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Diffstat (limited to 'regress/lib/libm/cephes/monotll.c')
| -rw-r--r-- | regress/lib/libm/cephes/monotll.c | 810 |
1 files changed, 810 insertions, 0 deletions
diff --git a/regress/lib/libm/cephes/monotll.c b/regress/lib/libm/cephes/monotll.c new file mode 100644 index 00000000000..ceccdc5da4e --- /dev/null +++ b/regress/lib/libm/cephes/monotll.c @@ -0,0 +1,810 @@ +/* $OpenBSD: monotll.c,v 1.1 2011/05/30 20:23:35 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* monotll.c + Floating point function test vectors. + 128-bit long double version. + + Arguments and function values are synthesized for NPTS points in + the vicinity of each given tabulated test point. The points are + chosen to be near and on either side of the likely function algorithm + domain boundaries. Since the function programs change their methods + at these points, major coding errors or monotonicity failures might be + detected. + + August, 1998 + S. L. Moshier */ + +#include <float.h> + +#if LDBL_MANT_DIG == 113 +/* Unit of error tolerance in test[i].thresh. */ +static long double MACHEPL = 1.9259299443872358530559779425849273185381E-34L; +/* How many times the above error to allow before printing a complaint. + If TOL < 0, consider absolute error instead of relative error. */ +#define TOL 4 +/* Number of test points to generate on each side of tabulated point. */ +#define NPTS 100 + + + +#include <stdio.h> +#include <string.h> + +/* Avoid including math.h. */ +long double frexpl (long double, int *); +long double ldexpl (long double, int); + +/* Functions of one variable. */ +long double expl (long double); +long double expm1l (long double); +long double logl (long double); +long double log1pl (long double); +long double sinl (long double); +long double cosl (long double); +long double tanl (long double); +long double atanl (long double); +long double asinl (long double); +long double acosl (long double); +long double sinhl (long double); +long double coshl (long double); +long double tanhl (long double); +long double asinhl (long double); +long double acoshl (long double); +long double atanhl (long double); +long double gammal (long double); +long double lgammal (long double); +long double tgammal (long double); +long double fabsl (long double); +long double floorl (long double); +long double j0l (long double); +long double y0l (long double); +long double j1l (long double); +long double y1l (long double); +long double jnl (int, long double); +long double ynl (int, long double); + +/* Data structure of the test. */ +struct oneargument + { + char *name; /* Name of the function. */ + long double (*func) (long double); /* Function call. */ + long double arg1; /* Function argument, assumed exact. */ + long double answer1; /* Exact number, close to function value. */ + long double answer2; /* answer1 + answer2 has extended precision. */ + long double derivative; /* dy/dx evaluated at x = arg1. */ + /* Error report threshold. 2 => 1 ulp approximately + if thresh < 0 then consider absolute error instead of relative error. */ + int thresh; + + }; + + + +static struct oneargument test1[] = +{ +#if 0 + {"exp", expl, 1.0L, 2.7182769775390625L, + 4.85091998273536028747135266249775725E-6L, + 2.71828182845904523536028747135266250E0L, TOL}, + {"exp", expl, -1.0L, 3.678741455078125e-1L, + 5.29566362982159552377016146086744581E-6L, + 3.67879441171442321595523770161460867E-1L, TOL}, + {"exp", expl, 0.5L, 1.648712158203125L, + 9.11249700314684865078781416357165378E-6L, + 1.64872127070012814684865078781416357L, TOL}, + {"exp", expl, -0.5L, 6.065216064453125e-1L, + 9.05326732092360379953499118045344192E-6L, + 6.06530659712633423603799534991180453E-1L, TOL}, + {"exp", expl, 