.c, histogram/gsl_histogram.h, histogram/gsl_histogram2d.h, histogram/init.c, histogram/init2d.c, histogram/maxval.c, histogram/maxval2d.c, histogram/oper.c, histogram/oper2d.c, histogram/params.c, histogram/params2d.c, histogram/pdf.c, histogram/pdf2d.c, 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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.
author: Joel Sherrill <joel.sherrill@OARcorp.com> 2011-04-08 17:33:11 +0000
committer: Joel Sherrill <joel.sherrill@OARcorp.com> 2011-04-08 17:33:11 +0000
commit: 73f643f3f4a55310b2c8c1a9858906b2dd676e72 (patch)
tree: b1df97f18dace4a5702b0bc7aafdfee8a2f25ada /gsl-1.9/specfunc/zeta.c
parent: ee523abdace8337d05ec4a179fcdf5de3fe0f634 (diff)
1 files changed, 1050 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/zeta.c b/gsl-1.9/specfunc/zeta.c
new file mode 100644
index 0000000..078d7d3
--- /dev/null
+++ b/gsl-1.9/specfunc/zeta.c
@@ -0,0 +1,1050 @@
+/* specfunc/zeta.c
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 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_elementary.h>
+#include <gsl/gsl_sf_exp.h>
+#include <gsl/gsl_sf_gamma.h>
+#include <gsl/gsl_sf_pow_int.h>
+#include <gsl/gsl_sf_zeta.h>
+
+#include "error.h"
+
+#include "chebyshev.h"
+#include "cheb_eval.c"
+
+#define LogTwoPi_  1.8378770664093454835606594728111235279723
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
+
+/* chebyshev fit for (s(t)-1)Zeta[s(t)]
+ * s(t)= (t+1)/2
+ * -1 <= t <= 1
+ */
+static double zeta_xlt1_data[14] = {
+  1.48018677156931561235192914649,
+  0.25012062539889426471999938167,
+  0.00991137502135360774243761467,
+ -0.00012084759656676410329833091,
+ -4.7585866367662556504652535281e-06,
+  2.2229946694466391855561441361e-07,
+ -2.2237496498030257121309056582e-09,
+ -1.0173226513229028319420799028e-10,
+  4.3756643450424558284466248449e-12,
+ -6.2229632593100551465504090814e-14,
+ -6.6116201003272207115277520305e-16,
+  4.9477279533373912324518463830e-17,
+ -1.0429819093456189719660003522e-18,
+  6.9925216166580021051464412040e-21,
+};
+static cheb_series zeta_xlt1_cs = {
+  zeta_xlt1_data,
+  13,
+  -1, 1,
+  8
+};
+
+/* chebyshev fit for (s(t)-1)Zeta[s(t)]
+ * s(t)= (19t+21)/2
+ * -1 <= t <= 1
+ */
+static double zeta_xgt1_data[30] = {
+  19.3918515726724119415911269006,
+   9.1525329692510756181581271500,
+   0.2427897658867379985365270155,
+  -0.1339000688262027338316641329,
+   0.0577827064065028595578410202,
+  -0.0187625983754002298566409700,
+   0.0039403014258320354840823803,
+  -0.0000581508273158127963598882,
+  -0.0003756148907214820704594549,
+   0.0001892530548109214349092999,
+  -0.0000549032199695513496115090,
+   8.7086484008939038610413331863e-6,
+   6.4609477924811889068410083425e-7,
+  -9.6749773915059089205835337136e-7,
+   3.6585400766767257736982342461e-7,
+  -8.4592516427275164351876072573e-8,
+   9.9956786144497936572288988883e-9,
+   1.4260036420951118112457144842e-9,
+  -1.1761968823382879195380320948e-9,
+   3.7114575899785204664648987295e-10,
+  -7.4756855194210961661210215325e-11,
+   7.8536934209183700456512982968e-12,
+   9.9827182259685539619810406271e-13,
+  -7.5276687030192221587850302453e-13,
+   2.1955026393964279988917878654e-13,
+  -4.1934859852834647427576319246e-14,
+   4.6341149635933550715779074274e-15,
+   2.3742488509048340106830309402e-16,
+  -2.7276516388124786119323824391e-16,
+   7.8473570134636044722154797225e-17
+};
+static cheb_series zeta_xgt1_cs = {
+  zeta_xgt1_data,
+  29,
+  -1, 1,
+  17
+};
+
+
+/* chebyshev fit for Ln[Zeta[s(t)] - 1 - 2^(-s(t))]
+ * s(t)= 10 + 5t
+ * -1 <= t <= 1; 5 <= s <= 15
+ */
+static double zetam1_inter_data[24] = {
+  -21.7509435653088483422022339374,
+  -5.63036877698121782876372020472,
+   0.0528041358684229425504861579635,
+  -0.0156381809179670789342700883562,
+   0.00408218474372355881195080781927,
+  -0.0010264867349474874045036628282,
+   0.000260469880409886900143834962387,
+  -0.0000676175847209968878098566819447,
+   0.0000179284472587833525426660171124,
+  -4.83238651318556188834107605116e-6,
+   1.31913788964999288471371329447e-6,
+  -3.63760500656329972578222188542e-7,
+   1.01146847513194744989748396574e-7,
+  -2.83215225141806501619105289509e-8,
+   7.97733710252021423361012829496e-9,
+  -2.25850168553956886676250696891e-9,
+   6.42269392950164306086395744145e-10,
+  -1.83363861846127284505060843614e-10,
+   5.25309763895283179960368072104e-11,
+  -1.50958687042589821074710575446e-11,
+   4.34997545516049244697776942981e-12,
