/* Autogenerated */ /* curve description: p256 */ /* requested operations: (all) */ /* 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 typedef unsigned char fiat_p256_uint1; typedef signed char fiat_p256_int1; typedef signed __int128 fiat_p256_int128; typedef unsigned __int128 fiat_p256_uint128; /* * 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)); uint64_t x3 = ((x2 & arg3) | ((~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; fiat_p256_uint1 x20; fiat_p256_addcarryx_u64(&x19, &x20, x18, x6, 0x0); uint64_t x21; uint64_t x22; fiat_p256_mulx_u64(&x21, &x22, x11, UINT64_C(0xffffffff00000001)); uint64_t x23; uint64_t x24; fiat_p256_mulx_u64(&x23, &x24, x11, UINT32_C(0xffffffff)); uint64_t x25; uint64_t x26; fiat_p256_mulx_u64(&x25, &x26, x11, UINT64_C(0xffffffffffffffff)); uint64_t x27; fiat_p256_uint1 x28; fiat_p256_addcarryx_u64(&x27, &x28, 0x0, x26, x23); uint64_t x29; fiat_p256_uint1 x30; fiat_p256_addcarryx_u64(&x29, &x30, x28, x24, 0x0); uint64_t x31; fiat_p256_uint1 x32; fiat_p256_addcarryx_u64(&x31, &x32, 0x0, x11, x25); uint64_t x33; fiat_p256_uint1 x34; fiat_p256_addcarryx_u64(&x33, &x34, x32, x13, x27); uint64_t x35; fiat_p256_uint1 x36; fiat_p256_addcarryx_u64(&x35, &x36, x34, x15, x29); uint64_t x37; fiat_p256_uint1 x38; fiat_p256_addcarryx_u64(&x37, &x38, x36, x17, x21); uint64_t x39; fiat_p256_uint1 x40; fiat_p256_addcarryx_u64(&x39, &x40, x38, x19, x22); uint64_t x41; fiat_p256_uint1 x42; fiat_p256_addcarryx_u64(&x41, &x42, x40, 0x0, 0x0); uint64_t x43; uint64_t x44; fiat_p256_mulx_u64(&x43, &x44, x1, (arg2[3])); uint64_t x45; uint64_t x46; fiat_p256_mulx_u64(&x45, &x46, x1, (arg2[2])); uint64_t x47; uint64_t x48; fiat_p256_mulx_u64(&x47, &x48, x1, (arg2[1])); uint64_t x49; uint64_t x50; fiat_p256_mulx_u64(&x49, &x50, x1, (arg2[0])); uint64_t x51; fiat_p256_uint1 x52; fiat_p256_addcarryx_u64(&x51, &x52, 0x0, x50, x47); uint64_t x53; fiat_p256_uint1 x54; fiat_p256_addcarryx_u64(&x53, &x54, x52, x48, x45); uint64_t x55; fiat_p256_uint1 x56; fiat_p256_addcarryx_u64(&x55, &x56, x54, x46, x43); uint64_t x57; fiat_p256_uint1 x58; fiat_p256_addcarryx_u64(&x57, &x58, x56, x44, 0x0); uint64_t x59; fiat_p256_uint1 x60; fiat_p256_addcarryx_u64(&x59, &x60, 0x0, x33, x49); uint64_t x61; fiat_p256_uint1 x62; fiat_p256_addcarryx_u64(&x61, &x62, x60, x35, x51); uint64_t x63; fiat_p256_uint1 x64; fiat_p256_addcarryx_u64(&x63, &x64, x62, x37, x53); uint64_t x65; fiat_p256_uint1 x66; fiat_p256_addcarryx_u64(&x65, &x66, x64, x39, x55); uint64_t x67; fiat_p256_uint1 x68; fiat_p256_addcarryx_u64(&x67, &x68, x66, (fiat_p256_uint1)x41, x57); uint64_t x69; uint64_t