2.0L, 7.3890533447265625L, + 2.75420408772723042746057500781318032E-6L, + 7.38905609893065022723042746057500781E0L, TOL}, + {"exp", expl, -2.0L, 1.353302001953125e-1L, + 5.08304130019189399949497248440340763E-6L, + 1.35335283236612691893999494972484403E-1L, TOL}, + {"expm1", expm1l, 1.0L, 1.7182769775390625L, + 4.85091998273536028747135266249775725E-6L, + 2.71828182845904523536028747135266250E0L, TOL}, + {"expm1", expm1l, 0.5L, 0.648712158203125L, + 9.11249700314684865078781416357165378E-6L, + 1.64872127070012814684865078781416357L, TOL}, + {"expm1", expm1l, 2.0L, 6.3890533447265625L, + 2.75420408772723042746057500781318032E-6L, + 7.38905609893065022723042746057500781E0L, TOL}, + {"log", logl, 1.41421356237309504880168872420969798L, + 3.465728759765625E-1L, + 7.14303410154708616060729088217412434E-7L, + 7.07106781186547524400844362104849086E-1L, TOL}, + {"log", logl, 7.07106781186547524400844362104848992E-1L, + -3.46588134765625E-1L, + 1.45444856523452913839392709116493369E-5L, + 1.41421356237309504880168872420969817E0L, TOL}, + {"log1p", log1pl, 0.41421356237309504880168872420969798L, + 3.465728759765625E-1L, + 7.14303410154708616060729088217412434E-7L, + 7.07106781186547524400844362104849086E-1L, TOL}, +#endif + {"sin", sinl, 7.85398163397448309615660845819875699E-1L, + 7.0709228515625E-1L, + 1.44960302975244008443621048490239551E-5L, + 7.07106781186547524400844362104849055E-1, TOL}, + {"sin", sinl, -7.85398163397448309615660845819875699E-1L, + -7.071075439453125E-1L, + 7.62758764975599155637895150976044903E-7L, + 7.07106781186547524400844362104849055E-1L, TOL}, + {"sin", sinl, 1.57079632679489661923132169163975140E0L, + 9.999847412109375E-1L, + 1.52587890625E-5L, + 0.0L, TOL}, + {"sin", sinl, -1.57079632679489661923132169163975140E0L, + -1.0L, + 0.0L, + 0.0L, TOL}, + {"sin", sinl, 4.71238898038468985769396507491925433E0L, + -1.0L, + 0.0L, + 0.0L, TOL}, + {"sin", sinl, -4.71238898038468985769396507491925420E0L, + 1.0L, + 0.0L, + 0.0L, TOL}, + {"cos", cosl, 3.92699081698724154807830422909937850E-1L, + 9.238739013671875E-1L, + 5.63114409925612818318939678829097061E-6L, + -3.82683432365089771728459984030398857E-1L, TOL}, + {"cos", cosl, 7.85398163397448309615660845819875699E-1L, + 7.0709228515625E-1L, + 1.44960302975244008443621048490546146E-5L, + -7.07106781186547524400844362104849024E-1L, TOL}, + {"cos", cosl, 1.17809724509617246442349126872981355E0L, + 3.826751708984375E-1L, + 8.26146665227172845998403039889680525E-6L, + -9.23879532511286756128183189396788274E-1L, TOL}, + {"cos", cosl, 1.96349540849362077403915211454968925E0L, + -3.826904296875E-1L, + 6.99732241022827154001596960118331183E-6L, + -9.23879532511286756128183189396788308E-1L, TOL}, + {"cos", cosl, 2.35619449019234492884698253745962710E0L, + -7.071075439453125E-1L, + 7.62758764975599155637895151006704382E-7L, + -7.07106781186547524400844362104849085E-1L, TOL}, + {"cos", cosl, 2.74889357189106908365481296036956495E0L, + -9.2388916015625E-1L, + 9.62764496324387181681060321174221497E-6L, + -3.82683432365089771728459984030398937E-1L, TOL}, + {"cos", cosl, 3.14159265358979323846264338327950280E0L, + -1.0L, + 0.0L, + 0.0L, TOL}, + {"tan", tanl, 7.8539816339744830961566084581987569936977E-1L, + 9.999847412109375E-1L, + 1.5258789062499999999999999999956640949349E-5L, + 2.0L, TOL}, + {"tan", tanl, 1.1780972450961724644234912687298135490547E0L, + 2.4141998291015625L, + 1.3733271532548801688724209697856514083701E-5L, + 6.8284271247461900976033774484193950849601E0L, TOL}, + {"tan", tanl, 1.96349540849362077403915211454968925E0L, + -2.414215087890625L, + 1.52551752995119831127579030155133768E-6L, + 6.82842712474619009760337744841939794E0L, TOL}, + {"tan", tanl, 