From e436ecbeb8ebe36767c26f70fc471182409718d5 Mon Sep 17 00:00:00 2001 From: Ignacio Hagopian Date: Sat, 26 Aug 2023 11:06:21 -0300 Subject: [PATCH] bn254: add scalar field implementation Signed-off-by: Ignacio Hagopian --- src/bn254/fr.zig | 2013 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 2013 insertions(+) create mode 100644 src/bn254/fr.zig diff --git a/src/bn254/fr.zig b/src/bn254/fr.zig new file mode 100644 index 0000000..512fa28 --- /dev/null +++ b/src/bn254/fr.zig @@ -0,0 +1,2013 @@ +// Autogenerated: './word_by_word_montgomery' --lang Zig --internal-static --public-function-case camelCase --private-function-case camelCase --public-type-case UpperCamelCase --private-type-case UpperCamelCase --no-prefix-fiat --package-name babyJubJubScalar '' 64 21888242871839275222246405745257275088548364400416034343698204186575808495617 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): babyJubJubScalar +// 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 = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001 (from "21888242871839275222246405745257275088548364400416034343698204186575808495617") +// +// 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 mode = @import("builtin").mode; // Checked arithmetic is disabled in non-debug modes to avoid side channels + +inline fn cast(comptime DestType: type, target: anytype) DestType { + @setEvalBranchQuota(10000); + if (@typeInfo(@TypeOf(target)) == .Int) { + const dest = @typeInfo(DestType).Int; + const source = @typeInfo(@TypeOf(target)).Int; + if (dest.bits < source.bits) { + return @bitCast(@as(std.meta.Int(source.signedness, dest.bits), @truncate(target))); + } else { + return @as(DestType, @bitCast(@as(std.meta.Int(source.signedness, dest.bits), target))); + } + } + return @as(DestType, target); +} + +// The type MontgomeryDomainFieldElement is a field element in the Montgomery domain. +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub const MontgomeryDomainFieldElement = [4]u64; + +// The type NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain. +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub const NonMontgomeryDomainFieldElement = [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] +inline fn addcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = ((cast(u128, arg1) + cast(u128, arg2)) + cast(u128, arg3)); + const x2 = cast(u64, (x1 & cast(u128, 0xffffffffffffffff))); + const x3 = cast(u1, (x1 >> 64)); + out1.* = x2; + out2.* = x3; +} + +/// 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] +inline fn subborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = ((cast(i128, arg2) - cast(i128, arg1)) - cast(i128, arg3)); + const x2 = cast(i1, (x1 >> 64)); + const x3 = cast(u64, (x1 & cast(i128, 0xffffffffffffffff))); + out1.* = x3; + out2.* = cast(u1, (cast(i2, 0x0) - cast(i2, x2))); +} + +/// 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] +inline fn mulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (cast(u128, arg1) * cast(u128, arg2)); + const x2 = cast(u64, (x1 & cast(u128, 0xffffffffffffffff))); + const x3 = cast(u64, (x1 >> 64)); + out1.* = x2; + out2.* = x3; +} + +/// 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] +inline fn cmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (~(~arg1)); + const x2 = cast(u64, (cast(i128, cast(i1, (cast(i2, 0x0) - cast(i2, x1)))) & cast(i128, 0xffffffffffffffff))); + const x3 = ((x2 & arg3) | ((~x2) & arg2)); + out1.* = x3; +} + +/// 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 +/// +pub fn mul(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) 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, 0xc2e1f593efffffff); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0x30644e72e131a029); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xb85045b68181585d); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0x2833e84879b97091); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0x30644e72e131a029); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xb85045b68181585d); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0x2833e84879b97091); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0x30644e72e131a029); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xb85045b68181585d); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0x2833e84879b97091); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0x30644e72e131a029); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xb85045b68181585d); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0x2833e84879b97091); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0x43e1f593f0000001); + 