/* Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --inline --static --use-value-barrier p256 64 '2^256 - 2^224 + 2^192 + 2^96 - 1' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp */ /* curve description: p256 */ /* machine_wordsize = 64 (from "64") */ /* requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp */ /* m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1") */ /* */ /* NOTE: In addition to the bounds specified above each function, all */ /* functions synthesized for this Montgomery arithmetic require the */ /* input to be strictly less than the prime modulus (m), and also */ /* require the input to be in the unique saturated representation. */ /* All functions also ensure that these two properties are true of */ /* return values. */ /* */ /* Computed values: */ /* eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) */ /* bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) */ /* twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in */ /* if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 */ #include typedef unsigned char fiat_p256_uint1; typedef signed char fiat_p256_int1; #if defined(__GNUC__) || defined(__clang__) # define FIAT_P256_FIAT_EXTENSION __extension__ # define FIAT_P256_FIAT_INLINE __inline__ #else # define FIAT_P256_FIAT_EXTENSION # define FIAT_P256_FIAT_INLINE #endif FIAT_P256_FIAT_EXTENSION typedef signed __int128 fiat_p256_int128; FIAT_P256_FIAT_EXTENSION typedef unsigned __int128 fiat_p256_uint128; /* The type fiat_p256_montgomery_domain_field_element is a field element in the Montgomery domain. */ /* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ typedef uint64_t fiat_p256_montgomery_domain_field_element[4]; /* The type fiat_p256_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. */ /* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ typedef uint64_t fiat_p256_non_montgomery_domain_field_element[4]; #if (-1 & 3) != 3 #error "This code only works on a two's complement system" #endif #if !defined(FIAT_P256_NO_ASM) && (defined(__GNUC__) || defined(__clang__)) static __inline__ uint64_t fiat_p256_value_barrier_u64(uint64_t a) { __asm__("" : "+r"(a) : /* no inputs */); return a; } #else # define fiat_p256_value_barrier_u64(x) (x) #endif /* * The function fiat_p256_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 FIAT_P256_FIAT_INLINE void fiat_p256_addcarryx_u64(uint64_t* out1, fiat_p256_uint1* out2, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_p256_uint128 x1; uint64_t x2; fiat_p256_uint1 x3; x1 = ((arg1 + (fiat_p256_uint128)arg2) + arg3); x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); x3 = (fiat_p256_uint1)(x1 >> 64); *out1 = x2; *out2 = x3; } /* * The function fiat_p256_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 FIAT_P256_FIAT_INLINE void fiat_p256_subborrowx_u64(uint64_t* out1, fiat_p256_uint1* out2, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_p256_int128 x1; fiat_p256_int1 x2; uint64_t x3; x1 = ((arg2 - (fiat_p256_int128)arg1) - arg3); x2 = (fiat_p256_int1)(x1 >> 64); x3 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); *out1 = x3; *out2 = (fiat_p256_uint1)(0x0 - x2); } /* * The function fiat_p256_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 FIAT_P256_FIAT_INLINE void fiat_p256_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) { fiat_p256_uint128 x1; uint64_t x2; uint64_t x3; x1 = ((fiat_p256_uint128)arg1 * arg2); x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); x3 = (uint64_t)(x1 >> 64); *out1 = x2; *out2 = x3; } /* * The function fiat_p256_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 FIAT_P256_FIAT_INLINE void fiat_p256_cmovznz_u64(uint64_t* out1, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_p256_uint1 x1; uint64_t x2; uint64_t x3; x1 = (!(!arg1)); x2 = ((fiat_p256_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff)); x3 = ((fiat_p256_value_barrier_u64(x2) & arg3) | (fiat_p256_value_barrier_u64((~x2)) & arg2)); *out1 = x3; } /* * The function fiat_p256_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 * */ static FIAT_P256_FIAT_INLINE void fiat_p256_mul(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) { uint64_t x1; uint64_t x2; uint64_t x3; uint64_t x4; uint64_t x5; uint64_t x6; uint64_t x7; uint64_t x8; uint64_t x9; uint64_t x10; uint64_t x11; uint64_t x12; uint64_t x13; fiat_p256_uint1 x14; uint64_t x15; fiat_p256_uint1 x16; uint64_t x17; fiat_p256_uint1 x18; uint64_t x19; uint64_t x20; uint64_t x21; uint64_t x22; uint64_t x23; uint64_t x24; uint64_t x25; uint64_t x26; fiat_p256_uint1 x27; uint64_t x28; uint64_t x29; fiat_p256_uint1 x30; uint64_t x31; fiat_p256_uint1 x32; uint64_t x33; fiat_p256_uint1 x34; uint64_t x35; fiat_p256_uint1 x36; uint64_t x37; fiat_p256_uint1 x38; uint64_t x39; uint64_t x40; uint64_t x41; uint64_t x42; uint64_t x43; uint64_t x44; uint64_t x45; uint64_t x46; uint64_t