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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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8
CHANGES
View File

@@ -128,7 +128,13 @@ The following are the changes from calc version 2.14.3.5 to date:
Added c_to_q(COMPLEX *c, bool cfree) to make is easier to convert
a COMPLEX value that is real (imag part is 0) into a NUMBER and
optionally free the COMPLEX value.
optionally free the COMPLEX value. The func.c code now uses c_to_q().
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.
The following are the changes from calc version 2.14.3.4 to 2.14.3.5:

105
cal/regress.cal
View File

@@ -3506,9 +3506,9 @@ define test_trig()
/* test 3401-3407 */
tnum = test3400(1, 3401);
vrfy(tnum++ == 3407, '3407: tnum == 3407');
pi = pi(1e-20);
/* test versed trigonometric sine */
pi = pi(1e-20);
vrfy(round(versin(0.2, 1e-10), 10) == 0.0199334222,
strcat(str(tnum++),
': round(versin(0.2, 1e-10), 10) == 0.0199334222'));
@@ -3533,8 +3533,20 @@ define test_trig()
strcat(str(tnum++),
': round(versin(2 + 3i, 1e-10), 10) == 5.189625691+9.1092278938i'));
/* test inverse versed trigonometric sine */
vrfy(round(aversin(0.5, 1e-10), 10) == 1.0471975512,
strcat(str(tnum++),
': round(aversin(0.5, 1e-10), 10) == 1.0471975512'));
vrfy(aversin(0) == 0,
strcat(str(tnum++), ': aversin(0) == 0'));
vrfy(round(aversin(-5, 1e-10), 10) == 2.4778887303i,
strcat(str(tnum++),
': round(aversin(-5, 1e-10), 10) == 2.4778887303i'));
vrfy(round(aversin(2 + 3i, 1e-10), 10) == 1.8783999763+1.8641615439i,
strcat(str(tnum++),
': round(aversin(2 + 3i, 1e-10), 10) == 1.8783999763+1.8641615439i'));
/* test coversed trigonometric sine */
pi = pi(1e-20);
vrfy(round(coversin(0.2, 1e-10), 10) == 0.8013306692,
strcat(str(tnum++),
': round(coversin(0.2, 1e-10), 10) == 0.8013306692'));
@@ -3559,19 +3571,6 @@ define test_trig()
strcat(str(tnum++),
': round(coversin(2 + 3i, 1e-10), 10) == -8.1544991469+4.16890696i'));
/* test inverse versed trigonometric sine */
vrfy(round(aversin(0.5, 1e-10), 10) == 1.0471975512,
strcat(str(tnum++),
': round(aversin(0.5, 1e-10), 10) == 1.0471975512'));
vrfy(aversin(0) == 0,
strcat(str(tnum++), ': aversin(0) == 0'));
vrfy(round(aversin(-5, 1e-10), 10) == 2.4778887303i,
strcat(str(tnum++),
': round(aversin(-5, 1e-10), 10) == 2.4778887303i'));
vrfy(round(aversin(2 + 3i, 1e-10), 10) == 1.8783999763+1.8641615439i,
strcat(str(tnum++),
': round(aversin(2 + 3i, 1e-10), 10) == 1.8783999763+1.8641615439i'));
/* test inverse coversed trigonometric sine */
vrfy(round(acoversin(0.5, 1e-10), 10) == 0.5235987756,
strcat(str(tnum++),
@@ -3585,6 +3584,82 @@ define test_trig()
strcat(str(tnum++),
': round(acoversin(2 + 3i, 1e-10), 10) == -0.3076036495-1.8641615442i'));
/* test versed trigonometric cosine */
vrfy(round(vercos(0.2, 1e-10), 10) == 1.9800665778,
strcat(str(tnum++),
': round(vercos(0.2, 1e-10), 10) == 1.9800665778'));
vrfy(round(vercos(3/7, 1e-10), 10) == 1.9095603517,
strcat(str(tnum++),
': round(vercos(3/7, 1e-10), 10) == 1.9095603517'));
