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 // Copyright 2009 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package math /* Floating-point arctangent. */ // The original C code, the long comment, and the constants below were // from http://netlib.sandia.gov/cephes/cmath/atan.c, available from // http://www.netlib.org/cephes/cmath.tgz. // The go code is a version of the original C. // // atan.c // Inverse circular tangent (arctangent) // // SYNOPSIS: // double x, y, atan(); // y = atan( x ); // // DESCRIPTION: // Returns radian angle between -pi/2 and +pi/2 whose tangent is x. // // Range reduction is from three intervals into the interval from zero to 0.66. // The approximant uses a rational function of degree 4/5 of the form // x + x**3 P(x)/Q(x). // // ACCURACY: // Relative error: // arithmetic domain # trials peak rms // DEC -10, 10 50000 2.4e-17 8.3e-18 // IEEE -10, 10 10^6 1.8e-16 5.0e-17 // // Cephes Math Library Release 2.8: June, 2000 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier // // The readme file at http://netlib.sandia.gov/cephes/ says: // Some software in this archive may be from the book _Methods and // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster // International, 1989) or from the Cephes Mathematical Library, a // commercial product. In either event, it is copyrighted by the author. // What you see here may be used freely but it comes with no support or // guarantee. // // The two known misprints in the book are repaired here in the // source listings for the gamma function and the incomplete beta // integral. // // Stephen L. Moshier // moshier@na-net.ornl.gov // xatan evaluates a series valid in the range [0, 0.66]. func xatan(x float64) float64 { const ( P0 = -8.750608600031904122785e-01 P1 = -1.615753718733365076637e+01 P2 = -7.500855792314704667340e+01 P3 = -1.228866684490136173410e+02 P4 = -6.485021904942025371773e+01 Q0 = +2.485846490142306297962e+01 Q1 = +1.650270098316988542046e+02 Q2 = +4.328810604912902668951e+02 Q3 = +4.853903996359136964868e+02 Q4 = +1.945506571482613964425e+02 ) z := x * x z = z * ((((P0*z+P1)*z+P2)*z+P3)*z + P4) / (((((z+Q0)*z+Q1)*z+Q2)*z+Q3)*z + Q4) z = x*z + x return z } // satan reduces its argument (known to be positive) // to the range [0, 0.66] and calls xatan. func satan(x float64) float64 { const ( Morebits = 6.123233995736765886130e-17 // pi/2 = PIO2 + Morebits Tan3pio8 = 2.41421356237309504880 // tan(3*pi/8) ) if x <= 0.66 { return xatan(x) } if x > Tan3pio8 { return Pi/2 - xatan(1/x) + Morebits } return Pi/4 + xatan((x-1)/(x+1)) + 0.5*Morebits } // Atan returns the arctangent, in radians, of x. // // Special cases are: // Atan(±0) = ±0 // Atan(±Inf) = ±Pi/2 func Atan(x float64) float64 func atan(x float64) float64 { if x == 0 { return x } if x > 0 { return satan(x) } return -satan(-x) }