1// Autogenerated: 'src/ExtractionOCaml/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 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
   2// curve description (via package name): p256
   3// machine_wordsize = 64 (from "64")
   4// requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp
   5// m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1")
   6//
   7// NOTE: In addition to the bounds specified above each function, all
   8//   functions synthesized for this Montgomery arithmetic require the
   9//   input to be strictly less than the prime modulus (m), and also
  10//   require the input to be in the unique saturated representation.
  11//   All functions also ensure that these two properties are true of
  12//   return values.
  13//
  14// Computed values:
  15//   eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192)
  16//   bytes_eval z = z[0]
  17//   + (z[1] << 8)
  18//   + (z[2] << 16)
  19//   + (z[3] << 24)
  20//   + (z[4] << 32)
  21//   + (z[5] << 40)
  22//   + (z[6] << 48)
  23//   + (z[7] << 56)
  24//   + (z[8] << 64)
  25//   + (z[9] << 72)
  26//   + (z[10] << 80)
  27//   + (z[11] << 88)
  28//   + (z[12] << 96)
  29//   + (z[13] << 104)
  30//   + (z[14] << 112)
  31//   + (z[15] << 120)
  32//   + (z[16] << 128)
  33//   + (z[17] << 136)
  34//   + (z[18] << 144)
  35//   + (z[19] << 152)
  36//   + (z[20] << 160)
  37//   + (z[21] << 168)
  38//   + (z[22] << 176)
  39//   + (z[23] << 184)
  40//   + (z[24] << 192)
  41//   + (z[25] << 200)
  42//   + (z[26] << 208)
  43//   + (z[27] << 216)
  44//   + (z[28] << 224)
  45//   + (z[29] << 232)
  46//   + (z[30] << 240)
  47//   + (z[31] << 248)
  48//   twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in
  49//                            if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
  50
  51const std = @import("std");
  52const mode = @import("builtin").mode; // Checked arithmetic is disabled in non-debug modes to avoid side channels
  53
  54// The type MontgomeryDomainFieldElement is a field element in the Montgomery domain.
  55// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
  56pub const MontgomeryDomainFieldElement = [4]u64;
  57
  58// The type NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain.
  59// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
  60pub const NonMontgomeryDomainFieldElement = [4]u64;
  61
  62/// The function addcarryxU64 is an addition with carry.
  63///
  64/// Postconditions:
  65///   out1 = (arg1 + arg2 + arg3) mod 2^64
  66///   out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋
  67///
  68/// Input Bounds:
  69///   arg1: [0x0 ~> 0x1]
  70///   arg2: [0x0 ~> 0xffffffffffffffff]
  71///   arg3: [0x0 ~> 0xffffffffffffffff]
  72/// Output Bounds:
  73///   out1: [0x0 ~> 0xffffffffffffffff]
  74///   out2: [0x0 ~> 0x1]
  75fn addcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void {
  76    const x = @as(u128, arg2) +% arg3 +% arg1;
  77    out1.* = @truncate(x);
  78    out2.* = @truncate(x >> 64);
  79}
  80
  81/// The function subborrowxU64 is a subtraction with borrow.
  82///
  83/// Postconditions:
  84///   out1 = (-arg1 + arg2 + -arg3) mod 2^64
  85///   out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋
  86///
  87/// Input Bounds:
  88///   arg1: [0x0 ~> 0x1]
  89///   arg2: [0x0 ~> 0xffffffffffffffff]
  90///   arg3: [0x0 ~> 0xffffffffffffffff]
  91/// Output Bounds:
  92///   out1: [0x0 ~> 0xffffffffffffffff]
  93///   out2: [0x0 ~> 0x1]
  94fn subborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void {
  95    const x = @as(u128, arg2) -% arg3 -% arg1;
  96    out1.* = @truncate(x);
  97    out2.* = @truncate(x >> 64);
  98}
  99
 100/// The function mulxU64 is a multiplication, returning the full double-width result.
 101///
 102/// Postconditions:
 103///   out1 = (arg1 * arg2) mod 2^64
 104///   out2 = ⌊arg1 * arg2 / 2^64⌋
 105///
 106/// Input Bounds:
 107///   arg1: [0x0 ~> 0xffffffffffffffff]
 108///   arg2: [0x0 ~> 0xffffffffffffffff]
 109/// Output Bounds:
 110///   out1: [0x0 ~> 0xffffffffffffffff]
 111///   out2: [0x0 ~> 0xffffffffffffffff]
 112fn mulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) void {
 113    @setRuntimeSafety(mode == .Debug);
 114
 115    const x = @as(u128, arg1) * @as(u128, arg2);
 116    out1.* = @as(u64, @truncate(x));
 117    out2.* = @as(u64, @truncate(x >> 64));
 118}
 119
 120/// The function cmovznzU64 is a single-word conditional move.
 121///
 122/// Postconditions:
 123///   out1 = (if arg1 = 0 then arg2 else arg3)
 124///
 125/// Input Bounds:
 126///   arg1: [0x0 ~> 0x1]
 127///   arg2: [0x0 ~> 0xffffffffffffffff]
 128///   arg3: [0x0 ~> 0xffffffffffffffff]
 129/// Output Bounds:
 130///   out1: [0x0 ~> 0xffffffffffffffff]
 131fn cmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) void {
 132    @setRuntimeSafety(mode == .Debug);
 133
 134    const mask = 0 -% @as(u64, arg1);
 135    out1.* = (mask & arg3) | ((~mask) & arg2);
 136}
 137
 138/// The function mul multiplies two field elements in the Montgomery domain.
 139///
 140/// Preconditions:
 141///   0 ≤ eval arg1 < m
 142///   0 ≤ eval arg2 < m
 143/// Postconditions:
 144///   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
 145///   0 ≤ eval out1 < m
 146///
 147pub fn mul(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void {
 148    @setRuntimeSafety(mode == .Debug);
 149
 150    const x1 = (arg1[1]);
 151    const x2 = (arg1[2]);
 152    const x3 = (arg1[3]);
 153    const x4 = (arg1[0]);
 154    var x5: u64 = undefined;
 155    var x6: u64 = undefined;
 156    mulxU64(&x5, &x6, x4, (arg2[3]));
 157    var x7: u64 = undefined;
 158    var x8: u64 = undefined;
 159    mulxU64(&x7, &x8, x4, (arg2[2]));
 160    var x9: u64 = undefined;
 161    var x10: u64 = undefined;
 162    mulxU64(&x9, &x10, x4, (arg2[1]));
 163    var x11: u64 = undefined;
 164    var x12: u64 = undefined;
 165    mulxU64(&x11, &x12, x4, (arg2[0]));
 166    var x13: u64 = undefined;
 167    var x14: u1 = undefined;
 168    addcarryxU64(&x13, &x14, 0x0, x12, x9);
 169    var x15: u64 = undefined;
 170    var x16: u1 = undefined;
 171    addcarryxU64(&x15, &x16, x14, x10, x7);
 172    var x17: u64 = undefined;
 173    var x18: u1 = undefined;
 174    addcarryxU64(&x17, &x18, x16, x8, x5);
 175    const x19 = (@as(u64, x18) + x6);
 176    var x20: u64 = undefined;
 177    var x21: u64 = undefined;
 178    mulxU64(&x20, &x21, x11, 0xffffffff00000001);
 179    var x22: u64 = undefined;
 180    var x23: u64 = undefined;
 181    mulxU64(&x22, &x23, x11, 0xffffffff);
 182    var x24: u64 = undefined;
 183    var x25: u64 = undefined;
 184    mulxU64(&x24, &x25, x11, 0xffffffffffffffff);
 185    var x26: u64 = undefined;
 186    var x27: u1 = undefined;
 187    addcarryxU64(&x26, &x27, 0x0, x25, x22);
 188    const x28 = (@as(u64, x27) + x23);
 189    var x29: u64 = undefined;
 190    var x30: u1 = undefined;
 191    addcarryxU64(&x29, &x30, 0x0, x11, x24);
 192    var x31: u64 = undefined;
 193    var x32: u1 = undefined;
 194    addcarryxU64(&x31, &x32, x30, x13, x26);
 195    var x33: u64 = undefined;
 196    var x34: u1 = undefined;
 197    addcarryxU64(&x33, &x34, x32, x15, x28);
 198    var x35: u64 = undefined;
 199    var x36: u1 = undefined;
 200    addcarryxU64(&x35, &x36, x34, x17, x20);
 201    var x37: u64 = undefined;
 202    var x38: u1 = undefined;
 203    addcarryxU64(&x37, &x38, x36, x19, x21);
 204    var x39: u64 = undefined;
 205    var x40: u64 = undefined;
 206    mulxU64(&x39, &x40, x1, (arg2[3]));
 207    var x41: u64 = undefined;
 208    var x42: u64 = undefined;
 209    mulxU64(&x41, &x42, x1, (arg2[2]));
 210    var x43: u64 = undefined;
 211    var x44: u64 = undefined;
 212    mulxU64(&x43, &x44, x1, (arg2[1]));
 213    var x45: u64 = undefined;
 214    var x46: u64 = undefined;
 215    mulxU64(&x45, &x46, x1, (arg2[0]));
 216    var x47: u64 = undefined;
 217    var x48: u1 = undefined;
 218    addcarryxU64(&x47, &x48, 0x0, x46, x43);
 219    var x49: u64 = undefined;
 220    var x50: u1 = undefined;
 221    addcarryxU64(&x49, &x50, x48, x44, x41);
 222    var x51: u64 = undefined;
 223    var x52: u1 = undefined;
 224    addcarryxU64(&x51, &x52, x50, x42, x39);
 225    const x53 = (@as(u64, x52) + x40);