2.35619449019234492884698253745962710E0L, + -1.0000152587890625L, + 1.52587890624999999999999999998699228E-5L, + 2.0L, TOL}, + {"tan", tanl, 2.74889357189106908365481296036956495E0L, + -4.14215087890625E-1L, + 1.52551752995119831127579030183253332E-6L, + 1.17157287525380990239662255158060392E0L, TOL}, + {"atan", atanl, 4.14213562373095048801688724209698081E-1L, + 3.926849365234375E-1L, + 1.41451752866548078304229099378622950E-5L, + 8.53553390593273762200422181052424518E-1L, TOL}, + {"atan", atanl, 1.0L, + 7.853851318359375E-1L, + 1.30315615108096156608458198757210493E-5L, + 0.5L, TOL}, + {"atan", atanl, 2.41421356237309504880168872420969818E0L, + 1.1780853271484375L, + 1.19179477349644234912687298135959800E-5L, + 1.46446609406726237799577818947575470E-1L, TOL}, + {"atan", atanl, -2.41421356237309504880168872420969818E0L, + -1.1781005859375L, + 3.34084132753557650873127018640402003E-6L, + 1.46446609406726237799577818947575470E-1L, TOL}, + {"atan", atanl, -1.0L, + -7.85400390625E-1L, + 2.22722755169038433915418012427895071E-6L, + 0.5L, TOL}, + {"atan", atanl, -4.14213562373095048801688724209698081E-1L, + -3.927001953125E-1L, + 1.11361377584519216957709006213770502E-6L, + 8.53553390593273762200422181052424518E-1L, TOL}, + {"asin", asinl, 3.82683432365089771728459984030398880E-1L, + 3.926849365234375E-1L, + 1.41451752866548078304229099378750938E-5L, + 1.08239220029239396879944641073277885E0L, TOL}, + {"asin", asinl, 0.5L, + 5.23590087890625E-1L, + 8.68770767387307710723054658381403286E-6L, + 1.15470053837925152901829756100391491E0L, TOL}, + {"asin", asinl, 7.07106781186547524400844362104848992E-1L, + 7.853851318359375E-1L, + 1.30315615108096156608458198756544240E-5L, + 1.41421356237309504880168872420969798E0L, TOL}, + {"asin", asinl, 9.23879532511286756128183189396788310E-1L, + 1.1780853271484375L, + 1.19179477349644234912687298136415266E-5L, + 2.61312592975275305571328634685437469E0L, TOL}, + {"asin", asinl, -0.5L, + -5.236053466796875E-1L, + 6.57108138862692289276945341618596714E-6L, + 1.15470053837925152901829756100391491E0L, TOL}, + {"asin", asinl, 1.16415321826934814453125E-10L, + 1.16415321826934814453125E-10L, + 2.62953635073670601805513180586984061E-31L, + 1.00000000000000000000677626357803440E0L, TOL}, + {"asin", asinl, 0.625L, + 6.751251220703125E-1L, + 6.41086671914720905626529438801420419E-6L, + 1.28102523044069706786602935814149630E0L, TOL}, + {"asin", asinl, 9.74999999999999999999999999999999981E-1L, + 1.346710205078125L, + 1.08364149523595315129076204973231659E-5L, + 4.50035160370409562029946413944745541E0L, TOL}, + {"acos", acosl, 1.95090322016128267848284868477022248E-1L, + 1.3744354248046875L, + 1.13611408470418274064801847825042255E-5L, + -1.01959115820831833788387960797568783E0L, TOL}, + {"acos", acosl, 3.82683432365089771728459984030398880E-1L, + 1.1780853271484375L, + 1.19179477349644234912687298135670048E-5L, + -1.08239220029239396879944641073277885E0L, TOL}, + {"acos", acosl, 0.5L, + 1.0471954345703125L, + 2.11662628524615421446109316762806572E-6L, + -1.15470053837925152901829756100391491E0L, TOL}, + {"acos", acosl, 7.07106781186547524400844362104848992E-1L, + 7.853851318359375E-1L, + 1.30315615108096156608458198757876746E-5L, + -1.41421356237309504880168872420969798E0L, TOL}, + {"acos", acosl, 9.23879532511286756128183189396788310E-1L, + 3.926849365234375E-1L, + 1.41451752866548078304229099378005720E-5L, + -2.61312592975275305571328634685437469E0L, TOL}, + {"acos", acosl, 9.80785280403230449126182236134239047E-1L, + 1.963348388671875E-1L, + 1.47019821745774039152114549688769794E-5L, + -5.12583089548301235759217259235540119E0L, TOL}, + {"acos", acosl, -0.5L, + 2.094390869140625L, + 4.23325257049230842892218633525613145E-6L, + -1.15470053837925152901829756100391491E0L, TOL}, +#if 