/* Autogenerated */ /* curve description: p224 */ /* requested operations: (all) */ /* m = 0xffffffffffffffffffffffffffffffff000000000000000000000001 (from "2^224 - 2^96 + 1") */ /* machine_wordsize = 64 (from "64") */ /* */ /* 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. */ #include typedef unsigned char fiat_p224_uint1; typedef signed char fiat_p224_int1; typedef signed __int128 fiat_p224_int128; typedef unsigned __int128 fiat_p224_uint128; /* * The function fiat_p224_addcarryx_u64 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] */ static void fiat_p224_addcarryx_u64(uint64_t* out1, fiat_p224_uint1* out2, fiat_p224_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_p224_uint128 x1 = ((arg1 + (fiat_p224_uint128)arg2) + arg3); uint64_t x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); fiat_p224_uint1 x3 = (fiat_p224_uint1)(x1 >> 64); *out1 = x2; *out2 = x3; } /* * The function fiat_p224_subborrowx_u64 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] */ static void fiat_p224_subborrowx_u64(uint64_t* out1, fiat_p224_uint1* out2, fiat_p224_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_p224_int128 x1 = ((arg2 - (fiat_p224_int128)arg1) - arg3); fiat_p224_int1 x2 = (fiat_p224_int1)(x1 >> 64); uint64_t x3 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); *out1 = x3; *out2 = (fiat_p224_uint1)(0x0 - x2); } /* * The function fiat_p224_mulx_u64 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] */ static void fiat_p224_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) { fiat_p224_uint128 x1 = ((fiat_p224_uint128)arg1 * arg2); uint64_t x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); uint64_t x3 = (uint64_t)(x1 >> 64); *out1 = x2; *out2 = x3; } /* * The function fiat_p224_cmovznz_u64 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] */ static void fiat_p224_cmovznz_u64(uint64_t* out1, fiat_p224_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_p224_uint1 x1 = (!(!arg1)); uint64_t x2 = ((fiat_p224_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff)); uint64_t x3 = ((x2 & arg3) | ((~x2) & arg2)); *out1 = x3; } /* * The function fiat_p224_mul multiplies two field elements in the Montgomery domain. * Preconditions: * 0 ≤ eval arg1 < m * 0 ≤ eval arg2 < m * Postconditions: * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m * 0 ≤ eval out1 < m * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p224_mul(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) { uint64_t x1 = (arg1[1]); uint64_t x2 = (arg1[2]); uint64_t x3 = (arg1[3]); uint64_t x4 = (arg1[0]); uint64_t x5; uint64_t x6; fiat_p224_mulx_u64(&x5, &x6, x4, (arg2[3])); uint64_t x7; uint64_t x8; fiat_p224_mulx_u64(&x7, &x8, x4, (arg2[2])); uint64_t x9; uint64_t x10; fiat_p224_mulx_u64(&x9, &x10, x4, (arg2[1])); uint64_t x11; uint64_t x12; fiat_p224_mulx_u64(&x11, &x12, x4, (arg2[0])); uint64_t x13; fiat_p224_uint1 x14; fiat_p224_addcarryx_u64(&x13, &x14, 0x0, x12, x9); uint64_t x15; fiat_p224_uint1 x16; fiat_p224_addcarryx_u64(&x15, &x16, x14, x10, x7); uint64_t x17; fiat_p224_uint1 x18; fiat_p224_addcarryx_u64(&x17, &x18, x16, x8, x5); uint64_t x19; fiat_p224_uint1 x20; fiat_p224_addcarryx_u64(&x19, &x20, x18, x6, 0x0); uint64_t x21; uint64_t x22; fiat_p224_mulx_u64(&x21, &x22, x11, UINT64_C(0xffffffffffffffff)); uint64_t x23; uint64_t x24; fiat_p224_mulx_u64(&x23, &x24, x21, UINT32_C(0xffffffff)); uint64_t x25; uint64_t x26; fiat_p224_mulx_u64(&x25, &x26, x21, UINT64_C(0xffffffffffffffff)); uint64_t x27; uint64_t x28; fiat_p224_mulx_u64(&x27, &x28, x21, UINT64_C(0xffffffff00000000)); uint64_t x29; fiat_p224_uint1 x30; fiat_p224_addcarryx_u64(&x29, &x30, 0x0, x28, x25); uint64_t x31; fiat_p224_uint1 x32; fiat_p224_addcarryx_u64(&x31, &x32, x30, x26, x23); uint64_t x33; fiat_p224_uint1 x34; fiat_p224_addcarryx_u64(&x33, &x34, x32, x24, 0x0); uint64_t x35; fiat_p224_uint1 x36; fiat_p224_addcarryx_u64(&x35, &x36, 0x0, x11, x21); uint64_t x37; fiat_p224_uint1 x38; fiat_p224_addcarryx_u64(&x37, &x38, x36, x13, x27); uint64_t x39; fiat_p224_uint1 x40; fiat_p224_addcarryx_u64(&x39, &x40, x38, x15, x29); uint64_t x41; fiat_p224_uint1 x42; fiat_p224_addcarryx_u64(&x41, &x42, x40, x17, x31); uint64_t x43; fiat_p224_uint1 x44; fiat_p224_addcarryx_u64(&x43, &x44, x42, x19, x33); uint64_t x45; fiat_p224_uint1 x46; fiat_p224_addcarryx_u64(&x45, &x46, x44, 0x0, 0x0); uint64_t x47; uint64_t x48; fiat_p224_mulx_u64(&x47, &x48, x1, (arg2[3])); uint64_t x49; uint64_t x50; fiat_p224_mulx_u64(&x49, &x50, x1, (arg2[2])); uint64_t x51; uint64_t x52; fiat_p224_mulx_u64(&x51, &x52, x1, (arg2[1])); uint64_t x53; uint64_t x54; fiat_p224_mulx_u64(&x53, &x54, x1, (arg2[0])); uint64_t x55; fiat_p224_uint1 x56; fiat_p224_addcarryx_u64(&x55, &x56, 0x0, x54, x51); uint64_t x57; fiat_p224_uint1 x58; fiat_p224_addcarryx_u64(&x57, &x58, x56, x52, x49); uint64_t x59; fiat_p224_uint1 