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); |
} |