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Diffstat (limited to 'libm/ldouble/monotl.c')
| -rw-r--r-- | libm/ldouble/monotl.c | 307 |
1 files changed, 307 insertions, 0 deletions
diff --git a/libm/ldouble/monotl.c b/libm/ldouble/monotl.c new file mode 100644 index 000000000..86b85eca1 --- /dev/null +++ b/libm/ldouble/monotl.c @@ -0,0 +1,307 @@ + +/* monot.c + Floating point function test vectors. + + 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 <stdio.h> + +/* Avoid including math.h. */ +long double frexpl (long double, int *); +long double ldexpl (long double, int); + +/* Number of test points to generate on each side of tabulated point. */ +#define NPTS 100 + +/* Functions of one variable. */ +long double expl (long double); +long double logl (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 fabsl (long double); +long double floorl (long double); + +struct oneargument + { + char *name; /* Name of the function. */ + long double (*func) (long double); + long double arg1; /* Function argument, assumed exact. */ + long double answer1; /* Exact, close to function value. */ + long double answer2; /* answer1 + answer2 has extended precision. */ + long double derivative; /* dy/dx evaluated at x = arg1. */ + int thresh; /* Error report threshold. 2 = 1 ULP approx. */ + }; + +/* Add this to error threshold test[i].thresh. */ +#define OKERROR 2 + +/* Unit of relative error in test[i].thresh. */ +static long double MACHEPL = 5.42101086242752217003726400434970855712890625E-20L; + +/* extern double MACHEP; */ + + +struct oneargument test1[] = +{ + {"exp", expl, 1.0L, 2.7182769775390625L, + 4.85091998273536028747e-6L, 2.71828182845904523536L, 1}, + {"exp", expl, -1.0L, 3.678741455078125e-1L, + 5.29566362982159552377e-6L, 3.678794411714423215955e-1L, 1}, + {"exp", expl, 0.5L, 1.648712158203125L, + 9.1124970031468486507878e-6L, 1.64872127070012814684865L, 1}, + {"exp", expl, -0.5L, 6.065216064453125e-1L, + 9.0532673209236037995e-6L, 6.0653065971263342360e-1L, 1}, + {"exp", expl, 2.0L, 7.3890533447265625L, + 2.75420408772723042746e-6L, 7.38905609893065022723L, 1}, + {"exp", expl, -2.0L, 1.353302001953125e-1L, + 5.08304130019189399949e-6L, 1.3533528323661269189e-1L, 1}, + {"log", logl, 1.41421356237309492343L, 3.465728759765625e-1L, + 7.1430341006605745676897e-7L, 7.0710678118654758708668e-1L, 1}, + {"log", logl, 7.07106781186547461715e-1L, -3.46588134765625e-1L, + 1.45444856522566402246e-5L, 1.41421356237309517417L, 1}, + {"sin", sinl, 7.85398163397448278999e-1L, 7.0709228515625e-1L, + 1.4496030297502751942956e-5L, 7.071067811865475460497e-1L, 1}, + {"sin", sinl, -7.85398163397448501044e-1L, -7.071075439453125e-1L, + 7.62758764840238811175e-7L, 7.07106781186547389040e-1L, 1}, + {"sin", sinl, 1.570796326794896558L, 9.999847412109375e-1L, + 1.52587890625e-5L, 6.12323399573676588613e-17L, 1}, + {"sin", sinl, -1.57079632679489678004L, -1.0L, + 1.29302922820150306903e-32L, -1.60812264967663649223e-16L, 1}, + {"sin", sinl, 4.712388980384689674L, -1.0L, + 1.68722975549458979398e-32L, -1.83697019872102976584e-16L, 1}, + {"sin", sinl, -4.71238898038468989604L, 9.999847412109375e-1L, + 1.52587890625e-5L, 3.83475850529283315008e-17L, 1}, + {"cos", cosl, 3.92699081698724139500E-1L, 9.23873901367187500000E-1L, + 5.63114409926198633370E-6L, -3.82683432365089757586E-1L, 1}, + {"cos", cosl, 7.85398163397448278999E-1L, 7.07092285156250000000E-1L, + 1.44960302975460497458E-5L, -7.07106781186547502752E-1L, 1}, + {"cos", cosl, 1.17809724509617241850E0L, 3.82675170898437500000E-1L, + 8.26146665231415693919E-6L, -9.23879532511286738554E-1L, 