/* Autogenerated: src/ExtractionOCaml/word_by_word_montgomery --static p256 '2^256 - 2^224 + 2^192 + 2^96 - 1' 64 mul square add sub opp from_montgomery nonzero selectznz to_bytes from_bytes */ /* curve description: p256 */ /* requested operations: mul, square, add, sub, opp, from_montgomery, nonzero, selectznz, to_bytes, from_bytes */ /* m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 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 <stdint.h> typedef unsigned char fiat_p256_uint1; typedef signed char fiat_p256_int1; typedef signed __int128 fiat_p256_int128; typedef unsigned __int128 fiat_p256_uint128; #if (-1 & 3) != 3 #error "This code only works on a two's complement system" #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 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 = ((arg1 + (fiat_p256_uint128)arg2) + arg3); uint64_t x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); fiat_p256_uint1 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 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 = ((arg2 - (fiat_p256_int128)arg1) - arg3); fiat_p256_int1 x2 = (fiat_p256_int1)(x1 >> 64); uint64_t 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 void fiat_p256_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) { fiat_p256_uint128 x1 = ((fiat_p256_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_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 void fiat_p256_cmovznz_u64(uint64_t* out1, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_p256_uint1 x1 = (!(!arg1)); uint64_t x2 = ((fiat_p256_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff)); // Note this line has been patched from the synthesized code to add value // barriers. // // Clang recognizes this pattern as a select. While it usually transforms it // to a cmov, it sometimes further transforms it into a branch, which we do // not want. uint64_t x3 = ((value_barrier_u64(x2) & arg3) | (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 * * 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_p256_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_p256_mulx_u64(&x5, &x6, x4, (arg2[3])); uint64_t x7; uint64_t x8; fiat_p256_mulx_u64(&x7, &x8, x4, (arg2[2])); uint64_t x9; uint64_t x10; fiat_p256_mulx_u64(&x9, &x10, x4, (arg2[1])); uint64_t x11; uint64_t x12; fiat_p256_mulx_u64(&x11, &x12, x4, (arg2[0])); uint64_t x13; fiat_p256_uint1 x14; fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9); uint64_t x15; fiat_p256_uint1 x16; fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7); uint64_t x17; fiat_p256_uint1 x18; fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5); uint64_t x19 = (x18 + x6); uint64_t x20; uint64_t x21; fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001)); uint64_t x22; uint64_t x23; fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff)); uint64_t x24; uint64_t x25; fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff)); uint64_t x26; fiat_p256_uint1 x27; fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22); uint64_t x28 = (x27 + x23); uint64_t x29; fiat_p256_uint1 x30; fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24); uint64_t x31; fiat_p256_uint1 x32; fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26); uint64_t x33; fiat_p256_uint1 x34; fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28); uint64_t x35; fiat_p256_uint1 x36; fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20); uint64_t x37; fiat_p256_uint1 x38; fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21); uint64_t x39; uint64_t x40; fiat_p256_mulx_u64(&x39, &x40, x1, (arg2[3])); uint64_t x41; uint64_t x42; fiat_p256_mulx_u64(&x41, &x42, x1, (arg2[2])); uint64_t x43; uint64_t x44; fiat_p256_mulx_u64(&x43, &x44, x1, (arg2[1])); uint64_t x45; uint64_t x46; fiat_p256_mulx_u64(&x45, &x46, x1, (arg2[0])); uint64_t x47; fiat_p256_uint1 x48; fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43); uint64_t x49; fiat_p256_uint1 x50; fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41); uint64_t x51; fiat_p256_uint1 x52; fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39); uint64_t x53 = (x52 + x40); uint64_t x54; fiat_p256_uint1 x55; fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45); uint64_t