 226    var x54: u64 = undefined;
 227    var x55: u1 = undefined;
 228    addcarryxU64(&x54, &x55, 0x0, x31, x45);
 229    var x56: u64 = undefined;
 230    var x57: u1 = undefined;
 231    addcarryxU64(&x56, &x57, x55, x33, x47);
 232    var x58: u64 = undefined;
 233    var x59: u1 = undefined;
 234    addcarryxU64(&x58, &x59, x57, x35, x49);
 235    var x60: u64 = undefined;
 236    var x61: u1 = undefined;
 237    addcarryxU64(&x60, &x61, x59, x37, x51);
 238    var x62: u64 = undefined;
 239    var x63: u1 = undefined;
 240    addcarryxU64(&x62, &x63, x61, @as(u64, x38), x53);
 241    var x64: u64 = undefined;
 242    var x65: u64 = undefined;
 243    mulxU64(&x64, &x65, x54, 0xffffffff00000001);
 244    var x66: u64 = undefined;
 245    var x67: u64 = undefined;
 246    mulxU64(&x66, &x67, x54, 0xffffffff);
 247    var x68: u64 = undefined;
 248    var x69: u64 = undefined;
 249    mulxU64(&x68, &x69, x54, 0xffffffffffffffff);
 250    var x70: u64 = undefined;
 251    var x71: u1 = undefined;
 252    addcarryxU64(&x70, &x71, 0x0, x69, x66);
 253    const x72 = (@as(u64, x71) + x67);
 254    var x73: u64 = undefined;
 255    var x74: u1 = undefined;
 256    addcarryxU64(&x73, &x74, 0x0, x54, x68);
 257    var x75: u64 = undefined;
 258    var x76: u1 = undefined;
 259    addcarryxU64(&x75, &x76, x74, x56, x70);
 260    var x77: u64 = undefined;
 261    var x78: u1 = undefined;
 262    addcarryxU64(&x77, &x78, x76, x58, x72);
 263    var x79: u64 = undefined;
 264    var x80: u1 = undefined;
 265    addcarryxU64(&x79, &x80, x78, x60, x64);
 266    var x81: u64 = undefined;
 267    var x82: u1 = undefined;
 268    addcarryxU64(&x81, &x82, x80, x62, x65);
 269    const x83 = (@as(u64, x82) + @as(u64, x63));
 270    var x84: u64 = undefined;
 271    var x85: u64 = undefined;
 272    mulxU64(&x84, &x85, x2, (arg2[3]));
 273    var x86: u64 = undefined;
 274    var x87: u64 = undefined;
 275    mulxU64(&x86, &x87, x2, (arg2[2]));
 276    var x88: u64 = undefined;
 277    var x89: u64 = undefined;
 278    mulxU64(&x88, &x89, x2, (arg2[1]));
 279    var x90: u64 = undefined;
 280    var x91: u64 = undefined;
 281    mulxU64(&x90, &x91, x2, (arg2[0]));
 282    var x92: u64 = undefined;
 283    var x93: u1 = undefined;
 284    addcarryxU64(&x92, &x93, 0x0, x91, x88);
 285    var x94: u64 = undefined;
 286    var x95: u1 = undefined;
 287    addcarryxU64(&x94, &x95, x93, x89, x86);
 288    var x96: u64 = undefined;
 289    var x97: u1 = undefined;
 290    addcarryxU64(&x96, &x97, x95, x87, x84);
 291    const x98 = (@as(u64, x97) + x85);
 292    var x99: u64 = undefined;
 293    var x100: u1 = undefined;
 294    addcarryxU64(&x99, &x100, 0x0, x75, x90);
 295    var x101: u64 = undefined;
 296    var x102: u1 = undefined;
 297    addcarryxU64(&x101, &x102, x100, x77, x92);
 298    var x103: u64 = undefined;
 299    var x104: u1 = undefined;
 300    addcarryxU64(&x103, &x104, x102, x79, x94);
 301    var x105: u64 = undefined;
 302    var x106: u1 = undefined;
 303    addcarryxU64(&x105, &x106, x104, x81, x96);
 304    var x107: u64 = undefined;
 305    var x108: u1 = undefined;
 306    addcarryxU64(&x107, &x108, x106, x83, x98);
 307    var x109: u64 = undefined;
 308    var x110: u64 = undefined;
 309    mulxU64(&x109, &x110, x99, 0xffffffff00000001);
 310    var x111: u64 = undefined;
 311    var x112: u64 = undefined;
 312    mulxU64(&x111, &x112, x99, 0xffffffff);
 313    var x113: u64 = undefined;
 314    var x114: u64 = undefined;
 315    mulxU64(&x113, &x114, x99, 0xffffffffffffffff);
 316    var x115: u64 = undefined;
 317    var x116: u1 = undefined;
 318    addcarryxU64(&x115, &x116, 0x0, x114, x111);
 319    const x117 = (@as(u64, x116) + x112);
 320    var x118: u64 = undefined;
 321    var x119: u1 = undefined;
 322    addcarryxU64(&x118, &x119, 0x0, x99, x113);
 323    var x120: u64 = undefined;
 324    var x121: u1 = undefined;
 325    addcarryxU64(&x120, &x121, x119, x101, x115);
 326    var x122: u64 = undefined;
 327    var x123: u1 = undefined;
 328    addcarryxU64(&x122, &x123, x121, x103, x117);
 329    var x124: u64 = undefined;
 330    var x125: u1 = undefined;
 331    addcarryxU64(&x124, &x125, x123, x105, x109);
 332    var x126: u64 = undefined;
 333    var x127: u1 = undefined;
 334    addcarryxU64(&x126, &x127, x125, x107, x110);
 335    const x128 = (@as(u64, x127) + @as(u64, x108));
 336    var x129: u64 = undefined;
 337    var x130: u64 = undefined;
 338    mulxU64(&x129, &x130, x3, (arg2[3]));
 339    var x131: u64 = undefined;
 340    var x132: u64 = undefined;
 341    mulxU64(&x131, &x132, x3, (arg2[2]));
 342    var x133: u64 = undefined;
 343    var x134: u64 = undefined;
 344    mulxU64(&x133, &x134, x3, (arg2[1]));
 345    var x135: u64 = undefined;
 346    var x136: u64 = undefined;
 347    mulxU64(&x135, &x136, x3, (arg2[0]));
 348    var x137: u64 = undefined;
 349    var x138: u1 = undefined;
 350    addcarryxU64(&x137, &x138, 0x0, x136, x133);
 351    var x139: u64 = undefined;
 352    var x140: u1 = undefined;
 353    addcarryxU64(&x139, &x140, x138, x134, x131);
 354    var x141: u64 = undefined;
 355    var x142: u1 = undefined;
 356    addcarryxU64(&x141, &x142, x140, x132, x129);
 357    const x143 = (@as(u64, x142) + x130);
 358    var x144: u64 = undefined;
 359    var x145: u1 = undefined;
 360    addcarryxU64(&x144, &x145, 0x0, x120, x135);
 361    var x146: u64 = undefined;
 362    var x147: u1 = undefined;
 363    addcarryxU64(&x146, &x147, x145, x122, x137);
 364    var x148: u64 = undefined;
 365    var x149: u1 = undefined;
 366    addcarryxU64(&x148, &x149, x147, x124, x139);
 367    var x150: u64 = undefined;
 368    var x151: u1 = undefined;
 369    addcarryxU64(&x150, &x151, x149, x126, x141);
 370    var x152: u64 = undefined;
 371    var x153: u1 = undefined;
 372    addcarryxU64(&x152, &x153, x151, x128, x143);
 373    var x154: u64 = undefined;
 374    var x155: u64 = undefined;
 375    mulxU64(&x154, &x155, x144, 0xffffffff00000001);
 376    var x156: u64 = undefined;
 377    var x157: u64 = undefined;
 378    mulxU64(&x156, &x157, x144, 0xffffffff);
 379    var x158: u64 = undefined;
 380    var x159: u64 = undefined;
 381    mulxU64(&x158, &x159, x144, 0xffffffffffffffff);
 382    var x160: u64 = undefined;
 383    var x161: u1 = undefined;
 384    addcarryxU64(&x160, &x161, 0x0, x159, x156);
 385    const x162 = (@as(u64, x161) + x157);
 386    var x163: u64 = undefined;
 387    var x164: u1 = undefined;
 388    addcarryxU64(&x163, &x164, 0x0, x144, x158);
 389    var x165: u64 = undefined;
 390    var x166: u1 = undefined;
 391    addcarryxU64(&x165, &x166, x164, x146, x160);
 392    var x167: u64 = undefined;
 393    var x168: u1 = undefined;
 394    addcarryxU64(&x167, &x168, x166, x148, x162);
 395    var x169: u64 = undefined;
 396    var x170: u1 = undefined;
 397    addcarryxU64(&x169, &x170, x168, x150, x154);
 398    var x171: u64 = undefined;
 399    var x172: u1 = undefined;
 400    addcarryxU64(&x171, &x172, x170, x152, x155);
 401    const x173 = (@as(u64, x172) + @as(u64, x153));
 402    var x174: u64 = undefined;
 403    var x175: u1 = undefined;
 404    subborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff);
 405    var x176: u64 = undefined;
 406    var x177: u1 = undefined;
 407    subborrowxU64(&x176, &x177, x175, x167, 0xffffffff);
 408    var x178: u64 = undefined;
 409    var x179: u1 = undefined;
 410    subborrowxU64(&x178, &x179, x177, x169, @as(u64, 0x0));
 411    var x180: u64 = undefined;
 412    var x181: u1 = undefined;
 413    subborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001);
 414    var x182: u64 = undefined;
 415    var x183: u1 = undefined;
 416    subborrowxU64(&x182, &x183, x181, x173, @as(u64, 0x0));
 417    var x184: u64 = undefined;
 418    cmovznzU64(&x184, x183, x174, x165);
 419    var x185: u64 = undefined;
 420    cmovznzU64(&x185, x183, x176, x167);
 421    var x186: u64 = undefined;
 422    cmovznzU64(&x186, x183, x178, x169);
 423    var x187: u64 = undefined;
 424    cmovznzU64(&x187, x183, x180, x171);
 425    out1[0] = x184;
 426    out1[1] = x185;
 427    out1[2] = x186;
 428    out1[3] = x187;
 429}
 430
 431/// The function square squares a field element in the Montgomery domain.