0 + {"sinh", sinhl, 1.0L, + 1.1751861572265625L, + 1.50364172389568823818505956008151557E-5L, + 1.54308063481524377847790562075706168E0L, TOL}, + {"sinh", sinhl, 11355.5L, + 2.13776152623792146713900550884909252E4931L, + 9.07106102767577900425552629248457689E4896L, + 2.13776152623792146713900550884909261E4931L, TOL}, + {"sinh", sinhl, 2.22044604925031308084726333618164062E-16L, + 2.22044604925031308084726333618164062E-16L, + 1.82460737542293889443193956157541613E-48L, + 1.00000000000000000000000000000002465E0L, TOL}, + {"sinh", sinhl, 40.0L, + 1.17692633418509992E17L, 7.039499553745174001302586809814832360E-1L, + 1.176926334185099927039499553745174044E17L, TOL}, + {"sinh", sinhl, 6.938893903907228377647697925567626953E-18L, /* 2^-57 */ + 6.938893903907228377647697925567626953E-18L, + 5.568259812692074262792784306565587261E-53L, 1.0L, TOL}, + {"sinh", sinhl, 11356.375L, + 5.1282233096855457613267954696602303826729E4931L, + 6.8582733554584347269625352341976754246942E4896L, + 5.1282233096855457613267954696602304512556E4931L, TOL}, + {"cosh", coshl, 40.0L, + 1.176926334185099927039499553745174054E17L, + -1.036733679609227143506056540471143597E-18L, + 1.176926334185099927039499553745174001E17L, TOL}, + {"cosh", coshl, 6.938893903907228377647697925567626953E-18L, + 1.0L, 2.407412430484044816319972428231159158E-35L, + 6.938893903907228377647697925567627009E-18L, TOL}, + {"cosh", coshl, 11356.375L, + 5.128223309685545761326795469660230383E4931L, + 6.858273355458434726962535234197675425E4896L, + 5.128223309685545761326795469660230451E4931L, TOL}, + {"cosh", coshl, 11355.5L, + 2.13776152623792146713900550884909252E4931L, + 9.07106102767577900425552629248457689E4896L, + 2.13776152623792146713900550884909261E4931L, TOL}, + {"cosh", coshl, 1.0L, + 1.5430755615234375L, + 5.07329180627847790562075706168260153E-6L, + 1.17520119364380145688238185059560082E0L, TOL}, + {"cosh", coshl, 0.5L, + 1.12762451171875L, + 1.45348763078522622516140267201254785E-6L, + 5.21095305493747361622425626411491559E-1L, TOL}, + {"tanh", tanhl, 0.5L, + 4.621124267578125E-1L, + 4.73050219725850231848364367254873029E-6L, + 7.86447732965927410149698934343636102E-1L, TOL}, + {"tanh", tanhl, 5.49306144334054845697622618461262805E-1L, + 4.999847412109375E-1L, + 1.52587890624999999999999999999648170E-5L, + 7.50000000000000000000000000000000035E-1L, TOL}, + {"tanh", tanhl, 0.625L, + 5.54595947265625E-1L, + 3.77508375729399903909532308359605810E-6L, + 6.92419147969988069630753311573341685E-1L, TOL}, + {"tanh", tanhl, 40.0L, + 1.0L, + -3.609702775690830344624256714700054777E-35L, + 7.219405551381660689248513429400109424E-35L, TOL}, + {"tanh", tanhl, 6.9388939039072283776476979255676269531250E-18L, /* 2^-57 */ + 6.9388939039072283776476979255676269531250E-18L, + -1.1136519625384148525585568613131174280582E-52L, + 9.9999999999999999999999999999999995185175E-1L, TOL}, + {"tanh", tanhl, 2.775557561562891351059079170227050781E-17L, /* 2^-55 */ + 2.775557561562891351059079170227050781E-17L, + -7.127372560245855056374763912403949481E-51L, + 9.999999999999999999999999999999992296E-1L, TOL}, + {"tanh", tanhl, 1.0L, + 7.615814208984375e-1L, + 1.273505732738811945828260479359041277E-5L, + 4.199743416140260693944967390417014449E-1L, TOL}, + {"asinh", asinhl, 0.5L, + 4.81201171875E-1L, + 1.06531846034474977589134243684231352E-5L, + 8.94427190999915878563669467492510494E-1L, TOL}, + {"asinh", asinhl, 1.0L, + 8.813629150390625E-1L, + 1.06719804805252326093249797923090282E-5L, + 7.07106781186547524400844362104849039E-1L, TOL}, + {"asinh", asinhl, 2.0L, + 1.443634033203125L, + 1.44197568534249327674027310526940555E-6L, + 4.47213595499957939281834733746255247E-1L, TOL}, + {"asinh", asinhl, 