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// Copyright 2021 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Code generated by addchain. DO NOT EDIT.
package fiat
// Invert sets e = 1/x, and returns e.
//
// If x == 0, Invert returns e = 0.
func (e *P521Element) Invert(x *P521Element) *P521Element {
// Inversion is implemented as exponentiation with exponent p − 2.
// The sequence of 13 multiplications and 520 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
//
// _10 = 2*1
// _11 = 1 + _10
// _1100 = _11 << 2
// _1111 = _11 + _1100
// _11110000 = _1111 << 4
// _11111111 = _1111 + _11110000
// x16 = _11111111 << 8 + _11111111
// x32 = x16 << 16 + x16
// x64 = x32 << 32 + x32
// x65 = 2*x64 + 1
// x129 = x65 << 64 + x64
// x130 = 2*x129 + 1
// x259 = x130 << 129 + x129
// x260 = 2*x259 + 1
// x519 = x260 << 259 + x259
// return x519 << 2 + 1
//
var z = new(P521Element).Set(e)
var t0 = new(P521Element)
z.Square(x)
z.Mul(x, z)
t0.Square(z)
for s := 1; s < 2; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
for s := 1; s < 4; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
for s := 1; s < 8; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
for s := 1; s < 16; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
for s := 1; s < 32; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
t0.Mul(x, t0)
for s := 0; s < 64; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
t0.Mul(x, t0)
for s := 0; s < 129; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
t0.Square(z)
t0.Mul(x, t0)
for s := 0; s < 259; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
for s := 0; s < 2; s++ {
z.Square(z)
}
z.Mul(x, z)
return e.Set(z)
}
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