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 // 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 }