 432///
 433/// Preconditions:
 434///   0 ≤ eval arg1 < m
 435/// Postconditions:
 436///   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m
 437///   0 ≤ eval out1 < m
 438///
 439pub fn square(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void {
 440    @setRuntimeSafety(mode == .Debug);
 441
 442    const x1 = (arg1[1]);
 443    const x2 = (arg1[2]);
 444    const x3 = (arg1[3]);
 445    const x4 = (arg1[0]);
 446    var x5: u64 = undefined;
 447    var x6: u64 = undefined;
 448    mulxU64(&x5, &x6, x4, (arg1[3]));
 449    var x7: u64 = undefined;
 450    var x8: u64 = undefined;
 451    mulxU64(&x7, &x8, x4, (arg1[2]));
 452    var x9: u64 = undefined;
 453    var x10: u64 = undefined;
 454    mulxU64(&x9, &x10, x4, (arg1[1]));
 455    var x11: u64 = undefined;
 456    var x12: u64 = undefined;
 457    mulxU64(&x11, &x12, x4, (arg1[0]));
 458    var x13: u64 = undefined;
 459    var x14: u1 = undefined;
 460    addcarryxU64(&x13, &x14, 0x0, x12, x9);
 461    var x15: u64 = undefined;
 462    var x16: u1 = undefined;
 463    addcarryxU64(&x15, &x16, x14, x10, x7);
 464    var x17: u64 = undefined;
 465    var x18: u1 = undefined;
 466    addcarryxU64(&x17, &x18, x16, x8, x5);
 467    const x19 = (@as(u64, x18) + x6);
 468    var x20: u64 = undefined;
 469    var x21: u64 = undefined;
 470    mulxU64(&x20, &x21, x11, 0xffffffff00000001);
 471    var x22: u64 = undefined;
 472    var x23: u64 = undefined;
 473    mulxU64(&x22, &x23, x11, 0xffffffff);
 474    var x24: u64 = undefined;
 475    var x25: u64 = undefined;
 476    mulxU64(&x24, &x25, x11, 0xffffffffffffffff);
 477    var x26: u64 = undefined;
 478    var x27: u1 = undefined;
 479    addcarryxU64(&x26, &x27, 0x0, x25, x22);
 480    const x28 = (@as(u64, x27) + x23);
 481    var x29: u64 = undefined;
 482    var x30: u1 = undefined;
 483    addcarryxU64(&x29, &x30, 0x0, x11, x24);
 484    var x31: u64 = undefined;
 485    var x32: u1 = undefined;
 486    addcarryxU64(&x31, &x32, x30, x13, x26);
 487    var x33: u64 = undefined;
 488    var x34: u1 = undefined;
 489    addcarryxU64(&x33, &x34, x32, x15, x28);
 490    var x35: u64 = undefined;
 491    var x36: u1 = undefined;
 492    addcarryxU64(&x35, &x36, x34, x17, x20);
 493    var x37: u64 = undefined;
 494    var x38: u1 = undefined;
 495    addcarryxU64(&x37, &x38, x36, x19, x21);
 496    var x39: u64 = undefined;
 497    var x40: u64 = undefined;
 498    mulxU64(&x39, &x40, x1, (arg1[3]));
 499    var x41: u64 = undefined;
 500    var x42: u64 = undefined;
 501    mulxU64(&x41, &x42, x1, (arg1[2]));
 502    var x43: u64 = undefined;
 503    var x44: u64 = undefined;
 504    mulxU64(&x43, &x44, x1, (arg1[1]));
 505    var x45: u64 = undefined;
 506    var x46: u64 = undefined;
 507    mulxU64(&x45, &x46, x1, (arg1[0]));
 508    var x47: u64 = undefined;
 509    var x48: u1 = undefined;
 510    addcarryxU64(&x47, &x48, 0x0, x46, x43);
 511    var x49: u64 = undefined;
 512    var x50: u1 = undefined;
 513    addcarryxU64(&x49, &x50, x48, x44, x41);
 514    var x51: u64 = undefined;
 515    var x52: u1 = undefined;
 516    addcarryxU64(&x51, &x52, x50, x42, x39);
 517    const x53 = (@as(u64, x52) + x40);
 518    var x54: u64 = undefined;
 519    var x55: u1 = undefined;
 520    addcarryxU64(&x54, &x55, 0x0, x31, x45);
 521    var x56: u64 = undefined;
 522    var x57: u1 = undefined;
 523    addcarryxU64(&x56, &x57, x55, x33, x47);
 524    var x58: u64 = undefined;
 525    var x59: u1 = undefined;
 526    addcarryxU64(&x58, &x59, x57, x35, x49);
 527    var x60: u64 = undefined;
 528    var x61: u1 = undefined;
 529    addcarryxU64(&x60, &x61, x59, x37, x51);
 530    var x62: u64 = undefined;
 531    var x63: u1 = undefined;
 532    addcarryxU64(&x62, &x63, x61, @as(u64, x38), x53);
 533    var x64: u64 = undefined;
 534    var x65: u64 = undefined;
 535    mulxU64(&x64, &x65, x54, 0xffffffff00000001);
 536    var x66: u64 = undefined;
 537    var x67: u64 = undefined;
 538    mulxU64(&x66, &x67, x54, 0xffffffff);
 539    var x68: u64 = undefined;
 540    var x69: u64 = undefined;
 541    mulxU64(&x68, &x69, x54, 0xffffffffffffffff);
 542    var x70: u64 = undefined;
 543    var x71: u1 = undefined;
 544    addcarryxU64(&x70, &x71, 0x0, x69, x66);
 545    const x72 = (@as(u64, x71) + x67);
 546    var x73: u64 = undefined;
 547    var x74: u1 = undefined;
 548    addcarryxU64(&x73, &x74, 0x0, x54, x68);
 549    var x75: u64 = undefined;
 550    var x76: u1 = undefined;
 551    addcarryxU64(&x75, &x76, x74, x56, x70);
 552    var x77: u64 = undefined;
 553    var x78: u1 = undefined;
 554    addcarryxU64(&x77, &x78, x76, x58, x72);
 555    var x79: u64 = undefined;
 556    var x80: u1 = undefined;
 557    addcarryxU64(&x79, &x80, x78, x60, x64);
 558    var x81: u64 = undefined;
 559    var x82: u1 = undefined;
 560    addcarryxU64(&x81, &x82, x80, x62, x65);
 561    const x83 = (@as(u64, x82) + @as(u64, x63));
 562    var x84: u64 = undefined;
 563    var x85: u64 = undefined;
 564    mulxU64(&x84, &x85, x2, (arg1[3]));
 565    var x86: u64 = undefined;
 566    var x87: u64 = undefined;
 567    mulxU64(&x86, &x87, x2, (arg1[2]));
 568    var x88: u64 = undefined;
 569    var x89: u64 = undefined;
 570    mulxU64(&x88, &x89, x2, (arg1[1]));
 571    var x90: u64 = undefined;
 572    var x91: u64 = undefined;
 573    mulxU64(&x90, &x91, x2, (arg1[0]));
 574    var x92: u64 = undefined;
 575    var x93: u1 = undefined;
 576    addcarryxU64(&x92, &x93, 0x0, x91, x88);
 577    var x94: u64 = undefined;
 578    var x95: u1 = undefined;
 579    addcarryxU64(&x94, &x95, x93, x89, x86);
 580    var x96: u64 = undefined;
 581    var x97: u1 = undefined;
 582    addcarryxU64(&x96, &x97, x95, x87, x84);
 583    const x98 = (@as(u64, x97) + x85);
 584    var x99: u64 = undefined;
 585    var x100: u1 = undefined;
 586    addcarryxU64(&x99, &x100, 0x0, x75, x90);
 587    var x101: u64 = undefined;
 588    var x102: u1 = undefined;
 589    addcarryxU64(&x101, &x102, x100, x77, x92);
 590    var x103: u64 = undefined;
 591    var x104: u1 = undefined;
 592    addcarryxU64(&x103, &x104, x102, x79, x94);
 593    var x105: u64 = undefined;
 594    var x106: u1 = undefined;
 595    addcarryxU64(&x105, &x106, x104, x81, x96);
 596    var x107: u64 = undefined;
 597    var x108: u1 = undefined;
 598    addcarryxU64(&x107, &x108, x106, x83, x98);
 599    var x109: u64 = undefined;
 600    var x110: u64 = undefined;
 601    mulxU64(&x109, &x110, x99, 0xffffffff00000001);
 602    var x111: u64 = undefined;
 603    var x112: u64 = undefined;
 604    mulxU64(&x111, &x112, x99, 0xffffffff);
 605    var x113: u64 = undefined;
 606    var x114: u64 = undefined;
 607    mulxU64(&x113, &x114, x99, 0xffffffffffffffff);
 608    var x115: u64 = undefined;
 609    var x116: u1 = undefined;
 610    addcarryxU64(&x115, &x116, 0x0, x114, x111);
 611    const x117 = (@as(u64, x116) + x112);
 612    var x118: u64 = undefined;
 613    var x119: u1 = undefined;
 614    addcarryxU64(&x118, &x119, 0x0, x99, x113);
 615    var x120: u64 = undefined;
 616    var x121: u1 = undefined;
 617    addcarryxU64(&x120, &x121, x119, x101, x115);
 618    var x122: u64 = undefined;
 619    var x123: u1 = undefined;
 620    addcarryxU64(&x122, &x123, x121, x103, x117);
 621    var x124: u64 = undefined;
 622    var x125: u1 = undefined;
 623    addcarryxU64(&x124, &x125, x123, x105, x109);
 624    var x126: u64 = undefined;
 625    var x127: u1 = undefined;
 626    addcarryxU64(&x126, &x127, x125, x107, x110);
 627    const x128 = (@as(u64, x127) + @as(u64, x108));
 628    var x129: u64 = undefined;
 629    var x130: u64 = undefined;
 630    mulxU64(&x129, &x130, x3, (arg1[3]));
 631    var x131: u64 = undefined;
 632    var x132: u64 = undefined;
 633    mulxU64(&x131, &x132, x3, (arg1[2]));
 634    var x133: u64 = undefined;
 635    var x134: u64 = undefined;
 636    mulxU64(&x133, &x134, x3, (arg1[1]));
 637    var x135: u64 = undefined;
 638    var x136: u64 = undefined;
 639    mulxU64(&x135, &x136, x3, (arg1[0]));
 640    var x137: u64 = undefined;
 641    var x138: u1 = undefined;
 642    addcarryxU64(&x137, &x138, 0x0, x136, x133);
 643    var x139: u64 = undefined;
 644    var x140: u1 = undefined;
 645    addcarryxU64(&x139, &x140, x138, x134, x131);
 646    var x141: u64 = undefined;
 647    var x142: u1 = undefined;
 648    addcarryxU64(&x141, &x142, x140, x132, x129);
 649    const x143 = (@as(u64, x142) + x130);
 650    var x144: u64 = undefined;
 651    var x145: u1 = undefined;
 652    addcarryxU64(&x144, &x145, 0x0, x120, x135);
 653    var x146: u64 = undefined;
 654    var x147: u1 = undefined;
 655    addcarryxU64(&x146, &x147, x145, x122, x137);
 656    var x148: u64 = undefined;
 657    var x149: u1 = undefined;
 658    addcarryxU64(&x148, &x149, x147, x124, x139);
 659    var x150: u64 = undefined;
 660    var x151: u1 = undefined;
 661    addcarryxU64(&x150, &x151, x149, x126, x141);
 662    var x152: u64 = undefined;
 663    var x153: u1 = undefined;
 664    addcarryxU64(&x152, &x153, x151, x128, x143);
 665    var x154: u64 = undefined;
 666    var x155: u64 = undefined;
 667    mulxU64(&x154, &x155, x144, 0xffffffff00000001);
 668    var x156: u64 = undefined;
 669    var x157: u64 = undefined;
 670    mulxU64(&x156, &x157, x144, 0xffffffff);
 671    var x158: u64 = undefined;
 672    var x159: u64 = undefined;
 673    mulxU64(&x158, &x159, x144, 0xffffffffffffffff);
 674    var x160: u64 = undefined;
 675    var x161: u1 = undefined;
 676    addcarryxU64(&x160, &x161, 0x0, x159, x156);
 677    const x162 = (@as(u64, x161) + x157);
 678    var x163: u64 = undefined;
 679    var x164: u1 = undefined;
 680    addcarryxU64(&x163, &x164, 0x0, x144, x158);
 681    var x165: u64 = undefined;
 682    var x166: u1 = undefined;
 683    addcarryxU64(&x165, &x166, x164, x146, x160);
 684    var x167: u64 = undefined;
 685    var x168: u1 = undefined;
 686    addcarryxU64(&x167, &x168, x166, x148, x162);
 687    var x169: u64 = undefined;
 688    var x170: u1 = undefined;
 689    addcarryxU64(&x169, &x170, x168, x150, x154);
 690    var x171: u64 = undefined;
 691    var x172: u1 = undefined;
 692    addcarryxU64(&x171, &x172, x170, x152, x155);
 693    const x173 = (@as(u64, x172) + @as(u64, x153));
 694    var x174: u64 = undefined;
 695    var x175: u1 = undefined;
 696    subborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff);
 697    var x176: u64 = undefined;
 698    var x177: u1 = undefined;
 699    subborrowxU64(&x176, &x177, x175, x167, 0xffffffff);
 700    var x178: u64 = undefined;
 701    var x179: u1 = undefined;
 702    subborrowxU64(&x178, &x179, x177, x169, @as(u64, 0x0));
 703    var x180: u64 = undefined;
 704    var x181: u1 = undefined;
 705    subborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001);
 706    var x182: u64 = undefined;
 707    var x183: u1 = undefined;
 708    subborrowxU64(&x182, &x183, x181, x173, @as(u64, 0x0));
 709    var x184: u64 = undefined;
 710    cmovznzU64(&x184, x183, x174, x165);
 711    var x185: u64 = undefined;
 712    cmovznzU64(&x185, x183, x176, x167);
 713    var x186: u64 = undefined;
 714    cmovznzU64(&x186, x183, x178, x169);
 715    var x187: u64 = undefined;
 716    cmovznzU64(&x187, x183, x180, x171);
 717    out1[0] = x184;
 718    out1[1] = x185;
 719    out1[2] = x186;
 720    out1[3] = x187;
 721}
 722
 723/// The function add adds two field elements in the Montgomery domain.
