From 97779442d0a551d96f2a0b1799e96944918af32e Mon Sep 17 00:00:00 2001 From: Frank Denis <124872+jedisct1@users.noreply.github.com> Date: Mon, 3 May 2021 09:57:45 +0200 Subject: [PATCH] Prepare std/crypto/pcurves for ecdsa and other curves (#8670) Functions generated by Fiat-crypto are not prefixed by their description any more. This matches an upstream change. We can now use a single type for different curves and implementations. The field type is now generic, so we can properly handle the base field and scalars without code duplication. --- lib/std/crypto/pcurves/common.zig | 284 +++ lib/std/crypto/pcurves/p256/field.zig | 261 +-- lib/std/crypto/pcurves/p256/p256_64.zig | 1308 +++++------ .../crypto/pcurves/p256/p256_scalar_64.zig | 2016 +++++++++++++++++ lib/std/crypto/pcurves/p256/scalar.zig | 34 +- 5 files changed, 3005 insertions(+), 898 deletions(-) create mode 100644 lib/std/crypto/pcurves/common.zig create mode 100644 lib/std/crypto/pcurves/p256/p256_scalar_64.zig diff --git a/lib/std/crypto/pcurves/common.zig b/lib/std/crypto/pcurves/common.zig new file mode 100644 index 0000000000..5a979fe3e5 --- /dev/null +++ b/lib/std/crypto/pcurves/common.zig @@ -0,0 +1,284 @@ +const std = @import("std"); +const builtin = std.builtin; +const crypto = std.crypto; +const debug = std.debug; +const mem = std.mem; +const meta = std.meta; + +const NonCanonicalError = crypto.errors.NonCanonicalError; +const NotSquareError = crypto.errors.NotSquareError; + +/// Parameters to create a finite field type. +pub const FieldParams = struct { + fiat: type, + field_order: comptime_int, + field_bits: comptime_int, + saturated_bits: comptime_int, + encoded_length: comptime_int, +}; + +/// A field element, internally stored in Montgomery domain. +pub fn Field(comptime params: FieldParams) type { + const fiat = params.fiat; + const Limbs = fiat.Limbs; + + return struct { + const Fe = @This(); + + limbs: Limbs, + + /// Field size. + pub const field_order = params.field_order; + + /// Number of bits to represent the set of all elements. + pub const field_bits = params.field_bits; + + /// Number of bits that can be saturated without overflowing. + pub const saturated_bits = params.saturated_bits; + + /// Number of bytes required to encode an element. + pub const encoded_length = params.encoded_length; + + /// Zero. + pub const zero: Fe = Fe{ .limbs = mem.zeroes(Limbs) }; + + /// One. + pub const one = comptime one: { + var fe: Fe = undefined; + fiat.setOne(&fe.limbs); + break :one fe; + }; + + /// Reject non-canonical encodings of an element. + pub fn rejectNonCanonical(s_: [encoded_length]u8, endian: builtin.Endian) NonCanonicalError!void { + var s = if (endian == .Little) s_ else orderSwap(s_); + const field_order_s = comptime fos: { + var fos: [encoded_length]u8 = undefined; + mem.writeIntLittle(std.meta.Int(.unsigned, encoded_length * 8), &fos, field_order); + break :fos fos; + }; + if (crypto.utils.timingSafeCompare(u8, &s, &field_order_s, .Little) != .lt) { + return error.NonCanonical; + } + } + + /// Swap the endianness of an encoded element. + pub fn orderSwap(s: [encoded_length]u8) [encoded_length]u8 { + var t = s; + for (s) |x, i| t[t.len - 1 - i] = x; + return t; + } + + /// Unpack a field element. + pub fn fromBytes(s_: [encoded_length]u8, endian: builtin.Endian) NonCanonicalError!Fe { + var s = if (endian == .Little) s_ else orderSwap(s_); + try rejectNonCanonical(s, .Little); + var limbs_z: Limbs = undefined; + fiat.fromBytes(&limbs_z, s); + var limbs: Limbs = undefined; + fiat.toMontgomery(&limbs, limbs_z); + return Fe{ .limbs = limbs }; + } + + /// Pack a field element. + pub fn toBytes(fe: Fe, endian: builtin.Endian) [encoded_length]u8 { + var limbs_z: Limbs = undefined; + fiat.fromMontgomery(&limbs_z, fe.limbs); + var s: [encoded_length]u8 = undefined; + fiat.toBytes(&s, limbs_z); + return if (endian == .Little) s else orderSwap(s); + } + + /// Element as an integer. + pub const IntRepr = meta.Int(.unsigned, params.field_bits); + + /// Create a field element from an integer. + pub fn fromInt(comptime x: IntRepr) NonCanonicalError!Fe { + var s: [encoded_length]u8 = undefined; + mem.writeIntLittle(IntRepr, &s, x); + return fromBytes(s, .Little); + } + + /// Return the field element as an integer. + pub fn toInt(fe: Fe) IntRepr { + const s = fe.toBytes(.Little); + return mem.readIntLittle(IntRepr, &s); + } + + /// Return true if the field element is zero. + pub fn isZero(fe: Fe) bool { + var z: @TypeOf(fe.limbs[0]) = undefined; + fiat.nonzero(&z, fe.limbs); + return z == 0; + } + + /// Return true if both field elements are equivalent. + pub fn equivalent(a: Fe, b: Fe) bool { + return a.sub(b).isZero(); + } + + /// Return true if the element is odd. + pub fn isOdd(fe: Fe) bool { + const s = fe.toBytes(.Little); + return @truncate(u1, s[0]) != 0; + } + + /// Conditonally replace a field element with `a` if `c` is positive. + pub fn cMov(fe: *Fe, a: Fe, c: u1) void { + fiat.selectznz(&fe.limbs, c, fe.limbs, a.limbs); + } + + /// Add field elements. + pub fn add(a: Fe, b: Fe) Fe { + var fe: Fe = undefined; + fiat.add(&fe.limbs, a.limbs, b.limbs); + return fe; + } + + /// Subtract field elements. + pub fn sub(a: Fe, b: Fe) Fe { + var fe: Fe = undefined; + fiat.sub(&fe.limbs, a.limbs, b.limbs); + return fe; + } + + /// Double a field element. + pub fn dbl(a: Fe) Fe { + var fe: Fe = undefined; + fiat.add(&fe.limbs, a.limbs, a.limbs); + return fe; + } + + /// Multiply field elements. + pub fn mul(a: Fe, b: Fe) Fe { + var fe: Fe = undefined; + fiat.mul(&fe.limbs, a.limbs, b.limbs); + return fe; + } + + /// Square a field element. + pub fn sq(a: Fe) Fe { + var fe: Fe = undefined; + fiat.square(&fe.limbs, a.limbs); + return fe; + } + + /// Square a field element n times. + fn sqn(a: Fe, comptime n: comptime_int) Fe { + var i: usize = 0; + var fe = a; + while (i < n) : (i += 1) { + fe = fe.sq(); + } + return fe; + } + + /// Compute a^n. + pub fn pow(a: Fe, comptime T: type, comptime n: T) Fe { + var fe = one; + var x: T = n; + var t = a; + while (true) { + if (@truncate(u1, x) != 0) fe = fe.mul(t); + x >>= 1; + if (x == 0) break; + t = t.sq(); + } + return fe; + } + + /// Negate a field element. + pub fn neg(a: Fe) Fe { + var fe: Fe = undefined; + fiat.opp(&fe.limbs, a.limbs); + return fe; + } + + /// Return the inverse of a field element, or 0 if a=0. + // Field inversion from https://eprint.iacr.org/2021/549.pdf + pub fn invert(a: Fe) Fe { + const iterations = (49 * field_bits + 57) / 17; + const Word = @TypeOf(a.limbs[0]); + const XLimbs = [a.limbs.len + 1]Word; + + var d: Word = 1; + var f: XLimbs = undefined; + fiat.msat(&f); + + var g: XLimbs = undefined; + fiat.fromMontgomery(g[0..a.limbs.len], a.limbs); + g[g.len - 1] = 0; + + var r: Limbs = undefined; + fiat.setOne(&r); + var v = mem.zeroes(Limbs); + + var precomp: Limbs = undefined; + fiat.divstepPrecomp(&precomp); + + var out1: Word = undefined; + var out2: XLimbs = undefined; + var out3: XLimbs = undefined; + var out4: Limbs = undefined; + var out5: Limbs = undefined; + + var i: usize = 0; + while (i < iterations - iterations % 2) : (i += 2) { + fiat.divstep(&out1, &out2, &out3, &out4, &out5, d, f, g, v, r); + fiat.divstep(&d, &f, &g, &v, &r, out1, out2, out3, out4, out5); + } + if (iterations % 2 != 0) { + fiat.divstep(&out1, &out2, &out3, &out4, &out5, d, f, g, v, r); + mem.copy(Word, &v, &out4); + mem.copy(Word, &f, &out2); + } + var v_opp: Limbs = undefined; + fiat.opp(&v_opp, v); + fiat.selectznz(&v, @truncate(u1, f[f.len - 1] >> (meta.bitCount(Word) - 1)), v, v_opp); + var fe: Fe = undefined; + fiat.mul(&fe.limbs, v, precomp); + return fe; + } + + /// Return true if the field element is a square. + pub fn isSquare(x2: Fe) bool { + if (field_order == 115792089210356248762697446949407573530086143415290314195533631308867097853951) { + const t110 = x2.mul(x2.sq()).sq(); + const t111 = x2.mul(t110); + const t111111 = t111.mul(x2.mul(t110).sqn(3)); + const x15 = t111111.sqn(6).mul(t111111).sqn(3).mul(t111); + const x16 = x15.sq().mul(x2); + const x53 = x16.sqn(16).mul(x16).sqn(15); + const x47 = x15.mul(x53); + const ls = x47.mul(((x53.sqn(17).mul(x2)).sqn(143).mul(x47)).sqn(47)).sq().mul(x2); + return ls.equivalent(Fe.one); + } else { + const ls = x2.pow(std.meta.Int(.unsigned, field_bits), (field_order - 1) / 2); // Legendre symbol + return ls.equivalent(Fe.one); + } + } + + // x=x2^((field_order+1)/4) w/ field order=3 (mod 4). + fn uncheckedSqrt(x2: Fe) Fe { + comptime debug.assert(field_order % 4 == 3); + if (field_order == 115792089210356248762697446949407573530086143415290314195533631308867097853951) { + const t11 = x2.mul(x2.sq()); + const t1111 = t11.mul(t11.sqn(2)); + const t11111111 = t1111.mul(t1111.sqn(4)); + const x16 = t11111111.sqn(8).mul(t11111111); + return x16.sqn(16).mul(x16).sqn(32).mul(x2).sqn(96).mul(x2).sqn(94); + } else { + return x2.pow(std.meta.Int(.unsigned, field_bits), (field_order + 1) / 4); + } + } + + /// Compute the square root of `x2`, returning `error.NotSquare` if `x2` was not a square. + pub fn sqrt(x2: Fe) NotSquareError!Fe { + const x = x2.uncheckedSqrt(); + if (x.sq().equivalent(x2)) { + return x; + } + return error.NotSquare; + } + }; +} diff --git a/lib/std/crypto/pcurves/p256/field.zig b/lib/std/crypto/pcurves/p256/field.zig index 68659e4601..15de1fe43e 100644 --- a/lib/std/crypto/pcurves/p256/field.zig +++ b/lib/std/crypto/pcurves/p256/field.zig @@ -5,257 +5,14 @@ // and substantial portions of the software. const std = @import("std"); -const builtin = std.builtin; -const crypto = std.crypto; -const debug = std.debug; -const mem = std.mem; -const meta = std.meta; +const common = @import("../common.zig"); -const fiat = @import("p256_64.zig"); +const Field = common.Field; -const NonCanonicalError = crypto.errors.NonCanonicalError; -const NotSquareError = crypto.errors.NotSquareError; - -const Limbs = fiat.Limbs; - -/// A field element, internally stored in Montgomery domain. -pub const Fe = struct { - limbs: Limbs, - - /// Field size. - pub const field_order = 115792089210356248762697446949407573530086143415290314195533631308867097853951; - - /// Numer of bits that can be saturated without overflowing. - pub const saturated_bits = 255; - - /// Zero. - pub const zero: Fe = Fe{ .limbs = mem.zeroes(Limbs) }; - - /// One. - pub const one = comptime one: { - var fe: Fe = undefined; - fiat.p256SetOne(&fe.limbs); - break :one fe; - }; - - /// Reject non-canonical encodings of an element. - pub fn rejectNonCanonical(s_: [32]u8, endian: builtin.Endian) NonCanonicalError!void { - var s = if (endian == .Little) s_ else orderSwap(s_); - const field_order_s = comptime fos: { - var fos: [32]u8 = undefined; - mem.writeIntLittle(u256, &fos, field_order); - break :fos fos; - }; - if (crypto.utils.timingSafeCompare(u8, &s, &field_order_s, .Little) != .lt) { - return error.NonCanonical; - } - } - - /// Swap the endianness of an encoded element. - pub fn orderSwap(s: [32]u8) [32]u8 { - var t = s; - for (s) |x, i| t[t.len - 1 - i] = x; - return t; - } - - /// Unpack a field element. - pub fn fromBytes(s_: [32]u8, endian: builtin.Endian) NonCanonicalError!Fe { - var s = if (endian == .Little) s_ else orderSwap(s_); - try rejectNonCanonical(s, .Little); - var limbs_z: Limbs = undefined; - fiat.p256FromBytes(&limbs_z, s); - var limbs: Limbs = undefined; - fiat.p256ToMontgomery(&limbs, limbs_z); - return Fe{ .limbs = limbs }; - } - - /// Pack a field element. - pub fn toBytes(fe: Fe, endian: builtin.Endian) [32]u8 { - var limbs_z: Limbs = undefined; - fiat.p256FromMontgomery(&limbs_z, fe.limbs); - var s: [32]u8 = undefined; - fiat.p256ToBytes(&s, limbs_z); - return if (endian == .Little) s else orderSwap(s); - } - - /// Create a field element from an integer. - pub fn fromInt(comptime x: u256) NonCanonicalError!Fe { - var s: [32]u8 = undefined; - mem.writeIntLittle(u256, &s, x); - return fromBytes(s, .Little); - } - - /// Return the field element as an integer. - pub fn toInt(fe: Fe) u256 { - const s = fe.toBytes(.Little); - return mem.readIntLittle(u256, &s); - } - - /// Return true if the field element is zero. - pub fn isZero(fe: Fe) bool { - var z: @TypeOf(fe.limbs[0]) = undefined; - fiat.p256Nonzero(&z, fe.limbs); - return z == 0; - } - - /// Return true if both field elements are equivalent. - pub fn equivalent(a: Fe, b: Fe) bool { - return a.sub(b).isZero(); - } - - /// Return true if the element is odd. - pub fn isOdd(fe: Fe) bool { - const s = fe.toBytes(.Little); - return @truncate(u1, s[0]) != 0; - } - - /// Conditonally replace a field element with `a` if `c` is positive. - pub fn cMov(fe: *Fe, a: Fe, c: u1) void { - fiat.p256Selectznz(&fe.limbs, c, fe.limbs, a.limbs); - } - - /// Add field elements. - pub fn add(a: Fe, b: Fe) Fe { - var fe: Fe = undefined; - fiat.p256Add(&fe.limbs, a.limbs, b.limbs); - return fe; - } - - /// Subtract field elements. - pub fn sub(a: Fe, b: Fe) Fe { - var fe: Fe = undefined; - fiat.p256Sub(&fe.limbs, a.limbs, b.limbs); - return fe; - } - - /// Double a field element. - pub fn dbl(a: Fe) Fe { - var fe: Fe = undefined; - fiat.p256Add(&fe.limbs, a.limbs, a.limbs); - return fe; - } - - /// Multiply field elements. - pub fn mul(a: Fe, b: Fe) Fe { - var fe: Fe = undefined; - fiat.p256Mul(&fe.limbs, a.limbs, b.limbs); - return fe; - } - - /// Square a field element. - pub fn sq(a: Fe) Fe { - var fe: Fe = undefined; - fiat.p256Square(&fe.limbs, a.limbs); - return fe; - } - - /// Square a field element n times. - fn sqn(a: Fe, comptime n: comptime_int) Fe { - var i: usize = 0; - var fe = a; - while (i < n) : (i += 1) { - fe = fe.sq(); - } - return fe; - } - - /// Compute a^n. - pub fn pow(a: Fe, comptime T: type, comptime n: T) Fe { - var fe = one; - var x: T = n; - var t = a; - while (true) { - if (@truncate(u1, x) != 0) fe = fe.mul(t); - x >>= 1; - if (x == 0) break; - t = t.sq(); - } - return fe; - } - - /// Negate a field element. - pub fn neg(a: Fe) Fe { - var fe: Fe = undefined; - fiat.p256Opp(&fe.limbs, a.limbs); - return fe; - } - - /// Return the inverse of a field element, or 0 if a=0. - // Field inversion from https://eprint.iacr.org/2021/549.pdf - pub fn invert(a: Fe) Fe { - const len_prime = 256; - const iterations = (49 * len_prime + 57) / 17; - const Word = @TypeOf(a.limbs[0]); - const XLimbs = [a.limbs.len + 1]Word; - - var d: Word = 1; - var f: XLimbs = undefined; - fiat.p256Msat(&f); - - var g: XLimbs = undefined; - fiat.p256FromMontgomery(g[0..a.limbs.len], a.limbs); - g[g.len - 1] = 0; - - var r: Limbs = undefined; - fiat.p256SetOne(&r); - var v = mem.zeroes(Limbs); - - var precomp: Limbs = undefined; - fiat.p256DivstepPrecomp(&precomp); - - var out1: Word = undefined; - var out2: XLimbs = undefined; - var out3: XLimbs = undefined; - var out4: Limbs = undefined; - var out5: Limbs = undefined; - - var i: usize = 0; - while (i < iterations - iterations % 2) : (i += 2) { - fiat.p256Divstep(&out1, &out2, &out3, &out4, &out5, d, f, g, v, r); - fiat.p256Divstep(&d, &f, &g, &v, &r, out1, out2, out3, out4, out5); - } - if (iterations % 2 != 0) { - fiat.p256Divstep(&out1, &out2, &out3, &out4, &out5, d, f, g, v, r); - mem.copy(Word, &v, &out4); - mem.copy(Word, &f, &out2); - } - var v_opp: Limbs = undefined; - fiat.p256Opp(&v_opp, v); - fiat.p256Selectznz(&v, @truncate(u1, f[f.len - 1] >> (meta.bitCount(Word) - 1)), v, v_opp); - var fe: Fe = undefined; - fiat.p256Mul(&fe.limbs, v, precomp); - return fe; - } - - /// Return true if the field element is a square. - pub fn isSquare(x2: Fe) bool { - const t110 = x2.mul(x2.sq()).sq(); - const t111 = x2.mul(t110); - const t111111 = t111.mul(x2.mul(t110).sqn(3)); - const x15 = t111111.sqn(6).mul(t111111).sqn(3).mul(t111); - const x16 = x15.sq().mul(x2); - const x53 = x16.sqn(16).mul(x16).sqn(15); - const x47 = x15.mul(x53); - const ls = x47.mul(((x53.sqn(17).mul(x2)).sqn(143).mul(x47)).sqn(47)).sq().mul(x2); // Legendre symbol, (p-1)/2 - return ls.equivalent(Fe.one); - } - - // x=x2^((field_order+1)/4) w/ field order=3 (mod 4). - fn uncheckedSqrt(x2: Fe) Fe { - comptime debug.assert(field_order % 4 == 3); - const t11 = x2.mul(x2.sq()); - const t1111 = t11.mul(t11.sqn(2)); - const t11111111 = t1111.mul(t1111.sqn(4)); - const x16 = t11111111.sqn(8).mul(t11111111); - return x16.sqn(16).mul(x16).sqn(32).mul(x2).sqn(96).mul(x2).sqn(94); - } - - /// Compute the square root of `x2`, returning `error.NotSquare` if `x2` was not a square. - pub fn sqrt(x2: Fe) NotSquareError!Fe { - const x = x2.uncheckedSqrt(); - if (x.sq().equivalent(x2)) { - return x; - } - return error.NotSquare; - } -}; +pub const Fe = Field(.{ + .fiat = @import("p256_64.zig"), + .field_order = 115792089210356248762697446949407573530086143415290314195533631308867097853951, + .field_bits = 256, + .saturated_bits = 255, + .encoded_length = 32, +}); diff --git a/lib/std/crypto/pcurves/p256/p256_64.zig b/lib/std/crypto/pcurves/p256/p256_64.zig index 9f3d6c22f8..ca04ee961d 100644 --- a/lib/std/crypto/pcurves/p256/p256_64.zig +++ b/lib/std/crypto/pcurves/p256/p256_64.zig @@ -1,11 +1,5 @@ -// SPDX-License-Identifier: MIT -// Copyright (c) 2015-2021 Zig Contributors -// This file is part of [zig](https://ziglang.org/), which is MIT licensed. -// The MIT license requires this copyright notice to be included in all copies -// and substantial portions of the software. - -// Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --lang Zig --internal-static --public-function-case camelCase --private-function-case camelCase p256 64 '2^256 - 2^224 + 2^192 + 2^96 - 1' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp -// curve description: p256 +// Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --lang Zig --internal-static --public-function-case camelCase --private-function-case camelCase --no-prefix-fiat --package-name p256 '' 64 '2^256 - 2^224 + 2^192 + 2^96 - 1' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp +// curve description (via package name): p256 // machine_wordsize = 64 (from "64") // requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp // m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1") @@ -20,10 +14,16 @@ // Computed values: // eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) // bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in +// if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 + +const std = @import("std"); +const cast = std.meta.cast; +const mode = std.builtin.mode; // Checked arithmetic is disabled in non-debug modes to avoid side channels pub const Limbs = [4]u64; -/// The function p256AddcarryxU64 is an addition with carry. +/// The function addcarryxU64 is an addition with carry. /// Postconditions: /// out1 = (arg1 + arg2 + arg3) mod 2^64 /// out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋ @@ -35,14 +35,16 @@ pub const Limbs = [4]u64; /// Output Bounds: /// out1: [0x0 ~> 0xffffffffffffffff] /// out2: [0x0 ~> 0x1] -fn p256AddcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { +fn addcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + var t: u64 = undefined; const carry1 = @addWithOverflow(u64, arg2, arg3, &t); const carry2 = @addWithOverflow(u64, t, arg1, out1); out2.* = @boolToInt(carry1) | @boolToInt(carry2); } -/// The function p256SubborrowxU64 is a subtraction with borrow. +/// The function subborrowxU64 is a subtraction with borrow. /// Postconditions: /// out1 = (-arg1 + arg2 + -arg3) mod 2^64 /// out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋ @@ -54,14 +56,16 @@ fn p256AddcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callc /// Output Bounds: /// out1: [0x0 ~> 0xffffffffffffffff] /// out2: [0x0 ~> 0x1] -fn p256SubborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { +fn subborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + var t: u64 = undefined; const carry1 = @subWithOverflow(u64, arg2, arg3, &t); const carry2 = @subWithOverflow(u64, t, arg1, out1); out2.* = @boolToInt(carry1) | @boolToInt(carry2); } -/// The function p256MulxU64 is a multiplication, returning the full double-width result. +/// The function mulxU64 is a multiplication, returning the full double-width result. /// Postconditions: /// out1 = (arg1 * arg2) mod 2^64 /// out2 = ⌊arg1 * arg2 / 2^64⌋ @@ -72,13 +76,15 @@ fn p256SubborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) call /// Output Bounds: /// out1: [0x0 ~> 0xffffffffffffffff] /// out2: [0x0 ~> 0xffffffffffffffff] -fn p256MulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) callconv(.Inline) void { +fn mulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + const x = @as(u128, arg1) * @as(u128, arg2); out1.* = @truncate(u64, x); out2.