newlib/libm/ld128/k_tanl.c

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