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add cas and cis trigonometric functions

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Added the following new trigonometric functions:

    cas(x [,eps])		trigonometric cosine plus sine
    cis(x [,eps])		Euler's formula
This commit is contained in:
Landon Curt Noll
2023-10-03 01:41:42 -07:00
parent 26fc394089
commit 2c4abcd2b7
48 changed files with 770 additions and 31 deletions
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58
cal/regress.cal
View File

@@ -4182,6 +4182,52 @@ define test_trig()
strcat(str(tnum++),
': round(acrd(2 + 3i, 1e-10), 10) == 1.0471975512+2.6339157938i'));
/* test cosine plus sine */
vrfy(cas(0, 1e-10) == 1,
strcat(str(tnum++), ': cas(0, 1e-10) == 1'));
vrfy(round(cas(0.2, 1e-10), 10) == 1.1787359086,
strcat(str(tnum++),
': round(cas(0.2, 1e-10), 10) == 1.1787359086'));
vrfy(round(cas(3/7, 1e-10), 10) == 1.3251322067,
strcat(str(tnum++),
': round(cas(3/7, 1e-10), 10) == 1.3251322067'));
vrfy(round(cas(-31, 1e-10), 10) == 1.3187800031,
strcat(str(tnum++),
': round(cas(-31, 1e-10), 10) == 1.3187800031'));
vrfy(cas(pi/2, 1e-10) == 1,
strcat(str(tnum++), ': cas(pi/2, 1e-10) == 1'));
vrfy(cas(pi, 1e-10) == -1,
strcat(str(tnum++), ': cas(pi, 1e-10) == -1'));
vrfy(cas(3*pi/2, 1e-10) == -1,
strcat(str(tnum++), ': cas(3*pi/2, 1e-10) == -1'));
vrfy(round(cas(1, 1e-10), 10) == 1.3817732907,
strcat(str(tnum++),
': round(cas(1, 1e-10), 10) == 1.3817732907'));
vrfy(round(cas(2 + 3i, 1e-10), 10) == 4.9648734559-13.2781348538i,
strcat(str(tnum++),
': round(cas(2 + 3i, 1e-10), 10) == 4.9648734559-13.2781348538i'));
/* test Euler's formula */
vrfy(cis(0, 1e-10) == 1,
strcat(str(tnum++), ': cis(0, 1e-10) == 1'));
vrfy(cis(pi/2, 1e-10) == 1i,
strcat(str(tnum++), ': cis(pi/2, 1e-10) == 1i'));
vrfy(round(cis(0.2, 1e-10), 10) == 0.9800665778+0.1986693308i,
strcat(str(tnum++),
': round(cis(0.2, 1e-10), 10) == 0.9800665778+0.1986693308i'));
vrfy(round(cis(3/7, 1e-10), 10) == 0.9095603517+0.415571855i,
strcat(str(tnum++),
': round(cis(3/7, 1e-10), 10) == 0.9095603517+0.415571855i'));
vrfy(round(cis(-31, 1e-10), 10) == 0.9147423578+0.4040376453i,
strcat(str(tnum++),
': round(cis(-31, 1e-10), 10) == 0.9147423578+0.4040376453i'));
vrfy(round(cis(1, 1e-10), 10) == 0.5403023059+0.8414709848i,
strcat(str(tnum++),
': round(cis(1, 1e-10), 10) == 0.5403023059+0.8414709848i'));
vrfy(round(cis(2 + 3i, 1e-10), 10) == -0.020718731+0.0452712532i,
strcat(str(tnum++),
': round(cis(2 + 3i, 1e-10), 10) == -0.020718731+0.0452712532i'));
print strcat(str(tnum++), ': Ending test_trig');
}
print '051: parsed test_trig()';
@@ -9879,9 +9925,11 @@ vrfy(verify_havercos(9513) == 0, '9513: verify_havercos(9513) == 0');
vrfy(verify_hacovercos(9514) == 0, '9514: verify_hacovercos(9514) == 0');
vrfy(verify_exsec(9515) == 0, '9515: verify_exsec(9515) == 0');
vrfy(verify_excsc(9516) == 0, '9516: verify_excsc(9516) == 0');
vrfy(verify_crd(9517) == 0, '9516: verify_excsc(9517) == 0');
vrfy(verify_crd(9517) == 0, '9517: verify_crd(9517) == 0');
vrfy(verify_cas(9518) == 0, '9518: verify_cas(9518) == 0');
vrfy(verify_cis(9519) == 0, '9519: verify_cis(9519) == 0');
print '9518: Ending trigonometric identities test set';
print '9520: Ending trigonometric identities test set';
/*
@@ -10890,6 +10938,12 @@ vrfy_errsym(10596, 10596, "E_CRD_3");
vrfy_errsym(10597, 10597, "E_ACRD_1");
vrfy_errsym(10598, 10598, "E_ACRD_2");
vrfy_errsym(10599, 10599, "E_ACRD_3");
vrfy_errsym(10600, 10600, "E_CAS_1");
vrfy_errsym(10601, 10601, "E_CAS_2");
vrfy_errsym(10602, 10602, "E_CAS_3");
vrfy_errsym(10603, 10603, "E_CIS_1");
vrfy_errsym(10604, 10604, "E_CIS_2");
vrfy_errsym(10605, 10605, "E_CIS_3");
/* ************************************************************** */
/* NOTE: Reserve thru test 10998 for calc computation error codes */

