// Use of this source code is governed by a BSD-style

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 the radian argument x.
//
// Special cases are:
//
//	Cos(±Inf) = NaN
//	Cos(NaN) = NaN
func ( float64) float64 {
if haveArchCos {
return archCos()
}
return cos()
}

func cos( float64) float64 {
const (
= 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
= 3.77489470793079817668e-8  // 0x3e64442d00000000,
= 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
)
// special cases
switch {
case IsNaN() || IsInf(, 0):
return NaN()
}

// make argument positive
:= false
= Abs()

var  uint64
var ,  float64
if  >= reduceThreshold {
,  = trigReduce()
} else {
= uint64( * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
= float64()           // integer part of x/(Pi/4), as float

// map zeros to origin
if &1 == 1 {
++
++
}
&= 7                               // octant modulo 2Pi radians (360 degrees)
= (( - *) - *) - * // Extended precision modular arithmetic
}

if  > 3 {
-= 4
= !
}
if  > 1 {
= !
}

:=  *
if  == 1 ||  == 2 {
=  + **((((((_sin[0]*)+_sin[1])*+_sin[2])*+_sin[3])*+_sin[4])*+_sin[5])
} else {
= 1.0 - 0.5* + **((((((_cos[0]*)+_cos[1])*+_cos[2])*+_cos[3])*+_cos[4])*+_cos[5])
}
if  {
= -
}
return
}

// Sin returns the sine of the radian argument x.
//
// Special cases are:
//
//	Sin(±0) = ±0
//	Sin(±Inf) = NaN
//	Sin(NaN) = NaN
func ( float64) float64 {
if haveArchSin {
return archSin()
}
return sin()
}

func sin( float64) float64 {
const (
= 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
= 3.77489470793079817668e-8  // 0x3e64442d00000000,
= 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
)
// special cases
switch {
case  == 0 || IsNaN():
return  // return ±0 || NaN()
case IsInf(, 0):
return NaN()
}

// make argument positive but save the sign
:= false
if  < 0 {
= -
= true
}

var  uint64
var ,  float64
if  >= reduceThreshold {
,  = trigReduce()
} else {
= uint64( * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
= float64()           // integer part of x/(Pi/4), as float

// map zeros to origin
if &1 == 1 {
++
++
}
&= 7                               // octant modulo 2Pi radians (360 degrees)
= (( - *) - *) - * // Extended precision modular arithmetic
}
// reflect in x axis
if  > 3 {
= !
-= 4
}
:=  *
if  == 1 ||  == 2 {
= 1.0 - 0.5* + **((((((_cos[0]*)+_cos[1])*+_cos[2])*+_cos[3])*+_cos[4])*+_cos[5])
} else {
=  + **((((((_sin[0]*)+_sin[1])*+_sin[2])*+_sin[3])*+_sin[4])*+_sin[5])
}
if  {
= -
}
return
}