1// Copyright 2021 The Go Authors. All rights reserved. 2// Use of this source code is governed by a BSD-style 3// license that can be found in the LICENSE file. 4 5// Code generated by addchain. DO NOT EDIT. 6 7package fiat 8 9// Invert sets e = 1/x, and returns e. 10// 11// If x == 0, Invert returns e = 0. 12func (e *P256Element) Invert(x *P256Element) *P256Element { 13 // Inversion is implemented as exponentiation with exponent p − 2. 14 // The sequence of 12 multiplications and 255 squarings is derived from the 15 // following addition chain generated with github.com/mmcloughlin/addchain v0.4.0. 16 // 17 // _10 = 2*1 18 // _11 = 1 + _10 19 // _110 = 2*_11 20 // _111 = 1 + _110 21 // _111000 = _111 << 3 22 // _111111 = _111 + _111000 23 // x12 = _111111 << 6 + _111111 24 // x15 = x12 << 3 + _111 25 // x16 = 2*x15 + 1 26 // x32 = x16 << 16 + x16 27 // i53 = x32 << 15 28 // x47 = x15 + i53 29 // i263 = ((i53 << 17 + 1) << 143 + x47) << 47 30 // return (x47 + i263) << 2 + 1 31 // 32 33 var z = new(P256Element).Set(e) 34 var t0 = new(P256Element) 35 var t1 = new(P256Element) 36 37 z.Square(x) 38 z.Mul(x, z) 39 z.Square(z) 40 z.Mul(x, z) 41 t0.Square(z) 42 for s := 1; s < 3; s++ { 43 t0.Square(t0) 44 } 45 t0.Mul(z, t0) 46 t1.Square(t0) 47 for s := 1; s < 6; s++ { 48 t1.Square(t1) 49 } 50 t0.Mul(t0, t1) 51 for s := 0; s < 3; s++ { 52 t0.Square(t0) 53 } 54 z.Mul(z, t0) 55 t0.Square(z) 56 t0.Mul(x, t0) 57 t1.Square(t0) 58 for s := 1; s < 16; s++ { 59 t1.Square(t1) 60 } 61 t0.Mul(t0, t1) 62 for s := 0; s < 15; s++ { 63 t0.Square(t0) 64 } 65 z.Mul(z, t0) 66 for s := 0; s < 17; s++ { 67 t0.Square(t0) 68 } 69 t0.Mul(x, t0) 70 for s := 0; s < 143; s++ { 71 t0.Square(t0) 72 } 73 t0.Mul(z, t0) 74 for s := 0; s < 47; s++ { 75 t0.Square(t0) 76 } 77 z.Mul(z, t0) 78 for s := 0; s < 2; s++ { 79 z.Square(z) 80 } 81 z.Mul(x, z) 82 83 return e.Set(z) 84} 85