+  -1.25597782748190416118082322061e-12,
+   3.61280740072222650030134104162e-13,
+  -9.66437239205745207188920348801e-14
+}; 
+static cheb_series zetam1_inter_cs = {
+  zetam1_inter_data,
+  22,
+  -1, 1,
+  12
+};
+
+
+
+/* assumes s >= 0 and s != 1.0 */
+inline
+static int
+riemann_zeta_sgt0(double s, gsl_sf_result * result)
+{
+  if(s < 1.0) {
+    gsl_sf_result c;
+    cheb_eval_e(&zeta_xlt1_cs, 2.0*s - 1.0, &c);
+    result->val = c.val / (s - 1.0);
+    result->err = c.err / fabs(s-1.0) + GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+  else if(s <= 20.0) {
+    double x = (2.0*s - 21.0)/19.0;
+    gsl_sf_result c;
+    cheb_eval_e(&zeta_xgt1_cs, x, &c);
+    result->val = c.val / (s - 1.0);
+    result->err = c.err / (s - 1.0) + GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+  else {
+    double f2 = 1.0 - pow(2.0,-s);
+    double f3 = 1.0 - pow(3.0,-s);
+    double f5 = 1.0 - pow(5.0,-s);
+    double f7 = 1.0 - pow(7.0,-s);
+    result->val = 1.0/(f2*f3*f5*f7);
+    result->err = 3.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+}
+
+
+inline
+static int
+riemann_zeta1ms_slt0(double s, gsl_sf_result * result)
+{
+  if(s > -19.0) {
+    double x = (-19 - 2.0*s)/19.0;
+    gsl_sf_result c;
+    cheb_eval_e(&zeta_xgt1_cs, x, &c);
+    result->val = c.val / (-s);
+    result->err = c.err / (-s) + GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+  else {
+    double f2 = 1.0 - pow(2.0,-(1.0-s));
+    double f3 = 1.0 - pow(3.0,-(1.0-s));
+    double f5 = 1.0 - pow(5.0,-(1.0-s));
+    double f7 = 1.0 - pow(7.0,-(1.0-s));
+    result->val = 1.0/(f2*f3*f5*f7);
+    result->err = 3.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+}
+
+
+/* works for 5 < s < 15*/
+static int
+riemann_zeta_minus_1_intermediate_s(double s, gsl_sf_result * result)
+{
+  double t = (s - 10.0)/5.0;
+  gsl_sf_result c;
+  cheb_eval_e(&zetam1_inter_cs, t, &c);
+  result->val = exp(c.val) + pow(2.0, -s);
+  result->err = (c.err + 2.0*GSL_DBL_EPSILON)*result->val;
+  return GSL_SUCCESS;
+}
+
+
+/* assumes s is large and positive
+ * write: zeta(s) - 1 = zeta(s) * (1 - 1/zeta(s))
+ * and expand a few terms of the product formula to evaluate 1 - 1/zeta(s)
+ *
+ * works well for s > 15
+ */
+static int
+riemann_zeta_minus1_large_s(double s, gsl_sf_result * result)
+{
+  double a = pow( 2.0,-s);
+  double b = pow( 3.0,-s);
+  double c = pow( 5.0,-s);
+  double d = pow( 7.0,-s);
+  double e = pow(11.0,-s);
+  double f = pow(13.0,-s);
+  double t1 = a + b + c + d + e + f;
+  double t2 = a*(b+c+d+e+f) + b*(c+d+e+f) + c*(d+e+f) + d*(e+f) + e*f;
+  /*
+  double t3 = a*(b*(c+d+e+f) + c*(d+e+f) + d*(e+f) + e*f) +
+              b*(c*(d+e+f) + d*(e+f) + e*f) +
+              c*(d*(e+f) + e*f) +
+              d*e*f;
+  double t4 = a*(b*(c*(d + e + f) + d*(e + f) + e*f) + c*(d*(e+f) + e*f) + d*e*f) +
+              b*(c*(d*(e+f) + e*f) + d*e*f) +
+              c*d*e*f;
+  double t5 = b*c*d*e*f + a*c*d*e*f+ a*b*d*e*f+ a*b*c*e*f+ a*b*c*d*f+ a*b*c*d*e;
+  double t6 = a*b*c*d*e*f;
+  */
+  double numt = t1 - t2 /* + t3 - t4 + t5 - t6 */;
+  double zeta = 1.0/((1.0-a)*(1.0-b)*(1.0-c)*(1.0-d)*(1.0-e)*(1.0-f));
+  result->val = numt*zeta;
+  result->err = (15.0/s + 1.0) * 6.0*GSL_DBL_EPSILON*result->val;
+  return GSL_SUCCESS;
+}
+
+
+#if 0
+/* zeta(n) */
+#define ZETA_POS_TABLE_NMAX   100
+static double zeta_pos_int_table_OLD[ZETA_POS_TABLE_NMAX+1] = {
+ -0.50000000000000000000000000000,       /* zeta(0) */
+  0.0 /* FIXME: DirectedInfinity() */,   /* zeta(1) */
+  1.64493406684822643647241516665,       /* ...     */
+  1.20205690315959428539973816151,
+  1.08232323371113819151600369654,
+  1.03692775514336992633136548646,
+  1.01734306198444913971451792979,
+  1.00834927738192282683979754985,
+  1.00407735619794433937868523851,
+  1.00200839282608221441785276923,
+  1.00099457512781808533714595890,
+  1.00049418860411946455870228253,
+  1.00024608655330804829863799805,
+  1.00012271334757848914675183653,
+  1.00006124813505870482925854511,
+  1.00003058823630702049355172851,
+  1.00001528225940865187173257149,
+  1.00000763719763789976227360029,
+  1.00000381729326499983985646164,
+  1.00000190821271655393892565696,
+  1.00000095396203387279611315204,
+  1.00000047693298678780646311672,
+  1.00000023845050272773299000365,
+  1.00000011921992596531107306779,
+  1.00000005960818905125947961244,
+  1.00000002980350351465228018606,
+  1.00000001490155482836504123466,
+  1.00000000745071178983542949198,