 724///
 725/// Preconditions:
 726///   0 ≤ eval arg1 < m
 727///   0 ≤ eval arg2 < m
 728/// Postconditions:
 729///   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
 730///   0 ≤ eval out1 < m
 731///
 732pub fn add(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void {
 733    @setRuntimeSafety(mode == .Debug);
 734
 735    var x1: u64 = undefined;
 736    var x2: u1 = undefined;
 737    addcarryxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
 738    var x3: u64 = undefined;
 739    var x4: u1 = undefined;
 740    addcarryxU64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
 741    var x5: u64 = undefined;
 742    var x6: u1 = undefined;
 743    addcarryxU64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
 744    var x7: u64 = undefined;
 745    var x8: u1 = undefined;
 746    addcarryxU64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
 747    var x9: u64 = undefined;
 748    var x10: u1 = undefined;
 749    subborrowxU64(&x9, &x10, 0x0, x1, 0xffffffffffffffff);
 750    var x11: u64 = undefined;
 751    var x12: u1 = undefined;
 752    subborrowxU64(&x11, &x12, x10, x3, 0xffffffff);
 753    var x13: u64 = undefined;
 754    var x14: u1 = undefined;
 755    subborrowxU64(&x13, &x14, x12, x5, @as(u64, 0x0));
 756    var x15: u64 = undefined;
 757    var x16: u1 = undefined;
 758    subborrowxU64(&x15, &x16, x14, x7, 0xffffffff00000001);
 759    var x17: u64 = undefined;
 760    var x18: u1 = undefined;
 761    subborrowxU64(&x17, &x18, x16, @as(u64, x8), @as(u64, 0x0));
 762    var x19: u64 = undefined;
 763    cmovznzU64(&x19, x18, x9, x1);
 764    var x20: u64 = undefined;
 765    cmovznzU64(&x20, x18, x11, x3);
 766    var x21: u64 = undefined;
 767    cmovznzU64(&x21, x18, x13, x5);
 768    var x22: u64 = undefined;
 769    cmovznzU64(&x22, x18, x15, x7);
 770    out1[0] = x19;
 771    out1[1] = x20;
 772    out1[2] = x21;
 773    out1[3] = x22;
 774}
 775
 776/// The function sub subtracts two field elements in the Montgomery domain.
 777///
 778/// Preconditions:
 779///   0 ≤ eval arg1 < m
 780///   0 ≤ eval arg2 < m
 781/// Postconditions:
 782///   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
 783///   0 ≤ eval out1 < m
 784///
 785pub fn sub(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void {
 786    @setRuntimeSafety(mode == .Debug);
 787
 788    var x1: u64 = undefined;
 789    var x2: u1 = undefined;
 790    subborrowxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
 791    var x3: u64 = undefined;
 792    var x4: u1 = undefined;
 793    subborrowxU64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
 794    var x5: u64 = undefined;
 795    var x6: u1 = undefined;
 796    subborrowxU64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
 797    var x7: u64 = undefined;
 798    var x8: u1 = undefined;
 799    subborrowxU64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
 800    var x9: u64 = undefined;
 801    cmovznzU64(&x9, x8, @as(u64, 0x0), 0xffffffffffffffff);
 802    var x10: u64 = undefined;
 803    var x11: u1 = undefined;
 804    addcarryxU64(&x10, &x11, 0x0, x1, x9);
 805    var x12: u64 = undefined;
 806    var x13: u1 = undefined;
 807    addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff));
 808    var x14: u64 = undefined;
 809    var x15: u1 = undefined;
 810    addcarryxU64(&x14, &x15, x13, x5, @as(u64, 0x0));
 811    var x16: u64 = undefined;
 812    var x17: u1 = undefined;
 813    addcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001));
 814    out1[0] = x10;
 815    out1[1] = x12;
 816    out1[2] = x14;
 817    out1[3] = x16;
 818}
 819
 820/// The function opp negates a field element in the Montgomery domain.
 821///
 822/// Preconditions:
 823///   0 ≤ eval arg1 < m
 824/// Postconditions:
 825///   eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
 826///   0 ≤ eval out1 < m
 827///
 828pub fn opp(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void {
 829    @setRuntimeSafety(mode == .Debug);
 830
 831    var x1: u64 = undefined;
 832    var x2: u1 = undefined;
 833    subborrowxU64(&x1, &x2, 0x0, @as(u64, 0x0), (arg1[0]));
 834    var x3: u64 = undefined;
 835    var x4: u1 = undefined;
 836    subborrowxU64(&x3, &x4, x2, @as(u64, 0x0), (arg1[1]));
 837    var x5: u64 = undefined;
 838    var x6: u1 = undefined;
 839    subborrowxU64(&x5, &x6, x4, @as(u64, 0x0), (arg1[2]));
 840    var x7: u64 = undefined;
 841    var x8: u1 = undefined;
 842    subborrowxU64(&x7, &x8, x6, @as(u64, 0x0), (arg1[3]));
 843    var x9: u64 = undefined;
 844    cmovznzU64(&x9, x8, @as(u64, 0x0), 0xffffffffffffffff);
 845    var x10: u64 = undefined;
 846    var x11: u1 = undefined;
 847    addcarryxU64(&x10, &x11, 0x0, x1, x9);
 848    var x12: u64 = undefined;
 849    var x13: u1 = undefined;
 850    addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff));
 851    var x14: u64 = undefined;
 852    var x15: u1 = undefined;
 853    addcarryxU64(&x14, &x15, x13, x5, @as(u64, 0x0));
 854    var x16: u64 = undefined;
 855    var x17: u1 = undefined;
 856    addcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001));
 857    out1[0] = x10;
 858    out1[1] = x12;
 859    out1[2] = x14;
 860    out1[3] = x16;
 861}
 862
 863/// The function fromMontgomery translates a field element out of the Montgomery domain.
 864///
 865/// Preconditions:
 866///   0 ≤ eval arg1 < m
 867/// Postconditions:
 868///   eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
 869///   0 ≤ eval out1 < m
 870///
 871pub fn fromMontgomery(out1: *NonMontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void {
 872    @setRuntimeSafety(mode == .Debug);
 873
 874    const x1 = (arg1[0]);
 875    var x2: u64 = undefined;
 876    var x3: u64 = undefined;
 877    mulxU64(&x2, &x3, x1, 0xffffffff00000001);
 878    var x4: u64 = undefined;
 879    var x5: u64 = undefined;
 880    mulxU64(&x4, &x5, x1, 0xffffffff);
 881    var x6: u64 = undefined;
 882    var x7: u64 = undefined;
 883    mulxU64(&x6, &x7, x1, 0xffffffffffffffff);
 884    var x8: u64 = undefined;
 885    var x9: u1 = undefined;
 886    addcarryxU64(&x8, &x9, 0x0, x7, x4);
 887    var x10: u64 = undefined;
 888    var x11: u1 = undefined;
 889    addcarryxU64(&x10, &x11, 0x0, x1, x6);
 890    var x12: u64 = undefined;
 891    var x13: u1 = undefined;
 892    addcarryxU64(&x12, &x13, x11, @as(u64, 0x0), x8);
 893    var x14: u64 = undefined;
 894    var x15: u1 = undefined;
 895    addcarryxU64(&x14, &x15, 0x0, x12, (arg1[1]));
 896    var x16: u64 = undefined;
 897    var x17: u64 = undefined;
 898    mulxU64(&x16, &x17, x14, 0xffffffff00000001);
 899    var x18: u64 = undefined;
 900    var x19: u64 = undefined;
 901    mulxU64(&x18, &x19, x14, 0xffffffff);
 902    var x20: u64 = undefined;
 903    var x21: u64 = undefined;
 904    mulxU64(&x20, &x21, x14, 0xffffffffffffffff);
 905    var x22: u64 = undefined;
 906    var x23: u1 = undefined;
 907    addcarryxU64(&x22, &x23, 0x0, x21, x18);
 908    var x24: u64 = undefined;
 909    var x25: u1 = undefined;
 910    addcarryxU64(&x24, &x25, 0x0, x14, x20);
 911    var x26: u64 = undefined;
 912    var x27: u1 = undefined;
 913    addcarryxU64(&x26, &x27, x25, (@as(u64, x15) + (@as(u64, x13) + (@as(u64, x9) + x5))), x22);
 914    var x28: u64 = undefined;
 915    var x29: u1 = undefined;
 916    addcarryxU64(&x28, &x29, x27, x2, (@as(u64, x23) + x19));
 917    var x30: u64 = undefined;
 918    var x31: u1 = undefined;
 919    addcarryxU64(&x30, &x31, x29, x3, x16);
 920    var x32: u64 = undefined;
 921    var x33: u1 = undefined;
 922    addcarryxU64(&x32, &x33, 0x0, x26, (arg1[2]));