x47; fiat_p256_uint1 x48; uint64_t x49; fiat_p256_uint1 x50; uint64_t x51; fiat_p256_uint1 x52; uint64_t x53; uint64_t x54; fiat_p256_uint1 x55; uint64_t x56; fiat_p256_uint1 x57; uint64_t x58; fiat_p256_uint1 x59; uint64_t x60; fiat_p256_uint1 x61; uint64_t x62; fiat_p256_uint1 x63; uint64_t x64; uint64_t x65; uint64_t x66; uint64_t x67; uint64_t x68; uint64_t x69; uint64_t x70; fiat_p256_uint1 x71; uint64_t x72; uint64_t x73; fiat_p256_uint1 x74; uint64_t x75; fiat_p256_uint1 x76; uint64_t x77; fiat_p256_uint1 x78; uint64_t x79; fiat_p256_uint1 x80; uint64_t x81; fiat_p256_uint1 x82; uint64_t x83; uint64_t x84; uint64_t x85; uint64_t x86; uint64_t x87; uint64_t x88; uint64_t x89; uint64_t x90; uint64_t x91; uint64_t x92; fiat_p256_uint1 x93; uint64_t x94; fiat_p256_uint1 x95; uint64_t x96; fiat_p256_uint1 x97; uint64_t x98; uint64_t x99; fiat_p256_uint1 x100; uint64_t x101; fiat_p256_uint1 x102; uint64_t x103; fiat_p256_uint1 x104; uint64_t x105; fiat_p256_uint1 x106; uint64_t x107; fiat_p256_uint1 x108; uint64_t x109; uint64_t x110; uint64_t x111; uint64_t x112; uint64_t x113; uint64_t x114; uint64_t x115; fiat_p256_uint1 x116; uint64_t x117; uint64_t x118; fiat_p256_uint1 x119; uint64_t x120; fiat_p256_uint1 x121; uint64_t x122; fiat_p256_uint1 x123; uint64_t x124; fiat_p256_uint1 x125; uint64_t x126; fiat_p256_uint1 x127; uint64_t x128; uint64_t x129; uint64_t x130; uint64_t x131; uint64_t x132; uint64_t x133; uint64_t x134; uint64_t x135; uint64_t x136; uint64_t x137; fiat_p256_uint1 x138; uint64_t x139; fiat_p256_uint1 x140; uint64_t x141; fiat_p256_uint1 x142; uint64_t x143; uint64_t x144; fiat_p256_uint1 x145; uint64_t x146; fiat_p256_uint1 x147; uint64_t x148; fiat_p256_uint1 x149; uint64_t x150; fiat_p256_uint1 x151; uint64_t x152; fiat_p256_uint1 x153; uint64_t x154; uint64_t x155; uint64_t x156; uint64_t x157; uint64_t x158; uint64_t x159; uint64_t x160; fiat_p256_uint1 x161; uint64_t x162; uint64_t x163; fiat_p256_uint1 x164; uint64_t x165; fiat_p256_uint1 x166; uint64_t x167; fiat_p256_uint1 x168; uint64_t x169; fiat_p256_uint1 x170; uint64_t x171; fiat_p256_uint1 x172; uint64_t x173; uint64_t x174; fiat_p256_uint1 x175; uint64_t x176; fiat_p256_uint1 x177; uint64_t x178; fiat_p256_uint1 x179; uint64_t x180; fiat_p256_uint1 x181; uint64_t x182; fiat_p256_uint1 x183; uint64_t x184; uint64_t x185; uint64_t x186; uint64_t x187; x1 = (arg1[1]); x2 = (arg1[2]); x3 = (arg1[3]); x4 = (arg1[0]); fiat_p256_mulx_u64(&x5, &x6, x4, (arg2[3])); fiat_p256_mulx_u64(&x7, &x8, x4, (arg2[2])); fiat_p256_mulx_u64(&x9, &x10, x4, (arg2[1])); fiat_p256_mulx_u64(&x11, &x12, x4, (arg2[0])); fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9); fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7); fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5); x19 = (x18 + x6); fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22); x28 = (x27 + x23); fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24); fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26); fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28); fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20); fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21); fiat_p256_mulx_u64(&x39, &x40, x1, (arg2[3])); fiat_p256_mulx_u64(&x41, &x42, x1, (arg2[2])); fiat_p256_mulx_u64(&x43, &x44, x1, (arg2[1])); fiat_p256_mulx_u64(&x45, &x46, x1, (arg2[0])); fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43); fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41); fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39); x53 = (x52 + x40); fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45); fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47); fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49); fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51); fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53); fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66); x72 = (x71 + x67); fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68); fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70); fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72); fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64); fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65); x83 = ((uint64_t)x82 + x63); fiat_p256_mulx_u64(&x84, &x85, x2, (arg2[3])); fiat_p256_mulx_u64(&x86, &x87, x2, (arg2[2])); fiat_p256_mulx_u64(&x88, &x89, x2, (arg2[1])); fiat_p256_mulx_u64(&x90, &x91, x2, (arg2[0])); fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88); fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86); fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84); x98 = (x97 + x85); fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90); fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92); fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94); fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96); fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98); fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111); x117 = (x116 + x112); fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113); fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115); fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117); fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109); fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110); x128 = ((uint64_t)x127 + x108); fiat_p256_mulx_u64(&x129, &x130, x3, (arg2[3])); fiat_p256_mulx_u64(&x131, &x132, x3, (arg2[2])); fiat_p256_mulx_u64(&x133, &x134, x3, (arg2[1])); fiat_p256_mulx_u64(&x135, &x136, x3, (arg2[0])); fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133); fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131); fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129); x143 = (x142 + x130); fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135); fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137); fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139); fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141); fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143); fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156); x162 = (x161 + x157); fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158); fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160); fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162); fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154); fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155); x173 = ((uint64_t)x172 + x153); fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff)); fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff)); fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0); fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001)); fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0); fiat_p256_cmovznz_u64(&x184, x183, x174, x165); fiat_p256_cmovznz_u64(&x185, x183, x176, x167); fiat_p256_cmovznz_u64(&x186, x183, x178, x169); fiat_p256_cmovznz_u64(&x187, x183, x180, x171); out1[0] = x184; out1[1] = x185; out1[2] = x186; out1[3] = x187; } /* * The function fiat_p256_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 * */ static FIAT_P256_FIAT_INLINE void fiat_p256_square(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) { uint64_t x1; uint64_t x2; uint64_t x3; uint64_t x4; uint64_t x5; uint64_t x6; uint64_t x7; uint64_t x8; uint64_t x9; uint64_t x10; uint64_t x11; uint64_t x12; uint64_t x13; fiat_p256_uint1 x14; uint64_t x15; fiat_p256_uint1 x16; uint64_t x17; fiat_p256_uint1 x18; uint64_t x19; uint64_t x20; uint64_t x21; uint64_t x22; uint64_t x23; uint64_t x24; uint64_t x25; uint64_t x26; fiat_p256_uint1 x27; uint64_t x28; uint64_t x29; fiat_p256_uint1 x30; uint64_t x31; fiat_p256_uint1 x32; uint64_t x33; fiat_p256_uint1 x34; uint64_t x35; fiat_p256_uint1 x36; uint64_t x37; fiat_p256_uint1 x38; uint64_t x39; uint64_t x40; uint64_t x41; uint64_t x42; uint64_t x43; uint64_t x44; uint64_t x45; uint64_t x46; uint64_t x47; fiat_p256_uint1 x48; uint64_t x49; fiat_p256_uint1 x50; uint64_t x51; fiat_p256_uint1 x52; uint64_t x53; uint64_t x54; fiat_p256_uint1 x55; uint64_t x56; fiat_p256_uint1 x57; uint64_t x58; fiat_p256_uint1 x59; uint64_t x60; fiat_p256_uint1 x61; uint64_t x62; fiat_p256_uint1 x63; uint64_t x64; uint64_t x65; uint64_t x66; uint64_t x67; uint64_t x68; uint64_t x69; uint64_t x70; fiat_p256_uint1 x71; uint64_t x72; uint64_t x73; fiat_p256_uint1 x74; uint64_t x75; fiat_p256_uint1 x76; uint64_t x77; fiat_p256_uint1 x78; uint64_t x79; fiat_p256_uint1 x80; uint64_t x81; fiat_p256_uint1 x82; uint64_t x83; uint64_t x84; uint64_t x85; uint64_t x86; uint64_t x87; uint64_t x88; uint64_t x89; uint64_t x90; uint64_t x91; uint64_t x92; fiat_p256_uint1 x93; uint64_t x94; fiat_p256_uint1 x95; uint64_t x96; fiat_p256_uint1 x97; uint64_t x98; uint64_t x99; fiat_p256_uint1 x100; uint64_t x101; fiat_p256_uint1 x102; uint64_t x103; fiat_p256_uint1 x104; uint64_t x105; fiat_p256_uint1 x106; uint64_t x107; fiat_p256_uint1 x108; uint64_t x109; uint64_t x110; uint64_t x111; uint64_t x112; uint64_t x113; uint64_t x114; uint64_t x115; fiat_p256_uint1 x116; uint64_t x117; uint64_t x118; fiat_p256_uint1 x119; uint64_t x120; fiat_p256_uint1 x121; uint64_t x122; fiat_p256_uint1 x123; uint64_t x124; fiat_p256_uint1 x125; uint64_t x126; fiat_p256_uint1 x127; uint64_t x128; uint64_t x129; uint64_t x130; uint64_t x131; uint64_t x132; uint64_t x133; uint64_t x134; uint64_t x135; uint64_t x136; uint64_t x137; fiat_p256_uint1 x138; uint64_t x139; fiat_p256_uint1 x140; uint64_t x141; fiat_p256_uint1 x142; uint64_t x143; uint64_t x144; fiat_p256_uint1 x145; uint64_t x146; fiat_p256_uint1 x147; uint64_t x148; fiat_p256_uint1 x149; uint64_t x150; fiat_p256_uint1 x151; uint64_t x152; fiat_p256_uint1 