x60; fiat_p224_addcarryx_u64(&x59, &x60, x58, x50, x47); uint64_t x61; fiat_p224_uint1 x62; fiat_p224_addcarryx_u64(&x61, &x62, x60, x48, 0x0); uint64_t x63; fiat_p224_uint1 x64; fiat_p224_addcarryx_u64(&x63, &x64, 0x0, x37, x53); uint64_t x65; fiat_p224_uint1 x66; fiat_p224_addcarryx_u64(&x65, &x66, x64, x39, x55); uint64_t x67; fiat_p224_uint1 x68; fiat_p224_addcarryx_u64(&x67, &x68, x66, x41, x57); uint64_t x69; fiat_p224_uint1 x70; fiat_p224_addcarryx_u64(&x69, &x70, x68, x43, x59); uint64_t x71; fiat_p224_uint1 x72; fiat_p224_addcarryx_u64(&x71, &x72, x70, (fiat_p224_uint1)x45, x61); uint64_t x73; uint64_t x74; fiat_p224_mulx_u64(&x73, &x74, x63, UINT64_C(0xffffffffffffffff)); uint64_t x75; uint64_t x76; fiat_p224_mulx_u64(&x75, &x76, x73, UINT32_C(0xffffffff)); uint64_t x77; uint64_t x78; fiat_p224_mulx_u64(&x77, &x78, x73, UINT64_C(0xffffffffffffffff)); uint64_t x79; uint64_t x80; fiat_p224_mulx_u64(&x79, &x80, x73, UINT64_C(0xffffffff00000000)); uint64_t x81; fiat_p224_uint1 x82; fiat_p224_addcarryx_u64(&x81, &x82, 0x0, x80, x77); uint64_t x83; fiat_p224_uint1 x84; fiat_p224_addcarryx_u64(&x83, &x84, x82, x78, x75); uint64_t x85; fiat_p224_uint1 x86; fiat_p224_addcarryx_u64(&x85, &x86, x84, x76, 0x0); uint64_t x87; fiat_p224_uint1 x88; fiat_p224_addcarryx_u64(&x87, &x88, 0x0, x63, x73); uint64_t x89; fiat_p224_uint1 x90; fiat_p224_addcarryx_u64(&x89, &x90, x88, x65, x79); uint64_t x91; fiat_p224_uint1 x92; fiat_p224_addcarryx_u64(&x91, &x92, x90, x67, x81); uint64_t x93; fiat_p224_uint1 x94; fiat_p224_addcarryx_u64(&x93, &x94, x92, x69, x83); uint64_t x95; fiat_p224_uint1 x96; fiat_p224_addcarryx_u64(&x95, &x96, x94, x71, x85); uint64_t x97; fiat_p224_uint1 x98; fiat_p224_addcarryx_u64(&x97, &x98, x96, x72, 0x0); uint64_t x99; uint64_t x100; fiat_p224_mulx_u64(&x99, &x100, x2, (arg2[3])); uint64_t x101; uint64_t x102; fiat_p224_mulx_u64(&x101, &x102, x2, (arg2[2])); uint64_t x103; uint64_t x104; fiat_p224_mulx_u64(&x103, &x104, x2, (arg2[1])); uint64_t x105; uint64_t x106; fiat_p224_mulx_u64(&x105, &x106, x2, (arg2[0])); uint64_t x107; fiat_p224_uint1 x108; fiat_p224_addcarryx_u64(&x107, &x108, 0x0, x106, x103); uint64_t x109; fiat_p224_uint1 x110; fiat_p224_addcarryx_u64(&x109, &x110, x108, x104, x101); uint64_t x111; fiat_p224_uint1 x112; fiat_p224_addcarryx_u64(&x111, &x112, x110, x102, x99); uint64_t x113; fiat_p224_uint1 x114; fiat_p224_addcarryx_u64(&x113, &x114, x112, x100, 0x0); uint64_t x115; fiat_p224_uint1 x116; fiat_p224_addcarryx_u64(&x115, &x116, 0x0, x89, x105); uint64_t x117; fiat_p224_uint1 x118; fiat_p224_addcarryx_u64(&x117, &x118, x116, x91, x107); uint64_t x119; fiat_p224_uint1 x120; fiat_p224_addcarryx_u64(&x119, &x120, x118, x93, x109); uint64_t x121; fiat_p224_uint1 x122; fiat_p224_addcarryx_u64(&x121, &x122, x120, x95, x111); uint64_t x123; fiat_p224_uint1 x124; fiat_p224_addcarryx_u64(&x123, &x124, x122, x97, x113); uint64_t x125; uint64_t x126; fiat_p224_mulx_u64(&x125, &x126, x115, UINT64_C(0xffffffffffffffff)); uint64_t x127; uint64_t x128; fiat_p224_mulx_u64(&x127, &x128, x125, UINT32_C(0xffffffff)); uint64_t x129; uint64_t x130; fiat_p224_mulx_u64(&x129, &x130, x125, UINT64_C(0xffffffffffffffff)); uint64_t x131; uint64_t x132; fiat_p224_mulx_u64(&x131, &x132, x125, UINT64_C(0xffffffff00000000)); uint64_t x133; fiat_p224_uint1 x134; fiat_p224_addcarryx_u64(&x133, &x134, 0x0, x132, x129); uint64_t x135; fiat_p224_uint1 x136; fiat_p224_addcarryx_u64(&x135, &x136, x134, x130, x127); uint64_t x137; fiat_p224_uint1 x138; fiat_p224_addcarryx_u64(&x137, &x138, x136, x128, 0x0); uint64_t x139; fiat_p224_uint1 x140; fiat_p224_addcarryx_u64(&x139, &x140, 0x0, x115, x125); uint64_t x141; fiat_p224_uint1 x142; fiat_p224_addcarryx_u64(&x141, &x142, x140, x117, x131); uint64_t x143; fiat_p224_uint1 x144; fiat_p224_addcarryx_u64(&x143, &x144, x142, x119, x133); uint64_t x145; fiat_p224_uint1 x146; fiat_p224_addcarryx_u64(&x145, &x146, x144, x121, x135); uint64_t x147; fiat_p224_uint1 x148; fiat_p224_addcarryx_u64(&x147, &x148, x146, x123, x137); uint64_t x149; fiat_p224_uint1 x150; fiat_p224_addcarryx_u64(&x149, &x150, x148, x124, 0x0); uint64_t x151; uint64_t x152; fiat_p224_mulx_u64(&x151, &x152, x3, (arg2[3])); uint64_t x153; uint64_t x154; fiat_p224_mulx_u64(&x153, &x154, x3, (arg2[2])); uint64_t x155; uint64_t x156; fiat_p224_mulx_u64(&x155, &x156, x3, (arg2[1])); uint64_t x157; uint64_t x158; fiat_p224_mulx_u64(&x157, &x158, x3, (arg2[0])); uint64_t x159; fiat_p224_uint1 x160; fiat_p224_addcarryx_u64(&x159, &x160, 0x0, x158, x155); uint64_t x161; fiat_p224_uint1 x162; fiat_p224_addcarryx_u64(&x161, &x162, x160, x156, x153); uint64_t x163; fiat_p224_uint1 x164; fiat_p224_addcarryx_u64(&x163, &x164, x162, x154, x151); uint64_t x165; fiat_p224_uint1 x166; fiat_p224_addcarryx_u64(&x165, &x166, x164, x152, 0x0); uint64_t x167; fiat_p224_uint1 