Index: fusl/src/math/__tan.c |
diff --git a/fusl/src/math/__tan.c b/fusl/src/math/__tan.c |
new file mode 100644 |
index 0000000000000000000000000000000000000000..8019844d3bc2dac0916290ecb5c05a63e8b7ffc8 |
--- /dev/null |
+++ b/fusl/src/math/__tan.c |
@@ -0,0 +1,110 @@ |
+/* origin: FreeBSD /usr/src/lib/msun/src/k_tan.c */ |
+/* |
+ * ==================================================== |
+ * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. |
+ * |
+ * Permission to use, copy, modify, and distribute this |
+ * software is freely granted, provided that this notice |
+ * is preserved. |
+ * ==================================================== |
+ */ |
+/* __tan( x, y, k ) |
+ * 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 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. |
+ * 2. Callers must return tan(-0) = -0 without calling here since our |
+ * odd polynomial is not evaluated in a way that preserves -0. |
+ * Callers may do the optimization tan(x) ~ x for tiny x. |
+ * 3. tan(x) is approximated by a odd polynomial of degree 27 on |
+ * [0,0.67434] |
+ * 3 27 |
+ * tan(x) ~ x + T1*x + ... + T13*x |
+ * where |
+ * |
+ * |tan(x) 2 4 26 | -59.2 |
+ * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 |
+ * | x | |
+ * |
+ * Note: tan(x+y) = tan(x) + tan'(x)*y |
+ * ~ tan(x) + (1+x*x)*y |
+ * Therefore, for better accuracy in computing tan(x+y), let |
+ * 3 2 2 2 2 |
+ * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) |
+ * then |
+ * 3 2 |
+ * tan(x+y) = x + (T1*x + (x *(r+y)+y)) |
+ * |
+ * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then |
+ * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) |
+ * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) |
+ */ |
+ |
+#include "libm.h" |
+ |
+static const double T[] = { |
+ 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ |
+ 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ |
+ 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ |
+ 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ |
+ 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ |
+ 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ |
+ 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ |
+ 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ |
+ 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ |
+ 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ |
+ 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ |
+ -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ |
+ 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ |
+}, |
+pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ |
+pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */ |
+ |
+double __tan(double x, double y, int odd) |
+{ |
+ 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); |
+} |