mirror of
https://github.com/lcn2/calc.git
synced 2025-08-16 01:03:29 +03:00
add half trigonometric functions
Fixed SEE ALSO typo in help randperm.
Added the following new trigonometric functions:
haversin(x [,eps]) half versed trigonometric sine
hacoversin(x [,eps]) half coversed trigonometric sine
havercos(x [,eps]) half versed trigonometric cosine
hacovercos(x [,eps]) half coversed trigonometric cosine
ahaversin(x [,eps]) inverse half versed trigonometric sine
ahacoversin(x [,eps]) inverse half coversed trigonometric sine
ahavercos(x [,eps]) inverse half versed trigonometric cosine
ahacovercos(x [,eps]) inverse half coversed trigonometric cosine
Fixed calc regression test 42dd to set the display value back to 20.
Added test 95dd and test9500.trigeq.cal to the calc regression test
suite to perform extensive test of trigonometric functions.
Fix and improve recently comments and variable names added new
trigonometric functions in comfunc.c, func.c, qtrans.c.
This commit is contained in:
Landon Curt Noll
474
comfunc.c
474
comfunc.c
@@ -1648,7 +1648,7 @@ c_ilog(COMPLEX *c, ZVALUE base)
|
||||
|
||||
|
||||
/*
|
||||
* c_versin - versed sine for COMPLEX values
|
||||
* c_versin - COMPLEX valued versed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -1684,13 +1684,13 @@ c_versin(COMPLEX *c, NUMBER *epsilon)
|
||||
*/
|
||||
ctmp = c_cos(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex cos for complex versin");
|
||||
math_error("Failed to compute complex cosine for complex versin");
|
||||
not_reached();
|
||||
}
|
||||
r = c_sub(&_cone_, ctmp);
|
||||
|
||||
/*
|
||||
* return complex 1 - cos(x)
|
||||
* return trigonometric result
|
||||
*/
|
||||
comfree(ctmp);
|
||||
return r;
|
||||
@@ -1698,7 +1698,7 @@ c_versin(COMPLEX *c, NUMBER *epsilon)
|
||||
|
||||
|
||||
/*
|
||||
* c_aversin - inverse versed sine for COMPLEX values
|
||||
* c_aversin - COMPLEX valued inverse versed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -1715,7 +1715,7 @@ COMPLEX *
|
||||
c_aversin(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *x; /* argument to inverse trig function */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
|
||||
/*
|
||||
* firewall
|
||||
@@ -1732,19 +1732,19 @@ c_aversin(COMPLEX *c, NUMBER *epsilon)
|
||||
/*
|
||||
* calculate complex inverse trig function value
|
||||
*/
|
||||
x = c_sub(&_cone_, c);
|
||||
r = c_acos(x, epsilon);
|
||||
comfree(x);
|
||||
ctmp = c_sub(&_cone_, c);
|
||||
r = c_acos(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return complex acos(1 - x)
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_coversin - coversed sine for COMPLEX values
|
||||
* c_coversin - COMPLEX valued coversed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -1780,21 +1780,21 @@ c_coversin(COMPLEX *c, NUMBER *epsilon)
|
||||
*/
|
||||
ctmp = c_sin(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex sin for complex coversin");
|
||||
math_error("Failed to compute complex sine for complex coversin");
|
||||
not_reached();
|
||||
}
|
||||
r = c_sub(&_cone_, ctmp);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return complex 1 - sin(x)
|
||||
* return trigonometric result
|
||||
*/
|
||||
comfree(ctmp);
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_acoversin - inverse versed sine for COMPLEX values
|
||||
* c_acoversin - COMPLEX valued inverse coversed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -1811,7 +1811,7 @@ COMPLEX *
|
||||
c_acoversin(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *x; /* argument to inverse trig function */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
|
||||
/*
|
||||
* firewall
|
||||
@@ -1828,19 +1828,19 @@ c_acoversin(COMPLEX *c, NUMBER *epsilon)
|
||||
/*
|
||||
* calculate complex inverse trig function value
|
||||
*/
|
||||
x = c_sub(&_cone_, c);
|
||||
r = c_asin(x, epsilon);
|
||||
comfree(x);
|
||||
ctmp = c_sub(&_cone_, c);
|
||||
r = c_asin(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return complex asin(1 - x)
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_vercos - versed sine for COMPLEX values
|
||||
* c_vercos - COMPLEX valued versed trigonometric cosine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -1876,21 +1876,21 @@ c_vercos(COMPLEX *c, NUMBER *epsilon)
|
||||
*/
|
||||
ctmp = c_cos(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex cos for complex vercos");
|
||||
math_error("Failed to compute complex cosine for complex vercos");
|
||||
not_reached();
|
||||
}
|
||||
r = c_add(&_cone_, ctmp);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return complex 1 + cos(x)
|
||||
* return trigonometric result
|
||||
*/
|
||||
comfree(ctmp);
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_avercos - inverse versed sine for COMPLEX values
|
||||
* c_avercos - COMPLEX valued inverse versed trigonometric cosine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -1907,7 +1907,7 @@ COMPLEX *
|
||||
c_avercos(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *x; /* argument to inverse trig function */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
|
||||
/*
|
||||
* firewall
|
||||
@@ -1924,19 +1924,19 @@ c_avercos(COMPLEX *c, NUMBER *epsilon)
|
||||
/*
|
||||
* calculate complex inverse trig function value
|
||||
*/
|
||||
x = c_sub(c, &_cone_);
|
||||
r = c_acos(x, epsilon);
|
||||
comfree(x);
|
||||
ctmp = c_sub(c, &_cone_);
|
||||
r = c_acos(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return complex acos(1 - x)
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_covercos - coversed sine for COMPLEX values
|
||||
* c_covercos - COMPLEX valued coversed trigonometric cosine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -1972,21 +1972,21 @@ c_covercos(COMPLEX *c, NUMBER *epsilon)