1}, + {"cos", cosl, 1.96349540849362069750E0L, -3.82690429687500000000E-1L, + 6.99732241029898567203E-6L, -9.23879532511286785419E-1L, 1}, + {"cos", cosl, 2.35619449019234483700E0L, -7.07107543945312500000E-1L, + 7.62758765040545859856E-7L, -7.07106781186547589348E-1L, 1}, + {"cos", cosl, 2.74889357189106897650E0L, -9.23889160156250000000E-1L, + 9.62764496328487887036E-6L, -3.82683432365089870728E-1L, 1}, + {"cos", cosl, 3.14159265358979311600E0L, -1.00000000000000000000E0L, + 7.49879891330928797323E-33L, -1.22464679914735317723E-16L, 1}, + {"tan", tanl, 7.85398163397448278999E-1L, 9.999847412109375e-1L, + 1.52587890624387676600E-5L, 1.99999999999999987754E0L, 1}, + {"tan", tanl, 1.17809724509617241850E0L, 2.41419982910156250000E0L, + 1.37332715322352112604E-5L, 6.82842712474618858345E0L, 1}, + {"tan", tanl, 1.96349540849362069750E0L, -2.41421508789062500000E0L, + 1.52551752942854759743E-6L, 6.82842712474619262118E0L, 1}, + {"tan", tanl, 2.35619449019234483700E0L, -1.00001525878906250000E0L, + 1.52587890623163029801E-5L, 2.00000000000000036739E0L, 1}, + {"tan", tanl, 2.74889357189106897650E0L, -4.14215087890625000000E-1L, + 1.52551752982565655126E-6L, 1.17157287525381000640E0L, 1}, + {"atan", atanl, 4.14213562373094923430E-1L, 3.92684936523437500000E-1L, + 1.41451752865477964149E-5L, 8.53553390593273837869E-1L, 1}, + {"atan", atanl, 1.0L, 7.85385131835937500000E-1L, + 1.30315615108096156608E-5L, 0.5L, 1}, + {"atan", atanl, 2.41421356237309492343E0L, 1.17808532714843750000E0L, + 1.19179477349460632350E-5L, 1.46446609406726250782E-1L, 1}, + {"atan", atanl, -2.41421356237309514547E0L, -1.17810058593750000000E0L, + 3.34084132752141908545E-6L, 1.46446609406726227789E-1L, 1}, + {"atan", atanl, -1.0L, -7.85400390625000000000E-1L, + 2.22722755169038433915E-6L, 0.5L, 1}, + {"atan", atanl, -4.14213562373095145475E-1L, -3.92700195312500000000E-1L, + 1.11361377576267665972E-6L, 8.53553390593273703853E-1L, 1}, + {"asin", asinl, 3.82683432365089615246E-1L, 3.92684936523437500000E-1L, + 1.41451752864854321970E-5L, 1.08239220029239389286E0L, 1}, + {"asin", asinl, 0.5L, 5.23590087890625000000E-1L, + 8.68770767387307710723E-6L, 1.15470053837925152902E0L, 1}, + {"asin", asinl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L, + 1.30315615107209645016E-5L, 1.41421356237309492343E0L, 1}, + {"asin", asinl, 9.23879532511286738483E-1L, 1.17808532714843750000E0L, + 1.19179477349183147612E-5L, 2.61312592975275276483E0L, 1}, + {"asin", asinl, -0.5L, -5.23605346679687500000E-1L, + 6.57108138862692289277E-6L, 1.15470053837925152902E0L, 1}, + {"acos", acosl, 1.95090322016128192573E-1L, 1.37443542480468750000E0L, + 1.13611408471185777914E-5L, -1.01959115820831832232E0L, 1}, + {"acos", acosl, 3.82683432365089615246E-1L, 1.17808532714843750000E0L, + 1.19179477351337991247E-5L, -1.08239220029239389286E0L, 1}, + {"acos", acosl, 0.5L, 1.04719543457031250000E0L, + 2.11662628524615421446E-6L, -1.15470053837925152902E0L, 1}, + {"acos", acosl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L, + 1.30315615108982668201E-5L, -1.41421356237309492343E0L, 1}, + {"acos", acosl, 9.23879532511286738483E-1L, 3.92684936523437500000E-1L, + 1.41451752867009165605E-5L, -2.61312592975275276483E0L, 1}, + {"acos", acosl, 9.80785280403230430579E-1L, 1.96334838867187500000E-1L, + 1.47019821746724723933E-5L, -5.12583089548300990774E0L, 1}, + {"acos", acosl, -0.5L, 2.09439086914062500000E0L, + 4.23325257049230842892E-6L, -1.15470053837925152902E0L, 1}, + {"sinh", sinhl, 1.0L, 1.17518615722656250000E0L, + 1.50364172389568823819E-5L, 1.54308063481524377848E0L, 