x153; uint64_t x154; uint64_t x155; uint64_t x156; uint64_t x157; uint64_t x158; uint64_t x159; uint64_t x160; fiat_p256_uint1 x161; uint64_t x162; uint64_t x163; fiat_p256_uint1 x164; uint64_t x165; fiat_p256_uint1 x166; uint64_t x167; fiat_p256_uint1 x168; uint64_t x169; fiat_p256_uint1 x170; uint64_t x171; fiat_p256_uint1 x172; uint64_t x173; uint64_t x174; fiat_p256_uint1 x175; uint64_t x176; fiat_p256_uint1 x177; uint64_t x178; fiat_p256_uint1 x179; uint64_t x180; fiat_p256_uint1 x181; uint64_t x182; fiat_p256_uint1 x183; uint64_t x184; uint64_t x185; uint64_t x186; uint64_t x187; x1 = (arg1[1]); x2 = (arg1[2]); x3 = (arg1[3]); x4 = (arg1[0]); fiat_p256_mulx_u64(&x5, &x6, x4, (arg1[3])); fiat_p256_mulx_u64(&x7, &x8, x4, (arg1[2])); fiat_p256_mulx_u64(&x9, &x10, x4, (arg1[1])); fiat_p256_mulx_u64(&x11, &x12, x4, (arg1[0])); fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9); fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7); fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5); x19 = (x18 + x6); fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22); x28 = (x27 + x23); fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24); fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26); fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28); fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20); fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21); fiat_p256_mulx_u64(&x39, &x40, x1, (arg1[3])); fiat_p256_mulx_u64(&x41, &x42, x1, (arg1[2])); fiat_p256_mulx_u64(&x43, &x44, x1, (arg1[1])); fiat_p256_mulx_u64(&x45, &x46, x1, (arg1[0])); fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43); fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41); fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39); x53 = (x52 + x40); fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45); fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47); fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49); fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51); fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53); fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66); x72 = (x71 + x67); fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68); fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70); fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72); fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64); fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65); x83 = ((uint64_t)x82 + x63); fiat_p256_mulx_u64(&x84, &x85, x2, (arg1[3])); fiat_p256_mulx_u64(&x86, &x87, x2, (arg1[2])); fiat_p256_mulx_u64(&x88, &x89, x2, (arg1[1])); fiat_p256_mulx_u64(&x90, &x91, x2, (arg1[0])); fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88); fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86); fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84); x98 = (x97 + x85); fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90); fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92); fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94); fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96); fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98); fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111); x117 = (x116 + x112); fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113); fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115); fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117); fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109); fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110); x128 = ((uint64_t)x127 + x108); fiat_p256_mulx_u64(&x129, &x130, x3, (arg1[3])); fiat_p256_mulx_u64(&x131, &x132, x3, (arg1[2])); fiat_p256_mulx_u64(&x133, &x134, x3, (arg1[1])); fiat_p256_mulx_u64(&x135, &x136, x3, (arg1[0])); fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133); fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131); fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129); x143 = (x142 + x130); fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135); fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137); fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139); fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141); fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143); fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001)); fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff)); fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156); x162 = (x161 + x157); fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158); fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160); fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162); fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154); fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155); x173 = ((uint64_t)x172 + x153); fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff)); fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff)); fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0); fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001)); fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0); fiat_p256_cmovznz_u64(&x184, x183, x174, x165); fiat_p256_cmovznz_u64(&x185, x183, x176, x167); fiat_p256_cmovznz_u64(&x186, x183, x178, x169); fiat_p256_cmovznz_u64(&x187, x183, x180, x171); out1[0] = x184; out1[1] = x185; out1[2] = x186; out1[3] = x187; } /* * The function fiat_p256_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 * */ static FIAT_P256_FIAT_INLINE void fiat_p256_add(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) { uint64_t x1; fiat_p256_uint1 x2; uint64_t x3; fiat_p256_uint1 x4; uint64_t x5; fiat_p256_uint1 x6; uint64_t x7; fiat_p256_uint1 x8; uint64_t x9; fiat_p256_uint1 x10; uint64_t x11; fiat_p256_uint1 x12; uint64_t x13; fiat_p256_uint1 x14; uint64_t x15; fiat_p256_uint1 x16; uint64_t x17; fiat_p256_uint1 x18; uint64_t x19; uint64_t x20; uint64_t x21; uint64_t x22; fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); fiat_p256_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); fiat_p256_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); fiat_p256_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); fiat_p256_subborrowx_u64(&x9, &x10, 0x0, x1, UINT64_C(0xffffffffffffffff)); fiat_p256_subborrowx_u64(&x11, &x12, x10, x3, UINT32_C(0xffffffff)); fiat_p256_subborrowx_u64(&x13, &x14, x12, x5, 0x0); fiat_p256_subborrowx_u64(&x15, &x16, x14, x7, UINT64_C(0xffffffff00000001)); fiat_p256_subborrowx_u64(&x17, &x18, x16, x8, 0x0); fiat_p256_cmovznz_u64(&x19, x18, x9, x1); fiat_p256_cmovznz_u64(&x20, x18, x11, x3); fiat_p256_cmovznz_u64(&x21, x18, x13, x5); fiat_p256_cmovznz_u64(&x22, x18, x15, x7); out1[0] = x19; out1[1] = x20; out1[2] = x21; out1[3] = x22; } /* * The function fiat_p256_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 * */ static FIAT_P256_FIAT_INLINE void fiat_p256_sub(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) { uint64_t x1; fiat_p256_uint1 x2; uint64_t x3; fiat_p256_uint1 x4; uint64_t x5; fiat_p256_uint1 x6; uint64_t x7; fiat_p256_uint1 x8; uint64_t x9; uint64_t x10; fiat_p256_uint1 x11; uint64_t x12; fiat_p256_uint1 x13; uint64_t x14; fiat_p256_uint1 x15; uint64_t x16; fiat_p256_uint1 x17; fiat_p256_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); fiat_p256_subborrowx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); fiat_p256_subborrowx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); fiat_p256_subborrowx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9); fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff))); fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0); fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001))); out1[0] = x10; out1[1] = x12; out1[2] = x14; out1[3] = x16; } /* * The function fiat_p256_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 * */ static FIAT_P256_FIAT_INLINE void fiat_p256_opp(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) { uint64_t x1; fiat_p256_uint1 x2; uint64_t x3; fiat_p256_uint1 x4; uint64_t x5; fiat_p256_uint1 x6; uint64_t x7; fiat_p256_uint1 x8; uint64_t x9; uint64_t x10; fiat_p256_uint1 x11; uint64_t x12; fiat_p256_uint1 x13; uint64_t x14; fiat_p256_uint1 x15; uint64_t x16; fiat_p256_uint1 x17; fiat_p256_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0])); fiat_p256_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1])); fiat_p256_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2])); fiat_p256_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3])); fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff)); fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9); fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff))); fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0); fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001))); out1[0] = x10; out1[1] = x12; out1[2] = x14; out1[3] = x16; } /* * The function fiat_p256_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 FIAT_P256_FIAT_INLINE void fiat_p256_nonzero(uint64_t* out1, const uint64_t arg1[4]) { uint64_t x1; x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3])))); *out1 = x1; } /* * The function fiat_p256_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 FIAT_P256_FIAT_INLINE void fiat_p256_selectznz(uint64_t out1[4], fiat_p256_uint1 arg1, const uint64_t arg2[4], const uint64_t arg3[4]) { uint64_t x1; uint64_t x2; uint64_t x3; uint64_t x4; fiat_p256_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0])); fiat_p256_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1])); fiat_p256_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2])); fiat_p256_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3])); out1[0] = x1; out1[1] = x2; out1[2] = x3; out1[3] = x4; }