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