diff options
Diffstat (limited to 'decimal.go')
| -rw-r--r-- | decimal.go | 221 |
1 files changed, 221 insertions, 0 deletions
@@ -1144,3 +1144,224 @@ func (d NullDecimal) MarshalJSON() ([]byte, error) { } return d.Decimal.MarshalJSON() } + +// Trig functions + +// Atan returns the arctangent, in radians, of x. +func (x Decimal) Atan() Decimal { + if x.Equal(NewFromFloat(0.0)) { + return x + } + if x.GreaterThan(NewFromFloat(0.0)) { + return x.satan() + } + return x.Neg().satan().Neg() +} + +func (d Decimal) xatan() Decimal { + P0 := NewFromFloat(-8.750608600031904122785e-01) + P1 := NewFromFloat(-1.615753718733365076637e+01) + P2 := NewFromFloat(-7.500855792314704667340e+01) + P3 := NewFromFloat(-1.228866684490136173410e+02) + P4 := NewFromFloat(-6.485021904942025371773e+01) + Q0 := NewFromFloat(2.485846490142306297962e+01) + Q1 := NewFromFloat(1.650270098316988542046e+02) + Q2 := NewFromFloat(4.328810604912902668951e+02) + Q3 := NewFromFloat(4.853903996359136964868e+02) + Q4 := NewFromFloat(1.945506571482613964425e+02) + z := d.Mul(d) + b1 := P0.Mul(z).Add(P1).Mul(z).Add(P2).Mul(z).Add(P3).Mul(z).Add(P4).Mul(z) + b2 := z.Add(Q0).Mul(z).Add(Q1).Mul(z).Add(Q2).Mul(z).Add(Q3).Mul(z).Add(Q4) + z = b1.Div(b2) + z = d.Mul(z).Add(d) + return z +} + +// satan reduces its argument (known to be positive) +// to the range [0, 0.66] and calls xatan. +func (d Decimal) satan() Decimal { + Morebits := NewFromFloat(6.123233995736765886130e-17) // pi/2 = PIO2 + Morebits + Tan3pio8 := NewFromFloat(2.41421356237309504880) // tan(3*pi/8) + pi := NewFromFloat(3.14159265358979323846264338327950288419716939937510582097494459) + + if d.LessThanOrEqual(NewFromFloat(0.66)) { + return d.xatan() + } + if d.GreaterThan(Tan3pio8) { + return pi.Div(NewFromFloat(2.0)).Sub(NewFromFloat(1.0).Div(d).xatan()).Add(Morebits) + } + return pi.Div(NewFromFloat(4.0)).Add((d.Sub(NewFromFloat(1.0)).Div(d.Add(NewFromFloat(1.0)))).xatan()).Add(NewFromFloat(0.5).Mul(Morebits)) +} + +// sin coefficients + var _sin = [...]Decimal{ + NewFromFloat(1.58962301576546568060E-10), // 0x3de5d8fd1fd19ccd + NewFromFloat(-2.50507477628578072866E-8), // 0xbe5ae5e5a9291f5d + NewFromFloat(2.75573136213857245213E-6), // 0x3ec71de3567d48a1 + NewFromFloat(-1.98412698295895385996E-4), // 0xbf2a01a019bfdf03 + NewFromFloat(8.33333333332211858878E-3), // 0x3f8111111110f7d0 + NewFromFloat(-1.66666666666666307295E-1), // 0xbfc5555555555548 + } + +// Sin returns the sine of the radian argument x. + func (d Decimal) Sin() Decimal { + PI4A := NewFromFloat(7.85398125648498535156E-1) // 0x3fe921fb40000000, Pi/4 split into three parts + PI4B := NewFromFloat(3.77489470793079817668E-8) // 0x3e64442d00000000, + PI4C := NewFromFloat(2.69515142907905952645E-15) // 0x3ce8469898cc5170, + M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi + + if d.Equal(NewFromFloat(0.0)) { + return d + } + // make argument positive but save the sign + sign := false + if d.LessThan(NewFromFloat(0.0)) { + d = d.Neg() + sign = true + } + + j := d.Mul(M4PI).IntPart() // integer part of x/(Pi/4), as integer for tests on the phase angle + y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float + + // map zeros to origin + if j&1 == 1 { + j++ + y = y.Add(NewFromFloat(1.0)) + } + j &= 7 // octant modulo 2Pi radians (360 degrees) + // reflect in x axis + if j > 3 { + sign = !sign + j -= 4 + } + z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic + zz := z.Mul(z) + + if j == 1 || j == 2 { + w := zz.Mul(zz).Mul(_cos[0].Mul(zz).Add(_cos[1]).Mul(zz).Add(_cos[2]).Mul(zz).Add(_cos[3]).Mul(zz).Add(_cos[4]).Mul(zz).Add(_cos[5])) + y = NewFromFloat(1.0).Sub(NewFromFloat(0.5).Mul(zz)).Add(w) + } else { + y = z.Add(z.Mul(zz).Mul(_sin[0].Mul(zz).Add(_sin[1]).Mul(zz).Add(_sin[2]).Mul(zz).Add(_sin[3]).Mul(zz).Add(_sin[4]).Mul(zz).Add(_sin[5]))) + } + if