| // 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 { | |
| if haveArchAtan { | |
| return archAtan(x) | |
| } | |
| return atan(x) | |
| } | |
| func atan(x float64) float64 { | |
| if x == 0 { | |
| return x | |
| } | |
| if x > 0 { | |
| return satan(x) | |
| } | |
| return -satan(-x) | |
| } | |