__tan.c File Reference

#include "libm.h"

Include dependency graph for __tan.c:

Go to the source code of this file.

Functions
double	__tan (double x, double y, int odd)

Variables
static const double	T []
static const double	pio4 = 7.85398163397448278999e-01
static const double	pio4lo = 3.06161699786838301793e-17

Function Documentation

__tan()

double __tan	(	double	x,
		double	y,
		int	odd
	)

Definition at line 76 of file __tan.c.

{
    double_t z, r, v, w, s, a;
    double w0, a0;
    uint32_t hx;
    int big, sign;
 
    GET_HIGH_WORD(hx,x);
    big = (hx&0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */
    if (big) {
        sign = hx>>31;
        if (sign) {
            x = -x;
            y = -y;
        }
        x = (pio4 - x) + (pio4lo - y);
        y = 0.0;
    }
    z = x * x;
    w = z * z;
    /*
     * Break x^5*(T[1]+x^2*T[2]+...) into
     * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
     * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
     */
    r = T[1] + w*(T[3] + w*(T[5] + w*(T[7] + w*(T[9] + w*T[11]))));
    v = z*(T[2] + w*(T[4] + w*(T[6] + w*(T[8] + w*(T[10] + w*T[12])))));
    s = z * x;
    r = y + z*(s*(r + v) + y) + s*T[0];
    w = x + r;
    if (big) {
        s = 1 - 2*odd;
        v = s - 2.0 * (x + (r - w*w/(w + s)));
        return sign ? -v : v;
    }
    if (!odd)
        return w;
    /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */
    w0 = w;
    SET_LOW_WORD(w0, 0);
    v = r - (w0 - x);       /* w0+v = r+x */
    a0 = a = -1.0 / w;
    SET_LOW_WORD(a0, 0);
    return a0 + a*(1.0 + a0*w0 + a0*v);
}

Referenced by tan().

Variable Documentation

pio4

const double pio4 = 7.85398163397448278999e-01

static

Definition at line 73 of file __tan.c.

Referenced by __tan().

pio4lo

const double pio4lo = 3.06161699786838301793e-17

static

Definition at line 74 of file __tan.c.

Referenced by __tan().

T

const double T[]

static

Initial value:

= {
             3.33333333333334091986e-01, 
             1.33333333333201242699e-01, 
             5.39682539762260521377e-02, 
             2.18694882948595424599e-02, 
             8.86323982359930005737e-03, 
             3.59207910759131235356e-03, 
             1.45620945432529025516e-03, 
             5.88041240820264096874e-04, 
             2.46463134818469906812e-04, 
             7.81794442939557092300e-05, 
             7.14072491382608190305e-05, 
            -1.85586374855275456654e-05, 
             2.59073051863633712884e-05, 
}

Definition at line 58 of file __tan.c.

Referenced by __tan().