+  1.00000000372533402478845705482,
+  1.00000000186265972351304900640,
+  1.00000000093132743241966818287,
+  1.00000000046566290650337840730,
+  1.00000000023283118336765054920,
+  1.00000000011641550172700519776,
+  1.00000000005820772087902700889,
+  1.00000000002910385044497099687,
+  1.00000000001455192189104198424,
+  1.00000000000727595983505748101,
+  1.00000000000363797954737865119,
+  1.00000000000181898965030706595,
+  1.00000000000090949478402638893,
+  1.00000000000045474737830421540,
+  1.00000000000022737368458246525,
+  1.00000000000011368684076802278,
+  1.00000000000005684341987627586,
+  1.00000000000002842170976889302,
+  1.00000000000001421085482803161,
+  1.00000000000000710542739521085,
+  1.00000000000000355271369133711,
+  1.00000000000000177635684357912,
+  1.00000000000000088817842109308,
+  1.00000000000000044408921031438,
+  1.00000000000000022204460507980,
+  1.00000000000000011102230251411,
+  1.00000000000000005551115124845,
+  1.00000000000000002775557562136,
+  1.00000000000000001387778780973,
+  1.00000000000000000693889390454,
+  1.00000000000000000346944695217,
+  1.00000000000000000173472347605,
+  1.00000000000000000086736173801,
+  1.00000000000000000043368086900,
+  1.00000000000000000021684043450,
+  1.00000000000000000010842021725,
+  1.00000000000000000005421010862,
+  1.00000000000000000002710505431,
+  1.00000000000000000001355252716,
+  1.00000000000000000000677626358,
+  1.00000000000000000000338813179,
+  1.00000000000000000000169406589,
+  1.00000000000000000000084703295,
+  1.00000000000000000000042351647,
+  1.00000000000000000000021175824,
+  1.00000000000000000000010587912,
+  1.00000000000000000000005293956,
+  1.00000000000000000000002646978,
+  1.00000000000000000000001323489,
+  1.00000000000000000000000661744,
+  1.00000000000000000000000330872,
+  1.00000000000000000000000165436,
+  1.00000000000000000000000082718,
+  1.00000000000000000000000041359,
+  1.00000000000000000000000020680,
+  1.00000000000000000000000010340,
+  1.00000000000000000000000005170,
+  1.00000000000000000000000002585,
+  1.00000000000000000000000001292,
+  1.00000000000000000000000000646,
+  1.00000000000000000000000000323,
+  1.00000000000000000000000000162,
+  1.00000000000000000000000000081,
+  1.00000000000000000000000000040,
+  1.00000000000000000000000000020,
+  1.00000000000000000000000000010,
+  1.00000000000000000000000000005,
+  1.00000000000000000000000000003,
+  1.00000000000000000000000000001,
+  1.00000000000000000000000000001,
+  1.00000000000000000000000000000,
+  1.00000000000000000000000000000,
+  1.00000000000000000000000000000
+};
+#endif /* 0 */
+
+
+/* zeta(n) - 1 */
+#define ZETA_POS_TABLE_NMAX   100
+static double zetam1_pos_int_table[ZETA_POS_TABLE_NMAX+1] = {
+ -1.5,                               /* zeta(0) */
+  0.0,       /* FIXME: Infinity */   /* zeta(1) - 1 */
+  0.644934066848226436472415166646,  /* zeta(2) - 1 */
+  0.202056903159594285399738161511,
+  0.082323233711138191516003696541,
+  0.036927755143369926331365486457,
+  0.017343061984449139714517929790,
+  0.008349277381922826839797549849,
+  0.004077356197944339378685238508,
+  0.002008392826082214417852769232,
+  0.000994575127818085337145958900,
+  0.000494188604119464558702282526,
+  0.000246086553308048298637998047,
+  0.000122713347578489146751836526,
+  0.000061248135058704829258545105,
+  0.000030588236307020493551728510,
+  0.000015282259408651871732571487,
+  7.6371976378997622736002935630e-6,
+  3.8172932649998398564616446219e-6,
+  1.9082127165539389256569577951e-6,
+  9.5396203387279611315203868344e-7,
+  4.7693298678780646311671960437e-7,
+  2.3845050272773299000364818675e-7,
+  1.1921992596531107306778871888e-7,
+  5.9608189051259479612440207935e-8,
+  2.9803503514652280186063705069e-8,
+  1.4901554828365041234658506630e-8,
+  7.4507117898354294919810041706e-9,
+  3.7253340247884570548192040184e-9,
+  1.8626597235130490064039099454e-9,
+  9.3132743241966818287176473502e-10,
+  4.6566290650337840729892332512e-10,
+  2.3283118336765054920014559759e-10,
+  1.1641550172700519775929738354e-10,
+  5.8207720879027008892436859891e-11,
+  2.9103850444970996869294252278e-11,
+  1.4551921891041984235929632245e-11,
+  7.2759598350574810145208690123e-12,
+  3.6379795473786511902372363558e-12,
+  1.8189896503070659475848321007e-12,
+  9.0949478402638892825331183869e-13,
+  4.5474737830421540267991120294e-13,
+  2.2737368458246525152268215779e-13,
+  1.1368684076802278493491048380e-13,
