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