func TestMathAcosh(t *testing.T) {
// This is just an interface to Go's function, so just a quick simple test
ctx := runtime.NewCtx(nil, nil)
mm := new(MathMod)
mm.SetCtx(ctx)
val := 1.12
ret := mm.math_Acosh(runtime.Number(val))
exp := math.Acosh(val)
if ret.Float() != exp {
t.Errorf("expected %f, got %f", exp, ret.Float())
}
}
//AcosH returns the inverse hyperbolic cosine of x
func AcosH(number float64) (float64, error) {
if number < 1 {
return 0.0, errors.New("#NUM! - Occurred because the supplied number argument is less than 1")
}
if math.IsNaN(number) {
return 0.0, errors.New("#VALUE! - Occurred because the supplied number argument is non-numeric")
}
return math.Acosh(number), nil
}
// Chebyshev biquad (2-poles) recursive coefficients
// Adapted from The Scientist and Engineer's Guide to Digital Signal Processing, Steven W. Smith
// poleIndex = [0, poleCount)
// percentRipple in the pass band can range from 0 for a butterworth to about 0.29. Something like 0.005 is a good trade-off.
func chebyshevBiquad(freq, percentRipple float64, poleIndex, poleCount int, highpass bool) (stageAs, stageBs []float64) {
// We start off by designing a low-pass filter with unity cut-off frequency
// Location of pole on unit circle, real and imaginary parts
// The maximally flat butterworth filter positions the poles so that
// they form a semi-circle on the left side of the s-plane (sigma < 0)
// The half offset keeps the poles evenly spaced and off of the sigma=0 line
// s-plane s = sigma + i * omega = poleR + i * poleI
poleI, poleR := math.Sincos((float64(poleIndex) + 0.5) * math.Pi / float64(poleCount))
poleR = -poleR
// The chebyshev filter uses an ellipse to move all of the poles closer to the sigma=0 line
// This causes pass-band ripple and sharpens the drop off
// Warp coordinates from being on a circle to an ellipse
if percentRipple != 0.0 {
e := math.Sqrt(1/((1-percentRipple)*(1-percentRipple)) - 1)
v := math.Asinh(1/e) / float64(poleCount)
k := math.Acosh(1/e) / float64(poleCount)
k = math.Cosh(k)
poleR = poleR * math.Sinh(v) / k
poleI = poleI * math.Cosh(v) / k
}
// bilinear s-domain to z-domain transformation
t := 2 * math.Tan(0.5)
w := 2 * math.Pi * freq
m := poleR*poleR + poleI*poleI
d := 4 - 4*poleR*t + m*t*t
x0 := t * t / d
x1 := 2 * t * t / d
x2 := t * t / d
y1 := (8 - 2*m*t*t) / d
y2 := (-4 - 4*poleR*t - m*t*t) / d
// We now have the coefficients of a low-pass filter with a cutoff frequency of 1 (2 times the nyquist)...
// We must now apply our desired frequency and convert to a high-pass filter if necessary
// as with the bilinear tranform, these are the results of a substitution in the transfer function...
var k float64
if highpass {
k = -math.Cos(w/2+0.5) / math.Cos(w/2-0.5)
} else {
k = math.Sin(0.5-w/2) / math.Sin(0.5+w/2)
}
d = 1 + (y1*k - y2*k*k)
a0 := (x0 - x1*k + x2*k*k) / d
a1 := (-2*x0*k + x1 + (x1*k*k - 2*x2*k)) / d
a2 := (x0*k*k - x1*k + x2) / d
b1 := (2*k + y1 + y1*k*k - 2*y2*k) / d
b2 := (-k*k - y1*k + y2) / d
if highpass {
a1, b1 = -a1, -b1
}
// we now have the desired coefficients of our low/high pass filter with the desired cutoff frequency
// however, the gain has not been normalized, if that is desired...
stageAs = []float64{a0, a1, a2}
stageBs = []float64{0, b1, b2}
return
}
// float32 version of math.Acoshf
func Acosh(x float32) float32 {
return float32(math.Acosh(float64(x)))
}
func (m *MathMod) math_Acosh(args ...runtime.Val) runtime.Val {
runtime.ExpectAtLeastNArgs(1, args)
return runtime.Number(math.Acosh(args[0].Float()))
}