text: /* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */
  /* origin: FreeBSD /usr/src/lib/msun/ld128/k_tanl.c */
  /*
   * ====================================================
   * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
   * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
   *
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  
  #include "libm.h"
  
  #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
  #if LDBL_MANT_DIG == 64
  /*
   * ld80 version of __tan.c.  See __tan.c for most comments.
   */
  /*
   * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22]
   * |tan(x)/x - t(x)| < 2**-71.9
   *
   * See __cosl.c for more details about the polynomial.
   */
  static const long double T3 = 0.333333333333333333180L, /*  0xaaaaaaaaaaaaaaa5.0p-65 */
      T5 = 0.133333333333333372290L,                      /*  0x88888888888893c3.0p-66 */
      T7 = 0.0539682539682504975744L,                     /*  0xdd0dd0dd0dc13ba2.0p-68 */
      pio4 = 0.785398163397448309628L,                    /*  0xc90fdaa22168c235.0p-64 */
      pio4lo = -1.25413940316708300586e-20L;              /* -0xece675d1fc8f8cbb.0p-130 */
  static const double T9 = 0.021869488536312216,          /*  0x1664f4882cc1c2.0p-58 */
      T11 = 0.0088632355256619590,                        /*  0x1226e355c17612.0p-59 */
      T13 = 0.0035921281113786528,                        /*  0x1d6d3d185d7ff8.0p-61 */
      T15 = 0.0014558334756312418,                        /*  0x17da354aa3f96b.0p-62 */
      T17 = 0.00059003538700862256,                       /*  0x13559358685b83.0p-63 */
      T19 = 0.00023907843576635544,                       /*  0x1f56242026b5be.0p-65 */
      T21 = 0.000097154625656538905,                      /*  0x1977efc26806f4.0p-66 */
      T23 = 0.000038440165747303162,                      /*  0x14275a09b3ceac.0p-67 */
      T25 = 0.000018082171885432524,                      /*  0x12f5e563e5487e.0p-68 */
      T27 = 0.0000024196006108814377,                     /*  0x144c0d80cc6896.0p-71 */
      T29 = 0.0000078293456938132840,                     /*  0x106b59141a6cb3.0p-69 */
      T31 = -0.0000032609076735050182,                    /* -0x1b5abef3ba4b59.0p-71 */
      T33 = 0.0000023261313142559411;                     /*  0x13835436c0c87f.0p-71 */
  #define RPOLY(w) \
    (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + w * (T25 + w * (T29 + w * T33)))))))
  #define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + w * (T27 + w * T31))))))
  #elif LDBL_MANT_DIG == 113
  /*
   * ld128 version of __tan.c.  See __tan.c for most comments.
   */
  /*
   * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
   * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
   *
   * See __cosl.c for more details about the polynomial.
   */
  static const long double T3 = 0x1.5555555555555555555555555553p-2L,
                           T5 = 0x1.1111111111111111111111111eb5p-3L,
                           T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
                           T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
                           T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
                           T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
                           T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
                           T17 = 0x1.355824803674477dfcf726649efep-11L,
                           T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
                           T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
                           T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
                           T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
                           T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
                           T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
                           T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
                           T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
                           T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
                           T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
                           pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
                           pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
  static const double T39 = 0.000000028443389121318352, /*  0x1e8a7592977938.0p-78 */
      T41 = 0.000000011981013102001973,                 /*  0x19baa1b1223219.0p-79 */
      T43 = 0.0000000038303578044958070,                /*  0x107385dfb24529.0p-80 */
      T45 = 0.0000000034664378216909893,                /*  0x1dc6c702a05262.0p-81 */
      T47 = -0.0000000015090641701997785,               /* -0x19ecef3569ebb6.0p-82 */
      T49 = 0.0000000029449552300483952,                /*  0x194c0668da786a.0p-81 */
      T51 = -0.0000000022006995706097711,               /* -0x12e763b8845268.0p-81 */
      T53 = 0.0000000015468200913196612,                /*  0x1a92fc98c29554.0p-82 */
      T55 = -0.00000000061311613386849674,              /* -0x151106cbc779a9.0p-83 */
      T57 = 1.4912469681508012e-10;                     /*  0x147edbdba6f43a.0p-85 */
  #define RPOLY(w)                                           \
    (T5 +                                                    \
     w * (T9 +                                               \
          w * (T13 +                                         \
               w * (T17 +                                    \
                    w * (T21 +                               \
                         w * (T25 +                          \
                              w * (T29 +                     \
                                   w * (T33 +                \
                                        w * (T37 +           \
                                             w * (T41 +      \
                                                  w * (T45 + \
                                                       w * (T49 + w * (T53 + w * T57)))))))))))))
  #define VPOLY(w)                                 \
    (T7 +                                          \
     w * (T11 +                                    \
          w * (T15 +                               \
               w * (T19 +                          \
                    w * (T23 +                     \
                         w * (T27 +                \
                              w * (T31 +           \
                                   w * (T35 +      \
                                        w * (T39 + \
                                             w * (T43 + w * (T47 + w * (T51 + w * T55))))))))))))
  #endif
  
  long double __tanl(long double x, long double y, int odd) {
    long double z, r, v, w, s, a, t;
    int big, sign;
  
    big = fabsl(x) >= 0.67434;
    if (big) {
      sign = 0;
      if (x < 0) {
        sign = 1;
        x = -x;
        y = -y;
      }
      x = (pio4 - x) + (pio4lo - y);
      y = 0.0;
    }
    z = x * x;
    w = z * z;
    r = RPOLY(w);
    v = z * VPOLY(w);
    s = z * x;
    r = y + z * (s * (r + v) + y) + T3 * s;
    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;
    /*
     * if allow error up to 2 ulp, simply return
     * -1.0 / (x+r) here
     */
    /* compute -1.0 / (x+r) accurately */
    z = w;
    z = z + 0x1p32 - 0x1p32;
    v = r - (z - x);  /* z+v = r+x */
    t = a = -1.0 / w; /* a = -1.0/w */
    t = t + 0x1p32 - 0x1p32;
    s = 1.0 + t * z;
    return t + a * (s + t * v);
  }
  #endif
  