x168; fiat_p224_addcarryx_u64(&x167, &x168, 0x0, x141, x157); uint64_t x169; fiat_p224_uint1 x170; fiat_p224_addcarryx_u64(&x169, &x170, x168, x143, x159); uint64_t x171; fiat_p224_uint1 x172; fiat_p224_addcarryx_u64(&x171, &x172, x170, x145, x161); uint64_t x173; fiat_p224_uint1 x174; fiat_p224_addcarryx_u64(&x173, &x174, x172, x147, x163); uint64_t x175; fiat_p224_uint1 x176; fiat_p224_addcarryx_u64(&x175, &x176, x174, x149, x165); uint64_t x177; uint64_t x178; fiat_p224_mulx_u64(&x177, &x178, x167, UINT64_C(0xffffffffffffffff)); uint64_t x179; uint64_t x180; fiat_p224_mulx_u64(&x179, &x180, x177, UINT32_C(0xffffffff)); uint64_t x181; uint64_t x182; fiat_p224_mulx_u64(&x181, &x182, x177, UINT64_C(0xffffffffffffffff)); uint64_t x183; uint64_t x184; fiat_p224_mulx_u64(&x183, &x184, x177, UINT64_C(0xffffffff00000000)); uint64_t x185; fiat_p224_uint1 x186; fiat_p224_addcarryx_u64(&x185, &x186, 0x0, x184, x181); uint64_t x187; fiat_p224_uint1 x188; fiat_p224_addcarryx_u64(&x187, &x188, x186, x182, x179); uint64_t x189; fiat_p224_uint1 x190; fiat_p224_addcarryx_u64(&x189, &x190, x188, x180, 0x0); uint64_t x191; fiat_p224_uint1 x192; fiat_p224_addcarryx_u64(&x191, &x192, 0x0, x167, x177); uint64_t x193; fiat_p224_uint1 x194; fiat_p224_addcarryx_u64(&x193, &x194, x192, x169, x183); uint64_t x195; fiat_p224_uint1 x196; fiat_p224_addcarryx_u64(&x195, &x196, x194, x171, x185); uint64_t x197; fiat_p224_uint1 x198; fiat_p224_addcarryx_u64(&x197, &x198, x196, x173, x187); uint64_t x199; fiat_p224_uint1 x200; fiat_p224_addcarryx_u64(&x199, &x200, x198, x175, x189); uint64_t x201; fiat_p224_uint1 x202; fiat_p224_addcarryx_u64(&x201, &x202, x200, x176, 0x0); uint64_t x203; fiat_p224_uint1 x204; fiat_p224_subborrowx_u64(&x203, &x204, 0x0, x193, 0x1); uint64_t x205; fiat_p224_uint1 x206; fiat_p224_subborrowx_u64(&x205, &x206, x204, x195, UINT64_C(0xffffffff00000000)); uint64_t x207; fiat_p224_uint1 x208; fiat_p224_subborrowx_u64(&x207, &x208, x206, x197, UINT64_C(0xffffffffffffffff)); uint64_t x209; fiat_p224_uint1 x210; fiat_p224_subborrowx_u64(&x209, &x210, x208, x199, UINT32_C(0xffffffff)); uint64_t x211; fiat_p224_uint1 x212; fiat_p224_subborrowx_u64(&x211, &x212, x210, x201, 0x0); uint64_t x213; fiat_p224_cmovznz_u64(&x213, x212, x203, x193); uint64_t x214; fiat_p224_cmovznz_u64(&x214, x212, x205, x195); uint64_t x215; fiat_p224_cmovznz_u64(&x215, x212, x207, x197); uint64_t x216; fiat_p224_cmovznz_u64(&x216, x212, x209, x199); out1[0] = x213; out1[1] = x214; out1[2] = x215; out1[3] = x216; } /* * The function fiat_p224_square squares a field element in the Montgomery domain. * Preconditions: * 0 ≤ eval arg1 < m * Postconditions: * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m * 0 ≤ eval out1 < m * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p224_square(uint64_t out1[4], const uint64_t arg1[4]) { uint64_t x1 = (arg1[1]); uint64_t x2 = (arg1[2]); uint64_t x3 = (arg1[3]); uint64_t x4 = (arg1[0]); uint64_t x5; uint64_t x6; fiat_p224_mulx_u64(&x5, &x6, x4, (arg1[3])); uint64_t x7; uint64_t x8; fiat_p224_mulx_u64(&x7, &x8, x4, (arg1[2])); uint64_t x9; uint64_t x10; fiat_p224_mulx_u64(&x9, &x10, x4, (arg1[1])); uint64_t x11; uint64_t x12; fiat_p224_mulx_u64(&x11, &x12, x4, (arg1[0])); uint64_t x13; fiat_p224_uint1 x14; fiat_p224_addcarryx_u64(&x13, &x14, 0x0, x12, x9); uint64_t x15; fiat_p224_uint1 x16; fiat_p224_addcarryx_u64(&x15, &x16, x14, x10, x7); uint64_t x17; fiat_p224_uint1 x18; fiat_p224_addcarryx_u64(&x17, &x18, x16, x8, x5); uint64_t x19; fiat_p224_uint1 x20; fiat_p224_addcarryx_u64(&x19, &x20, x18, x6, 0x0); uint64_t x21; uint64_t x22; fiat_p224_mulx_u64(&x21, &x22, x11, UINT64_C(0xffffffffffffffff)); uint64_t x23; uint64_t x24; fiat_p224_mulx_u64(&x23, &x24, x21, UINT32_C(0xffffffff)); uint64_t x25; uint64_t x26; fiat_p224_mulx_u64(&x25, &x26, x21, UINT64_C(0xffffffffffffffff)); uint64_t x27; uint64_t x28; fiat_p224_mulx_u64(&x27, &x28, x21, UINT64_C(0xffffffff00000000)); uint64_t x29; fiat_p224_uint1 x30; fiat_p224_addcarryx_u64(&x29, &x30, 0x0, x28, x25); uint64_t x31; fiat_p224_uint1 x32; fiat_p224_addcarryx_u64(&x31, &x32, x30, x26, x23); uint64_t x33; fiat_p224_uint1 x34; fiat_p224_addcarryx_u64(&x33, &x34, x32, x24, 0x0); uint64_t x35; fiat_p224_uint1 x36; fiat_p224_addcarryx_u64(&x35, &x36, 0x0, x11, x21); uint64_t x37; fiat_p224_uint1 x38; fiat_p224_addcarryx_u64(&x37, &x38, x36, x13, x27); uint64_t x39; fiat_p224_uint1 x40; fiat_p224_addcarryx_u64(&x39, &x40, x38, x15, x29); uint64_t x41; fiat_p224_uint1 x42; fiat_p224_addcarryx_u64(&x41, &x42, x40, x17, x31); uint64_t x43; fiat_p224_uint1 x44; fiat_p224_addcarryx_u64(&x43, &x44, x42, x19, x33); uint64_t x45; fiat_p224_uint1 x46; fiat_p224_addcarryx_u64(&x45, &x46, x44, 0x0, 0x0); uint64_t x47; uint64_t x48; fiat_p224_mulx_u64(&x47, &x48, x1, (arg1[3])); uint64_t x49; uint64_t x50; fiat_p224_mulx_u64(&x49, &x50, x1, (arg1[2])); uint64_t