double
atan(double x)
{
/* Algorithm and coefficients from:
"Software manual for the elementary functions"
by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
static double p[] = {
-0.13688768894191926929e+2,
-0.20505855195861651981e+2,
-0.84946240351320683534e+1,
-0.83758299368150059274e+0
};
static double q[] = {
0.41066306682575781263e+2,
0.86157349597130242515e+2,
0.59578436142597344465e+2,
0.15024001160028576121e+2,
1.0
};
static double a[] = {
0.0,
0.52359877559829887307710723554658381, /* pi/6 */
M_PI_2,
1.04719755119659774615421446109316763 /* pi/3 */
};
int neg = x < 0;
int n;
double g;
if (__IsNan(x)) {
errno = EDOM;
return x;
}
if (neg) {
x = -x;
}
if (x > 1.0) {
x = 1.0/x;
n = 2;
}
else n = 0;
if (x > 0.26794919243112270647) { /* 2-sqtr(3) */
n = n + 1;
x = (((0.73205080756887729353*x-0.5)-0.5)+x)/
(1.73205080756887729353+x);
}
/* ??? avoid underflow ??? */
g = x * x;
x += x * g * POLYNOM3(g, p) / POLYNOM4(g, q);
if (n > 1) x = -x;
x += a[n];
return neg ? -x : x;
}
static double
asin_acos(double x, int cosfl)
{
int negative = x < 0;
int i;
double g;
static double p[] = {
-0.27368494524164255994e+2,
0.57208227877891731407e+2,
-0.39688862997540877339e+2,
0.10152522233806463645e+2,
-0.69674573447350646411e+0
};
static double q[] = {
-0.16421096714498560795e+3,
0.41714430248260412556e+3,
-0.38186303361750149284e+3,
0.15095270841030604719e+3,
-0.23823859153670238830e+2,
1.0
};
if (__IsNan(x)) {
errno = EDOM;
return x;
}
if (negative) {
x = -x;
}
if (x > 0.5) {
i = 1;
if (x > 1) {
errno = EDOM;
return 0;
}
g = 0.5 - 0.5 * x;
x = - sqrt(g);
x += x;
}
else {
/* ??? avoid underflow ??? */
i = 0;
g = x * x;
}
x += x * g * POLYNOM4(g, p) / POLYNOM5(g, q);
if (cosfl) {
if (! negative) x = -x;
}
if ((cosfl == 0) == (i == 1)) {
x = (x + M_PI_4) + M_PI_4;
}
else if (cosfl && negative && i == 1) {
x = (x + M_PI_2) + M_PI_2;
}
if (! cosfl && negative) x = -x;
return x;
}
/****** BEGIN ************************************************************* */
float mymathAtan(float x) {
static float p[] = { -0.13688768894191926929e+2, -0.20505855195861651981e+2,
-0.84946240351320683534e+1, -0.83758299368150059274e+0 };
static float q[] = { 0.41066306682575781263e+2, 0.86157349597130242515e+2,
0.59578436142597344465e+2, 0.15024001160028576121e+2, 1.0 };
static float a[] = { 0.0,
MATH_PI6, /* pi/6 */
MATH_PI2, /* pi/2 */
MATH_PI3 /* pi/3 */
};
int32_t neg = x < 0;
int32_t n;
float g;
if (neg) {
x = -x;
}
if (x > 1.0) {
x = 1.0 / x;
n = 2;
} else
n = 0;
if (x > 0.26794919243112270647) { /* 2-sqtr(3) */
n = n + 1;
x = (((0.73205080756887729353 * x - 0.5) - 0.5) + x)
/ (1.73205080756887729353 + x);
}
g = x * x;
x += x * g * POLYNOM3(g, p) / POLYNOM4(g, q);
if (n > 1)
x = -x;
x += a[n];
return neg ? -x : x;
}
double
tan(double x)
{
/* Algorithm and coefficients from:
"Software manual for the elementary functions"
by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
int negative = x < 0;
int invert = 0;
double y;
static double p[] = {
1.0,
-0.13338350006421960681e+0,
0.34248878235890589960e-2,
-0.17861707342254426711e-4
};
static double q[] = {
1.0,
-0.46671683339755294240e+0,
0.25663832289440112864e-1,
-0.31181531907010027307e-3,
0.49819433993786512270e-6
};
if (__IsNan(x)) {
errno = EDOM;
return x;
}
if (negative) x = -x;
/* ??? avoid loss of significance, error if x is too large ??? */
y = x * M_2_PI + 0.5;
if (y >= DBL_MAX/M_PI_2) return 0.0;
/* Use extended precision to calculate reduced argument.
Here we used 12 bits of the mantissa for a1.
Also split x in integer part x1 and fraction part x2.
*/
#define A1 1.57080078125
#define A2 -4.454455103380768678308e-6
{
double x1, x2;
modf(y, &y);
if (modf(0.5*y, &x1)) invert = 1;
x2 = modf(x, &x1);
x = x1 - y * A1;
x += x2;
x -= y * A2;
#undef A1
#undef A2
}
/* ??? avoid underflow ??? */
y = x * x;
x += x * y * POLYNOM2(y, p+1);
y = POLYNOM4(y, q);
if (negative) x = -x;
return invert ? -y/x : x/y;
}
