diff options
Diffstat (limited to 'src/math/__tan.c')
| -rw-r--r-- | src/math/__tan.c | 57 |
1 files changed, 24 insertions, 33 deletions
diff --git a/src/math/__tan.c b/src/math/__tan.c index fc739f95..8019844d 100644 --- a/src/math/__tan.c +++ b/src/math/__tan.c @@ -12,7 +12,7 @@ * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 * Input x is assumed to be bounded by ~pi/4 in magnitude. * Input y is the tail of x. - * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned. + * Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned. * * Algorithm * 1. Since tan(-x) = -tan(x), we need only to consider positive x. @@ -63,21 +63,22 @@ static const double T[] = { pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */ -double __tan(double x, double y, int iy) +double __tan(double x, double y, int odd) { - double_t z, r, v, w, s, sign; - int32_t ix, hx; + double_t z, r, v, w, s, a; + double w0, a0; + uint32_t hx; + int big, sign; GET_HIGH_WORD(hx,x); - ix = hx & 0x7fffffff; /* high word of |x| */ - if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ - if (hx < 0) { + big = (hx&0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */ + if (big) { + sign = hx>>31; + if (sign) { x = -x; y = -y; } - z = pio4 - x; - w = pio4lo - y; - x = z + w; + x = (pio4 - x) + (pio4lo - y); y = 0.0; } z = x * x; @@ -90,30 +91,20 @@ double __tan(double x, double y, int iy) 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); - r += T[0] * s; + r = y + z*(s*(r + v) + y) + s*T[0]; w = x + r; - if (ix >= 0x3FE59428) { - v = iy; - sign = 1 - ((hx >> 30) & 2); - return sign * (v - 2.0 * (x - (w * w / (w + v) - r))); + if (big) { + s = 1 - 2*odd; + v = s - 2.0 * (x + (r - w*w/(w + s))); + return sign ? -v : v; } - if (iy == 1) + if (!odd) return w; - else { - /* - * if allow error up to 2 ulp, simply return - * -1.0 / (x+r) here - */ - /* compute -1.0 / (x+r) accurately */ - double_t a; - double z, t; - z = w; - SET_LOW_WORD(z,0); - v = r - (z - x); /* z+v = r+x */ - t = a = -1.0 / w; /* a = -1.0/w */ - SET_LOW_WORD(t,0); - s = 1.0 + t * z; - return t + a * (s + t * v); - } + /* -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); } |