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[/] [openrisc/] [trunk/] [gnu-dev/] [or1k-gcc/] [libquadmath/] [math/] [tanq.c] - Blame information for rev 775

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1 740 jeremybenn
/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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/*
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  Long double expansions are
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  Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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  and are incorporated herein by permission of the author.  The author
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  reserves the right to distribute this material elsewhere under different
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  copying permissions.  These modifications are distributed here under
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  the following terms:
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    This library is free software; you can redistribute it and/or
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    modify it under the terms of the GNU Lesser General Public
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    License as published by the Free Software Foundation; either
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    version 2.1 of the License, or (at your option) any later version.
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    This library is distributed in the hope that it will be useful,
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    but WITHOUT ANY WARRANTY; without even the implied warranty of
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    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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    Lesser General Public License for more details.
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    You should have received a copy of the GNU Lesser General Public
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    License along with this library; if not, write to the Free Software
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    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307  USA */
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/* __quadmath_kernel_tanq( x, y, k )
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 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
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 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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 * Input y is the tail of x.
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 * Input k indicates whether tan (if k=1) or
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 * -1/tan (if k= -1) is returned.
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 *
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 * Algorithm
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 *      1. Since tan(-x) = -tan(x), we need only to consider positive x.
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 *      2. if x < 2^-57, return x with inexact if x!=0.
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 *      3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
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 *          on [0,0.67433].
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 *
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 *         Note: tan(x+y) = tan(x) + tan'(x)*y
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 *                        ~ tan(x) + (1+x*x)*y
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 *         Therefore, for better accuracy in computing tan(x+y), let
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 *              r = x^3 * R(x^2)
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 *         then
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 *              tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
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 *
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 *      4. For x in [0.67433,pi/4],  let y = pi/4 - x, then
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 *              tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
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 *                     = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
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 */
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#include "quadmath-imp.h"
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static const __float128
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  one = 1.0Q,
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  pio4hi = 7.8539816339744830961566084581987569936977E-1Q,
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  pio4lo = 2.1679525325309452561992610065108379921906E-35Q,
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  /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
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     Peak relative error 8.0e-36  */
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 TH =  3.333333333333333333333333333333333333333E-1Q,
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 T0 = -1.813014711743583437742363284336855889393E7Q,
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 T1 =  1.320767960008972224312740075083259247618E6Q,
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 T2 = -2.626775478255838182468651821863299023956E4Q,
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 T3 =  1.764573356488504935415411383687150199315E2Q,
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 T4 = -3.333267763822178690794678978979803526092E-1Q,
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 U0 = -1.359761033807687578306772463253710042010E8Q,
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 U1 =  6.494370630656893175666729313065113194784E7Q,
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 U2 = -4.180787672237927475505536849168729386782E6Q,
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 U3 =  8.031643765106170040139966622980914621521E4Q,
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 U4 = -5.323131271912475695157127875560667378597E2Q;
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  /* 1.000000000000000000000000000000000000000E0 */
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static __float128
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__quadmath_kernel_tanq (__float128 x, __float128 y, int iy)
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{
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  __float128 z, r, v, w, s;
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  int32_t ix, sign = 1;
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  ieee854_float128 u, u1;
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  u.value = x;
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  ix = u.words32.w0 & 0x7fffffff;
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  if (ix < 0x3fc60000)          /* x < 2**-57 */
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    {
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      if ((int) x == 0)
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        {                       /* generate inexact */
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          if ((ix | u.words32.w1 | u.words32.w2 | u.words32.w3
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               | (iy + 1)) == 0)
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            return one / fabsq (x);
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          else
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            return (iy == 1) ? x : -one / x;
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        }
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    }
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  if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */
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    {
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      if ((u.words32.w0 & 0x80000000) != 0)
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        {
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          x = -x;
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          y = -y;
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          sign = -1;
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        }
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      else
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        sign = 1;
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      z = pio4hi - x;
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      w = pio4lo - y;
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      x = z + w;
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      y = 0.0;
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    }
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  z = x * x;
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  r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
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  v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
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  r = r / v;
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  s = z * x;
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  r = y + z * (s * r + y);
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  r += TH * s;
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  w = x + r;
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  if (ix >= 0x3ffe5942)
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    {
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      v = (__float128) iy;
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      w = (v - 2.0Q * (x - (w * w / (w + v) - r)));
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      if (sign < 0)
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        w = -w;
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      return w;
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    }
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  if (iy == 1)
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    return w;
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  else
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    {                           /* if allow error up to 2 ulp,
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                                   simply return -1.0/(x+r) here */
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      /*  compute -1.0/(x+r) accurately */
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      u1.value = w;
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      u1.words32.w2 = 0;
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      u1.words32.w3 = 0;
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      v = r - (u1.value - x);           /* u1+v = r+x */
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      z = -1.0 / w;
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      u.value = z;
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      u.words32.w2 = 0;
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      u.words32.w3 = 0;
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      s = 1.0 + u.value * u1.value;
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      return u.value + z * (s + u.value * v);
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    }
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}
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/* s_tanl.c -- long double version of s_tan.c.
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 * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
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 */
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/* @(#)s_tan.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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/* tanl(x)
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 * Return tangent function of x.
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 *
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 * kernel function:
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 *      __kernel_tanq           ... tangent function on [-pi/4,pi/4]
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 *      __ieee754_rem_pio2q     ... argument reduction routine
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 *
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 * Method.
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 *      Let S,C and T denote the sin, cos and tan respectively on
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 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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 *      in [-pi/4 , +pi/4], and let n = k mod 4.
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 *      We have
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 *
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 *          n        sin(x)      cos(x)        tan(x)
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 *     ----------------------------------------------------------
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 *          0          S           C             T
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 *          1          C          -S            -1/T
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 *          2         -S          -C             T
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 *          3         -C           S            -1/T
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 *     ----------------------------------------------------------
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 *
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 * Special cases:
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 *      Let trig be any of sin, cos, or tan.
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 *      trig(+-INF)  is NaN, with signals;
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 *      trig(NaN)    is that NaN;
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 *
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 * Accuracy:
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 *      TRIG(x) returns trig(x) nearly rounded
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 */
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__float128
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tanq (__float128 x)
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{
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        __float128 y[2],z=0.0Q;
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        int64_t n, ix;
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    /* High word of x. */
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        GET_FLT128_MSW64(ix,x);
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219
    /* |x| ~< pi/4 */
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        ix &= 0x7fffffffffffffffLL;
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        if(ix <= 0x3ffe921fb54442d1LL) return __quadmath_kernel_tanq(x,z,1);
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    /* tanl(Inf or NaN) is NaN */
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        else if (ix>=0x7fff000000000000LL) {
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            if (ix == 0x7fff000000000000LL) {
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                GET_FLT128_LSW64(n,x);
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            }
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            return x-x;         /* NaN */
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        }
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    /* argument reduction needed */
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        else {
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            n = __quadmath_rem_pio2q(x,y);
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                                        /*   1 -- n even, -1 -- n odd */
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            return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1));
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        }
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}

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