pebble/third_party/jerryscript/jerry-libm/asin.c

/* Copyright 2016 Samsung Electronics Co., Ltd.
 * Copyright 2016 University of Szeged
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * This file is based on work under the following copyright and permission
 * notice:
 *
 *     Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 *     Developed at SunSoft, a Sun Microsystems, Inc. business.
 *     Permission to use, copy, modify, and distribute this
 *     software is freely granted, provided that this notice
 *     is preserved.
 *
 *     @(#)e_asin.c 1.3 95/01/18
 */

#include "jerry-libm-internal.h"

/* asin(x)
 *
 * Method:
 *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
 *      we approximate asin(x) on [0,0.5] by
 *              asin(x) = x + x*x^2*R(x^2)
 *      where
 *              R(x^2) is a rational approximation of (asin(x)-x)/x^3
 *      and its remez error is bounded by
 *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
 *
 *      For x in [0.5,1]
 *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
 *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
 *      then for x>0.98
 *              asin(x) = pi/2 - 2*(s+s*z*R(z))
 *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
 *      For x<=0.98, let pio4_hi = pio2_hi/2, then
 *              f = hi part of s;
 *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
 *      and
 *              asin(x) = pi/2 - 2*(s+s*z*R(z))
 *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
 *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
 *
 * Special cases:
 *      if x is NaN, return x itself;
 *      if |x|>1, return NaN with invalid signal.
 */

#define one      1.00000000000000000000e+00 /* 0x3FF00000, 0x00000000 */
#define huge     1.000e+300
#define pio2_hi  1.57079632679489655800e+00 /* 0x3FF921FB, 0x54442D18 */
#define pio2_lo  6.12323399573676603587e-17 /* 0x3C91A626, 0x33145C07 */
#define pio4_hi  7.85398163397448278999e-01 /* 0x3FE921FB, 0x54442D18 */
/* coefficient for R(x^2) */
#define pS0      1.66666666666666657415e-01 /* 0x3FC55555, 0x55555555 */
#define pS1     -3.25565818622400915405e-01 /* 0xBFD4D612, 0x03EB6F7D */
#define pS2      2.01212532134862925881e-01 /* 0x3FC9C155, 0x0E884455 */
#define pS3     -4.00555345006794114027e-02 /* 0xBFA48228, 0xB5688F3B */
#define pS4      7.91534994289814532176e-04 /* 0x3F49EFE0, 0x7501B288 */
#define pS5      3.47933107596021167570e-05 /* 0x3F023DE1, 0x0DFDF709 */
#define qS1     -2.40339491173441421878e+00 /* 0xC0033A27, 0x1C8A2D4B */
#define qS2      2.02094576023350569471e+00 /* 0x40002AE5, 0x9C598AC8 */
#define qS3     -6.88283971605453293030e-01 /* 0xBFE6066C, 0x1B8D0159 */
#define qS4      7.70381505559019352791e-02 /* 0x3FB3B8C5, 0xB12E9282 */

double
asin (double x)
{
  double t, w, p, q, c, r, s;
  int hx, ix;

  hx = __HI (x);
  ix = hx & 0x7fffffff;
  if (ix >= 0x3ff00000) /* |x| >= 1 */
  {
    if (((ix - 0x3ff00000) | __LO (x)) == 0) /* asin(1) = +-pi/2 with inexact */
    {
      return x * pio2_hi + x * pio2_lo;
    }
    return (x - x) / (x - x); /* asin(|x|>1) is NaN */
  }
  else if (ix < 0x3fe00000) /* |x| < 0.5 */
  {
    if (ix < 0x3e400000) /* if |x| < 2**-27 */
    {
      if (huge + x > one) /* return x with inexact if x != 0 */
      {
        return x;
      }
    }
    t = x * x;
    p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
    q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
    w = p / q;
    return x + x * w;
  }
  /* 1 > |x| >= 0.5 */
  w = one - fabs (x);
  t = w * 0.5;
  p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
  q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
  s = sqrt (t);
  if (ix >= 0x3FEF3333) /* if |x| > 0.975 */
  {
    w = p / q;
    t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
  }
  else
  {
    w = s;
    __LO (w) = 0;
    c = (t - w * w) / (s + w);
    r = p / q;
    p = 2.0 * s * r - (pio2_lo - 2.0 * c);
    q = pio4_hi - 2.0 * w;
    t = pio4_hi - (p - q);
  }
  if (hx > 0)
  {
    return t;
  }
  else
  {
    return -t;
  }
} /* asin */

#undef one
#undef huge
#undef pio2_hi
#undef pio2_lo
#undef pio4_hi
#undef pS0
#undef pS1
#undef pS2
#undef pS3
#undef pS4
#undef pS5
#undef qS1
#undef qS2
#undef qS3
#undef qS4