x70; fiat_p256_mulx_u64(&x69, &x70, x59, UINT64_C(0xffffffff00000001)); uint64_t x71; uint64_t x72; fiat_p256_mulx_u64(&x71, &x72, x59, UINT32_C(0xffffffff)); uint64_t x73; uint64_t x74; fiat_p256_mulx_u64(&x73, &x74, x59, UINT64_C(0xffffffffffffffff)); uint64_t x75; fiat_p256_uint1 x76; fiat_p256_addcarryx_u64(&x75, &x76, 0x0, x74, x71); uint64_t x77; fiat_p256_uint1 x78; fiat_p256_addcarryx_u64(&x77, &x78, x76, x72, 0x0); uint64_t x79; fiat_p256_uint1 x80; fiat_p256_addcarryx_u64(&x79, &x80, 0x0, x59, x73); uint64_t x81; fiat_p256_uint1 x82; fiat_p256_addcarryx_u64(&x81, &x82, x80, x61, x75); uint64_t x83; fiat_p256_uint1 x84; fiat_p256_addcarryx_u64(&x83, &x84, x82, x63, x77); uint64_t x85; fiat_p256_uint1 x86; fiat_p256_addcarryx_u64(&x85, &x86, x84, x65, x69); uint64_t x87; fiat_p256_uint1 x88; fiat_p256_addcarryx_u64(&x87, &x88, x86, x67, x70); uint64_t x89; fiat_p256_uint1 x90; fiat_p256_addcarryx_u64(&x89, &x90, x88, x68, 0x0); uint64_t x91; uint64_t x92; fiat_p256_mulx_u64(&x91, &x92, x2, (arg2[3])); uint64_t x93; uint64_t x94; fiat_p256_mulx_u64(&x93, &x94, x2, (arg2[2])); uint64_t x95; uint64_t x96; fiat_p256_mulx_u64(&x95, &x96, x2, (arg2[1])); uint64_t x97; uint64_t x98; fiat_p256_mulx_u64(&x97, &x98, x2, (arg2[0])); uint64_t x99; fiat_p256_uint1 x100; fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x98, x95); uint64_t x101; fiat_p256_uint1 x102; fiat_p256_addcarryx_u64(&x101, &x102, x100, x96, x93); uint64_t x103; fiat_p256_uint1 x104; fiat_p256_addcarryx_u64(&x103, &x104, x102, x94, x91); uint64_t x105; fiat_p256_uint1 x106; fiat_p256_addcarryx_u64(&x105, &x106, x104, x92, 0x0); uint64_t x107; fiat_p256_uint1 x108; fiat_p256_addcarryx_u64(&x107, &x108, 0x0, x81, x97); uint64_t x109; fiat_p256_uint1 x110; fiat_p256_addcarryx_u64(&x109, &x110, x108, x83, x99); uint64_t x111; fiat_p256_uint1 x112; fiat_p256_addcarryx_u64(&x111, &x112, x110, x85, x101); uint64_t x113; fiat_p256_uint1 x114; fiat_p256_addcarryx_u64(&x113, &x114, x112, x87, x103); uint64_t x115; fiat_p256_uint1 x116; fiat_p256_addcarryx_u64(&x115, &x116, x114, x89, x105); uint64_t x117; uint64_t x118; fiat_p256_mulx_u64(&x117, &x118, x107, UINT64_C(0xffffffff00000001)); uint64_t x119; uint64_t x120; fiat_p256_mulx_u64(&x119, &x120, x107, UINT32_C(0xffffffff)); uint64_t x121; uint64_t x122; fiat_p256_mulx_u64(&x121, &x122, x107, UINT64_C(0xffffffffffffffff)); uint64_t x123; fiat_p256_uint1 x124; fiat_p256_addcarryx_u64(&x123, &x124, 0x0, x122, x119); uint64_t x125; fiat_p256_uint1 x126; fiat_p256_addcarryx_u64(&x125, &x126, x124, x120, 0x0); uint64_t x127; fiat_p256_uint1 x128; fiat_p256_addcarryx_u64(&x127, &x128, 0x0, x107, x121); uint64_t