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package bigfloat
import (
"math"
"math/big"
)
// Exp returns a big.Float representation of exp(z). Precision is
// the same as the one of the argument. The function returns +Inf
// when z = +Inf, and 0 when z = -Inf.
func Exp(z *big.Float) *big.Float {
// exp(0) == 1
if z.Sign() == 0 {
return big.NewFloat(1).SetPrec(z.Prec())
}
// Exp(+Inf) = +Inf
if z.IsInf() && z.Sign() > 0 {
return big.NewFloat(math.Inf(+1)).SetPrec(z.Prec())
}
// Exp(-Inf) = 0
if z.IsInf() && z.Sign() < 0 {
return big.NewFloat(0).SetPrec(z.Prec())
}
guess := new(big.Float)
// try to get initial estimate using IEEE-754 math
zf, _ := z.Float64()
if zfs := math.Exp(zf); zfs == math.Inf(+1) || zfs == 0 {
// too big or too small for IEEE-754 math,
// perform argument reduction using
// e^{2z} = (e^z)²
halfZ := new(big.Float).Mul(z, big.NewFloat(0.5))
halfExp := Exp(halfZ.SetPrec(z.Prec() + 64))
return new(big.Float).Mul(halfExp, halfExp).SetPrec(z.Prec())
} else {
// we got a nice IEEE-754 estimate
guess.SetFloat64(zfs)
}
// f(t)/f'(t) = t*(log(t) - z)
f := func(t *big.Float) *big.Float {
x := new(big.Float)
x.Sub(Log(t), z)
return x.Mul(x, t)
}
x := newton(f, guess, z.Prec())
return x
}
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