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Diffstat (limited to 'src/pkg/math/cmplx/tan.go')
| -rw-r--r-- | src/pkg/math/cmplx/tan.go | 184 |
1 files changed, 0 insertions, 184 deletions
diff --git a/src/pkg/math/cmplx/tan.go b/src/pkg/math/cmplx/tan.go deleted file mode 100644 index 9485315d8..000000000 --- a/src/pkg/math/cmplx/tan.go +++ /dev/null @@ -1,184 +0,0 @@ -// Copyright 2010 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 cmplx - -import "math" - -// The original C code, the long comment, and the constants -// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c. -// The go code is a simplified version of the original C. -// -// 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 - -// Complex circular tangent -// -// DESCRIPTION: -// -// If -// z = x + iy, -// -// then -// -// sin 2x + i sinh 2y -// w = --------------------. -// cos 2x + cosh 2y -// -// On the real axis the denominator is zero at odd multiples -// of PI/2. The denominator is evaluated by its Taylor -// series near these points. -// -// ctan(z) = -i ctanh(iz). -// -// ACCURACY: -// -// Relative error: -// arithmetic domain # trials peak rms -// DEC -10,+10 5200 7.1e-17 1.6e-17 -// IEEE -10,+10 30000 7.2e-16 1.2e-16 -// Also tested by ctan * ccot = 1 and catan(ctan(z)) = z. - -// Tan returns the tangent of x. -func Tan(x complex128) complex128 { - d := math.Cos(2*real(x)) + math.Cosh(2*imag(x)) - if math.Abs(d) < 0.25 { - d = tanSeries(x) - } - if d == 0 { - return Inf() - } - return complex(math.Sin(2*real(x))/d, math.Sinh(2*imag(x))/d) -} - -// Complex hyperbolic tangent -// -// DESCRIPTION: -// -// tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) . -// -// ACCURACY: -// -// Relative error: -// arithmetic domain # trials peak rms -// IEEE -10,+10 30000 1.7e-14 2.4e-16 - -// Tanh returns the hyperbolic tangent of x. -func Tanh(x complex128) complex128 { - d := math.Cosh(2*real(x)) + math.Cos(2*imag(x)) - if d == 0 { - return Inf() - } - return complex(math.Sinh(2*real(x))/d, math.Sin(2*imag(x))/d) -} - -// Program to subtract nearest integer multiple of PI -func reducePi(x float64) float64 { - const ( - // extended precision value of PI: - DP1 = 3.14159265160560607910E0 // ?? 0x400921fb54000000 - DP2 = 1.98418714791870343106E-9 // ?? 0x3e210b4610000000 - DP3 = 1.14423774522196636802E-17 // ?? 0x3c6a62633145c06e - ) - t := x / math.Pi - if t >= 0 { - t += 0.5 - } else { - t -= 0.5 - } - t = float64(int64(t)) // int64(t) = the multiple - return ((x - t*DP1) - t*DP2) - t*DP3 -} - -// Taylor series expansion for cosh(2y) - cos(2x) -func tanSeries(z complex128) float64 { - const MACHEP = 1.0 / (1 << 53) - x := math.Abs(2 * real(z)) - y := math.Abs(2 * imag(z)) - x = reducePi(x) - x = x * x - y = y * y - x2 := 1.0 - y2 := 1.0 - f := 1.0 - rn := 0.0 - d := 0.0 - for { - rn += 1 - f *= rn - rn += 1 - f *= rn - x2 *= x - y2 *= y - t := y2 + x2 - t /= f - d += t - - rn += 1 - f *= rn - rn += 1 - f *= rn - x2 *= x - y2 *= y - t = y2 - x2 - t /= f - d += t - if math.Abs(t/d) <= MACHEP { - break - } - } - return d -} - -// Complex circular cotangent -// -// DESCRIPTION: -// -// If -// z = x + iy, -// -// then -// -// sin 2x - i sinh 2y -// w = --------------------. -// cosh 2y - cos 2x -// -// On the real axis, the denominator has zeros at even -// multiples of PI/2. Near these points it is evaluated -// by a Taylor series. -// -// ACCURACY: -// -// Relative error: -// arithmetic domain # trials peak rms -// DEC -10,+10 3000 6.5e-17 1.6e-17 -// IEEE -10,+10 30000 9.2e-16 1.2e-16 -// Also tested by ctan * ccot = 1 + i0. - -// Cot returns the cotangent of x. -func Cot(x complex128) complex128 { - d := math.Cosh(2*imag(x)) - math.Cos(2*real(x)) - if math.Abs(d) < 0.25 { - d = tanSeries(x) - } - if d == 0 { - return Inf() - } - return complex(math.Sin(2*real(x))/d, -math.Sinh(2*imag(x))/d) -} |