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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 sine and cosine.

*/

// 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.

//

//      sin.c

//

//      Circular sine

//

// SYNOPSIS:

//

// double x, y, sin();

// y = sin( x );

//

// DESCRIPTION:

//

// Range reduction is into intervals of pi/4.  The reduction error is nearly

// eliminated by contriving an extended precision modular arithmetic.

//

// Two polynomial approximating functions are employed.

// Between 0 and pi/4 the sine is approximated by

//      x  +  x**3 P(x**2).

// Between pi/4 and pi/2 the cosine is represented as

//      1  -  x**2 Q(x**2).

//

// ACCURACY:

//

//                      Relative error:

// arithmetic   domain      # trials      peak         rms

//    DEC       0, 10       150000       3.0e-17     7.8e-18

//    IEEE -1.07e9,+1.07e9  130000       2.1e-16     5.4e-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.

//

//      cos.c

//

//      Circular cosine

//

// SYNOPSIS:

//

// double x, y, cos();

// y = cos( x );

//

// DESCRIPTION:

//

// Range reduction is into intervals of pi/4.  The reduction error is nearly

// eliminated by contriving an extended precision modular arithmetic.

//

// Two polynomial approximating functions are employed.

// Between 0 and pi/4 the cosine is approximated by

//      1  -  x**2 Q(x**2).

// Between pi/4 and pi/2 the sine is represented as

//      x  +  x**3 P(x**2).

//

// ACCURACY:

//

//                      Relative error:

// arithmetic   domain      # trials      peak         rms

//    IEEE -1.07e9,+1.07e9  130000       2.1e-16     5.4e-17

//    DEC        0,+1.07e9   17000       3.0e-17     7.2e-18

//

// 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

// sin coefficients

var _sin = [...]float64{

        1.58962301576546568060E-10, // 0x3de5d8fd1fd19ccd

        -2.50507477628578072866E-8, // 0xbe5ae5e5a9291f5d

        2.75573136213857245213E-6,  // 0x3ec71de3567d48a1

        -1.98412698295895385996E-4, // 0xbf2a01a019bfdf03

        8.33333333332211858878E-3,  // 0x3f8111111110f7d0

        -1.66666666666666307295E-1, // 0xbfc5555555555548

}

// cos coefficients

var _cos = [...]float64{

        -1.13585365213876817300E-11, // 0xbda8fa49a0861a9b

        2.08757008419747316778E-9,   // 0x3e21ee9d7b4e3f05

        -2.75573141792967388112E-7,  // 0xbe927e4f7eac4bc6

        2.48015872888517045348E-5,   // 0x3efa01a019c844f5

        -1.38888888888730564116E-3,  // 0xbf56c16c16c14f91

        4.16666666666665929218E-2,   // 0x3fa555555555554b

}

// Cos returns the cosine of x.

//

// Special cases are:

//      Cos(±Inf) = NaN

//      Cos(NaN) = NaN

//extern cos

func libc_cos(float64) float64

func Cos(x float64) float64 {

        return libc_cos(x)

}

func cos(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 IsNaN(x) || IsInf(x, 0):

                return NaN()

        }

        // make argument positive

        sign := false

        if x < 0 {

                x = -x

        }

        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 to origin

        if j&1 == 1 {

                j += 1

                y += 1

        }

        j &= 7 // octant modulo 2Pi radians (360 degrees)

        if j > 3 {

                j -= 4

                sign = !sign

        }

        if j > 1 {

                sign = !sign

        }

        z := ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic

        zz := z * z

        if j == 1 || j == 2 {

                y = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])

        } else {

                y = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])

        }

        if sign {

                y = -y

        }

        return y

}

// Sin returns the sine of x.

//

// Special cases are:

//      Sin(±0) = ±0

//      Sin(±Inf) = NaN

//      Sin(NaN) = NaN

//extern sin

func libc_sin(float64) float64

func Sin(x float64) float64 {

        return libc_sin(x)

}

func sin(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 to origin

        if j&1 == 1 {

                j += 1

                y += 1

        }

        j &= 7 // octant modulo 2Pi radians (360 degrees)

        // reflect in x axis

        if j > 3 {

                sign = !sign

                j -= 4

        }

        z := ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic

        zz := z * z

        if j == 1 || j == 2 {

                y = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])

        } else {

                y = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])

        }

        if sign {

                y = -y

        }

        return y

}