 923    var x34: u64 = undefined;
 924    var x35: u1 = undefined;
 925    addcarryxU64(&x34, &x35, x33, x28, @as(u64, 0x0));
 926    var x36: u64 = undefined;
 927    var x37: u1 = undefined;
 928    addcarryxU64(&x36, &x37, x35, x30, @as(u64, 0x0));
 929    var x38: u64 = undefined;
 930    var x39: u64 = undefined;
 931    mulxU64(&x38, &x39, x32, 0xffffffff00000001);
 932    var x40: u64 = undefined;
 933    var x41: u64 = undefined;
 934    mulxU64(&x40, &x41, x32, 0xffffffff);
 935    var x42: u64 = undefined;
 936    var x43: u64 = undefined;
 937    mulxU64(&x42, &x43, x32, 0xffffffffffffffff);
 938    var x44: u64 = undefined;
 939    var x45: u1 = undefined;
 940    addcarryxU64(&x44, &x45, 0x0, x43, x40);
 941    var x46: u64 = undefined;
 942    var x47: u1 = undefined;
 943    addcarryxU64(&x46, &x47, 0x0, x32, x42);
 944    var x48: u64 = undefined;
 945    var x49: u1 = undefined;
 946    addcarryxU64(&x48, &x49, x47, x34, x44);
 947    var x50: u64 = undefined;
 948    var x51: u1 = undefined;
 949    addcarryxU64(&x50, &x51, x49, x36, (@as(u64, x45) + x41));
 950    var x52: u64 = undefined;
 951    var x53: u1 = undefined;
 952    addcarryxU64(&x52, &x53, x51, (@as(u64, x37) + (@as(u64, x31) + x17)), x38);
 953    var x54: u64 = undefined;
 954    var x55: u1 = undefined;
 955    addcarryxU64(&x54, &x55, 0x0, x48, (arg1[3]));
 956    var x56: u64 = undefined;
 957    var x57: u1 = undefined;
 958    addcarryxU64(&x56, &x57, x55, x50, @as(u64, 0x0));
 959    var x58: u64 = undefined;
 960    var x59: u1 = undefined;
 961    addcarryxU64(&x58, &x59, x57, x52, @as(u64, 0x0));
 962    var x60: u64 = undefined;
 963    var x61: u64 = undefined;
 964    mulxU64(&x60, &x61, x54, 0xffffffff00000001);
 965    var x62: u64 = undefined;
 966    var x63: u64 = undefined;
 967    mulxU64(&x62, &x63, x54, 0xffffffff);
 968    var x64: u64 = undefined;
 969    var x65: u64 = undefined;
 970    mulxU64(&x64, &x65, x54, 0xffffffffffffffff);
 971    var x66: u64 = undefined;
 972    var x67: u1 = undefined;
 973    addcarryxU64(&x66, &x67, 0x0, x65, x62);
 974    var x68: u64 = undefined;
 975    var x69: u1 = undefined;
 976    addcarryxU64(&x68, &x69, 0x0, x54, x64);
 977    var x70: u64 = undefined;
 978    var x71: u1 = undefined;
 979    addcarryxU64(&x70, &x71, x69, x56, x66);
 980    var x72: u64 = undefined;
 981    var x73: u1 = undefined;
 982    addcarryxU64(&x72, &x73, x71, x58, (@as(u64, x67) + x63));
 983    var x74: u64 = undefined;
 984    var x75: u1 = undefined;
 985    addcarryxU64(&x74, &x75, x73, (@as(u64, x59) + (@as(u64, x53) + x39)), x60);
 986    const x76 = (@as(u64, x75) + x61);
 987    var x77: u64 = undefined;
 988    var x78: u1 = undefined;
 989    subborrowxU64(&x77, &x78, 0x0, x70, 0xffffffffffffffff);
 990    var x79: u64 = undefined;
 991    var x80: u1 = undefined;
 992    subborrowxU64(&x79, &x80, x78, x72, 0xffffffff);
 993    var x81: u64 = undefined;
 994    var x82: u1 = undefined;
 995    subborrowxU64(&x81, &x82, x80, x74, @as(u64, 0x0));
 996    var x83: u64 = undefined;
 997    var x84: u1 = undefined;
 998    subborrowxU64(&x83, &x84, x82, x76, 0xffffffff00000001);
 999    var x85: u64 = undefined;
1000    var x86: u1 = undefined;
1001    subborrowxU64(&x85, &x86, x84, @as(u64, 0x0), @as(u64, 0x0));
1002    var x87: u64 = undefined;
1003    cmovznzU64(&x87, x86, x77, x70);
1004    var x88: u64 = undefined;
1005    cmovznzU64(&x88, x86, x79, x72);
1006    var x89: u64 = undefined;
1007    cmovznzU64(&x89, x86, x81, x74);
1008    var x90: u64 = undefined;
1009    cmovznzU64(&x90, x86, x83, x76);
1010    out1[0] = x87;
1011    out1[1] = x88;
1012    out1[2] = x89;
1013    out1[3] = x90;
1014}
1015
1016/// The function toMontgomery translates a field element into the Montgomery domain.
1017///
1018/// Preconditions:
1019///   0 ≤ eval arg1 < m
1020/// Postconditions:
1021///   eval (from_montgomery out1) mod m = eval arg1 mod m
1022///   0 ≤ eval out1 < m
1023///
1024pub fn toMontgomery(out1: *MontgomeryDomainFieldElement, arg1: NonMontgomeryDomainFieldElement) void {
1025    @setRuntimeSafety(mode == .Debug);
1026
1027    const x1 = (arg1[1]);
1028    const x2 = (arg1[2]);
1029    const x3 = (arg1[3]);
1030    const x4 = (arg1[0]);
1031    var x5: u64 = undefined;
1032    var x6: u64 = undefined;
1033    mulxU64(&x5, &x6, x4, 0x4fffffffd);
1034    var x7: u64 = undefined;
1035    var x8: u64 = undefined;
1036    mulxU64(&x7, &x8, x4, 0xfffffffffffffffe);
1037    var x9: u64 = undefined;
1038    var x10: u64 = undefined;
1039    mulxU64(&x9, &x10, x4, 0xfffffffbffffffff);
1040    var x11: u64 = undefined;
1041    var x12: u64 = undefined;
1042    mulxU64(&x11, &x12, x4, 0x3);
1043    var x13: u64 = undefined;
1044    var x14: u1 = undefined;
1045    addcarryxU64(&x13, &x14, 0x0, x12, x9);
1046    var x15: u64 = undefined;
1047    var x16: u1 = undefined;
1048    addcarryxU64(&x15, &x16, x14, x10, x7);
1049    var x17: u64 = undefined;
1050    var x18: u1 = undefined;
1051    addcarryxU64(&x17, &x18, x16, x8, x5);
1052    var x19: u64 = undefined;
1053    var x20: u64 = undefined;
1054    mulxU64(&x19, &x20, x11, 0xffffffff00000001);
1055    var x21: u64 = undefined;
1056    var x22: u64 = undefined;
1057    mulxU64(&x21, &x22, x11, 0xffffffff);
1058    var x23: u64 = undefined;
1059    var x24: u64 = undefined;
1060    mulxU64(&x23, &x24, x11, 0xffffffffffffffff);
1061    var x25: u64 = undefined;
1062    var x26: u1 = undefined;
1063    addcarryxU64(&x25, &x26, 0x0, x24, x21);
1064    var x27: u64 = undefined;
1065    var x28: u1 = undefined;
1066    addcarryxU64(&x27, &x28, 0x0, x11, x23);
1067    var x29: u64 = undefined;
1068    var x30: u1 = undefined;
1069    addcarryxU64(&x29, &x30, x28, x13, x25);
1070    var x31: u64 = undefined;
1071    var x32: u1 = undefined;
1072    addcarryxU64(&x31, &x32, x30, x15, (@as(u64, x26) + x22));
1073    var x33: u64 = undefined;
1074    var x34: u1 = undefined;
1075    addcarryxU64(&x33, &x34, x32, x17, x19);
1076    var x35: u64 = undefined;
1077    var x36: u1 = undefined;
1078    addcarryxU64(&x35, &x36, x34, (@as(u64, x18) + x6), x20);
1079    var x37: u64 = undefined;
1080    var x38: u64 = undefined;
1081    mulxU64(&x37, &x38, x1, 0x4fffffffd);
1082    var x39: u64 = undefined;
1083    var x40: u64 = undefined;
1084    mulxU64(&x39, &x40, x1, 0xfffffffffffffffe);
1085    var x41: u64 = undefined;
1086    var x42: u64 = undefined;
1087    mulxU64(&x41, &x42, x1, 0xfffffffbffffffff);
1088    var x43: u64 = undefined;
1089    var x44: u64 = undefined;
1090    mulxU64(&x43, &x44, x1, 0x3);
1091    var x45: u64 = undefined;
1092    var x46: u1 = undefined;
1093    addcarryxU64(&x45, &x46, 0x0, x44, x41);
1094    var x47: u64 = undefined;
1095    var x48: u1 = undefined;
1096    addcarryxU64(&x47, &x48, x46, x42, x39);
1097    var x49: u64 = undefined;
1098    var x50: u1 = undefined;
1099    addcarryxU64(&x49, &x50, x48, x40, x37);
1100    var x51: u64 = undefined;
1101    var x52: u1 = undefined;
1102    addcarryxU64(&x51, &x52, 0x0, x29, x43);
1103    var x53: u64 = undefined;
1104    var x54: u1 = undefined;
1105    addcarryxU64(&x53, &x54, x52, x31, x45);
1106    var x55: u64 = undefined;
1107    var x56: u1 = undefined;
1108    addcarryxU64(&x55, &x56, x54, x33, x47);
1109    var x57: u64 = undefined;
1110    var x58: u1 = undefined;
1111    addcarryxU64(&x57, &x58, x56, x35, x49);
1112    var x59: u64 = undefined;
1113    var x60: u64 = undefined;
1114    mulxU64(&x59, &x60, x51, 0xffffffff00000001);
1115    var x61: u64 = undefined;
1116    var x62: u64 = undefined;
1117    mulxU64(&x61, &x62, x51, 0xffffffff);
