codekingpro/portable-devtools

1// Copyright 2009 The Go Authors. All rights reserved.2// Use of this source code is governed by a BSD-style3// license that can be found in the LICENSE file.4 5package math6 7/*8	Floating-point arctangent.9*/10 11// The original C code, the long comment, and the constants below were12// from http://netlib.sandia.gov/cephes/cmath/atan.c, available from13// http://www.netlib.org/cephes/cmath.tgz.14// The go code is a version of the original C.15//16// atan.c17// Inverse circular tangent (arctangent)18//19// SYNOPSIS:20// double x, y, atan();21// y = atan( x );22//23// DESCRIPTION:24// Returns radian angle between -pi/2 and +pi/2 whose tangent is x.25//26// Range reduction is from three intervals into the interval from zero to 0.66.27// The approximant uses a rational function of degree 4/5 of the form28// x + x**3 P(x)/Q(x).29//30// ACCURACY:31//                      Relative error:32// arithmetic   domain    # trials  peak     rms33//    DEC       -10, 10   50000     2.4e-17  8.3e-1834//    IEEE      -10, 10   10^6      1.8e-16  5.0e-1735//36// Cephes Math Library Release 2.8:  June, 200037// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier38//39// The readme file at http://netlib.sandia.gov/cephes/ says:40//    Some software in this archive may be from the book _Methods and41// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster42// International, 1989) or from the Cephes Mathematical Library, a43// commercial product. In either event, it is copyrighted by the author.44// What you see here may be used freely but it comes with no support or45// guarantee.46//47//   The two known misprints in the book are repaired here in the48// source listings for the gamma function and the incomplete beta49// integral.50//51//   Stephen L. Moshier52//   moshier@na-net.ornl.gov53 54// xatan evaluates a series valid in the range [0, 0.66].55func xatan(x float64) float64 {56	const (57		P0 = -8.750608600031904122785e-0158		P1 = -1.615753718733365076637e+0159		P2 = -7.500855792314704667340e+0160		P3 = -1.228866684490136173410e+0261		P4 = -6.485021904942025371773e+0162		Q0 = +2.485846490142306297962e+0163		Q1 = +1.650270098316988542046e+0264		Q2 = +4.328810604912902668951e+0265		Q3 = +4.853903996359136964868e+0266		Q4 = +1.945506571482613964425e+0267	)68	z := x * x69	z = z * ((((P0*z+P1)*z+P2)*z+P3)*z + P4) / (((((z+Q0)*z+Q1)*z+Q2)*z+Q3)*z + Q4)70	z = x*z + x71	return z72}73 74// satan reduces its argument (known to be positive)75// to the range [0, 0.66] and calls xatan.76func satan(x float64) float64 {77	const (78		Morebits = 6.123233995736765886130e-17 // pi/2 = PIO2 + Morebits79		Tan3pio8 = 2.41421356237309504880      // tan(3*pi/8)80	)81	if x <= 0.66 {82		return xatan(x)83	}84	if x > Tan3pio8 {85		return Pi/2 - xatan(1/x) + Morebits86	}87	return Pi/4 + xatan((x-1)/(x+1)) + 0.5*Morebits88}89 90// Atan returns the arctangent, in radians, of x.91//92// Special cases are:93//94//	Atan(±0) = ±095//	Atan(±Inf) = ±Pi/296func Atan(x float64) float64 {97	if haveArchAtan {98		return archAtan(x)99	}100	return atan(x)101}102 103func atan(x float64) float64 {104	if x == 0 {105		return x106	}107	if x > 0 {108		return satan(x)109	}110	return -satan(-x)111}112