Source: tan.go in package math


package math

Floating-point tangent.

The original C code, the long comment, and the constants below were from http://netlib.sandia.gov/cephes/cmath/sin.c, available from http://www.netlib.org/cephes/cmath.tgz. The go code is a simplified version of the original C. tan.c Circular tangent SYNOPSIS: double x, y, tan(); y = tan( x ); DESCRIPTION: Returns the circular tangent of the radian argument x. Range reduction is modulo pi/4. A rational function x + x**3 P(x**2)/Q(x**2) is employed in the basic interval [0, pi/4]. ACCURACY: Relative error: arithmetic domain # trials peak rms DEC +-1.07e9 44000 4.1e-17 1.0e-17 IEEE +-1.07e9 30000 2.9e-16 8.1e-17 Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9. The loss is not gradual, but jumps suddenly to about 1 part in 10e7. Results may be meaningless for x > 2**49 = 5.6e14. [Accuracy loss statement from sin.go comments.] 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

tan coefficients

var _tanP = [...]float64{
	-1.30936939181383777646e4, // 0xc0c992d8d24f3f38
	1.15351664838587416140e6,  // 0x413199eca5fc9ddd
	-1.79565251976484877988e7, // 0xc1711fead3299176
}
var _tanQ = [...]float64{
	1.00000000000000000000e0,
	1.36812963470692954678e4,  //0x40cab8a5eeb36572
	-1.32089234440210967447e6, //0xc13427bc582abc96
	2.50083801823357915839e7,  //0x4177d98fc2ead8ef
	-5.38695755929454629881e7, //0xc189afe03cbe5a31
}

Tan returns the tangent of the radian argument x. Special cases are: Tan(±0) = ±0 Tan(±Inf) = NaN Tan(NaN) = NaN

func Tan(x float64) float64

func tan(x float64) float64 {
	const (
		PI4A = 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
		PI4B = 3.77489470793079817668e-8  // 0x3e64442d00000000,
		PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,

special cases

	switch {
	case x == 0 || IsNaN(x):
		return x // return ±0 || NaN()
	case IsInf(x, 0):
		return NaN()
	}

make argument positive but save the sign

	sign := false
	if x < 0 {
		x = -x
		sign = true
	}
	var j uint64
	var y, z float64
	if x >= reduceThreshold {
		j, z = trigReduce(x)
	} else {
		j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
		y = float64(j)           // integer part of x/(Pi/4), as float

map zeros and singularities to origin

		if j&1 == 1 {
			j++
			y++
		}

		z = ((x - y*PI4A) - y*PI4B) - y*PI4C
	}
	zz := z * z

	if zz > 1e-14 {
		y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
	} else {
		y = z
	}
	if j&2 == 2 {
		y = -1 / y
	}
	if sign {
		y = -y
	}
	return y