x129; fiat_p256_uint1 x130; fiat_p256_addcarryx_u64(&x129, &x130, x128, x109, x123); uint64_t x131; fiat_p256_uint1 x132; fiat_p256_addcarryx_u64(&x131, &x132, x130, x111, x125); uint64_t x133; fiat_p256_uint1 x134; fiat_p256_addcarryx_u64(&x133, &x134, x132, x113, x117); uint64_t x135; fiat_p256_uint1 x136; fiat_p256_addcarryx_u64(&x135, &x136, x134, x115, x118); uint64_t x137; fiat_p256_uint1 x138; fiat_p256_addcarryx_u64(&x137, &x138, x136, x116, 0x0); uint64_t x139; uint64_t x140; fiat_p256_mulx_u64(&x139, &x140, x3, (arg2[3])); uint64_t x141; uint64_t x142; fiat_p256_mulx_u64(&x141, &x142, x3, (arg2[2])); uint64_t x143; uint64_t x144; fiat_p256_mulx_u64(&x143, &x144, x3, (arg2[1])); uint64_t x145; uint64_t x146; fiat_p256_mulx_u64(&x145, &x146, x3, (arg2[0])); uint64_t x147; fiat_p256_uint1 x148; fiat_p256_addcarryx_u64(&x147, &x148, 0x0, x146, x143); uint64_t x149; fiat_p256_uint1 x150; fiat_p256_addcarryx_u64(&x149, &x150, x148, x144, x141); uint64_t x151; fiat_p256_uint1 x152; fiat_p256_addcarryx_u64(&x151, &x152, x150, x142, x139); uint64_t x153; fiat_p256_uint1 x154; fiat_p256_addcarryx_u64(&x153, &x154, x152, x140, 0x0); uint64_t x155; fiat_p256_uint1 x156; fiat_p256_addcarryx_u64(&x155, &x156, 0x0, x129, x145); uint64_t x157; fiat_p256_uint1 x158; fiat_p256_addcarryx_u64(&x157, &x158, x156, x131, x147); uint64_t x159; fiat_p256_uint1 x160; fiat_p256_addcarryx_u64(&x159, &x160, x158, x133, x149); uint64_t x161; fiat_p256_uint1 x162; fiat_p256_addcarryx_u64(&x161, &x162, x160, x135, x151); uint64_t x163; fiat_p256_uint1 x164; fiat_p256_addcarryx_u64(&x163, &x164, x162, x137, x153); uint64_t x165; uint64_t x166; fiat_p256_mulx_u64(&x165, &x166, x155, UINT64_C(0xffffffff00000001)); uint64_t x167; uint64_t x168; fiat_p256_mulx_u64(&x167, &x168, x155, UINT32_C(0xffffffff)); uint64_t x169; uint64_t x170; fiat_p256_mulx_u64(&x169, &x170, x155, UINT64_C(0xffffffffffffffff)); uint64_t x171; fiat_p256_uint1 x172; fiat_p256_addcarryx_u64(&x171, &x172, 0x0, x170, x167); uint64_t x173; fiat_p256_uint1 x174; fiat_p256_addcarryx_u64(&x173, &x174, x172, x168, 0x0); uint64_t x175; fiat_p256_uint1 x176; fiat_p256_addcarryx_u64(&x175, &x176, 0x0, x155, x169); uint64_t x177; fiat_p256_uint1 x178; fiat_p256_addcarryx_u64(&x177, &x178, x176, x157, x171); uint64_t x179; fiat_p256_uint1 x180; fiat_p256_addcarryx_u64(&x179, &x180, x178, x159, x173); uint64_t x181; fiat_p256_uint1 x182; fiat_p256_addcarryx_u64(&x181, &x182, x180, x161, x165); uint64_t x183; fiat_p256_uint1 x184; fiat_p256_addcarryx_u64(&x183, &x184, x182, x163, x166); uint64_t x185; fiat_p256_uint1 x186; fiat_p256_addcarryx_u64(&x185, &x186, x184, x164, 