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| -rw-r--r-- | src/math/tan.go | 140 |
1 files changed, 140 insertions, 0 deletions
diff --git a/src/math/tan.go b/src/math/tan.go new file mode 100644 index 0000000..8f6e71e --- /dev/null +++ b/src/math/tan.go @@ -0,0 +1,140 @@ +// 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 { + if haveArchTan { + return archTan(x) + } + return tan(x) +} + +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 +} |