* = @truncate(u64, x >> 64); } -/// The function p256CmovznzU64 is a single-word conditional move. +/// The function cmovznzU64 is a single-word conditional move. /// Postconditions: /// out1 = (if arg1 = 0 then arg2 else arg3) /// @@ -88,12 +94,14 @@ fn p256MulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) callconv(.Inline) v /// arg3: [0x0 ~> 0xffffffffffffffff] /// Output Bounds: /// out1: [0x0 ~> 0xffffffffffffffff] -fn p256CmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { +fn cmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + const mask = 0 -% @as(u64, arg1); out1.* = (mask & arg3) | ((~mask) & arg2); } -/// The function p256Mul multiplies two field elements in the Montgomery domain. +/// The function mul multiplies two field elements in the Montgomery domain. /// Preconditions: /// 0 ≤ eval arg1 < m /// 0 ≤ eval arg2 < m @@ -106,289 +114,291 @@ fn p256CmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) /// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Mul(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { - const x1: u64 = (arg1[1]); - const x2: u64 = (arg1[2]); - const x3: u64 = (arg1[3]); - const x4: u64 = (arg1[0]); +pub fn mul(out1: *[4]u64, arg1: [4]u64, arg2: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); var x5: u64 = undefined; var x6: u64 = undefined; - p256MulxU64(&x5, &x6, x4, (arg2[3])); + mulxU64(&x5, &x6, x4, (arg2[3])); var x7: u64 = undefined; var x8: u64 = undefined; - p256MulxU64(&x7, &x8, x4, (arg2[2])); + mulxU64(&x7, &x8, x4, (arg2[2])); var x9: u64 = undefined; var x10: u64 = undefined; - p256MulxU64(&x9, &x10, x4, (arg2[1])); + mulxU64(&x9, &x10, x4, (arg2[1])); var x11: u64 = undefined; var x12: u64 = undefined; - p256MulxU64(&x11, &x12, x4, (arg2[0])); + mulxU64(&x11, &x12, x4, (arg2[0])); var x13: u64 = undefined; var x14: u1 = undefined; - p256AddcarryxU64(&x13, &x14, 0x0, x12, x9); + addcarryxU64(&x13, &x14, 0x0, x12, x9); var x15: u64 = undefined; var x16: u1 = undefined; - p256AddcarryxU64(&x15, &x16, x14, x10, x7); + addcarryxU64(&x15, &x16, x14, x10, x7); var x17: u64 = undefined; var x18: u1 = undefined; - p256AddcarryxU64(&x17, &x18, x16, x8, x5); - const x19: u64 = (@intCast(u64, x18) + x6); + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (cast(u64, x18) + x6); var x20: u64 = undefined; var x21: u64 = undefined; - p256MulxU64(&x20, &x21, x11, 0xffffffff00000001); + mulxU64(&x20, &x21, x11, 0xffffffff00000001); var x22: u64 = undefined; var x23: u64 = undefined; - p256MulxU64(&x22, &x23, x11, 0xffffffff); + mulxU64(&x22, &x23, x11, 0xffffffff); var x24: u64 = undefined; var x25: u64 = undefined; - p256MulxU64(&x24, &x25, x11, 0xffffffffffffffff); + mulxU64(&x24, &x25, x11, 0xffffffffffffffff); var x26: u64 = undefined; var x27: u1 = undefined; - p256AddcarryxU64(&x26, &x27, 0x0, x25, x22); - const x28: u64 = (@intCast(u64, x27) + x23); + addcarryxU64(&x26, &x27, 0x0, x25, x22); + const x28 = (cast(u64, x27) + x23); var x29: u64 = undefined; var x30: u1 = undefined; - p256AddcarryxU64(&x29, &x30, 0x0, x11, x24); + addcarryxU64(&x29, &x30, 0x0, x11, x24); var x31: u64 = undefined; var x32: u1 = undefined; - p256AddcarryxU64(&x31, &x32, x30, x13, x26); + addcarryxU64(&x31, &x32, x30, x13, x26); var x33: u64 = undefined; var x34: u1 = undefined; - p256AddcarryxU64(&x33, &x34, x32, x15, x28); + addcarryxU64(&x33, &x34, x32, x15, x28); var x35: u64 = undefined; var x36: u1 = undefined; - p256AddcarryxU64(&x35, &x36, x34, x17, x20); + addcarryxU64(&x35, &x36, x34, x17, x20); var x37: u64 = undefined; var x38: u1 = undefined; - p256AddcarryxU64(&x37, &x38, x36, x19, x21); + addcarryxU64(&x37, &x38, x36, x19, x21); var x39: u64 = undefined; var x40: u64 = undefined; - p256MulxU64(&x39, &x40, x1, (arg2[3])); + mulxU64(&x39, &x40, x1, (arg2[3])); var x41: u64 = undefined; var x42: u64 = undefined; - p256MulxU64(&x41, &x42, x1, (arg2[2])); + mulxU64(&x41, &x42, x1, (arg2[2])); var x43: u64 = undefined; var x44: u64 = undefined; - p256MulxU64(&x43, &x44, x1, (arg2[1])); + mulxU64(&x43, &x44, x1, (arg2[1])); var x45: u64 = undefined; var x46: u64 = undefined; - p256MulxU64(&x45, &x46, x1, (arg2[0])); + mulxU64(&x45, &x46, x1, (arg2[0])); var x47: u64 = undefined; var x48: u1 = undefined; - p256AddcarryxU64(&x47, &x48, 0x0, x46, x43); + addcarryxU64(&x47, &x48, 0x0, x46, x43); var x49: u64 = undefined; var x50: u1 = undefined; - p256AddcarryxU64(&x49, &x50, x48, x44, x41); + addcarryxU64(&x49, &x50, x48, x44, x41); var x51: u64 = undefined; var x52: u1 = undefined; - p256AddcarryxU64(&x51, &x52, x50, x42, x39); - const x53: u64 = (@intCast(u64, x52) + x40); + addcarryxU64(&x51, &x52, x50, x42, x39); + const x53 = (cast(u64, x52) + x40); var x54: u64 = undefined; var x55: u1 = undefined; - p256AddcarryxU64(&x54, &x55, 0x0, x31, x45); + addcarryxU64(&x54, &x55, 0x0, x31, x45); var x56: u64 = undefined; var x57: u1 = undefined; - p256AddcarryxU64(&x56, &x57, x55, x33, x47); + addcarryxU64(&x56, &x57, x55, x33, x47); var x58: u64 = undefined; var x59: u1 = undefined; - p256AddcarryxU64(&x58, &x59, x57, x35, x49); + addcarryxU64(&x58, &x59, x57, x35, x49); var x60: u64 = undefined; var x61: u1 = undefined; - p256AddcarryxU64(&x60, &x61, x59, x37, x51); + addcarryxU64(&x60, &x61, x59, x37, x51); var x62: u64 = undefined; var x63: u1 = undefined; - p256AddcarryxU64(&x62, &x63, x61, @intCast(u64, x38), x53); + addcarryxU64(&x62, &x63, x61, cast(u64, x38), x53); var x64: u64 = undefined; var x65: u64 = undefined; - p256MulxU64(&x64, &x65, x54, 0xffffffff00000001); + mulxU64(&x64, &x65, x54, 0xffffffff00000001); var x66: u64 = undefined; var x67: u64 = undefined; - p256MulxU64(&x66, &x67, x54, 0xffffffff); + mulxU64(&x66, &x67, x54, 0xffffffff); var x68: u64 = undefined; var x69: u64 = undefined; - p256MulxU64(&x68, &x69, x54, 0xffffffffffffffff); + mulxU64(&x68, &x69, x54, 0xffffffffffffffff); var x70: u64 = undefined; var x71: u1 = undefined; - p256AddcarryxU64(&x70, &x71, 0x0, x69, x66); - const x72: u64 = (@intCast(u64, x71) + x67); + addcarryxU64(&x70, &x71, 0x0, x69, x66); + const x72 = (cast(u64, x71) + x67); var x73: u64 = undefined; var x74: u1 = undefined; - p256AddcarryxU64(&x73, &x74, 0x0, x54, x68); + addcarryxU64(&x73, &x74, 0x0, x54, x68); var x75: u64 = undefined; var x76: u1 = undefined; - p256AddcarryxU64(&x75, &x76, x74, x56, x70); + addcarryxU64(&x75, &x76, x74, x56, x70); var x77: u64 = undefined; var x78: u1 = undefined; - p256AddcarryxU64(&x77, &x78, x76, x58, x72); + addcarryxU64(&x77, &x78, x76, x58, x72); var x79: u64 = undefined; var x80: u1 = undefined; - p256AddcarryxU64(&x79, &x80, x78, x60, x64); + addcarryxU64(&x79, &x80, x78, x60, x64); var x81: u64 = undefined; var x82: u1 = undefined; - p256AddcarryxU64(&x81, &x82, x80, x62, x65); - const x83: u64 = (@intCast(u64, x82) + @intCast(u64, x63)); + addcarryxU64(&x81, &x82, x80, x62, x65); + const x83 = (cast(u64, x82) + cast(u64, x63)); var x84: u64 = undefined; var x85: u64 = undefined; - p256MulxU64(&x84, &x85, x2, (arg2[3])); + mulxU64(&x84, &x85, x2, (arg2[3])); var x86: u64 = undefined; var x87: u64 = undefined; - p256MulxU64(&x86, &x87, x2, (arg2[2])); + mulxU64(&x86, &x87, x2, (arg2[2])); var x88: u64 = undefined; var x89: u64 = undefined; - p256MulxU64(&x88, &x89, x2, (arg2[1])); + mulxU64(&x88, &x89, x2, (arg2[1])); var x90: u64 = undefined; var x91: u64 = undefined; - p256MulxU64(&x90, &x91, x2, (arg2[0])); + mulxU64(&x90, &x91, x2, (arg2[0])); var x92: u64 = undefined; var x93: u1 = undefined; - p256AddcarryxU64(&x92, &x93, 0x0, x91, x88); + addcarryxU64(&x92, &x93, 0x0, x91, x88); var x94: u64 = undefined; var x95: u1 = undefined; - p256AddcarryxU64(&x94, &x95, x93, x89, x86); + addcarryxU64(&x94, &x95, x93, x89, x86); var x96: u64 = undefined; var x97: u1 = undefined; - p256AddcarryxU64(&x96, &x97, x95, x87, x84); - const x98: u64 = (@intCast(u64, x97) + x85); + addcarryxU64(&x96, &x97, x95, x87, x84); + const x98 = (cast(u64, x97) + x85); var x99: u64 = undefined; var x100: u1 = undefined; - p256AddcarryxU64(&x99, &x100, 0x0, x75, x90); + addcarryxU64(&x99, &x100, 0x0, x75, x90); var x101: u64 = undefined; var x102: u1 = undefined; - p256AddcarryxU64(&x101, &x102, x100, x77, x92); + addcarryxU64(&x101, &x102, x100, x77, x92); var x103: u64 = undefined; var x104: u1 = undefined; - p256AddcarryxU64(&x103, &x104, x102, x79, x94); + addcarryxU64(&x103, &x104, x102, x79, x94); var x105: u64 = undefined; var x106: u1 = undefined; - p256AddcarryxU64(&x105, &x106, x104, x81, x96); + addcarryxU64(&x105, &x106, x104, x81, x96); var x107: u64 = undefined; var x108: u1 = undefined; - p256AddcarryxU64(&x107, &x108, x106, x83, x98); + addcarryxU64(&x107, &x108, x106, x83, x98); var x109: u64 = undefined; var x110: u64 = undefined; - p256MulxU64(&x109, &x110, x99, 0xffffffff00000001); + mulxU64(&x109, &x110, x99, 0xffffffff00000001); var x111: u64 = undefined; var x112: u64 = undefined; - p256MulxU64(&x111, &x112, x99, 0xffffffff); + mulxU64(&x111, &x112, x99, 0xffffffff); var x113: u64 = undefined; var x114: u64 = undefined; - p256MulxU64(&x113, &x114, x99, 0xffffffffffffffff); + mulxU64(&x113, &x114, x99, 0xffffffffffffffff); var x115: u64 = undefined; var x116: u1 = undefined; - p256AddcarryxU64(&x115, &x116, 0x0, x114, x111); - const x117: u64 = (@intCast(u64, x116) + x112); + addcarryxU64(&x115, &x116, 0x0, x114, x111); + const x117 = (cast(u64, x116) + x112); var x118: u64 = undefined; var x119: u1 = undefined; - p256AddcarryxU64(&x118, &x119, 0x0, x99, x113); + addcarryxU64(&x118, &x119, 0x0, x99, x113); var x120: u64 = undefined; var x121: u1 = undefined; - p256AddcarryxU64(&x120, &x121, x119, x101, x115); + addcarryxU64(&x120, &x121, x119, x101, x115); var x122: u64 = undefined; var x123: u1 = undefined; - p256AddcarryxU64(&x122, &x123, x121, x103, x117); + addcarryxU64(&x122, &x123, x121, x103, x117); var x124: u64 = undefined; var x125: u1 = undefined; - p256AddcarryxU64(&x124, &x125, x123, x105, x109); + addcarryxU64(&x124, &x125, x123, x105, x109); var x126: u64 = undefined; var x127: u1 = undefined; - p256AddcarryxU64(&x126, &x127, x125, x107, x110); - const x128: u64 = (@intCast(u64, x127) + @intCast(u64, x108)); + addcarryxU64(&x126, &x127, x125, x107, x110); + const x128 = (cast(u64, x127) + cast(u64, x108)); var x129: u64 = undefined; var x130: u64 = undefined; - p256MulxU64(&x129, &x130, x3, (arg2[3])); + mulxU64(&x129, &x130, x3, (arg2[3])); var x131: u64 = undefined; var x132: u64 = undefined; - p256MulxU64(&x131, &x132, x3, (arg2[2])); + mulxU64(&x131, &x132, x3, (arg2[2])); var x133: u64 = undefined; var x134: u64 = undefined; - p256MulxU64(&x133, &x134, x3, (arg2[1])); + mulxU64(&x133, &x134, x3, (arg2[1])); var x135: u64 = undefined; var x136: u64 = undefined; - p256MulxU64(&x135, &x136, x3, (arg2[0])); + mulxU64(&x135, &x136, x3, (arg2[0])); var x137: u64 = undefined; var x138: u1 = undefined; - p256AddcarryxU64(&x137, &x138, 0x0, x136, x133); + addcarryxU64(&x137, &x138, 0x0, x136, x133); var x139: u64 = undefined; var x140: u1 = undefined; - p256AddcarryxU64(&x139, &x140, x138, x134, x131); + addcarryxU64(&x139, &x140, x138, x134, x131); var x141: u64 = undefined; var x142: u1 = undefined; - p256AddcarryxU64(&x141, &x142, x140, x132, x129); - const x143: u64 = (@intCast(u64, x142) + x130); + addcarryxU64(&x141, &x142, x140, x132, x129); + const x143 = (cast(u64, x142) + x130); var x144: u64 = undefined; var x145: u1 = undefined; - p256AddcarryxU64(&x144, &x145, 0x0, x120, x135); + addcarryxU64(&x144, &x145, 0x0, x120, x135); var x146: u64 = undefined; var x147: u1 = undefined; - p256AddcarryxU64(&x146, &x147, x145, x122, x137); + addcarryxU64(&x146, &x147, x145, x122, x137); var x148: u64 = undefined; var x149: u1 = undefined; - p256AddcarryxU64(&x148, &x149, x147, x124, x139); + addcarryxU64(&x148, &x149, x147, x124, x139); var x150: u64 = undefined; var x151: u1 = undefined; - p256AddcarryxU64(&x150, &x151, x149, x126, x141); + addcarryxU64(&x150, &x151, x149, x126, x141); var x152: u64 = undefined; var x153: u1 = undefined; - p256AddcarryxU64(&x152, &x153, x151, x128, x143); + addcarryxU64(&x152, &x153, x151, x128, x143); var x154: u64 = undefined; var x155: u64 = undefined; - p256MulxU64(&x154, &x155, x144, 0xffffffff00000001); + mulxU64(&x154, &x155, x144, 0xffffffff00000001); var x156: u64 = undefined; var x157: u64 = undefined; - p256MulxU64(&x156, &x157, x144, 0xffffffff); + mulxU64(&x156, &x157, x144, 0xffffffff); var x158: u64 = undefined; var x159: u64 = undefined; - p256MulxU64(&x158, &x159, x144, 0xffffffffffffffff); + mulxU64(&x158, &x159, x144, 0xffffffffffffffff); var x160: u64 = undefined; var x161: u1 = undefined; - p256AddcarryxU64(&x160, &x161, 0x0, x159, x156); - const x162: u64 = (@intCast(u64, x161) + x157); + addcarryxU64(&x160, &x161, 0x0, x159, x156); + const x162 = (cast(u64, x161) + x157); var x163: u64 = undefined; var x164: u1 = undefined; - p256AddcarryxU64(&x163, &x164, 0x0, x144, x158); + addcarryxU64(&x163, &x164, 0x0, x144, x158); var x165: u64 = undefined; var x166: u1 = undefined; - p256AddcarryxU64(&x165, &x166, x164, x146, x160); + addcarryxU64(&x165, &x166, x164, x146, x160); var x167: u64 = undefined; var x168: u1 = undefined; - p256AddcarryxU64(&x167, &x168, x166, x148, x162); + addcarryxU64(&x167, &x168, x166, x148, x162); var x169: u64 = undefined; var x170: u1 = undefined; - p256AddcarryxU64(&x169, &x170, x168, x150, x154); + addcarryxU64(&x169, &x170, x168, x150, x154); var x171: u64 = undefined; var x172: u1 = undefined; - p256AddcarryxU64(&x171, &x172, x170, x152, x155); - const x173: u64 = (@intCast(u64, x172) + @intCast(u64, x153)); + addcarryxU64(&x171, &x172, x170, x152, x155); + const x173 = (cast(u64, x172) + cast(u64, x153)); var x174: u64 = undefined; var x175: u1 = undefined; - p256SubborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff); + subborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff); var x176: u64 = undefined; var x177: u1 = undefined; - p256SubborrowxU64(&x176, &x177, x175, x167, 0xffffffff); + subborrowxU64(&x176, &x177, x175, x167, 0xffffffff); var x178: u64 = undefined; var x179: u1 = undefined; - p256SubborrowxU64(&x178, &x179, x177, x169, @intCast(u64, 0x0)); + subborrowxU64(&x178, &x179, x177, x169, cast(u64, 0x0)); var x180: u64 = undefined; var x181: u1 = undefined; - p256SubborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001); + subborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001); var x182: u64 = undefined; var x183: u1 = undefined; - p256SubborrowxU64(&x182, &x183, x181, x173, @intCast(u64, 0x0)); + subborrowxU64(&x182, &x183, x181, x173, cast(u64, 0x0)); var x184: u64 = undefined; - p256CmovznzU64(&x184, x183, x174, x165); + cmovznzU64(&x184, x183, x174, x165); var x185: u64 = undefined; - p256CmovznzU64(&x185, x183, x176, x167); + cmovznzU64(&x185, x183, x176, x167); var x186: u64 = undefined; - p256CmovznzU64(&x186, x183, x178, x169); + cmovznzU64(&x186, x183, x178, x169); var x187: u64 = undefined; - p256CmovznzU64(&x187, x183, x180, x171); + cmovznzU64(&x187, x183, x180, x171); out1[0] = x184; out1[1] = x185; out1[2] = x186; out1[3] = x187; } -/// The function p256Square squares a field element in the Montgomery domain. +/// The function square squares a field element in the Montgomery domain. /// Preconditions: /// 0 ≤ eval arg1 < m /// Postconditions: @@ -399,289 +409,291 @@ pub fn p256Mul(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { /// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Square(out1: *Limbs, arg1: Limbs) void { - const x1: u64 = (arg1[1]); - const x2: u64 = (arg1[2]); - const x3: u64 = (arg1[3]); - const x4: u64 = (arg1[0]); +pub fn square(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); var x5: u64 = undefined; var x6: u64 = undefined; - p256MulxU64(&x5, &x6, x4, (arg1[3])); + mulxU64(&x5, &x6, x4, (arg1[3])); var x7: u64 = undefined; var x8: u64 = undefined; - p256MulxU64(&x7, &x8, x4, (arg1[2])); + mulxU64(&x7, &x8, x4, (arg1[2])); var x9: u64 = undefined; var x10: u64 = undefined; - p256MulxU64(&x9, &x10, x4, (arg1[1])); + mulxU64(&x9, &x10, x4, (arg1[1])); var x11: u64 = undefined; var x12: u64 = undefined; - p256MulxU64(&x11, &x12, x4, (arg1[0])); + mulxU64(&x11, &x12, x4, (arg1[0])); var x13: u64 = undefined; var x14: u1 = undefined; - p256AddcarryxU64(&x13, &x14, 0x0, x12, x9); + addcarryxU64(&x13, &x14, 0x0, x12, x9); var x15: u64 = undefined; var x16: u1 = undefined; - p256AddcarryxU64(&x15, &x16, x14, x10, x7); + addcarryxU64(&x15, &x16, x14, x10, x7); var x17: u64 = undefined; var x18: u1 = undefined; - p256AddcarryxU64(&x17, &x18, x16, x8, x5); - const x19: u64 = (@intCast(u64, x18) + x6); + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (cast(u64, x18) + x6); var x20: u64 = undefined; var x21: u64 = undefined; - p256MulxU64(&x20, &x21, x11, 0xffffffff00000001); + mulxU64(&x20, &x21, x11, 0xffffffff00000001); var x22: u64 = undefined; var x23: u64 = undefined; - p256MulxU64(&x22, &x23, x11, 0xffffffff); + mulxU64(&x22, &x23, x11, 0xffffffff); var x24: u64 = undefined; var x25: u64 = undefined; - p256MulxU64(&x24, &x25, x11, 0xffffffffffffffff); + mulxU64(&x24, &x25, x11, 0xffffffffffffffff); var x26: u64 = undefined; var x27: u1 = undefined; - p256AddcarryxU64(&x26, &x27, 0x0, x25, x22); - const x28: u64 = (@intCast(u64, x27) + x23); + addcarryxU64(&x26, &x27, 0x0, x25, x22); + const x28 = (cast(u64, x27) + x23); var x29: u64 = undefined; var x30: u1 = undefined; - p256AddcarryxU64(&x29, &x30, 0x0, x11, x24); + addcarryxU64(&x29, &x30, 0x0, x11, x24); var x31: u64 = undefined; var x32: u1 = undefined; - p256AddcarryxU64(&x31, &x32, x30, x13, x26); + addcarryxU64(&x31, &x32, x30, x13, x26); var x33: u64 = undefined; var x34: u1 = undefined; - p256AddcarryxU64(&x33, &x34, x32, x15, x28); + addcarryxU64(&x33, &x34, x32, x15, x28); var x35: u64 = undefined; var x36: u1 = undefined; - p256AddcarryxU64(&x35, &x36, x34, x17, x20); + addcarryxU64(&x35, &x36, x34, x17, x20); var x37: u64 = undefined; var x38: u1 = undefined; - p256AddcarryxU64(&x37, &x38, x36, x19, x21); + addcarryxU64(&x37, &x38, x36, x19, x21); var x39: u64 = undefined; var x40: u64 = undefined; - p256MulxU64(&x39, &x40, x1, (arg1[3])); + mulxU64(&x39, &x40, x1, (arg1[3])); var x41: u64 = undefined; var x42: u64 = undefined; - p256MulxU64(&x41, &x42, x1, (arg1[2])); + mulxU64(&x41, &x42, x1, (arg1[2])); var x43: u64 = undefined; var x44: u64 = undefined; - p256MulxU64(&x43, &x44, x1, (arg1[1])); + mulxU64(&x43, &x44, x1, (arg1[1])); var x45: u64 = undefined; var x46: u64 = undefined; - p256MulxU64(&x45, &x46, x1, (arg1[0])); + mulxU64(&x45, &x46, x1, (arg1[0])); var x47: u64 = undefined; var x48: u1 = undefined; - p256AddcarryxU64(&x47, &x48, 0x0, x46, x43); + addcarryxU64(&x47, &x48, 0x0, x46, x43); var x49: u64 = undefined; var x50: u1 = undefined; - p256AddcarryxU64(&x49, &x50, x48, x44, x41); + addcarryxU64(&x49, &x50, x48, x44, x41); var x51: u64 = undefined; var x52: u1 = undefined; - p256AddcarryxU64(&x51, &x52, x50, x42, x39); - const x53: u64 = (@intCast(u64, x52) + x40); + addcarryxU64(&x51, &x52, x50, x42, x39); + const x53 = (cast(u64, x52) + x40); var x54: u64 = undefined; var x55: u1 = undefined; - p256AddcarryxU64(&x54, &x55, 0x0, x31, x45); + addcarryxU64(&x54, &x55, 0x0, x31, x45); var x56: u64 = undefined; var x57: u1 = undefined; - p256AddcarryxU64(&x56, &x57, x55, x33, x47); + addcarryxU64(&x56, &x57, x55, x33, x47); var x58: u64 = undefined; var x59: u1 = undefined; - p256AddcarryxU64(&x58, &x59, x57, x35, x49); + addcarryxU64(&x58, &x59, x57, x35, x49); var x60: u64 = undefined; var x61: u1 = undefined; - p256AddcarryxU64(&x60, &x61, x59, x37, x51); + addcarryxU64(&x60, &x61, x59, x37, x51); var x62: u64 = undefined; var x63: u1 = undefined; - p256AddcarryxU64(&x62, &x63, x61, @intCast(u64, x38), x53); + addcarryxU64(&x62, &x63, x61, cast(u64, x38), x53); var x64: u64 = undefined; var x65: u64 = undefined; - p256MulxU64(&x64, &x65, x54, 0xffffffff00000001); + mulxU64(&x64, &x65, x54, 0xffffffff00000001); var x66: u64 = undefined; var x67: u64 = undefined; - p256MulxU64(&x66, &x67, x54, 0xffffffff); + mulxU64(&x66, &x67, x54, 0xffffffff); var x68: u64 = undefined; var x69: u64 = undefined; - p256MulxU64(&x68, &x69, x54, 0xffffffffffffffff); + mulxU64(&x68, &x69, x54, 0xffffffffffffffff); var x70: u64 = undefined; var x71: u1 = undefined; - p256AddcarryxU64(&x70, &x71, 0x0, x69, x66); - const x72: u64 = (@intCast(u64, x71) + x67); + addcarryxU64(&x70, &x71, 0x0, x69, x66); + const x72 = (cast(u64, x71) + x67); var x73: u64 = undefined; var x74: u1 = undefined; - p256AddcarryxU64(&x73, &x74, 0x0, x54, x68); + addcarryxU64(&x73, &x74, 0x0, x54, x68); var x75: u64 = undefined; var x76: u1 = undefined; - p256AddcarryxU64(&x75, &x76, x74, x56, x70); + addcarryxU64(&x75, &x76, x74, x56, x70); var x77: u64 = undefined; var x78: u1 = undefined; - p256AddcarryxU64(&x77, &x78, x76, x58, x72); + addcarryxU64(&x77, &x78, x76, x58, x72); var x79: u64 = undefined; var x80: u1 = undefined; - p256AddcarryxU64(&x79, &x80, x78, x60, x64); + addcarryxU64(&x79, &x80, x78, x60, x64); var x81: u64 = undefined; var x82: u1 = undefined; - p256AddcarryxU64(&x81, &x82, x80, x62, x65); - const x83: u64 = (@intCast(u64, x82) + @intCast(u64, x63)); + addcarryxU64(&x81, &x82, x80, x62, x65); + const x83 = (cast(u64, x82) + cast(u64, x63)); var x84: u64 = undefined; var x85: u64 = undefined; - p256MulxU64(&x84, &x85, x2, (arg1[3])); + mulxU64(&x84, &x85, x2, (arg1[3])); var x86: u64 = undefined; var x87: u64 = undefined; - p256MulxU64(&x86, &x87, x2, (arg1[2])); + mulxU64(&x86, &x87, x2, (arg1[2])); var x88: u64 = undefined; var x89: u64 = undefined; - p256MulxU64(&x88, &x89, x2, (arg1[1])); + mulxU64(&x88, &x89, x2, (arg1[1])); var x90: u64 = undefined; var x91: u64 = undefined; - p256MulxU64(&x90, &x91, x2, (arg1[0])); + mulxU64(&x90, &x91, x2, (arg1[0])); var x92: u64 = undefined; var x93: u1 = undefined; - p256AddcarryxU64(&x92, &x93, 0x0, x91, x88); + addcarryxU64(&x92, &x93, 0x0, x91, x88); var x94: u64 = undefined; var x95: u1 = undefined; - p256AddcarryxU64(&x94, &x95, x93, x89, x86); + addcarryxU64(&x94, &x95, x93, x89, x86); var x96: u64 = undefined; var x97: u1 = undefined; - p256AddcarryxU64(&x96, &x97, x95, x87, x84); - const x98: u64 = (@intCast(u64, x97) + x85); + addcarryxU64(&x96, &x97, x95, x87, x84); + const x98 = (cast(u64, x97) + x85); var x99: u64 = undefined; var x100: u1 = undefined; - p256AddcarryxU64(&x99, &x100, 0x0, x75, x90); + addcarryxU64(&x99, &x100, 0x0, x75, x90); var x101: u64 = undefined; var x102: u1 = undefined; - p256AddcarryxU64(&x101, &x102, x100, x77, x92); + addcarryxU64(&x101, &x102, x100, x77, x92); var x103: u64 = undefined; var x104: u1 = undefined; - p256AddcarryxU64(&x103, &x104, x102, x79, x94); + addcarryxU64(&x103, &x104, x102, x79, x94); var x105: u64 = undefined; var x106: u1 = undefined; - p256AddcarryxU64(&x105, &x106, x104, x81, x96); + addcarryxU64(&x105, &x106, x104, x81, x96); var x107: u64 = undefined; var x108: u1 = undefined; - p256AddcarryxU64(&x107, &x108, x106, x83, x98); + addcarryxU64(&x107, &x108, x106, x83, x98); var x109: u64 = undefined; var x110: u64 = undefined; - p256MulxU64(&x109, &x110, x99, 0xffffffff00000001); + mulxU64(&x109, &x110, x99, 0xffffffff00000001); var x111: u64 = undefined; var x112: u64 = undefined; - p256MulxU64(&x111, &x112, x99, 0xffffffff); + mulxU64(&x111, &x112, x99, 0xffffffff); var x113: u64 = undefined; var x114: u64 = undefined; - p256MulxU64(&x113, &x114, x99, 0xffffffffffffffff); + mulxU64(&x113, &x114, x99, 0xffffffffffffffff); var x115: u64 = undefined; var x116: u1 = undefined; - p256AddcarryxU64(&x115, &x116, 0x0, x114, x111); - const x117: u64 = (@intCast(u64, x116) + x112); + addcarryxU64(&x115, &x116, 0x0, x114, x111); + const x117 = (cast(u64, x116) + x112); var x118: u64 = undefined; var x119: u1 = undefined; - p256AddcarryxU64(&x118, &x119, 0x0, x99, x113); + addcarryxU64(&x118, &x119, 0x0, x99, x113); var x120: u64 = undefined; var x121: u1 = undefined; - p256AddcarryxU64(&x120, &x121, x119, x101, x115); + addcarryxU64(&x120, &x121, x119, x101, x115); var x122: u64 = undefined; var x123: u1 = undefined; - p256AddcarryxU64(&x122, &x123, x121, x103, x117); + addcarryxU64(&x122, &x123, x121, x103, x117); var x124: u64 = undefined; var x125: u1 = undefined; - p256AddcarryxU64(&x124, &x125, x123, x105, x109); + addcarryxU64(&x124, &x125, x123, x105, x109); var x126: u64 = undefined; var x127: u1 = undefined; - p256AddcarryxU64(&x126, &x127, x125, x107, x110); - const x128: u64 = (@intCast(u64, x127) + @intCast(u64, x108)); + addcarryxU64(&x126, &x127, x125, x107, x110); + const x128 = (cast(u64, x127) + cast(u64, x108)); var x129: u64 = undefined; var x130: u64 = undefined; - p256MulxU64(&x129, &x130, x3, (arg1[3])); + mulxU64(&x129, &x130, x3, (arg1[3])); var x131: u64 = undefined; var x132: u64 = undefined; - p256MulxU64(&x131, &x132, x3, (arg1[2])); + mulxU64(&x131, &x132, x3, (arg1[2])); var x133: u64 = undefined; var x134: u64 = undefined; - p256MulxU64(&x133, &x134, x3, (arg1[1])); + mulxU64(&x133, &x134, x3, (arg1[1])); var x135: u64 = undefined; var x136: u64 = undefined; - p256MulxU64(&x135, &x136, x3, (arg1[0])); + mulxU64(&x135, &x136, x3, (arg1[0])); var x137: u64 = undefined; var x138: u1 = undefined; - p256AddcarryxU64(&x137, &x138, 0x0, x136, x133); + addcarryxU64(&x137, &x138, 0x0, x136, x133); var x139: u64 = undefined; var x140: u1 = undefined; - p256AddcarryxU64(&x139, &x140, x138, x134, x131); + addcarryxU64(&x139, &x140, x138, x134, x131); var x141: u64 = undefined; var x142: u1 = undefined; - p256AddcarryxU64(&x141, &x142, x140, x132, x129); - const x143: u64 = (@intCast(u64, x142) + x130); + addcarryxU64(&x141, &x142, x140, x132, x129); + const x143 = (cast(u64, x142) + x130); var x144: u64 = undefined; var x145: u1 = undefined; - p256AddcarryxU64(&x144, &x145, 0x0, x120, x135); + addcarryxU64(&x144, &x145, 0x0, x120, x135); var x146: u64 = undefined; var x147: u1 = undefined; - p256AddcarryxU64(&x146, &x147, x145, x122, x137); + addcarryxU64(&x146, &x147, x145, x122, x137); var x148: u64 = undefined; var x149: u1 = undefined; - p256AddcarryxU64(&x148, &x149, x147, x124, x139); + addcarryxU64(&x148, &x149, x147, x124, x139); var x150: u64 = undefined; var x151: u1 = undefined; - p256AddcarryxU64(&x150, &x151, x149, x126, x141); + addcarryxU64(&x150, &x151, x149, x126, x141); var x152: u64 = undefined; var x153: u1 = undefined; - p256AddcarryxU64(&x152, &x153, x151, x128, x143); + addcarryxU64(&x152, &x153, x151, x128, x143); var x154: u64 = undefined; var x155: u64 = undefined; - p256MulxU64(&x154, &x155, x144, 0xffffffff00000001); + mulxU64(&x154, &x155, x144, 0xffffffff00000001); var x156: u64 = undefined; var x157: u64 = undefined; - p256MulxU64(&x156, &x157, x144, 0xffffffff); + mulxU64(&x156, &x157, x144, 0xffffffff); var x158: u64 = undefined; var x159: u64 = undefined; - p256MulxU64(&x158, &x159, x144, 0xffffffffffffffff); + mulxU64(&x158, &x159, x144, 0xffffffffffffffff); var x160: u64 = undefined; var x161: u1 = undefined; - p256AddcarryxU64(&x160, &x161, 0x0, x159, x156); - const x162: u64 = (@intCast(u64, x161) + x157); + addcarryxU64(&x160, &x161, 0x0, x159, x156); + const x162 = (cast(u64, x161) + x157); var x163: u64 = undefined; var x164: u1 = undefined; - p256AddcarryxU64(&x163, &x164, 0x0, x144, x158); + addcarryxU64(&x163, &x164, 0x0, x144, x158); var x165: u64 = undefined; var x166: u1 = undefined; - p256AddcarryxU64(&x165, &x166, x164, x146, x160); + addcarryxU64(&x165, &x166, x164, x146, x160); var x167: u64 = undefined; var x168: u1 = undefined; - p256AddcarryxU64(&x167, &x168, x166, x148, x162); + addcarryxU64(&x167, &x168, x166, x148, x162); var x169: u64 = undefined; var x170: u1 = undefined; - p256AddcarryxU64(&x169, &x170, x168, x150, x154); + addcarryxU64(&x169, &x170, x168, x150, x154); var x171: u64 = undefined; var x172: u1 = undefined; - p256AddcarryxU64(&x171, &x172, x170, x152, x155); - const x173: u64 = (@intCast(u64, x172) + @intCast(u64, x153)); + addcarryxU64(&x171, &x172, x170, x152, x155); + const x173 = (cast(u64, x172) + cast(u64, x153)); var x174: u64 = undefined; var x175: u1 = undefined; - p256SubborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff); + subborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff); var x176: u64 = undefined; var x177: u1 = undefined; - p256SubborrowxU64(&x176, &x177, x175, x167, 0xffffffff); + subborrowxU64(&x176, &x177, x175, x167, 0xffffffff); var x178: u64 = undefined; var x179: u1 = undefined; - p256SubborrowxU64(&x178, &x179, x177, x169, @intCast(u64, 0x0)); + subborrowxU64(&x178, &x179, x177, x169, cast(u64, 0x0)); var x180: u64 = undefined; var x181: u1 = undefined; - p256SubborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001); + subborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001); var x182: u64 = undefined; var x183: u1 = undefined; - p256SubborrowxU64(&x182, &x183, x181, x173, @intCast(u64, 0x0)); + subborrowxU64(&x182, &x183, x181, x173, cast(u64, 0x0)); var x184: u64 = undefined; - p256CmovznzU64(&x184, x183, x174, x165); + cmovznzU64(&x184, x183, x174, x165); var x185: u64 = undefined; - p256CmovznzU64(&x185, x183, x176, x167); + cmovznzU64(&x185, x183, x176, x167); var x186: u64 = undefined; - p256CmovznzU64(&x186, x183, x178, x169); + cmovznzU64(&x186, x183, x178, x169); var x187: u64 = undefined; - p256CmovznzU64(&x187, x183, x180, x171); + cmovznzU64(&x187, x183, x180, x171); out1[0] = x184; out1[1] = x185; out1[2] = x186; out1[3] = x187; } -/// The function p256Add adds two field elements in the Montgomery domain. +/// The function add adds two field elements in the Montgomery domain. /// Preconditions: /// 0 ≤ eval arg1 < m /// 0 ≤ eval arg2 < m @@ -694,49 +706,51 @@ pub fn p256Square(out1: *Limbs, arg1: Limbs) void { /// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Add(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { +pub fn add(out1: *[4]u64, arg1: [4]u64, arg2: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + var x1: u64 = undefined; var x2: u1 = undefined; - p256AddcarryxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + addcarryxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); var x3: u64 = undefined; var x4: u1 = undefined; - p256AddcarryxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + addcarryxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); var x5: u64 = undefined; var x6: u1 = undefined; - p256AddcarryxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + addcarryxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); var x7: u64 = undefined; var x8: u1 = undefined; - p256AddcarryxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + addcarryxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); var x9: u64 = undefined; var x10: u1 = undefined; - p256SubborrowxU64(&x9, &x10, 0x0, x1, 0xffffffffffffffff); + subborrowxU64(&x9, &x10, 0x0, x1, 0xffffffffffffffff); var x11: u64 = undefined; var x12: u1 = undefined; - p256SubborrowxU64(&x11, &x12, x10, x3, 0xffffffff); + subborrowxU64(&x11, &x12, x10, x3, 0xffffffff); var x13: u64 = undefined; var x14: u1 = undefined; - p256SubborrowxU64(&x13, &x14, x12, x5, @intCast(u64, 0x0)); + subborrowxU64(&x13, &x14, x12, x5, cast(u64, 0x0)); var x15: u64 = undefined; var x16: u1 = undefined; - p256SubborrowxU64(&x15, &x16, x14, x7, 0xffffffff00000001); + subborrowxU64(&x15, &x16, x14, x7, 0xffffffff00000001); var x17: u64 = undefined; var x18: u1 = undefined; - p256SubborrowxU64(&x17, &x18, x16, @intCast(u64, x8), @intCast(u64, 0x0)); + subborrowxU64(&x17, &x18, x16, cast(u64, x8), cast(u64, 0x0)); var x19: u64 = undefined; - p256CmovznzU64(&x19, x18, x9, x1); + cmovznzU64(&x19, x18, x9, x1); var x20: u64 = undefined; - p256CmovznzU64(&x20, x18, x11, x3); + cmovznzU64(&x20, x18, x11, x3); var x21: u64 = undefined; - p256CmovznzU64(&x21, x18, x13, x5); + cmovznzU64(&x21, x18, x13, x5); var x22: u64 = undefined; - p256CmovznzU64(&x22, x18, x15, x7); + cmovznzU64(&x22, x18, x15, x7); out1[0] = x19; out1[1] = x20; out1[2] = x21; out1[3] = x22; } -/// The function p256Sub subtracts two field elements in the Montgomery domain. +/// The function sub subtracts two field elements in the Montgomery domain. /// Preconditions: /// 0 ≤ eval arg1 < m /// 0 ≤ eval arg2 < m @@ -749,40 +763,42 @@ pub fn p256Add(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { /// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Sub(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { +pub fn sub(out1: *[4]u64, arg1: [4]u64, arg2: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + var x1: u64 = undefined; var x2: u1 = undefined; - p256SubborrowxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + subborrowxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); var x3: u64 = undefined; var x4: u1 = undefined; - p256SubborrowxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + subborrowxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); var x5: u64 = undefined; var x6: u1 = undefined; - p256SubborrowxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + subborrowxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); var x7: u64 = undefined; var x8: u1 = undefined; - p256SubborrowxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + subborrowxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); var x9: u64 = undefined; - p256CmovznzU64(&x9, x8, @intCast(u64, 0x0), 0xffffffffffffffff); + cmovznzU64(&x9, x8, cast(u64, 0x0), 0xffffffffffffffff); var x10: u64 = undefined; var x11: u1 = undefined; - p256AddcarryxU64(&x10, &x11, 0x0, x1, x9); + addcarryxU64(&x10, &x11, 0x0, x1, x9); var x12: u64 = undefined; var x13: u1 = undefined; - p256AddcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff)); + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff)); var x14: u64 = undefined; var x15: u1 = undefined; - p256AddcarryxU64(&x14, &x15, x13, x5, @intCast(u64, 0x0)); + addcarryxU64(&x14, &x15, x13, x5, cast(u64, 0x0)); var x16: u64 = undefined; var x17: u1 = undefined; - p256AddcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001)); + addcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001)); out1[0] = x10; out1[1] = x12; out1[2] = x14; out1[3] = x16; } -/// The function p256Opp negates a field element in the Montgomery domain. +/// The function opp negates a field element in the Montgomery domain. /// Preconditions: /// 0 ≤ eval arg1 < m /// Postconditions: @@ -793,40 +809,42 @@ pub fn p256Sub(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { /// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Opp(out1: *Limbs, arg1: Limbs) void { +pub fn opp(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + var x1: u64 = undefined; var x2: u1 = undefined; - p256SubborrowxU64(&x1, &x2, 0x0, @intCast(u64, 0x0), (arg1[0])); + subborrowxU64(&x1, &x2, 0x0, cast(u64, 0x0), (arg1[0])); var x3: u64 = undefined; var x4: u1 = undefined; - p256SubborrowxU64(&x3, &x4, x2, @intCast(u64, 0x0), (arg1[1])); + subborrowxU64(&x3, &x4, x2, cast(u64, 0x0), (arg1[1])); var x5: u64 = undefined; var x6: u1 = undefined; - p256SubborrowxU64(&x5, &x6, x4, @intCast(u64, 0x0), (arg1[2])); + subborrowxU64(&x5, &x6, x4, cast(u64, 0x0), (arg1[2])); var x7: u64 = undefined; var x8: u1 = undefined; - p256SubborrowxU64(&x7, &x8, x6, @intCast(u64, 0x0), (arg1[3])); + subborrowxU64(&x7, &x8, x6, cast(u64, 0x0), (arg1[3])); var x9: u64 = undefined; - p256CmovznzU64(&x9, x8, @intCast(u64, 0x0), 0xffffffffffffffff); + cmovznzU64(&x9, x8, cast(u64, 0x0), 0xffffffffffffffff); var x10: u64 = undefined; var x11: u1 = undefined; - p256AddcarryxU64(&x10, &x11, 0x0, x1, x9); + addcarryxU64(&x10, &x11, 0x0, x1, x9); var x12: u64 = undefined; var x13: u1 = undefined; - p256AddcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff)); + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff)); var x14: u64 = undefined; var x15: u1 = undefined; - p256AddcarryxU64(&x14, &x15, x13, x5, @intCast(u64, 0x0)); + addcarryxU64(&x14, &x15, x13, x5, cast(u64, 0x0)); var x16: u64 = undefined; var x17: u1 = undefined; - p256AddcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001)); + addcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001)); out1[0] = x10; out1[1] = x12; out1[2] = x14; out1[3] = x16; } -/// The function p256FromMontgomery translates a field element out of the Montgomery domain. +/// The function fromMontgomery translates a field element out of the Montgomery domain. /// Preconditions: /// 0 ≤ eval arg1 < m /// Postconditions: @@ -837,150 +855,152 @@ pub fn p256Opp(out1: *Limbs, arg1: Limbs) void { /// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256FromMontgomery(out1: *Limbs, arg1: Limbs) void { - const x1: u64 = (arg1[0]); +pub fn fromMontgomery(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[0]); var x2: u64 = undefined; var x3: u64 = undefined; - p256MulxU64(&x2, &x3, x1, 0xffffffff00000001); + mulxU64(&x2, &x3, x1, 0xffffffff00000001); var x4: u64 = undefined; var x5: u64 = undefined; - p256MulxU64(&x4, &x5, x1, 0xffffffff); + mulxU64(&x4, &x5, x1, 0xffffffff); var x6: u64 = undefined; var x7: u64 = undefined; - p256MulxU64(&x6, &x7, x1, 0xffffffffffffffff); + mulxU64(&x6, &x7, x1, 0xffffffffffffffff); var x8: u64 = undefined; var x9: u1 = undefined; - p256AddcarryxU64(&x8, &x9, 0x0, x7, x4); + addcarryxU64(&x8, &x9, 0x0, x7, x4); var x10: u64 = undefined; var x11: u1 = undefined; - p256AddcarryxU64(&x10, &x11, 0x0, x1, x6); + addcarryxU64(&x10, &x11, 0x0, x1, x6); var x12: u64 = undefined; var x13: u1 = undefined; - p256AddcarryxU64(&x12, &x13, x11, @intCast(u64, 0x0), x8); + addcarryxU64(&x12, &x13, x11, cast(u64, 0x0), x8); var x14: u64 = undefined; var x15: u1 = undefined; - p256AddcarryxU64(&x14, &x15, 0x0, x12, (arg1[1])); + addcarryxU64(&x14, &x15, 0x0, x12, (arg1[1])); var x16: u64 = undefined; var x17: u64 = undefined; - p256MulxU64(&x16, &x17, x14, 0xffffffff00000001); + mulxU64(&x16, &x17, x14, 0xffffffff00000001); var x18: u64 = undefined; var x19: u64 = undefined; - p256MulxU64(&x18, &x19, x14, 0xffffffff); + mulxU64(&x18, &x19, x14, 0xffffffff); var x20: u64 = undefined; var x21: u64 = undefined; - p256MulxU64(&x20, &x21, x14, 0xffffffffffffffff); + mulxU64(&x20, &x21, x14, 0xffffffffffffffff); var x22: u64 = undefined; var x23: u1 = undefined; - p256AddcarryxU64(&x22, &x23, 0x0, x21, x18); + addcarryxU64(&x22, &x23, 0x0, x21, x18); var x24: u64 = undefined; var x25: u1 = undefined; - p256AddcarryxU64(&x24, &x25, 0x0, x14, x20); + addcarryxU64(&x24, &x25, 0x0, x14, x20); var x26: u64 = undefined; var x27: u1 = undefined; - p256AddcarryxU64(&x26, &x27, x25, (@intCast(u64, x15) + (@intCast(u64, x13) + (@intCast(u64, x9) + x5))), x22); + addcarryxU64(&x26, &x27, x25, (cast(u64, x15) + (cast(u64, x13) + (cast(u64, x9) + x5))), x22); var x28: u64 = undefined; var x29: u1 = undefined; - p256AddcarryxU64(&x28, &x29, x27, x2, (@intCast(u64, x23) + x19)); + addcarryxU64(&x28, &x29, x27, x2, (cast(u64, x23) + x19)); var x30: u64 = undefined; var x31: u1 = undefined; - p256AddcarryxU64(&x30, &x31, x29, x3, x16); + addcarryxU64(&x30, &x31, x29, x3, x16); var x32: u64 = undefined; var x33: u1 = undefined; - p256AddcarryxU64(&x32, &x33, 0x0, x26, (arg1[2])); + addcarryxU64(&x32, &x33, 0x0, x26, (arg1[2])); var x34: u64 = undefined; var x35: u1 = undefined; - p256AddcarryxU64(&x34, &x35, x33, x28, @intCast(u64, 0x0)); + addcarryxU64(&x34, &x35, x33, x28, cast(u64, 0x0)); var x36: u64 = undefined; var x37: u1 = undefined; - p256AddcarryxU64(&x36, &x37, x35, x30, @intCast(u64, 0x0)); + addcarryxU64(&x36, &x37, x35, x30, cast(u64, 0x0)); var x38: u64 = undefined; var x39: u64 = undefined; - p256MulxU64(&x38, &x39, x32, 0xffffffff00000001); + mulxU64(&x38, &x39, x32, 0xffffffff00000001); var x40: u64 = undefined; var x41: u64 = undefined; - p256MulxU64(&x40, &x41, x32, 0xffffffff); + mulxU64(&x40, &x41, x32, 0xffffffff); var x42: u64 = undefined; var x43: u64 = undefined; - p256MulxU64(&x42, &x43, x32, 0xffffffffffffffff); + mulxU64(&x42, &x43, x32, 0xffffffffffffffff); var x44: u64 = undefined; var x45: u1 = undefined; - p256AddcarryxU64(&x44, &x45, 0x0, x43, x40); + addcarryxU64(&x44, &x45, 0x0, x43, x40); var x46: u64 = undefined; var x47: u1 = undefined; - p256AddcarryxU64(&x46, &x47, 0x0, x32, x42); + addcarryxU64(&x46, &x47, 0x0, x32, x42); var x48: u64 = undefined; var x49: u1 = undefined; - p256AddcarryxU64(&x48, &x49, x47, x34, x44); + addcarryxU64(&x48, &x49, x47, x34, x44); var x50: u64 = undefined; var x51: u1 = undefined; - p256AddcarryxU64(&x50, &x51, x49, x36, (@intCast(u64, x45) + x41)); + addcarryxU64(&x50, &x51, x49, x36, (cast(u64, x45) + x41)); var x52: u64 = undefined; var x53: u1 = undefined; - p256AddcarryxU64(&x52, &x53, x51, (@intCast(u64, x37) + (@intCast(u64, x31) + x17)), x38); + addcarryxU64(&x52, &x53, x51, (cast(u64, x37) + (cast(u64, x31) + x17)), x38); var x54: u64 = undefined; var x55: u1 = undefined; - p256AddcarryxU64(&x54, &x55, 0x0, x48, (arg1[3])); + addcarryxU64(&x54, &x55, 0x0, x48, (arg1[3])); var x56: u64 = undefined; var x57: u1 = undefined; - p256AddcarryxU64(&x56, &x57, x55, x50, @intCast(u64, 0x0)); + addcarryxU64(&x56, &x57, x55, x50, cast(u64, 0x0)); var x58: u64 = undefined; var x59: u1 = undefined; - p256AddcarryxU64(&x58, &x59, x57, x52, @intCast(u64, 0x0)); + addcarryxU64(&x58, &x59, x57, x52, cast(u64, 0x0)); var x60: u64 = undefined; var x61: u64 = undefined; - p256MulxU64(&x60, &x61, x54, 0xffffffff00000001); + mulxU64(&x60, &x61, x54, 0xffffffff00000001); var x62: u64 = undefined; var x63: u64 = undefined; - p256MulxU64(&x62, &x63, x54, 0xffffffff); + mulxU64(&x62, &x63, x54, 0xffffffff); var x64: u64 = undefined; var x65: u64 = undefined; - p256MulxU64(&x64, &x65, x54, 0xffffffffffffffff); + mulxU64(&x64, &x65, x54, 0xffffffffffffffff); var