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, 0x43e1f593f0000001); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0x2833e84879b97091); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xb85045b68181585d); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0x30644e72e131a029); + 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 +/// +pub fn square(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) 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, 0xc2e1f593efffffff); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0x30644e72e131a029); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xb85045b68181585d); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0x2833e84879b97091); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0x30644e72e131a029); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xb85045b68181585d); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0x2833e84879b97091); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0x30644e72e131a029); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xb85045b68181585d); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0x2833e84879b97091); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0x30644e72e131a029); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xb85045b68181585d); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0x2833e84879b97091); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0x43e1f593f0000001); + 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, 0x43e1f593f0000001); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0x2833e84879b97091); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xb85045b68181585d); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0x30644e72e131a029); + 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 +/// +pub fn add(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) 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, 0x43e1f593f0000001); + var x11: u64 = undefined; + var x12: u1 = undefined; + subborrowxU64(&x11, &x12, x10, x3, 0x2833e84879b97091); + var x13: u64 = undefined; + var x14: u1 = undefined; + subborrowxU64(&x13, &x14, x12, x5, 0xb85045b68181585d); + var x15: u64 = undefined; + var x16: u1 = undefined; + subborrowxU64(&x15, &x16, x14, x7, 0x30644e72e131a029); + 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 +/// +pub fn sub(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) 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 & 0x43e1f593f0000001)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0x2833e84879b97091)); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, (x9 & 0xb85045b68181585d)); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, (x9 & 0x30644e72e131a029)); + 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 +/// +pub fn opp(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) 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 & 0x43e1f593f0000001)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0x2833e84879b97091)); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, (x9 & 0xb85045b68181585d)); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, (x9 & 0x30644e72e131a029)); + 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 +/// +pub fn fromMontgomery(out1: *NonMontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[0]); + var x2: u64 = undefined; + var x3: u64 = undefined; + mulxU64(&x2, &x3, x1, 0xc2e1f593efffffff); + var x4: u64 = undefined; + var x5: u64 = undefined; + mulxU64(&x4, &x5, x2, 0x30644e72e131a029); + var x6: u64 = undefined; + var x7: u64 = undefined; + mulxU64(&x6, &x7, x2, 0xb85045b68181585d); + var x8: u64 = undefined; + var x9: u64 = undefined; + mulxU64(&x8, &x9, x2, 0x2833e84879b97091); + var x10: u64 = undefined; + var x11: u64 = undefined; + mulxU64(&x10, &x11, x2, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x34: u64 = undefined; + var x35: u64 = undefined; + mulxU64(&x34, &x35, x32, 0x30644e72e131a029); + var x36: u64 = undefined; + var x37: u64 = undefined; + mulxU64(&x36, &x37, x32, 0xb85045b68181585d); + var x38: u64 = undefined; + var x39: u64 = undefined; + mulxU64(&x38, &x39, x32, 