mirror of
https://github.com/autc04/Retro68.git
synced 2024-11-30 19:53:46 +00:00
137 lines
3.7 KiB
Go
137 lines
3.7 KiB
Go
// Copyright 2011 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
|
|
|
|
/*
|
|
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
|
|
|
|
//extern tan
|
|
func libc_tan(float64) float64
|
|
|
|
func Tan(x float64) float64 {
|
|
return libc_tan(x)
|
|
}
|
|
|
|
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,
|
|
M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi
|
|
)
|
|
// 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
|
|
}
|
|
|
|
j := int64(x * M4PI) // 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 += 1
|
|
y += 1
|
|
}
|
|
|
|
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
|
|
}
|