sign { + y = y.Neg() + } + return y + } + + // cos coefficients + var _cos = [...]Decimal{ + NewFromFloat(-1.13585365213876817300E-11), // 0xbda8fa49a0861a9b + NewFromFloat(2.08757008419747316778E-9), // 0x3e21ee9d7b4e3f05 + NewFromFloat(-2.75573141792967388112E-7), // 0xbe927e4f7eac4bc6 + NewFromFloat(2.48015872888517045348E-5), // 0x3efa01a019c844f5 + NewFromFloat(-1.38888888888730564116E-3), // 0xbf56c16c16c14f91 + NewFromFloat(4.16666666666665929218E-2), // 0x3fa555555555554b + } + + // Cos returns the cosine of the radian argument x. + func (d Decimal) Cos() Decimal { + + PI4A := NewFromFloat(7.85398125648498535156E-1) // 0x3fe921fb40000000, Pi/4 split into three parts + PI4B := NewFromFloat(3.77489470793079817668E-8) // 0x3e64442d00000000, + PI4C := NewFromFloat(2.69515142907905952645E-15) // 0x3ce8469898cc5170, + M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi + + // make argument positive + sign := false + if d.LessThan(NewFromFloat(0.0)) { + d = d.Neg() + } + + j := d.Mul(M4PI).IntPart() // integer part of x/(Pi/4), as integer for tests on the phase angle + y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float + + // map zeros to origin + if j&1 == 1 { + j++ + y = y.Add(NewFromFloat(1.0)) + } + j &= 7 // octant modulo 2Pi radians (360 degrees) + // reflect in x axis + if j > 3 { + sign = !sign + j -= 4 + } + if j > 1 { + sign = !sign + } + + z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic + zz := z.Mul(z) + + if j == 1 || j == 2 { + y = z.Add(z.Mul(zz).Mul(_sin[0].Mul(zz).Add(_sin[1]).Mul(zz).Add(_sin[2]).Mul(zz).Add(_sin[3]).Mul(zz).Add(_sin[4]).Mul(zz).Add(_sin[5]))) + } else { + w := zz.Mul(zz).Mul(_cos[0].Mul(zz).Add(_cos[1]).Mul(zz).Add(_cos[2]).Mul(zz).Add(_cos[3]).Mul(zz).Add(_cos[4]).Mul(zz).Add(_cos[5])) + y = NewFromFloat(1.0).Sub(NewFromFloat(0.5).Mul(zz)).Add(w) + } + if sign { + y = y.Neg() + } + return y + } + + var _tanP = [...]Decimal{ + NewFromFloat(-1.30936939181383777646E+4), // 0xc0c992d8d24f3f38 + NewFromFloat(1.15351664838587416140E+6), // 0x413199eca5fc9ddd + NewFromFloat(-1.79565251976484877988E+7), // 0xc1711fead3299176 + } + var _tanQ = [...]Decimal{ + NewFromFloat(1.00000000000000000000E+0), + NewFromFloat(1.36812963470692954678E+4), //0x40cab8a5eeb36572 + NewFromFloat(-1.32089234440210967447E+6), //0xc13427bc582abc96 + NewFromFloat(2.50083801823357915839E+7), //0x4177d98fc2ead8ef + NewFromFloat(-5.38695755929454629881E+7), //0xc189afe03cbe5a31 + } + + // Tan returns the tangent of the radian argument x. + func (d Decimal) Tan() Decimal { + + PI4A := NewFromFloat(7.85398125648498535156E-1) // 0x3fe921fb40000000, Pi/4 split into three parts + PI4B := NewFromFloat(3.77489470793079817668E-8) // 0x3e64442d00000000, + PI4C := NewFromFloat(2.69515142907905952645E-15) // 0x3ce8469898cc5170, + M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi + + if d.Equal(NewFromFloat(0.0)) { + return d + } + + // make argument positive but save the sign + sign := false + if d.LessThan(NewFromFloat(0.0)) { + d = d.Neg() + sign = true + } + + j := d.Mul(M4PI).IntPart() // integer part of x/(Pi/4), as integer for tests on the phase angle + y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float + + // map zeros to origin + if j&1 == 1 { + j++ + y = y.Add(NewFromFloat(1.0)) + } + + z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic + zz := z.Mul(z) + + if zz.GreaterThan(NewFromFloat(1e-14)) { + w := zz.Mul(_tanP[0].Mul(zz).Add(_tanP[1]).Mul(zz).Add(_tanP[2])) + x := zz.Add(_tanQ[1]).Mul(zz).Add(_tanQ[2]).Mul(zz).Add(_tanQ[3]).Mul(zz).Add(_tanQ[4]) + y = z.Add(z.Mul(w.Div(x))) + } else { + y = z + } + if j&2 == 2 { + y = NewFromFloat(-1.0).Div(y) + } + if sign { + y = y.Neg() + } + return y + } |