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add trigonometric chord of a unit circle functions

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Improve builtin function strings, as printed by help builtin,
that use an optional accuracy (epsilon) arg by adding a comma.

Added the following new trigonometric functions:

    crd(x [,eps])		trigonometric chord of a unit circle
    acrd(x [,eps])		inverse trigonometric chord of a unit circle
This commit is contained in:
Landon Curt Noll
2023-10-02 22:43:33 -07:00
parent c78a893862
commit 26fc394089
44 changed files with 1246 additions and 118 deletions
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156
qtrans.c
View File

@@ -3467,3 +3467,159 @@ qaexcsc(NUMBER *q, NUMBER *epsilon)
*/
return res;
}
/*
* qcrd - trigonometric chord of a unit circle
*
* This uses the formula:
*
* crd(x) = 2 * sin(x / 2)
*
* given:
* q real value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* returns:
* real value result of trig function on q with error epsilon
*/
NUMBER *
qcrd(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *qdiv2; /* q/2 */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
*/
if (q == NULL) {
math_error("q is NULL for %s", __func__);
not_reached();
}
if (check_epsilon(epsilon) == false) {
math_error("Invalid epsilon arg for %s", __func__);
not_reached();
}
/*
* calculate trig function value
*/
qdiv2 = qdivi(q, 2);
qtmp = qsin(qdiv2, epsilon);
qfree(qdiv2);
res = qmuli(qtmp, 2);
qfree(qtmp);
/*
* return trigonometric result
*/
return res;
}
/*
* qacrd_or_NULL - return NULL or non-complex inverse trigonometric chord of a unit circle
*
* This uses the formula:
*
* acrd(x) = 2 * asin(x / 2)
*
* given:
* q real value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* returns:
* real value result of trig function on q with error epsilon
*
* returns:
* != NULL ==> real value result of trig function on q with error epsilon,
* NULL ==> trig function value cannot be expressed as a NUMBER
*
* NOTE: If this function returns NULL, consider calling the equivalent
* COMPLEX function from comfunc.c. See the help file for the
* related builtin for details.
*/
NUMBER *
qacrd_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *qdiv2; /* q/2 */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
*/
if (q == NULL) {
math_error("q is NULL for %s", __func__);
not_reached();
}
if (check_epsilon(epsilon) == false) {
math_error("Invalid epsilon arg for %s", __func__);
not_reached();
}
/*
* calculate inverse trig function value
*/
qdiv2 = qdivi(q, 2);
qtmp = qasin(qdiv2, epsilon);
qfree(qdiv2);
if (qtmp == NULL) {
return NULL;
}
res = qmuli(qtmp, 2);
qfree(qtmp);
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qacrd - non-complex inverse trigonometric chord of a unit circle
*
* This uses the formula:
*
* acrd(x) = 2 * asin(x / 2)
*
* given:
* q real value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* returns:
* real value result of trig function on q with error epsilon
*/
NUMBER *
qacrd(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
/*
* firewall
*/
if (q == NULL) {
math_error("q is NULL for %s", __func__);
not_reached();
}
if (check_epsilon(epsilon) == false) {
math_error("Invalid epsilon arg for %s", __func__);
not_reached();
}
/*
* calculate inverse trig function value
*/
res = qacrd_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse sine for acrd");
not_reached();
}
/*
* return inverse trigonometric result
*/
return res;
}