x56; fiat_p256_uint1 x57; fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47); uint64_t x58; fiat_p256_uint1 x59; fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49); uint64_t x60; fiat_p256_uint1 x61; fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51); uint64_t x62; fiat_p256_uint1 x63; fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53); uint64_t x64; uint64_t x65; fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001)); uint64_t x66; uint64_t x67; fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff)); uint64_t x68; uint64_t x69; fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff)); uint64_t x70; fiat_p256_uint1 x71; fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66); uint64_t x72 = (x71 + x67); uint64_t x73; fiat_p256_uint1 x74; fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68); uint64_t x75; fiat_p256_uint1 x76; fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70); uint64_t x77; fiat_p256_uint1 x78; fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72); uint64_t x79; fiat_p256_uint1 x80; fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64); uint64_t x81; fiat_p256_uint1 x82; fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65); uint64_t x83 = ((uint64_t)x82 + x63); uint64_t x84; uint64_t x85; fiat_p256_mulx_u64(&x84, &x85, x2, (arg2[3])); uint64_t x86; uint64_t x87; fiat_p256_mulx_u64(&x86, &x87, x2, (arg2[2])); uint64_t x88; uint64_t x89; fiat_p256_mulx_u64(&x88, &x89, x2, (arg2[1])); uint64_t x90; uint64_t x91; fiat_p256_mulx_u64(&x90, &x91, x2, (arg2[0])); uint64_t x92; fiat_p256_uint1 x93; fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88); uint64_t x94; fiat_p256_uint1 x95; fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86); uint64_t x96; fiat_p256_uint1 x97; fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84); uint64_t x98 = (x97 + x85); uint64_t x99; fiat_p256_uint1 x100; fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90); uint64_t x101; fiat_p256_uint1 x102; fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92); uint64_t x103; fiat_p256_uint1 x104; fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94); uint64_t x105; fiat_p256_uint1 x106; fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96); uint64_t x107; fiat_p256_uint1 x108; fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98); uint64_t x109; uint64_t x110; fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001)); uint64_t x111; uint64_t x112; fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff)); uint64_t x113; uint64_t x114; fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff)); uint64_t x115; fiat_p256_uint1 x116; fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111); uint64_t x117 = (x116 + x112); uint64_t x118; fiat_p256_uint1 x119; fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113); uint64_t x120; fiat_p256_uint1 x121; fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115); uint64_t x122; fiat_p256_uint1 x123; fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117); uint64_t x124; fiat_p256_uint1 x125; fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109); uint64_t x126; fiat_p256_uint1 x127; fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110); uint64_t x128 = ((uint64_t)x127 + x108); uint64_t x129; uint64_t x130; fiat_p256_mulx_u64(&x129, &x130, x3, (arg2[3])); uint64_t x131; uint64_t x132; fiat_p256_mulx_u64(&x131, &x132, x3, (arg2[2])); uint64_t x133; uint64_t x134; fiat_p256_mulx_u64(&x133, &x134, x3, (arg2[1])); uint64_t x135; uint64_t x136; fiat_p256_mulx_u64(&x135, &x136, x3, (arg2[0])); uint64_t x137; fiat_p256_uint1 x138; fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133); uint64_t x139; fiat_p256_uint1 x140; fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131); uint64_t x141; fiat_p256_uint1 x142; fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129); uint64_t x143 = (x142 + x130); uint64_t x144; fiat_p256_uint1 x145; fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135); uint64_t x146; fiat_p256_uint1 x147; fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137); uint64_t x148; fiat_p256_uint1 x149; fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139); uint64_t x150; fiat_p256_uint1 