vrfy(round(vercos(-31, 1e-10), 10) == 1.9147423578,
strcat(str(tnum++),
': round(vercos(-31, 1e-10), 10) == 1.9147423578'));
vrfy(vercos(pi/3, 1e-10) == 1.5,
strcat(str(tnum++), ': vercos(pi/3, 1e-10) == 1.5'));
vrfy(vercos(pi/2, 1e-10) == 1,
strcat(str(tnum++), ': vercos(pi/2, 1e-10) == 1'));
vrfy(vercos(pi, 1e-10) == 0,
strcat(str(tnum++), ': vercos(pi, 1e-10) == 0'));
vrfy(vercos(3*pi/2, 1e-10) == 1,
strcat(str(tnum++), ': vercos(3*pi/2, 1e-10) == 1'));
vrfy(round(vercos(1, 1e-10), 10) == 1.5403023059,
strcat(str(tnum++),
': round(vercos(1, 1e-10), 10) == 1.5403023059'));
vrfy(round(vercos(2 + 3i, 1e-10), 10) == -3.189625691-9.1092278938i,
strcat(str(tnum++),
': round(vercos(2 + 3i, 1e-10), 10) == -3.189625691-9.1092278938i'));
/* test inverse versed trigonometric cosine */
vrfy(round(avercos(0.5, 1e-10), 10) == 2.0943951024,
strcat(str(tnum++),
': round(avercos(0.5, 1e-10), 10) == 2.0943951024'));
vrfy(avercos(2) == 0,
strcat(str(tnum++), ': avercos(2) == 0'));
vrfy(round(avercos(-5, 1e-10), 10) == 3.1415926536-2.4778887303i,
strcat(str(tnum++),
': round(avercos(-5, 1e-10), 10) == 3.1415926536-2.4778887303i'));
vrfy(round(avercos(2 + 3i, 1e-10), 10) == 1.2631926773-1.8641615442i,
strcat(str(tnum++),
': round(avercos(2 + 3i, 1e-10), 10) == 1.2631926773-1.8641615442i'));
/* test coversed trigonometric cosine */
vrfy(round(covercos(0.2, 1e-10), 10) == 1.1986693308,
strcat(str(tnum++),
': round(covercos(0.2, 1e-10), 10) == 1.1986693308'));
vrfy(round(covercos(3/7, 1e-10), 10) == 1.415571855,
strcat(str(tnum++),
': round(covercos(3/7, 1e-10), 10) == 1.415571855'));
vrfy(round(covercos(-31, 1e-10), 10) == 1.4040376453,
strcat(str(tnum++),
': round(covercos(-31, 1e-10), 10) == 1.4040376453'));
vrfy(covercos(pi/6, 1e-10) == 1.5,
strcat(str(tnum++), ': covercos(pi/6, 1e-10) == 1.5'));
vrfy(covercos(pi/2, 1e-10) == 2,
strcat(str(tnum++), ': covercos(pi/2, 1e-10) == 2'));
vrfy(covercos(pi, 1e-10) == 1,
strcat(str(tnum++), ': covercos(pi, 1e-10) == 1'));
vrfy(covercos(3*pi/2, 1e-10) == 0,
strcat(str(tnum++), ': covercos(3*pi/2, 1e-10) == 0'));
vrfy(round(covercos(1, 1e-10), 10) == 1.8414709848,
strcat(str(tnum++),
': round(covercos(1, 1e-10), 10) == 1.8414709848'));
vrfy(round(covercos(2 + 3i, 1e-10), 10) == 10.1544991469-4.16890696i,
strcat(str(tnum++),
': round(covercos(2 + 3i, 1e-10), 10) == 10.1544991469-4.16890696i'));
/* test inverse coversed trigonometric cosine */
vrfy(round(acovercos(0.5, 1e-10), 10) == 0.5235987756,
strcat(str(tnum++),
': round(acovercos(0.5, 1e-10), 10) == 0.5235987756'));
vrfy(acovercos(1) == 0,
strcat(str(tnum++), ': acovercos(1) == 0'));
vrfy(round(acovercos(-5, 1e-10), 10) == -1.5707963268+2.4778887303i,
strcat(str(tnum++),
': round(acovercos(-5, 1e-10), 10) == -1.5707963268+2.4778887303i'));
vrfy(round(acovercos(2 + 3i, 1e-10), 10) == 0.3076036495+1.8641615442i,
strcat(str(tnum++),
': round(acovercos(2 + 3i, 1e-10), 10) == 0.3076036495+1.8641615442i'));
print strcat(str(tnum++), ': Ending test_trig');
}
print '051: parsed test_trig()';

