63 lines
1.5 KiB
Go
63 lines
1.5 KiB
Go
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// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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/*
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Floating-point arctangent.
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Atan returns the value of the arctangent of its
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argument in the range [-pi/2,pi/2].
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There are no error returns.
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Coefficients are #5077 from Hart & Cheney. (19.56D)
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*/
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// xatan evaluates a series valid in the
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// range [-0.414...,+0.414...]. (tan(pi/8))
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func xatan(arg float64) float64 {
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const (
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P4 = .161536412982230228262e2
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P3 = .26842548195503973794141e3
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P2 = .11530293515404850115428136e4
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P1 = .178040631643319697105464587e4
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P0 = .89678597403663861959987488e3
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Q4 = .5895697050844462222791e2
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Q3 = .536265374031215315104235e3
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Q2 = .16667838148816337184521798e4
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Q1 = .207933497444540981287275926e4
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Q0 = .89678597403663861962481162e3
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)
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sq := arg * arg
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value := ((((P4*sq+P3)*sq+P2)*sq+P1)*sq + P0)
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value = value / (((((sq+Q4)*sq+Q3)*sq+Q2)*sq+Q1)*sq + Q0)
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return value * arg
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}
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// satan reduces its argument (known to be positive)
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// to the range [0,0.414...] and calls xatan.
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func satan(arg float64) float64 {
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if arg < Sqrt2-1 {
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return xatan(arg)
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}
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if arg > Sqrt2+1 {
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return Pi/2 - xatan(1/arg)
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}
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return Pi/4 + xatan((arg-1)/(arg+1))
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}
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// Atan returns the arctangent of x.
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//
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// Special cases are:
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// Atan(±0) = ±0
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// Atan(±Inf) = ±Pi/2
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func Atan(x float64) float64 {
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if x == 0 {
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return x
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}
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if x > 0 {
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return satan(x)
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}
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return -satan(-x)
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}
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