x66: u64 = undefined; var x67: u1 = undefined; - p256AddcarryxU64(&x66, &x67, 0x0, x65, x62); + addcarryxU64(&x66, &x67, 0x0, x65, x62); var x68: u64 = undefined; var x69: u1 = undefined; - p256AddcarryxU64(&x68, &x69, 0x0, x54, x64); + addcarryxU64(&x68, &x69, 0x0, x54, x64); var x70: u64 = undefined; var x71: u1 = undefined; - p256AddcarryxU64(&x70, &x71, x69, x56, x66); + addcarryxU64(&x70, &x71, x69, x56, x66); var x72: u64 = undefined; var x73: u1 = undefined; - p256AddcarryxU64(&x72, &x73, x71, x58, (@intCast(u64, x67) + x63)); + addcarryxU64(&x72, &x73, x71, x58, (cast(u64, x67) + x63)); var x74: u64 = undefined; var x75: u1 = undefined; - p256AddcarryxU64(&x74, &x75, x73, (@intCast(u64, x59) + (@intCast(u64, x53) + x39)), x60); - const x76: u64 = (@intCast(u64, x75) + x61); + addcarryxU64(&x74, &x75, x73, (cast(u64, x59) + (cast(u64, x53) + x39)), x60); + const x76 = (cast(u64, x75) + x61); var x77: u64 = undefined; var x78: u1 = undefined; - p256SubborrowxU64(&x77, &x78, 0x0, x70, 0xffffffffffffffff); + subborrowxU64(&x77, &x78, 0x0, x70, 0xffffffffffffffff); var x79: u64 = undefined; var x80: u1 = undefined; - p256SubborrowxU64(&x79, &x80, x78, x72, 0xffffffff); + subborrowxU64(&x79, &x80, x78, x72, 0xffffffff); var x81: u64 = undefined; var x82: u1 = undefined; - p256SubborrowxU64(&x81, &x82, x80, x74, @intCast(u64, 0x0)); + subborrowxU64(&x81, &x82, x80, x74, cast(u64, 0x0)); var x83: u64 = undefined; var x84: u1 = undefined; - p256SubborrowxU64(&x83, &x84, x82, x76, 0xffffffff00000001); + subborrowxU64(&x83, &x84, x82, x76, 0xffffffff00000001); var x85: u64 = undefined; var x86: u1 = undefined; - p256SubborrowxU64(&x85, &x86, x84, @intCast(u64, 0x0), @intCast(u64, 0x0)); + subborrowxU64(&x85, &x86, x84, cast(u64, 0x0), cast(u64, 0x0)); var x87: u64 = undefined; - p256CmovznzU64(&x87, x86, x77, x70); + cmovznzU64(&x87, x86, x77, x70); var x88: u64 = undefined; - p256CmovznzU64(&x88, x86, x79, x72); + cmovznzU64(&x88, x86, x79, x72); var x89: u64 = undefined; - p256CmovznzU64(&x89, x86, x81, x74); + cmovznzU64(&x89, x86, x81, x74); var x90: u64 = undefined; - p256CmovznzU64(&x90, x86, x83, x76); + cmovznzU64(&x90, x86, x83, x76); out1[0] = x87; out1[1] = x88; out1[2] = x89; out1[3] = x90; } -/// The function p256ToMontgomery translates a field element into the Montgomery domain. +/// The function toMontgomery translates a field element into the Montgomery domain. /// Preconditions: /// 0 ≤ eval arg1 < m /// Postconditions: @@ -991,269 +1011,271 @@ pub fn p256FromMontgomery(out1: *Limbs, arg1: Limbs) void { /// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256ToMontgomery(out1: *Limbs, arg1: Limbs) void { - const x1: u64 = (arg1[1]); - const x2: u64 = (arg1[2]); - const x3: u64 = (arg1[3]); - const x4: u64 = (arg1[0]); +pub fn toMontgomery(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); var x5: u64 = undefined; var x6: u64 = undefined; - p256MulxU64(&x5, &x6, x4, 0x4fffffffd); + mulxU64(&x5, &x6, x4, 0x4fffffffd); var x7: u64 = undefined; var x8: u64 = undefined; - p256MulxU64(&x7, &x8, x4, 0xfffffffffffffffe); + mulxU64(&x7, &x8, x4, 0xfffffffffffffffe); var x9: u64 = undefined; var x10: u64 = undefined; - p256MulxU64(&x9, &x10, x4, 0xfffffffbffffffff); + mulxU64(&x9, &x10, x4, 0xfffffffbffffffff); var x11: u64 = undefined; var x12: u64 = undefined; - p256MulxU64(&x11, &x12, x4, 0x3); + mulxU64(&x11, &x12, x4, 0x3); var x13: u64 = undefined; var x14: u1 = undefined; - p256AddcarryxU64(&x13, &x14, 0x0, x12, x9); + addcarryxU64(&x13, &x14, 0x0, x12, x9); var x15: u64 = undefined; var x16: u1 = undefined; - p256AddcarryxU64(&x15, &x16, x14, x10, x7); + addcarryxU64(&x15, &x16, x14, x10, x7); var x17: u64 = undefined; var x18: u1 = undefined; - p256AddcarryxU64(&x17, &x18, x16, x8, x5); + addcarryxU64(&x17, &x18, x16, x8, x5); var x19: u64 = undefined; var x20: u64 = undefined; - p256MulxU64(&x19, &x20, x11, 0xffffffff00000001); + mulxU64(&x19, &x20, x11, 0xffffffff00000001); var x21: u64 = undefined; var x22: u64 = undefined; - p256MulxU64(&x21, &x22, x11, 0xffffffff); + mulxU64(&x21, &x22, x11, 0xffffffff); var x23: u64 = undefined; var x24: u64 = undefined; - p256MulxU64(&x23, &x24, x11, 0xffffffffffffffff); + mulxU64(&x23, &x24, x11, 0xffffffffffffffff); var x25: u64 = undefined; var x26: u1 = undefined; - p256AddcarryxU64(&x25, &x26, 0x0, x24, x21); + addcarryxU64(&x25, &x26, 0x0, x24, x21); var x27: u64 = undefined; var x28: u1 = undefined; - p256AddcarryxU64(&x27, &x28, 0x0, x11, x23); + addcarryxU64(&x27, &x28, 0x0, x11, x23); var x29: u64 = undefined; var x30: u1 = undefined; - p256AddcarryxU64(&x29, &x30, x28, x13, x25); + addcarryxU64(&x29, &x30, x28, x13, x25); var x31: u64 = undefined; var x32: u1 = undefined; - p256AddcarryxU64(&x31, &x32, x30, x15, (@intCast(u64, x26) + x22)); + addcarryxU64(&x31, &x32, x30, x15, (cast(u64, x26) + x22)); var x33: u64 = undefined; var x34: u1 = undefined; - p256AddcarryxU64(&x33, &x34, x32, x17, x19); + addcarryxU64(&x33, &x34, x32, x17, x19); var x35: u64 = undefined; var x36: u1 = undefined; - p256AddcarryxU64(&x35, &x36, x34, (@intCast(u64, x18) + x6), x20); + addcarryxU64(&x35, &x36, x34, (cast(u64, x18) + x6), x20); var x37: u64 = undefined; var x38: u64 = undefined; - p256MulxU64(&x37, &x38, x1, 0x4fffffffd); + mulxU64(&x37, &x38, x1, 0x4fffffffd); var x39: u64 = undefined; var x40: u64 = undefined; - p256MulxU64(&x39, &x40, x1, 0xfffffffffffffffe); + mulxU64(&x39, &x40, x1, 0xfffffffffffffffe); var x41: u64 = undefined; var x42: u64 = undefined; - p256MulxU64(&x41, &x42, x1, 0xfffffffbffffffff); + mulxU64(&x41, &x42, x1, 0xfffffffbffffffff); var x43: u64 = undefined; var x44: u64 = undefined; - p256MulxU64(&x43, &x44, x1, 0x3); + mulxU64(&x43, &x44, x1, 0x3); var x45: u64 = undefined; var x46: u1 = undefined; - p256AddcarryxU64(&x45, &x46, 0x0, x44, x41); + addcarryxU64(&x45, &x46, 0x0, x44, x41); var x47: u64 = undefined; var x48: u1 = undefined; - p256AddcarryxU64(&x47, &x48, x46, x42, x39); + addcarryxU64(&x47, &x48, x46, x42, x39); var x49: u64 = undefined; var x50: u1 = undefined; - p256AddcarryxU64(&x49, &x50, x48, x40, x37); + addcarryxU64(&x49, &x50, x48, x40, x37); var x51: u64 = undefined; var x52: u1 = undefined; - p256AddcarryxU64(&x51, &x52, 0x0, x29, x43); + addcarryxU64(&x51, &x52, 0x0, x29, x43); var x53: u64 = undefined; var x54: u1 = undefined; - p256AddcarryxU64(&x53, &x54, x52, x31, x45); + addcarryxU64(&x53, &x54, x52, x31, x45); var x55: u64 = undefined; var x56: u1 = undefined; - p256AddcarryxU64(&x55, &x56, x54, x33, x47); + addcarryxU64(&x55, &x56, x54, x33, x47); var x57: u64 = undefined; var x58: u1 = undefined; - p256AddcarryxU64(&x57, &x58, x56, x35, x49); + addcarryxU64(&x57, &x58, x56, x35, x49); var x59: u64 = undefined; var x60: u64 = undefined; - p256MulxU64(&x59, &x60, x51, 0xffffffff00000001); + mulxU64(&x59, &x60, x51, 0xffffffff00000001); var x61: u64 = undefined; var x62: u64 = undefined; - p256MulxU64(&x61, &x62, x51, 0xffffffff); + mulxU64(&x61, &x62, x51, 0xffffffff); var x63: u64 = undefined; var x64: u64 = undefined; - p256MulxU64(&x63, &x64, x51, 0xffffffffffffffff); + mulxU64(&x63, &x64, x51, 0xffffffffffffffff); var x65: u64 = undefined; var x66: u1 = undefined; - p256AddcarryxU64(&x65, &x66, 0x0, x64, x61); + addcarryxU64(&x65, &x66, 0x0, x64, x61); var x67: u64 = undefined; var x68: u1 = undefined; - p256AddcarryxU64(&x67, &x68, 0x0, x51, x63); + addcarryxU64(&x67, &x68, 0x0, x51, x63); var x69: u64 = undefined; var x70: u1 = undefined; - p256AddcarryxU64(&x69, &x70, x68, x53, x65); + addcarryxU64(&x69, &x70, x68, x53, x65); var x71: u64 = undefined; var x72: u1 = undefined; - p256AddcarryxU64(&x71, &x72, x70, x55, (@intCast(u64, x66) + x62)); + addcarryxU64(&x71, &x72, x70, x55, (cast(u64, x66) + x62)); var x73: u64 = undefined; var x74: u1 = undefined; - p256AddcarryxU64(&x73, &x74, x72, x57, x59); + addcarryxU64(&x73, &x74, x72, x57, x59); var x75: u64 = undefined; var x76: u1 = undefined; - p256AddcarryxU64(&x75, &x76, x74, ((@intCast(u64, x58) + @intCast(u64, x36)) + (@intCast(u64, x50) + x38)), x60); + addcarryxU64(&x75, &x76, x74, ((cast(u64, x58) + cast(u64, x36)) + (cast(u64, x50) + x38)), x60); var x77: u64 = undefined; var x78: u64 = undefined; - p256MulxU64(&x77, &x78, x2, 0x4fffffffd); + mulxU64(&x77, &x78, x2, 0x4fffffffd); var x79: u64 = undefined; var x80: u64 = undefined; - p256MulxU64(&x79, &x80, x2, 0xfffffffffffffffe); + mulxU64(&x79, &x80, x2, 0xfffffffffffffffe); var x81: u64 = undefined; var x82: u64 = undefined; - p256MulxU64(&x81, &x82, x2, 0xfffffffbffffffff); + mulxU64(&x81, &x82, x2, 0xfffffffbffffffff); var x83: u64 = undefined; var x84: u64 = undefined; - p256MulxU64(&x83, &x84, x2, 0x3); + mulxU64(&x83, &x84, x2, 0x3); var x85: u64 = undefined; var x86: u1 = undefined; - p256AddcarryxU64(&x85, &x86, 0x0, x84, x81); + addcarryxU64(&x85, &x86, 0x0, x84, x81); var x87: u64 = undefined; var x88: u1 = undefined; - p256AddcarryxU64(&x87, &x88, x86, x82, x79); + addcarryxU64(&x87, &x88, x86, x82, x79); var x89: u64 = undefined; var x90: u1 = undefined; - p256AddcarryxU64(&x89, &x90, x88, x80, x77); + addcarryxU64(&x89, &x90, x88, x80, x77); var x91: u64 = undefined; var x92: u1 = undefined; - p256AddcarryxU64(&x91, &x92, 0x0, x69, x83); + addcarryxU64(&x91, &x92, 0x0, x69, x83); var x93: u64 = undefined; var x94: u1 = undefined; - p256AddcarryxU64(&x93, &x94, x92, x71, x85); + addcarryxU64(&x93, &x94, x92, x71, x85); var x95: u64 = undefined; var x96: u1 = undefined; - p256AddcarryxU64(&x95, &x96, x94, x73, x87); + addcarryxU64(&x95, &x96, x94, x73, x87); var x97: u64 = undefined; var x98: u1 = undefined; - p256AddcarryxU64(&x97, &x98, x96, x75, x89); + addcarryxU64(&x97, &x98, x96, x75, x89); var x99: u64 = undefined; var x100: u64 = undefined; - p256MulxU64(&x99, &x100, x91, 0xffffffff00000001); + mulxU64(&x99, &x100, x91, 0xffffffff00000001); var x101: u64 = undefined; var x102: u64 = undefined; - p256MulxU64(&x101, &x102, x91, 0xffffffff); + mulxU64(&x101, &x102, x91, 0xffffffff); var x103: u64 = undefined; var x104: u64 = undefined; - p256MulxU64(&x103, &x104, x91, 0xffffffffffffffff); + mulxU64(&x103, &x104, x91, 0xffffffffffffffff); var x105: u64 = undefined; var x106: u1 = undefined; - p256AddcarryxU64(&x105, &x106, 0x0, x104, x101); + addcarryxU64(&x105, &x106, 0x0, x104, x101); var x107: u64 = undefined; var x108: u1 = undefined; - p256AddcarryxU64(&x107, &x108, 0x0, x91, x103); + addcarryxU64(&x107, &x108, 0x0, x91, x103); var x109: u64 = undefined; var x110: u1 = undefined; - p256AddcarryxU64(&x109, &x110, x108, x93, x105); + addcarryxU64(&x109, &x110, x108, x93, x105); var x111: u64 = undefined; var x112: u1 = undefined; - p256AddcarryxU64(&x111, &x112, x110, x95, (@intCast(u64, x106) + x102)); + addcarryxU64(&x111, &x112, x110, x95, (cast(u64, x106) + x102)); var x113: u64 = undefined; var x114: u1 = undefined; - p256AddcarryxU64(&x113, &x114, x112, x97, x99); + addcarryxU64(&x113, &x114, x112, x97, x99); var x115: u64 = undefined; var x116: u1 = undefined; - p256AddcarryxU64(&x115, &x116, x114, ((@intCast(u64, x98) + @intCast(u64, x76)) + (@intCast(u64, x90) + x78)), x100); + addcarryxU64(&x115, &x116, x114, ((cast(u64, x98) + cast(u64, x76)) + (cast(u64, x90) + x78)), x100); var x117: u64 = undefined; var x118: u64 = undefined; - p256MulxU64(&x117, &x118, x3, 0x4fffffffd); + mulxU64(&x117, &x118, x3, 0x4fffffffd); var x119: u64 = undefined; var x120: u64 = undefined; - p256MulxU64(&x119, &x120, x3, 0xfffffffffffffffe); + mulxU64(&x119, &x120, x3, 0xfffffffffffffffe); var x121: u64 = undefined; var x122: u64 = undefined; - p256MulxU64(&x121, &x122, x3, 0xfffffffbffffffff); + mulxU64(&x121, &x122, x3, 0xfffffffbffffffff); var x123: u64 = undefined; var x124: u64 = undefined; - p256MulxU64(&x123, &x124, x3, 0x3); + mulxU64(&x123, &x124, x3, 0x3); var x125: u64 = undefined; var x126: u1 = undefined; - p256AddcarryxU64(&x125, &x126, 0x0, x124, x121); + addcarryxU64(&x125, &x126, 0x0, x124, x121); var x127: u64 = undefined; var x128: u1 = undefined; - p256AddcarryxU64(&x127, &x128, x126, x122, x119); + addcarryxU64(&x127, &x128, x126, x122, x119); var x129: u64 = undefined; var x130: u1 = undefined; - p256AddcarryxU64(&x129, &x130, x128, x120, x117); + addcarryxU64(&x129, &x130, x128, x120, x117); var x131: u64 = undefined; var x132: u1 = undefined; - p256AddcarryxU64(&x131, &x132, 0x0, x109, x123); + addcarryxU64(&x131, &x132, 0x0, x109, x123); var x133: u64 = undefined; var x134: u1 = undefined; - p256AddcarryxU64(&x133, &x134, x132, x111, x125); + addcarryxU64(&x133, &x134, x132, x111, x125); var x135: u64 = undefined; var x136: u1 = undefined; - p256AddcarryxU64(&x135, &x136, x134, x113, x127); + addcarryxU64(&x135, &x136, x134, x113, x127); var x137: u64 = undefined; var x138: u1 = undefined; - p256AddcarryxU64(&x137, &x138, x136, x115, x129); + addcarryxU64(&x137, &x138, x136, x115, x129); var x139: u64 = undefined; var x140: u64 = undefined; - p256MulxU64(&x139, &x140, x131, 0xffffffff00000001); + mulxU64(&x139, &x140, x131, 0xffffffff00000001); var x141: u64 = undefined; var x142: u64 = undefined; - p256MulxU64(&x141, &x142, x131, 0xffffffff); + mulxU64(&x141, &x142, x131, 0xffffffff); var x143: u64 = undefined; var x144: u64 = undefined; - p256MulxU64(&x143, &x144, x131, 0xffffffffffffffff); + mulxU64(&x143, &x144, x131, 0xffffffffffffffff); var x145: u64 = undefined; var x146: u1 = undefined; - p256AddcarryxU64(&x145, &x146, 0x0, x144, x141); + addcarryxU64(&x145, &x146, 0x0, x144, x141); var x147: u64 = undefined; var x148: u1 = undefined; - p256AddcarryxU64(&x147, &x148, 0x0, x131, x143); + addcarryxU64(&x147, &x148, 0x0, x131, x143); var x149: u64 = undefined; var x150: u1 = undefined; - p256AddcarryxU64(&x149, &x150, x148, x133, x145); + addcarryxU64(&x149, &x150, x148, x133, x145); var x151: u64 = undefined; var x152: u1 = undefined; - p256AddcarryxU64(&x151, &x152, x150, x135, (@intCast(u64, x146) + x142)); + addcarryxU64(&x151, &x152, x150, x135, (cast(u64, x146) + x142)); var x153: u64 = undefined; var x154: u1 = undefined; - p256AddcarryxU64(&x153, &x154, x152, x137, x139); + addcarryxU64(&x153, &x154, x152, x137, x139); var x155: u64 = undefined; var x156: u1 = undefined; - p256AddcarryxU64(&x155, &x156, x154, ((@intCast(u64, x138) + @intCast(u64, x116)) + (@intCast(u64, x130) + x118)), x140); + addcarryxU64(&x155, &x156, x154, ((cast(u64, x138) + cast(u64, x116)) + (cast(u64, x130) + x118)), x140); var x157: u64 = undefined; var x158: u1 = undefined; - p256SubborrowxU64(&x157, &x158, 0x0, x149, 0xffffffffffffffff); + subborrowxU64(&x157, &x158, 0x0, x149, 0xffffffffffffffff); var x159: u64 = undefined; var x160: u1 = undefined; - p256SubborrowxU64(&x159, &x160, x158, x151, 0xffffffff); + subborrowxU64(&x159, &x160, x158, x151, 0xffffffff); var x161: u64 = undefined; var x162: u1 = undefined; - p256SubborrowxU64(&x161, &x162, x160, x153, @intCast(u64, 0x0)); + subborrowxU64(&x161, &x162, x160, x153, cast(u64, 0x0)); var x163: u64 = undefined; var x164: u1 = undefined; - p256SubborrowxU64(&x163, &x164, x162, x155, 0xffffffff00000001); + subborrowxU64(&x163, &x164, x162, x155, 0xffffffff00000001); var x165: u64 = undefined; var x166: u1 = undefined; - p256SubborrowxU64(&x165, &x166, x164, @intCast(u64, x156), @intCast(u64, 0x0)); + subborrowxU64(&x165, &x166, x164, cast(u64, x156), cast(u64, 0x0)); var x167: u64 = undefined; - p256CmovznzU64(&x167, x166, x157, x149); + cmovznzU64(&x167, x166, x157, x149); var x168: u64 = undefined; - p256CmovznzU64(&x168, x166, x159, x151); + cmovznzU64(&x168, x166, x159, x151); var x169: u64 = undefined; - p256CmovznzU64(&x169, x166, x161, x153); + cmovznzU64(&x169, x166, x161, x153); var x170: u64 = undefined; - p256CmovznzU64(&x170, x166, x163, x155); + cmovznzU64(&x170, x166, x163, x155); out1[0] = x167; out1[1] = x168; out1[2] = x169; out1[3] = x170; } -/// The function p256Nonzero outputs a single non-zero word if the input is non-zero and zero otherwise. +/// The function nonzero outputs a single non-zero word if the input is non-zero and zero otherwise. /// Preconditions: /// 0 ≤ eval arg1 < m /// Postconditions: @@ -1263,12 +1285,14 @@ pub fn p256ToMontgomery(out1: *Limbs, arg1: Limbs) void { /// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [0x0 ~> 0xffffffffffffffff] -pub fn p256Nonzero(out1: *u64, arg1: Limbs) void { - const x1: u64 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3])))); +pub fn nonzero(out1: *u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3])))); out1.* = x1; } -/// The function p256Selectznz is a multi-limb conditional select. +/// The function selectznz is a multi-limb conditional select. /// Postconditions: /// eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) /// @@ -1278,22 +1302,24 @@ pub fn p256Nonzero(out1: *u64, arg1: Limbs) void { /// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Selectznz(out1: *Limbs, arg1: u1, arg2: Limbs, arg3: Limbs) void { +pub fn selectznz(out1: *[4]u64, arg1: u1, arg2: [4]u64, arg3: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + var x1: u64 = undefined; - p256CmovznzU64(&x1, arg1, (arg2[0]), (arg3[0])); + cmovznzU64(&x1, arg1, (arg2[0]), (arg3[0])); var x2: u64 = undefined; - p256CmovznzU64(&x2, arg1, (arg2[1]), (arg3[1])); + cmovznzU64(&x2, arg1, (arg2[1]), (arg3[1])); var x3: u64 = undefined; - p256CmovznzU64(&x3, arg1, (arg2[2]), (arg3[2])); + cmovznzU64(&x3, arg1, (arg2[2]), (arg3[2])); var x4: u64 = undefined; - p256CmovznzU64(&x4, arg1, (arg2[3]), (arg3[3])); + cmovznzU64(&x4, arg1, (arg2[3]), (arg3[3])); out1[0] = x1; out1[1] = x2; out1[2] = x3; out1[3] = x4; } -/// The function p256ToBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. +/// The function toBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. /// Preconditions: /// 0 ≤ eval arg1 < m /// Postconditions: @@ -1303,67 +1329,69 @@ pub fn p256Selectznz(out1: *Limbs, arg1: u1, arg2: Limbs, arg3: Limbs) void { /// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// Output Bounds: /// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] -pub fn p256ToBytes(out1: *[32]u8, arg1: Limbs) void { - const x1: u64 = (arg1[3]); - const x2: u64 = (arg1[2]); - const x3: u64 = (arg1[1]); - const x4: u64 = (arg1[0]); - const x5: u8 = @intCast(u8, (x4 & @intCast(u64, 0xff))); - const x6: u64 = (x4 >> 8); - const x7: u8 = @intCast(u8, (x6 & @intCast(u64, 0xff))); - const x8: u64 = (x6 >> 8); - const x9: u8 = @intCast(u8, (x8 & @intCast(u64, 0xff))); - const x10: u64 = (x8 >> 8); - const x11: u8 = @intCast(u8, (x10 & @intCast(u64, 0xff))); - const x12: u64 = (x10 >> 8); - const x13: u8 = @intCast(u8, (x12 & @intCast(u64, 0xff))); - const x14: u64 = (x12 >> 8); - const x15: u8 = @intCast(u8, (x14 & @intCast(u64, 0xff))); - const x16: u64 = (x14 >> 8); - const x17: u8 = @intCast(u8, (x16 & @intCast(u64, 0xff))); - const x18: u8 = @intCast(u8, (x16 >> 8)); - const x19: u8 = @intCast(u8, (x3 & @intCast(u64, 0xff))); - const x20: u64 = (x3 >> 8); - const x21: u8 = @intCast(u8, (x20 & @intCast(u64, 0xff))); - const x22: u64 = (x20 >> 8); - const x23: u8 = @intCast(u8, (x22 & @intCast(u64, 0xff))); - const x24: u64 = (x22 >> 8); - const x25: u8 = @intCast(u8, (x24 & @intCast(u64, 0xff))); - const x26: u64 = (x24 >> 8); - const x27: u8 = @intCast(u8, (x26 & @intCast(u64, 0xff))); - const x28: u64 = (x26 >> 8); - const x29: u8 = @intCast(u8, (x28 & @intCast(u64, 0xff))); - const x30: u64 = (x28 >> 8); - const x31: u8 = @intCast(u8, (x30 & @intCast(u64, 0xff))); - const x32: u8 = @intCast(u8, (x30 >> 8)); - const x33: u8 = @intCast(u8, (x2 & @intCast(u64, 0xff))); - const x34: u64 = (x2 >> 8); - const x35: u8 = @intCast(u8, (x34 & @intCast(u64, 0xff))); - const x36: u64 = (x34 >> 8); - const x37: u8 = @intCast(u8, (x36 & @intCast(u64, 0xff))); - const x38: u64 = (x36 >> 8); - const x39: u8 = @intCast(u8, (x38 & @intCast(u64, 0xff))); - const x40: u64 = (x38 >> 8); - const x41: u8 = @intCast(u8, (x40 & @intCast(u64, 0xff))); - const x42: u64 = (x40 >> 8); - const x43: u8 = @intCast(u8, (x42 & @intCast(u64, 0xff))); - const x44: u64 = (x42 >> 8); - const x45: u8 = @intCast(u8, (x44 & @intCast(u64, 0xff))); - const x46: u8 = @intCast(u8, (x44 >> 8)); - const x47: u8 = @intCast(u8, (x1 & @intCast(u64, 0xff))); - const x48: u64 = (x1 >> 8); - const x49: u8 = @intCast(u8, (x48 & @intCast(u64, 0xff))); - const x50: u64 = (x48 >> 8); - const x51: u8 = @intCast(u8, (x50 & @intCast(u64, 0xff))); - const x52: u64 = (x50 >> 8); - const x53: u8 = @intCast(u8, (x52 & @intCast(u64, 0xff))); - const x54: u64 = (x52 >> 8); - const x55: u8 = @intCast(u8, (x54 & @intCast(u64, 0xff))); - const x56: u64 = (x54 >> 8); - const x57: u8 = @intCast(u8, (x56 & @intCast(u64, 0xff))); - const x58: u64 = (x56 >> 8); - const x59: u8 = @intCast(u8, (x58 & @intCast(u64, 