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// Copyright ©2018 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package hyperdual
import (
"fmt"
"math"
"strings"
)
// Number is a float64 precision hyperdual number.
type Number struct {
Real, E1mag, E2mag, E1E2mag float64
}
var negZero = math.Float64frombits(1 << 63)
// Format implements fmt.Formatter.
func (d Number) Format(fs fmt.State, c rune) {
prec, pOk := fs.Precision()
if !pOk {
prec = -1
}
width, wOk := fs.Width()
if !wOk {
width = -1
}
switch c {
case 'v':
if fs.Flag('#') {
fmt.Fprintf(fs, "%T{Real:%#v, E1mag:%#v, E2mag:%#v, E1E2mag:%#v}", d, d.Real, d.E1mag, d.E2mag, d.E1E2mag)
return
}
if fs.Flag('+') {
fmt.Fprintf(fs, "{Real:%+v, E1mag:%+v, E2mag:%+v, E1E2mag:%+v}", d.Real, d.E1mag, d.E2mag, d.E1E2mag)
return
}
c = 'g'
prec = -1
fallthrough
case 'e', 'E', 'f', 'F', 'g', 'G':
fre := fmtString(fs, c, prec, width, false)
fim := fmtString(fs, c, prec, width, true)
fmt.Fprintf(fs, fmt.Sprintf("(%s%[2]sϵ₁%[2]sϵ₂%[2]sϵ₁ϵ₂)", fre, fim), d.Real, d.E1mag, d.E2mag, d.E1E2mag)
default:
fmt.Fprintf(fs, "%%!%c(%T=%[2]v)", c, d)
return
}
}
// This is horrible, but it's what we have.
func fmtString(fs fmt.State, c rune, prec, width int, wantPlus bool) string {
var b strings.Builder
b.WriteByte('%')
for _, f := range "0+- " {
if fs.Flag(int(f)) || (f == '+' && wantPlus) {
b.WriteByte(byte(f))
}
}
if width >= 0 {
fmt.Fprint(&b, width)
}
if prec >= 0 {
b.WriteByte('.')
if prec > 0 {
fmt.Fprint(&b, prec)
}
}
b.WriteRune(c)
return b.String()
}
// Add returns the sum of x and y.
func Add(x, y Number) Number {
return Number{
Real: x.Real + y.Real,
E1mag: x.E1mag + y.E1mag,
E2mag: x.E2mag + y.E2mag,
E1E2mag: x.E1E2mag + y.E1E2mag,
}
}
// Sub returns the difference of x and y, x-y.
func Sub(x, y Number) Number {
return Number{
Real: x.Real - y.Real,
E1mag: x.E1mag - y.E1mag,
E2mag: x.E2mag - y.E2mag,
E1E2mag: x.E1E2mag - y.E1E2mag,
}
}
// Mul returns the hyperdual product of x and y.
func Mul(x, y Number) Number {
return Number{
Real: x.Real * y.Real,
E1mag: x.Real*y.E1mag + x.E1mag*y.Real,
E2mag: x.Real*y.E2mag + x.E2mag*y.Real,
E1E2mag: x.Real*y.E1E2mag + x.E1mag*y.E2mag + x.E2mag*y.E1mag + x.E1E2mag*y.Real,
}
}
// Inv returns the hyperdual inverse of d.
//
// Special cases are:
//
// Inv(±Inf) = ±0-0ϵ₁-0ϵ₂±0ϵ₁ϵ₂
// Inv(±0) = ±Inf-Infϵ₁-Infϵ₂±Infϵ₁ϵ₂
func Inv(d Number) Number {
if d.Real == 0 {
return Number{
Real: 1 / d.Real,
E1mag: math.Inf(-1),
E2mag: math.Inf(-1),
E1E2mag: 1 / d.Real, // Return a signed inf from a signed zero.
}
}
d2 := d.Real * d.Real
return Number{
Real: 1 / d.Real,
E1mag: -d.E1mag / d2,
E2mag: -d.E2mag / d2,
E1E2mag: -d.E1E2mag/d2 + 2*d.E1mag*d.E2mag/(d2*d.Real),
}
}
// Scale returns d scaled by f.
func Scale(f float64, d Number) Number {
return Number{Real: f * d.Real, E1mag: f * d.E1mag, E2mag: f * d.E2mag, E1E2mag: f * d.E1E2mag}
}
// Abs returns the absolute value of d.
func Abs(d Number) Number {
if math.Float64bits(d.Real)&(1<<63) == 0 {
return d
}
return Scale(-1, d)
}
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