1118    var x63: u64 = undefined;
1119    var x64: u64 = undefined;
1120    mulxU64(&x63, &x64, x51, 0xffffffffffffffff);
1121    var x65: u64 = undefined;
1122    var x66: u1 = undefined;
1123    addcarryxU64(&x65, &x66, 0x0, x64, x61);
1124    var x67: u64 = undefined;
1125    var x68: u1 = undefined;
1126    addcarryxU64(&x67, &x68, 0x0, x51, x63);
1127    var x69: u64 = undefined;
1128    var x70: u1 = undefined;
1129    addcarryxU64(&x69, &x70, x68, x53, x65);
1130    var x71: u64 = undefined;
1131    var x72: u1 = undefined;
1132    addcarryxU64(&x71, &x72, x70, x55, (@as(u64, x66) + x62));
1133    var x73: u64 = undefined;
1134    var x74: u1 = undefined;
1135    addcarryxU64(&x73, &x74, x72, x57, x59);
1136    var x75: u64 = undefined;
1137    var x76: u1 = undefined;
1138    addcarryxU64(&x75, &x76, x74, ((@as(u64, x58) + @as(u64, x36)) + (@as(u64, x50) + x38)), x60);
1139    var x77: u64 = undefined;
1140    var x78: u64 = undefined;
1141    mulxU64(&x77, &x78, x2, 0x4fffffffd);
1142    var x79: u64 = undefined;
1143    var x80: u64 = undefined;
1144    mulxU64(&x79, &x80, x2, 0xfffffffffffffffe);
1145    var x81: u64 = undefined;
1146    var x82: u64 = undefined;
1147    mulxU64(&x81, &x82, x2, 0xfffffffbffffffff);
1148    var x83: u64 = undefined;
1149    var x84: u64 = undefined;
1150    mulxU64(&x83, &x84, x2, 0x3);
1151    var x85: u64 = undefined;
1152    var x86: u1 = undefined;
1153    addcarryxU64(&x85, &x86, 0x0, x84, x81);
1154    var x87: u64 = undefined;
1155    var x88: u1 = undefined;
1156    addcarryxU64(&x87, &x88, x86, x82, x79);
1157    var x89: u64 = undefined;
1158    var x90: u1 = undefined;
1159    addcarryxU64(&x89, &x90, x88, x80, x77);
1160    var x91: u64 = undefined;
1161    var x92: u1 = undefined;
1162    addcarryxU64(&x91, &x92, 0x0, x69, x83);
1163    var x93: u64 = undefined;
1164    var x94: u1 = undefined;
1165    addcarryxU64(&x93, &x94, x92, x71, x85);
1166    var x95: u64 = undefined;
1167    var x96: u1 = undefined;
1168    addcarryxU64(&x95, &x96, x94, x73, x87);
1169    var x97: u64 = undefined;
1170    var x98: u1 = undefined;
1171    addcarryxU64(&x97, &x98, x96, x75, x89);
1172    var x99: u64 = undefined;
1173    var x100: u64 = undefined;
1174    mulxU64(&x99, &x100, x91, 0xffffffff00000001);
1175    var x101: u64 = undefined;
1176    var x102: u64 = undefined;
1177    mulxU64(&x101, &x102, x91, 0xffffffff);
1178    var x103: u64 = undefined;
1179    var x104: u64 = undefined;
1180    mulxU64(&x103, &x104, x91, 0xffffffffffffffff);
1181    var x105: u64 = undefined;
1182    var x106: u1 = undefined;
1183    addcarryxU64(&x105, &x106, 0x0, x104, x101);
1184    var x107: u64 = undefined;
1185    var x108: u1 = undefined;
1186    addcarryxU64(&x107, &x108, 0x0, x91, x103);
1187    var x109: u64 = undefined;
1188    var x110: u1 = undefined;
1189    addcarryxU64(&x109, &x110, x108, x93, x105);
1190    var x111: u64 = undefined;
1191    var x112: u1 = undefined;
1192    addcarryxU64(&x111, &x112, x110, x95, (@as(u64, x106) + x102));
1193    var x113: u64 = undefined;
1194    var x114: u1 = undefined;
1195    addcarryxU64(&x113, &x114, x112, x97, x99);
1196    var x115: u64 = undefined;
1197    var x116: u1 = undefined;
1198    addcarryxU64(&x115, &x116, x114, ((@as(u64, x98) + @as(u64, x76)) + (@as(u64, x90) + x78)), x100);
1199    var x117: u64 = undefined;
1200    var x118: u64 = undefined;
1201    mulxU64(&x117, &x118, x3, 0x4fffffffd);
1202    var x119: u64 = undefined;
1203    var x120: u64 = undefined;
1204    mulxU64(&x119, &x120, x3, 0xfffffffffffffffe);
1205    var x121: u64 = undefined;
1206    var x122: u64 = undefined;
1207    mulxU64(&x121, &x122, x3, 0xfffffffbffffffff);
1208    var x123: u64 = undefined;
1209    var x124: u64 = undefined;
1210    mulxU64(&x123, &x124, x3, 0x3);
1211    var x125: u64 = undefined;
1212    var x126: u1 = undefined;
1213    addcarryxU64(&x125, &x126, 0x0, x124, x121);
1214    var x127: u64 = undefined;
1215    var x128: u1 = undefined;
1216    addcarryxU64(&x127, &x128, x126, x122, x119);
1217    var x129: u64 = undefined;
1218    var x130: u1 = undefined;
1219    addcarryxU64(&x129, &x130, x128, x120, x117);
1220    var x131: u64 = undefined;
1221    var x132: u1 = undefined;
1222    addcarryxU64(&x131, &x132, 0x0, x109, x123);
1223    var x133: u64 = undefined;
1224    var x134: u1 = undefined;
1225    addcarryxU64(&x133, &x134, x132, x111, x125);
1226    var x135: u64 = undefined;
1227    var x136: u1 = undefined;
1228    addcarryxU64(&x135, &x136, x134, x113, x127);
1229    var x137: u64 = undefined;
1230    var x138: u1 = undefined;
1231    addcarryxU64(&x137, &x138, x136, x115, x129);
1232    var x139: u64 = undefined;
1233    var x140: u64 = undefined;
1234    mulxU64(&x139, &x140, x131, 0xffffffff00000001);
1235    var x141: u64 = undefined;
1236    var x142: u64 = undefined;
1237    mulxU64(&x141, &x142, x131, 0xffffffff);
1238    var x143: u64 = undefined;
1239    var x144: u64 = undefined;
1240    mulxU64(&x143, &x144, x131, 0xffffffffffffffff);
1241    var x145: u64 = undefined;
1242    var x146: u1 = undefined;
1243    addcarryxU64(&x145, &x146, 0x0, x144, x141);
1244    var x147: u64 = undefined;
1245    var x148: u1 = undefined;
1246    addcarryxU64(&x147, &x148, 0x0, x131, x143);
1247    var x149: u64 = undefined;
1248    var x150: u1 = undefined;
1249    addcarryxU64(&x149, &x150, x148, x133, x145);
1250    var x151: u64 = undefined;
1251    var x152: u1 = undefined;
1252    addcarryxU64(&x151, &x152, x150, x135, (@as(u64, x146) + x142));
1253    var x153: u64 = undefined;
1254    var x154: u1 = undefined;
1255    addcarryxU64(&x153, &x154, x152, x137, x139);
1256    var x155: u64 = undefined;
1257    var x156: u1 = undefined;
1258    addcarryxU64(&x155, &x156, x154, ((@as(u64, x138) + @as(u64, x116)) + (@as(u64, x130) + x118)), x140);
1259    var x157: u64 = undefined;
1260    var x158: u1 = undefined;
1261    subborrowxU64(&x157, &x158, 0x0, x149, 0xffffffffffffffff);
1262    var x159: u64 = undefined;
1263    var x160: u1 = undefined;
1264    subborrowxU64(&x159, &x160, x158, x151, 0xffffffff);
1265    var x161: u64 = undefined;
1266    var x162: u1 = undefined;
1267    subborrowxU64(&x161, &x162, x160, x153, @as(u64, 0x0));
1268    var x163: u64 = undefined;
1269    var x164: u1 = undefined;
1270    subborrowxU64(&x163, &x164, x162, x155, 0xffffffff00000001);
1271    var x165: u64 = undefined;
1272    var x166: u1 = undefined;
1273    subborrowxU64(&x165, &x166, x164, @as(u64, x156), @as(u64, 0x0));
1274    var x167: u64 = undefined;
1275    cmovznzU64(&x167, x166, x157, x149);
1276    var x168: u64 = undefined;
1277    cmovznzU64(&x168, x166, x159, x151);
1278    var x169: u64 = undefined;
1279    cmovznzU64(&x169, x166, x161, x153);
1280    var x170: u64 = undefined;
1281    cmovznzU64(&x170, x166, x163, x155);
1282    out1[0] = x167;
1283    out1[1] = x168;
1284    out1[2] = x169;
1285    out1[3] = x170;
1286}
1287
1288/// The function nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
1289///
1290/// Preconditions:
1291///   0 ≤ eval arg1 < m
1292/// Postconditions:
1293///   out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0
1294///
1295/// Input Bounds:
1296///   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1297/// Output Bounds:
1298///   out1: [0x0 ~> 0xffffffffffffffff]
1299pub fn nonzero(out1: *u64, arg1: [4]u64) void {
1300    @setRuntimeSafety(mode == .Debug);
1301
1302    const x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3]))));
1303    out1.* = x1;
1304}
1305
1306/// The function selectznz is a multi-limb conditional select.