0x2833e84879b97091); + var x40: u64 = undefined; + var x41: u64 = undefined; + mulxU64(&x40, &x41, x32, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x64: u64 = undefined; + var x65: u64 = undefined; + mulxU64(&x64, &x65, x62, 0x30644e72e131a029); + var x66: u64 = undefined; + var x67: u64 = undefined; + mulxU64(&x66, &x67, x62, 0xb85045b68181585d); + var x68: u64 = undefined; + var x69: u64 = undefined; + mulxU64(&x68, &x69, x62, 0x2833e84879b97091); + var x70: u64 = undefined; + var x71: u64 = undefined; + mulxU64(&x70, &x71, x62, 0x43e1f593f0000001); + 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, 0xc2e1f593efffffff); + var x94: u64 = undefined; + var x95: u64 = undefined; + mulxU64(&x94, &x95, x92, 0x30644e72e131a029); + var x96: u64 = undefined; + var x97: u64 = undefined; + mulxU64(&x96, &x97, x92, 0xb85045b68181585d); + var x98: u64 = undefined; + var x99: u64 = undefined; + mulxU64(&x98, &x99, x92, 0x2833e84879b97091); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x92, 0x43e1f593f0000001); + 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, 0x43e1f593f0000001); + var x119: u64 = undefined; + var x120: u1 = undefined; + subborrowxU64(&x119, &x120, x118, x112, 0x2833e84879b97091); + var x121: u64 = undefined; + var x122: u1 = undefined; + subborrowxU64(&x121, &x122, x120, x114, 0xb85045b68181585d); + var x123: u64 = undefined; + var x124: u1 = undefined; + subborrowxU64(&x123, &x124, x122, x116, 0x30644e72e131a029); + 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 +/// +pub fn toMontgomery(out1: *MontgomeryDomainFieldElement, arg1: NonMontgomeryDomainFieldElement) 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, 0x216d0b17f4e44a5); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, 0x8c49833d53bb8085); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, 0x53fe3ab1e35c59e3); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, 0x1bb8e645ae216da7); + 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, 0xc2e1f593efffffff); + var x21: u64 = undefined; + var x22: u64 = undefined; + mulxU64(&x21, &x22, x19, 0x30644e72e131a029); + var x23: u64 = undefined; + var x24: u64 = undefined; + mulxU64(&x23, &x24, x19, 0xb85045b68181585d); + var x25: u64 = undefined; + var x26: u64 = undefined; + mulxU64(&x25, &x26, x19, 0x2833e84879b97091); + var x27: u64 = undefined; + var x28: u64 = undefined; + mulxU64(&x27, &x28, x19, 0x43e1f593f0000001); + 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: u64 = undefined; + mulxU64(&x43, &x44, x1, 0x216d0b17f4e44a5); + var x45: u64 = undefined; + var x46: u64 = undefined; + mulxU64(&x45, &x46, x1, 0x8c49833d53bb8085); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, 0x53fe3ab1e35c59e3); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, 0x1bb8e645ae216da7); + var x51: u64 = undefined; + var x52: u1 = undefined; + addcarryxU64(&x51, &x52, 0x0, x50, x47); + var x53: u64 = undefined; + var x54: u1 = undefined; + addcarryxU64(&x53, &x54, x52, x48, x45); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, x54, x46, x43); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, 0x0, x37, x49); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x39, x51); + var x61: u64 = undefined; + var x62: u1 = undefined; + addcarryxU64(&x61, &x62, x60, x41, x53); + var x63: u64 = undefined; + var x64: u1 = undefined; + addcarryxU64(&x63, &x64, x62, ((cast(u64, x42) + (cast(u64, x18) + x6)) + (cast(u64, x34) + x22)), x55); + var x65: u64 = undefined; + var x66: u64 = undefined; + mulxU64(&x65, &x66, x57, 0xc2e1f593efffffff); + var x67: u64 = undefined; + var x68: u64 = undefined; + mulxU64(&x67, &x68, x65, 0x30644e72e131a029); + var x69: u64 = undefined; + var x70: u64 = undefined; + mulxU64(&x69, &x70, x65, 0xb85045b68181585d); + var x71: u64 = undefined; + var x72: u64 = undefined; + mulxU64(&x71, &x72, x65, 0x2833e84879b97091); + var x73: u64 = undefined; + var x74: u64 = undefined; + mulxU64(&x73, &x74, x65, 0x43e1f593f0000001); + var x75: u64 = undefined; + var x76: u1 = undefined; + addcarryxU64(&x75, &x76, 0x0, x74, x71); + var x77: u64 = undefined; + var x78: u1 = undefined; + addcarryxU64(&x77, &x78, x76, x72, x69); + var x79: u64 = undefined; + var x80: u1 = undefined; + addcarryxU64(&x79, &x80, x78, x70, x67); + var x81: u64 = undefined; + var x82: u1 = undefined; + addcarryxU64(&x81, &x82, 