A program to compute inverses of numbers (requires Go 1.13+ for floating-point hex)

heron.go

package main

import (
    "fmt"
    "os"
    "strconv"
)

const (
    eps1m01 float64 = 1.0 - 0x1P-01
    eps1p01 float64 = 1.0 + 0x1P-01
    eps1m24 float64 = 1.0 - 0x1P-24
    eps1p24 float64 = 1.0 + 0x1P-24
)

func main() {
    for i := 1; i < len(os.Args); i++ { // Process args
        a, _ := strconv.ParseFloat(os.Args[i], 64) // arg -> double
        x := 1.0
        for { // By powers of 2
            prod := a * x
            if prod < eps1m01 {
                x *= 2.0
            } else if eps1p01 < prod {
                x *= 0.5
            } else {
                break
            }
        }
        for { // Heron approximation
            prod := a * x
            if prod < eps1m24 || eps1p24 < prod {
                x *= 2.0 - prod
            } else {
                break
            }
        }
        fmt.Printf("heron: a=%.5e,\tx=%.5e,\ta*x=%.12f\n", a, x, a*x)
    }
}