static double
sinh_cosh(double x, int cosh_flag)
{
/* Algorithm and coefficients from:
"Software manual for the elementary functions"
by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
static double p[] = {
-0.35181283430177117881e+6,
-0.11563521196851768270e+5,
-0.16375798202630751372e+3,
-0.78966127417357099479e+0
};
static double q[] = {
-0.21108770058106271242e+7,
0.36162723109421836460e+5,
-0.27773523119650701167e+3,
1.0
};
int negative = x < 0;
double y = negative ? -x : x;
if (__IsNan(x)) {
errno = EDOM;
return x;
}
if (! cosh_flag && y <= 1.0) {
/* ??? check for underflow ??? */
y = y * y;
return x + x * y * POLYNOM3(y, p)/POLYNOM3(y,q);
}
if (y >= M_LN_MAX_D) {
/* exp(y) would cause overflow */
#define LNV 0.69316101074218750000e+0
#define VD2M1 0.52820835025874852469e-4
double w = y - LNV;
if (w < M_LN_MAX_D+M_LN2-LNV) {
x = exp(w);
x += VD2M1 * x;
}
else {
errno = ERANGE;
x = HUGE_VAL;
}
}
else {
double z = exp(y);
x = 0.5 * (z + (cosh_flag ? 1.0 : -1.0)/z);
}
return negative ? -x : x;
}
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;
}
double
exp(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[] = {
0.25000000000000000000e+0,
0.75753180159422776666e-2,
0.31555192765684646356e-4
};
static double q[] = {
0.50000000000000000000e+0,
0.56817302698551221787e-1,
0.63121894374398503557e-3,
0.75104028399870046114e-6
};
double xn, g;
int n;
int negative = x < 0;
if (__IsNan(x)) {
errno = EDOM;
return x;
}
if (x < M_LN_MIN_D) {
errno = ERANGE;
return 0.0;
}
if (x > M_LN_MAX_D) {
errno = ERANGE;
return HUGE_VAL;
}
if (negative) x = -x;
/* ??? avoid underflow ??? */
n = x * M_LOG2E + 0.5; /* 1/ln(2) = log2(e), 0.5 added for rounding */
xn = n;
{
double x1 = (long) x;
double x2 = x - x1;
g = ((x1-xn*0.693359375)+x2) - xn*(-2.1219444005469058277e-4);
}
if (negative) {
g = -g;
n = -n;
}
xn = g * g;
x = g * POLYNOM2(xn, p);
n += 1;
return (ldexp(0.5 + x/(POLYNOM3(xn, q) - x), n));
}
double
log(double x)
{
/* Algorithm and coefficients from:
"Software manual for the elementary functions"
by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
static double a[] = {
-0.64124943423745581147e2,
0.16383943563021534222e2,
-0.78956112887491257267e0
};
static double b[] = {
-0.76949932108494879777e3,
0.31203222091924532844e3,
-0.35667977739034646171e2,
1.0
};
double znum, zden, z, w;
int exponent;
if (__IsNan(x)) {
errno = EDOM;
return x;
}
if (x < 0) {
errno = EDOM;
return -HUGE_VAL;
}
else if (x == 0) {
errno = ERANGE;
return -HUGE_VAL;
}
if (x <= DBL_MAX) {
}
else return x; /* for infinity and Nan */
x = frexp(x, &exponent);
if (x > M_1_SQRT2) {
znum = (x - 0.5) - 0.5;
zden = x * 0.5 + 0.5;
}
else {
znum = x - 0.5;
zden = znum * 0.5 + 0.5;
exponent--;
}
z = znum/zden; w = z * z;
x = z + z * w * (POLYNOM2(w,a)/POLYNOM3(w,b));
z = exponent;
x += z * (-2.121944400546905827679e-4);
return x + z * 0.693359375;
}
double
tanh(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[] = {
-0.16134119023996228053e+4,
-0.99225929672236083313e+2,
-0.96437492777225469787e+0
};
static double q[] = {
0.48402357071988688686e+4,
0.22337720718962312926e+4,
0.11274474380534949335e+3,
1.0
};
int negative = x < 0;
if (__IsNan(x)) {
errno = EDOM;
return x;
}
if (negative) x = -x;
if (x >= 0.5*M_LN_MAX_D) {
x = 1.0;
}
#define LN3D2 0.54930614433405484570e+0 /* ln(3)/2 */
else if (x > LN3D2) {
x = 0.5 - 1.0/(exp(x+x)+1.0);
x += x;
}
else {
/* ??? avoid underflow ??? */
double g = x*x;
x += x * g * POLYNOM2(g, p)/POLYNOM3(g, q);
}
return negative ? -x : 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;
}