x151; fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141); uint64_t x152; fiat_p256_uint1 x153; fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143); uint64_t x154; uint64_t x155; fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001)); uint64_t x156; uint64_t x157; fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff)); uint64_t x158; uint64_t x159; fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff)); uint64_t x160; fiat_p256_uint1 x161; fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156); uint64_t x162 = (x161 + x157); uint64_t x163; fiat_p256_uint1 x164; fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158); uint64_t x165; fiat_p256_uint1 x166; fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160); uint64_t x167; fiat_p256_uint1 x168; fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162); uint64_t x169; fiat_p256_uint1 x170; fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154); uint64_t x171; fiat_p256_uint1 x172; fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155); uint64_t x173 = ((uint64_t)x172 + x153); uint64_t x174; fiat_p256_uint1 x175; fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff)); uint64_t x176; fiat_p256_uint1 x177; fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff)); uint64_t x178; fiat_p256_uint1 x179; fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0); uint64_t x180; fiat_p256_uint1 x181; fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001)); uint64_t x182; fiat_p256_uint1 x183; fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0); uint64_t x184; fiat_p256_cmovznz_u64(&x184, x183, x174, x165); uint64_t x185; fiat_p256_cmovznz_u64(&x185, x183, x176, x167); uint64_t x186; fiat_p256_cmovznz_u64(&x186, x183, x178, x169); uint64_t x187; 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 * * 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_p256_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_p256_mulx_u64(&x5, &x6, x4, (arg1[3])); uint64_t x7; uint64_t x8; fiat_p256_mulx_u64(&x7, &x8, x4, (arg1[2])); uint64_t x9; uint64_t x10; fiat_p256_mulx_u64(&x9, &x10, x4, (arg1[1])); uint64_t x11; uint64_t x12; fiat_p256_mulx_u64(&x11, &x12, x4, (arg1[0])); uint64_t x13; fiat_p256_uint1 x14; fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9); uint64_t x15; fiat_p256_uint1 x16; fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7); uint64_t x17; fiat_p256_uint1 x18; fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5); uint64_t x19 = (x18 + x6); uint64_t x20; uint64_t x21; fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001)); uint64_t x22; uint64_t x23; fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff)); uint64_t x24; uint64_t x25; fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff)); uint64_t x26; fiat_p256_uint1 x27; fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22); uint64_t x28 = (x27 + x23); uint64_t x29; fiat_p256_uint1 x30; fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24); uint64_t x31; fiat_p256_uint1 x32; fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26); uint64_t x33; fiat_p256_uint1 x34; fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28); uint64_t x35; fiat_p256_uint1 x36; fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20); uint64_t x37; fiat_p256_uint1 x38; fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21); uint64_t x39; uint64_t x40; fiat_p256_mulx_u64(&x39, &x40, x1, (arg1[3])); uint64_t x41; uint64_t x42; fiat_p256_mulx_u64(&x41, &x42, x1, (arg1[2])); uint64_t x43; uint64_t x44; fiat_p256_mulx_u64(&x43, &x44, x1, (arg1[1])); uint64_t x45; uint64_t x46; fiat_p256_mulx_u64(&x45, &x46, x1, (arg1[0])); uint64_t x47; fiat_p256_uint1 x48; fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43); uint64_t x49; fiat_p256_uint1 x50; fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41); uint64_t x51; fiat_p256_uint1 x52; fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39); uint64_t x53 = (x52 + x40); uint64_t x54; fiat_p256_uint1 x55; fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45); uint64_t x56; fiat_p256_uint1 x57; fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47); uint64_t x58; fiat_p256_uint1 