diff options
Diffstat (limited to 'libc-top-half/musl/src/math/__tan.c')
| -rw-r--r-- | libc-top-half/musl/src/math/__tan.c | 110 |
1 files changed, 110 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/__tan.c b/libc-top-half/musl/src/math/__tan.c new file mode 100644 index 0000000..8019844 --- /dev/null +++ b/libc-top-half/musl/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); +} |