0x0); uint64_t x187; fiat_p256_uint1 x188; fiat_p256_subborrowx_u64(&x187, &x188, 0x0, x177, UINT64_C(0xffffffffffffffff)); uint64_t x189; fiat_p256_uint1 x190; fiat_p256_subborrowx_u64(&x189, &x190, x188, x179, UINT32_C(0xffffffff)); uint64_t x191; fiat_p256_uint1 x192; fiat_p256_subborrowx_u64(&x191, &x192, x190, x181, 0x0); uint64_t x193; fiat_p256_uint1 x194; fiat_p256_subborrowx_u64(&x193, &x194, x192, x183, UINT64_C(0xffffffff00000001)); uint64_t x195; fiat_p256_uint1 x196; fiat_p256_subborrowx_u64(&x195, &x196, x194, x185, 0x0); uint64_t x197; fiat_p256_cmovznz_u64(&x197, x196, x187, x177); uint64_t x198; fiat_p256_cmovznz_u64(&x198, x196, x189, x179); uint64_t x199; fiat_p256_cmovznz_u64(&x199, x196, x191, x181); uint64_t x200; fiat_p256_cmovznz_u64(&x200, x196, x193, x183); out1[0] = x197; out1[1] = x198; out1[2] = x199; out1[3] = x200; } /* * 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; fiat_p256_uint1 x20; fiat_p256_addcarryx_u64(&x19, &x20, x18, x6, 0x0); uint64_t x21; uint64_t x22; fiat_p256_mulx_u64(&x21, &x22, x11, UINT64_C(0xffffffff00000001)); uint64_t x23; uint64_t x24; fiat_p256_mulx_u64(&x23, &x24, x11, UINT32_C(0xffffffff)); uint64_t x25; uint64_t x26; fiat_p256_mulx_u64(&x25, &x26, x11, UINT64_C(0xffffffffffffffff)); uint64_t x27; fiat_p256_uint1 x28; fiat_p256_addcarryx_u64(&x27, &x28, 0x0, x26, x23); uint64_t x29; fiat_p256_uint1 x30; fiat_p256_addcarryx_u64(&x29, &x30, x28, x24, 0x0); uint64_t x31; fiat_p256_uint1 x32; fiat_p256_addcarryx_u64(&x31, &x32, 0x0, x11, x25); uint64_t x33; fiat_p256_uint1 x34; fiat_p256_addcarryx_u64(&x33, &x34, x32, x13, x27); uint64_t x35; fiat_p256_uint1 x36; fiat_p256_addcarryx_u64(&x35, &x36, x34, x15, x29); uint64_t x37; fiat_p256_uint1 x38; fiat_p256_addcarryx_u64(&x37, &x38, x36, x17, x21); uint64_t x39; fiat_p256_uint1 x40; fiat_p256_addcarryx_u64(&x39, &x40, x38, x19, x22); uint64_t x41; fiat_p256_uint1 x42; fiat_p256_addcarryx_u64(&x41, &x42, x40, 0x0, 0x0); uint64_t x43; uint64_t x44; fiat_p256_mulx_u64(&x43, &x44, x1, (arg1[3])); uint64_t x45; uint64_t x46; fiat_p256_mulx_u64(&x45, &x46, x1, (arg1[2])); uint64_t x47; uint64_t x48; fiat_p256_mulx_u64(&x47, &x48, x1, (arg1[1])); uint64_t x49; uint64_t x50; fiat_p256_mulx_u64(&x49, &x50, x1, (arg1[0])); uint64_t x51; fiat_p256_uint1 x52; fiat_p256_addcarryx_u64(&x51, &x52, 0x0, x50, x47); uint64_t x53; fiat_p256_uint1 x54; fiat_p256_addcarryx_u64(&x53, &x54, x52, x48, x45); uint64_t x55; fiat_p256_uint1 x56; fiat_p256_addcarryx_u64(&x55, &x56, x54, x46, x43); uint64_t x57; fiat_p256_uint1 x58; fiat_p256_addcarryx_u64(&x57, &x58, x56, x44, 0x0); uint64_t x59; fiat_p256_uint1 