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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 x.

//

// Special cases are:

//      Tan(±0) = ±0

//      Tan(±Inf) = NaN

//      Tan(NaN) = NaN

//extern tan

func libc_tan(float64) float64

func Tan(x float64) float64 {

        return libc_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,

                M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi

        )

        // 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

        }

        j := int64(x * M4PI) // 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 += 1

                y += 1

        }

        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

}