| // 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 |
| |
| export atan |
| |
| /* |
| * floating-point arctangent |
| * |
| * atan returns the value of the arctangent of its |
| * argument in the range [-pi/2,pi/2]. |
| * there are no error returns. |
| * coefficients are #5077 from Hart & Cheney. (19.56D) |
| */ |
| |
| |
| const |
| ( |
| p4 = .161536412982230228262e2; |
| p3 = .26842548195503973794141e3; |
| p2 = .11530293515404850115428136e4; |
| p1 = .178040631643319697105464587e4; |
| p0 = .89678597403663861959987488e3; |
| q4 = .5895697050844462222791e2; |
| q3 = .536265374031215315104235e3; |
| q2 = .16667838148816337184521798e4; |
| q1 = .207933497444540981287275926e4; |
| q0 = .89678597403663861962481162e3; |
| pio2 = .15707963267948966192313216e1; |
| pio4 = .7853981633974483096156608e0; |
| sq2p1 = .2414213562373095048802e1; // sqrt(2)+1 |
| sq2m1 = .414213562373095048802e0; // sqrt(2)-1 |
| ) |
| |
| /* |
| * xatan evaluates a series valid in the |
| * range [-0.414...,+0.414...]. (tan(pi/8)) |
| */ |
| func |
| xatan(arg float64) float64 |
| { |
| var argsq, value float64; |
| |
| argsq = arg*arg; |
| value = ((((p4*argsq + p3)*argsq + p2)*argsq + p1)*argsq + p0); |
| value = value/(((((argsq + q4)*argsq + q3)*argsq + q2)*argsq + q1)*argsq + q0); |
| return value*arg; |
| } |
| |
| /* |
| * satan reduces its argument (known to be positive) |
| * to the range [0,0.414...] and calls xatan. |
| */ |
| func |
| satan(arg float64) float64 |
| { |
| |
| if arg < sq2m1 { |
| return xatan(arg); |
| } |
| if arg > sq2p1 { |
| return pio2 - xatan(1/arg); |
| } |
| return pio4 + xatan((arg-1)/(arg+1)); |
| } |
| |
| /* |
| * atan makes its argument positive and |
| * calls the inner routine satan. |
| */ |
| func |
| atan(arg float64) float64 |
| { |
| |
| if arg > 0 { |
| return satan(arg); |
| } |
| return -satan(-arg); |
| } |