x51; uint64_t x52; fiat_p224_mulx_u64(&x51, &x52, x1, (arg1[1])); uint64_t x53; uint64_t x54; fiat_p224_mulx_u64(&x53, &x54, x1, (arg1[0])); uint64_t x55; fiat_p224_uint1 x56; fiat_p224_addcarryx_u64(&x55, &x56, 0x0, x54, x51); uint64_t x57; fiat_p224_uint1 x58; fiat_p224_addcarryx_u64(&x57, &x58, x56, x52, x49); uint64_t x59; fiat_p224_uint1 x60; fiat_p224_addcarryx_u64(&x59, &x60, x58, x50, x47); uint64_t x61; fiat_p224_uint1 x62; fiat_p224_addcarryx_u64(&x61, &x62, x60, x48, 0x0); uint64_t x63; fiat_p224_uint1 x64; fiat_p224_addcarryx_u64(&x63, &x64, 0x0, x37, x53); uint64_t x65; fiat_p224_uint1 x66; fiat_p224_addcarryx_u64(&x65, &x66, x64, x39, x55); uint64_t x67; fiat_p224_uint1 x68; fiat_p224_addcarryx_u64(&x67, &x68, x66, x41, x57); uint64_t x69; fiat_p224_uint1 x70; fiat_p224_addcarryx_u64(&x69, &x70, x68, x43, x59); uint64_t x71; fiat_p224_uint1 x72; fiat_p224_addcarryx_u64(&x71, &x72, x70, (fiat_p224_uint1)x45, x61); uint64_t x73; uint64_t x74; fiat_p224_mulx_u64(&x73, &x74, x63, UINT64_C(0xffffffffffffffff)); uint64_t x75; uint64_t x76; fiat_p224_mulx_u64(&x75, &x76, x73, UINT32_C(0xffffffff)); uint64_t x77; uint64_t x78; fiat_p224_mulx_u64(&x77, &x78, x73, UINT64_C(0xffffffffffffffff)); uint64_t x79; uint64_t x80; fiat_p224_mulx_u64(&x79, &x80, x73, UINT64_C(0xffffffff00000000)); uint64_t x81; fiat_p224_uint1 x82; fiat_p224_addcarryx_u64(&x81, &x82, 0x0, x80, x77); uint64_t x83; fiat_p224_uint1 x84; fiat_p224_addcarryx_u64(&x83, &x84, x82, x78, x75); uint64_t x85; fiat_p224_uint1 x86; fiat_p224_addcarryx_u64(&x85, &x86, x84, x76, 0x0); uint64_t x87; fiat_p224_uint1 x88; fiat_p224_addcarryx_u64(&x87, &x88, 0x0, x63, x73); uint64_t x89; fiat_p224_uint1 x90; fiat_p224_addcarryx_u64(&x89, &x90, x88, x65, x79); uint64_t x91; fiat_p224_uint1 x92; fiat_p224_addcarryx_u64(&x91, &x92, x90, x67, x81); uint64_t x93; fiat_p224_uint1 x94; fiat_p224_addcarryx_u64(&x93, &x94, x92, x69, x83); uint64_t x95; fiat_p224_uint1 x96; fiat_p224_addcarryx_u64(&x95, &x96, x94, x71, x85); uint64_t x97; fiat_p224_uint1 x98; fiat_p224_addcarryx_u64(&x97, &x98, x96, x72, 0x0); uint64_t x99; uint64_t x100; fiat_p224_mulx_u64(&x99, &x100, x2, (arg1[3])); uint64_t x101; uint64_t x102; fiat_p224_mulx_u64(&x101, &x102, x2, (arg1[2])); uint64_t x103; uint64_t x104; fiat_p224_mulx_u64(&x103, &x104, x2, (arg1[1])); uint64_t x105; uint64_t x106; fiat_p224_mulx_u64(&x105, &x106, x2, (arg1[0])); uint64_t x107; fiat_p224_uint1 x108; fiat_p224_addcarryx_u64(&x107, &x108, 0x0, x106, x103); uint64_t x109; fiat_p224_uint1 x110; fiat_p224_addcarryx_u64(&x109, &x110, x108, x104, x101); uint64_t x111; fiat_p224_uint1 x112; fiat_p224_addcarryx_u64(&x111, &x112, x110, x102, x99); uint64_t x113; fiat_p224_uint1 x114; fiat_p224_addcarryx_u64(&x113, &x114, x112, x100, 0x0); uint64_t x115; fiat_p224_uint1 x116; fiat_p224_addcarryx_u64(&x115, &x116, 0x0, x89, x105); uint64_t x117; fiat_p224_uint1 x118; fiat_p224_addcarryx_u64(&x117, &x118, x116, x91, x107); uint64_t x119; fiat_p224_uint1 x120; fiat_p224_addcarryx_u64(&x119, &x120, x118, x93, x109); uint64_t x121; fiat_p224_uint1 x122; fiat_p224_addcarryx_u64(&x121, &x122, x120, x95, x111); uint64_t x123; fiat_p224_uint1 x124; fiat_p224_addcarryx_u64(&x123, &x124, x122, x97, x113); uint64_t x125; uint64_t x126; fiat_p224_mulx_u64(&x125, &x126, x115, UINT64_C(0xffffffffffffffff)); uint64_t x127; uint64_t x128; fiat_p224_mulx_u64(&x127, &x128, x125, UINT32_C(0xffffffff)); uint64_t x129; uint64_t x130; fiat_p224_mulx_u64(&x129, &x130, x125, UINT64_C(0xffffffffffffffff)); uint64_t x131; uint64_t x132; fiat_p224_mulx_u64(&x131, &x132, x125, UINT64_C(0xffffffff00000000)); uint64_t x133; fiat_p224_uint1 x134; fiat_p224_addcarryx_u64(&x133, &x134, 0x0, x132, x129); uint64_t x135; fiat_p224_uint1 x136; fiat_p224_addcarryx_u64(&x135, &x136, x134, x130, x127); uint64_t x137; fiat_p224_uint1 x138; fiat_p224_addcarryx_u64(&x137, &x138, x136, x128, 0x0); uint64_t x139; fiat_p224_uint1 x140; fiat_p224_addcarryx_u64(&x139, &x140, 0x0, x115, x125); uint64_t x141; fiat_p224_uint1 x142; fiat_p224_addcarryx_u64(&x141, &x142, x140, x117, x131); uint64_t x143; fiat_p224_uint1 x144; fiat_p224_addcarryx_u64(&x143, &x144, x142, x119, x133); uint64_t x145; fiat_p224_uint1 x146; fiat_p224_addcarryx_u64(&x145, &x146, x144, x121, x135); uint64_t x147; fiat_p224_uint1 x148; fiat_p224_addcarryx_u64(&x147, &x148, x146, x123, x137); uint64_t x149; fiat_p224_uint1 x150; fiat_p224_addcarryx_u64(&x149, &x150, x148, x124, 0x0); uint64_t x151; uint64_t x152; fiat_p224_mulx_u64(&x151, &x152, x3, (arg1[3])); uint64_t x153; uint64_t x154; fiat_p224_mulx_u64(&x153, &x154, x3, (arg1[2])); uint64_t x155; uint64_t x156; fiat_p224_mulx_u64(&x155, &x156, x3, (arg1[1])); uint64_t x157; uint64_t x158; fiat_p224_mulx_u64(&x157, &x158, x3, (arg1[0])); uint64_t x159; fiat_p224_uint1 x160; fiat_p224_addcarryx_u64(&x159, &x160, 