x60; fiat_p256_addcarryx_u64(&x59, &x60, 0x0, x33, x49); uint64_t x61; fiat_p256_uint1 x62; fiat_p256_addcarryx_u64(&x61, &x62, x60, x35, x51); uint64_t x63; fiat_p256_uint1 x64; fiat_p256_addcarryx_u64(&x63, &x64, x62, x37, x53); uint64_t x65; fiat_p256_uint1 x66; fiat_p256_addcarryx_u64(&x65, &x66, x64, x39, x55); uint64_t x67; fiat_p256_uint1 x68; fiat_p256_addcarryx_u64(&x67, &x68, x66, (fiat_p256_uint1)x41, x57); uint64_t x69; uint64_t x70; fiat_p256_mulx_u64(&x69, &x70, x59, UINT64_C(0xffffffff00000001)); uint64_t x71; uint64_t x72; fiat_p256_mulx_u64(&x71, &x72, x59, UINT32_C(0xffffffff)); uint64_t x73; uint64_t x74; fiat_p256_mulx_u64(&x73, &x74, x59, UINT64_C(0xffffffffffffffff)); uint64_t x75; fiat_p256_uint1 x76; fiat_p256_addcarryx_u64(&x75, &x76, 0x0, x74, x71); uint64_t x77; fiat_p256_uint1 x78; fiat_p256_addcarryx_u64(&x77, &x78, x76, x72, 0x0); uint64_t x79; fiat_p256_uint1 x80; fiat_p256_addcarryx_u64(&x79, &x80, 0x0, x59, x73); uint64_t x81; fiat_p256_uint1 x82; fiat_p256_addcarryx_u64(&x81, &x82, x80, x61, x75); uint64_t x83; fiat_p256_uint1 x84; fiat_p256_addcarryx_u64(&x83, &x84, x82, x63, x77); uint64_t x85; fiat_p256_uint1 x86; fiat_p256_addcarryx_u64(&x85, &x86, x84, x65, x69); uint64_t x87; fiat_p256_uint1 x88; fiat_p256_addcarryx_u64(&x87, &x88, x86, x67, x70); uint64_t x89; fiat_p256_uint1 x90; fiat_p256_addcarryx_u64(&x89, &x90, x88, x68, 0x0); uint64_t x91; uint64_t x92; fiat_p256_mulx_u64(&x91, &x92, x2, (arg1[3])); uint64_t x93; uint64_t x94; fiat_p256_mulx_u64(&x93, &x94, x2, (arg1[2])); uint64_t x95; uint64_t x96; fiat_p256_mulx_u64(&x95, &x96, x2, (arg1[1])); uint64_t x97; uint64_t x98; fiat_p256_mulx_u64(&x97, &x98, x2, (arg1[0])); uint64_t x99; fiat_p256_uint1 x100; fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x98, x95); uint64_t x101; fiat_p256_uint1 x102; fiat_p256_addcarryx_u64(&x101, &x102, x100, x96, x93); uint64_t x103; fiat_p256_uint1 x104; fiat_p256_addcarryx_u64(&x103, &x104, x102, x94, x91); uint64_t x105; fiat_p256_uint1 x106; fiat_p256_addcarryx_u64(&x105, &x106, x104, x92, 0x0); uint64_t x107; fiat_p256_uint1 x108; fiat_p256_addcarryx_u64(&x107, &x108, 0x0, x81, x97); uint64_t x109; fiat_p256_uint1 x110; fiat_p256_addcarryx_u64(&x109, &x110, x108, x83, x99); uint64_t x111; fiat_p256_uint1 x112; fiat_p256_addcarryx_u64(&x111, &x112, x110, x85, x101); uint64_t x113; fiat_p256_uint1 x114; fiat_p256_addcarryx_u64(&x113, &x114, x112, x87, x103); uint64_t x115; fiat_p256_uint1 x116; fiat_p256_addcarryx_u64(&x115, &x116, x114, x89, x105); uint64_t x117; uint64_t x118; fiat_p256_mulx_u64(&x117, &x118, x107, UINT64_C(0xffffffff00000001)); uint64_t x119; uint64_t