+  5.6843419876275856092771829675e-14,
+  2.8421709768893018554550737049e-14,
+  1.4210854828031606769834307141e-14,
+  7.1054273952108527128773544799e-15,
+  3.5527136913371136732984695340e-15,
+  1.7763568435791203274733490144e-15,
+  8.8817842109308159030960913863e-16,
+  4.4408921031438133641977709402e-16,
+  2.2204460507980419839993200942e-16,
+  1.1102230251410661337205445699e-16,
+  5.5511151248454812437237365905e-17,
+  2.7755575621361241725816324538e-17,
+  1.3877787809725232762839094906e-17,
+  6.9388939045441536974460853262e-18,
+  3.4694469521659226247442714961e-18,
+  1.7347234760475765720489729699e-18,
+  8.6736173801199337283420550673e-19,
+  4.3368086900206504874970235659e-19,
+  2.1684043449972197850139101683e-19,
+  1.0842021724942414063012711165e-19,
+  5.4210108624566454109187004043e-20,
+  2.7105054312234688319546213119e-20,
+  1.3552527156101164581485233996e-20,
+  6.7762635780451890979952987415e-21,
+  3.3881317890207968180857031004e-21,
+  1.6940658945097991654064927471e-21,
+  8.4703294725469983482469926091e-22,
+  4.2351647362728333478622704833e-22,
+  2.1175823681361947318442094398e-22,
+  1.0587911840680233852265001539e-22,
+  5.2939559203398703238139123029e-23,
+  2.6469779601698529611341166842e-23,
+  1.3234889800848990803094510250e-23,
+  6.6174449004244040673552453323e-24,
+  3.3087224502121715889469563843e-24,
+  1.6543612251060756462299236771e-24,
+  8.2718061255303444036711056167e-25,
+  4.1359030627651609260093824555e-25,
+  2.0679515313825767043959679193e-25,
+  1.0339757656912870993284095591e-25,
+  5.1698788284564313204101332166e-26,
+  2.5849394142282142681277617708e-26,
+  1.2924697071141066700381126118e-26,
+  6.4623485355705318034380021611e-27,
+  3.2311742677852653861348141180e-27,
+  1.6155871338926325212060114057e-27,
+  8.0779356694631620331587381863e-28,
+  4.0389678347315808256222628129e-28,
+  2.0194839173657903491587626465e-28,
+  1.0097419586828951533619250700e-28,
+  5.0487097934144756960847711725e-29,
+  2.5243548967072378244674341938e-29,
+  1.2621774483536189043753999660e-29,
+  6.3108872417680944956826093943e-30,
+  3.1554436208840472391098412184e-30,
+  1.5777218104420236166444327830e-30,
+  7.8886090522101180735205378276e-31
+};
+
+
+#define ZETA_NEG_TABLE_NMAX  99
+#define ZETA_NEG_TABLE_SIZE  50
+static double zeta_neg_int_table[ZETA_NEG_TABLE_SIZE] = {
+ -0.083333333333333333333333333333,     /* zeta(-1) */
+  0.008333333333333333333333333333,     /* zeta(-3) */
+ -0.003968253968253968253968253968,     /* ...      */
+  0.004166666666666666666666666667,
+ -0.007575757575757575757575757576,
+  0.021092796092796092796092796093,
+ -0.083333333333333333333333333333,
+  0.44325980392156862745098039216,
+ -3.05395433027011974380395433027,
+  26.4562121212121212121212121212,
+ -281.460144927536231884057971014,
+  3607.5105463980463980463980464,
+ -54827.583333333333333333333333,
+  974936.82385057471264367816092,
+ -2.0052695796688078946143462272e+07,
+  4.7238486772162990196078431373e+08,
+ -1.2635724795916666666666666667e+10,
+  3.8087931125245368811553022079e+11,
+ -1.2850850499305083333333333333e+13,
+  4.8241448354850170371581670362e+14,
+ -2.0040310656516252738108421663e+16,
+  9.1677436031953307756992753623e+17,
+ -4.5979888343656503490437943262e+19,
+  2.5180471921451095697089023320e+21,
+ -1.5001733492153928733711440151e+23,
+  9.6899578874635940656497942895e+24,
+ -6.7645882379292820990945242302e+26,
+  5.0890659468662289689766332916e+28,
+ -4.1147288792557978697665486068e+30,
+  3.5666582095375556109684574609e+32,
+ -3.3066089876577576725680214670e+34,
+  3.2715634236478716264211227016e+36,
+ -3.4473782558278053878256455080e+38,
+  3.8614279832705258893092720200e+40,
+ -4.5892974432454332168863989006e+42,
+  5.7775386342770431824884825688e+44,
+ -7.6919858759507135167410075972e+46,
+  1.0813635449971654696354033351e+49,
+ -1.6029364522008965406067102346e+51,
+  2.5019479041560462843656661499e+53,
+ -4.1067052335810212479752045004e+55,
+  7.0798774408494580617452972433e+57,
+ -1.2804546887939508790190849756e+60,
+  2.4267340392333524078020892067e+62,
+ -4.8143218874045769355129570066e+64,
+  9.9875574175727530680652777408e+66,
+ -2.1645634868435185631335136160e+69,
+  4.8962327039620553206849224516e+71,    /* ...        */
+ -1.1549023923963519663954271692e+74,    /* zeta(-97)  */
+  2.8382249570693706959264156336e+76     /* zeta(-99)  */
+};
+
+
+/* coefficients for Maclaurin summation in hzeta()
+ * B_{2j}/(2j)!