0x0, x158, x155); uint64_t x161; fiat_p224_uint1 x162; fiat_p224_addcarryx_u64(&x161, &x162, x160, x156, x153); uint64_t x163; fiat_p224_uint1 x164; fiat_p224_addcarryx_u64(&x163, &x164, x162, x154, x151); uint64_t x165; fiat_p224_uint1 x166; fiat_p224_addcarryx_u64(&x165, &x166, x164, x152, 0x0); uint64_t x167; fiat_p224_uint1 x168; fiat_p224_addcarryx_u64(&x167, &x168, 0x0, x141, x157); uint64_t x169; fiat_p224_uint1 x170; fiat_p224_addcarryx_u64(&x169, &x170, x168, x143, x159); uint64_t x171; fiat_p224_uint1 x172; fiat_p224_addcarryx_u64(&x171, &x172, x170, x145, x161); uint64_t x173; fiat_p224_uint1 x174; fiat_p224_addcarryx_u64(&x173, &x174, x172, x147, x163); uint64_t x175; fiat_p224_uint1 x176; fiat_p224_addcarryx_u64(&x175, &x176, x174, x149, x165); uint64_t x177; uint64_t x178; fiat_p224_mulx_u64(&x177, &x178, x167, UINT64_C(0xffffffffffffffff)); uint64_t x179; uint64_t x180; fiat_p224_mulx_u64(&x179, &x180, x177, UINT32_C(0xffffffff)); uint64_t x181; uint64_t x182; fiat_p224_mulx_u64(&x181, &x182, x177, UINT64_C(0xffffffffffffffff)); uint64_t x183; uint64_t x184; fiat_p224_mulx_u64(&x183, &x184, x177, UINT64_C(0xffffffff00000000)); uint64_t x185; fiat_p224_uint1 x186; fiat_p224_addcarryx_u64(&x185, &x186, 0x0, x184, x181); uint64_t x187; fiat_p224_uint1 x188; fiat_p224_addcarryx_u64(&x187, &x188, x186, x182, x179); uint64_t x189; fiat_p224_uint1 x190; fiat_p224_addcarryx_u64(&x189, &x190, x188, x180, 0x0); uint64_t x191; fiat_p224_uint1 x192; fiat_p224_addcarryx_u64(&x191, &x192, 0x0, x167, x177); uint64_t x193; fiat_p224_uint1 x194; fiat_p224_addcarryx_u64(&x193, &x194, x192, x169, x183); uint64_t x195; fiat_p224_uint1 x196; fiat_p224_addcarryx_u64(&x195, &x196, x194, x171, x185); uint64_t x197; fiat_p224_uint1 x198; fiat_p224_addcarryx_u64(&x197, &x198, x196, x173, x187); uint64_t x199; fiat_p224_uint1 x200; fiat_p224_addcarryx_u64(&x199, &x200, x198, x175, x189); uint64_t x201; fiat_p224_uint1 x202; fiat_p224_addcarryx_u64(&x201, &x202, x200, x176, 0x0); uint64_t x203; fiat_p224_uint1 x204; fiat_p224_subborrowx_u64(&x203, &x204, 0x0, x193, 0x1); uint64_t x205; fiat_p224_uint1 x206; fiat_p224_subborrowx_u64(&x205, &x206, x204, x195, UINT64_C(0xffffffff00000000)); uint64_t x207; fiat_p224_uint1 x208; fiat_p224_subborrowx_u64(&x207, &x208, x206, x197, UINT64_C(0xffffffffffffffff)); uint64_t x209; fiat_p224_uint1 x210; fiat_p224_subborrowx_u64(&x209, &x210, x208, x199, UINT32_C(0xffffffff)); uint64_t x211; fiat_p224_uint1 x212; fiat_p224_subborrowx_u64(&x211, &x212, x210, x201, 0x0); uint64_t x213; fiat_p224_cmovznz_u64(&x213, x212, x203, x193); uint64_t x214; fiat_p224_cmovznz_u64(&x214, x212, x205, x195); uint64_t x215; fiat_p224_cmovznz_u64(&x215, x212, x207, x197); uint64_t x216; fiat_p224_cmovznz_u64(&x216, x212, x209, x199); out1[0] = x213; out1[1] = x214; out1[2] = x215; out1[3] = x216; } /* * The function fiat_p224_add adds two field elements in the Montgomery domain. * Preconditions: * 0 ≤ eval arg1 < m * 0 ≤ eval arg2 < m * Postconditions: * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m * 0 ≤ eval out1 < m * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p224_add(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) { uint64_t x1; fiat_p224_uint1 x2; fiat_p224_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); uint64_t x3; fiat_p224_uint1 x4; fiat_p224_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); uint64_t x5; fiat_p224_uint1 x6; fiat_p224_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); uint64_t x7; fiat_p224_uint1 x8; fiat_p224_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); uint64_t x9; fiat_p224_uint1 x10; fiat_p224_subborrowx_u64(&x9, &x10, 0x0, x1, 0x1); uint64_t x11; fiat_p224_uint1 x12; fiat_p224_subborrowx_u64(&x11, &x12, x10, x3, UINT64_C(0xffffffff00000000)); uint64_t x13; fiat_p224_uint1 x14; fiat_p224_subborrowx_u64(&x13, &x14, x12, x5, UINT64_C(0xffffffffffffffff)); uint64_t x15; fiat_p224_uint1 x16; fiat_p224_subborrowx_u64(&x15, &x16, x14, x7, UINT32_C(0xffffffff)); uint64_t x17; fiat_p224_uint1 x18; fiat_p224_subborrowx_u64(&x17, &x18, x16, x8, 0x0); uint64_t x19; fiat_p224_cmovznz_u64(&x19, x18, x9, x1); uint64_t x20; fiat_p224_cmovznz_u64(&x20, x18, x11, x3); uint64_t x21; fiat_p224_cmovznz_u64(&x21, x18, x13, x5); uint64_t x22; fiat_p224_cmovznz_u64(&x22, x18, x15, x7); out1[0] = x19; out1[1] = x20; out1[2] = x21; out1[3] = x22; } /* * The function fiat_p224_sub subtracts two field elements in the Montgomery domain. * Preconditions: * 0 ≤ eval arg1 < m * 0 ≤ eval arg2 < m * Postconditions: * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m * 0 ≤ eval out1 < m * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p224_sub(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) { uint64_t x1; fiat_p224_uint1 x2; fiat_p224_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); uint64_t