x59; fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49); uint64_t x60; fiat_p256_uint1 x61; fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51); uint64_t x62; fiat_p256_uint1 x63; fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53); uint64_t x64; uint64_t x65; fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001)); uint64_t x66; uint64_t x67; fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff)); uint64_t x68; uint64_t x69; fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff)); uint64_t x70; fiat_p256_uint1 x71; fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66); uint64_t x72 = (x71 + x67); uint64_t x73; fiat_p256_uint1 x74; fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68); uint64_t x75; fiat_p256_uint1 x76; fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70); uint64_t x77; fiat_p256_uint1 x78; fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72); uint64_t x79; fiat_p256_uint1 x80; fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64); uint64_t x81; fiat_p256_uint1 x82; fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65); uint64_t x83 = ((uint64_t)x82 + x63); uint64_t x84; uint64_t x85; fiat_p256_mulx_u64(&x84, &x85, x2, (arg1[3])); uint64_t x86; uint64_t x87; fiat_p256_mulx_u64(&x86, &x87, x2, (arg1[2])); uint64_t x88; uint64_t x89; fiat_p256_mulx_u64(&x88, &x89, x2, (arg1[1])); uint64_t x90; uint64_t x91; fiat_p256_mulx_u64(&x90, &x91, x2, (arg1[0])); uint64_t x92; fiat_p256_uint1 x93; fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88); uint64_t x94; fiat_p256_uint1 x95; fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86); uint64_t x96; fiat_p256_uint1 x97; fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84); uint64_t x98 = (x97 + x85); uint64_t x99; fiat_p256_uint1 x100; fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90); uint64_t x101; fiat_p256_uint1 x102; fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92); uint64_t x103; fiat_p256_uint1 x104; fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94); uint64_t x105; fiat_p256_uint1 x106; fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96); uint64_t x107; fiat_p256_uint1 x108; fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98); uint64_t x109; uint64_t x110; fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001)); uint64_t x111; uint64_t x112; fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff)); uint64_t x113; uint64_t x114; fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff)); uint64_t x115; fiat_p256_uint1 x116; fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111); uint64_t x117 = (x116 + x112); uint64_t x118; fiat_p256_uint1 x119; fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113); uint64_t x120; fiat_p256_uint1 x121; fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115); uint64_t x122; fiat_p256_uint1 x123; fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117); uint64_t x124; fiat_p256_uint1 x125; fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109); uint64_t x126; fiat_p256_uint1 x127; fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110); uint64_t x128 = ((uint64_t)x127 + x108); uint64_t x129; uint64_t x130; fiat_p256_mulx_u64(&x129, &x130, x3, (arg1[3])); uint64_t x131; uint64_t x132; fiat_p256_mulx_u64(&x131, &x132, x3, (arg1[2])); uint64_t x133; uint64_t x134; fiat_p256_mulx_u64(&x133, &x134, x3, (arg1[1])); uint64_t x135; uint64_t x136; fiat_p256_mulx_u64(&x135, &x136, x3, (arg1[0])); uint64_t x137; fiat_p256_uint1 x138; fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133); uint64_t x139; fiat_p256_uint1 x140; fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131); uint64_t x141; fiat_p256_uint1 x142; fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129); uint64_t x143 = (x142 + x130); uint64_t x144; fiat_p256_uint1 x145; fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135); uint64_t x146; fiat_p256_uint1 x147; fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137); uint64_t x148; fiat_p256_uint1 x149; fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139); uint64_t x150; fiat_p256_uint1 x151; fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141); uint64_t x152; fiat_p256_uint1 