0xff))); - const x60: u8 = @intCast(u8, (x58 >> 8)); +pub fn toBytes(out1: *[32]u8, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[3]); + const x2 = (arg1[2]); + const x3 = (arg1[1]); + const x4 = (arg1[0]); + const x5 = cast(u8, (x4 & cast(u64, 0xff))); + const x6 = (x4 >> 8); + const x7 = cast(u8, (x6 & cast(u64, 0xff))); + const x8 = (x6 >> 8); + const x9 = cast(u8, (x8 & cast(u64, 0xff))); + const x10 = (x8 >> 8); + const x11 = cast(u8, (x10 & cast(u64, 0xff))); + const x12 = (x10 >> 8); + const x13 = cast(u8, (x12 & cast(u64, 0xff))); + const x14 = (x12 >> 8); + const x15 = cast(u8, (x14 & cast(u64, 0xff))); + const x16 = (x14 >> 8); + const x17 = cast(u8, (x16 & cast(u64, 0xff))); + const x18 = cast(u8, (x16 >> 8)); + const x19 = cast(u8, (x3 & cast(u64, 0xff))); + const x20 = (x3 >> 8); + const x21 = cast(u8, (x20 & cast(u64, 0xff))); + const x22 = (x20 >> 8); + const x23 = cast(u8, (x22 & cast(u64, 0xff))); + const x24 = (x22 >> 8); + const x25 = cast(u8, (x24 & cast(u64, 0xff))); + const x26 = (x24 >> 8); + const x27 = cast(u8, (x26 & cast(u64, 0xff))); + const x28 = (x26 >> 8); + const x29 = cast(u8, (x28 & cast(u64, 0xff))); + const x30 = (x28 >> 8); + const x31 = cast(u8, (x30 & cast(u64, 0xff))); + const x32 = cast(u8, (x30 >> 8)); + const x33 = cast(u8, (x2 & cast(u64, 0xff))); + const x34 = (x2 >> 8); + const x35 = cast(u8, (x34 & cast(u64, 0xff))); + const x36 = (x34 >> 8); + const x37 = cast(u8, (x36 & cast(u64, 0xff))); + const x38 = (x36 >> 8); + const x39 = cast(u8, (x38 & cast(u64, 0xff))); + const x40 = (x38 >> 8); + const x41 = cast(u8, (x40 & cast(u64, 0xff))); + const x42 = (x40 >> 8); + const x43 = cast(u8, (x42 & cast(u64, 0xff))); + const x44 = (x42 >> 8); + const x45 = cast(u8, (x44 & cast(u64, 0xff))); + const x46 = cast(u8, (x44 >> 8)); + const x47 = cast(u8, (x1 & cast(u64, 0xff))); + const x48 = (x1 >> 8); + const x49 = cast(u8, (x48 & cast(u64, 0xff))); + const x50 = (x48 >> 8); + const x51 = cast(u8, (x50 & cast(u64, 0xff))); + const x52 = (x50 >> 8); + const x53 = cast(u8, (x52 & cast(u64, 0xff))); + const x54 = (x52 >> 8); + const x55 = cast(u8, (x54 & cast(u64, 0xff))); + const x56 = (x54 >> 8); + const x57 = cast(u8, (x56 & cast(u64, 0xff))); + const x58 = (x56 >> 8); + const x59 = cast(u8, (x58 & cast(u64, 0xff))); + const x60 = cast(u8, (x58 >> 8)); out1[0] = x5; out1[1] = x7; out1[2] = x9; @@ -1398,7 +1426,7 @@ pub fn p256ToBytes(out1: *[32]u8, arg1: Limbs) void { out1[31] = x60; } -/// The function p256FromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. +/// The function fromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. /// Preconditions: /// 0 ≤ bytes_eval arg1 < m /// Postconditions: @@ -1409,74 +1437,76 @@ pub fn p256ToBytes(out1: *[32]u8, arg1: Limbs) void { /// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256FromBytes(out1: *Limbs, arg1: [32]u8) void { - const x1: u64 = (@intCast(u64, (arg1[31])) << 56); - const x2: u64 = (@intCast(u64, (arg1[30])) << 48); - const x3: u64 = (@intCast(u64, (arg1[29])) << 40); - const x4: u64 = (@intCast(u64, (arg1[28])) << 32); - const x5: u64 = (@intCast(u64, (arg1[27])) << 24); - const x6: u64 = (@intCast(u64, (arg1[26])) << 16); - const x7: u64 = (@intCast(u64, (arg1[25])) << 8); - const x8: u8 = (arg1[24]); - const x9: u64 = (@intCast(u64, (arg1[23])) << 56); - const x10: u64 = (@intCast(u64, (arg1[22])) << 48); - const x11: u64 = (@intCast(u64, (arg1[21])) << 40); - const x12: u64 = (@intCast(u64, (arg1[20])) << 32); - const x13: u64 = (@intCast(u64, (arg1[19])) << 24); - const x14: u64 = (@intCast(u64, (arg1[18])) << 16); - const x15: u64 = (@intCast(u64, (arg1[17])) << 8); - const x16: u8 = (arg1[16]); - const x17: u64 = (@intCast(u64, (arg1[15])) << 56); - const x18: u64 = (@intCast(u64, (arg1[14])) << 48); - const x19: u64 = (@intCast(u64, (arg1[13])) << 40); - const x20: u64 = (@intCast(u64, (arg1[12])) << 32); - const x21: u64 = (@intCast(u64, (arg1[11])) << 24); - const x22: u64 = (@intCast(u64, (arg1[10])) << 16); - const x23: u64 = (@intCast(u64, (arg1[9])) << 8); - const x24: u8 = (arg1[8]); - const x25: u64 = (@intCast(u64, (arg1[7])) << 56); - const x26: u64 = (@intCast(u64, (arg1[6])) << 48); - const x27: u64 = (@intCast(u64, (arg1[5])) << 40); - const x28: u64 = (@intCast(u64, (arg1[4])) << 32); - const x29: u64 = (@intCast(u64, (arg1[3])) << 24); - const x30: u64 = (@intCast(u64, (arg1[2])) << 16); - const x31: u64 = (@intCast(u64, (arg1[1])) << 8); - const x32: u8 = (arg1[0]); - const x33: u64 = (x31 + @intCast(u64, x32)); - const x34: u64 = (x30 + x33); - const x35: u64 = (x29 + x34); - const x36: u64 = (x28 + x35); - const x37: u64 = (x27 + x36); - const x38: u64 = (x26 + x37); - const x39: u64 = (x25 + x38); - const x40: u64 = (x23 + @intCast(u64, x24)); - const x41: u64 = (x22 + x40); - const x42: u64 = (x21 + x41); - const x43: u64 = (x20 + x42); - const x44: u64 = (x19 + x43); - const x45: u64 = (x18 + x44); - const x46: u64 = (x17 + x45); - const x47: u64 = (x15 + @intCast(u64, x16)); - const x48: u64 = (x14 + x47); - const x49: u64 = (x13 + x48); - const x50: u64 = (x12 + x49); - const x51: u64 = (x11 + x50); - const x52: u64 = (x10 + x51); - const x53: u64 = (x9 + x52); - const x54: u64 = (x7 + @intCast(u64, x8)); - const x55: u64 = (x6 + x54); - const x56: u64 = (x5 + x55); - const x57: u64 = (x4 + x56); - const x58: u64 = (x3 + x57); - const x59: u64 = (x2 + x58); - const x60: u64 = (x1 + x59); +pub fn fromBytes(out1: *[4]u64, arg1: [32]u8) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (cast(u64, (arg1[31])) << 56); + const x2 = (cast(u64, (arg1[30])) << 48); + const x3 = (cast(u64, (arg1[29])) << 40); + const x4 = (cast(u64, (arg1[28])) << 32); + const x5 = (cast(u64, (arg1[27])) << 24); + const x6 = (cast(u64, (arg1[26])) << 16); + const x7 = (cast(u64, (arg1[25])) << 8); + const x8 = (arg1[24]); + const x9 = (cast(u64, (arg1[23])) << 56); + const x10 = (cast(u64, (arg1[22])) << 48); + const x11 = (cast(u64, (arg1[21])) << 40); + const x12 = (cast(u64, (arg1[20])) << 32); + const x13 = (cast(u64, (arg1[19])) << 24); + const x14 = (cast(u64, (arg1[18])) << 16); + const x15 = (cast(u64, (arg1[17])) << 8); + const x16 = (arg1[16]); + const x17 = (cast(u64, (arg1[15])) << 56); + const x18 = (cast(u64, (arg1[14])) << 48); + const x19 = (cast(u64, (arg1[13])) << 40); + const x20 = (cast(u64, (arg1[12])) << 32); + const x21 = (cast(u64, (arg1[11])) << 24); + const x22 = (cast(u64, (arg1[10])) << 16); + const x23 = (cast(u64, (arg1[9])) << 8); + const x24 = (arg1[8]); + const x25 = (cast(u64, (arg1[7])) << 56); + const x26 = (cast(u64, (arg1[6])) << 48); + const x27 = (cast(u64, (arg1[5])) << 40); + const x28 = (cast(u64, (arg1[4])) << 32); + const x29 = (cast(u64, (arg1[3])) << 24); + const x30 = (cast(u64, (arg1[2])) << 16); + const x31 = (cast(u64, (arg1[1])) << 8); + const x32 = (arg1[0]); + const x33 = (x31 + cast(u64, x32)); + const x34 = (x30 + x33); + const x35 = (x29 + x34); + const x36 = (x28 + x35); + const x37 = (x27 + x36); + const x38 = (x26 + x37); + const x39 = (x25 + x38); + const x40 = (x23 + cast(u64, x24)); + const x41 = (x22 + x40); + const x42 = (x21 + x41); + const x43 = (x20 + x42); + const x44 = (x19 + x43); + const x45 = (x18 + x44); + const x46 = (x17 + x45); + const x47 = (x15 + cast(u64, x16)); + const x48 = (x14 + x47); + const x49 = (x13 + x48); + const x50 = (x12 + x49); + const x51 = (x11 + x50); + const x52 = (x10 + x51); + const x53 = (x9 + x52); + const x54 = (x7 + cast(u64, x8)); + const x55 = (x6 + x54); + const x56 = (x5 + x55); + const x57 = (x4 + x56); + const x58 = (x3 + x57); + const x59 = (x2 + x58); + const x60 = (x1 + x59); out1[0] = x39; out1[1] = x46; out1[2] = x53; out1[3] = x60; } -/// The function p256SetOne returns the field element one in the Montgomery domain. +/// The function setOne returns the field element one in the Montgomery domain. /// Postconditions: /// eval (from_montgomery out1) mod m = 1 mod m /// 0 ≤ eval out1 < m @@ -1484,14 +1514,16 @@ pub fn p256FromBytes(out1: *Limbs, arg1: [32]u8) void { /// Input Bounds: /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256SetOne(out1: *Limbs) void { - out1[0] = @intCast(u64, 0x1); +pub fn setOne(out1: *[4]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = cast(u64, 0x1); out1[1] = 0xffffffff00000000; out1[2] = 0xffffffffffffffff; out1[3] = 0xfffffffe; } -/// The function p256Msat returns the saturated representation of the prime modulus. +/// The function msat returns the saturated representation of the prime modulus. /// Postconditions: /// twos_complement_eval out1 = m /// 0 ≤ eval out1 < m @@ -1499,15 +1531,17 @@ pub fn p256SetOne(out1: *Limbs) void { /// Input Bounds: /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Msat(out1: *[5]u64) void { +pub fn msat(out1: *[5]u64) void { + @setRuntimeSafety(mode == .Debug); + out1[0] = 0xffffffffffffffff; out1[1] = 0xffffffff; - out1[2] = @intCast(u64, 0x0); + out1[2] = cast(u64, 0x0); out1[3] = 0xffffffff00000001; - out1[4] = @intCast(u64, 0x0); + out1[4] = cast(u64, 0x0); } -/// The function p256Divstep computes a divstep. +/// The function divstep computes a divstep. /// Preconditions: /// 0 ≤ eval arg4 < m /// 0 ≤ eval arg5 < m @@ -1534,209 +1568,211 @@ pub fn p256Msat(out1: *[5]u64) void { /// out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] /// out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256Divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *Limbs, out5: *Limbs, arg1: u64, arg2: [5]u64, arg3: [5]u64, arg4: Limbs, arg5: Limbs) void { +pub fn divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *[4]u64, out5: *[4]u64, arg1: u64, arg2: [5]u64, arg3: [5]u64, arg4: [4]u64, arg5: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + var x1: u64 = undefined; var x2: u1 = undefined; - p256AddcarryxU64(&x1, &x2, 0x0, (~arg1), @intCast(u64, 0x1)); - const x3: u1 = (@intCast(u1, (x1 >> 63)) & @intCast(u1, ((arg3[0]) & @intCast(u64, 0x1)))); + addcarryxU64(&x1, &x2, 0x0, (~arg1), cast(u64, 0x1)); + const x3 = (cast(u1, (x1 >> 63)) & cast(u1, ((arg3[0]) & cast(u64, 0x1)))); var x4: u64 = undefined; var x5: u1 = undefined; - p256AddcarryxU64(&x4, &x5, 0x0, (~arg1), @intCast(u64, 0x1)); + addcarryxU64(&x4, &x5, 0x0, (~arg1), cast(u64, 0x1)); var x6: u64 = undefined; - p256CmovznzU64(&x6, x3, arg1, x4); + cmovznzU64(&x6, x3, arg1, x4); var x7: u64 = undefined; - p256CmovznzU64(&x7, x3, (arg2[0]), (arg3[0])); + cmovznzU64(&x7, x3, (arg2[0]), (arg3[0])); var x8: u64 = undefined; - p256CmovznzU64(&x8, x3, (arg2[1]), (arg3[1])); + cmovznzU64(&x8, x3, (arg2[1]), (arg3[1])); var x9: u64 = undefined; - p256CmovznzU64(&x9, x3, (arg2[2]), (arg3[2])); + cmovznzU64(&x9, x3, (arg2[2]), (arg3[2])); var x10: u64 = undefined; - p256CmovznzU64(&x10, x3, (arg2[3]), (arg3[3])); + cmovznzU64(&x10, x3, (arg2[3]), (arg3[3])); var x11: u64 = undefined; - p256CmovznzU64(&x11, x3, (arg2[4]), (arg3[4])); + cmovznzU64(&x11, x3, (arg2[4]), (arg3[4])); var x12: u64 = undefined; var x13: u1 = undefined; - p256AddcarryxU64(&x12, &x13, 0x0, @intCast(u64, 0x1), (~(arg2[0]))); + addcarryxU64(&x12, &x13, 0x0, cast(u64, 0x1), (~(arg2[0]))); var x14: u64 = undefined; var x15: u1 = undefined; - p256AddcarryxU64(&x14, &x15, x13, @intCast(u64, 0x0), (~(arg2[1]))); + addcarryxU64(&x14, &x15, x13, cast(u64, 0x0), (~(arg2[1]))); var x16: u64 = undefined; var x17: u1 = undefined; - p256AddcarryxU64(&x16, &x17, x15, @intCast(u64, 0x0), (~(arg2[2]))); + addcarryxU64(&x16, &x17, x15, cast(u64, 0x0), (~(arg2[2]))); var x18: u64 = undefined; var x19: u1 = undefined; - p256AddcarryxU64(&x18, &x19, x17, @intCast(u64, 0x0), (~(arg2[3]))); + addcarryxU64(&x18, &x19, x17, cast(u64, 0x0), (~(arg2[3]))); var x20: u64 = undefined; var x21: u1 = undefined; - p256AddcarryxU64(&x20, &x21, x19, @intCast(u64, 0x0), (~(arg2[4]))); + addcarryxU64(&x20, &x21, x19, cast(u64, 0x0), (~(arg2[4]))); var x22: u64 = undefined; - p256CmovznzU64(&x22, x3, (arg3[0]), x12); + cmovznzU64(&x22, x3, (arg3[0]), x12); var x23: u64 = undefined; - p256CmovznzU64(&x23, x3, (arg3[1]), x14); + cmovznzU64(&x23, x3, (arg3[1]), x14); var x24: u64 = undefined; - p256CmovznzU64(&x24, x3, (arg3[2]), x16); + cmovznzU64(&x24, x3, (arg3[2]), x16); var x25: u64 = undefined; - p256CmovznzU64(&x25, x3, (arg3[3]), x18); + cmovznzU64(&x25, x3, (arg3[3]), x18); var x26: u64 = undefined; - p256CmovznzU64(&x26, x3, (arg3[4]), x20); + cmovznzU64(&x26, x3, (arg3[4]), x20); var x27: u64 = undefined; - p256CmovznzU64(&x27, x3, (arg4[0]), (arg5[0])); + cmovznzU64(&x27, x3, (arg4[0]), (arg5[0])); var x28: u64 = undefined; - p256CmovznzU64(&x28, x3, (arg4[1]), (arg5[1])); + cmovznzU64(&x28, x3, (arg4[1]), (arg5[1])); var x29: u64 = undefined; - p256CmovznzU64(&x29, x3, (arg4[2]), (arg5[2])); + cmovznzU64(&x29, x3, (arg4[2]), (arg5[2])); var x30: u64 = undefined; - p256CmovznzU64(&x30, x3, (arg4[3]), (arg5[3])); + cmovznzU64(&x30, x3, (arg4[3]), (arg5[3])); var x31: u64 = undefined; var x32: u1 = undefined; - p256AddcarryxU64(&x31, &x32, 0x0, x27, x27); + addcarryxU64(&x31, &x32, 0x0, x27, x27); var x33: u64 = undefined; var x34: u1 = undefined; - p256AddcarryxU64(&x33, &x34, x32, x28, x28); + addcarryxU64(&x33, &x34, x32, x28, x28); var x35: u64 = undefined; var x36: u1 = undefined; - p256AddcarryxU64(&x35, &x36, x34, x29, x29); + addcarryxU64(&x35, &x36, x34, x29, x29); var x37: u64 = undefined; var x38: u1 = undefined; - p256AddcarryxU64(&x37, &x38, x36, x30, x30); + addcarryxU64(&x37, &x38, x36, x30, x30); var x39: u64 = undefined; var x40: u1 = undefined; - p256SubborrowxU64(&x39, &x40, 0x0, x31, 0xffffffffffffffff); + subborrowxU64(&x39, &x40, 0x0, x31, 0xffffffffffffffff); var x41: u64 = undefined; var x42: u1 = undefined; - p256SubborrowxU64(&x41, &x42, x40, x33, 0xffffffff); + subborrowxU64(&x41, &x42, x40, x33, 0xffffffff); var x43: u64 = undefined; var x44: u1 = undefined; - p256SubborrowxU64(&x43, &x44, x42, x35, @intCast(u64, 0x0)); + subborrowxU64(&x43, &x44, x42, x35, cast(u64, 0x0)); var x45: u64 = undefined; var x46: u1 = undefined; - p256SubborrowxU64(&x45, &x46, x44, x37, 0xffffffff00000001); + subborrowxU64(&x45, &x46, x44, x37, 0xffffffff00000001); var x47: u64 = undefined; var x48: u1 = undefined; - p256SubborrowxU64(&x47, &x48, x46, @intCast(u64, x38), @intCast(u64, 0x0)); - const x49: u64 = (arg4[3]); - const x50: u64 = (arg4[2]); - const x51: u64 = (arg4[1]); - const x52: u64 = (arg4[0]); + subborrowxU64(&x47, &x48, x46, cast(u64, x38), cast(u64, 0x0)); + const x49 = (arg4[3]); + const x50 = (arg4[2]); + const x51 = (arg4[1]); + const x52 = (arg4[0]); var x53: u64 = undefined; var x54: u1 = undefined; - p256SubborrowxU64(&x53, &x54, 0x0, @intCast(u64, 0x0), x52); + subborrowxU64(&x53, &x54, 0x0, cast(u64, 0x0), x52); var x55: u64 = undefined; var x56: u1 = undefined; - p256SubborrowxU64(&x55, &x56, x54, @intCast(u64, 0x0), x51); + subborrowxU64(&x55, &x56, x54, cast(u64, 0x0), x51); var x57: u64 = undefined; var x58: u1 = undefined; - p256SubborrowxU64(&x57, &x58, x56, @intCast(u64, 0x0), x50); + subborrowxU64(&x57, &x58, x56, cast(u64, 0x0), x50); var x59: u64 = undefined; var x60: u1 = undefined; - p256SubborrowxU64(&x59, &x60, x58, @intCast(u64, 0x0), x49); + subborrowxU64(&x59, &x60, x58, cast(u64, 0x0), x49); var x61: u64 = undefined; - p256CmovznzU64(&x61, x60, @intCast(u64, 0x0), 0xffffffffffffffff); + cmovznzU64(&x61, x60, cast(u64, 0x0), 0xffffffffffffffff); var x62: u64 = undefined; var x63: u1 = undefined; - p256AddcarryxU64(&x62, &x63, 0x0, x53, x61); + addcarryxU64(&x62, &x63, 0x0, x53, x61); var x64: u64 = undefined; var x65: u1 = undefined; - p256AddcarryxU64(&x64, &x65, x63, x55, (x61 & 0xffffffff)); + addcarryxU64(&x64, &x65, x63, x55, (x61 & 0xffffffff)); var x66: u64 = undefined; var x67: u1 = undefined; - p256AddcarryxU64(&x66, &x67, x65, x57, @intCast(u64, 0x0)); + addcarryxU64(&x66, &x67, x65, x57, cast(u64, 0x0)); var x68: u64 = undefined; var x69: u1 = undefined; - p256AddcarryxU64(&x68, &x69, x67, x59, (x61 & 0xffffffff00000001)); + addcarryxU64(&x68, &x69, x67, x59, (x61 & 0xffffffff00000001)); var x70: u64 = undefined; - p256CmovznzU64(&x70, x3, (arg5[0]), x62); + cmovznzU64(&x70, x3, (arg5[0]), x62); var x71: u64 = undefined; - p256CmovznzU64(&x71, x3, (arg5[1]), x64); + cmovznzU64(&x71, x3, (arg5[1]), x64); var x72: u64 = undefined; - p256CmovznzU64(&x72, x3, (arg5[2]), x66); + cmovznzU64(&x72, x3, (arg5[2]), x66); var x73: u64 = undefined; - p256CmovznzU64(&x73, x3, (arg5[3]), x68); - const x74: u1 = @intCast(u1, (x22 & @intCast(u64, 0x1))); + cmovznzU64(&x73, x3, (arg5[3]), x68); + const x74 = cast(u1, (x22 & cast(u64, 0x1))); var x75: u64 = undefined; - p256CmovznzU64(&x75, x74, @intCast(u64, 0x0), x7); + cmovznzU64(&x75, x74, cast(u64, 0x0), x7); var x76: u64 = undefined; - p256CmovznzU64(&x76, x74, @intCast(u64, 0x0), x8); + cmovznzU64(&x76, x74, cast(u64, 0x0), x8); var x77: u64 = undefined; - p256CmovznzU64(&x77, x74, @intCast(u64, 0x0), x9); + cmovznzU64(&x77, x74, cast(u64, 0x0), x9); var x78: u64 = undefined; - p256CmovznzU64(&x78, x74, @intCast(u64, 0x0), x10); + cmovznzU64(&x78, x74, cast(u64, 0x0), x10); var x79: u64 = undefined; - p256CmovznzU64(&x79, x74, @intCast(u64, 0x0), x11); + cmovznzU64(&x79, x74, cast(u64, 0x0), x11); var x80: u64 = undefined; var x81: u1 = undefined; - p256AddcarryxU64(&x80, &x81, 0x0, x22, x75); + addcarryxU64(&x80, &x81, 0x0, x22, x75); var x82: u64 = undefined; var x83: u1 = undefined; - p256AddcarryxU64(&x82, &x83, x81, x23, x76); + addcarryxU64(&x82, &x83, x81, x23, x76); var x84: u64 = undefined; var x85: u1 = undefined; - p256AddcarryxU64(&x84, &x85, x83, x24, x77); + addcarryxU64(&x84, &x85, x83, x24, x77); var x86: u64 = undefined; var x87: u1 = undefined; - p256AddcarryxU64(&x86, &x87, x85, x25, x78); + addcarryxU64(&x86, &x87, x85, x25, x78); var x88: u64 = undefined; var x89: u1 = undefined; - p256AddcarryxU64(&x88, &x89, x87, x26, x79); + addcarryxU64(&x88, &x89, x87, x26, x79); var x90: u64 = undefined; - p256CmovznzU64(&x90, x74, @intCast(u64, 0x0), x27); + cmovznzU64(&x90, x74, cast(u64, 0x0), x27); var x91: u64 = undefined; - p256CmovznzU64(&x91, x74, @intCast(u64, 0x0), x28); + cmovznzU64(&x91, x74, cast(u64, 0x0), x28); var x92: u64 = undefined; - p256CmovznzU64(&x92, x74, @intCast(u64, 0x0), x29); + cmovznzU64(&x92, x74, cast(u64, 0x0), x29); var x93: u64 = undefined; - p256CmovznzU64(&x93, x74, @intCast(u64, 0x0), x30); + cmovznzU64(&x93, x74, cast(u64, 0x0), x30); var x94: u64 = undefined; var x95: u1 = undefined; - p256AddcarryxU64(&x94, &x95, 0x0, x70, x90); + addcarryxU64(&x94, &x95, 0x0, x70, x90); var x96: u64 = undefined; var x97: u1 = undefined; - p256AddcarryxU64(&x96, &x97, x95, x71, x91); + addcarryxU64(&x96, &x97, x95, x71, x91); var x98: u64 = undefined; var x99: u1 = undefined; - p256AddcarryxU64(&x98, &x99, x97, x72, x92); + addcarryxU64(&x98, &x99, x97, x72, x92); var x100: u64 = undefined; var x101: u1 = undefined; - p256AddcarryxU64(&x100, &x101, x99, x73, x93); + addcarryxU64(&x100, &x101, x99, x73, x93); var x102: u64 = undefined; var x103: u1 = undefined; - p256SubborrowxU64(&x102, &x103, 0x0, x94, 0xffffffffffffffff); + subborrowxU64(&x102, &x103, 0x0, x94, 0xffffffffffffffff); var x104: u64 = undefined; var x105: u1 = undefined; - p256SubborrowxU64(&x104, &x105, x103, x96, 0xffffffff); + subborrowxU64(&x104, &x105, x103, x96, 0xffffffff); var x106: u64 = undefined; var x107: u1 = undefined; - p256SubborrowxU64(&x106, &x107, x105, x98, @intCast(u64, 0x0)); + subborrowxU64(&x106, &x107, x105, x98, cast(u64, 0x0)); var x108: u64 = undefined; var x109: u1 = undefined; - p256SubborrowxU64(&x108, &x109, x107, x100, 0xffffffff00000001); + subborrowxU64(&x108, &x109, x107, x100, 0xffffffff00000001); var x110: u64 = undefined; var x111: u1 = undefined; - p256SubborrowxU64(&x110, &x111, x109, @intCast(u64, x101), @intCast(u64, 0x0)); + subborrowxU64(&x110, &x111, x109, cast(u64, x101), cast(u64, 0x0)); var x112: u64 = undefined; var x113: u1 = undefined; - p256AddcarryxU64(&x112, &x113, 0x0, x6, @intCast(u64, 0x1)); - const x114: u64 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff)); - const x115: u64 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff)); - const x116: u64 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff)); - const x117: u64 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff)); - const x118: u64 = ((x88 & 0x8000000000000000) | (x88 >> 1)); + addcarryxU64(&x112, &x113, 0x0, x6, cast(u64, 0x1)); + const x114 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff)); + const x115 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff)); + const x116 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff)); + const x117 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff)); + const x118 = ((x88 & 0x8000000000000000) | (x88 >> 1)); var x119: u64 = undefined; - p256CmovznzU64(&x119, x48, x39, x31); + cmovznzU64(&x119, x48, x39, x31); var x120: u64 = undefined; - p256CmovznzU64(&x120, x48, x41, x33); + cmovznzU64(&x120, x48, x41, x33); var x121: u64 = undefined; - p256CmovznzU64(&x121, x48, x43, x35); + cmovznzU64(&x121, x48, x43, x35); var x122: u64 = undefined; - p256CmovznzU64(&x122, x48, x45, x37); + cmovznzU64(&x122, x48, x45, x37); var x123: u64 = undefined; - p256CmovznzU64(&x123, x111, x102, x94); + cmovznzU64(&x123, x111, x102, x94); var x124: u64 = undefined; - p256CmovznzU64(&x124, x111, x104, x96); + cmovznzU64(&x124, x111, x104, x96); var x125: u64 = undefined; - p256CmovznzU64(&x125, x111, x106, x98); + cmovznzU64(&x125, x111, x106, x98); var x126: u64 = undefined; - p256CmovznzU64(&x126, x111, x108, x100); + cmovznzU64(&x126, x111, x108, x100); out1.