Subversion Repositories openrisc

// 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
}