x153; fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143); uint64_t x154; uint64_t x155; fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001)); uint64_t x156; uint64_t x157; fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff)); uint64_t x158; uint64_t x159; fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff)); uint64_t x160; fiat_p256_uint1 x161; fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156); uint64_t x162 = (x161 + x157); uint64_t x163; fiat_p256_uint1 x164; fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158); uint64_t x165; fiat_p256_uint1 x166; fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160); uint64_t x167; fiat_p256_uint1 x168; fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162); uint64_t x169; fiat_p256_uint1 x170; fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154); uint64_t x171; fiat_p256_uint1 x172; fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155); uint64_t x173 = ((uint64_t)x172 + x153); uint64_t x174; fiat_p256_uint1 x175; fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff)); uint64_t x176; fiat_p256_uint1 x177; fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff)); uint64_t x178; fiat_p256_uint1 x179; fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0); uint64_t x180; fiat_p256_uint1 x181; fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001)); uint64_t x182; fiat_p256_uint1 x183; fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0); uint64_t x184; fiat_p256_cmovznz_u64(&x184, x183, x174, x165); uint64_t x185; fiat_p256_cmovznz_u64(&x185, x183, x176, x167); uint64_t x186; fiat_p256_cmovznz_u64(&x186, x183, x178, x169); uint64_t x187; 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 * * 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_p256_add(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) { uint64_t x1; fiat_p256_uint1 x2; fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); uint64_t x3; fiat_p256_uint1 x4; fiat_p256_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); uint64_t x5; fiat_p256_uint1 x6; fiat_p256_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); uint64_t x7; fiat_p256_uint1 x8; fiat_p256_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); uint64_t x9; fiat_p256_uint1 x10; fiat_p256_subborrowx_u64(&x9, &x10, 0x0, x1, UINT64_C(0xffffffffffffffff)); uint64_t x11; fiat_p256_uint1 x12; fiat_p256_subborrowx_u64(&x11, &x12, x10, x3, UINT32_C(0xffffffff)); uint64_t x13; fiat_p256_uint1 x14; fiat_p256_subborrowx_u64(&x13, &x14, x12, x5, 0x0); uint64_t x15; fiat_p256_uint1 x16; fiat_p256_subborrowx_u64(&x15, &x16, x14, x7, UINT64_C(0xffffffff00000001)); uint64_t x17; fiat_p256_uint1 x18; fiat_p256_subborrowx_u64(&x17, &x18, x16, x8, 0x0); uint64_t x19; fiat_p256_cmovznz_u64(&x19, x18, x9, x1); uint64_t x20; fiat_p256_cmovznz_u64(&x20, x18, x11, x3); uint64_t x21; fiat_p256_cmovznz_u64(&x21, x18, x13, x5); uint64_t x22; 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 * * 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_p256_sub(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) { uint64_t x1; fiat_p256_uint1 x2; fiat_p256_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); uint64_t x3; fiat_p256_uint1 x4; fiat_p256_subborrowx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); uint64_t x5; fiat_p256_uint1 x6; fiat_p256_subborrowx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); uint64_t x7; fiat_p256_uint1 x8; fiat_p256_subborrowx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); uint64_t x9; fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff)); uint64_t x10; fiat_p256_uint1 x11; fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, (x9 & UINT64_C(0xffffffffffffffff))); uint64_t x12; fiat_p256_uint1 x13; fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff))); uint64_t x14; fiat_p256_uint1 x15; fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0); uint64_t x16; fiat_p256_uint1 x17; 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 * * 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_p256_opp(uint64_t out1[4], const uint64_t arg1[4]) { uint64_t x1; fiat_p256_uint1 x2; fiat_p256_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0])); uint64_t x3; fiat_p256_uint1 