1.3877787807814456755295395851135253906250E-17L, /*2^-56*/ + 1.3877787807814456755295395851135253906250E-17L, + -4.4546078501536594102342274452524694119585E-52L, + 9.9999999999999999999999999999999990370350E-1L, TOL}, + {"asinh", asinhl, 1.8014398509481984E16L, + 38.1230926513671875L, + 2.2794298045179477666801997120145244851447E-6L, + 5.5511151231257827021181583404540930096529E-17L, TOL}, + {"acosh", acoshl, 2.0L, + 1.31695556640625L, + 2.33051856670862504634730796844402698E-6L, + 5.77350269189625764509148780501957456E-1L, TOL}, + {"acosh", acoshl, 1.5L, + 9.624176025390625E-1L, + 6.04758014439499551782684873684627037E-6L, + 8.94427190999915878563669467492510494E-1L, TOL}, + {"acosh", acoshl, 1.03125L, + 2.493438720703125E-1L, + 9.62177257298785143907541001884302707E-6L, + 3.96911150685467059808817882107262579E0L, TOL}, + {"acosh", acoshl, 2.68435456e8L, /* 2 ^ 28 */ + 20.10125732421875L, + 1.091201966396963028457033350626731006E-5L, + 3.725290298461914088349394142282115109E-9L, TOL}, + {"acosh", acoshl, 1.8014398509481984e16L, /* 2 ^ 54 */ + 38.1230926513671875L, + 2.279429804517947766680199710473780530E-6L, + 5.551115123125782702118158340454110115E-17L, TOL}, + {"acosh", acoshl, 1.073741824e9L, /* 2^30 */ + 21.487548828125L, + 1.376923330459171735533070637272346848E-5L, + 9.313225746154785160288967834731580446E-10L, TOL}, + {"atanh", atanhl, 0.5L, + 5.493011474609375E-1L, + 4.99687311734569762261846126285232375E-6L, + 1.33333333333333333333333333333333333E0L, TOL}, + {"atanh", atanhl, 6.938893903907228377647697925567626953125E-18, + 6.938893903907228377647697925567626953125E-18, /* 2^-57 */ + 1.1136519625384148525585568613131174816786E-52, 1.0, TOL}, + {"j0", j0l, 16.0L, -1.749114990234375e-1L, + 1.24250398083151715974822741805925455E-5L, + -9.03971756613041862386833024580760244E-2L, -2}, + {"j0", j0l, 8.0L, 1.716461181640625E-1L, + 4.68897349140609086940785197200106842E-6L, + -2.34636346853914624381276651590454612E-1L, -2}, + {"j0", j0l, 5.33333333333333333333333333333333333E0L, + -6.427001953125e-2L, + 2.71515994768793872858212682917411767E-6L, + 3.46125605116223455248039758589625114E-1L, -2}, + {"j0", j0l, 4.0L, -3.9715576171875e-1L, + 5.95185490262771340923154830195802438E-6L, + 6.60433280235491361431854208032750287E-2L, -2}, + {"j0", j0l, 3.2L, -3.201904296875e-1L, + 2.26003037709271056745460231434000663E-6L, + -2.61343248780504837362986742359905319E-1L, -2}, + {"j0", j0l, 2.66666666666666666666666666666666667E0L, + -1.275634765625e-1L, + 2.48895584953746034929481550434723427E-6L, + -4.51651148392987785778929732830311060E-1L, -2}, + {"j0", j0l, 2.28571428571428571428571428571428571E0L, + 6.3262939453125e-2L, + 7.41898014310740285267270594759284975E-6L, + -5.42395540605083481518545728422177515E-1L, -2}, + {"j0", j0l, 2.0L, + 2.23876953125e-1L, + 1.38260162356680518274546499486258252E-5L, + -5.76724807756873387202448242269137087E-1L, -2}, + {"y0", y0l, 16.0L, + 9.58099365234375e-2L, + 1.06055727490314207096590322941832776E-6L, + -1.77975168939416859630601904359871915E-1L, -2}, + {"y0", y0l, 8.0L, + 2.235107421875e-1L, + 1.07472000662205273234004986203592748E-5L, + 1.58060461731247494255555266187483550E-1L, -2}, + {"y0", y0l, 5.33333333333333333333333333333333333E0L, + -3.387451171875e-1L, + 1.48763307492243286439161163883136261E-5L, + -3.30338692743198039852173817311267913E-2L, -2}, + {"y0", y0l, 4.0L, + -1.69525146484375E-2L, + 1.17753233725080963648655528467817595E-5L, + -3.97925710557100005253979972450791852E-1L, -2}, + {"y0", y0l, 3.2L, + 3.070526123046875E-1L, + 6.37827715583546999256417236405953385E-7L, + -3.70711338441274693924314235987044508E-1L, -2}, + {"y0", y0l, 2.66666666666666666666666666666666667E0L, + 4.67864990234375E-1L, + 