Adding upstream version 1.16.10.upstream/1.16.10upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 134 insertions, 0 deletions

diff --git a/src/math/tan.go b/src/math/tan.go
new file mode 100644
index 0000000..49b1239
--- /dev/null
+++ b/src/math/tan.go
@@ -0,0 +1,134 @@
+// 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
+
+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
+}