x3; fiat_p224_uint1 x4; fiat_p224_subborrowx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); uint64_t x5; fiat_p224_uint1 x6; fiat_p224_subborrowx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); uint64_t x7; fiat_p224_uint1 x8; fiat_p224_subborrowx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); uint64_t x9; fiat_p224_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff)); uint64_t x10; fiat_p224_uint1 x11; fiat_p224_addcarryx_u64(&x10, &x11, 0x0, x1, (fiat_p224_uint1)(x9 & 0x1)); uint64_t x12; fiat_p224_uint1 x13; fiat_p224_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT64_C(0xffffffff00000000))); uint64_t x14; fiat_p224_uint1 x15; fiat_p224_addcarryx_u64(&x14, &x15, x13, x5, (x9 & UINT64_C(0xffffffffffffffff))); uint64_t x16; fiat_p224_uint1 x17; fiat_p224_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT32_C(0xffffffff))); out1[0] = x10; out1[1] = x12; out1[2] = x14; out1[3] = x16; } /* * The function fiat_p224_opp negates a field element in the Montgomery domain. * Preconditions: * 0 ≤ eval arg1 < m * Postconditions: * eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m * 0 ≤ eval out1 < m * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p224_opp(uint64_t out1[4], const uint64_t arg1[4]) { uint64_t x1; fiat_p224_uint1 x2; fiat_p224_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0])); uint64_t x3; fiat_p224_uint1 x4; fiat_p224_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1])); uint64_t x5; fiat_p224_uint1 x6; fiat_p224_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2])); uint64_t x7; fiat_p224_uint1 x8; fiat_p224_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3])); uint64_t x9; fiat_p224_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff)); uint64_t x10; fiat_p224_uint1 x11; fiat_p224_addcarryx_u64(&x10, &x11, 0x0, x1, (fiat_p224_uint1)(x9 & 0x1)); uint64_t x12; fiat_p224_uint1 x13; fiat_p224_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT64_C(0xffffffff00000000))); uint64_t x14; fiat_p224_uint1 x15; fiat_p224_addcarryx_u64(&x14, &x15, x13, x5, (x9 & UINT64_C(0xffffffffffffffff))); uint64_t x16; fiat_p224_uint1 x17; fiat_p224_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT32_C(0xffffffff))); out1[0] = x10; out1[1] = x12; out1[2] = x14; out1[3] = x16; } /* * The function fiat_p224_from_montgomery translates a field element out of the Montgomery domain. * Preconditions: * 0 ≤ eval arg1 < m * Postconditions: * eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m * 0 ≤ eval out1 < m * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p224_from_montgomery(uint64_t out1[4], const uint64_t arg1[4]) { uint64_t x1 = (arg1[0]); uint64_t x2; uint64_t x3; fiat_p224_mulx_u64(&x2, &x3, x1, UINT64_C(0xffffffffffffffff)); uint64_t x4; uint64_t x5; fiat_p224_mulx_u64(&x4, &x5, x2, UINT32_C(0xffffffff)); uint64_t x6; uint64_t x7; fiat_p224_mulx_u64(&x6, &x7, x2, UINT64_C(0xffffffffffffffff)); uint64_t x8; uint64_t x9; fiat_p224_mulx_u64(&x8, &x9, x2, UINT64_C(0xffffffff00000000)); uint64_t x10; fiat_p224_uint1 x11; fiat_p224_addcarryx_u64(&x10, &x11, 0x0, x9, x6); uint64_t x12; fiat_p224_uint1 x13; fiat_p224_addcarryx_u64(&x12, &x13, x11, x7, x4); uint64_t x14; fiat_p224_uint1 x15; fiat_p224_addcarryx_u64(&x14, &x15, 0x0, x1, x2); uint64_t x16; fiat_p224_uint1 x17; fiat_p224_addcarryx_u64(&x16, &x17, x15, 0x0, x8); uint64_t x18; fiat_p224_uint1 x19; fiat_p224_addcarryx_u64(&x18, &x19, x17, 0x0, x10); uint64_t x20; fiat_p224_uint1 x21; fiat_p224_addcarryx_u64(&x20, &x21, x19, 0x0, x12); uint64_t x22; fiat_p224_uint1 x23; fiat_p224_addcarryx_u64(&x22, &x23, 0x0, x16, (arg1[1])); uint64_t x24; fiat_p224_uint1 x25; fiat_p224_addcarryx_u64(&x24, &x25, x23, x18, 0x0); uint64_t x26; fiat_p224_uint1 x27; fiat_p224_addcarryx_u64(&x26, &x27, x25, x20, 0x0); uint64_t x28; uint64_t x29; fiat_p224_mulx_u64(&x28, &x29, x22, UINT64_C(0xffffffffffffffff)); uint64_t x30; uint64_t x31; fiat_p224_mulx_u64(&x30, &x31, x28, UINT32_C(0xffffffff)); uint64_t x32; uint64_t x33; fiat_p224_mulx_u64(&x32, &x33, x28, UINT64_C(0xffffffffffffffff)); uint64_t x34; uint64_t x35; fiat_p224_mulx_u64(&x34, &x35, x28, UINT64_C(0xffffffff00000000)); uint64_t x36; fiat_p224_uint1 x37; fiat_p224_addcarryx_u64(&x36, &x37, 0x0, x35, x32); uint64_t x38; fiat_p224_uint1 x39; fiat_p224_addcarryx_u64(&x38, &x39, x37, x33, x30); uint64_t x40; fiat_p224_uint1 x41; fiat_p224_addcarryx_u64(&x40, &x41, 0x0, x22, x28); uint64_t x42; fiat_p224_uint1 x43; fiat_p224_addcarryx_u64(&x42, &x43, x41, x24, x34); uint64_t x44; fiat_p224_uint1 x45; fiat_p224_addcarryx_u64(&x44, &x45, x43, x26, x36); uint64_t x46; fiat_p224_uint1 x47; fiat_p224_addcarryx_u64(&x46, &x47, x13, x5, 0x0); uint64_t x48; fiat_p224_uint1 x49; fiat_p224_addcarryx_u64(&x48, &x49, x21, 0x0, x46); uint64_t x50; fiat_p224_uint1 x51; fiat_p224_addcarryx_u64(&x50, &x51, x27, x48, 0x0); uint64_t