0x0, x57, x73); + var x83: u64 = undefined; + var x84: u1 = undefined; + addcarryxU64(&x83, &x84, x82, 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: u64 = undefined; + mulxU64(&x89, &x90, x2, 0x216d0b17f4e44a5); + var x91: u64 = undefined; + var x92: u64 = undefined; + mulxU64(&x91, &x92, x2, 0x8c49833d53bb8085); + var x93: u64 = undefined; + var x94: u64 = undefined; + mulxU64(&x93, &x94, x2, 0x53fe3ab1e35c59e3); + var x95: u64 = undefined; + var x96: u64 = undefined; + mulxU64(&x95, &x96, x2, 0x1bb8e645ae216da7); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, 0x0, x96, x93); + var x99: u64 = undefined; + var x100: u1 = undefined; + addcarryxU64(&x99, &x100, x98, x94, x91); + var x101: u64 = undefined; + var x102: u1 = undefined; + addcarryxU64(&x101, &x102, x100, x92, x89); + var x103: u64 = undefined; + var x104: u1 = undefined; + addcarryxU64(&x103, &x104, 0x0, x83, x95); + var x105: u64 = undefined; + var x106: u1 = undefined; + addcarryxU64(&x105, &x106, x104, x85, x97); + var x107: u64 = undefined; + var x108: u1 = undefined; + addcarryxU64(&x107, &x108, x106, x87, x99); + var x109: u64 = undefined; + var x110: u1 = undefined; + addcarryxU64(&x109, &x110, x108, ((cast(u64, x88) + (cast(u64, x64) + (cast(u64, x56) + x44))) + (cast(u64, x80) + x68)), x101); + var x111: u64 = undefined; + var x112: u64 = undefined; + mulxU64(&x111, &x112, x103, 0xc2e1f593efffffff); + var x113: u64 = undefined; + var x114: u64 = undefined; + mulxU64(&x113, &x114, x111, 0x30644e72e131a029); + var x115: u64 = undefined; + var x116: u64 = undefined; + mulxU64(&x115, &x116, x111, 0xb85045b68181585d); + var x117: u64 = undefined; + var x118: u64 = undefined; + mulxU64(&x117, &x118, x111, 0x2833e84879b97091); + var x119: u64 = undefined; + var x120: u64 = undefined; + mulxU64(&x119, &x120, x111, 0x43e1f593f0000001); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, 0x0, x120, x117); + var x123: u64 = undefined; + var x124: u1 = undefined; + addcarryxU64(&x123, &x124, x122, x118, x115); + var x125: u64 = undefined; + var x126: u1 = undefined; + addcarryxU64(&x125, &x126, x124, x116, x113); + var x127: u64 = undefined; + var x128: u1 = undefined; + addcarryxU64(&x127, &x128, 0x0, x103, x119); + var x129: u64 = undefined; + var x130: u1 = undefined; + addcarryxU64(&x129, &x130, x128, x105, x121); + var x131: u64 = undefined; + var x132: u1 = undefined; + addcarryxU64(&x131, &x132, x130, x107, x123); + var x133: u64 = undefined; + var x134: u1 = undefined; + addcarryxU64(&x133, &x134, x132, x109, x125); + var x135: u64 = undefined; + var x136: u64 = undefined; + mulxU64(&x135, &x136, x3, 0x216d0b17f4e44a5); + var x137: u64 = undefined; + var x138: u64 = undefined; + mulxU64(&x137, &x138, x3, 0x8c49833d53bb8085); + var x139: u64 = undefined; + var x140: u64 = undefined; + mulxU64(&x139, &x140, x3, 0x53fe3ab1e35c59e3); + var x141: u64 = undefined; + var x142: u64 = undefined; + mulxU64(&x141, &x142, x3, 0x1bb8e645ae216da7); + var x143: u64 = undefined; + var x144: u1 = undefined; + addcarryxU64(&x143, &x144, 0x0, x142, x139); + var x145: u64 = undefined; + var x146: u1 = undefined; + addcarryxU64(&x145, &x146, x144, x140, x137); + var x147: u64 = undefined; + var x148: u1 = undefined; + addcarryxU64(&x147, &x148, x146, x138, x135); + var x149: u64 = undefined; + var x150: u1 = undefined; + addcarryxU64(&x149, &x150, 0x0, x129, x141); + var x151: u64 = undefined; + var x152: u1 = undefined; + addcarryxU64(&x151, &x152, x150, x131, x143); + var x153: u64 = undefined; + var x154: u1 = undefined; + addcarryxU64(&x153, &x154, x152, x133, x145); + var x155: u64 = undefined; + var x156: u1 = undefined; + addcarryxU64(&x155, &x156, x154, ((cast(u64, x134) + (cast(u64, x110) + (cast(u64, x102) + x90))) + (cast(u64, x126) + x114)), x147); + var x157: u64 = undefined; + var x158: u64 = undefined; + mulxU64(&x157, &x158, x149, 0xc2e1f593efffffff); + var x159: u64 = undefined; + var x160: u64 = undefined; + mulxU64(&x159, &x160, x157, 0x30644e72e131a029); + var x161: u64 = undefined; + var x162: u64 = undefined; + mulxU64(&x161, &x162, x157, 0xb85045b68181585d); + var x163: u64 = undefined; + var x164: u64 = undefined; + mulxU64(&x163, &x164, x157, 0x2833e84879b97091); + var x165: u64 = undefined; + var x166: u64 = undefined; + mulxU64(&x165, &x166, x157, 0x43e1f593f0000001); + var x167: u64 = undefined; + var x168: u1 = undefined; + addcarryxU64(&x167, &x168, 0x0, x166, x163); + var x169: u64 = undefined; + var x170: u1 = undefined; + addcarryxU64(&x169, &x170, x168, x164, x161); + var x171: u64 = undefined; + var x172: u1 = undefined; + addcarryxU64(&x171, &x172, x170, x162, x159); + var x173: u64 = undefined; + var x174: u1 = undefined; + addcarryxU64(&x173, &x174, 0x0, x149, x165); + var x175: u64 = undefined; + var x176: u1 = undefined; + addcarryxU64(&x175, &x176, x174, x151, x167); + var x177: u64 = undefined; + var x178: u1 = undefined; + addcarryxU64(&x177, &x178, x176, x153, x169); + var x179: u64 = undefined; + var x180: u1 = undefined; + addcarryxU64(&x179, &x180, x178, x155, x171); + const x181 = ((cast(u64, x180) + (cast(u64, x156) + (cast(u64, x148) + x136))) + (cast(u64, x172) + x160)); + var x182: u64 = undefined; + var x183: u1 = undefined; + subborrowxU64(&x182, &x183, 0x0, x175, 0x43e1f593f0000001); + var x184: u64 = undefined; + var x185: u1 = undefined; + subborrowxU64(&x184, &x185, x183, x177, 0x2833e84879b97091); + var x186: u64 = undefined; + var x187: u1 = undefined; + subborrowxU64(&x186, &x187, x185, x179, 0xb85045b68181585d); + var x188: u64 = undefined; + var x189: u1 = undefined; + subborrowxU64(&x188, &x189, x187, x181, 0x30644e72e131a029); + var x190: u64 = undefined; + var x191: u1 = undefined; + subborrowxU64(&x190, &x191, x189, cast(u64, 0x0), cast(u64, 0x0)); + var x192: u64 = undefined; + cmovznzU64(&x192, x191, x182, x175); + var x193: u64 = undefined; + cmovznzU64(&x193, x191, x184, x177); + var x194: u64 = undefined; + cmovznzU64(&x194, x191, x186, x179); + var x195: u64 = undefined; + cmovznzU64(&x195, x191, x188, x181); + out1[0] = x192; + out1[1] = x193; + out1[2] = x194; + out1[3] = x195; +} + +/// 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: +/// out1 = (if arg1 = 0 then arg2 else 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 ~> 0x3fffffffffffffff]] +/// 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 ~> 0x3f]] +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 ~> 0x3f]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x3fffffffffffffff]] +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 +/// +pub fn setOne(out1: *MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xac96341c4ffffffb; + out1[1] = 0x36fc76959f60cd29; + out1[2] = 0x666ea36f7879462e; + out1[3] = 0xe0a77c19a07df2f; +} + +/// The function msat returns the saturated representation of the prime modulus. +/// +/// Postconditions: +/// twos_complement_eval out1 = m +/// 0 ≤ eval out1 < m +/// +/// 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] = 0x43e1f593f0000001; + out1[1] = 0x2833e84879b97091; + out1[2] = 0xb85045b68181585d; + out1[3] = 0x30644e72e131a029; + out1[4] = cast(u64, 0x0); +} + +/// 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, 0x43e1f593f0000001); + var x41: u64 = undefined; + var x42: u1 = undefined; + subborrowxU64(&x41, &x42, x40, x33, 0x2833e84879b97091); + var x43: u64 = undefined; + var x44: u1 = undefined; + subborrowxU64(&x43, &x44, x42, x35, 0xb85045b68181585d); + var x45: u64 = undefined; + var x46: u1 = undefined; + subborrowxU64(&x45, &x46, x44, x37, 0x30644e72e131a029); + 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 & 0x43e1f593f0000001)); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x55, (x61 & 0x2833e84879b97091)); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x57, (x61 & 0xb85045b68181585d)); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x59, (x61 & 0x30644e72e131a029)); + 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, 0x43e1f593f0000001); + var x104: u64 = undefined; + var x105: u1 = undefined; + subborrowxU64(&x104, &x105, x103, x96, 0x2833e84879b97091); + var x106: u64 = undefined; + var x107: u1 = undefined; + subborrowxU64(&x106, &x107, x105, x98, 0xb85045b68181585d); + var x108: u64 = undefined; + var x109: u1 = undefined; + subborrowxU64(&x108, &x109, x107, x100, 0x30644e72e131a029); + 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; +} + +/// 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 +/// +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn divstepPrecomp(out1: *[4]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0x99ddb8c9f8b62554; + out1[1] = 0x9d24a395a4811e46; + out1[2] = 0x241215ce0ed81b0; + out1[3] = 0x2e6a72a316e4cfb6; +}