dualfroz
dbeea4d2e3
MonomialEval started Horner evaluation from poly[len-2] instead of the highest-degree coefficient poly[len-1], so it silently ignored the top coefficient (1 + 2x at x=3 gave 1 instead of 7) and indexed poly[-1] on a constant polynomial, panicking. Start from poly[n] and iterate from n-1, matching the documented y = sum x^i * poly[i]. Closes #579
52 lines
1.1 KiB
Go
52 lines
1.1 KiB
Go
package bignum
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import (
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"math/big"
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)
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// MonomialEval evaluates y = sum x^i * poly[i].
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func MonomialEval(x *big.Float, poly []*big.Float) (y *big.Float) {
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n := len(poly) - 1
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y = new(big.Float).Set(poly[n])
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for i := n - 1; i >= 0; i-- {
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y.Mul(y, x)
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y.Add(y, poly[i])
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}
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return
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}
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// ChebyshevEval evaluates y = sum Ti(x) * poly[i], where T0(x) = 1, T1(x) = (2x-a-b)/(b-a) and T{i+j}(x) = 2TiTj(x)- T|i-j|(x).
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func ChebyshevEval(x *big.Float, poly []*big.Float, inter Interval) (y *big.Float) {
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precision := x.Prec()
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two := NewFloat(2, precision)
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var tmp, u = new(big.Float), new(big.Float)
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var T, Tprev, Tnext = new(big.Float), new(big.Float), new(big.Float)
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// u = (2*x - (a+b))/(b-a)
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u.Set(x)
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u.Mul(u, two)
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u.Sub(u, &inter.A)
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u.Sub(u, &inter.B)
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tmp.Set(&inter.B)
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tmp.Sub(tmp, &inter.A)
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u.Quo(u, tmp)
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Tprev.SetPrec(precision)
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Tprev.SetFloat64(1)
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T.Set(u)
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y = new(big.Float).Set(poly[0])
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for i := 1; i < len(poly); i++ {
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y.Add(y, tmp.Mul(T, poly[i]))
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Tnext.Mul(two, u)
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Tnext.Mul(Tnext, T)
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Tnext.Sub(Tnext, Tprev)
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Tprev.Set(T)
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T.Set(Tnext)
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}
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return
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}
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