1307///
1308/// Postconditions:
1309///   eval out1 = (if arg1 = 0 then eval arg2 else eval arg3)
1310///
1311/// Input Bounds:
1312///   arg1: [0x0 ~> 0x1]
1313///   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1314///   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1315/// Output Bounds:
1316///   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1317pub fn selectznz(out1: *[4]u64, arg1: u1, arg2: [4]u64, arg3: [4]u64) void {
1318    @setRuntimeSafety(mode == .Debug);
1319
1320    var x1: u64 = undefined;
1321    cmovznzU64(&x1, arg1, (arg2[0]), (arg3[0]));
1322    var x2: u64 = undefined;
1323    cmovznzU64(&x2, arg1, (arg2[1]), (arg3[1]));
1324    var x3: u64 = undefined;
1325    cmovznzU64(&x3, arg1, (arg2[2]), (arg3[2]));
1326    var x4: u64 = undefined;
1327    cmovznzU64(&x4, arg1, (arg2[3]), (arg3[3]));
1328    out1[0] = x1;
1329    out1[1] = x2;
1330    out1[2] = x3;
1331    out1[3] = x4;
1332}
1333
1334/// The function toBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
1335///
1336/// Preconditions:
1337///   0 ≤ eval arg1 < m
1338/// Postconditions:
1339///   out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
1340///
1341/// Input Bounds:
1342///   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1343/// Output Bounds:
1344///   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]]
1345pub fn toBytes(out1: *[32]u8, arg1: [4]u64) void {
1346    @setRuntimeSafety(mode == .Debug);
1347
1348    const x1 = (arg1[3]);
1349    const x2 = (arg1[2]);
1350    const x3 = (arg1[1]);
1351    const x4 = (arg1[0]);
1352    const x5 = @as(u8, @truncate((x4 & @as(u64, 0xff))));
1353    const x6 = (x4 >> 8);
1354    const x7 = @as(u8, @truncate((x6 & @as(u64, 0xff))));
1355    const x8 = (x6 >> 8);
1356    const x9 = @as(u8, @truncate((x8 & @as(u64, 0xff))));
1357    const x10 = (x8 >> 8);
1358    const x11 = @as(u8, @truncate((x10 & @as(u64, 0xff))));
1359    const x12 = (x10 >> 8);
1360    const x13 = @as(u8, @truncate((x12 & @as(u64, 0xff))));
1361    const x14 = (x12 >> 8);
1362    const x15 = @as(u8, @truncate((x14 & @as(u64, 0xff))));
1363    const x16 = (x14 >> 8);
1364    const x17 = @as(u8, @truncate((x16 & @as(u64, 0xff))));
1365    const x18 = @as(u8, @truncate((x16 >> 8)));
1366    const x19 = @as(u8, @truncate((x3 & @as(u64, 0xff))));
1367    const x20 = (x3 >> 8);
1368    const x21 = @as(u8, @truncate((x20 & @as(u64, 0xff))));
1369    const x22 = (x20 >> 8);
1370    const x23 = @as(u8, @truncate((x22 & @as(u64, 0xff))));
1371    const x24 = (x22 >> 8);
1372    const x25 = @as(u8, @truncate((x24 & @as(u64, 0xff))));
1373    const x26 = (x24 >> 8);
1374    const x27 = @as(u8, @truncate((x26 & @as(u64, 0xff))));
1375    const x28 = (x26 >> 8);
1376    const x29 = @as(u8, @truncate((x28 & @as(u64, 0xff))));
1377    const x30 = (x28 >> 8);
1378    const x31 = @as(u8, @truncate((x30 & @as(u64, 0xff))));
1379    const x32 = @as(u8, @truncate((x30 >> 8)));
1380    const x33 = @as(u8, @truncate((x2 & @as(u64, 0xff))));
1381    const x34 = (x2 >> 8);
1382    const x35 = @as(u8, @truncate((x34 & @as(u64, 0xff))));
1383    const x36 = (x34 >> 8);
1384    const x37 = @as(u8, @truncate((x36 & @as(u64, 0xff))));
1385    const x38 = (x36 >> 8);
1386    const x39 = @as(u8, @truncate((x38 & @as(u64, 0xff))));
1387    const x40 = (x38 >> 8);
1388    const x41 = @as(u8, @truncate((x40 & @as(u64, 0xff))));
1389    const x42 = (x40 >> 8);
1390    const x43 = @as(u8, @truncate((x42 & @as(u64, 0xff))));
1391    const x44 = (x42 >> 8);
1392    const x45 = @as(u8, @truncate((x44 & @as(u64, 0xff))));
1393    const x46 = @as(u8, @truncate((x44 >> 8)));
1394    const x47 = @as(u8, @truncate((x1 & @as(u64, 0xff))));
1395    const x48 = (x1 >> 8);
1396    const x49 = @as(u8, @truncate((x48 & @as(u64, 0xff))));
1397    const x50 = (x48 >> 8);
1398    const x51 = @as(u8, @truncate((x50 & @as(u64, 0xff))));
1399    const x52 = (x50 >> 8);
1400    const x53 = @as(u8, @truncate((x52 & @as(u64, 0xff))));
1401    const x54 = (x52 >> 8);
1402    const x55 = @as(u8, @truncate((x54 & @as(u64, 0xff))));
1403    const x56 = (x54 >> 8);
1404    const x57 = @as(u8, @truncate((x56 & @as(u64, 0xff))));
1405    const x58 = (x56 >> 8);
1406    const x59 = @as(u8, @truncate((x58 & @as(u64, 0xff))));
1407    const x60 = @as(u8, @truncate((x58 >> 8)));
1408    out1[0] = x5;
1409    out1[1] = x7;
1410    out1[2] = x9;
1411    out1[3] = x11;
1412    out1[4] = x13;
1413    out1[5] = x15;
1414    out1[6] = x17;
1415    out1[7] = x18;
1416    out1[8] = x19;
1417    out1[9] = x21;
1418    out1[10] = x23;
1419    out1[11] = x25;
1420    out1[12] = x27;
1421    out1[13] = x29;
1422    out1[14] = x31;
1423    out1[15] = x32;
1424    out1[16] = x33;
1425    out1[17] = x35;
1426    out1[18] = x37;
1427    out1[19] = x39;
1428    out1[20] = x41;
1429    out1[21] = x43;
1430    out1[22] = x45;
1431    out1[23] = x46;
1432    out1[24] = x47;
1433    out1[25] = x49;
1434    out1[26] = x51;
1435    out1[27] = x53;
1436    out1[28] = x55;
1437    out1[29] = x57;
1438    out1[30] = x59;
1439    out1[31] = x60;
1440}
1441
1442/// The function fromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
1443///
1444/// Preconditions:
1445///   0 ≤ bytes_eval arg1 < m
1446/// Postconditions:
1447///   eval out1 mod m = bytes_eval arg1 mod m
1448///   0 ≤ eval out1 < m
1449///
1450/// Input Bounds:
1451///   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]]
1452/// Output Bounds:
1453///   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1454pub fn fromBytes(out1: *[4]u64, arg1: [32]u8) void {
1455    @setRuntimeSafety(mode == .Debug);
1456
1457    const x1 = (@as(u64, (arg1[31])) << 56);
1458    const x2 = (@as(u64, (arg1[30])) << 48);
1459    const x3 = (@as(u64, (arg1[29])) << 40);
1460    const x4 = (@as(u64, (arg1[28])) << 32);
1461    const x5 = (@as(u64, (arg1[27])) << 24);
1462    const x6 = (@as(u64, (arg1[26])) << 16);
1463    const x7 = (@as(u64, (arg1[25])) << 8);
1464    const x8 = (arg1[24]);
1465    const x9 = (@as(u64, (arg1[23])) << 56);
1466    const x10 = (@as(u64, (arg1[22])) << 48);
1467    const x11 = (@as(u64, (arg1[21])) << 40);
1468    const x12 = (@as(u64, (arg1[20])) << 32);
1469    const x13 = (@as(u64, (arg1[19])) << 24);
1470    const x14 = (@as(u64, (arg1[18])) << 16);
1471    const x15 = (@as(u64, (arg1[17])) << 8);
1472    const x16 = (arg1[16]);
1473    const x17 = (@as(u64, (arg1[15])) << 56);
1474    const x18 = (@as(u64, (arg1[14])) << 48);
1475    const x19 = (@as(u64, (arg1[13])) << 40);
1476    const x20 = (@as(u64, (arg1[12])) << 32);
1477    const x21 = (@as(u64, (arg1[11])) << 24);
1478    const x22 = (@as(u64, (arg1[10])) << 16);
1479    const x23 = (@as(u64, (arg1[9])) << 8);
1480    const x24 = (arg1[8]);
1481    const x25 = (@as(u64, (arg1[7])) << 56);
1482    const x26 = (@as(u64, (arg1[6])) << 48);
1483    const x27 = (@as(u64, (arg1[5])) << 40);
1484    const x28 = (@as(u64, (arg1[4])) << 32);
1485    const x29 = (@as(u64, (arg1[3])) << 24);
1486    const x30 = (@as(u64, (arg1[2])) << 16);
1487    const x31 = (@as(u64, (arg1[1])) << 8);
1488    const x32 = (arg1[0]);
1489    const x33 = (x31 + @as(u64, x32));
1490    const x34 = (x30 + x33);
1491    const x35 = (x29 + x34);
1492    const x36 = (x28 + x35);
1493    const x37 = (x27 + x36);
1494    const x38 = (x26 + x37);
1495    const x39 = (x25 + x38);
1496    const x40 = (x23 + @as(u64, x24));
1497    const x41 = (x22 + x40);
1498    const x42 = (x21 + x41);
1499    const x43 = (x20 + x42);
1500    const x44 = (x19 + x43);
1501    const x45 = (x18 + x44);
1502    const x46 = (x17 + x45);
1503    const x47 = (x15 + @as(u64, x16));
1504    const x48 = (x14 + x47);
1505    const x49 = (x13 + x48);
1506    const x50 = (x12 + x49);
1507    const x51 = (x11 + x50);
1508    const x52 = (x10 + x51);
1509    const x53 = (x9 + x52);
1510    const x54 = (x7 + @as(u64, x8));
1511    const x55 = (x6 + x54);
1512    const x56 = (x5 + x55);
1513    const x57 = (x4 + x56);
1514    const x58 = (x3 + x57);
1515    const x59 = (x2 + x58);
1516    const x60 = (x1 + x59);
1517    out1[0] = x39;
1518    out1[1] = x46;
1519    out1[2] = x53;
1520    out1[3] = x60;
1521}
1522
1523/// The function setOne returns the field element one in the Montgomery domain.
1524///
1525/// Postconditions:
1526///   eval (from_montgomery out1) mod m = 1 mod m
1527///   0 ≤ eval out1 < m
1528///
1529pub fn setOne(out1: *MontgomeryDomainFieldElement) void {
1530    @setRuntimeSafety(mode == .Debug);
1531
1532    out1[0] = @as(u64, 0x1);
1533    out1[1] = 0xffffffff00000000;
1534    out1[2] = 0xffffffffffffffff;
1535    out1[3] = 0xfffffffe;
1536}
1537
1538/// The function msat returns the saturated representation of the prime modulus.
1539///
1540/// Postconditions:
1541///   twos_complement_eval out1 = m
1542///   0 ≤ eval out1 < m
1543///
1544/// Output Bounds:
1545///   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1546pub fn msat(out1: *[5]u64) void {
1547    @setRuntimeSafety(mode == .Debug);
1548
1549    out1[0] = 0xffffffffffffffff;
1550    out1[1] = 0xffffffff;
1551    out1[2] = @as(u64, 0x0);
1552    out1[3] = 0xffffffff00000001;
1553    out1[4] = @as(u64, 0x0);
1554}
1555
1556/// The function divstep computes a divstep.
