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add vercos(), avercos(), covercos(), acovercos()

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Improved trig help files.

Added new vercos(x, [,eps]) for versed cosine and covercos(x, [,eps])
for inverse versed cosine.

Added new avercos(x, [,eps]) for inverse versed cosine and acovercos(x, [,eps])
for inverse coversed cosine.
This commit is contained in:
Landon Curt Noll
2023-09-06 00:52:37 -07:00
parent ea5b5e0b53
commit fdbf53d7e8
28 changed files with 1218 additions and 59 deletions
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194
comfunc.c
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@@ -1428,7 +1428,7 @@ c_aversin(COMPLEX *c, NUMBER *epsilon)
*
* This uses the formula:
*
* coversin(x) = 1 - sin(x)
* coversin(x) = 1 - cos(x)
*
* given:
* q complex value to pass to the trig function
@@ -1517,3 +1517,195 @@ c_acoversin(COMPLEX *c, NUMBER *epsilon)
*/
return r;
}
/*
* c_vercos - versed sine for COMPLEX values
*
* This uses the formula:
*
* vercos(x) = 1 + cos(x)
*
* given:
* q complex value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* returns:
* complex value result of trig function on q with error epsilon
*/
COMPLEX *
c_vercos(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *r; /* return COMPLEX value */
COMPLEX *ctmp; /* complex cos(c) */
/*
* firewall
*/
if (c == NULL) {
math_error("%s: c is NULL", __func__);
not_reached();
}
if (check_epsilon(epsilon) == false) {
math_error("Invalid epsilon arg for %s", __func__);
not_reached();
}
/*
* calculate complex trig function value
*/
ctmp = c_cos(c, epsilon);
if (ctmp == NULL) {
math_error("Failed to compute complex cos for complex vercos");
not_reached();
}
r = c_add(&_cone_, ctmp);
/*
* return complex 1 + cos(x)
*/
comfree(ctmp);
return r;
}
/*
* c_avercos - inverse versed sine for COMPLEX values
*
* This uses the formula:
*
* avercos(x) = acos(x - 1)
*
* given:
* q complex value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* returns:
* complex value result of trig function on q with error epsilon
*/
COMPLEX *
c_avercos(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *r; /* inverse trig value result */
COMPLEX *x; /* argument to inverse trig function */
/*
* firewall
*/
if (c == NULL) {
math_error("%s: c is NULL", __func__);
not_reached();
}
if (check_epsilon(epsilon) == false) {
math_error("Invalid epsilon arg for %s", __func__);
not_reached();
}
/*
* calculate complex inverse trig function value
*/
x = c_sub(c, &_cone_);
r = c_acos(x, epsilon);
comfree(x);
/*
* return complex acos(1 - x)
*/
return r;
}
/*
* c_covercos - coversed sine for COMPLEX values
*
* This uses the formula:
*
* covercos(x) = 1 + sin(x)
*
* given:
* q complex value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* returns:
* complex value result of trig function on q with error epsilon
*/
COMPLEX *
c_covercos(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *r; /* return COMPLEX value */
COMPLEX *ctmp; /* complex sin(c) */
/*
* firewall
*/
if (c == NULL) {
math_error("%s: c is NULL", __func__);
not_reached();
}
if (check_epsilon(epsilon) == false) {
math_error("Invalid epsilon arg for %s", __func__);
not_reached();
}
/*
* calculate complex trig function value
*/
ctmp = c_sin(c, epsilon);
if (ctmp == NULL) {
math_error("Failed to compute complex sin for complex covercos");
not_reached();
}
r = c_add(&_cone_, ctmp);
/*
* return complex 1 + sin(x)
*/
comfree(ctmp);
return r;
}
/*
* c_acovercos - inverse versed sine for COMPLEX values
*
* This uses the formula:
*
* acovercos(x) = asin(x - 1)
*
* given:
* q complex value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* returns:
* complex value result of trig function on q with error epsilon
*/
COMPLEX *
c_acovercos(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *r; /* inverse trig value result */
COMPLEX *x; /* argument to inverse trig function */
/*
* firewall
*/
if (c == NULL) {
math_error("%s: c is NULL", __func__);
not_reached();
}
if (check_epsilon(epsilon) == false) {
math_error("Invalid epsilon arg for %s", __func__);
not_reached();
}
/*
* calculate complex inverse trig function value
*/
x = c_sub(c, &_cone_);
r = c_asin(x, epsilon);
comfree(x);
/*
* return complex asin(x - 1)
*/
return r;
}