+ */
+static double hzeta_c[15] = {
+  1.00000000000000000000000000000,
+  0.083333333333333333333333333333,
+ -0.00138888888888888888888888888889,
+  0.000033068783068783068783068783069,
+ -8.2671957671957671957671957672e-07,
+  2.0876756987868098979210090321e-08,
+ -5.2841901386874931848476822022e-10,
+  1.3382536530684678832826980975e-11,
+ -3.3896802963225828668301953912e-13,
+  8.5860620562778445641359054504e-15,
+ -2.1748686985580618730415164239e-16,
+  5.5090028283602295152026526089e-18,
+ -1.3954464685812523340707686264e-19,
+  3.5347070396294674716932299778e-21,
+ -8.9535174270375468504026113181e-23
+};
+
+#define ETA_POS_TABLE_NMAX  100
+static double eta_pos_int_table[ETA_POS_TABLE_NMAX+1] = {
+0.50000000000000000000000000000,  /* eta(0) */
+M_LN2,                            /* eta(1) */
+0.82246703342411321823620758332,  /* ...    */
+0.90154267736969571404980362113,
+0.94703282949724591757650323447,
+0.97211977044690930593565514355,
+0.98555109129743510409843924448,
+0.99259381992283028267042571313,
+0.99623300185264789922728926008,
+0.99809429754160533076778303185,
+0.99903950759827156563922184570,
+0.99951714349806075414409417483,
+0.99975768514385819085317967871,
+0.99987854276326511549217499282,
+0.99993917034597971817095419226,
+0.99996955121309923808263293263,
+0.99998476421490610644168277496,
+0.99999237829204101197693787224,
+0.99999618786961011347968922641,
+0.99999809350817167510685649297,
+0.99999904661158152211505084256,
+0.99999952325821554281631666433,
+0.99999976161323082254789720494,
+0.99999988080131843950322382485,
+0.99999994039889239462836140314,
+0.99999997019885696283441513311,
+0.99999998509923199656878766181,
+0.99999999254955048496351585274,
+0.99999999627475340010872752767,
+0.99999999813736941811218674656,
+0.99999999906868228145397862728,
+0.99999999953434033145421751469,
+0.99999999976716989595149082282,
+0.99999999988358485804603047265,
+0.99999999994179239904531592388,
+0.99999999997089618952980952258,
+0.99999999998544809143388476396,
+0.99999999999272404460658475006,
+0.99999999999636202193316875550,
+0.99999999999818101084320873555,
+0.99999999999909050538047887809,
+0.99999999999954525267653087357,
+0.99999999999977262633369589773,
+0.99999999999988631316532476488,
+0.99999999999994315658215465336,
+0.99999999999997157829090808339,
+0.99999999999998578914539762720,
+0.99999999999999289457268000875,
+0.99999999999999644728633373609,
+0.99999999999999822364316477861,
+0.99999999999999911182158169283,
+0.99999999999999955591079061426,
+0.99999999999999977795539522974,
+0.99999999999999988897769758908,
+0.99999999999999994448884878594,
+0.99999999999999997224442439010,
+0.99999999999999998612221219410,
+0.99999999999999999306110609673,
+0.99999999999999999653055304826,
+0.99999999999999999826527652409,
+0.99999999999999999913263826204,
+0.99999999999999999956631913101,
+0.99999999999999999978315956551,
+0.99999999999999999989157978275,
+0.99999999999999999994578989138,
+0.99999999999999999997289494569,
+0.99999999999999999998644747284,
+0.99999999999999999999322373642,
+0.99999999999999999999661186821,
+0.99999999999999999999830593411,
+0.99999999999999999999915296705,
+0.99999999999999999999957648353,
+0.99999999999999999999978824176,
+0.99999999999999999999989412088,
+0.99999999999999999999994706044,
+0.99999999999999999999997353022,
+0.99999999999999999999998676511,
+0.99999999999999999999999338256,
+0.99999999999999999999999669128,
+0.99999999999999999999999834564,
+0.99999999999999999999999917282,
+0.99999999999999999999999958641,
+0.99999999999999999999999979320,
+0.99999999999999999999999989660,
+0.99999999999999999999999994830,
+0.99999999999999999999999997415,
+0.99999999999999999999999998708,
+0.99999999999999999999999999354,
+0.99999999999999999999999999677,
+0.99999999999999999999999999838,
+0.99999999999999999999999999919,
+0.99999999999999999999999999960,
+0.99999999999999999999999999980,
+0.99999999999999999999999999990,
+0.99999999999999999999999999995,
+0.99999999999999999999999999997,
+0.99999999999999999999999999999,
+0.99999999999999999999999999999,
+1.00000000000000000000000000000,
