gitee.com/quant1x/num@v0.3.2/math32/atan.go (about)

     1  package math32
     2  
     3  func Atan(x float32) float32 {
     4  	if x == 0 {
     5  		return x
     6  	}
     7  	if x > 0 {
     8  		return satan(x)
     9  	}
    10  	return -satan(-x)
    11  }
    12  
    13  // The original C code, the long comment, and the constants below were
    14  // from http://netlib.sandia.gov/cephes/cmath/atan.c, available from
    15  // http://www.netlib.org/cephes/cmath.tgz.
    16  // The go code is a version of the original C.
    17  //
    18  // atan.c
    19  // Inverse circular tangent (arctangent)
    20  //
    21  // SYNOPSIS:
    22  // double x, y, atan();
    23  // y = atan( x );
    24  //
    25  // DESCRIPTION:
    26  // Returns radian angle between -pi/2 and +pi/2 whose tangent is x.
    27  //
    28  // Range reduction is from three intervals into the interval from zero to 0.66.
    29  // The approximant uses a rational function of degree 4/5 of the form
    30  // x + x**3 P(x)/Q(x).
    31  //
    32  // ACCURACY:
    33  //                      Relative error:
    34  // arithmetic   domain    # trials  peak     rms
    35  //    DEC       -10, 10   50000     2.4e-17  8.3e-18
    36  //    IEEE      -10, 10   10^6      1.8e-16  5.0e-17
    37  //
    38  // Cephes Math Library Release 2.8:  June, 2000
    39  // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
    40  //
    41  // The readme file at http://netlib.sandia.gov/cephes/ says:
    42  //    Some software in this archive may be from the book _Methods and
    43  // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
    44  // International, 1989) or from the Cephes Mathematical Library, a
    45  // commercial product. In either event, it is copyrighted by the author.
    46  // What you see here may be used freely but it comes with no support or
    47  // guarantee.
    48  //
    49  //   The two known misprints in the book are repaired here in the
    50  // source listings for the gamma function and the incomplete beta
    51  // integral.
    52  //
    53  //   Stephen L. Moshier
    54  //   moshier@na-net.ornl.gov
    55  
    56  // xatan evaluates a series valid in the range [0, 0.66].
    57  func xatan(x float32) float32 {
    58  	const (
    59  		P0 = -8.750608600031904122785e-01
    60  		P1 = -1.615753718733365076637e+01
    61  		P2 = -7.500855792314704667340e+01
    62  		P3 = -1.228866684490136173410e+02
    63  		P4 = -6.485021904942025371773e+01
    64  		Q0 = +2.485846490142306297962e+01
    65  		Q1 = +1.650270098316988542046e+02
    66  		Q2 = +4.328810604912902668951e+02
    67  		Q3 = +4.853903996359136964868e+02
    68  		Q4 = +1.945506571482613964425e+02
    69  	)
    70  	z := x * x
    71  	z = z * ((((P0*z+P1)*z+P2)*z+P3)*z + P4) / (((((z+Q0)*z+Q1)*z+Q2)*z+Q3)*z + Q4)
    72  	z = x*z + x
    73  	return z
    74  }
    75  
    76  // satan reduces its argument (known to be positive)
    77  // to the range [0, 0.66] and calls xatan.
    78  func satan(x float32) float32 {
    79  	const (
    80  		Morebits float32 = 6.123233995736765886130e-17 // pi/2 = PIO2 + Morebits
    81  		Tan3pio8 float32 = 2.41421356237309504880      // tan(3*pi/8)
    82  	)
    83  	if x <= 0.66 {
    84  		return xatan(x)
    85  	}
    86  	if x > Tan3pio8 {
    87  		return Pi/2 - xatan(1/x) + Morebits
    88  	}
    89  	return Pi/4 + xatan((x-1)/(x+1)) + 0.5*Morebits
    90  }