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      1 /* From: @(#)k_tan.c 1.5 04/04/22 SMI */
      2 
      3 /*
      4  * ====================================================
      5  * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
      6  * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
      7  *
      8  * Permission to use, copy, modify, and distribute this
      9  * software is freely granted, provided that this notice
     10  * is preserved.
     11  * ====================================================
     12  */
     13 
     14 #include <sys/cdefs.h>
     15 /*
     16  * ld128 version of k_tan.c.  See ../src/k_tan.c for most comments.
     17  */
     18 
     19 #include "math.h"
     20 #include "math_private.h"
     21 
     22 /*
     23  * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
     24  * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
     25  *
     26  * See ../ld80/k_cosl.c for more details about the polynomial.
     27  */
     28 static const long double
     29 T3 = 0x1.5555555555555555555555555553p-2L,
     30 T5 = 0x1.1111111111111111111111111eb5p-3L,
     31 T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
     32 T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
     33 T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
     34 T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
     35 T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
     36 T17 = 0x1.355824803674477dfcf726649efep-11L,
     37 T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
     38 T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
     39 T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
     40 T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
     41 T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
     42 T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
     43 T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
     44 T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
     45 T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
     46 T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
     47 pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
     48 pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
     49 
     50 static const double
     51 T39 =  0.000000028443389121318352,	/*  0x1e8a7592977938.0p-78 */
     52 T41 =  0.000000011981013102001973,	/*  0x19baa1b1223219.0p-79 */
     53 T43 =  0.0000000038303578044958070,	/*  0x107385dfb24529.0p-80 */
     54 T45 =  0.0000000034664378216909893,	/*  0x1dc6c702a05262.0p-81 */
     55 T47 = -0.0000000015090641701997785,	/* -0x19ecef3569ebb6.0p-82 */
     56 T49 =  0.0000000029449552300483952,	/*  0x194c0668da786a.0p-81 */
     57 T51 = -0.0000000022006995706097711,	/* -0x12e763b8845268.0p-81 */
     58 T53 =  0.0000000015468200913196612,	/*  0x1a92fc98c29554.0p-82 */
     59 T55 = -0.00000000061311613386849674,	/* -0x151106cbc779a9.0p-83 */
     60 T57 =  1.4912469681508012e-10;		/*  0x147edbdba6f43a.0p-85 */
     61 
     62 long double
     63 __kernel_tanl(long double x, long double y, int iy) {
     64 	long double z, r, v, w, s;
     65 	long double osign;
     66 	int i;
     67 
     68 	iy = (iy == 1 ? -1 : 1);	/* XXX recover original interface */
     69 	osign = (x >= 0 ? 1.0 : -1.0);	/* XXX slow, probably wrong for -0 */
     70 	if (fabsl(x) >= 0.67434) {
     71 		if (x < 0) {
     72 			x = -x;
     73 			y = -y;
     74 		}
     75 		z = pio4 - x;
     76 		w = pio4lo - y;
     77 		x = z + w;
     78 		y = 0.0;
     79 		i = 1;
     80 	} else
     81 		i = 0;
     82 	z = x * x;
     83 	w = z * z;
     84 	r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
     85 	    w * (T25 + w * (T29 + w * (T33 +
     86 	    w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 +
     87 	    w * T57))))))))))));
     88 	v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
     89 	    w * (T27 + w * (T31 + w * (T35 +
     90 	    w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55))))))))))));
     91 	s = z * x;
     92 	r = y + z * (s * (r + v) + y);
     93 	r += T3 * s;
     94 	w = x + r;
     95 	if (i == 1) {
     96 		v = (long double) iy;
     97 		return osign *
     98 			(v - 2.0 * (x - (w * w / (w + v) - r)));
     99 	}
    100 	if (iy == 1)
    101 		return w;
    102 	else {
    103 		/*
    104 		 * if allow error up to 2 ulp, simply return
    105 		 * -1.0 / (x+r) here
    106 		 */
    107 		/* compute -1.0 / (x+r) accurately */
    108 		long double a, t;
    109 		z = w;
    110 		z = z + 0x1p32 - 0x1p32;
    111 		v = r - (z - x);	/* z+v = r+x */
    112 		t = a = -1.0 / w;	/* a = -1.0/w */
    113 		t = t + 0x1p32 - 0x1p32;
    114 		s = 1.0 + t * z;
    115 		return t + a * (s + t * v);
    116 	}
    117 }
    118