12
calcerr.tbl
View File

@@ -562,3 +562,15 @@ E_COVERSIN3 Too-large im(argument) for coversin
E_ACOVERSIN1 Bad epsilon for acoversin
E_ACOVERSIN2 Bad first argument for acoversin
E_ACOVERSIN3 Too-large im(argument) for acoversin
E_VERCOS1 Bad epsilon for vercos
E_VERCOS2 Bad first argument for vercos
E_VERCOS3 Too-large im(argument) for vercos
E_AVERCOS1 Bad epsilon for avercos
E_AVERCOS2 Bad first argument for avercos
E_AVERCOS3 Too-large im(argument) for avercos
E_COVERCOS1 Bad epsilon for covercos
E_COVERCOS2 Bad first argument for covercos
E_COVERCOS3 Too-large im(argument) for covercos
E_ACOVERCOS1 Bad epsilon for acovercos
E_ACOVERCOS2 Bad first argument for acovercos
E_ACOVERCOS3 Too-large im(argument) for acovercos

4
cmath.h
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@@ -127,6 +127,10 @@ E_FUNC COMPLEX *c_versin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_aversin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_coversin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acoversin(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_vercos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_avercos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_covercos(COMPLEX *c, NUMBER *epsilon);
E_FUNC COMPLEX *c_acovercos(COMPLEX *c, NUMBER *epsilon);