119
cal/test9500.trigeq.cal
View File

@@ -1312,3 +1312,122 @@ define verify_crd(testnum)
}
return error_count;
}
/*
* verify_cas - verify cosine plus sine
*
* We use the following trigonometric identity:
*
* cas(x) = cos(x) + sin(x)
*
* given:
* testnum regression test number being performed
*
* returns:
* number of tests that failed
*/
define verify_cas(testnum)
{
local tval_len; /* current length of the tval[] array */
local ident_val; /* computed trig value trigonometric identity */
local trig_val; /* computed value from the trigonometric function */
local error_count; /* number of compare errors detected */
local i;
/*
* firewall
*/
if (size(sin_tval) <= 0) {
precompute_trig();
}
if (size(cos_tval) <= 0) {
precompute_trig();
}
/*
* for each test value, verify the trigonometric identity within epsilon
*/
tval_len = size(tval);
for (i=0; i < tval_len; ++i) {
/* compute trigonometric identity */
ident_val = cos_tval[i] + sin_tval[i];
/* compute trigonometric function */
trig_val = cas(tval[i]);
/* compare trigonometric identity with trigonometric function value */
if (compare(ident_val, trig_val, "cas", i, testnum)) {
++error_count;
}
}
/*
* report test results
*/
if (error_count != 0) {
print '**** test', testnum : ': cas test failure count:', error_count;
}
return error_count;
}
/*
* verify_cis - verify Euler's formula
*
* We use the following trigonometric identity:
*
* cis(x) = cos(x) + i*sin(x)
* cis(x) = exp(1i * x)
*
* given:
* testnum regression test number being performed
*
* returns:
* number of tests that failed
*/
define verify_cis(testnum)
{
local tval_len; /* current length of the tval[] array */
local ident_val; /* computed trig value trigonometric identity */
local trig_val; /* computed value from the trigonometric function */
local error_count; /* number of compare errors detected */
local i;
/*
* firewall
*/
if (size(sin_tval) <= 0) {
precompute_trig();
}
if (size(cos_tval) <= 0) {
precompute_trig();
}
/*
* for each test value, verify the trigonometric identity within epsilon
*/
tval_len = size(tval);
for (i=0; i < tval_len; ++i) {
/* compute trigonometric identity */
ident_val = cos_tval[i] + 1i*sin_tval[i];
/* compute trigonometric function */
trig_val = cis(tval[i]);
/* compare trigonometric identity with trigonometric function value */
if (compare(ident_val, trig_val, "cis", i, testnum)) {
++error_count;
}
}
/*
* report test results
*/
if (error_count != 0) {
print '**** test', testnum : ': cis test failure count:', error_count;
}
return error_count;
}