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Diffstat (limited to 'src/math/sin.go')
| -rw-r--r-- | src/math/sin.go | 224 |
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diff --git a/src/math/sin.go b/src/math/sin.go new file mode 100644 index 000000000..ed85f21be --- /dev/null +++ b/src/math/sin.go @@ -0,0 +1,224 @@ +// 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 += 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 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 += 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 +} |