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Diffstat (limited to 'src/pkg/math/cmplx/asin.go')
| -rw-r--r-- | src/pkg/math/cmplx/asin.go | 170 |
1 files changed, 0 insertions, 170 deletions
diff --git a/src/pkg/math/cmplx/asin.go b/src/pkg/math/cmplx/asin.go deleted file mode 100644 index 61880a257..000000000 --- a/src/pkg/math/cmplx/asin.go +++ /dev/null @@ -1,170 +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 arc sine -// -// DESCRIPTION: -// -// Inverse complex sine: -// 2 -// w = -i clog( iz + csqrt( 1 - z ) ). -// -// casin(z) = -i casinh(iz) -// -// ACCURACY: -// -// Relative error: -// arithmetic domain # trials peak rms -// DEC -10,+10 10100 2.1e-15 3.4e-16 -// IEEE -10,+10 30000 2.2e-14 2.7e-15 -// Larger relative error can be observed for z near zero. -// Also tested by csin(casin(z)) = z. - -// Asin returns the inverse sine of x. -func Asin(x complex128) complex128 { - if imag(x) == 0 { - if math.Abs(real(x)) > 1 { - return complex(math.Pi/2, 0) // DOMAIN error - } - return complex(math.Asin(real(x)), 0) - } - ct := complex(-imag(x), real(x)) // i * x - xx := x * x - x1 := complex(1-real(xx), -imag(xx)) // 1 - x*x - x2 := Sqrt(x1) // x2 = sqrt(1 - x*x) - w := Log(ct + x2) - return complex(imag(w), -real(w)) // -i * w -} - -// Asinh returns the inverse hyperbolic sine of x. -func Asinh(x complex128) complex128 { - // TODO check range - if imag(x) == 0 { - if math.Abs(real(x)) > 1 { - return complex(math.Pi/2, 0) // DOMAIN error - } - return complex(math.Asinh(real(x)), 0) - } - xx := x * x - x1 := complex(1+real(xx), imag(xx)) // 1 + x*x - return Log(x + Sqrt(x1)) // log(x + sqrt(1 + x*x)) -} - -// Complex circular arc cosine -// -// DESCRIPTION: -// -// w = arccos z = PI/2 - arcsin z. -// -// ACCURACY: -// -// Relative error: -// arithmetic domain # trials peak rms -// DEC -10,+10 5200 1.6e-15 2.8e-16 -// IEEE -10,+10 30000 1.8e-14 2.2e-15 - -// Acos returns the inverse cosine of x. -func Acos(x complex128) complex128 { - w := Asin(x) - return complex(math.Pi/2-real(w), -imag(w)) -} - -// Acosh returns the inverse hyperbolic cosine of x. -func Acosh(x complex128) complex128 { - w := Acos(x) - if imag(w) <= 0 { - return complex(-imag(w), real(w)) // i * w - } - return complex(imag(w), -real(w)) // -i * w -} - -// Complex circular arc tangent -// -// DESCRIPTION: -// -// If -// z = x + iy, -// -// then -// 1 ( 2x ) -// Re w = - arctan(-----------) + k PI -// 2 ( 2 2) -// (1 - x - y ) -// -// ( 2 2) -// 1 (x + (y+1) ) -// Im w = - log(------------) -// 4 ( 2 2) -// (x + (y-1) ) -// -// Where k is an arbitrary integer. -// -// catan(z) = -i catanh(iz). -// -// ACCURACY: -// -// Relative error: -// arithmetic domain # trials peak rms -// DEC -10,+10 5900 1.3e-16 7.8e-18 -// IEEE -10,+10 30000 2.3e-15 8.5e-17 -// The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, -// had peak relative error 1.5e-16, rms relative error -// 2.9e-17. See also clog(). - -// Atan returns the inverse tangent of x. -func Atan(x complex128) complex128 { - if real(x) == 0 && imag(x) > 1 { - return NaN() - } - - x2 := real(x) * real(x) - a := 1 - x2 - imag(x)*imag(x) - if a == 0 { - return NaN() - } - t := 0.5 * math.Atan2(2*real(x), a) - w := reducePi(t) - - t = imag(x) - 1 - b := x2 + t*t - if b == 0 { - return NaN() - } - t = imag(x) + 1 - c := (x2 + t*t) / b - return complex(w, 0.25*math.Log(c)) -} - -// Atanh returns the inverse hyperbolic tangent of x. -func Atanh(x complex128) complex128 { - z := complex(-imag(x), real(x)) // z = i * x - z = Atan(z) - return complex(imag(z), -real(z)) // z = -i * z -} |