1.52461165366402773840048623192120982E-5L, + -2.14907152209457967672108494960545800E-1L, -2}, + {"y0", y0l, 2.28571428571428571428571428571428571E0L, + 5.18768310546875E-1L, + 3.23404086137065314580351322765266943E-6L, + -4.51747395962233519705260050662299281E-2L, -2}, + {"y0", y0l, 2.0L, + 5.103607177734375E-1L, + 1.49548763076195966065927271578732681E-5L, + 1.07032431540937546888370772277476637E-1L, -2}, + {"j1", j1l, 16.0L, + 9.039306640625e-2L, + 4.1092550541862386833024580760244495945291E-6L, + -1.8054889746246069646832022412944915898260E-1L, -2}, + {"j1", j1l, 8.0L, + 2.346343994140625e-1L, + 1.9474398521243812766515904546115487521615E-6L, + 1.4232126378081457804320982640316517462483E-1L, -2}, + {"j1", j1l, 5.3333333333333333333333333333333330765427E0L, + -3.4613037109375e-1L, + 4.7659775265447519602414103748858036315250E-6L, + 6.3124658798958579773603686238379727242328E-4L, -2}, + {"j1", j1l, 4.0L, + -6.60552978515625e-2L, + 1.1969828013363856814579196724971272576580E-5L, + -3.8063897785796008825079441325087928479376E-1L, -2}, + {"j1", j1l, 3.2000000000000000000000000000000001540744E0L, + 2.613372802734375e-1L, + 5.9685070673373629867423599052573498655055E-6L, + -4.0185793490103066896536590238515608924925E-1L, -2}, + {"j1", j1l, 2.6666666666666666666666666666666665382713E0L, + 4.516448974609375e-1L, + 6.2509320502857789297328303110978154167062E-6L, + -2.9693016825402088220674935499586226461144E-1L, -2}, + {"j1", j1l, 2.2857142857142857142857142857142856042326E0L, + 5.42388916015625e-1L, + 6.6245894584815185457284221775341820978577E-6L, + -1.7402769058145591576151108347875503008807E-1L, -2}, + {"j1", j1l, 2.0L, + 5.7672119140625e-1L, + 3.6163506233872024482422691370869203026897E-6L, + -6.4471624737201025549396666484619917634997E-2L, -2}, + {"y1", y1l, 16.0L, + 1.779632568359375e-1L, + 1.1912103479359630601904359871915459722520E-5L, + 8.4687549021998849415158346880737423611524E-2L, -2}, + {"y1", y1l, 8.0L, + -1.580657958984375e-1L, + 5.3341671900057444447338125164496726559505E-6L, + 2.4327904710397215730926780877205580306573E-1L, -2}, + {"y1", y1l, 5.3333333333333333333333333333333330765427E0L, + 3.302001953125e-2L, + 1.3849743069803985217381731126879849266308E-5L, + -3.4492409134568573891858434295819796816112E-1L, -2}, + {"y1", y1l, 4.0L, + 3.97918701171875e-1L, + 7.0093852250052539799724507918522711891816E-6L, + -1.1642216696433999321713012755985118130829E-1L, -2}, + {"y1", y1l, 3.2000000000000000000000000000000001540744E0L, + 3.70697021484375e-1L, + 1.4316956899693924314235987044537888863453E-5L, + 1.9120595686950474169565105767128493632383E-1L, -2}, + {"y1", y1l, 2.6666666666666666666666666666666665382713E0L, + 2.1490478515625e-1L, + 2.3670532079676721084949605457501811641711E-6L, + 3.8729005427236490240034331925211457949310E-1L, -2}, + {"y1", y1l, 2.2857142857142857142857142857142856042326E0L, + 4.5166015625e-2L, + 8.7239712233519705260050662298731987015100E-6L, + 4.9900759601438865416604067629675208716502E-1L, -2}, + {"y1", y1l, 2.0L, + -1.070404052734375e-1L, + 7.9737324999531116292277225233633125191018E-6L, + 5.6389188842021389304079197886589619161188E-1L, -2}, + {"jnl", NULL, 6.9388939039072283776476979255676269531250E-18L, + 6.9602982143332406209530299018670212642178E-54L, + 2.6551531852207537950481339962774251294400E-59L, + 3.0092655e-36L, -2}, +#endif +#if 0 + {"lgamma", lgammal, 8.0L, 8.525146484375L, + 1.4876690414300165531036347125050759667737E-5L, + 2.0156414779556099965363450527747404656959E0L, 4}, + {"lgamma", lgammal, 0.125L, 2.0194091796875E0L, + 9.1778662963453202905211670995899482809521E-6L, + -8.3884926632958548678027429230863429642684E0L, 4}, + {"lgamma", lgammal, 0.375L, 8.63067626953125E-1L, + 