/* * (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands. * See the copyright notice in the ACK home directory, in the file "Copyright". * * Author: Ceriel J.H. Jacobs */ #include #include int nerrors; #define EPS_D 5.0e-14 main() { testsqrt(); testtrig(); testexplog(); testgamma(); testbessel(); exit(nerrors); } dotest(s, x, d, v) char *s; double x, d, v; { double fabs(); if (fabs((v - d) / (fabs(v) < EPS_D ? 1.0 : v)) > EPS_D) { printf(s, x); printf(" = %.16e, should be %.16e\n", d, v); nerrors++; } } testsqrt() { #define SQRT2 M_SQRT2 #define SQRT10 3.16227766016837933199889354443271853 double x, val; extern double sqrt(); printf("testing sqrt ... \n"); dotest("sqrt(%.1f)", 2.0, sqrt(2.0), SQRT2); dotest("sqrt(%.1f)", 10.0, sqrt(10.0), SQRT10); for (x = 0.1; x < 0.1e20; x += x) { val = sqrt(x); dotest("sqrt(%.1f)^2", x, val*val, x); } } testtrig() { #define SINPI_24 0.13052619222005159154840622789548901 #define SINPI_16 0.19509032201612826784828486847702224 #define SINPI_12 0.25881904510252076234889883762404832 #define SINPI_6 0.5 #define SINPI_4 M_1_SQRT2 #define SINPI_3 0.86602540378443864676372317075293618 #define SINPI_2 1.0 #define SIN0 0.0 double x; extern double sin(), cos(), tan(), asin(), acos(), atan(), fabs(); printf("testing sin, cos, tan, asin, acos, atan ... \n"); dotest("sin(0)", 0.0, sin(0.0), SIN0); dotest("sin(pi/24)", M_PI/24 , sin(M_PI/24), SINPI_24); dotest("sin(pi/16)", M_PI/16 , sin(M_PI/16), SINPI_16); dotest("sin(pi/12)", M_PI/12 , sin(M_PI/12), SINPI_12); dotest("sin(pi/6)", M_PI/6 , sin(M_PI/6), SINPI_6); dotest("sin(pi/4)", M_PI_4 , sin(M_PI_4), SINPI_4); dotest("sin(pi/3)", M_PI/3 , sin(M_PI/3), SINPI_3); dotest("sin(pi/2)", M_PI_2 , sin(M_PI_2), SINPI_2); dotest("sin(pi)", 0.0, sin(M_PI), SIN0); dotest("sin(3*pi/2)", 0.0, sin(M_PI+M_PI_2), -SINPI_2); dotest("sin(-pi/24)", -M_PI/24 , sin(-M_PI/24), -SINPI_24); dotest("sin(-pi/16)", -M_PI/16 , sin(-M_PI/16), -SINPI_16); dotest("sin(-pi/12)", -M_PI/12 , sin(-M_PI/12), -SINPI_12); dotest("sin(-pi/6)", -M_PI/6 , sin(-M_PI/6), -SINPI_6); dotest("sin(-pi/4)", -M_PI_4 , sin(-M_PI_4), -SINPI_4); dotest("sin(-pi/3)", -M_PI/3 , sin(-M_PI/3), -SINPI_3); dotest("sin(-pi/2)", -M_PI_2 , sin(-M_PI_2), -SINPI_2); dotest("cos(pi/2)", M_PI_2, cos(M_PI_2), SIN0); dotest("cos(11pi/24)", M_PI/24 , cos(11*M_PI/24), SINPI_24); dotest("cos(7pi/16)", M_PI/16 , cos(7*M_PI/16), SINPI_16); dotest("cos(5pi/12)", M_PI/12 , cos(5*M_PI/12), SINPI_12); dotest("cos(pi/3)", M_PI/6 , cos(M_PI/3), SINPI_6); dotest("cos(pi/4)", M_PI_4 , cos(M_PI_4), SINPI_4); dotest("cos(pi/6)", M_PI/3 , cos(M_PI/6), SINPI_3); dotest("cos(0)", M_PI_2 , cos(0), SINPI_2); dotest("cos(pi)", M_PI , cos(M_PI), -SINPI_2); dotest("cos(3pi/2)", M_PI , cos(M_PI+M_PI_2), SIN0); dotest("cos(-pi/2)", M_PI_2, cos(-M_PI_2), SIN0); dotest("cos(-11pi/24)", M_PI/24 , cos(-11*M_PI/24), SINPI_24); dotest("cos(-7pi/16)", M_PI/16 , cos(-7*M_PI/16), SINPI_16); dotest("cos(-5pi/12)", M_PI/12 , cos(-5*M_PI/12), SINPI_12); dotest("cos(-pi/3)", M_PI/6 , cos(-M_PI/3), SINPI_6); dotest("cos(-pi/4)", M_PI_4 , cos(-M_PI_4), SINPI_4); dotest("cos(-pi/6)", M_PI/3 , cos(-M_PI/6), SINPI_3); for (x = -10; x <= 10; x += 0.5) { dotest("sin+2*pi-sin(%.2f)", x, sin(x+M_2PI)-sin(x), 0.0); dotest("cos+2*pi-cos(%.2f)", x, cos(x+M_2PI)-cos(x), 0.0); dotest("tan+2*pi-tan(%.2f)", x, tan(x+M_2PI)-tan(x), 0.0); dotest("tan+pi-tan(%.2f)", x, tan(x+M_PI)-tan(x), 0.0); } for (x = -1.5; x <= 1.5; x += 0.1) { dotest("asin(sin(%.2f))", x, asin(sin(x)), x); dotest("acos(cos(%.2f))", x, acos(cos(x)), fabs(x)); dotest("atan(tan(%.2f))", x, atan(tan(x)), x); } } testexplog() { #define EXPMIN1 0.36787944117144232159552377016146087 /* exp(-1) */ #define EXPMIN1_4 0.77880078307140486824517026697832065 /* exp(-1/4) */ #define EXP0 1.0 /* exp(0) */ #define EXP1_4 1.28402541668774148407342056806243646 /* exp(1/4) */ #define EXP1 M_E /* exp(1) */ #define LN1 0.0 /* log(1) */ #define LN2 M_LN2 /* log(2) */ #define LN4 1.38629436111989061883446424291635313 /* log(4) */ #define LNE 1.0 /* log(e) */ #define LN10 M_LN10 /* log(10) */ extern double exp(), log(); double x; printf("testing exp and log ...\n"); dotest("exp(%.2f)", -1.0, exp(-1.0), EXPMIN1); dotest("exp(%.2f)", -0.25, exp(-0.25), EXPMIN1_4); dotest("exp(%.2f)", 0.0, exp(0.0), EXP0); dotest("exp(%.2f)", 0.25, exp(0.25), EXP1_4); dotest("exp(%.2f)", 1.0, exp(1.0), EXP1); dotest("log(%.2f)", 1.0, log(1.0), LN1); dotest("log(%.2f)", 2.0, log(2.0), LN2); dotest("log(%.2f)", 4.0, log(4.0), LN4); dotest("log(%.2f)", 10.0, log(10.0), LN10); dotest("log(e)", M_E, log(M_E), LNE); for (x = -30.0; x <= 30.0; x += 0.5) { dotest("log(exp(%.2f))", x, log(exp(x)), x); } } testgamma() { double x, xfac; extern double gamma(), exp(); printf("testing gamma ...\n"); for (x = 1.0, xfac = 1.0; x < 30.0; x += 1.0) { dotest("exp(gamma(%.2f))", x, exp(gamma(x)), xfac); xfac *= x; } } testbessel() { #define J0__PI_4 0.85163191370480801270040601506092607 /* j0(pi/4) */ #define J0__PI_2 0.47200121576823476744766838787250096 /* j0(pi/2) */ #define J1__PI_4 0.36318783834686733179559374778892472 /* j1(pi/4) */ #define J1__PI_2 0.56682408890587393771124496346716028 /* j1(pi/2) */ #define J10__PI_4 0.00000000002369974904082422018721148 /* j10(p1/4) */ #define J10__PI_2 0.00000002326614794865976450546482206 /* j10(pi/2) */ extern double j0(), j1(), jn(), yn(); register int n; double x; extern char *sprintf(); char buf[100]; printf("testing bessel ...\n"); dotest("j0(pi/4)", M_PI_4, j0(M_PI_4), J0__PI_4); dotest("j0(pi/2)", M_PI_2, j0(M_PI_2), J0__PI_2); dotest("j1(pi/4)", M_PI_4, j1(M_PI_4), J1__PI_4); dotest("j1(pi/2)", M_PI_2, j1(M_PI_2), J1__PI_2); dotest("j10(pi/4)", M_PI_4, jn(10,M_PI_4), J10__PI_4); dotest("j10(pi/2)", M_PI_2, jn(10,M_PI_2), J10__PI_2); /* Also check consistency using the Wronskian relation jn(n+1,x)*yn(n, x) - jn(n,x)*yn(n+1,x) = 2/(pi*x) */ for (x = 0.1; x < 20.0; x += 0.5) { double two_over_pix = M_2_PI/x; for (n = 0; n <= 10; n++) { dotest(sprintf(buf, "jn(%d,%.2f)*yn(%d,%.2f)-jn(%d,%.2f)*yn(%d,%.2f)",n+1,x,n,x,n,x,n+1,x), x, jn(n+1,x)*yn(n,x)-jn(n,x)*yn(n+1,x),M_2_PI/x); } } }