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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/doc/math.texi
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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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.
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+@cindex elementary functions
+@cindex mathematical functions, elementary
+
+This chapter describes basic mathematical functions. Some of these
+functions are present in system libraries, but the alternative versions
+given here can be used as a substitute when the system functions are not
+available.
+
+The functions and macros described in this chapter are defined in the
+header file @file{gsl_math.h}.
+
+@menu
+* Mathematical Constants::
+* Infinities and Not-a-number::
+* Elementary Functions::
+* Small integer powers::
+* Testing the Sign of Numbers::
+* Testing for Odd and Even Numbers::
+* Maximum and Minimum functions::
+* Approximate Comparison of Floating Point Numbers::
+@end menu
+
+@node Mathematical Constants
+@section Mathematical Constants
+@cindex mathematical constants, defined as macros
+@cindex numerical constants, defined as macros
+@cindex constants, mathematical---defined as macros
+@cindex macros for mathematical constants
+The library ensures that the standard @sc{bsd} mathematical constants
+are defined. For reference, here is a list of the constants:
+
+@table @code
+@item M_E
+@cindex e, defined as a macro
+The base of exponentials, @math{e}
+
+@item M_LOG2E
+The base-2 logarithm of @math{e}, @math{\log_2 (e)}
+
+@item M_LOG10E
+The base-10 logarithm of @math{e}, @c{$\log_{10}(e)$}
+@math{\log_10 (e)}
+
+@item M_SQRT2
+The square root of two, @math{\sqrt 2}
+
+@item M_SQRT1_2
+The square root of one-half, @c{$\sqrt{1/2}$}
+@math{\sqrt@{1/2@}}
+
+@item M_SQRT3
+The square root of three, @math{\sqrt 3}
+
+@item M_PI
+@cindex pi, defined as a macro
+The constant pi, @math{\pi}
+
+@item M_PI_2
+Pi divided by two, @math{\pi/2}
+
+@item M_PI_4
+Pi divided by four, @math{\pi/4}
+
+@item M_SQRTPI
+The square root of pi, @math{\sqrt\pi}
+
+@item M_2_SQRTPI
+Two divided by the square root of pi, @math{2/\sqrt\pi}
+
+@item M_1_PI
+The reciprocal of pi, @math{1/\pi}
+
+@item M_2_PI
+Twice the reciprocal of pi, @math{2/\pi}
+
+@item M_LN10
+The natural logarithm of ten, @math{\ln(10)}
+
+@item M_LN2
+The natural logarithm of two, @math{\ln(2)}
+
+@item M_LNPI
+The natural logarithm of pi, @math{\ln(\pi)}
+
+@item M_EULER
+@cindex Euler's constant, defined as a macro
+Euler's constant, @math{\gamma}
+
+@end table
+
+@node Infinities and Not-a-number
+@section Infinities and Not-a-number
+
+@cindex infinity, defined as a macro
+@cindex IEEE infinity, defined as a macro
+@cindex NaN, defined as a macro
+@cindex Not-a-number, defined as a macro
+@cindex IEEE NaN, defined as a macro
+
+@defmac GSL_POSINF
+This macro contains the IEEE representation of positive infinity,
+@math{+\infty}. It is computed from the expression @code{+1.0/0.0}.
+@end defmac
+
+@defmac GSL_NEGINF
+This macro contains the IEEE representation of negative infinity,
+@math{-\infty}. It is computed from the expression @code{-1.0/0.0}.
+@end defmac
+
+@defmac GSL_NAN
+This macro contains the IEEE representation of the Not-a-Number symbol,
+@code{NaN}. It is computed from the ratio @code{0.0/0.0}.
+@end defmac
+
+@deftypefun int gsl_isnan (const double @var{x})
+This function returns 1 if @var{x} is not-a-number.
+@end deftypefun
+
+@deftypefun int gsl_isinf (const double @var{x})
+This function returns @math{+1} if @var{x} is positive infinity,
+@math{-1} if @var{x} is negative infinity and 0 otherwise.
+@end deftypefun
+
+@deftypefun int gsl_finite (const double @var{x})
+This function returns 1 if @var{x} is a real number, and 0 if it is
+infinite or not-a-number.
+@end deftypefun
+
+
+@node Elementary Functions
+@section Elementary Functions
+
+The following routines provide portable implementations of functions
+found in the BSD math library. When native versions are not available
+the functions described here can be used instead. The substitution can
+be made automatically if you use @code{autoconf} to compile your
+application (@pxref{Portability functions}).
