atan.c

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/*
 * PROJECT:     ReactOS CRT
 * LICENSE:     MIT (https://spdx.org/licenses/MIT)
 * PURPOSE:     Implementation of atan.
 * COPYRIGHT:   Imported from musl libc
 *              https://git.musl-libc.org/cgit/musl/tree/src/math/atan.c
 *              blob: 63b0ab25e3cf02ea81bab5a9ee4d99d6c40bb582
 *              See https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
 */
 
/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
/* atan(x)
 * Method
 *   1. Reduce x to positive by atan(x) = -atan(-x).
 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
 *      is further reduced to one of the following intervals and the
 *      arctangent of t is evaluated by the corresponding formula:
 *
 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */
 
 
#include "libm.h"
 
#ifdef _MSC_VER
#pragma function(atan)
#endif
 
static const double atanhi[] = {
  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};
 
static const double atanlo[] = {
  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};
 
static const double aT[] = {
  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};
 
double atan(double x)
{
    double_t w,s1,s2,z;
    uint32_t ix,sign;
    int id;
 
    GET_HIGH_WORD(ix, x);
    sign = ix >> 31;
    ix &= 0x7fffffff;
    if (ix >= 0x44100000) {   /* if |x| >= 2^66 */
        if (isnan(x))
            return x;
        z = atanhi[3] + 0x1p-120f;
        return sign ? -z : z;
    }
    if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */
        if (ix < 0x3e400000) {  /* |x| < 2^-27 */
            if (ix < 0x00100000)
                /* raise underflow for subnormal x */
                FORCE_EVAL((float)x);
            return x;
        }
        id = -1;
    } else {
        x = fabs(x);
        if (ix < 0x3ff30000) {  /* |x| < 1.1875 */
            if (ix < 0x3fe60000) {  /*  7/16 <= |x| < 11/16 */
                id = 0;
                x = (2.0*x-1.0)/(2.0+x);
            } else {                /* 11/16 <= |x| < 19/16 */
                id = 1;
                x = (x-1.0)/(x+1.0);
            }
        } else {
            if (ix < 0x40038000) {  /* |x| < 2.4375 */
                id = 2;
                x = (x-1.5)/(1.0+1.5*x);
            } else {                /* 2.4375 <= |x| < 2^66 */
                id = 3;
                x = -1.0/x;
            }
        }
    }
    /* end of argument reduction */
    z = x*x;
    w = z*z;
    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
    s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
    s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
    if (id < 0)
        return x - x*(s1+s2);
    z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x);
    return sign ? -z : z;
}