x4; fiat_p256_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1])); uint64_t x5; fiat_p256_uint1 x6; fiat_p256_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2])); uint64_t x7; fiat_p256_uint1 x8; fiat_p256_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3])); uint64_t x9; fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff)); uint64_t x10; fiat_p256_uint1 x11; fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, (x9 & UINT64_C(0xffffffffffffffff))); uint64_t x12; fiat_p256_uint1 x13; fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff))); uint64_t x14; fiat_p256_uint1 x15; fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0); uint64_t x16; fiat_p256_uint1 x17; 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_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_p256_from_montgomery(uint64_t out1[4], const uint64_t arg1[4]) { uint64_t x1 = (arg1[0]); uint64_t x2; uint64_t x3; fiat_p256_mulx_u64(&x2, &x3, x1, UINT64_C(0xffffffff00000001)); uint64_t x4; uint64_t x5; fiat_p256_mulx_u64(&x4, &x5, x1, UINT32_C(0xffffffff)); uint64_t x6; uint64_t x7; fiat_p256_mulx_u64(&x6, &x7, x1, UINT64_C(0xffffffffffffffff)); uint64_t x8; fiat_p256_uint1 x9; fiat_p256_addcarryx_u64(&x8, &x9, 0x0, x7, x4); uint64_t x10; fiat_p256_uint1 x11; fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x6); uint64_t x12; fiat_p256_uint1 x13; fiat_p256_addcarryx_u64(&x12, &x13, x11, 0x0, x8); uint64_t x14; fiat_p256_uint1 x15; fiat_p256_addcarryx_u64(&x14, &x15, 0x0, x12, (arg1[1])); uint64_t x16; uint64_t x17; fiat_p256_mulx_u64(&x16, &x17, x14, UINT64_C(0xffffffff00000001)); uint64_t x18; uint64_t x19; fiat_p256_mulx_u64(&x18, &x19, x14, UINT32_C(0xffffffff)); uint64_t x20; uint64_t x21; fiat_p256_mulx_u64(&x20, &x21, x14, UINT64_C(0xffffffffffffffff)); uint64_t x22; fiat_p256_uint1 x23; fiat_p256_addcarryx_u64(&x22, &x23, 0x0, x21, x18); uint64_t x24; fiat_p256_uint1 x25; fiat_p256_addcarryx_u64(&x24, &x25, 0x0, x14, x20); uint64_t x26; fiat_p256_uint1 x27; fiat_p256_addcarryx_u64(&x26, &x27, x25, (x15 + (x13 + (x9 + x5))), x22); uint64_t x28; fiat_p256_uint1 x29; fiat_p256_addcarryx_u64(&x28, &x29, x27, x2, (x23 + x19)); uint64_t x30; fiat_p256_uint1 x31; fiat_p256_addcarryx_u64(&x30, &x31, x29, x3, x16); uint64_t x32; fiat_p256_uint1 x33; fiat_p256_addcarryx_u64(&x32, &x33, 0x0, x26, (arg1[2])); uint64_t x34; fiat_p256_uint1 x35; fiat_p256_addcarryx_u64(&x34, &x35, x33, x28, 0x0); uint64_t x36; fiat_p256_uint1 x37; fiat_p256_addcarryx_u64(&x36, &x37, x35, x30, 0x0); uint64_t x38; uint64_t x39; fiat_p256_mulx_u64(&x38, &x39, x32, UINT64_C(0xffffffff00000001)); uint64_t x40; uint64_t x41; fiat_p256_mulx_u64(&x40, &x41, x32, UINT32_C(0xffffffff)); uint64_t x42; uint64_t x43; fiat_p256_mulx_u64(&x42, &x43, x32, UINT64_C(0xffffffffffffffff)); uint64_t x44; fiat_p256_uint1 x45; fiat_p256_addcarryx_u64(&x44, &x45, 0x0, x43, x40); uint64_t x46; fiat_p256_uint1 x47; fiat_p256_addcarryx_u64(&x46, &x47, 0x0, x32, x42); uint64_t x48; fiat_p256_uint1 x49; fiat_p256_addcarryx_u64(&x48, &x49, x47, x34, x44); uint64_t x50; fiat_p256_uint1 x51; fiat_p256_addcarryx_u64(&x50, &x51, x49, x36, (x45 + x41)); uint64_t x52; fiat_p256_uint1 x53; fiat_p256_addcarryx_u64(&x52, &x53, x51, (x37 + (x31 + x17)), x38); uint64_t x54; fiat_p256_uint1 x55; fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x48, (arg1[3])); uint64_t x56; fiat_p256_uint1 x57; fiat_p256_addcarryx_u64(&x56, &x57, x55, x50, 0x0); uint64_t x58; fiat_p256_uint1 x59; fiat_p256_addcarryx_u64(&x58, &x59, x57, x52, 0x0); uint64_t x60; uint64_t x61; fiat_p256_mulx_u64(&x60, &x61, x54, UINT64_C(0xffffffff00000001)); uint64_t x62; uint64_t x63; fiat_p256_mulx_u64(&x62, &x63, x54, UINT32_C(0xffffffff)); uint64_t x64; uint64_t x65; fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffffffffffff)); uint64_t x66; fiat_p256_uint1 x67; fiat_p256_addcarryx_u64(&x66, &x67, 0x0, x65, x62); uint64_t x68; fiat_p256_uint1 x69; fiat_p256_addcarryx_u64(&x68, &x69, 0x0, x54, x64); uint64_t x70; fiat_p256_uint1 x71; fiat_p256_addcarryx_u64(&x70, &x71, x69, x56, x66); uint64_t x72; fiat_p256_uint1 x73; fiat_p256_addcarryx_u64(&x72, &x73, x71, x58, (x67 + x63)); uint64_t x74; fiat_p256_uint1 x75; fiat_p256_addcarryx_u64(&x74, &x75, x73, (x59 + (x53 + x39)), x60); uint64_t x76 = (x75 + x61); uint64_t x77; fiat_p256_uint1 x78; fiat_p256_subborrowx_u64(&x77, &x78, 0x0, x70, UINT64_C(0xffffffffffffffff)); uint64_t x79; fiat_p256_uint1 x80; fiat_p256_subborrowx_u64(&x79, &x80, x78, x72, UINT32_C(0xffffffff)); uint64_t x81; fiat_p256_uint1 x82; fiat_p256_subborrowx_u64(&x81, &x82, x80, x74, 0x0); uint64_t x83; fiat_p256_uint1 x84; fiat_p256_subborrowx_u64(&x83, &x84, x82, x76, UINT64_C(0xffffffff00000001)); uint64_t x85; fiat_p256_uint1 x86; fiat_p256_subborrowx_u64(&x85, &x86, x84, 0x0, 0x0); uint64_t x87; fiat_p256_cmovznz_u64(&x87, x86, x77, x70); uint64_t x88; fiat_p256_cmovznz_u64(&x88, x86, x79, x72); uint64_t x89; fiat_p256_cmovznz_u64(&x89, x86, x81, x74); uint64_t x90; fiat_p256_cmovznz_u64(&x90, x86, x83, x76); out1[0] = x87; out1[1] = x88; out1[2] = x89; out1[3] = x90; } /* * 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 void fiat_p256_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_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 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; fiat_p256_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0])); uint64_t x2; fiat_p256_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1])); uint64_t x3; fiat_p256_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2])); uint64_t x4; fiat_p256_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3])); out1[0] = x1; out1[1] = x2; out1[2] = x3; out1[3] = x4; } /* * The function fiat_p256_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 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] */ static void fiat_p256_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)); uint64_t x54 = (x52 >> 8); uint8_t x55 = (uint8_t)(x52 & UINT8_C(0xff)); uint64_t x56 = (x54 >> 8); uint8_t x57 = (uint8_t)(x54 & UINT8_C(0xff)); uint64_t x58 = (x56 >> 8); uint8_t x59 = (uint8_t)(x56 & UINT8_C(0xff)); uint64_t x60 = (x58 >> 8); uint8_t x61 = (uint8_t)(x58 & UINT8_C(0xff)); uint8_t x62 = (uint8_t)(x60 >> 8); uint8_t x63 = (uint8_t)(x60 & 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] = x57; out1[28] = x59; out1[29] = x61; out1[30] = x63; out1[31] = x62; } /* * The function fiat_p256_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 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_p256_from_bytes(uint64_t out1[4], const uint8_t arg1[32]) { uint64_t x1 = ((uint64_t)(arg1[31]) << 56); uint64_t x2 = ((uint64_t)(arg1[30]) << 48); uint64_t x3 = ((uint64_t)(arg1[29]) << 40); uint64_t x4 = ((uint64_t)(arg1[28]) << 32); uint64_t x5 = ((uint64_t)(arg1[27]) << 24); uint64_t x6 = ((uint64_t)(arg1[26]) << 16); uint64_t x7 = ((uint64_t)(arg1[25]) << 8); uint8_t x8 = (arg1[24]); uint64_t x9 = ((uint64_t)(arg1[23]) << 56); uint64_t x10 = ((uint64_t)(arg1[22]) << 48); uint64_t x11 = ((uint64_t)(arg1[21]) << 40); uint64_t x12 = ((uint64_t)(arg1[20]) << 32); uint64_t x13 = ((uint64_t)(arg1[19]) << 24); uint64_t x14 = ((uint64_t)(arg1[18]) << 16); uint64_t x15 = ((uint64_t)(arg1[17]) << 8); uint8_t x16 = (arg1[16]); uint64_t x17 = ((uint64_t)(arg1[15]) << 56); uint64_t x18 = ((uint64_t)(arg1[14]) << 48); uint64_t x19 = ((uint64_t)(arg1[13]) << 40); uint64_t x20 = ((uint64_t)(arg1[12]) << 32); uint64_t x21 = ((uint64_t)(arg1[11]) << 24); uint64_t x22 = ((uint64_t)(arg1[10]) << 16); uint64_t x23 = ((uint64_t)(arg1[9]) << 8); uint8_t x24 = (arg1[8]); uint64_t x25 = ((uint64_t)(arg1[7]) << 56); uint64_t x26 = ((uint64_t)(arg1[6]) << 48); uint64_t x27 = ((uint64_t)(arg1[5]) << 40); uint64_t x28 = ((uint64_t)(arg1[4]) << 32); uint64_t x29 = ((uint64_t)(arg1[3]) << 24); uint64_t x30 = ((uint64_t)(arg1[2]) << 16); uint64_t x31 = ((uint64_t)(arg1[1]) << 8); uint8_t x32 = (arg1[0]); uint64_t x33 = (x32 + (x31 + (x30 + (x29 + (x28 + (x27 + (x26 + x25))))))); uint64_t x34 = (x33 & UINT64_C(0xffffffffffffffff)); uint64_t x35 = (x8 + (x7 + (x6 + (x5 + (x4 + (x3 + (x2 + x1))))))); uint64_t x36 = (x16 + (x15 + (x14 + (x13 + (x12 + (x11 + (x10 + x9))))))); uint64_t x37 = (x24 + (x23 + (x22 + (x21 + (x20 + (x19 + (x18 + x17))))))); uint64_t x38 = (x37 & UINT64_C(0xffffffffffffffff)); uint64_t x39 = (x36 & UINT64_C(0xffffffffffffffff)); out1[0] = x34; out1[1] = x38; out1[2] = x39; out1[3] = x35; }