x52; fiat_p224_uint1 x53; fiat_p224_addcarryx_u64(&x52, &x53, x45, x50, x38); uint64_t x54; fiat_p224_uint1 x55; fiat_p224_addcarryx_u64(&x54, &x55, 0x0, x42, (arg1[2])); uint64_t x56; fiat_p224_uint1 x57; fiat_p224_addcarryx_u64(&x56, &x57, x55, x44, 0x0); uint64_t x58; fiat_p224_uint1 x59; fiat_p224_addcarryx_u64(&x58, &x59, x57, x52, 0x0); uint64_t x60; uint64_t x61; fiat_p224_mulx_u64(&x60, &x61, x54, UINT64_C(0xffffffffffffffff)); uint64_t x62; uint64_t x63; fiat_p224_mulx_u64(&x62, &x63, x60, UINT32_C(0xffffffff)); uint64_t x64; uint64_t x65; fiat_p224_mulx_u64(&x64, &x65, x60, UINT64_C(0xffffffffffffffff)); uint64_t x66; uint64_t x67; fiat_p224_mulx_u64(&x66, &x67, x60, UINT64_C(0xffffffff00000000)); uint64_t x68; fiat_p224_uint1 x69; fiat_p224_addcarryx_u64(&x68, &x69, 0x0, x67, x64); uint64_t x70; fiat_p224_uint1 x71; fiat_p224_addcarryx_u64(&x70, &x71, x69, x65, x62); uint64_t x72; fiat_p224_uint1 x73; fiat_p224_addcarryx_u64(&x72, &x73, 0x0, x54, x60); uint64_t x74; fiat_p224_uint1 x75; fiat_p224_addcarryx_u64(&x74, &x75, x73, x56, x66); uint64_t x76; fiat_p224_uint1 x77; fiat_p224_addcarryx_u64(&x76, &x77, x75, x58, x68); uint64_t x78; fiat_p224_uint1 x79; fiat_p224_addcarryx_u64(&x78, &x79, x39, x31, 0x0); uint64_t x80; fiat_p224_uint1 x81; fiat_p224_addcarryx_u64(&x80, &x81, x53, 0x0, x78); uint64_t x82; fiat_p224_uint1 x83; fiat_p224_addcarryx_u64(&x82, &x83, x59, x80, 0x0); uint64_t x84; fiat_p224_uint1 x85; fiat_p224_addcarryx_u64(&x84, &x85, x77, x82, x70); uint64_t x86; fiat_p224_uint1 x87; fiat_p224_addcarryx_u64(&x86, &x87, 0x0, x74, (arg1[3])); uint64_t x88; fiat_p224_uint1 x89; fiat_p224_addcarryx_u64(&x88, &x89, x87, x76, 0x0); uint64_t x90; fiat_p224_uint1 x91; fiat_p224_addcarryx_u64(&x90, &x91, x89, x84, 0x0); uint64_t x92; uint64_t x93; fiat_p224_mulx_u64(&x92, &x93, x86, UINT64_C(0xffffffffffffffff)); uint64_t x94; uint64_t x95; fiat_p224_mulx_u64(&x94, &x95, x92, UINT32_C(0xffffffff)); uint64_t x96; uint64_t x97; fiat_p224_mulx_u64(&x96, &x97, x92, UINT64_C(0xffffffffffffffff)); uint64_t x98; uint64_t x99; fiat_p224_mulx_u64(&x98, &x99, x92, UINT64_C(0xffffffff00000000)); uint64_t x100; fiat_p224_uint1 x101; fiat_p224_addcarryx_u64(&x100, &x101, 0x0, x99, x96); uint64_t x102; fiat_p224_uint1 x103; fiat_p224_addcarryx_u64(&x102, &x103, x101, x97, x94); uint64_t x104; fiat_p224_uint1 x105; fiat_p224_addcarryx_u64(&x104, &x105, 0x0, x86, x92); uint64_t x106; fiat_p224_uint1 x107; fiat_p224_addcarryx_u64(&x106, &x107, x105, x88, x98); uint64_t x108; fiat_p224_uint1 x109; fiat_p224_addcarryx_u64(&x108, &x109, x107, x90, x100); uint64_t x110; fiat_p224_uint1 x111; fiat_p224_addcarryx_u64(&x110, &x111, x71, x63, 0x0); uint64_t x112; fiat_p224_uint1 x113; fiat_p224_addcarryx_u64(&x112, &x113, x85, 0x0, x110); uint64_t x114; fiat_p224_uint1 x115; fiat_p224_addcarryx_u64(&x114, &x115, x91, x112, 0x0); uint64_t x116; fiat_p224_uint1 x117; fiat_p224_addcarryx_u64(&x116, &x117, x109, x114, x102); uint64_t x118; fiat_p224_uint1 x119; fiat_p224_addcarryx_u64(&x118, &x119, x103, x95, 0x0); uint64_t x120; fiat_p224_uint1 x121; fiat_p224_addcarryx_u64(&x120, &x121, x117, 0x0, x118); uint64_t x122; fiat_p224_uint1 x123; fiat_p224_subborrowx_u64(&x122, &x123, 0x0, x106, 0x1); uint64_t x124; fiat_p224_uint1 x125; fiat_p224_subborrowx_u64(&x124, &x125, x123, x108, UINT64_C(0xffffffff00000000)); uint64_t x126; fiat_p224_uint1 x127; fiat_p224_subborrowx_u64(&x126, &x127, x125, x116, UINT64_C(0xffffffffffffffff)); uint64_t x128; fiat_p224_uint1 x129; fiat_p224_subborrowx_u64(&x128, &x129, x127, x120, UINT32_C(0xffffffff)); uint64_t x130; fiat_p224_uint1 x131; fiat_p224_subborrowx_u64(&x130, &x131, x129, 0x0, 0x0); uint64_t x132; fiat_p224_cmovznz_u64(&x132, x131, x122, x106); uint64_t x133; fiat_p224_cmovznz_u64(&x133, x131, x124, x108); uint64_t x134; fiat_p224_cmovznz_u64(&x134, x131, x126, x116); uint64_t x135; fiat_p224_cmovznz_u64(&x135, x131, x128, x120); out1[0] = x132; out1[1] = x133; out1[2] = x134; out1[3] = x135; } /* * The function fiat_p224_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] */ static void fiat_p224_nonzero(uint64_t* out1, const uint64_t arg1[4]) { uint64_t x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | ((arg1[3]) | (uint64_t)0x0)))); *out1 = x1; } /* * The function fiat_p224_selectznz is a multi-limb conditional select. * Postconditions: * eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p224_selectznz(uint64_t out1[4], fiat_p224_uint1 arg1, const uint64_t arg2[4], const uint64_t arg3[4]) { uint64_t x1; fiat_p224_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0])); uint64_t x2; fiat_p224_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1])); uint64_t x3; fiat_p224_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2])); uint64_t x4; fiat_p224_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3])); out1[0] = x1; out1[1] = x2; out1[2] = x3; out1[3] = x4; } /* * The