| // 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) |
| } |