+1.00000000000000000000000000000,
+1.00000000000000000000000000000,
+};
+
+
+#define ETA_NEG_TABLE_NMAX  99
+#define ETA_NEG_TABLE_SIZE  50
+static double eta_neg_int_table[ETA_NEG_TABLE_SIZE] = {
+ 0.25000000000000000000000000000,   /* eta(-1) */
+-0.12500000000000000000000000000,   /* eta(-3) */
+ 0.25000000000000000000000000000,   /* ...      */
+-1.06250000000000000000000000000,
+ 7.75000000000000000000000000000,
+-86.3750000000000000000000000000,
+ 1365.25000000000000000000000000,
+-29049.0312500000000000000000000,
+ 800572.750000000000000000000000,
+-2.7741322625000000000000000000e+7,
+ 1.1805291302500000000000000000e+9,
+-6.0523980051687500000000000000e+10,
+ 3.6794167785377500000000000000e+12,
+-2.6170760990658387500000000000e+14,
+ 2.1531418140800295250000000000e+16,
+-2.0288775575173015930156250000e+18,
+ 2.1708009902623770590275000000e+20,
+-2.6173826968455814932120125000e+22,
+ 3.5324148876863877826668602500e+24,
+-5.3042033406864906641493838981e+26,
+ 8.8138218364311576767253114668e+28,
+-1.6128065107490778547354654864e+31,
+ 3.2355470001722734208527794569e+33,
+-7.0876727476537493198506645215e+35,
+ 1.6890450341293965779175629389e+38,
+-4.3639690731216831157655651358e+40,
+ 1.2185998827061261322605065672e+43,
+-3.6670584803153006180101262324e+45,
+ 1.1859898526302099104271449748e+48,
+-4.1120769493584015047981746438e+50,
+ 1.5249042436787620309090168687e+53,
+-6.0349693196941307074572991901e+55,
+ 2.5437161764210695823197691519e+58,
+-1.1396923802632287851130360170e+61,
+ 5.4180861064753979196802726455e+63,
+-2.7283654799994373847287197104e+66,
+ 1.4529750514918543238511171663e+69,
+-8.1705519371067450079777183386e+71,
+ 4.8445781606678367790247757259e+74,
+-3.0246694206649519336179448018e+77,
+ 1.9858807961690493054169047970e+80,
+-1.3694474620720086994386818232e+83,
+ 9.9070382984295807826303785989e+85,
+-7.5103780796592645925968460677e+88,
+ 5.9598418264260880840077992227e+91,
+-4.9455988887500020399263196307e+94,
+ 4.2873596927020241277675775935e+97,
+-3.8791952037716162900707994047e+100,
+ 3.6600317773156342245401829308e+103,
+-3.5978775704117283875784869570e+106    /* eta(-99)  */
+};
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
+
+
+int gsl_sf_hzeta_e(const double s, const double q, gsl_sf_result * result)
+{
+  /* CHECK_POINTER(result) */
+
+  if(s <= 1.0 || q <= 0.0) {
+    DOMAIN_ERROR(result);
+  }
+  else {
+    const double max_bits = 54.0;
+    const double ln_term0 = -s * log(q);  
+
+    if(ln_term0 < GSL_LOG_DBL_MIN + 1.0) {
+      UNDERFLOW_ERROR(result);
+    }
+    else if(ln_term0 > GSL_LOG_DBL_MAX - 1.0) {
+      OVERFLOW_ERROR (result);
+    }
+    else if((s > max_bits && q < 1.0) || (s > 0.5*max_bits && q < 0.25)) {
+      result->val = pow(q, -s);
+      result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+      return GSL_SUCCESS;
+    }
+    else if(s > 0.5*max_bits && q < 1.0) {
+      const double p1 = pow(q, -s);
+      const double p2 = pow(q/(1.0+q), s);
+      const double p3 = pow(q/(2.0+q), s);
+      result->val = p1 * (1.0 + p2 + p3);
+      result->err = GSL_DBL_EPSILON * (0.5*s + 2.0) * fabs(result->val);
+      return GSL_SUCCESS;
+    }
+    else {
+      /* Euler-Maclaurin summation formula 
+       * [Moshier, p. 400, with several typo corrections]
+       */
+      const int jmax = 12;
+      const int kmax = 10;
+      int j, k;
+      const double pmax  = pow(kmax + q, -s);
+      double scp = s;
+      double pcp = pmax / (kmax + q);
+      double ans = pmax*((kmax+q)/(s-1.0) + 0.5);
+
+      for(k=0; k<kmax; k++) {
+        ans += pow(k + q, -s);
+      }
+
+      for(j=0; j<=jmax; j++) {
+        double delta = hzeta_c[j+1] * scp * pcp;
+        ans += delta;
+        if(fabs(delta/ans) < 0.5*GSL_DBL_EPSILON) break;
+        scp *= (s+2*j+1)*(s+2*j+2);
+        pcp /= (kmax + q)*(kmax + q);
+      }
+
+      result->val = ans;
+      result->err = 2.0 * (jmax + 1.0) * GSL_DBL_EPSILON * fabs(ans);
+      return GSL_SUCCESS;
+    }
+  }
+}
+
+
+int gsl_sf_zeta_e(const double s, gsl_sf_result * result)
+{
+  /* CHECK_POINTER(result) */
+
+  if(s == 1.0) {
+    DOMAIN_ERROR(result);
+  }
