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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
import "math"
/*
* 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)
*/
/*
* xatan evaluates a series valid in the
* range [-0.414...,+0.414...]. (tan(pi/8))
*/
func xatan(arg float64) float64 {
const
(
P4 = .161536412982230228262e2;
P3 = .26842548195503973794141e3;
P2 = .11530293515404850115428136e4;
P1 = .178040631643319697105464587e4;
P0 = .89678597403663861959987488e3;
Q4 = .5895697050844462222791e2;
Q3 = .536265374031215315104235e3;
Q2 = .16667838148816337184521798e4;
Q1 = .207933497444540981287275926e4;
Q0 = .89678597403663861962481162e3;
)
sq := arg*arg;
value := ((((P4*sq + P3)*sq + P2)*sq + P1)*sq + P0);
value = value/(((((sq + Q4)*sq + Q3)*sq + Q2)*sq + Q1)*sq + 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 < Sqrt2 - 1 {
return xatan(arg);
}
if arg > Sqrt2 + 1 {
return Pi/2 - xatan(1/arg);
}
return Pi/4 + xatan((arg-1)/(arg+1));
}
/*
* atan makes its argument positive and
* calls the inner routine satan.
*/
// Atan returns the arc tangent of x.
func Atan(x float64) float64 {
if x > 0 {
return satan(x);
}
return -satan(-x);
}
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