* = x112; out2[0] = x7; out2[1] = x8; @@ -1758,7 +1794,7 @@ pub fn p256Divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *Limbs, out5: out5[3] = x126; } -/// The function p256DivstepPrecomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form). +/// The function divstepPrecomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form). /// Postconditions: /// eval (from_montgomery out1) = ⌊(m - 1) / 2⌋^(if (log2 m) + 1 < 46 then ⌊(49 * ((log2 m) + 1) + 80) / 17⌋ else ⌊(49 * ((log2 m) + 1) + 57) / 17⌋) /// 0 ≤ eval out1 < m @@ -1766,7 +1802,9 @@ pub fn p256Divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *Limbs, out5: /// Input Bounds: /// Output Bounds: /// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] -pub fn p256DivstepPrecomp(out1: *Limbs) void { +pub fn divstepPrecomp(out1: *[4]u64) void { + @setRuntimeSafety(mode == .Debug); + out1[0] = 0x67ffffffb8000000; out1[1] = 0xc000000038000000; out1[2] = 0xd80000007fffffff; diff --git a/lib/std/crypto/pcurves/p256/p256_scalar_64.zig b/lib/std/crypto/pcurves/p256/p256_scalar_64.zig new file mode 100644 index 0000000000..7e3cc211f5 --- /dev/null +++ b/lib/std/crypto/pcurves/p256/p256_scalar_64.zig @@ -0,0 +1,2016 @@ +// Autogenerated: './src/ExtractionOCaml/word_by_word_montgomery' --lang Zig --internal-static --public-function-case camelCase --private-function-case camelCase --no-prefix-fiat --package-name p256-scalar '' 64 115792089210356248762697446949407573529996955224135760342422259061068512044369 +// curve description (via package name): p256-scalar +// machine_wordsize = 64 (from "64") +// requested operations: (all) +// m = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 (from "115792089210356248762697446949407573529996955224135760342422259061068512044369") +// +// NOTE: In addition to the bounds specified above each function, all +// functions synthesized for this Montgomery arithmetic require the +// input to be strictly less than the prime modulus (m), and also +// require the input to be in the unique saturated representation. +// All functions also ensure that these two properties are true of +// return values. +// +// Computed values: +// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) +// bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in +// if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 + +const std = @import("std"); +const cast = std.meta.cast; +const mode = std.builtin.mode; // Checked arithmetic is disabled in non-debug modes to avoid side channels + +pub const Limbs = [4]u64; + +/// The function addcarryxU64 is an addition with carry. +/// Postconditions: +/// out1 = (arg1 + arg2 + arg3) mod 2^64 +/// out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0x1] +fn addcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + + var t: u64 = undefined; + const carry1 = @addWithOverflow(u64, arg2, arg3, &t); + const carry2 = @addWithOverflow(u64, t, arg1, out1); + out2.* = @boolToInt(carry1) | @boolToInt(carry2); +} + +/// The function subborrowxU64 is a subtraction with borrow. +/// Postconditions: +/// out1 = (-arg1 + arg2 + -arg3) mod 2^64 +/// out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0x1] +fn subborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + + var t: u64 = undefined; + const carry1 = @subWithOverflow(u64, arg2, arg3, &t); + const carry2 = @subWithOverflow(u64, t, arg1, out1); + out2.* = @boolToInt(carry1) | @boolToInt(carry2); +} + +/// The function mulxU64 is a multiplication, returning the full double-width result. +/// Postconditions: +/// out1 = (arg1 * arg2) mod 2^64 +/// out2 = ⌊arg1 * arg2 / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0xffffffffffffffff] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0xffffffffffffffff] +fn mulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + + const x = @as(u128, arg1) * @as(u128, arg2); + out1.* = @truncate(u64, x); + out2.* = @truncate(u64, x >> 64); +} + +/// The function cmovznzU64 is a single-word conditional move. +/// Postconditions: +/// out1 = (if arg1 = 0 then arg2 else arg3) +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +fn cmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + @setRuntimeSafety(mode == .Debug); + + const mask = 0 -% @as(u64, arg1); + out1.* = (mask & arg3) | ((~mask) & arg2); +} + +/// The function mul multiplies two field elements in the Montgomery domain. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn mul(out1: *[4]u64, arg1: [4]u64, arg2: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, (arg2[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, (arg2[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, (arg2[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, (arg2[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (cast(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + mulxU64(&x20, &x21, x11, 0xccd1c8aaee00bc4f); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0xffffffff00000000); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xffffffffffffffff); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0xbce6faada7179e84); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0xf3b9cac2fc632551); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, 0x0, x29, x26); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x27, x24); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x25, x22); + const x36 = (cast(u64, x35) + x23); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, 0x0, x11, x28); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x13, x30); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x15, x32); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, x17, x34); + var x45: u64 = undefined; + var x46: u1 = undefined; + addcarryxU64(&x45, &x46, x44, x19, x36); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, (arg2[3])); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, (arg2[2])); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, (arg2[1])); + var x53: u64 = undefined; + var x54: u64 = undefined; + mulxU64(&x53, &x54, x1, (arg2[0])); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, 0x0, x54, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x52, x49); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x50, x47); + const x61 = (cast(u64, x60) + x48); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x39, x53); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x41, x55); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x43, x57); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x45, x59); + var x70: u64 = undefined; + var x71: u1 = undefined; + addcarryxU64(&x70, &x71, x69, cast(u64, x46), x61); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x62, 0xccd1c8aaee00bc4f); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0xffffffff00000000); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xffffffffffffffff); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0xbce6faada7179e84); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0xf3b9cac2fc632551); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, 0x0, x81, x78); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x79, x76); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x77, x74); + const x88 = (cast(u64, x87) + x75); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, 0x0, x62, x80); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, x64, x82); + var x93: u64 = undefined; + var x94: u1 = undefined; + addcarryxU64(&x93, &x94, x92, x66, x84); + var x95: u64 = undefined; + var x96: u1 = undefined; + addcarryxU64(&x95, &x96, x94, x68, x86); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, x96, x70, x88); + const x99 = (cast(u64, x98) + cast(u64, x71)); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x2, (arg2[3])); + var x102: u64 = undefined; + var x103: u64 = undefined; + mulxU64(&x102, &x103, x2, (arg2[2])); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x2, (arg2[1])); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x2, (arg2[0])); + var x108: u64 = undefined; + var x109: u1 = undefined; + addcarryxU64(&x108, &x109, 0x0, x107, x104); + var x110: u64 = undefined; + var x111: u1 = undefined; + addcarryxU64(&x110, &x111, x109, x105, x102); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, x111, x103, x100); + const x114 = (cast(u64, x113) + x101); + var x115: u64 = undefined; + var x116: u1 = undefined; + addcarryxU64(&x115, &x116, 0x0, x91, x106); + var x117: u64 = undefined; + var x118: u1 = undefined; + addcarryxU64(&x117, &x118, x116, x93, x108); + var x119: u64 = undefined; + var x120: u1 = undefined; + addcarryxU64(&x119, &x120, x118, x95, x110); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, x120, x97, x112); + var x123: u64 = undefined; + var x124: u1 = undefined; + addcarryxU64(&x123, &x124, x122, x99, x114); + var x125: u64 = undefined; + var x126: u64 = undefined; + mulxU64(&x125, &x126, x115, 0xccd1c8aaee00bc4f); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0xffffffff00000000); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xffffffffffffffff); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0xbce6faada7179e84); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0xf3b9cac2fc632551); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, 0x0, x134, x131); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x132, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, x130, x127); + const x141 = (cast(u64, x140) + x128); + var x142: u64 = undefined; + var x143: u1 = undefined; + addcarryxU64(&x142, &x143, 0x0, x115, x133); + var x144: u64 = undefined; + var x145: u1 = undefined; + addcarryxU64(&x144, &x145, x143, x117, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + addcarryxU64(&x146, &x147, x145, x119, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + addcarryxU64(&x148, &x149, x147, x121, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + addcarryxU64(&x150, &x151, x149, x123, x141); + const x152 = (cast(u64, x151) + cast(u64, x124)); + var x153: u64 = undefined; + var x154: u64 = undefined; + mulxU64(&x153, &x154, x3, (arg2[3])); + var x155: u64 = undefined; + var x156: u64 = undefined; + mulxU64(&x155, &x156, x3, (arg2[2])); + var x157: u64 = undefined; + var x158: u64 = undefined; + mulxU64(&x157, &x158, x3, (arg2[1])); + var x159: u64 = undefined; + var x160: u64 = undefined; + mulxU64(&x159, &x160, x3, (arg2[0])); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, 0x0, x160, x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + addcarryxU64(&x163, &x164, x162, x158, x155); + var x165: u64 = undefined; + var x166: u1 = undefined; + addcarryxU64(&x165, &x166, x164, x156, x153); + const x167 = (cast(u64, x166) + x154); + var x168: u64 = undefined; + var x169: u1 = undefined; + addcarryxU64(&x168, &x169, 0x0, x144, x159); + var x170: u64 = undefined; + var x171: u1 = undefined; + addcarryxU64(&x170, &x171, x169, x146, x161); + var x172: u64 = undefined; + var x173: u1 = undefined; + addcarryxU64(&x172, &x173, x171, x148, x163); + var x174: u64 = undefined; + var x175: u1 = undefined; + addcarryxU64(&x174, &x175, x173, x150, x165); + var x176: u64 = undefined; + var x177: u1 = undefined; + addcarryxU64(&x176, &x177, x175, x152, x167); + var x178: u64 = undefined; + var x179: u64 = undefined; + mulxU64(&x178, &x179, x168, 0xccd1c8aaee00bc4f); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0xffffffff00000000); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xffffffffffffffff); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0xbce6faada7179e84); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0xf3b9cac2fc632551); + var x188: u64 = undefined; + var x189: u1 = undefined; + addcarryxU64(&x188, &x189, 0x0, x187, x184); + var x190: u64 = undefined; + var x191: u1 = undefined; + addcarryxU64(&x190, &x191, x189, x185, x182); + var x192: u64 = undefined; + var x193: u1 = undefined; + addcarryxU64(&x192, &x193, x191, x183, x180); + const x194 = (cast(u64, x193) + x181); + var x195: u64 = undefined; + var x196: u1 = undefined; + addcarryxU64(&x195, &x196, 0x0, x168, x186); + var x197: u64 = undefined; + var x198: u1 = undefined; + addcarryxU64(&x197, &x198, x196, x170, x188); + var x199: u64 = undefined; + var x200: u1 = undefined; + addcarryxU64(&x199, &x200, x198, x172, x190); + var x201: u64 = undefined; + var x202: u1 = undefined; + addcarryxU64(&x201, &x202, x200, x174, x192); + var x203: u64 = undefined; + var x204: u1 = undefined; + addcarryxU64(&x203, &x204, x202, x176, x194); + const x205 = (cast(u64, x204) + cast(u64, x177)); + var x206: u64 = undefined; + var x207: u1 = undefined; + subborrowxU64(&x206, &x207, 0x0, x197, 0xf3b9cac2fc632551); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0xbce6faada7179e84); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xffffffffffffffff); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0xffffffff00000000); + var x214: u64 = undefined; + var x215: u1 = undefined; + subborrowxU64(&x214, &x215, x213, x205, cast(u64, 0x0)); + var x216: u64 = undefined; + cmovznzU64(&x216, x215, x206, x197); + var x217: u64 = undefined; + cmovznzU64(&x217, x215, x208, x199); + var x218: u64 = undefined; + cmovznzU64(&x218, x215, x210, x201); + var x219: u64 = undefined; + cmovznzU64(&x219, x215, x212, x203); + out1[0] = x216; + out1[1] = x217; + out1[2] = x218; + out1[3] = x219; +} + +/// The function square squares a field element in the Montgomery domain. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn square(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, (arg1[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, (arg1[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, (arg1[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, (arg1[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (cast(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + mulxU64(&x20, &x21, x11, 0xccd1c8aaee00bc4f); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0xffffffff00000000); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xffffffffffffffff); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0xbce6faada7179e84); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0xf3b9cac2fc632551); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, 0x0, x29, x26); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x27, x24); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x25, x22); + const x36 = (cast(u64, x35) + x23); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, 0x0, x11, x28); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x13, x30); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x15, x32); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, x17, x34); + var x45: u64 = undefined; + var x46: u1 = undefined; + addcarryxU64(&x45, &x46, x44, x19, x36); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, (arg1[3])); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, (arg1[2])); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, (arg1[1])); + var x53: u64 = undefined; + var x54: u64 = undefined; + mulxU64(&x53, &x54, x1, (arg1[0])); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, 0x0, x54, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x52, x49); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x50, x47); + const x61 = (cast(u64, x60) + x48); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x39, x53); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x41, x55); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x43, x57); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x45, x59); + var x70: u64 = undefined; + var x71: u1 = undefined; + addcarryxU64(&x70, &x71, x69, cast(u64, x46), x61); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x62, 0xccd1c8aaee00bc4f); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0xffffffff00000000); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xffffffffffffffff); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0xbce6faada7179e84); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0xf3b9cac2fc632551); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, 0x0, x81, x78); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x79, x76); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x77, x74); + const x88 = (cast(u64, x87) + x75); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, 0x0, x62, x80); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, x64, x82); + var x93: u64 = undefined; + var x94: u1 = undefined; + addcarryxU64(&x93, &x94, x92, x66, x84); + var x95: u64 = undefined; + var x96: u1 = undefined; + addcarryxU64(&x95, &x96, x94, x68, x86); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, x96, x70, x88); + const x99 = (cast(u64, x98) + cast(u64, x71)); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x2, (arg1[3])); + var x102: u64 = undefined; + var x103: u64 = undefined; + mulxU64(&x102, &x103, x2, (arg1[2])); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x2, (arg1[1])); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x2, (arg1[0])); + var x108: u64 = undefined; + var x109: u1 = undefined; + addcarryxU64(&x108, &x109, 0x0, x107, x104); + var x110: u64 = undefined; + var x111: u1 = undefined; + addcarryxU64(&x110, &x111, x109, x105, x102); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, x111, x103, x100); + const x114 = (cast(u64, x113) + x101); + var x115: u64 = undefined; + var x116: u1 = undefined; + addcarryxU64(&x115, &x116, 0x0, x91, x106); + var x117: u64 = undefined; + var x118: u1 = undefined; + addcarryxU64(&x117, &x118, x116, x93, x108); + var x119: u64 = undefined; + var x120: u1 = undefined; + addcarryxU64(&x119, &x120, x118, x95, x110); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, x120, x97, x112); + var x123: u64 = undefined; + var x124: u1 = undefined; + addcarryxU64(&x123, &x124, x122, x99, x114); + var x125: u64 = undefined; + var x126: u64 = undefined; + mulxU64(&x125, &x126, x115, 0xccd1c8aaee00bc4f); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0xffffffff00000000); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xffffffffffffffff); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0xbce6faada7179e84); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0xf3b9cac2fc632551); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, 0x0, x134, x131); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x132, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, x130, x127); + const x141 = (cast(u64, x140) + x128); + var x142: u64 = undefined; + var x143: u1 = undefined; + addcarryxU64(&x142, &x143, 0x0, x115, x133); + var x144: u64 = undefined; + var x145: u1 = undefined; + addcarryxU64(&x144, &x145, x143, x117, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + addcarryxU64(&x146, &x147, x145, x119, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + addcarryxU64(&x148, &x149, x147, x121, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + addcarryxU64(&x150, &x151, x149, x123, x141); + const x152 = (cast(u64, x151) + cast(u64, x124)); + var x153: u64 = undefined; + var x154: u64 = undefined; + mulxU64(&x153, &x154, x3, (arg1[3])); + var x155: u64 = undefined; + var x156: u64 = undefined; + mulxU64(&x155, &x156, x3, (arg1[2])); + var x157: u64 = undefined; + var x158: u64 = undefined; + mulxU64(&x157, &x158, x3, (arg1[1])); + var x159: u64 = undefined; + var x160: u64 = undefined; + mulxU64(&x159, &x160, x3, (arg1[0])); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, 0x0, x160, x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + addcarryxU64(&x163, &x164, x162, x158, x155); + var x165: u64 = undefined; + var x166: u1 = undefined; + addcarryxU64(&x165, &x166, x164, x156, x153); + const x167 = (cast(u64, x166) + x154); + var x168: u64 = undefined; + var x169: u1 = undefined; + addcarryxU64(&x168, &x169, 0x0, x144, x159); + var x170: u64 = undefined; + var x171: u1 = undefined; + addcarryxU64(&x170, &x171, x169, x146, x161); + var x172: u64 = undefined; + var x173: u1 = undefined; + addcarryxU64(&x172, &x173, x171, x148, x163); + var x174: u64 = undefined; + var x175: u1 = undefined; + addcarryxU64(&x174, &x175, x173, x150, x165); + var x176: u64 = undefined; + var x177: u1 = undefined; + addcarryxU64(&x176, &x177, x175, x152, x167); + var x178: u64 = undefined; + var x179: u64 = undefined; + mulxU64(&x178, &x179, x168, 0xccd1c8aaee00bc4f); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0xffffffff00000000); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xffffffffffffffff); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0xbce6faada7179e84); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0xf3b9cac2fc632551); + var x188: u64 = undefined; + var x189: u1 = undefined; + addcarryxU64(&x188, &x189, 0x0, x187, x184); + var x190: u64 = undefined; + var x191: u1 = undefined; + addcarryxU64(&x190, &x191, x189, x185, x182); + var x192: u64 = undefined; + var x193: u1 = undefined; + addcarryxU64(&x192, &x193, x191, x183, x180); + const x194 = (cast(u64, x193) + x181); + var x195: u64 = undefined; + var x196: u1 = undefined; + addcarryxU64(&x195, &x196, 0x0, x168, x186); + var x197: u64 = undefined; + var x198: u1 = undefined; + addcarryxU64(&x197, &x198, x196, x170, x188); + var x199: u64 = undefined; + var x200: u1 = undefined; + addcarryxU64(&x199, &x200, x198, x172, x190); + var x201: u64 = undefined; + var x202: u1 = undefined; + addcarryxU64(&x201, &x202, x200, x174, x192); + var x203: u64 = undefined; + var x204: u1 = undefined; + addcarryxU64(&x203, &x204, x202, x176, x194); + const x205 = (cast(u64, x204) + cast(u64, x177)); + var x206: u64 = undefined; + var x207: u1 = undefined; + subborrowxU64(&x206, &x207, 0x0, x197, 0xf3b9cac2fc632551); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0xbce6faada7179e84); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xffffffffffffffff); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0xffffffff00000000); + var x214: u64 = undefined; + var x215: u1 = undefined; + subborrowxU64(&x214, &x215, x213, x205, cast(u64, 0x0)); + var x216: u64 = undefined; + cmovznzU64(&x216, x215, x206, x197); + var x217: u64 = undefined; + cmovznzU64(&x217, x215, x208, x199); + var x218: u64 = undefined; + cmovznzU64(&x218, x215, x210, x201); + var x219: u64 = undefined; + cmovznzU64(&x219, x215, x212, x203); + out1[0] = x216; + out1[1] = x217; + out1[2] = x218; + out1[3] = x219; +} + +/// The function add adds two field elements in the Montgomery domain. