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add half trigonometric functions

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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
2023-09-28 23:46:53 -07:00
parent ab95e47c0a
commit 5d62e58704
12 changed files with 3040 additions and 139 deletions
Download Patch File Download Diff File Expand all files Collapse all files

725
qtrans.c
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@@ -1979,7 +1979,7 @@ qacoth(NUMBER *q, NUMBER *epsilon)
/*
* qversin - versed sine for NUMBER values
* qversin - versed trigonometric sine
*
* This uses the formula:
*
@@ -1995,8 +1995,8 @@ qacoth(NUMBER *q, NUMBER *epsilon)
NUMBER *
qversin(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res;
NUMBER *cos;
NUMBER *res; /* inverse trig value result */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2013,19 +2013,19 @@ qversin(NUMBER *q, NUMBER *epsilon)
/*
* calculate trig function value
*/
cos = qcos(q, epsilon);
res = qsub(&_qone_, cos);
qfree(cos);
qtmp = qcos(q, epsilon);
res = qsub(&_qone_, qtmp);
qfree(qtmp);
/*
* return 1 - cos(x)
* return trigonometric result
*/
return res;
}
/*
* qaversin_or_NULL - inverse versed sine for NUMBER values
* qaversin_or_NULL - return NULL or non-complex inverse versed trigonometric sine
*
* This uses the formula:
*
@@ -2047,7 +2047,7 @@ NUMBER *
qaversin_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *x; /* argument to inverse trig function */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2064,22 +2064,22 @@ qaversin_or_NULL(NUMBER *q, NUMBER *epsilon)
/*
* calculate inverse trig function value
*/
x = qsub(&_qone_, q);
res = qacos(x, epsilon);
qfree(x);
qtmp = qsub(&_qone_, q);
res = qacos(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return acos(1 - x)
* return inverse trigonometric result
*/
return res;
}
/*
* qaversin - inverse versed sine for NUMBER values
* qaversin - non-complex inverse versed trigonometric sine
*
* This uses the formula:
*
@@ -2114,19 +2114,19 @@ qaversin(NUMBER *q, NUMBER *epsilon)
*/
res = qaversin_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse cos for aversin");
math_error("cannot compute inverse cosine for aversin");
not_reached();
}
/*
* return acos(1 - x)
* return inverse trigonometric result
*/
return res;
}
/*
* qcoversin - coversed sine for NUMBER values
* qcoversin - coversed trigonometric sine
*
* This uses the formula:
*
@@ -2142,7 +2142,8 @@ qaversin(NUMBER *q, NUMBER *epsilon)
NUMBER *
qcoversin(NUMBER *q, NUMBER *epsilon)
{
NUMBER *sin, *res;
NUMBER *res; /* inverse trig value result */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2159,19 +2160,19 @@ qcoversin(NUMBER *q, NUMBER *epsilon)
/*
* calculate trig function value
*/
sin = qsin(q, epsilon);
res = qsub(&_qone_, sin);
qfree(sin);
qtmp = qsin(q, epsilon);
res = qsub(&_qone_, qtmp);
qfree(qtmp);
/*
* return 1 - sin(x)
* return trigonometric result
*/
return res;
}
/*
* qacoversin_or_NULL - inverse coversed sine for NUMBER values
* qacoversin_or_NULL - return NULL or non-complex inverse coversed trigonometric sine
*
* This uses the formula:
*
@@ -2196,7 +2197,7 @@ NUMBER *
qacoversin_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *x; /* argument to inverse trig function */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2213,22 +2214,22 @@ qacoversin_or_NULL(NUMBER *q, NUMBER *epsilon)
/*
* calculate inverse trig function value
*/
x = qsub(&_qone_, q);
res = qasin(x, epsilon);
qfree(x);
qtmp = qsub(&_qone_, q);
res = qasin(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return asin(1 - x)
* return inverse trigonometric result
*/
return res;
}
/*
* qacoversin - inverse coversed sine for NUMBER values
* qacoversin - non-complex inverse coversed trigonometric sine
*
* This uses the formula:
*
@@ -2263,19 +2264,19 @@ qacoversin(NUMBER *q, NUMBER *epsilon)
*/
res = qacoversin_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse sin for acoversin");
math_error("cannot compute inverse sine for acoversin");
not_reached();
}
/*
* return asin(1 - x)
* return inverse trigonometric result
*/
return res;
}
/*
* qvercos - versed sine for NUMBER values
* qvercos - versed trigonometric cosine
*
* This uses the formula:
*
@@ -2291,7 +2292,8 @@ qacoversin(NUMBER *q, NUMBER *epsilon)
NUMBER *
qvercos(NUMBER *q, NUMBER *epsilon)
{
NUMBER *cos, *res;
