...
Run Format

Source file src/math/sin.go

  // 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 Cos(x float64) float64
  
  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++
  		y++
  	}
  	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 the radian argument x.
  //
  // Special cases are:
  //	Sin(±0) = ±0
  //	Sin(±Inf) = NaN
  //	Sin(NaN) = NaN
  func Sin(x float64) float64
  
  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++
  		y++
  	}
  	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
  }
  

View as plain text