6.3553175224624050890941340154953324706293E-6L, + -2.7539990491451395757640192188045680759926E0L, 4}, + {"lgamma", lgammal, 0.625L, 3.608245849609375E-1L, + 4.9105280026811849576858227794878573691202E-6L, + -1.4527087645765665672107816120233772668729E0L, 4}, + {"lgamma", lgammal, 0.875L, 8.5845947265625E-2L, + 1.2759959709323502365583769487702269719126E-5L, + -8.0401707154769538232421854974614639758707E-1L, 4}, + {"lgamma", lgammal, 1.0L, 0.0L, + 0.0L, -5.7721566490153286060651209008240239144696E-1L, -4}, + {"lgamma", lgammal, 1.125L, -6.0028076171875E-2L, + 4.8920458354170685941567925698857217805491E-6L, + -3.8849266329585486780274292308634296426837E-1L, 4}, + {"lgamma", lgammal, 1.375L, -1.17767333984375E-1L, + 1.2063243296225548637966682011495753460784E-5L, + -8.7332382478472909097352552137901409325952E-2L, 4}, + {"lgamma", lgammal, 1.625L, -1.091766357421875E-1L, + 2.5019853921275340206546744374231564700714E-6L, + 1.4729123542343343278921838797662273312715E-1L, 4}, + {"lgamma", lgammal, 1.875L, -4.76837158203125E-2L, + 1.1030421124200356021962838137727680303452E-5L, + 3.3884007130944747481863859311099645955579E-1L, 4}, + {"lgamma", lgammal, 2.375L, 2.0068359375E-1L, + 1.4866627455841358885180272611091348667235E-5L, + 6.3994034479425436362992017513482586340132E-1L, 4}, + {"lgamma", lgammal, 2.75L, 4.752044677734375E-1L, + 1.0199141499630313102466395428861742242065E-5L, + 8.1890102497543259227787514194472409043081E-1L, 4}, + {"lgamma", lgammal, 3.5L, 1.2009735107421875E0L, + 9.1604886724816021881450712995770238915468E-8L, + 1.1031566406452431872256903336679111259463E0L, 4}, + {"lgamma", lgammal, 4.5L, 2.4537353515625E0L, + 1.2192799422205041425034357161573318235107E-6L, + 1.3888709263595289015114046193821968402320E0L, 4}, + {"lgamma", lgammal, 5.5L, 3.9578094482421875E0L, + 4.5193765287938774008558225909985513044920E-6L, + 1.6110931485817511237336268416044190624542E0L, 4}, + {"lgamma", lgammal, 6.5L, 5.6625518798828125E0L, + 1.0179974329028522112312329543730297511212E-5L, + 1.7929113303999329419154450234226008806361E0L, 4}, + {"lgamma", lgammal, 7.5L, 7.53436279296875E0L, + 1.4437899829551583676324366857670272790220E-6L, + 1.9467574842460867880692911772687547267899E0L, 4}, + {"lgamma", lgammal, 8.5L, 9.54925537109375E0L, + 1.1886207247711737140081127222543124870800E-5L, + 2.0800908175794201214026245106020880601232E0L, 4}, + {"lgamma", lgammal, 9.5L, 1.16893310546875E1L, + 2.3661097684825694425775421725106375736779E-6L, + 2.1977378764029495331673303929550292365938E0L, 4}, + {"lgamma", lgammal, 10.5L, 1.394061279296875E1L, + 1.2426435013633161237887971849479799452805E-5L, + 2.3030010342976863752725935508497660786991E0L, 4}, + {"lgamma", lgammal, 11.5L, 1.62919921875E1L, + 8.2890672413202446037468793783460085279579E-6L, + 2.3982391295357816133678316460878613167943E0L, 4}, + {"lgamma", lgammal, 12.5L, 1.8734344482421875E1L, + 3.0295145707016341244572313978963754081384E-6L, + 2.4851956512749120481504403417400352298378E0L, 4}, + {"lgamma", lgammal, 13.5L, 2.126007080078125E1L, + 5.3554634511414184110022255966073511107125E-6L, + 2.5651956512749120481504403417400352298378E0, 4}, + {"lgamma", lgammal, -0.5L, 1.2655029296875E0L, + 9.1937971453964889457971347059238991475408E-6L, + 3.6489973978576520559023667001244459279636E-2L, 4}, + {"lgamma", lgammal, -1.5L, 8.6004638671875E-1L, + 6.2865773101451093268167035678732715711736E-7L, + 7.0315664064524318722569033366791112594630E-1L, 4}, + {"lgamma", lgammal, -2.5L, -5.6243896484375E-2L, + 1.7998670094932740546990234571587705589745E-7L, + 1.1031566406452431872256903336679111259463E0L, -4}, + {"lgamma", lgammal, -3.5L,-1.30902099609375E0L, + 1.4311100707953639284847917342554315471302E-5L, + 1.3888709263595289015114046193821968402320E0L, -4}, + {"lgamma", lgammal, 