NUMBER *res; /* inverse trig value result */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2308,19 +2310,19 @@ qvercos(NUMBER *q, NUMBER *epsilon)
/*
* calculate trig function value
*/
cos = qcos(q, epsilon);
res = qqadd(&_qone_, cos);
qfree(cos);
qtmp = qcos(q, epsilon);
res = qqadd(&_qone_, qtmp);
qfree(qtmp);
/*
* return 1 + cos(x)
* return trigonometric result
*/
return res;
}
/*
* qavercos_or_NULL - inverse versed sine for NUMBER values
* qavercos_or_NULL - return NULL or non-complex inverse versed trigonometric cosine
*
* This uses the formula:
*
@@ -2342,7 +2344,7 @@ NUMBER *
qavercos_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *x; /* argument to inverse trig function */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2359,22 +2361,22 @@ qavercos_or_NULL(NUMBER *q, NUMBER *epsilon)
/*
* calculate inverse trig function value
*/
x = qsub(q, &_qone_);
res = qacos(x, epsilon);
qfree(x);
qtmp = qsub(q, &_qone_);
res = qacos(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return acos(x - 1)
* return inverse trigonometric result
*/
return res;
}
/*
* qavercos - inverse versed sine for NUMBER values
* qavercos - non-complex inverse versed trigonometric cosine
*
* This uses the formula:
*
@@ -2409,19 +2411,19 @@ qavercos(NUMBER *q, NUMBER *epsilon)
*/
res = qavercos_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse cos for avercos");
math_error("cannot compute inverse cosine for avercos");
not_reached();
}
/*
* return acos(x - 1)
* return inverse trigonometric result
*/
return res;
}
/*
* qcovercos - coversed sine for NUMBER values
* qcovercos - coversed trigonometric cosine
*
* This uses the formula:
*
@@ -2437,7 +2439,8 @@ qavercos(NUMBER *q, NUMBER *epsilon)
NUMBER *
qcovercos(NUMBER *q, NUMBER *epsilon)
{
NUMBER *sin, *res;
NUMBER *res; /* inverse trig value result */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2454,19 +2457,19 @@ qcovercos(NUMBER *q, NUMBER *epsilon)
/*
* calculate trig function value
*/
sin = qsin(q, epsilon);
res = qqadd(&_qone_, sin);
qfree(sin);
qtmp = qsin(q, epsilon);
res = qqadd(&_qone_, qtmp);
qfree(qtmp);
/*
* return 1 + sin(x)
* return trigonometric result
*/
return res;
}
/*
* qacovercos_or_NULL - inverse coversed sine for NUMBER values
* qacovercos_or_NULL - return NULL or non-complex inverse coversed trigonometric cosine
*
* This uses the formula:
*
@@ -2491,7 +2494,7 @@ NUMBER *
qacovercos_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *x; /* argument to inverse trig function */
NUMBER *qtmp; /* argument to inverse trig function */
/*
* firewall
@@ -2508,22 +2511,22 @@ qacovercos_or_NULL(NUMBER *q, NUMBER *epsilon)
/*
* calculate inverse trig function value
*/
x = qsub(&_qone_, q);
res = qasin(x, epsilon);
qfree(x);
qtmp = qsub(&_qone_, q);
res = qasin(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return asin(x - 1)
* return inverse trigonometric result
*/
return res;
}
/*
* qacovercos - inverse coversed sine for NUMBER values
* qacovercos - non-complex inverse coversed trigonometric cosine
*
* This uses the formula:
*
@@ -2558,12 +2561,612 @@ qacovercos(NUMBER *q, NUMBER *epsilon)
*/
res = qacovercos_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse sin for acovercos");
math_error("cannot compute inverse sine for acovercos");
not_reached();
}
/*
* return asin(x - 1)
* return inverse trigonometric result
*/
return res;
}
/*
* qhaversin - half versed trigonometric sine
*
* This uses the formula:
*
* haversin(x) = versin(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 *
qhaversin(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
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
*/
qtmp = qversin(q, epsilon);
res = qdivi(qtmp, 2);
qfree(qtmp);
/*
* return trigonometric result
*/
return res;
}
/*
* qahaversin_or_NULL - return NULL or non-complex inverse half versed trigonometric sine
*
* This uses the formula:
*
* ahaversin(x) = acos(1 - 2*x)
*
* given:
* q real value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* 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 *
qahaversin_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *qtmp; /* argument to inverse trig function */
NUMBER *x2; /* twice x */
/*
* 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
*/
x2 = qmuli(q, 2);
qtmp = qsub(&_qone_, x2);
qfree(x2);
res = qacos(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qahaversin - non-complex inverse half versed trigonometric sine
