c2047754c3
Compiler changes:
* Change map assignment to use mapassign and assign value directly.
* Change string iteration to use decoderune, faster for ASCII strings.
* Change makeslice to take int, and use makeslice64 for larger values.
* Add new noverflow field to hmap struct used for maps.
Unresolved problems, to be fixed later:
* Commented out test in go/types/sizes_test.go that doesn't compile.
* Commented out reflect.TestStructOf test for padding after zero-sized field.
Reviewed-on: https://go-review.googlesource.com/35231
gotools/:
Updates for Go 1.8rc1.
* Makefile.am (go_cmd_go_files): Add bug.go.
(s-zdefaultcc): Write defaultPkgConfig.
* Makefile.in: Rebuild.
From-SVN: r244456
187 lines
4.4 KiB
Go
187 lines
4.4 KiB
Go
// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package cmplx
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import "math"
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// The original C code, the long comment, and the constants
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// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
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// The go code is a simplified version of the original C.
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//
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// Cephes Math Library Release 2.8: June, 2000
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// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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//
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// The readme file at http://netlib.sandia.gov/cephes/ says:
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// Some software in this archive may be from the book _Methods and
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// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
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// International, 1989) or from the Cephes Mathematical Library, a
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// commercial product. In either event, it is copyrighted by the author.
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// What you see here may be used freely but it comes with no support or
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// guarantee.
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//
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// The two known misprints in the book are repaired here in the
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// source listings for the gamma function and the incomplete beta
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// integral.
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//
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// Stephen L. Moshier
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// moshier@na-net.ornl.gov
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// Complex circular tangent
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//
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// DESCRIPTION:
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//
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// If
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// z = x + iy,
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//
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// then
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//
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// sin 2x + i sinh 2y
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// w = --------------------.
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// cos 2x + cosh 2y
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//
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// On the real axis the denominator is zero at odd multiples
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// of PI/2. The denominator is evaluated by its Taylor
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// series near these points.
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//
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// ctan(z) = -i ctanh(iz).
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//
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// ACCURACY:
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//
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// Relative error:
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// arithmetic domain # trials peak rms
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// DEC -10,+10 5200 7.1e-17 1.6e-17
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// IEEE -10,+10 30000 7.2e-16 1.2e-16
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// Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
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// Tan returns the tangent of x.
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func Tan(x complex128) complex128 {
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d := math.Cos(2*real(x)) + math.Cosh(2*imag(x))
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if math.Abs(d) < 0.25 {
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d = tanSeries(x)
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}
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if d == 0 {
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return Inf()
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}
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return complex(math.Sin(2*real(x))/d, math.Sinh(2*imag(x))/d)
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}
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// Complex hyperbolic tangent
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//
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// DESCRIPTION:
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//
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// tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) .
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//
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// ACCURACY:
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//
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// Relative error:
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// arithmetic domain # trials peak rms
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// IEEE -10,+10 30000 1.7e-14 2.4e-16
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// Tanh returns the hyperbolic tangent of x.
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func Tanh(x complex128) complex128 {
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d := math.Cosh(2*real(x)) + math.Cos(2*imag(x))
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if d == 0 {
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return Inf()
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}
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return complex(math.Sinh(2*real(x))/d, math.Sin(2*imag(x))/d)
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}
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// Program to subtract nearest integer multiple of PI
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func reducePi(x float64) float64 {
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const (
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// extended precision value of PI:
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DP1 = 3.14159265160560607910E0 // ?? 0x400921fb54000000
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DP2 = 1.98418714791870343106E-9 // ?? 0x3e210b4610000000
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DP3 = 1.14423774522196636802E-17 // ?? 0x3c6a62633145c06e
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)
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t := x / math.Pi
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if t >= 0 {
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t += 0.5
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} else {
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t -= 0.5
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}
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t = float64(int64(t)) // int64(t) = the multiple
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return ((x - t*DP1) - t*DP2) - t*DP3
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}
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// Taylor series expansion for cosh(2y) - cos(2x)
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func tanSeries(z complex128) float64 {
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const MACHEP = 1.0 / (1 << 53)
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x := math.Abs(2 * real(z))
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y := math.Abs(2 * imag(z))
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x = reducePi(x)
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x = x * x
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y = y * y
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x2 := 1.0
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y2 := 1.0
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f := 1.0
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rn := 0.0
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d := 0.0
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for {
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rn++
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f *= rn
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rn++
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f *= rn
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x2 *= x
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y2 *= y
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t := y2 + x2
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t /= f
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d += t
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rn++
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f *= rn
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rn++
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f *= rn
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x2 *= x
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y2 *= y
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t = y2 - x2
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t /= f
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d += t
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if !(math.Abs(t/d) > MACHEP) {
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// Caution: Use ! and > instead of <= for correct behavior if t/d is NaN.
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// See issue 17577.
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break
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}
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}
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return d
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}
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// Complex circular cotangent
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//
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// DESCRIPTION:
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//
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// If
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// z = x + iy,
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//
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// then
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//
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// sin 2x - i sinh 2y
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// w = --------------------.
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// cosh 2y - cos 2x
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//
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// On the real axis, the denominator has zeros at even
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// multiples of PI/2. Near these points it is evaluated
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// by a Taylor series.
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//
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// ACCURACY:
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//
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// Relative error:
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// arithmetic domain # trials peak rms
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// DEC -10,+10 3000 6.5e-17 1.6e-17
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// IEEE -10,+10 30000 9.2e-16 1.2e-16
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// Also tested by ctan * ccot = 1 + i0.
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// Cot returns the cotangent of x.
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func Cot(x complex128) complex128 {
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d := math.Cosh(2*imag(x)) - math.Cos(2*real(x))
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if math.Abs(d) < 0.25 {
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d = tanSeries(x)
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}
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if d == 0 {
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return Inf()
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}
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return complex(math.Sin(2*real(x))/d, -math.Sinh(2*imag(x))/d)
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}
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