Source File
sin.go
Belonging Package
math
// 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 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
}
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