+  else if(s >= 0.0) {
+    return riemann_zeta_sgt0(s, result);
+  }
+  else {
+    /* reflection formula, [Abramowitz+Stegun, 23.2.5] */
+
+    gsl_sf_result zeta_one_minus_s;
+    const int stat_zoms = riemann_zeta1ms_slt0(s, &zeta_one_minus_s);
+    const double sin_term = (fmod(s,2.0) == 0.0) ? 0.0 : sin(0.5*M_PI*fmod(s,4.0))/M_PI;
+
+    if(sin_term == 0.0) {
+      result->val = 0.0;
+      result->err = 0.0;
+      return GSL_SUCCESS;
+    }
+    else if(s > -170) {
+      /* We have to be careful about losing digits
+       * in calculating pow(2 Pi, s). The gamma
+       * function is fine because we were careful
+       * with that implementation.
+       * We keep an array of (2 Pi)^(10 n).
+       */
+      const double twopi_pow[18] = { 1.0,
+                                     9.589560061550901348e+007,
+                                     9.195966217409212684e+015,
+                                     8.818527036583869903e+023,
+                                     8.456579467173150313e+031,
+                                     8.109487671573504384e+039,
+                                     7.776641909496069036e+047,
+                                     7.457457466828644277e+055,
+                                     7.151373628461452286e+063,
+                                     6.857852693272229709e+071,
+                                     6.576379029540265771e+079,
+                                     6.306458169130020789e+087,
+                                     6.047615938853066678e+095,
+                                     5.799397627482402614e+103,
+                                     5.561367186955830005e+111,
+                                     5.333106466365131227e+119,
+                                     5.114214477385391780e+127,
+                                     4.904306689854036836e+135
+                                    };
+      const int n = floor((-s)/10.0);
+      const double fs = s + 10.0*n;
+      const double p = pow(2.0*M_PI, fs) / twopi_pow[n];
+
+      gsl_sf_result g;
+      const int stat_g = gsl_sf_gamma_e(1.0-s, &g);
+      result->val  = p * g.val * sin_term * zeta_one_minus_s.val;
+      result->err  = fabs(p * g.val * sin_term) * zeta_one_minus_s.err;
+      result->err += fabs(p * sin_term * zeta_one_minus_s.val) * g.err;
+      result->err += GSL_DBL_EPSILON * (fabs(s)+2.0) * fabs(result->val);
+      return GSL_ERROR_SELECT_2(stat_g, stat_zoms);
+    }
+    else {
+      /* The actual zeta function may or may not
+       * overflow here. But we have no easy way
+       * to calculate it when the prefactor(s)
+       * overflow. Trying to use log's and exp
+       * is no good because we loose a couple
+       * digits to the exp error amplification.
+       * When we gather a little more patience,
+       * we can implement something here. Until
+       * then just give up.
+       */
+      OVERFLOW_ERROR(result);
+    }
+  }
+}
+
+
+int gsl_sf_zeta_int_e(const int n, gsl_sf_result * result)
+{
+  /* CHECK_POINTER(result) */
+
+  if(n < 0) {
+    if(!GSL_IS_ODD(n)) {
+      result->val = 0.0; /* exactly zero at even negative integers */
+      result->err = 0.0;
+      return GSL_SUCCESS;
+    }
+    else if(n > -ZETA_NEG_TABLE_NMAX) {
+      result->val = zeta_neg_int_table[-(n+1)/2];
+      result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+      return GSL_SUCCESS;
+    }
+    else {
+      return gsl_sf_zeta_e((double)n, result);
+    }
+  }
+  else if(n == 1){
+    DOMAIN_ERROR(result);
+  }
+  else if(n <= ZETA_POS_TABLE_NMAX){
+    result->val = 1.0 + zetam1_pos_int_table[n];
+    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+  else {
+    result->val = 1.0;
+    result->err = GSL_DBL_EPSILON;
+    return GSL_SUCCESS;
+  }
+}
+
+
+int gsl_sf_zetam1_e(const double s, gsl_sf_result * result)
+{
+  if(s <= 5.0)
+  {
+    int stat = gsl_sf_zeta_e(s, result);
+    result->val = result->val - 1.0;
+    return stat;
+  }
+  else if(s < 15.0)
+  {
+    return riemann_zeta_minus_1_intermediate_s(s, result);
+  }
+  else
+  {
+    return riemann_zeta_minus1_large_s(s, result);
