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Unified Diff: src/base/ieee754.cc

Issue 2083453002: [builtins] Introduce proper Float64Tan operator. (Closed) Base URL: https://chromium.googlesource.com/v8/v8.git@master
Patch Set: Created 4 years, 6 months ago
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Index: src/base/ieee754.cc
diff --git a/src/base/ieee754.cc b/src/base/ieee754.cc
index 67c0c89671aaf9a9ba7b89eeb81399eb12f3b99b..81a6fd5649d9c628b6cb719734b5950b9c9af1ec 100644
--- a/src/base/ieee754.cc
+++ b/src/base/ieee754.cc
@@ -761,6 +761,143 @@ V8_INLINE double __kernel_sin(double x, double y, int iy) {
}
}
+/* __kernel_tan( x, y, k )
+ * kernel tan function on [-pi/4, pi/4], 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.
+ *
+ * Algorithm
+ * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
+ * 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)))
+ */
+double __kernel_tan(double x, double y, int iy) {
+ static const double xxx[] = {
+ 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 */
+ /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
+ /* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
+ /* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
+ };
+#define one xxx[13]
+#define pio4 xxx[14]
+#define pio4lo xxx[15]
+#define T xxx
+
+ double z, r, v, w, s;
+ int32_t ix, hx;
+
+ GET_HIGH_WORD(hx, x); /* high word of x */
+ ix = hx & 0x7fffffff; /* high word of |x| */
+ if (ix < 0x3e300000) { /* x < 2**-28 */
+ if (static_cast<int>(x) == 0) { /* generate inexact */
+ u_int32_t low;
+ GET_LOW_WORD(low, x);
+ if (((ix | low) | (iy + 1)) == 0) {
+ return one / fabs(x);
+ } else {
+ if (iy == 1) {
+ return x;
+ } else { /* compute -1 / (x+y) carefully */
+ double a, t;
+
+ z = w = x + y;
+ SET_LOW_WORD(z, 0);
+ v = y - (z - x);
+ t = a = -one / w;
+ SET_LOW_WORD(t, 0);
+ s = one + t * z;
+ return t + a * (s + t * v);
+ }
+ }
+ }
+ }
+ if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
+ if (hx < 0) {
+ x = -x;
+ y = -y;
+ }
+ z = pio4 - x;
+ w = pio4lo - y;
+ x = z + w;
+ 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);
+ r += T[0] * s;
+ w = x + r;
+ if (ix >= 0x3FE59428) {
+ v = iy;
+ return (1 - ((hx >> 30) & 2)) * (v - 2.0 * (x - (w * w / (w + v) - r)));
+ }
+ if (iy == 1) {
+ return w;
+ } else {
+ /*
+ * if allow error up to 2 ulp, simply return
+ * -1.0 / (x+r) here
+ */
+ /* compute -1.0 / (x+r) accurately */
+ double a, 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);
+ }
+
+#undef one
+#undef pio4
+#undef pio4lo
+#undef T
+}
+
} // namespace
/* atan(x)
@@ -2123,6 +2260,57 @@ double sin(double x) {
}
}
+/* tan(x)
+ * Return tangent function of x.
+ *
+ * kernel function:
+ * __kernel_tan ... tangent function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+double tan(double x) {
+ double y[2], z = 0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix, x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if (ix <= 0x3fe921fb) {
+ return __kernel_tan(x, z, 1);
+ } else if (ix >= 0x7ff00000) {
+ /* tan(Inf or NaN) is NaN */
+ return x - x; /* NaN */
+ } else {
+ /* argument reduction needed */
+ n = __ieee754_rem_pio2(x, y);
+ /* 1 -> n even, -1 -> n odd */
+ return __kernel_tan(y[0], y[1], 1 - ((n & 1) << 1));
+ }
+}
+
} // namespace ieee754
} // namespace base
} // namespace v8
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