194
comfunc.c
View File

@@ -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;
}

288
func.c
View File

@@ -10841,6 +10841,286 @@ f_acoversin(int count, VALUE **vals)
}
/*
* f_vercos - versed cosine
*/
S_FUNC VALUE
f_vercos(int count, VALUE **vals)
{
VALUE result;
COMPLEX *c;
NUMBER *eps;
/* initialize VALUE */
result.v_subtype = V_NOSUBTYPE;
/*
* set error tolerance for builtin function
*
* Use eps VALUE arg if given and value is in a valid range.
*/
eps = conf->epsilon;
if (count == 2) {
if (verify_eps(vals[1]) == false) {
return error_value(E_VERCOS1);
}
eps = vals[1]->v_num;
}
/*
* compute trig function to a given error tolerance
*/
switch (vals[0]->v_type) {
case V_NUM:
result.v_num = qvercos(vals[0]->v_num, eps);
result.v_type = V_NUM;
break;
case V_COM:
c = c_vercos(vals[0]->v_com, eps);
if (c == NULL) {
return error_value(E_VERCOS3);
}
result.v_com = c;
result.v_type = V_COM;
/*
* case: complex trig function returned real, convert result to NUMBER
*/
if (cisreal(c)) {
result.v_num = c_to_q(c, true);
result.v_type = V_NUM;
}
break;
default:
return error_value(E_VERCOS2);
}
return result;
}
/*
* f_avercos - inverse versed cosine
*/
S_FUNC VALUE
f_avercos(int count, VALUE **vals)
{
VALUE arg1; /* 1st arg if it is a COMPLEX value */
VALUE result; /* value to return */
COMPLEX *c; /* COMPLEX trig result */
NUMBER *eps; /* epsilon error tolerance */
/* initialize VALUE */
result.v_subtype = V_NOSUBTYPE;
/*
* set error tolerance for builtin function
*
* Use eps VALUE arg if given and value is in a valid range.
*/
eps = conf->epsilon;
if (count == 2) {
if (verify_eps(vals[1]) == false) {
return error_value(E_AVERCOS1);
}
eps = vals[1]->v_num;
}
/*
* compute inverse trig function to a given error tolerance
*/
arg1 = *vals[0];
if (arg1.v_type == V_NUM) {
/* try to compute result using real triv function */
result.v_num = qavercos_or_NULL(arg1.v_num, eps);
/*
* case: trig function returned a NUMBER
*/
if (result.v_num != NULL) {
result.v_type = V_NUM;
/*
* case: trig function returned NULL - need to try COMPLEX trig function
*/
} else {
/* convert NUMBER argument from NUMBER to COMPLEX */
arg1.v_com = qqtoc(arg1.v_num, &_qzero_);
arg1.v_type = V_COM;
}
}
if (arg1.v_type == V_COM) {
/*
* case: argument was COMPLEX or
* trig function returned NULL and argument was converted to COMPLEX
*/
c = c_avercos(arg1.v_com, eps);
if (c == NULL) {
return error_value(E_AVERCOS3);
}
result.v_com = c;
result.v_type = V_COM;
/*
* case: complex trig function returned real, convert result to NUMBER
*/
if (cisreal(c)) {
result.v_num = c_to_q(c, true);
result.v_type = V_NUM;
}
}
if (arg1.v_type != V_NUM && arg1.v_type != V_COM) {
/*
* case: argument type is not valid for this function
*/
return error_value(E_AVERCOS2);
}
return result;
}
/*
* f_covercos - coversed cosine
*/
S_FUNC VALUE
f_covercos(int count, VALUE **vals)
{
VALUE result;
COMPLEX *c;
NUMBER *eps;
/* initialize VALUE */
result.v_subtype = V_NOSUBTYPE;
/*
* set error tolerance for builtin function
*
* Use eps VALUE arg if given and value is in a valid range.
*/
eps = conf->epsilon;
if (count == 2) {
if (verify_eps(vals[1]) == false) {
return error_value(E_COVERCOS1);
}
eps = vals[1]->v_num;
}
/*
* compute trig function to a given error tolerance
*/
switch (vals[0]->v_type) {
case V_NUM:
result.v_num = qcovercos(vals[0]->v_num, eps);
result.v_type = V_NUM;
break;
case V_COM:
c = c_covercos(vals[0]->v_com, eps);
if (c == NULL) {
return error_value(E_COVERCOS3);
}
result.v_com = c;
result.v_type = V_COM;
/*
* case: complex trig function returned real, convert result to NUMBER
*/
if (cisreal(c)) {
result.v_num = c_to_q(c, true);
result.v_type = V_NUM;
}
break;
default:
return error_value(E_COVERCOS2);
}
return result;
}
/*
* f_acovercos - inverse coversed cosine
*/
S_FUNC VALUE
f_acovercos(int count, VALUE **vals)
