summaryrefslogtreecommitdiffstats
path: root/src/math/tan.go
diff options
context:
space:
mode:
Diffstat (limited to '')
-rw-r--r--src/math/tan.go140
1 files changed, 140 insertions, 0 deletions
diff --git a/src/math/tan.go b/src/math/tan.go
new file mode 100644
index 0000000..8f6e71e
--- /dev/null
+++ b/src/math/tan.go
@@ -0,0 +1,140 @@
+// 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
+func Tan(x float64) float64 {
+ if haveArchTan {
+ return archTan(x)
+ }
+ return 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,
+ )
+ // 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
+}