1}, + {"sinh", sinhl, 7.09089565712818057364E2L, 4.49423283712885057274E307L, + 4.25947714184369757620E208L, 4.49423283712885057274E307L, 1}, + {"sinh", sinhl, 2.22044604925031308085E-16L, 0.00000000000000000000E0L, + 2.22044604925031308085E-16L, 1.00000000000000000000E0L, 1}, + {"cosh", coshl, 7.09089565712818057364E2L, 4.49423283712885057274E307L, + 4.25947714184369757620E208L, 4.49423283712885057274E307L, 1}, + {"cosh", coshl, 1.0L, 1.54307556152343750000E0L, + 5.07329180627847790562E-6L, 1.17520119364380145688E0L, 1}, + {"cosh", coshl, 0.5L, 1.12762451171875000000E0L, + 1.45348763078522622516E-6L, 5.21095305493747361622E-1L, 1}, + {"tanh", tanhl, 0.5L, 4.62112426757812500000E-1L, + 4.73050219725850231848E-6L, 7.86447732965927410150E-1L, 1}, + {"tanh", tanhl, 5.49306144334054780032E-1L, 4.99984741210937500000E-1L, + 1.52587890624507506378E-5L, 7.50000000000000049249E-1L, 1}, + {"tanh", tanhl, 0.625L, 5.54595947265625000000E-1L, + 3.77508375729399903910E-6L, 6.92419147969988069631E-1L, 1}, + {"asinh", asinhl, 0.5L, 4.81201171875000000000E-1L, + 1.06531846034474977589E-5L, 8.94427190999915878564E-1L, 1}, + {"asinh", asinhl, 1.0L, 8.81362915039062500000E-1L, + 1.06719804805252326093E-5L, 7.07106781186547524401E-1L, 1}, + {"asinh", asinhl, 2.0L, 1.44363403320312500000E0L, + 1.44197568534249327674E-6L, 4.47213595499957939282E-1L, 1}, + {"acosh", acoshl, 2.0L, 1.31695556640625000000E0L, + 2.33051856670862504635E-6L, 5.77350269189625764509E-1L, 1}, + {"acosh", acoshl, 1.5L, 9.62417602539062500000E-1L, + 6.04758014439499551783E-6L, 8.94427190999915878564E-1L, 1}, + {"acosh", acoshl, 1.03125L, 2.49343872070312500000E-1L, + 9.62177257298785143908E-6L, 3.96911150685467059809E0L, 1}, + {"atanh", atanhl, 0.5L, 5.49301147460937500000E-1L, + 4.99687311734569762262E-6L, 1.33333333333333333333E0L, 1}, +#if 0 + {"gamma", gammal, 1.0L, 1.0L, + 0.0L, -5.772156649015328606e-1L, 1}, + {"gamma", gammal, 2.0L, 1.0L, + 0.0L, 4.2278433509846713939e-1L, 1}, + {"gamma", gammal, 3.0L, 2.0L, + 0.0L, 1.845568670196934279L, 1}, + {"gamma", gammal, 4.0L, 6.0L, + 0.0L, 7.536706010590802836L, 1}, +#endif + {"null", NULL, 0.0L, 0.0L, 0.0L, 1}, +}; + +/* These take care of extra-precise floating point register problems. */ +volatile long double volat1; +volatile long double volat2; + + +/* Return the next nearest floating point value to X + in the direction of UPDOWN (+1 or -1). + (Fails if X is denormalized.) */ + +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 +main () +{ + long double (*fun1) (long double); + int i, j, errs, tests; + long double x, x0, y, dy, err; + + errs = 0; + tests = 0; + i = 0; + + for (;;) + { + fun1 = test1[i].func; + if (fun1 == NULL) + break; + volat1 = test1[i].arg1; + x0 = volat1; + x = volat1; + for (j = 0; j <= NPTS; j++) + { + volat1 = x - x0; + dy = volat1 * test1[i].derivative; + dy = test1[i].answer2 + dy; + volat1 = test1[i].answer1 + dy; + volat2 = (*(fun1)) (x); + if (volat2 != volat1) + { + /* Report difference between program result + and extended precision function value. */ + err = volat2 - test1[i].answer1; + err = err - dy; + err = err / volat1; + if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL)) + { + printf ("%d %s(%.19Le) = %.19Le, 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; + volat2 = (*(fun1)) (x); + if (volat2 != volat1) + { + err = volat2 - test1[i].answer1; + err = err - dy; + err = err / volat1; + if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL)) + { + printf ("%d %s(%.19Le) = %.19Le, 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); +} |