{
VALUE arg1; /* 1st arg if it is a COMPLEX value */
VALUE result; /* value to return */
COMPLEX *c; /* COMPLEX trig result */
NUMBER *eps; /* epsilon error tolerance */
/* initialize VALUE */
result.v_subtype = V_NOSUBTYPE;
/*
* set error tolerance for builtin function
*
* Use eps VALUE arg if given and value is in a valid range.
*/
eps = conf->epsilon;
if (count == 2) {
if (verify_eps(vals[1]) == false) {
return error_value(E_ACOVERCOS1);
}
eps = vals[1]->v_num;
}
/*
* compute inverse trig function to a given error tolerance
*/
arg1 = *vals[0];
if (arg1.v_type == V_NUM) {
/* try to compute result using real triv function */
result.v_num = qacovercos_or_NULL(arg1.v_num, eps);
/*
* case: trig function returned a NUMBER
*/
if (result.v_num != NULL) {
result.v_type = V_NUM;
/*
* case: trig function returned NULL - need to try COMPLEX trig function
*/
} else {
/* convert NUMBER argument from NUMBER to COMPLEX */
arg1.v_com = qqtoc(arg1.v_num, &_qzero_);
arg1.v_type = V_COM;
}
}
if (arg1.v_type == V_COM) {
/*
* case: argument was COMPLEX or
* trig function returned NULL and argument was converted to COMPLEX
*/
c = c_acovercos(arg1.v_com, eps);
if (c == NULL) {
return error_value(E_ACOVERCOS3);
}
result.v_com = c;
result.v_type = V_COM;
/*
* case: complex trig function returned real, convert result to NUMBER
*/
if (cisreal(c)) {
result.v_num = c_to_q(c, true);
result.v_type = V_NUM;
}
}
if (arg1.v_type != V_NUM && arg1.v_type != V_COM) {
/*
* case: argument type is not valid for this function
*/
return error_value(E_ACOVERCOS2);
}
return result;
}
#endif /* !FUNCLIST */
@@ -10893,6 +11173,8 @@ STATIC CONST struct builtin builtins[] = {
"inverse cotangent of a within accuracy b"},
{"acoth", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_acoth},
"inverse hyperbolic cotangent of a within accuracy b"},
{"acovercos", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_acovercos},
"inverse coversed cosine of a within accuracy b"},
{"acoversin", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_acoversin},
"inverse coversed sine of a within accuracy b"},
{"acsc", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_acsc},
@@ -10925,6 +11207,8 @@ STATIC CONST struct builtin builtins[] = {
"angle to point (b,a) within accuracy c"},
{"atanh", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_atanh},
"inverse hyperbolic tangent of a within accuracy b"},
{"avercos", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_avercos},
"inverse versed cosine of a within accuracy b"},
{"aversin", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_aversin},
"inverse versed sine of a within accuracy b"},
{"avg", 0, IN, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_avg},
@@ -10988,6 +11272,8 @@ STATIC CONST struct builtin builtins[] = {
"hyperbolic cotangent of a within accuracy b"},
{"count", 2, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_2 = f_count},
"count listr/matrix elements satisfying some condition"},
{"covercos", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_covercos},
"coversed cosine of value a within accuracy b"},
{"coversin", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_coversin},
"coversed sine of value a within accuracy b"},
{"cp", 2, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_2 = f_cp},
@@ -11547,6 +11833,8 @@ STATIC CONST struct builtin builtins[] = {
"unget char read from file"},
{"usertime", 0, 0, 0, OP_NOP, {.numfunc_0 = f_usertime}, {.null = NULL},
"user mode CPU time in seconds"},
{"vercos", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_vercos},
"versed cosine of value a within accuracy b"},
{"versin", 1, 2, 0, OP_NOP, {.null = NULL}, {.valfunc_cnt = f_versin},
"versed sine of value a within accuracy b"},
{"version", 0, 0, 0, OP_NOP, {.null = NULL}, {.valfunc_0 = f_version},