+
+@deftypefun double gsl_log1p (const double @var{x})
+@cindex log1p
+@cindex logarithm, computed accurately near 1
+This function computes the value of @math{\log(1+x)} in a way that is
+accurate for small @var{x}. It provides an alternative to the BSD math
+function @code{log1p(x)}.
+@end deftypefun
+
+@deftypefun double gsl_expm1 (const double @var{x})
+@cindex expm1
+@cindex exponential, difference from 1 computed accurately
+This function computes the value of @math{\exp(x)-1} in a way that is
+accurate for small @var{x}. It provides an alternative to the BSD math
+function @code{expm1(x)}.
+@end deftypefun
+
+@deftypefun double gsl_hypot (const double @var{x}, const double @var{y})
+@cindex hypot
+@cindex euclidean distance function, hypot
+@cindex length, computed accurately using hypot
+This function computes the value of
+@c{$\sqrt{x^2 + y^2}$}
+@math{\sqrt@{x^2 + y^2@}} in a way that avoids overflow. It provides an
+alternative to the BSD math function @code{hypot(x,y)}.
+@end deftypefun
+
+@deftypefun double gsl_acosh (const double @var{x})
+@cindex acosh
+@cindex hyperbolic cosine, inverse
+@cindex inverse hyperbolic cosine
+This function computes the value of @math{\arccosh(x)}. It provides an
+alternative to the standard math function @code{acosh(x)}.
+@end deftypefun
+
+@deftypefun double gsl_asinh (const double @var{x})
+@cindex asinh
+@cindex hyperbolic sine, inverse
+@cindex inverse hyperbolic sine
+This function computes the value of @math{\arcsinh(x)}. It provides an
+alternative to the standard math function @code{asinh(x)}.
+@end deftypefun
+
+@deftypefun double gsl_atanh (const double @var{x})
+@cindex atanh
+@cindex hyperbolic tangent, inverse
+@cindex inverse hyperbolic tangent
+This function computes the value of @math{\arctanh(x)}. It provides an
+alternative to the standard math function @code{atanh(x)}.
+@end deftypefun
+
+
+@deftypefun double gsl_ldexp (double @var{x}, int @var{e})
+@cindex ldexp
+This function computes the value of @math{x * 2^e}. It provides an
+alternative to the standard math function @code{ldexp(x,e)}.
+@end deftypefun
+
+@deftypefun double gsl_frexp (double @var{x}, int * @var{e})
+@cindex frexp
+This function splits the number @math{x} into its normalized fraction
+@math{f} and exponent @math{e}, such that @math{x = f * 2^e} and
+@c{$0.5 \le f < 1$}
+@math{0.5 <= f < 1}. The function returns @math{f} and stores the
+exponent in @math{e}. If @math{x} is zero, both @math{f} and @math{e}
+are set to zero. This function provides an alternative to the standard
+math function @code{frexp(x, e)}.
+@end deftypefun
+
+@node Small integer powers
+@section Small integer powers
+
+A common complaint about the standard C library is its lack of a
+function for calculating (small) integer powers. GSL provides some simple
+functions to fill this gap. For reasons of efficiency, these functions
+do not check for overflow or underflow conditions.
+
+@deftypefun double gsl_pow_int (double @var{x}, int @var{n})
+This routine computes the power @math{x^n} for integer @var{n}. The
+power is computed efficiently---for example, @math{x^8} is computed as
+@math{((x^2)^2)^2}, requiring only 3 multiplications. A version of this
+function which also computes the numerical error in the result is
+available as @code{gsl_sf_pow_int_e}.
+@end deftypefun
+
+@deftypefun double gsl_pow_2 (const double @var{x})
+@deftypefunx double gsl_pow_3 (const double @var{x})
+@deftypefunx double gsl_pow_4 (const double @var{x})
+@deftypefunx double gsl_pow_5 (const double @var{x})
+@deftypefunx double gsl_pow_6 (const double @var{x})
+@deftypefunx double gsl_pow_7 (const double @var{x})
+@deftypefunx double gsl_pow_8 (const double @var{x})
+@deftypefunx double gsl_pow_9 (const double @var{x})
+These functions can be used to compute small integer powers @math{x^2},
+@math{x^3}, etc. efficiently. The functions will be inlined when
+possible so that use of these functions should be as efficient as
+explicitly writing the corresponding product expression.
