Adding upstream version 1.16.10.upstream/1.16.10upstream

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

1 files changed, 232 insertions, 0 deletions

diff --git a/src/math/sin.go b/src/math/sin.go
new file mode 100644
index 0000000..3b6dbe3
--- /dev/null
+++ b/src/math/sin.go
@@ -0,0 +1,232 @@
+// 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 sine and cosine.
+*/
+
+// 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.
+//
+//      sin.c
+//
+//      Circular sine
+//
+// SYNOPSIS:
+//
+// double x, y, sin();
+// y = sin( x );
+//
+// DESCRIPTION:
+//
+// Range reduction is into intervals of pi/4.  The reduction error is nearly
+// eliminated by contriving an extended precision modular arithmetic.
+//
+// Two polynomial approximating functions are employed.
+// Between 0 and pi/4 the sine is approximated by
+//      x  +  x**3 P(x**2).
+// Between pi/4 and pi/2 the cosine is represented as
+//      1  -  x**2 Q(x**2).
+//
+// ACCURACY:
+//
+//                      Relative error:
+// arithmetic   domain      # trials      peak         rms
+//    DEC       0, 10       150000       3.0e-17     7.8e-18
+//    IEEE -1.07e9,+1.07e9  130000       2.1e-16     5.4e-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.
+//
+//      cos.c
+//
+//      Circular cosine
+//
+// SYNOPSIS:
+//
+// double x, y, cos();
+// y = cos( x );
+//
+// DESCRIPTION:
+//
+// Range reduction is into intervals of pi/4.  The reduction error is nearly
+// eliminated by contriving an extended precision modular arithmetic.
+//
+// Two polynomial approximating functions are employed.
+// Between 0 and pi/4 the cosine is approximated by
+//      1  -  x**2 Q(x**2).
+// Between pi/4 and pi/2 the sine is represented as
+//      x  +  x**3 P(x**2).
+//
+// ACCURACY:
+//
+//                      Relative error:
+// arithmetic   domain      # trials      peak         rms
+//    IEEE -1.07e9,+1.07e9  130000       2.1e-16     5.4e-17
+//    DEC        0,+1.07e9   17000       3.0e-17     7.2e-18
+//
+// 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
+
+// sin coefficients
+var _sin = [...]float64{
+	1.58962301576546568060e-10, // 0x3de5d8fd1fd19ccd
+	-2.50507477628578072866e-8, // 0xbe5ae5e5a9291f5d
+	2.75573136213857245213e-6,  // 0x3ec71de3567d48a1
+	-1.98412698295895385996e-4, // 0xbf2a01a019bfdf03
+	8.33333333332211858878e-3,  // 0x3f8111111110f7d0
+	-1.66666666666666307295e-1, // 0xbfc5555555555548
+}
+
+// cos coefficients
+var _cos = [...]float64{
+	-1.13585365213876817300e-11, // 0xbda8fa49a0861a9b
+	2.08757008419747316778e-9,   // 0x3e21ee9d7b4e3f05
+	-2.75573141792967388112e-7,  // 0xbe927e4f7eac4bc6
+	2.48015872888517045348e-5,   // 0x3efa01a019c844f5
+	-1.38888888888730564116e-3,  // 0xbf56c16c16c14f91
+	4.16666666666665929218e-2,   // 0x3fa555555555554b
+}
+
+// Cos returns the cosine of the radian argument x.
+//
+// Special cases are:
+//	Cos(±Inf) = NaN
+//	Cos(NaN) = NaN
+func Cos(x float64) float64
+
+func cos(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 IsNaN(x) || IsInf(x, 0):
+		return NaN()
+	}
+
+	// make argument positive
+	sign := false
+	x = Abs(x)
+
+	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 to origin
+		if j&1 == 1 {
+			j++
+			y++
+		}
+		j &= 7                               // octant modulo 2Pi radians (360 degrees)
+		z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
+	}
+
+	if j > 3 {
+		j -= 4
+		sign = !sign
+	}
+	if j > 1 {
+		sign = !sign
+	}
+
+	zz := z * z
+	if j == 1 || j == 2 {
+		y = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
+	} else {
+		y = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])
+	}
+	if sign {
+		y = -y
+	}
+	return y
+}
+
+// Sin returns the sine of the radian argument x.
+//
+// Special cases are:
+//	Sin(±0) = ±0
+//	Sin(±Inf) = NaN
+//	Sin(NaN) = NaN
+func Sin(x float64) float64
+
+func sin(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 to origin
+		if j&1 == 1 {
+			j++
+			y++
+		}
+		j &= 7                               // octant modulo 2Pi radians (360 degrees)
+		z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
+	}
+	// reflect in x axis
+	if j > 3 {
+		sign = !sign
+		j -= 4
+	}
+	zz := z * z
+	if j == 1 || j == 2 {
+		y = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])
+	} else {
+		y = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
+	}
+	if sign {
+		y = -y
+	}
+	return y
+}