4
help/acos
View File

@@ -36,8 +36,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2023 Landon Curt Noll

4
help/acot
View File

@@ -34,8 +34,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll

62
help/acovercos Normal file
View File

@@ -0,0 +1,62 @@
NAME
acovercos - inverse coversed trigonometric cosine
SYNOPSIS
acovercos(x [,eps])
TYPES
x number (real or complex)
eps 0 < real < 1, defaults to epsilon()
return number
DESCRIPTION
Calculate the inverse coversed trigonometric cosine of x to a multiple of eps with error less in
absolute value than .75 * eps.
This function is sometimes called acvc, or arccovercos, is equivalent to:
acovercos(x) = asin(x - 1)
EXAMPLE
; print acovercos(.5, 1e-5), acovercos(.5, 1e-10), acovercos(.5, 1e-15), acovercos(.5, 1e-20)
0.5236 0.5235987756 0.523598775598299 0.52359877559829887308
; print acovercos(1), acovercos(-5), acovercos(2 + 3i)
0 -1.57079632679489661923+2.47788873028847500485i 0.30760364953071124992+1.86416154415788242834i
LIMITS
0 < eps < 1
LINK LIBRARY
NUMBER *qacovercos(NUMBER *x, NUMBER *eps)
COMPLEX *c_acovercos(COMPLEX *x, NUMBER *eps)
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 2023 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 2023/09/05 23:30:08
## File existed as early as: 2023
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/

9
help/acoversin
View File

@@ -11,11 +11,10 @@ TYPES
return number
DESCRIPTION
Calculate the inverse coversed sine of x to a multiple of eps with error less in
Calculate the inverse coversed trigonometric sine of x to a multiple of eps with error less in
absolute value than .75 * eps.
The coversed sine function is sometimes called covers, or acosiv, or acvs,
may be defined as:
This function is sometimes called acovers, or acvs, or arccoversin, is equivalent to:
acoversin(x) = asin(1 - x)
@@ -36,8 +35,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin
aversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 2023 Landon Curt Noll

4
help/acsc
View File

@@ -34,8 +34,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll

4
help/asec
View File

@@ -34,8 +34,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll

4
help/asin
View File

@@ -36,8 +36,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
acos, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll

4
help/atan
View File

@@ -34,8 +34,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2023 Landon Curt Noll

63
help/avercos Normal file
View File

@@ -0,0 +1,63 @@
NAME
avercos - inverse versed trigonometric cosine
SYNOPSIS
avercos(x [,eps])
TYPES
x number (real or complex)
eps 0 < real < 1, defaults to epsilon()
return real
DESCRIPTION
Returns the inverse versed trigonometric cosine of x to a multiple of eps with error less in
absolute value than .75 * eps.
This function is sometimes called averc, or arcvercos, is equivalent to:
avercos(x) = acos(x - 1)
EXAMPLE
; print avercos(.5, 1e-5), avercos(.5, 1e-10), avercos(.5, 1e-15), avercos(.5, 1e-20)
2.0944 2.0943951024 2.094395102393195 2.09439510239319549231
; print avercos(2), avercos(-5), avercos(2 + 3i)
0 3.14159265358979323846-2.47788873028847500481i 1.26319267726418536931-1.86416154415788242834i
LIMITS
0 < eps < 1
LINK LIBRARY
NUMBER *qavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
NUMBER *qavercos(NUMBER *q, NUMBER *epsilon);
COMPLEX *c_avercos(COMPLEX *c, NUMBER *epsilon);
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 2023 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 2023/09/05 23:40:24
## File existed as early as: 2023
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/

5
help/aversin
View File

@@ -11,11 +11,10 @@ TYPES
return real
DESCRIPTION
Returns the inverse versed sine of x to a multiple of eps with error less in
Returns the inverse versed trigonometric sine of x to a multiple of eps with error less in
absolute value than .75 * eps.
The inverse versed sine function is sometimes called avers, sometimes called aver,
may be defined as:
This function is sometimes called avers, or arcversin, is equivalent to:
aversin(x) = acos(1 - x)

4
help/cos
View File

@@ -35,8 +35,8 @@ LINK LIBRARY
SEE ALSO
sin, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll

4
help/cot
View File

@@ -28,8 +28,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll

69
help/covercos Normal file
View File

@@ -0,0 +1,69 @@
NAME
covercos - coversed trigonometric cosine
SYNOPSIS
covercos(x [,eps])
TYPES
x number (real or complex)
eps 0 < real < 1, defaults to epsilon()
return number
DESCRIPTION
Calculate the coversed trigonometric cosine of x to a multiple of eps with error less in
absolute value than .75 * eps.
This function is sometimes called cvc, is equivalent to:
covercos(x) = 1 + sin(x)
EXAMPLE
; print covercos(0.2), covercos(3/7), covercos(-31)
1.19866933079506121546 1.41557185499305200807 1.40403764532306500605
; print covercos(1, 1e-5), covercos(1, 1e-10), covercos(1, 1e-15), covercos(1, 1e-20)
1.84147 1.8414709848 1.841470984807896 1.84147098480789650665
; print covercos(2 + 3i, 1e-5), covercos(2 + 3i, 1e-10)
10.1545-4.16891i 10.1544991469-4.16890696i
; pi = pi(1e-20)
; print covercos(pi/6, 1e-10), covercos(pi/2, 1e-10), covercos(pi, 1e-10), covercos(3*pi/2, 1e-10)
1.5 2 1 0
LIMITS
0 < eps < 1
LINK LIBRARY
NUMBER *qcovercos(NUMBER *x, NUMBER *eps)
COMPLEX *c_covercos(COMPLEX *x, NUMBER *eps)
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 2023 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 2023/09/05 23:31:08
## File existed as early as: 2023
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/

9
help/coversin
View File

@@ -11,11 +11,10 @@ TYPES
return number
DESCRIPTION
Calculate the coversed sine of x to a multiple of eps with error less in
Calculate the coversed trigonometric sine of x to a multiple of eps with error less in
absolute value than .75 * eps.
The coversed sine function is sometimes called covers, or cosiv, or cvs,
may be defined as:
This function is sometimes called covers, or cvs, is equivalent to:
coversin(x) = 1 - sin(x)
@@ -43,8 +42,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 2023 Landon Curt Noll

4
help/csc
View File

@@ -27,8 +27,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec
asin, acos, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2023 Landon Curt Noll

4
help/sec
View File

@@ -28,8 +28,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, csc
asin, acos, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2023 Landon Curt Noll

4
help/sin
View File

@@ -35,8 +35,8 @@ LINK LIBRARY
SEE ALSO
cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll

4
help/tan
View File

@@ -29,8 +29,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 1999,2023 Landon Curt Noll

69
help/vercos Normal file
View File

@@ -0,0 +1,69 @@
NAME
vercos - versed trigonometric cosine
SYNOPSIS
vercos(x [,eps])
TYPES
x number (real or complex)
eps 0 < real < 1, defaults to epsilon()
return number
DESCRIPTION
Calculate the versed trigonometric cosine of x to a multiple of eps with error less in
absolute value than .75 * eps.
This function is sometimes called verc, is equivalent to:
vercos(x) = 1 + cos(x)
EXAMPLE
; print vercos(0.2), vercos(3/7), vercos(-31)
1.98006657784124163112 1.90956035167416667403 1.91474235780453127896
; print vercos(1, 1e-5), vercos(1, 1e-10), vercos(1, 1e-15), vercos(1, 1e-20)
1.5403 1.5403023059 1.54030230586814 1.5403023058681397174
; print vercos(2 + 3i, 1e-5), vercos(2 + 3i, 1e-10)
-3.18963-9.10923i -3.189625691-9.1092278938i
; pi = pi(1e-20)
; print vercos(pi/3, 1e-10), vercos(pi/2, 1e-10), vercos(pi, 1e-10), vercos(3*pi/2, 1e-10)
1.5 1 0 1
LIMITS
0 < eps < 1
LINK LIBRARY
NUMBER *qvercos(NUMBER *x, NUMBER *eps)
COMPLEX *c_vercos(COMPLEX *x, NUMBER *eps)
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 2023 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 2023/09/05 23:25:28
## File existed as early as: 2023
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/

