| Index: fusl/src/math/__tan.c
|
| diff --git a/fusl/src/math/__tan.c b/fusl/src/math/__tan.c
|
| index 8019844d3bc2dac0916290ecb5c05a63e8b7ffc8..543ac8723661f6e5a1d245aa7dfe1eaba122d32c 100644
|
| --- a/fusl/src/math/__tan.c
|
| +++ b/fusl/src/math/__tan.c
|
| @@ -12,7 +12,8 @@
|
| * 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.
|
| + * 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.
|
| @@ -45,66 +46,67 @@
|
|
|
| #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 */
|
| +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 */
|
| + 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;
|
| +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);
|
| + 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);
|
| }
|
|
|