+  }
+}
+
+
+int gsl_sf_zetam1_int_e(const int n, gsl_sf_result * result)
+{
+  if(n < 0) {
+    if(!GSL_IS_ODD(n)) {
+      result->val = -1.0; /* at even negative integers zetam1 == -1 since zeta is exactly zero */
+      result->err = 0.0;
+      return GSL_SUCCESS;
+    }
+    else if(n > -ZETA_NEG_TABLE_NMAX) {
+      result->val = zeta_neg_int_table[-(n+1)/2] - 1.0;
+      result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+      return GSL_SUCCESS;
+    }
+    else {
+      /* could use gsl_sf_zetam1_e here but subtracting 1 makes no difference
+         for such large values, so go straight to the result */
+      return gsl_sf_zeta_e((double)n, result);  
+    }
+  }
+  else if(n == 1){
+    DOMAIN_ERROR(result);
+  }
+  else if(n <= ZETA_POS_TABLE_NMAX){
+    result->val = zetam1_pos_int_table[n];
+    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+  else {
+    return gsl_sf_zetam1_e(n, result);
+  }
+}
+
+
+int gsl_sf_eta_int_e(int n, gsl_sf_result * result)
+{
+  if(n > ETA_POS_TABLE_NMAX) {
+    result->val = 1.0;
+    result->err = GSL_DBL_EPSILON;
+    return GSL_SUCCESS;
+  }
+  else if(n >= 0) {
+    result->val = eta_pos_int_table[n];
+    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+  else {
+    /* n < 0 */
+
+    if(!GSL_IS_ODD(n)) {
+      /* exactly zero at even negative integers */
+      result->val = 0.0;
+      result->err = 0.0;
+      return GSL_SUCCESS;
+    }
+    else if(n > -ETA_NEG_TABLE_NMAX) {
+      result->val = eta_neg_int_table[-(n+1)/2];
+      result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+      return GSL_SUCCESS;
+    }
+    else {
+      gsl_sf_result z;
+      gsl_sf_result p;
+      int stat_z = gsl_sf_zeta_int_e(n, &z);
+      int stat_p = gsl_sf_exp_e((1.0-n)*M_LN2, &p);
+      int stat_m = gsl_sf_multiply_e(-p.val, z.val, result);
+      result->err  = fabs(p.err * (M_LN2*(1.0-n)) * z.val) + z.err * fabs(p.val);
+      result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+      return GSL_ERROR_SELECT_3(stat_m, stat_p, stat_z);
+    }
+  }
+}
+
+
+int gsl_sf_eta_e(const double s, gsl_sf_result * result)
+{
+  /* CHECK_POINTER(result) */
+
+  if(s > 100.0) {
+    result->val = 1.0;
+    result->err = GSL_DBL_EPSILON;
+    return GSL_SUCCESS;
+  }
+  else if(fabs(s-1.0) < 10.0*GSL_ROOT5_DBL_EPSILON) {
+    double del = s-1.0;
+    double c0  = M_LN2;
+    double c1  = M_LN2 * (M_EULER - 0.5*M_LN2);
+    double c2  = -0.0326862962794492996;
+    double c3  =  0.0015689917054155150;
+    double c4  =  0.00074987242112047532;
+    result->val = c0 + del * (c1 + del * (c2 + del * (c3 + del * c4)));
+    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
+  }
+  else {
+    gsl_sf_result z;
+    gsl_sf_result p;
+    int stat_z = gsl_sf_zeta_e(s, &z);
+    int stat_p = gsl_sf_exp_e((1.0-s)*M_LN2, &p);
+    int stat_m = gsl_sf_multiply_e(1.0-p.val, z.val, result);
+    result->err  = fabs(p.err * (M_LN2*(1.0-s)) * z.val) + z.err * fabs(p.val);
+    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_ERROR_SELECT_3(stat_m, stat_p, stat_z);
+  }
+}
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"
+
+double gsl_sf_zeta(const double s)
+{
+  EVAL_RESULT(gsl_sf_zeta_e(s, &result));
+}
+
+double gsl_sf_hzeta(const double s, const double a)
+{
+  EVAL_RESULT(gsl_sf_hzeta_e(s, a, &result));
+}
+
+double gsl_sf_zeta_int(const int s)
+{
+  EVAL_RESULT(gsl_sf_zeta_int_e(s, &result));
+}
+
+double gsl_sf_zetam1(const double s)
+{
+  EVAL_RESULT(gsl_sf_zetam1_e(s, &result));
+}
+
+double gsl_sf_zetam1_int(const int s)
+{
+  EVAL_RESULT(gsl_sf_zetam1_int_e(s, &result));
+}
+
+double gsl_sf_eta_int(const int s)
+{
+  EVAL_RESULT(gsl_sf_eta_int_e(s, &result));
+}
+
+double gsl_sf_eta(const double s)
+{
+  EVAL_RESULT(gsl_sf_eta_e(s, &result));
+}
author	Joel Sherrill <joel.sherrill@OARcorp.com>	2011-04-08 17:33:11 +0000
committer	Joel Sherrill <joel.sherrill@OARcorp.com>	2011-04-08 17:33:11 +0000
commit	73f643f3f4a55310b2c8c1a9858906b2dd676e72 (patch)
tree	b1df97f18dace4a5702b0bc7aafdfee8a2f25ada /gsl-1.9/specfunc/zeta.c
parent	ee523abdace8337d05ec4a179fcdf5de3fe0f634 (diff)