9
help/versin
View File

@@ -11,11 +11,10 @@ TYPES
return number
DESCRIPTION
Calculate the versed sine of x to a multiple of eps with error less in
Calculate the versed trigonometric sine of x to a multiple of eps with error less in
absolute value than .75 * eps.
The versed sine function is sometimes called vers, sometimes called ver,
may be defined as:
This function is sometimes called vers, is equivalent to:
versin(x) = 1 - cos(x)
@@ -43,8 +42,8 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
coversin
aversin. acoversin
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
epsilon
## Copyright (C) 2023 Landon Curt Noll

6
qmath.h
View File

@@ -232,6 +232,12 @@ E_FUNC NUMBER *qaversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcoversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacoversin_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacoversin(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qvercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qavercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qcovercos(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacovercos_or_NULL(NUMBER *q, NUMBER *epsilon);
E_FUNC NUMBER *qacovercos(NUMBER *q, NUMBER *epsilon);
/*

317
qtrans.c
View File

@@ -2293,3 +2293,320 @@ qacoversin(NUMBER *q, NUMBER *epsilon)
*/
return res;
}
/*
* qvercos - versed sine for NUMBER values
*
* This uses the formula:
*
* vercos(x) = 1 + cos(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 *
qvercos(NUMBER *q, NUMBER *epsilon)
{
NUMBER *sin, *cos, *res;
NUMBER *vercos;
long n;
/*
* 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
*/
n = -qilog2(epsilon);
qsincos(q, n + 2, &sin, &cos);
qfree(sin);
vercos = qqadd(&_qone_, cos);
qfree(cos);
/*
* round value to nearest epsilon
*/
res = qmappr(vercos, epsilon, 24);
qfree(vercos);
/*
* return 1 + cos(x)
*/
return res;
}
/*
* qavercos_or_NULL - inverse versed sine for NUMBER values
*
* This uses the formula:
*
* avercos(x) = acos(x - 1)
*
* 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 *
qavercos_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *x; /* 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
*/
x = qsub(q, &_qone_);
res = qacos(x, epsilon);
qfree(x);
if (res == NULL) {
return NULL;
}
/*
* return acos(x - 1)
*/
return res;
}
/*
* qavercos - inverse versed sine for NUMBER values
*
* This uses the formula:
*
* avercos(x) = acos(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 *
qavercos(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 = qavercos_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse cos for avercos");
not_reached();
}
/*
* return acos(x - 1)
*/
return res;
}
/*
* qcovercos - coversed sine for NUMBER values
*
* This uses the formula:
*
* covercos((x) = 1 + sin(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 *
qcovercos(NUMBER *q, NUMBER *epsilon)
{
NUMBER *sin, *cos, *res;
NUMBER *covercos;
long n;
/*
* 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
*/
n = -qilog2(epsilon);
if (qiszero(q) || n < 0)
return qlink(&_qzero_);
qsincos(q, n + 2, &sin, &cos);
qfree(cos);
covercos = qqadd(&_qone_, sin);
qfree(sin);
/*
* round value to nearest epsilon
*/
res = qmappr(covercos, epsilon, 24);
qfree(covercos);
/*
* return 1 + sin(x)
*/
return res;
}
/*
* qacovercos_or_NULL - inverse coversed sine for NUMBER values
*
* This uses the formula:
*
* acovercos(x) = asin(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 *
qacovercos_or_NULL(NUMBER *q, NUMBER *epsilon)
{
NUMBER *res; /* inverse trig value result */
NUMBER *x; /* 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
*/
x = qsub(&_qone_, q);
res = qasin(x, epsilon);
qfree(x);
if (res == NULL) {
return NULL;
}
/*
* return asin(x - 1)
*/
return res;
}
/*
* qacovercos - inverse coversed sine for NUMBER values
*
* This uses the formula:
*
* acovercos(x) = asin(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 *
qacovercos(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 = qacovercos_or_NULL(q, epsilon);
if (res == NULL) {
math_error("cannot compute inverse sin for acovercos");
not_reached();
}
/*
* return asin(x - 1)
*/
return res;
}