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;
}
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;
}
