Source file src/pkg/math/atan.go
1 // Copyright 2009 The Go Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 package math 6 7 /* 8 Floating-point arctangent. 9 10 Atan returns the value of the arctangent of its 11 argument in the range [-pi/2,pi/2]. 12 There are no error returns. 13 Coefficients are #5077 from Hart & Cheney. (19.56D) 14 */ 15 16 // xatan evaluates a series valid in the 17 // range [-0.414...,+0.414...]. (tan(pi/8)) 18 func xatan(arg float64) float64 { 19 const ( 20 P4 = .161536412982230228262e2 21 P3 = .26842548195503973794141e3 22 P2 = .11530293515404850115428136e4 23 P1 = .178040631643319697105464587e4 24 P0 = .89678597403663861959987488e3 25 Q4 = .5895697050844462222791e2 26 Q3 = .536265374031215315104235e3 27 Q2 = .16667838148816337184521798e4 28 Q1 = .207933497444540981287275926e4 29 Q0 = .89678597403663861962481162e3 30 ) 31 sq := arg * arg 32 value := ((((P4*sq+P3)*sq+P2)*sq+P1)*sq + P0) 33 value = value / (((((sq+Q4)*sq+Q3)*sq+Q2)*sq+Q1)*sq + Q0) 34 return value * arg 35 } 36 37 // satan reduces its argument (known to be positive) 38 // to the range [0,0.414...] and calls xatan. 39 func satan(arg float64) float64 { 40 if arg < Sqrt2-1 { 41 return xatan(arg) 42 } 43 if arg > Sqrt2+1 { 44 return Pi/2 - xatan(1/arg) 45 } 46 return Pi/4 + xatan((arg-1)/(arg+1)) 47 } 48 49 // Atan returns the arctangent of x. 50 // 51 // Special cases are: 52 // Atan(±0) = ±0 53 // Atan(±Inf) = ±Pi/2 54 func Atan(x float64) float64 55 56 func atan(x float64) float64 { 57 if x == 0 { 58 return x 59 } 60 if x > 0 { 61 return satan(x) 62 } 63 return -satan(-x) 64 }