initial check-in, version 0.5.0 v0.5.0

1 files changed, 149 insertions, 0 deletions

diff --git a/src/math/k_tan.c b/src/math/k_tan.c
new file mode 100644
index 00000000..f721ae6d
--- /dev/null
+++ b/src/math/k_tan.c
@@ -0,0 +1,149 @@
+/* @(#)k_tan.c 1.5 04/04/22 SMI */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* __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)))
+ */
+
+#include <math.h>
+#include "math_private.h"
+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
+/* INDENT ON */
+
+double
+__kernel_tan(double x, double y, int iy) {
+        double z, r, v, w, s;
+        int32_t ix, hx;
+
+        GET_HIGH_WORD(hx,x);
+        ix = hx & 0x7fffffff;                   /* high word of |x| */
+        if (ix < 0x3e300000) {                  /* x < 2**-28 */
+                if ((int) x == 0) {             /* generate inexact */
+                        uint32_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 = (double) iy;
+                return (double) (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);
+        }
+}