+@end deftypefun
+
+@example
+#include <gsl/gsl_math.h>
+double y = gsl_pow_4 (3.141) /* compute 3.141**4 */
+@end example
+
+@node Testing the Sign of Numbers
+@section Testing the Sign of Numbers
+
+@defmac GSL_SIGN (x)
+This macro returns the sign of @var{x}. It is defined as @code{((x) >= 0
+? 1 : -1)}. Note that with this definition the sign of zero is positive
+(regardless of its @sc{ieee} sign bit).
+@end defmac
+
+@node Testing for Odd and Even Numbers
+@section Testing for Odd and Even Numbers
+
+@defmac GSL_IS_ODD (n)
+This macro evaluates to 1 if @var{n} is odd and 0 if @var{n} is
+even. The argument @var{n} must be of integer type.
+@end defmac
+
+@defmac GSL_IS_EVEN (n)
+This macro is the opposite of @code{GSL_IS_ODD(n)}. It evaluates to 1 if
+@var{n} is even and 0 if @var{n} is odd. The argument @var{n} must be of
+integer type.
+@end defmac
+
+@node Maximum and Minimum functions
+@section Maximum and Minimum functions
+
+@defmac GSL_MAX (a, b)
+@cindex maximum of two numbers
+This macro returns the maximum of @var{a} and @var{b}. It is defined as
+@code{((a) > (b) ? (a):(b))}.
+@end defmac
+
+@defmac GSL_MIN (a, b)
+@cindex minimum of two numbers
+This macro returns the minimum of @var{a} and @var{b}. It is defined as
+@code{((a) < (b) ? (a):(b))}.
+@end defmac
+
+@deftypefun {extern inline double} GSL_MAX_DBL (double @var{a}, double @var{b})
+This function returns the maximum of the double precision numbers
+@var{a} and @var{b} using an inline function. The use of a function
+allows for type checking of the arguments as an extra safety feature. On
+platforms where inline functions are not available the macro
+@code{GSL_MAX} will be automatically substituted.
+@end deftypefun
+
+@deftypefun {extern inline double} GSL_MIN_DBL (double @var{a}, double @var{b})
+This function returns the minimum of the double precision numbers
+@var{a} and @var{b} using an inline function. The use of a function
+allows for type checking of the arguments as an extra safety feature. On
+platforms where inline functions are not available the macro
+@code{GSL_MIN} will be automatically substituted.
+@end deftypefun
+
+@deftypefun {extern inline int} GSL_MAX_INT (int @var{a}, int @var{b})
+@deftypefunx {extern inline int} GSL_MIN_INT (int @var{a}, int @var{b})
+These functions return the maximum or minimum of the integers @var{a}
+and @var{b} using an inline function. On platforms where inline
+functions are not available the macros @code{GSL_MAX} or @code{GSL_MIN}
+will be automatically substituted.
+@end deftypefun
+
+@deftypefun {extern inline long double} GSL_MAX_LDBL (long double @var{a}, long double @var{b})
+@deftypefunx {extern inline long double} GSL_MIN_LDBL (long double @var{a}, long double @var{b})
+These functions return the maximum or minimum of the long doubles @var{a}
+and @var{b} using an inline function. On platforms where inline
+functions are not available the macros @code{GSL_MAX} or @code{GSL_MIN}
+will be automatically substituted.
+@end deftypefun
+
+@node Approximate Comparison of Floating Point Numbers
+@section Approximate Comparison of Floating Point Numbers
+
+It is sometimes useful to be able to compare two floating point numbers
+approximately, to allow for rounding and truncation errors. The following
+function implements the approximate floating-point comparison algorithm
+proposed by D.E. Knuth in Section 4.2.2 of @cite{Seminumerical
+Algorithms} (3rd edition).
+
+@deftypefun int gsl_fcmp (double @var{x}, double @var{y}, double @var{epsilon})
+@cindex approximate comparison of floating point numbers
+@cindex safe comparison of floating point numbers
+@cindex floating point numbers, approximate comparison
+This function determines whether @math{x} and @math{y} are approximately
+equal to a relative accuracy @var{epsilon}.
+
+The relative accuracy is measured using an interval of size @math{2
+\delta}, where @math{\delta = 2^k \epsilon} and @math{k} is the
+maximum base-2 exponent of @math{x} and @math{y} as computed by the
+function @code{frexp}.
+
+If @math{x} and @math{y} lie within this interval, they are considered
+approximately equal and the function returns 0. Otherwise if @math{x <
+y}, the function returns @math{-1}, or if @math{x > y}, the function returns
+@math{+1}.
+
+The implementation is based on the package @code{fcmp} by T.C. Belding.
+@end deftypefun