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn add(out1: *[4]u64, arg1: [4]u64, arg2: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + addcarryxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + addcarryxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + addcarryxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + addcarryxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + var x10: u1 = undefined; + subborrowxU64(&x9, &x10, 0x0, x1, 0xf3b9cac2fc632551); + var x11: u64 = undefined; + var x12: u1 = undefined; + subborrowxU64(&x11, &x12, x10, x3, 0xbce6faada7179e84); + var x13: u64 = undefined; + var x14: u1 = undefined; + subborrowxU64(&x13, &x14, x12, x5, 0xffffffffffffffff); + var x15: u64 = undefined; + var x16: u1 = undefined; + subborrowxU64(&x15, &x16, x14, x7, 0xffffffff00000000); + var x17: u64 = undefined; + var x18: u1 = undefined; + subborrowxU64(&x17, &x18, x16, cast(u64, x8), cast(u64, 0x0)); + var x19: u64 = undefined; + cmovznzU64(&x19, x18, x9, x1); + var x20: u64 = undefined; + cmovznzU64(&x20, x18, x11, x3); + var x21: u64 = undefined; + cmovznzU64(&x21, x18, x13, x5); + var x22: u64 = undefined; + cmovznzU64(&x22, x18, x15, x7); + out1[0] = x19; + out1[1] = x20; + out1[2] = x21; + out1[3] = x22; +} + +/// The function sub subtracts two field elements in the Montgomery domain. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn sub(out1: *[4]u64, arg1: [4]u64, arg2: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + subborrowxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + subborrowxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + subborrowxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + subborrowxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + cmovznzU64(&x9, x8, cast(u64, 0x0), 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + addcarryxU64(&x10, &x11, 0x0, x1, (x9 & 0xf3b9cac2fc632551)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xbce6faada7179e84)); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, x9); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000000)); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function opp negates a field element in the Montgomery domain. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn opp(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + subborrowxU64(&x1, &x2, 0x0, cast(u64, 0x0), (arg1[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + subborrowxU64(&x3, &x4, x2, cast(u64, 0x0), (arg1[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + subborrowxU64(&x5, &x6, x4, cast(u64, 0x0), (arg1[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + subborrowxU64(&x7, &x8, x6, cast(u64, 0x0), (arg1[3])); + var x9: u64 = undefined; + cmovznzU64(&x9, x8, cast(u64, 0x0), 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + addcarryxU64(&x10, &x11, 0x0, x1, (x9 & 0xf3b9cac2fc632551)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xbce6faada7179e84)); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, x9); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000000)); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function fromMontgomery translates a field element out of the Montgomery domain. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn fromMontgomery(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[0]); + var x2: u64 = undefined; + var x3: u64 = undefined; + mulxU64(&x2, &x3, x1, 0xccd1c8aaee00bc4f); + var x4: u64 = undefined; + var x5: u64 = undefined; + mulxU64(&x4, &x5, x2, 0xffffffff00000000); + var x6: u64 = undefined; + var x7: u64 = undefined; + mulxU64(&x6, &x7, x2, 0xffffffffffffffff); + var x8: u64 = undefined; + var x9: u64 = undefined; + mulxU64(&x8, &x9, x2, 0xbce6faada7179e84); + var x10: u64 = undefined; + var x11: u64 = undefined; + mulxU64(&x10, &x11, x2, 0xf3b9cac2fc632551); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, 0x0, x11, x8); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x9, x6); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, x4); + var x18: u64 = undefined; + var x19: u1 = undefined; + addcarryxU64(&x18, &x19, 0x0, x1, x10); + var x20: u64 = undefined; + var x21: u1 = undefined; + addcarryxU64(&x20, &x21, x19, cast(u64, 0x0), x12); + var x22: u64 = undefined; + var x23: u1 = undefined; + addcarryxU64(&x22, &x23, x21, cast(u64, 0x0), x14); + var x24: u64 = undefined; + var x25: u1 = undefined; + addcarryxU64(&x24, &x25, x23, cast(u64, 0x0), x16); + var x26: u64 = undefined; + var x27: u1 = undefined; + addcarryxU64(&x26, &x27, 0x0, x20, (arg1[1])); + var x28: u64 = undefined; + var x29: u1 = undefined; + addcarryxU64(&x28, &x29, x27, x22, cast(u64, 0x0)); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, x29, x24, cast(u64, 0x0)); + var x32: u64 = undefined; + var x33: u64 = undefined; + mulxU64(&x32, &x33, x26, 0xccd1c8aaee00bc4f); + var x34: u64 = undefined; + var x35: u64 = undefined; + mulxU64(&x34, &x35, x32, 0xffffffff00000000); + var x36: u64 = undefined; + var x37: u64 = undefined; + mulxU64(&x36, &x37, x32, 0xffffffffffffffff); + var x38: u64 = undefined; + var x39: u64 = undefined; + mulxU64(&x38, &x39, x32, 0xbce6faada7179e84); + var x40: u64 = undefined; + var x41: u64 = undefined; + mulxU64(&x40, &x41, x32, 0xf3b9cac2fc632551); + var x42: u64 = undefined; + var x43: u1 = undefined; + addcarryxU64(&x42, &x43, 0x0, x41, x38); + var x44: u64 = undefined; + var x45: u1 = undefined; + addcarryxU64(&x44, &x45, x43, x39, x36); + var x46: u64 = undefined; + var x47: u1 = undefined; + addcarryxU64(&x46, &x47, x45, x37, x34); + var x48: u64 = undefined; + var x49: u1 = undefined; + addcarryxU64(&x48, &x49, 0x0, x26, x40); + var x50: u64 = undefined; + var x51: u1 = undefined; + addcarryxU64(&x50, &x51, x49, x28, x42); + var x52: u64 = undefined; + var x53: u1 = undefined; + addcarryxU64(&x52, &x53, x51, x30, x44); + var x54: u64 = undefined; + var x55: u1 = undefined; + addcarryxU64(&x54, &x55, x53, (cast(u64, x31) + (cast(u64, x25) + (cast(u64, x17) + x5))), x46); + var x56: u64 = undefined; + var x57: u1 = undefined; + addcarryxU64(&x56, &x57, 0x0, x50, (arg1[2])); + var x58: u64 = undefined; + var x59: u1 = undefined; + addcarryxU64(&x58, &x59, x57, x52, cast(u64, 0x0)); + var x60: u64 = undefined; + var x61: u1 = undefined; + addcarryxU64(&x60, &x61, x59, x54, cast(u64, 0x0)); + var x62: u64 = undefined; + var x63: u64 = undefined; + mulxU64(&x62, &x63, x56, 0xccd1c8aaee00bc4f); + var x64: u64 = undefined; + var x65: u64 = undefined; + mulxU64(&x64, &x65, x62, 0xffffffff00000000); + var x66: u64 = undefined; + var x67: u64 = undefined; + mulxU64(&x66, &x67, x62, 0xffffffffffffffff); + var x68: u64 = undefined; + var x69: u64 = undefined; + mulxU64(&x68, &x69, x62, 0xbce6faada7179e84); + var x70: u64 = undefined; + var x71: u64 = undefined; + mulxU64(&x70, &x71, x62, 0xf3b9cac2fc632551); + var x72: u64 = undefined; + var x73: u1 = undefined; + addcarryxU64(&x72, &x73, 0x0, x71, x68); + var x74: u64 = undefined; + var x75: u1 = undefined; + addcarryxU64(&x74, &x75, x73, x69, x66); + var x76: u64 = undefined; + var x77: u1 = undefined; + addcarryxU64(&x76, &x77, x75, x67, x64); + var x78: u64 = undefined; + var x79: u1 = undefined; + addcarryxU64(&x78, &x79, 0x0, x56, x70); + var x80: u64 = undefined; + var x81: u1 = undefined; + addcarryxU64(&x80, &x81, x79, x58, x72); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, x81, x60, x74); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, (cast(u64, x61) + (cast(u64, x55) + (cast(u64, x47) + x35))), x76); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, 0x0, x80, (arg1[3])); + var x88: u64 = undefined; + var x89: u1 = undefined; + addcarryxU64(&x88, &x89, x87, x82, cast(u64, 0x0)); + var x90: u64 = undefined; + var x91: u1 = undefined; + addcarryxU64(&x90, &x91, x89, x84, cast(u64, 0x0)); + var x92: u64 = undefined; + var x93: u64 = undefined; + mulxU64(&x92, &x93, x86, 0xccd1c8aaee00bc4f); + var x94: u64 = undefined; + var x95: u64 = undefined; + mulxU64(&x94, &x95, x92, 0xffffffff00000000); + var x96: u64 = undefined; + var x97: u64 = undefined; + mulxU64(&x96, &x97, x92, 0xffffffffffffffff); + var x98: u64 = undefined; + var x99: u64 = undefined; + mulxU64(&x98, &x99, x92, 0xbce6faada7179e84); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x92, 0xf3b9cac2fc632551); + var x102: u64 = undefined; + var x103: u1 = undefined; + addcarryxU64(&x102, &x103, 0x0, x101, x98); + var x104: u64 = undefined; + var x105: u1 = undefined; + addcarryxU64(&x104, &x105, x103, x99, x96); + var x106: u64 = undefined; + var x107: u1 = undefined; + addcarryxU64(&x106, &x107, x105, x97, x94); + var x108: u64 = undefined; + var x109: u1 = undefined; + addcarryxU64(&x108, &x109, 0x0, x86, x100); + var x110: u64 = undefined; + var x111: u1 = undefined; + addcarryxU64(&x110, &x111, x109, x88, x102); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, x111, x90, x104); + var x114: u64 = undefined; + var x115: u1 = undefined; + addcarryxU64(&x114, &x115, x113, (cast(u64, x91) + (cast(u64, x85) + (cast(u64, x77) + x65))), x106); + const x116 = (cast(u64, x115) + (cast(u64, x107) + x95)); + var x117: u64 = undefined; + var x118: u1 = undefined; + subborrowxU64(&x117, &x118, 0x0, x110, 0xf3b9cac2fc632551); + var x119: u64 = undefined; + var x120: u1 = undefined; + subborrowxU64(&x119, &x120, x118, x112, 0xbce6faada7179e84); + var x121: u64 = undefined; + var x122: u1 = undefined; + subborrowxU64(&x121, &x122, x120, x114, 0xffffffffffffffff); + var x123: u64 = undefined; + var x124: u1 = undefined; + subborrowxU64(&x123, &x124, x122, x116, 0xffffffff00000000); + var x125: u64 = undefined; + var x126: u1 = undefined; + subborrowxU64(&x125, &x126, x124, cast(u64, 0x0), cast(u64, 0x0)); + var x127: u64 = undefined; + cmovznzU64(&x127, x126, x117, x110); + var x128: u64 = undefined; + cmovznzU64(&x128, x126, x119, x112); + var x129: u64 = undefined; + cmovznzU64(&x129, x126, x121, x114); + var x130: u64 = undefined; + cmovznzU64(&x130, x126, x123, x116); + out1[0] = x127; + out1[1] = x128; + out1[2] = x129; + out1[3] = x130; +} + +/// The function toMontgomery translates a field element into the Montgomery domain. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = eval arg1 mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn toMontgomery(out1: *[4]u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, 0x66e12d94f3d95620); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, 0x2845b2392b6bec59); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, 0x4699799c49bd6fa6); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, 0x83244c95be79eea2); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + var x19: u64 = undefined; + var x20: u64 = undefined; + mulxU64(&x19, &x20, x11, 0xccd1c8aaee00bc4f); + var x21: u64 = undefined; + var x22: u64 = undefined; + mulxU64(&x21, &x22, x19, 0xffffffff00000000); + var x23: u64 = undefined; + var x24: u64 = undefined; + mulxU64(&x23, &x24, x19, 0xffffffffffffffff); + var x25: u64 = undefined; + var x26: u64 = undefined; + mulxU64(&x25, &x26, x19, 0xbce6faada7179e84); + var x27: u64 = undefined; + var x28: u64 = undefined; + mulxU64(&x27, &x28, x19, 0xf3b9cac2fc632551); + var x29: u64 = undefined; + var x30: u1 = undefined; + addcarryxU64(&x29, &x30, 0x0, x28, x25); + var x31: u64 = undefined; + var x32: u1 = undefined; + addcarryxU64(&x31, &x32, x30, x26, x23); + var x33: u64 = undefined; + var x34: u1 = undefined; + addcarryxU64(&x33, &x34, x32, x24, x21); + var x35: u64 = undefined; + var x36: u1 = undefined; + addcarryxU64(&x35, &x36, 0x0, x11, x27); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, x36, x13, x29); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x15, x31); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x17, x33); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, (cast(u64, x18) + x6), (cast(u64, x34) + x22)); + var x45: u64 = undefined; + var x46: u64 = undefined; + mulxU64(&x45, &x46, x1, 0x66e12d94f3d95620); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, 0x2845b2392b6bec59); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, 0x4699799c49bd6fa6); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, 0x83244c95be79eea2); + var x53: u64 = undefined; + var x54: u1 = undefined; + addcarryxU64(&x53, &x54, 0x0, x52, x49); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, x54, x50, x47); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x48, x45); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, 0x0, x37, x51); + var x61: u64 = undefined; + var x62: u1 = undefined; + addcarryxU64(&x61, &x62, x60, x39, x53); + var x63: u64 = undefined; + var x64: u1 = undefined; + addcarryxU64(&x63, &x64, x62, x41, x55); + var x65: u64 = undefined; + var x66: u1 = undefined; + addcarryxU64(&x65, &x66, x64, x43, x57); + var x67: u64 = undefined; + var x68: u64 = undefined; + mulxU64(&x67, &x68, x59, 0xccd1c8aaee00bc4f); + var x69: u64 = undefined; + var x70: u64 = undefined; + mulxU64(&x69, &x70, x67, 0xffffffff00000000); + var x71: u64 = undefined; + var x72: u64 = undefined; + mulxU64(&x71, &x72, x67, 0xffffffffffffffff); + var x73: u64 = undefined; + var x74: u64 = undefined; + mulxU64(&x73, &x74, x67, 0xbce6faada7179e84); + var x75: u64 = undefined; + var x76: u64 = undefined; + mulxU64(&x75, &x76, x67, 0xf3b9cac2fc632551); + var x77: u64 = undefined; + var x78: u1 = undefined; + addcarryxU64(&x77, &x78, 0x0, x76, x73); + var x79: u64 = undefined; + var x80: u1 = undefined; + addcarryxU64(&x79, &x80, x78, x74, x71); + var x81: u64 = undefined; + var x82: u1 = undefined; + addcarryxU64(&x81, &x82, x80, x72, x69); + var x83: u64 = undefined; + var x84: u1 = undefined; + addcarryxU64(&x83, &x84, 0x0, x59, x75); + var x85: u64 = undefined; + var x86: u1 = undefined; + addcarryxU64(&x85, &x86, x84, x61, x77); + var x87: u64 = undefined; + var x88: u1 = undefined; + addcarryxU64(&x87, &x88, x86, x63, x79); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, x88, x65, x81); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, ((cast(u64, x66) + cast(u64, x44)) + (cast(u64, x58) + x46)), (cast(u64, x82) + x70)); + var x93: u64 = undefined; + var x94: u64 = undefined; + mulxU64(&x93, &x94, x2, 0x66e12d94f3d95620); + var x95: u64 = undefined; + var x96: u64 = undefined; + mulxU64(&x95, &x96, x2, 0x2845b2392b6bec59); + var x97: u64 = undefined; + var x98: u64 = undefined; + mulxU64(&x97, &x98, x2, 0x4699799c49bd6fa6); + var x99: u64 = undefined; + var x100: u64 = undefined; + mulxU64(&x99, &x100, x2, 0x83244c95be79eea2); + var x101: u64 = undefined; + var x102: u1 = undefined; + addcarryxU64(&x101, &x102, 0x0, x100, x97); + var x103: u64 = undefined; + var x104: u1 = undefined; + addcarryxU64(&x103, &x104, x102, x98, x95); + var x105: u64 = undefined; + var x106: u1 = undefined; + addcarryxU64(&x105, &x106, x104, x96, x93); + var x107: u64 = undefined; + var x108: u1 = undefined; + addcarryxU64(&x107, &x108, 0x0, x85, x99); + var x109: u64 = undefined; + var x110: u1 = undefined; + addcarryxU64(&x109, &x110, x108, x87, x101); + var x111: u64 = undefined; + var x112: u1 = undefined; + addcarryxU64(&x111, &x112, x110, x89, x103); + var x113: u64 = undefined; + var x114: u1 = undefined; + addcarryxU64(&x113, &x114, x112, x91, x105); + var x115: u64 = undefined; + var x116: u64 = undefined; + mulxU64(&x115, &x116, x107, 0xccd1c8aaee00bc4f); + var x117: u64 = undefined; + var x118: u64 = undefined; + mulxU64(&x117, &x118, x115, 0xffffffff00000000); + var x119: u64 = undefined; + var x120: u64 = undefined; + mulxU64(&x119, &x120, x115, 0xffffffffffffffff); + var x121: u64 = undefined; + var x122: u64 = undefined; + mulxU64(&x121, &x122, x115, 0xbce6faada7179e84); + var x123: u64 = undefined; + var x124: u64 = undefined; + mulxU64(&x123, &x124, x115, 0xf3b9cac2fc632551); + var x125: u64 = undefined; + var x126: u1 = undefined; + addcarryxU64(&x125, &x126, 0x0, x124, x121); + var x127: u64 = undefined; + var x128: u1 = undefined; + addcarryxU64(&x127, &x128, x126, x122, x119); + var x129: u64 = undefined; + var x130: u1 = undefined; + addcarryxU64(&x129, &x130, x128, x120, x117); + var x131: u64 = undefined; + var x132: u1 = undefined; + addcarryxU64(&x131, &x132, 0x0, x107, x123); + var x133: u64 = undefined; + var x134: u1 = undefined; + addcarryxU64(&x133, &x134, x132, x109, x125); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, x134, x111, x127); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x113, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, ((cast(u64, x114) + cast(u64, x92)) + (cast(u64, x106) + x94)), (cast(u64, x130) + x118)); + var x141: u64 = undefined; + var x142: u64 = undefined; + mulxU64(&x141, &x142, x3, 0x66e12d94f3d95620); + var x143: u64 = undefined; + var x144: u64 = undefined; + mulxU64(&x143, &x144, x3, 0x2845b2392b6bec59); + var x145: u64 = undefined; + var x146: u64 = undefined; + mulxU64(&x145, &x146, x3, 0x4699799c49bd6fa6); + var x147: u64 = undefined; + var x148: u64 = undefined; + mulxU64(&x147, &x148, x3, 0x83244c95be79eea2); + var x149: u64 = undefined; + var x150: u1 = undefined; + addcarryxU64(&x149, &x150, 0x0, x148, x145); + var x151: u64 = undefined; + var x152: u1 = undefined; + addcarryxU64(&x151, &x152, x150, x146, x143); + var x153: u64 = undefined; + var x154: u1 = undefined; + addcarryxU64(&x153, &x154, x152, x144, x141); + var x155: u64 = undefined; + var x156: u1 = undefined; + addcarryxU64(&x155, &x156, 0x0, x133, x147); + var x157: u64 = undefined; + var x158: u1 = undefined; + addcarryxU64(&x157, &x158, x156, x135, x149); + var x159: u64 = undefined; + var x160: u1 = undefined; + addcarryxU64(&x159, &x160, x158, x137, x151); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, x160, x139, x153); + var x163: u64 = undefined; + var x164: u64 = undefined; + mulxU64(&x163, &x164, x155, 0xccd1c8aaee00bc4f); + var x165: u64 = undefined; + var x166: u64 = undefined; + mulxU64(&x165, &x166, x163, 0xffffffff00000000); + var x167: u64 = undefined; + var x168: u64 = undefined; + mulxU64(&x167, &x168, x163, 0xffffffffffffffff); + var x169: u64 = undefined; + var x170: u64 = undefined; + mulxU64(&x169, &x170, x163, 0xbce6faada7179e84); + var x171: u64 = undefined; + var x172: u64 = undefined; + mulxU64(&x171, &x172, x163, 0xf3b9cac2fc632551); + var x173: u64 = undefined; + var x174: u1 = undefined; + addcarryxU64(&x173, &x174, 0x0, x172, x169); + var x175: u64 = undefined; + var x176: u1 = undefined; + addcarryxU64(&x175, &x176, x174, x170, x167); + var x177: u64 = undefined; + var x178: u1 = undefined; + addcarryxU64(&x177, &x178, x176, x168, x165); + var x179: u64 = undefined; + var x180: u1 = undefined; + addcarryxU64(&x179, &x180, 0x0, x155, x171); + var x181: u64 = undefined; + var x182: u1 = undefined; + addcarryxU64(&x181, &x182, x180, x157, x173); + var x183: u64 = undefined; + var x184: u1 = undefined; + addcarryxU64(&x183, &x184, x182, x159, x175); + var x185: u64 = undefined; + var x186: u1 = undefined; + addcarryxU64(&x185, &x186, x184, x161, x177); + var x187: u64 = undefined; + var x188: u1 = undefined; + addcarryxU64(&x187, &x188, x186, ((cast(u64, x162) + cast(u64, x140)) + (cast(u64, x154) + x142)), (cast(u64, x178) + x166)); + var x189: u64 = undefined; + var x190: u1 = undefined; + subborrowxU64(&x189, &x190, 0x0, x181, 0xf3b9cac2fc632551); + var x191: u64 = undefined; + var x192: u1 = undefined; + subborrowxU64(&x191, &x192, x190, x183, 0xbce6faada7179e84); + var x193: u64 = undefined; + var x194: u1 = undefined; + subborrowxU64(&x193, &x194, x192, x185, 0xffffffffffffffff); + var x195: u64 = undefined; + var x196: u1 = undefined; + subborrowxU64(&x195, &x196, x194, x187, 0xffffffff00000000); + var x197: u64 = undefined; + var x198: u1 = undefined; + subborrowxU64(&x197, &x198, x196, cast(u64, x188), cast(u64, 0x0)); + var x199: u64 = undefined; + cmovznzU64(&x199, x198, x189, x181); + var x200: u64 = undefined; + cmovznzU64(&x200, x198, x191, x183); + var x201: u64 = undefined; + cmovznzU64(&x201, x198, x193, x185); + var x202: u64 = undefined; + cmovznzU64(&x202, x198, x195, x187); + out1[0] = x199; + out1[1] = x200; + out1[2] = x201; + out1[3] = x202; +} + +/// The function nonzero outputs a single non-zero word if the input is non-zero and zero otherwise. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +pub fn nonzero(out1: *u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3])))); + out1.* = x1; +} + +/// The function selectznz is a multi-limb conditional select. +/// Postconditions: +/// eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn selectznz(out1: *[4]u64, arg1: u1, arg2: [4]u64, arg3: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + cmovznzU64(&x1, arg1, (arg2[0]), (arg3[0])); + var x2: u64 = undefined; + cmovznzU64(&x2, arg1, (arg2[1]), (arg3[1])); + var x3: u64 = undefined; + cmovznzU64(&x3, arg1, (arg2[2]), (arg3[2])); + var x4: u64 = undefined; + cmovznzU64(&x4, arg1, (arg2[3]), (arg3[3])); + out1[0] = x1; + out1[1] = x2; + out1[2] = x3; + out1[3] = x4; +} + +/// The function toBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31] +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +pub fn toBytes(out1: *[32]u8, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[3]); + const x2 = (arg1[2]); + const x3 = (arg1[1]); + const x4 = (arg1[0]); + const x5 = cast(u8, (x4 & cast(u64, 0xff))); + const x6 = (x4 >> 8); + const x7 = cast(u8, (x6 & cast(u64, 0xff))); + const x8 = (x6 >> 8); + const x9 = cast(u8, (x8 & cast(u64, 0xff))); + const x10 = (x8 >> 8); + const x11 = cast(u8, (x10 & cast(u64, 0xff))); + const x12 = (x10 >> 8); + const x13 = cast(u8, (x12 & cast(u64, 0xff))); + const x14 = (x12 >> 8); + const x15 = cast(u8, (x14 & cast(u64, 0xff))); + const x16 = (x14 >> 8); + const x17 = cast(u8, (x16 & cast(u64, 0xff))); + const x18 = cast(u8, (x16 >> 8)); + const x19 = cast(u8, (x3 & cast(u64, 0xff))); + const x20 = (x3 >> 8); + const x21 = cast(u8, (x20 & cast(u64, 0xff))); + const x22 = (x20 >> 8); + const x23 = cast(u8, (x22 & cast(u64, 0xff))); + const x24 = (x22 >> 8); + const x25 = cast(u8, (x24 & cast(u64, 0xff))); + const x26 = (x24 >> 8); + const x27 = cast(u8, (x26 & cast(u64, 0xff))); + const x28 = (x26 >> 8); + const x29 = cast(u8, (x28 & cast(u64, 0xff))); + const x30 = (x28 >> 8); + const x31 = cast(u8, (x30 & cast(u64, 0xff))); + const x32 = cast(u8, (x30 >> 8)); + const x33 = cast(u8, (x2 & cast(u64, 0xff))); + const x34 = (x2 >> 8); + const x35 = cast(u8, (x34 & cast(u64, 0xff))); + const x36 = (x34 >> 8); + const x37 = cast(u8, (x36 & cast(u64, 0xff))); + const x38 = (x36 >> 8); + const x39 = cast(u8, (x38 & cast(u64, 0xff))); + const x40 = (x38 >> 8); + const x41 = cast(u8, (x40 & cast(u64, 0xff))); + const x42 = (x40 >> 8); + const x43 = cast(u8, (x42 & cast(u64, 0xff))); + const x44 = (x42 >> 8); + const x45 = cast(u8, (x44 & cast(u64, 0xff))); + const x46 = cast(u8, (x44 >> 8)); + const x47 = cast(u8, (x1 & cast(u64, 0xff))); + const x48 = (x1 >> 8); + const x49 = cast(u8, (x48 & cast(u64, 0xff))); + const x50 = (x48 >> 8); + const x51 = cast(u8, (x50 & cast(u64, 0xff))); + const x52 = (x50 >> 8); + const x53 = cast(u8, (x52 & cast(u64, 0xff))); + const x54 = (x52 >> 8); + const x55 = cast(u8, (x54 & cast(u64, 0xff))); + const x56 = (x54 >> 8); + const x57 = cast(u8, (x56 & cast(u64, 0xff))); + const x58 = (x56 >> 8); + const x59 = cast(u8, (x58 & cast(u64, 0xff))); + const x60 = cast(u8, (x58 >> 8)); + out1[0] = x5; + out1[1] = x7; + out1[2] = x9; + out1[3] = x11; + out1[4] = x13; + out1[5] = x15; + out1[6] = x17; + out1[7] = x18; + out1[8] = x19; + out1[9] = x21; + out1[10] = x23; + out1[11] = x25; + out1[12] = x27; + out1[13] = x29; + out1[14] = x31; + out1[15] = x32; + out1[16] = x33; + out1[17] = x35; + out1[18] = x37; + out1[19] = x39; + out1[20] = x41; + out1[21] = x43; + out1[22] = x45; + out1[23] = x46; + out1[24] = x47; + out1[25] = x49; + out1[26] = x51; + out1[27] = x53; + out1[28] = x55; + out1[29] = x57; + out1[30] = x59; + out1[31] = x60; +} + +/// The function fromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. +/// Preconditions: +/// 0 ≤ bytes_eval arg1 < m +/// Postconditions: +/// eval out1 mod m = bytes_eval arg1 mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn fromBytes(out1: *[4]u64, arg1: [32]u8) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (cast(u64, (arg1[31])) << 56); + const x2 = (cast(u64, (arg1[30])) << 48); + const x3 = (cast(u64, (arg1[29])) << 40); + const x4 = (cast(u64, (arg1[28])) << 32); + const x5 = (cast(u64, (arg1[27])) << 24); + const x6 = (cast(u64, (arg1[26])) << 16); + const x7 = (cast(u64, (arg1[25])) << 8); + const x8 = (arg1[24]); + const x9 = (cast(u64, (arg1[23])) << 56); + const x10 = (cast(u64, (arg1[22])) << 48); + const x11 = (cast(u64, (arg1[21])) << 40); + const x12 = (cast(u64, (arg1[20])) << 32); + const x13 = (cast(u64, (arg1[19])) << 24); + const x14 = (cast(u64, (arg1[18])) << 16); + const x15 = (cast(u64, (arg1[17])) << 8); + const x16 = (arg1[16]); + const x17 = (cast(u64, (arg1[15])) << 56); + const x18 = (cast(u64, (arg1[14])) << 48); + const x19 = (cast(u64, (arg1[13])) << 40); + const x20 = (cast(u64, (arg1[12])) << 32); + const x21 = (cast(u64, (arg1[11])) << 24); + const x22 = (cast(u64, (arg1[10])) << 16); + const x23 = (cast(u64, (arg1[9])) << 8); + const x24 = (arg1[8]); + const x25 = (cast(u64, (arg1[7])) << 56); + const x26 = (cast(u64, (arg1[6])) << 48); + const x27 = (cast(u64, (arg1[5])) << 40); + const x28 = (cast(u64, (arg1[4])) << 32); + const x29 = (cast(u64, (arg1[3])) << 24); + const x30 = (cast(u64, (arg1[2])) << 16); + const x31 = (cast(u64, (arg1[1])) << 8); + const x32 = (arg1[0]); + const x33 = (x31 + cast(u64, x32)); + const x34 = (x30 + x33); + const x35 = (x29 + x34); + const x36 = (x28 + x35); + const x37 = (x27 + x36); + const x38 = (x26 + x37); + const x39 = (x25 + x38); + const x40 = (x23 + cast(u64, x24)); + const x41 = (x22 + x40); + const x42 = (x21 + x41); + const x43 = (x20 + x42); + const x44 = (x19 + x43); + const x45 = (x18 + x44); + const x46 = (x17 + x45); + const x47 = (x15 + cast(u64, x16)); + const x48 = (x14 + x47); + const x49 = (x13 + x48); + const x50 = (x12 + x49); + const x51 = (x11 + x50); + const x52 = (x10 + x51); + const x53 = (x9 + x52); + const x54 = (x7 + cast(u64, x8)); + const x55 = (x6 + x54); + const x56 = (x5 + x55); + const x57 = (x4 + x56); + const x58 = (x3 + x57); + const x59 = (x2 + x58); + const x60 = (x1 + x59); + out1[0] = x39; + out1[1] = x46; + out1[2] = x53; + out1[3] = x60; +} + +/// The function setOne returns the field element one in the Montgomery domain. +/// Postconditions: +/// eval (from_montgomery out1) mod m = 1 mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn setOne(out1: *[4]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xc46353d039cdaaf; + out1[1] = 0x4319055258e8617b; + out1[2] = cast(u64, 0x0); + out1[3] = 0xffffffff; +} + +/// The function msat returns the saturated representation of the prime modulus. +/// Postconditions: +/// twos_complement_eval out1 = m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn msat(out1: *[5]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xf3b9cac2fc632551; + out1[1] = 0xbce6faada7179e84; + out1[2] = 0xffffffffffffffff; + out1[3] = 0xffffffff00000000; + out1[4] = cast(u64, 0x0); +} + +/// The function divstepPrecomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form). +/// Postconditions: +/// eval (from_montgomery out1) = ⌊(m - 1) / 2⌋^(if (log2 m) + 1 < 46 then ⌊(49 * ((log2 m) + 1) + 80) / 17⌋ else ⌊(49 * ((log2 m) + 1) + 57) / 17⌋) +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn divstepPrecomp(out1: *[4]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xd739262fb7fcfbb5; + out1[1] = 0x8ac6f75d20074414; + out1[2] = 0xc67428bfb5e3c256; + out1[3] = 0x444962f2eda7aedf; +} + +/// The function divstep computes a divstep. +/// Preconditions: +/// 0 ≤ eval arg4 < m +/// 0 ≤ eval arg5 < m +/// Postconditions: +/// out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1) +/// twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2) +/// twos_complement_eval out3 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then ⌊(twos_complement_eval arg3 - twos_complement_eval arg2) / 2⌋ else ⌊(twos_complement_eval arg3 + (twos_complement_eval arg3 mod 2) * twos_complement_eval arg2) / 2⌋) +/// eval (from_montgomery out4) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (2 * eval (from_montgomery arg5)) mod m else (2 * eval (from_montgomery arg4)) mod m) +/// eval (from_montgomery out5) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (eval (from_montgomery arg4) - eval (from_montgomery arg4)) mod m else (eval (from_montgomery arg5) + (twos_complement_eval arg3 mod 2) * eval (from_montgomery arg4)) mod m) +/// 0 ≤ eval out5 < m +/// 0 ≤ eval out5 < m +/// 0 ≤ eval out2 < m +/// 0 ≤ eval out3 < m +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0xffffffffffffffff] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *[4]u64, out5: *[4]u64, arg1: u64, arg2: [5]u64, arg3: [5]u64, arg4: [4]u64, arg5: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + addcarryxU64(&x1, &x2, 0x0, (~arg1), cast(u64, 0x1)); + const x3 = (cast(u1, (x1 >> 63)) & cast(u1, ((arg3[0]) & cast(u64, 0x1)))); + var x4: u64 = undefined; + var x5: u1 = undefined; + addcarryxU64(&x4, &x5, 0x0, (~arg1), cast(u64, 0x1)); + var x6: u64 = undefined; + cmovznzU64(&x6, x3, arg1, x4); + var x7: u64 = undefined; + cmovznzU64(&x7, x3, (arg2[0]), (arg3[0])); + var x8: u64 = undefined; + cmovznzU64(&x8, x3, (arg2[1]), (arg3[1])); + var x9: u64 = undefined; + cmovznzU64(&x9, x3, (arg2[2]), (arg3[2])); + var x10: u64 = undefined; + cmovznzU64(&x10, x3, (arg2[3]), (arg3[3])); + var x11: u64 = undefined; + cmovznzU64(&x11, x3, (arg2[4]), (arg3[4])); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, 0x0, cast(u64, 0x1), (~(arg2[0]))); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, cast(u64, 0x0), (~(arg2[1]))); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, cast(u64, 0x0), (~(arg2[2]))); + var x18: u64 = undefined; + var x19: u1 = undefined; + addcarryxU64(&x18, &x19, x17, cast(u64, 0x0), (~(arg2[3]))); + var x20: u64 = undefined; + var x21: u1 = undefined; + addcarryxU64(&x20, &x21, x19, cast(u64, 0x0), (~(arg2[4]))); + var x22: u64 = undefined; + cmovznzU64(&x22, x3, (arg3[0]), x12); + var x23: u64 = undefined; + cmovznzU64(&x23, x3, (arg3[1]), x14); + var x24: u64 = undefined; + cmovznzU64(&x24, x3, (arg3[2]), x16); + var x25: u64 = undefined; + cmovznzU64(&x25, x3, (arg3[3]), x18); + var x26: u64 = undefined; + cmovznzU64(&x26, x3, (arg3[4]), x20); + var x27: u64 = undefined; + cmovznzU64(&x27, x3, (arg4[0]), (arg5[0])); + var x28: u64 = undefined; + cmovznzU64(&x28, x3, (arg4[1]), (arg5[1])); + var x29: u64 = undefined; + cmovznzU64(&x29, x3, (arg4[2]), (arg5[2])); + var x30: u64 = undefined; + cmovznzU64(&x30, x3, (arg4[3]), (arg5[3])); + var x31: u64 = undefined; + var x32: u1 = undefined; + addcarryxU64(&x31, &x32, 0x0, x27, x27); + var x33: u64 = undefined; + var x34: u1 = undefined; + addcarryxU64(&x33, &x34, x32, x28, x28); + var x35: u64 = undefined; + var x36: u1 = undefined; + addcarryxU64(&x35, &x36, x34, x29, x29); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, x36, x30, x30); + var x39: u64 = undefined; + var x40: u1 = undefined; + subborrowxU64(&x39, &x40, 0x0, x31, 0xf3b9cac2fc632551); + var x41: u64 = undefined; + var x42: u1 = undefined; + subborrowxU64(&x41, &x42, x40, x33, 0xbce6faada7179e84); + var x43: u64 = undefined; + var x44: u1 = undefined; + subborrowxU64(&x43, &x44, x42, x35, 0xffffffffffffffff); + var x45: u64 = undefined; + var x46: u1 = undefined; + subborrowxU64(&x45, &x46, x44, x37, 0xffffffff00000000); + var x47: u64 = undefined; + var x48: u1 = undefined; + subborrowxU64(&x47, &x48, x46, cast(u64, x38), cast(u64, 0x0)); + const x49 = (arg4[3]); + const x50 = (arg4[2]); + const x51 = (arg4[1]); + const x52 = (arg4[0]); + var x53: u64 = undefined; + var x54: u1 = undefined; + subborrowxU64(&x53, &x54, 0x0, cast(u64, 0x0), x52); + var x55: u64 = undefined; + var x56: u1 = undefined; + subborrowxU64(&x55, &x56, x54, cast(u64, 0x0), x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + subborrowxU64(&x57, &x58, x56, cast(u64, 0x0), x50); + var x59: u64 = undefined; + var x60: u1 = undefined; + subborrowxU64(&x59, &x60, x58, cast(u64, 0x0), x49); + var x61: u64 = undefined; + cmovznzU64(&x61, x60, cast(u64, 0x0), 0xffffffffffffffff); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x53, (x61 & 0xf3b9cac2fc632551)); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x55, (x61 & 0xbce6faada7179e84)); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x57, x61); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x59, (x61 & 0xffffffff00000000)); + var x70: u64 = undefined; + cmovznzU64(&x70, x3, (arg5[0]), x62); + var x71: u64 = undefined; + cmovznzU64(&x71, x3, (arg5[1]), x64); + var x72: u64 = undefined; + cmovznzU64(&x72, x3, (arg5[2]), x66); + var x73: u64 = undefined; + cmovznzU64(&x73, x3, (arg5[3]), x68); + const x74 = cast(u1, (x22 & cast(u64, 0x1))); + var x75: u64 = undefined; + cmovznzU64(&x75, x74, cast(u64, 0x0), x7); + var x76: u64 = undefined; + cmovznzU64(&x76, x74, cast(u64, 0x0), x8); + var x77: u64 = undefined; + cmovznzU64(&x77, x74, cast(u64, 0x0), x9); + var x78: u64 = undefined; + cmovznzU64(&x78, x74, cast(u64, 0x0), x10); + var x79: u64 = undefined; + cmovznzU64(&x79, x74, cast(u64, 0x0), x11); + var x80: u64 = undefined; + var x81: u1 = undefined; + addcarryxU64(&x80, &x81, 0x0, x22, x75); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, x81, x23, x76); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x24, x77); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x25, x78); + var x88: u64 = undefined; + var x89: u1 = undefined; + addcarryxU64(&x88, &x89, x87, x26, x79); + var x90: u64 = undefined; + cmovznzU64(&x90, x74, cast(u64, 0x0), x27); + var x91: u64 = undefined; + cmovznzU64(&x91, x74, cast(u64, 0x0), x28); + var x92: u64 = undefined; + cmovznzU64(&x92, x74, cast(u64, 0x0), x29); + var x93: u64 = undefined; + cmovznzU64(&x93, x74, cast(u64, 0x0), x30); + var x94: u64 = undefined; + var x95: u1 = undefined; + addcarryxU64(&x94, &x95, 0x0, x70, x90); + var x96: u64 = undefined; + var x97: u1 = undefined; + addcarryxU64(&x96, &x97, x95, x71, x91); + var x98: u64 = undefined; + var x99: u1 = undefined; + addcarryxU64(&x98, &x99, x97, x72, x92); + var x100: u64 = undefined; + var x101: u1 = undefined; + addcarryxU64(&x100, &x101, x99, x73, x93); + var x102: u64 = undefined; + var x103: u1 = undefined; + subborrowxU64(&x102, &x103, 0x0, x94, 0xf3b9cac2fc632551); + var x104: u64 = undefined; + var x105: u1 = undefined; + subborrowxU64(&x104, &x105, x103, x96, 0xbce6faada7179e84); + var x106: u64 = undefined; + var x107: u1 = undefined; + subborrowxU64(&x106, &x107, x105, x98, 0xffffffffffffffff); + var x108: u64 = undefined; + var x109: u1 = undefined; + subborrowxU64(&x108, &x109, x107, x100, 0xffffffff00000000); + var x110: u64 = undefined; + var x111: u1 = undefined; + subborrowxU64(&x110, &x111, x109, cast(u64, x101), cast(u64, 0x0)); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, 0x0, x6, cast(u64, 0x1)); + const x114 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff)); + const x115 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff)); + const x116 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff)); + const x117 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff)); + const x118 = ((x88 & 0x8000000000000000) | (x88 >> 1)); + var x119: u64 = undefined; + cmovznzU64(&x119, x48, x39, x31); + var x120: u64 = undefined; + cmovznzU64(&x120, x48, x41, x33); + var x121: u64 = undefined; + cmovznzU64(&x121, x48, x43, x35); + var x122: u64 = undefined; + cmovznzU64(&x122, x48, x45, x37); + var x123: u64 = undefined; + cmovznzU64(&x123, x111, x102, x94); + var x124: u64 = undefined; + cmovznzU64(&x124, x111, x104, x96); + var x125: u64 = undefined; + cmovznzU64(&x125, x111, x106, x98); + var x126: u64 = undefined; + cmovznzU64(&x126, x111, x108, x100); + out1.* = x112; + out2[0] = x7; + out2[1] = x8; + out2[2] = x9; + out2[3] = x10; + out2[4] = x11; + out3[0] = x114; + out3[1] = x115; + out3[2] = x116; + out3[3] = x117; + out3[4] = x118; + out4[0] = x119; + out4[1] = x120; + out4[2] = x121; + out4[3] = x122; + out5[0] = x123; + out5[1] = x124; + out5[2] = x125; + out5[3] = x126; +} diff --git a/lib/std/crypto/pcurves/p256/scalar.zig b/lib/std/crypto/pcurves/p256/scalar.zig index e047f6a8d6..3cd6689897 100644 --- a/lib/std/crypto/pcurves/p256/scalar.zig +++ b/lib/std/crypto/pcurves/p256/scalar.zig @@ -6,32 +6,44 @@ const std = @import("std"); const builtin = std.builtin; +const common = @import("../common.zig"); const crypto = std.crypto; const debug = std.debug; const math = std.math; const mem = std.mem; -const Fe = @import("field.zig").Fe; +const Field = common.Field; const NonCanonicalError = std.crypto.errors.NonCanonicalError; const NotSquareError = std.crypto.errors.NotSquareError; +/// Number of bytes required to encode a scalar. +pub const encoded_length = 32; + /// A compressed scalar, in canonical form. -pub const CompressedScalar = [32]u8; +pub const CompressedScalar = [encoded_length]u8; + +const Fe = Field(.{ + .fiat = @import("p256_scalar_64.zig"), + .field_order = 115792089210356248762697446949407573529996955224135760342422259061068512044369, + .field_bits = 256, + .saturated_bits = 255, + .encoded_length = encoded_length, +}); /// Reject a scalar whose encoding is not canonical. -pub fn rejectNonCanonical(s: CompressedScalar) NonCanonicalError!void { - return Fe.rejectNonCanonical(s); +pub fn rejectNonCanonical(s: CompressedScalar, endian: builtin.Endian) NonCanonicalError!void { + return Fe.rejectNonCanonical(s, endian); } /// Reduce a 48-bytes scalar to the field size. -pub fn reduce48(s: [48]u8) CompressedScalar { - return Scalar.fromBytes48(s).toBytes(); +pub fn reduce48(s: [48]u8, endian: builtin.Endian) CompressedScalar { + return Scalar.fromBytes48(s, endian).toBytes(endian); } /// Reduce a 64-bytes scalar to the field size. -pub fn reduce64(s: [64]u8) CompressedScalar { - return ScalarDouble.fromBytes64(s).toBytes(); +pub fn reduce64(s: [64]u8, endian: builtin.Endian) CompressedScalar { + return ScalarDouble.fromBytes64(s, endian).toBytes(endian); } /// Return a*b (mod L) @@ -183,19 +195,19 @@ const ScalarDouble = struct { } var t = ScalarDouble{ .x1 = undefined, .x2 = Fe.zero, .x3 = Fe.zero }; { - var b = [_]u8{0} ** 32; + var b = [_]u8{0} ** encoded_length; const len = math.min(s.len, 24); mem.copy(u8, b[0..len], s[0..len]); t.x1 = Fe.fromBytes(b, .Little) catch unreachable; } if (s_.len >= 24) { - var b = [_]u8{0} ** 32; + var b = [_]u8{0} ** encoded_length; const len = math.min(s.len - 24, 24); mem.copy(u8, b[0..len], s[24..][0..len]); t.x2 = Fe.fromBytes(b, .Little) catch unreachable; } if (s_.len >= 48) { - var b = [_]u8{0} ** 32; + var b = [_]u8{0} ** encoded_length; const len = s.len - 48; mem.copy(u8, b[0..len], s[48..][0..len]); t.x3 = Fe.fromBytes(b, .Little) catch unreachable;