*
* This uses the formula:
*
* ahaversin(x) = acos(1 - 2*x)
*
* 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 *
qahaversin(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 = qahaversin_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse cosine for ahaversin");
not_reached();
}
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qhacoversin - coversed trigonometric sine
*
* This uses the formula:
*
* hacoversin((x) = coversin(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 *
qhacoversin(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
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
*/
qtmp = qcoversin(q, epsilon);
res = qdivi(qtmp, 2);
qfree(qtmp);
/*
* return trigonometric result
*/
return res;
}
/*
* qahacoversin_or_NULL - return NULL or non-complex inverse coversed trigonometric sine
*
* This uses the formula:
*
* ahacoversin(x) = asin(1 - 2*x)
*
* 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 *
qahacoversin_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
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
*/
qtmp = qsub(&_qone_, q);
res = qasin(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qahacoversin - non-complex inverse coversed trigonometric sine
*
* This uses the formula:
*
* ahacoversin(x) = asin(1 - 2*x)
*
* 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 *
qahacoversin(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 = qahacoversin_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse sine for ahacoversin");
not_reached();
}
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qhavercos - half versed trigonometric cosine
*
* This uses the formula:
*
* havercos(x) = vercos(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 *
qhavercos(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
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
*/
qtmp = qvercos(q, epsilon);
res = qdivi(qtmp, 2);
qfree(qtmp);
/*
* return trigonometric result
*/
return res;
}
/*
* qahavercos_or_NULL - return NULL or non-complex inverse half versed trigonometric cosine
*
* This uses the formula:
*
* ahavercos(x) = acos(1 - 2*x)
*
* given:
* q real value to pass to the trig function
* epsilon error tolerance / precision for trig calculation
*
* 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 *
qahavercos_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *qtmp; /* argument to inverse trig function */
NUMBER *x2; /* twice x */
/*
* 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
*/
x2 = qmuli(q, 2);
qtmp = qsub(&_qone_, x2);
qfree(x2);
res = qacos(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qahavercos - non-complex inverse half versed trigonometric cosine
*
* This uses the formula:
*
* ahavercos(x) = acos(1 - 2*x)
*
* 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 *
qahavercos(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 = qahaversin_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse cocosine for ahavercos");
not_reached();
}
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qhacovercos - half coversed trigonometric cosine
*
* This uses the formula:
*
* hacovercos((x) = covercos(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 *
qhacovercos(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
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
*/
qtmp = qcovercos(q, epsilon);
res = qdivi(qtmp, 2);
qfree(qtmp);
/*
* return trigonometric result
*/
return res;
}
/*
* qahacovercos_or_NULL - return NULL or non-complex inverse half coversed trigonometric cosine
*
* This uses the formula:
*
* ahacovercos(x) = acos(2*x - 1)
*
* 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 *
qahacovercos_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
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
*/
qtmp = qsub(&_qone_, q);
res = qacos(qtmp, epsilon);
qfree(qtmp);
if (res == NULL) {
return NULL;
}
/*
* return inverse trigonometric result
*/
return res;
}
/*
* qahacovercos - non-complex inverse half coversed trigonometric cosine
*
* This uses the formula:
*
* ahacovercos(x) = acos(2*x - 1)
*
* 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 *
qahacovercos(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 = qahacoversin_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse cosine for ahacovercos");
not_reached();
}
/*
* return inverse trigonometric result
*/
return res;
}