|
||||
*/
|
||||
ctmp = c_sin(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex sin for complex covercos");
|
||||
math_error("Failed to compute complex sine for complex covercos");
|
||||
not_reached();
|
||||
}
|
||||
r = c_add(&_cone_, ctmp);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return complex 1 + sin(x)
|
||||
* return trigonometric result
|
||||
*/
|
||||
comfree(ctmp);
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_acovercos - inverse versed sine for COMPLEX values
|
||||
* c_acovercos - COMPLEX valued inverse coversed trigonometric cosine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
@@ -2003,7 +2003,7 @@ COMPLEX *
|
||||
c_acovercos(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *x; /* argument to inverse trig function */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
|
||||
/*
|
||||
* firewall
|
||||
@@ -2020,12 +2020,408 @@ c_acovercos(COMPLEX *c, NUMBER *epsilon)
|
||||
/*
|
||||
* calculate complex inverse trig function value
|
||||
*/
|
||||
x = c_sub(c, &_cone_);
|
||||
r = c_asin(x, epsilon);
|
||||
comfree(x);
|
||||
ctmp = c_sub(c, &_cone_);
|
||||
r = c_asin(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return complex asin(x - 1)
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_haversin - COMPLEX valued half versed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* haversin(x) = versin(x) / 2
|
||||
*
|
||||
* 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_haversin(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_versin(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex versed sine for complex haversin");
|
||||
not_reached();
|
||||
}
|
||||
r = c_divq(ctmp, &_qtwo_);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_ahaversin - COMPLEX valued inverse half versed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* ahaversin(x) = acos(1 - 2*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_ahaversin(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
COMPLEX *x2; /* twice x */
|
||||
|
||||
/*
|
||||
* 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
|
||||
*/
|
||||
x2 = c_mulq(c, &_qtwo_);
|
||||
ctmp = c_sub(&_cone_, x2);
|
||||
comfree(x2);
|
||||
r = c_acos(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_hacoversin - COMPLEX valued half coversed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* hacoversin(x) = coversin(x) / 2
|
||||
*
|
||||
* 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_hacoversin(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_coversin(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex coversed sine for complex hacoversin");
|
||||
not_reached();
|
||||
}
|
||||
r = c_divq(ctmp, &_qtwo_);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_ahacoversin - COMPLEX valued inverse half coversed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* ahacoversin(x) = asin(1 - 2*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_ahacoversin(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
COMPLEX *x2; /* twice x */
|
||||
|
||||
/*
|
||||
* 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
|
||||
*/
|
||||
x2 = c_mulq(c, &_qtwo_);
|
||||
ctmp = c_sub(&_cone_, x2);
|
||||
comfree(x2);
|
||||
r = c_asin(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_havercos - COMPLEX valued half coversed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* havercos(x) = vercos(x) / 2
|
||||
*
|
||||
* 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_havercos(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_vercos(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex versed cosine for complex havercos");
|
||||
not_reached();
|
||||
}
|
||||
r = c_divq(ctmp, &_qtwo_);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_ahavercos - COMPLEX valued inverse half coversed trigonometric sine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* ahavercos(x) = acos(2*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_ahavercos(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
COMPLEX *x2; /* twice x */
|
||||
|
||||
/*
|
||||
* 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
|
||||
*/
|
||||
x2 = c_mulq(c, &_qtwo_);
|
||||
ctmp = c_sub(&_cone_, x2);
|
||||
comfree(x2);
|
||||
r = c_acos(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_hacovercos - COMPLEX valued half coversed trigonometric cosine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* hacovercos(x) = covercos(x) / 2
|
||||
*
|
||||
* 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_hacovercos(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_covercos(c, epsilon);
|
||||
if (ctmp == NULL) {
|
||||
math_error("Failed to compute complex coversed cosine for complex hacovercos");
|
||||
not_reached();
|
||||
}
|
||||
r = c_divq(ctmp, &_qtwo_);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* c_ahacovercos - COMPLEX valued inverse half coversed trigonometric cosine
|
||||
*
|
||||
* This uses the formula:
|
||||
*
|
||||
* ahacovercos(x) = asin(2*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_ahacovercos(COMPLEX *c, NUMBER *epsilon)
|
||||
{
|
||||
COMPLEX *r; /* inverse trig value result */
|
||||
COMPLEX *ctmp; /* argument to inverse trig function */
|
||||
COMPLEX *x2; /* twice x */
|
||||
|
||||
/*
|
||||
* 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
|
||||
*/
|
||||
x2 = c_mulq(c, &_qtwo_);
|
||||
ctmp = c_sub(&_cone_, x2);
|
||||
comfree(x2);
|
||||
r = c_asin(ctmp, epsilon);
|
||||
comfree(ctmp);
|
||||
|
||||
/*
|
||||
* return inverse trigonometric result
|
||||
*/
|
||||
return r;
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user