1.0e18L, 4.0446531673037733888E19L, + 8.5508840451951888057681732252156677289759E8L, + 4.1446531673892822311823846184318555736736E1, 4}, +#endif /* 0 */ +#if 0 +#define gammal tgammal /* Yuck. */ + {"gamma", gammal, 1.0L, 1.0L, + 0.0L, -5.772156649015328606e-1L, 4}, + {"gamma", gammal, 2.0L, 1.0L, + 0.0L, 4.2278433509846713939e-1L, 4}, + {"gamma", gammal, 3.0L, 2.0L, + 0.0L, 1.845568670196934279L, 4}, + {"gamma", gammal, 4.0L, 6.0L, + 0.0L, 7.536706010590802836L, 4}, +#endif + {NULL, NULL, 0.0L, 0.0L, 0.0L, 1}, +}; + +/* These take care of extra-precise floating point register problems. */ +static volatile long double volat1; +static volatile long double volat2; + + +/* Return the next nearest floating point value to X + in the direction of UPDOWN (+1 or -1). + (Might fail if X is denormalized.) */ + +static long double +nextval (x, updown) + long double x; + int updown; +{ + long double m; + int i; + + volat1 = x; + m = 0.25L * MACHEPL * volat1 * updown; + volat2 = volat1 + m; + if (volat2 != volat1) + printf ("successor failed\n"); + + for (i = 2; i < 10; i++) + { + volat2 = volat1 + i * m; + if (volat1 != volat2) + return volat2; + } + + printf ("nextval failed\n"); + return volat1; +} + + + + +int +monotll () +{ + long double (*fun1) (long double); + int i, j, errs, tests, err_thresh; + long double x, x0, dy, err; + + errs = 0; + tests = 0; + i = 0; + + for (;;) + { + /* Function call reference. */ + fun1 = test1[i].func; + if (test1[i].name == NULL) + break; + /* + if (fun1 == NULL) + break; + */ + /* Function argument. */ + volat1 = test1[i].arg1; + /* x0 is the given argument, x scans from slightly below to above x0. */ + x0 = volat1; + x = volat1; + for (j = 0; j <= NPTS; j++) + { + /* delta x */ + volat1 = x - x0; + /* delta y */ + dy = volat1 * test1[i].derivative; + /* y + delta y */ + dy = test1[i].answer2 + dy; + volat1 = test1[i].answer1 + dy; + /* Run the function under test. */ + if (fun1 == NULL) + { +#if 0 + if (! strcmp (test1[i].name, "jnl")) + volat2 = jnl (3, x); + else +#endif + break; + } + else + volat2 = (*(fun1)) (x); + if (volat2 != volat1) + { + /* Estimate difference between program result + and extended precision function value. */ + err = volat2 - test1[i].answer1; + err = err - dy; + /* Compare difference with reporting threshold. */ + err_thresh = test1[i].thresh; + if (err_thresh >= 0) + err = err / volat1; /* relative error */ + else + { + err_thresh = -err_thresh; /* absolute error */ + /* ...but relative error if function value > 1 */ + if (fabsl(volat1) > 1.0L) + err = err / volat1; + } + if (fabsl (err) > (err_thresh * MACHEPL)) + { + printf ("%d %s(%.36Le) = %.36Le, rel err = %.3Le\n", + j, test1[i].name, x, volat2, err); + errs += 1; + } + } + x = nextval (x, 1); + tests += 1; + } + + x = x0; + x = nextval (x, -1); + for (j = 1; j < NPTS; j++) + { + volat1 = x - x0; + dy = volat1 * test1[i].derivative; + dy = test1[i].answer2 + dy; + volat1 = test1[i].answer1 + dy; + if (fun1 == NULL) + { +#if 0 + if (! strcmp (test1[i].name, "jnl")) + volat2 = jnl (3, x); + else +#endif + break; + } + else + volat2 = (*(fun1)) (x); + if (volat2 != volat1) + { + err = volat2 - test1[i].answer1; + err = err - dy; + err_thresh = test1[i].thresh; + if (err_thresh >= 0) + err = err / volat1; /* relative error */ + else + { + err_thresh = -err_thresh; + if (fabsl(volat1) > 1.0L) + err = err / volat1; + } + if (fabsl (err) > (err_thresh * MACHEPL)) + { + printf ("%d %s(%.36Le) = %.36Le, rel err = %.3Le\n", + j, test1[i].name, x, volat2, err); + errs += 1; + } + } + x = nextval (x, -1); + tests += 1; + } + i += 1; + } + printf ("%d errors in %d tests\n", errs, tests); + return (errs); +} +#endif /* LDBL_MANT_DIG == 113 */ |