1557///
1558/// Preconditions:
1559///   0 ≤ eval arg4 < m
1560///   0 ≤ eval arg5 < m
1561/// Postconditions:
1562///   out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1)
1563///   twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2)
1564///   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⌋)
1565///   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)
1566///   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)
1567///   0 ≤ eval out5 < m
1568///   0 ≤ eval out5 < m
1569///   0 ≤ eval out2 < m
1570///   0 ≤ eval out3 < m
1571///
1572/// Input Bounds:
1573///   arg1: [0x0 ~> 0xffffffffffffffff]
1574///   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1575///   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1576///   arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1577///   arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1578/// Output Bounds:
1579///   out1: [0x0 ~> 0xffffffffffffffff]
1580///   out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1581///   out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1582///   out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1583///   out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1584pub 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 {
1585    @setRuntimeSafety(mode == .Debug);
1586
1587    var x1: u64 = undefined;
1588    var x2: u1 = undefined;
1589    addcarryxU64(&x1, &x2, 0x0, (~arg1), @as(u64, 0x1));
1590    const x3 = (@as(u1, @truncate((x1 >> 63))) & @as(u1, @truncate(((arg3[0]) & @as(u64, 0x1)))));
1591    var x4: u64 = undefined;
1592    var x5: u1 = undefined;
1593    addcarryxU64(&x4, &x5, 0x0, (~arg1), @as(u64, 0x1));
1594    var x6: u64 = undefined;
1595    cmovznzU64(&x6, x3, arg1, x4);
1596    var x7: u64 = undefined;
1597    cmovznzU64(&x7, x3, (arg2[0]), (arg3[0]));
1598    var x8: u64 = undefined;
1599    cmovznzU64(&x8, x3, (arg2[1]), (arg3[1]));
1600    var x9: u64 = undefined;
1601    cmovznzU64(&x9, x3, (arg2[2]), (arg3[2]));
1602    var x10: u64 = undefined;
1603    cmovznzU64(&x10, x3, (arg2[3]), (arg3[3]));
1604    var x11: u64 = undefined;
1605    cmovznzU64(&x11, x3, (arg2[4]), (arg3[4]));
1606    var x12: u64 = undefined;
1607    var x13: u1 = undefined;
1608    addcarryxU64(&x12, &x13, 0x0, @as(u64, 0x1), (~(arg2[0])));
1609    var x14: u64 = undefined;
1610    var x15: u1 = undefined;
1611    addcarryxU64(&x14, &x15, x13, @as(u64, 0x0), (~(arg2[1])));
1612    var x16: u64 = undefined;
1613    var x17: u1 = undefined;
1614    addcarryxU64(&x16, &x17, x15, @as(u64, 0x0), (~(arg2[2])));
1615    var x18: u64 = undefined;
1616    var x19: u1 = undefined;
1617    addcarryxU64(&x18, &x19, x17, @as(u64, 0x0), (~(arg2[3])));
1618    var x20: u64 = undefined;
1619    var x21: u1 = undefined;
1620    addcarryxU64(&x20, &x21, x19, @as(u64, 0x0), (~(arg2[4])));
1621    var x22: u64 = undefined;
1622    cmovznzU64(&x22, x3, (arg3[0]), x12);
1623    var x23: u64 = undefined;
1624    cmovznzU64(&x23, x3, (arg3[1]), x14);
1625    var x24: u64 = undefined;
1626    cmovznzU64(&x24, x3, (arg3[2]), x16);
1627    var x25: u64 = undefined;
1628    cmovznzU64(&x25, x3, (arg3[3]), x18);
1629    var x26: u64 = undefined;
1630    cmovznzU64(&x26, x3, (arg3[4]), x20);
1631    var x27: u64 = undefined;
1632    cmovznzU64(&x27, x3, (arg4[0]), (arg5[0]));
1633    var x28: u64 = undefined;
1634    cmovznzU64(&x28, x3, (arg4[1]), (arg5[1]));
1635    var x29: u64 = undefined;
1636    cmovznzU64(&x29, x3, (arg4[2]), (arg5[2]));
1637    var x30: u64 = undefined;
1638    cmovznzU64(&x30, x3, (arg4[3]), (arg5[3]));
1639    var x31: u64 = undefined;
1640    var x32: u1 = undefined;
1641    addcarryxU64(&x31, &x32, 0x0, x27, x27);
1642    var x33: u64 = undefined;
1643    var x34: u1 = undefined;
1644    addcarryxU64(&x33, &x34, x32, x28, x28);
1645    var x35: u64 = undefined;
1646    var x36: u1 = undefined;
1647    addcarryxU64(&x35, &x36, x34, x29, x29);
1648    var x37: u64 = undefined;
1649    var x38: u1 = undefined;
1650    addcarryxU64(&x37, &x38, x36, x30, x30);
1651    var x39: u64 = undefined;
1652    var x40: u1 = undefined;
1653    subborrowxU64(&x39, &x40, 0x0, x31, 0xffffffffffffffff);
1654    var x41: u64 = undefined;
1655    var x42: u1 = undefined;
1656    subborrowxU64(&x41, &x42, x40, x33, 0xffffffff);
1657    var x43: u64 = undefined;
1658    var x44: u1 = undefined;
1659    subborrowxU64(&x43, &x44, x42, x35, @as(u64, 0x0));
1660    var x45: u64 = undefined;
1661    var x46: u1 = undefined;
1662    subborrowxU64(&x45, &x46, x44, x37, 0xffffffff00000001);
1663    var x47: u64 = undefined;
1664    var x48: u1 = undefined;
1665    subborrowxU64(&x47, &x48, x46, @as(u64, x38), @as(u64, 0x0));
1666    const x49 = (arg4[3]);
1667    const x50 = (arg4[2]);
1668    const x51 = (arg4[1]);
1669    const x52 = (arg4[0]);
1670    var x53: u64 = undefined;
1671    var x54: u1 = undefined;
1672    subborrowxU64(&x53, &x54, 0x0, @as(u64, 0x0), x52);
1673    var x55: u64 = undefined;
1674    var x56: u1 = undefined;
1675    subborrowxU64(&x55, &x56, x54, @as(u64, 0x0), x51);
1676    var x57: u64 = undefined;
1677    var x58: u1 = undefined;
1678    subborrowxU64(&x57, &x58, x56, @as(u64, 0x0), x50);
1679    var x59: u64 = undefined;
1680    var x60: u1 = undefined;
1681    subborrowxU64(&x59, &x60, x58, @as(u64, 0x0), x49);
1682    var x61: u64 = undefined;
1683    cmovznzU64(&x61, x60, @as(u64, 0x0), 0xffffffffffffffff);
1684    var x62: u64 = undefined;
1685    var x63: u1 = undefined;
1686    addcarryxU64(&x62, &x63, 0x0, x53, x61);
1687    var x64: u64 = undefined;
1688    var x65: u1 = undefined;
1689    addcarryxU64(&x64, &x65, x63, x55, (x61 & 0xffffffff));
1690    var x66: u64 = undefined;
1691    var x67: u1 = undefined;
1692    addcarryxU64(&x66, &x67, x65, x57, @as(u64, 0x0));
1693    var x68: u64 = undefined;
1694    var x69: u1 = undefined;
1695    addcarryxU64(&x68, &x69, x67, x59, (x61 & 0xffffffff00000001));
1696    var x70: u64 = undefined;
1697    cmovznzU64(&x70, x3, (arg5[0]), x62);
1698    var x71: u64 = undefined;
1699    cmovznzU64(&x71, x3, (arg5[1]), x64);
1700    var x72: u64 = undefined;
1701    cmovznzU64(&x72, x3, (arg5[2]), x66);
1702    var x73: u64 = undefined;
1703    cmovznzU64(&x73, x3, (arg5[3]), x68);
1704    const x74 = @as(u1, @truncate((x22 & @as(u64, 0x1))));
1705    var x75: u64 = undefined;
1706    cmovznzU64(&x75, x74, @as(u64, 0x0), x7);
1707    var x76: u64 = undefined;
1708    cmovznzU64(&x76, x74, @as(u64, 0x0), x8);
1709    var x77: u64 = undefined;
1710    cmovznzU64(&x77, x74, @as(u64, 0x0), x9);
1711    var x78: u64 = undefined;
1712    cmovznzU64(&x78, x74, @as(u64, 0x0), x10);
1713    var x79: u64 = undefined;
1714    cmovznzU64(&x79, x74, @as(u64, 0x0), x11);
1715    var x80: u64 = undefined;
1716    var x81: u1 = undefined;
1717    addcarryxU64(&x80, &x81, 0x0, x22, x75);
1718    var x82: u64 = undefined;
1719    var x83: u1 = undefined;
1720    addcarryxU64(&x82, &x83, x81, x23, x76);
1721    var x84: u64 = undefined;
1722    var x85: u1 = undefined;
1723    addcarryxU64(&x84, &x85, x83, x24, x77);
1724    var x86: u64 = undefined;
1725    var x87: u1 = undefined;
1726    addcarryxU64(&x86, &x87, x85, x25, x78);
1727    var x88: u64 = undefined;
1728    var x89: u1 = undefined;
1729    addcarryxU64(&x88, &x89, x87, x26, x79);
1730    var x90: u64 = undefined;
1731    cmovznzU64(&x90, x74, @as(u64, 0x0), x27);
1732    var x91: u64 = undefined;
1733    cmovznzU64(&x91, x74, @as(u64, 0x0), x28);
1734    var x92: u64 = undefined;
1735    cmovznzU64(&x92, x74, @as(u64, 0x0), x29);
1736    var x93: u64 = undefined;
1737    cmovznzU64(&x93, x74, @as(u64, 0x0), x30);
1738    var x94: u64 = undefined;
1739    var x95: u1 = undefined;
1740    addcarryxU64(&x94, &x95, 0x0, x70, x90);
1741    var x96: u64 = undefined;
1742    var x97: u1 = undefined;
1743    addcarryxU64(&x96, &x97, x95, x71, x91);
1744    var x98: u64 = undefined;
1745    var x99: u1 = undefined;
1746    addcarryxU64(&x98, &x99, x97, x72, x92);
1747    var x100: u64 = undefined;
1748    var x101: u1 = undefined;
1749    addcarryxU64(&x100, &x101, x99, x73, x93);
1750    var x102: u64 = undefined;
1751    var x103: u1 = undefined;
1752    subborrowxU64(&x102, &x103, 0x0, x94, 0xffffffffffffffff);
1753    var x104: u64 = undefined;
1754    var x105: u1 = undefined;
1755    subborrowxU64(&x104, &x105, x103, x96, 0xffffffff);
1756    var x106: u64 = undefined;
1757    var x107: u1 = undefined;
1758    subborrowxU64(&x106, &x107, x105, x98, @as(u64, 0x0));
1759    var x108: u64 = undefined;
1760    var x109: u1 = undefined;
1761    subborrowxU64(&x108, &x109, x107, x100, 0xffffffff00000001);
1762    var x110: u64 = undefined;
1763    var x111: u1 = undefined;
1764    subborrowxU64(&x110, &x111, x109, @as(u64, x101), @as(u64, 0x0));
1765    var x112: u64 = undefined;
1766    var x113: u1 = undefined;
1767    addcarryxU64(&x112, &x113, 0x0, x6, @as(u64, 0x1));
1768    const x114 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff));
1769    const x115 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff));
1770    const x116 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff));
1771    const x117 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff));
1772    const x118 = ((x88 & 0x8000000000000000) | (x88 >> 1));
1773    var x119: u64 = undefined;
1774    cmovznzU64(&x119, x48, x39, x31);
1775    var x120: u64 = undefined;
1776    cmovznzU64(&x120, x48, x41, x33);
1777    var x121: u64 = undefined;
1778    cmovznzU64(&x121, x48, x43, x35);
1779    var x122: u64 = undefined;
1780    cmovznzU64(&x122, x48, x45, x37);
1781    var x123: u64 = undefined;
1782    cmovznzU64(&x123, x111, x102, x94);
1783    var x124: u64 = undefined;
1784    cmovznzU64(&x124, x111, x104, x96);
1785    var x125: u64 = undefined;
1786    cmovznzU64(&x125, x111, x106, x98);
1787    var x126: u64 = undefined;
1788    cmovznzU64(&x126, x111, x108, x100);
1789    out1.* = x112;
1790    out2[0] = x7;
1791    out2[1] = x8;
1792    out2[2] = x9;
1793    out2[3] = x10;
1794    out2[4] = x11;
1795    out3[0] = x114;
1796    out3[1] = x115;
1797    out3[2] = x116;
1798    out3[3] = x117;
1799    out3[4] = x118;
1800    out4[0] = x119;
1801    out4[1] = x120;
1802    out4[2] = x121;
1803    out4[3] = x122;
1804    out5[0] = x123;
1805    out5[1] = x124;
1806    out5[2] = x125;
1807    out5[3] = x126;
1808}
1809
1810/// The function divstepPrecomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).
1811///
1812/// Postconditions:
1813///   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⌋)
1814///   0 ≤ eval out1 < m
1815///
1816/// Output Bounds:
1817///   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1818pub fn divstepPrecomp(out1: *[4]u64) void {
1819    @setRuntimeSafety(mode == .Debug);
1820
1821    out1[0] = 0x67ffffffb8000000;
1822    out1[1] = 0xc000000038000000;
1823    out1[2] = 0xd80000007fffffff;
1824    out1[3] = 0x2fffffffffffffff;
1825}