function fiat_p224_to_bytes serializes a field element 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 ~> 0xffffffff]] * 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 ~> 0x0], [0x0 ~> 0x0], [0x0 ~> 0x0], [0x0 ~> 0x0]] */ static void fiat_p224_to_bytes(uint8_t out1[32], const uint64_t arg1[4]) { uint64_t x1 = (arg1[3]); uint64_t x2 = (arg1[2]); uint64_t x3 = (arg1[1]); uint64_t x4 = (arg1[0]); uint64_t x5 = (x4 >> 8); uint8_t x6 = (uint8_t)(x4 & UINT8_C(0xff)); uint64_t x7 = (x5 >> 8); uint8_t x8 = (uint8_t)(x5 & UINT8_C(0xff)); uint64_t x9 = (x7 >> 8); uint8_t x10 = (uint8_t)(x7 & UINT8_C(0xff)); uint64_t x11 = (x9 >> 8); uint8_t x12 = (uint8_t)(x9 & UINT8_C(0xff)); uint64_t x13 = (x11 >> 8); uint8_t x14 = (uint8_t)(x11 & UINT8_C(0xff)); uint64_t x15 = (x13 >> 8); uint8_t x16 = (uint8_t)(x13 & UINT8_C(0xff)); uint8_t x17 = (uint8_t)(x15 >> 8); uint8_t x18 = (uint8_t)(x15 & UINT8_C(0xff)); uint8_t x19 = (uint8_t)(x17 & UINT8_C(0xff)); uint64_t x20 = (x3 >> 8); uint8_t x21 = (uint8_t)(x3 & UINT8_C(0xff)); uint64_t x22 = (x20 >> 8); uint8_t x23 = (uint8_t)(x20 & UINT8_C(0xff)); uint64_t x24 = (x22 >> 8); uint8_t x25 = (uint8_t)(x22 & UINT8_C(0xff)); uint64_t x26 = (x24 >> 8); uint8_t x27 = (uint8_t)(x24 & UINT8_C(0xff)); uint64_t x28 = (x26 >> 8); uint8_t x29 = (uint8_t)(x26 & UINT8_C(0xff)); uint64_t x30 = (x28 >> 8); uint8_t x31 = (uint8_t)(x28 & UINT8_C(0xff)); uint8_t x32 = (uint8_t)(x30 >> 8); uint8_t x33 = (uint8_t)(x30 & UINT8_C(0xff)); uint8_t x34 = (uint8_t)(x32 & UINT8_C(0xff)); uint64_t x35 = (x2 >> 8); uint8_t x36 = (uint8_t)(x2 & UINT8_C(0xff)); uint64_t x37 = (x35 >> 8); uint8_t x38 = (uint8_t)(x35 & UINT8_C(0xff)); uint64_t x39 = (x37 >> 8); uint8_t x40 = (uint8_t)(x37 & UINT8_C(0xff)); uint64_t x41 = (x39 >> 8); uint8_t x42 = (uint8_t)(x39 & UINT8_C(0xff)); uint64_t x43 = (x41 >> 8); uint8_t x44 = (uint8_t)(x41 & UINT8_C(0xff)); uint64_t x45 = (x43 >> 8); uint8_t x46 = (uint8_t)(x43 & UINT8_C(0xff)); uint8_t x47 = (uint8_t)(x45 >> 8); uint8_t x48 = (uint8_t)(x45 & UINT8_C(0xff)); uint8_t x49 = (uint8_t)(x47 & UINT8_C(0xff)); uint64_t x50 = (x1 >> 8); uint8_t x51 = (uint8_t)(x1 & UINT8_C(0xff)); uint64_t x52 = (x50 >> 8); uint8_t x53 = (uint8_t)(x50 & UINT8_C(0xff)); uint8_t x54 = (uint8_t)(x52 >> 8); uint8_t x55 = (uint8_t)(x52 & UINT8_C(0xff)); uint8_t x56 = (uint8_t)(x54 & UINT8_C(0xff)); out1[0] = x6; out1[1] = x8; out1[2] = x10; out1[3] = x12; out1[4] = x14; out1[5] = x16; out1[6] = x18; out1[7] = x19; out1[8] = x21; out1[9] = x23; out1[10] = x25; out1[11] = x27; out1[12] = x29; out1[13] = x31; out1[14] = x33; out1[15] = x34; out1[16] = x36; out1[17] = x38; out1[18] = x40; out1[19] = x42; out1[20] = x44; out1[21] = x46; out1[22] = x48; out1[23] = x49; out1[24] = x51; out1[25] = x53; out1[26] = x55; out1[27] = x56; out1[28] = 0x0; out1[29] = 0x0; out1[30] = 0x0; out1[31] = 0x0; } /* * The function fiat_p224_from_bytes deserializes a field element 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 ~> 0x0], [0x0 ~> 0x0], [0x0 ~> 0x0], [0x0 ~> 0x0]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffff]] */ static void fiat_p224_from_bytes(uint64_t out1[4], const uint8_t arg1[32]) { uint64_t x1 = ((uint64_t)(arg1[27]) << 24); uint64_t x2 = ((uint64_t)(arg1[26]) << 16); uint64_t x3 = ((uint64_t)(arg1[25]) << 8); uint8_t x4 = (arg1[24]); uint64_t x5 = ((uint64_t)(arg1[23]) << 56); uint64_t x6 = ((uint64_t)(arg1[22]) << 48); uint64_t x7 = ((uint64_t)(arg1[21]) << 40); uint64_t x8 = ((uint64_t)(arg1[20]) << 32); uint64_t x9 = ((uint64_t)(arg1[19]) << 24); uint64_t x10 = ((uint64_t)(arg1[18]) << 16); uint64_t x11 = ((uint64_t)(arg1[17]) << 8); uint8_t x12 = (arg1[16]); uint64_t x13 = ((uint64_t)(arg1[15]) << 56); uint64_t x14 = ((uint64_t)(arg1[14]) << 48); uint64_t x15 = ((uint64_t)(arg1[13]) << 40); uint64_t x16 = ((uint64_t)(arg1[12]) << 32); uint64_t x17 = ((uint64_t)(arg1[11]) << 24); uint64_t x18 = ((uint64_t)(arg1[10]) << 16); uint64_t x19 = ((uint64_t)(arg1[9]) << 8); uint8_t x20 = (arg1[8]); uint64_t x21 = ((uint64_t)(arg1[7]) << 56); uint64_t x22 = ((uint64_t)(arg1[6]) << 48); uint64_t x23 = ((uint64_t)(arg1[5]) << 40); uint64_t x24 = ((uint64_t)(arg1[4]) << 32); uint64_t x25 = ((uint64_t)(arg1[3]) << 24); uint64_t x26 = ((uint64_t)(arg1[2]) << 16); uint64_t x27 = ((uint64_t)(arg1[1]) << 8); uint8_t x28 = (arg1[0]); uint64_t x29 = (x28 + (x27 + (x26 + (x25 + (x24 + (x23 + (x22 + x21))))))); uint64_t x30 = (x29 & UINT64_C(0xffffffffffffffff)); uint64_t x31 = (x4 + (x3 + (x2 + x1))); uint64_t x32 = (x12 + (x11 + (x10 + (x9 + (x8 + (x7 + (x6 + x5))))))); uint64_t x33 = (x20 + (x19 + (x18 + (x17 + (x16 + (x15 + (x14 + x13))))))); uint64_t x34 = (x33 & UINT64_C(0xffffffffffffffff)); uint64_t x35 = (x32 & UINT64_C(0xffffffffffffffff)); out1[0] = x30; out1[1] = x34; out1[2] = x35; out1[3] = x31; }