x120; fiat_p256_mulx_u64(&x119, &x120, x107, UINT32_C(0xffffffff)); uint64_t x121; uint64_t x122; fiat_p256_mulx_u64(&x121, &x122, x107, UINT64_C(0xffffffffffffffff)); uint64_t x123; fiat_p256_uint1 x124; fiat_p256_addcarryx_u64(&x123, &x124, 0x0, x122, x119); uint64_t x125; fiat_p256_uint1 x126; fiat_p256_addcarryx_u64(&x125, &x126, x124, x120, 0x0); uint64_t x127; fiat_p256_uint1 x128; fiat_p256_addcarryx_u64(&x127, &x128, 0x0, x107, x121); uint64_t x129; fiat_p256_uint1 x130; fiat_p256_addcarryx_u64(&x129, &x130, x128, x109, x123); uint64_t x131; fiat_p256_uint1 x132; fiat_p256_addcarryx_u64(&x131, &x132, x130, x111, x125); uint64_t x133; fiat_p256_uint1 x134; fiat_p256_addcarryx_u64(&x133, &x134, x132, x113, x117); uint64_t x135; fiat_p256_uint1 x136; fiat_p256_addcarryx_u64(&x135, &x136, x134, x115, x118); uint64_t x137; fiat_p256_uint1 x138; fiat_p256_addcarryx_u64(&x137, &x138, x136, x116, 0x0); uint64_t x139; uint64_t x140; fiat_p256_mulx_u64(&x139, &x140, x3, (arg1[3])); uint64_t x141; uint64_t x142; fiat_p256_mulx_u64(&x141, &x142, x3, (arg1[2])); uint64_t x143; uint64_t x144; fiat_p256_mulx_u64(&x143, &x144, x3, (arg1[1])); uint64_t x145; uint64_t x146; fiat_p256_mulx_u64(&x145, &x146, x3, (arg1[0])); uint64_t x147; fiat_p256_uint1 x148; fiat_p256_addcarryx_u64(&x147, &x148, 0x0, x146, x143); uint64_t x149; fiat_p256_uint1 x150; fiat_p256_addcarryx_u64(&x149, &x150, x148, x144, x141); uint64_t x151; fiat_p256_uint1 x152; fiat_p256_addcarryx_u64(&x151, &x152, x150, x142, x139); uint64_t x153; fiat_p256_uint1 x154; fiat_p256_addcarryx_u64(&x153, &x154, x152, x140, 0x0); uint64_t x155; fiat_p256_uint1 x156; fiat_p256_addcarryx_u64(&x155, &x156, 0x0, x129, x145); uint64_t x157; fiat_p256_uint1 x158; fiat_p256_addcarryx_u64(&x157, &x158, x156, x131, x147); uint64_t x159; fiat_p256_uint1 x160; fiat_p256_addcarryx_u64(&x159, &x160, x158, x133, x149); uint64_t x161; fiat_p256_uint1 x162; fiat_p256_addcarryx_u64(&x161, &x162, x160, x135, x151); uint64_t x163; fiat_p256_uint1 x164; fiat_p256_addcarryx_u64(&x163, &x164, x162, x137, x153); uint64_t x165; uint64_t x166; fiat_p256_mulx_u64(&x165, &x166, x155, UINT64_C(0xffffffff00000001)); uint64_t x167; uint64_t x168; fiat_p256_mulx_u64(&x167, &x168, x155, UINT32_C(0xffffffff)); uint64_t x169; uint64_t x170; fiat_p256_mulx_u64(&x169, &x170, x155, UINT64_C(0xffffffffffffffff)); uint64_t x171; fiat_p256_uint1 x172; fiat_p256_addcarryx_u64(&x171, &x172, 0x0, x170, x167); uint64_t x173; fiat_p256_uint1 x174; fiat_p256_addcarryx_u64(&x173, &x174, x172, x168, 0x0); uint64_t x175; fiat_p256_uint1 x176; fiat_p256_addcarryx_u64(&x175, &x176, 0x0, x155, x169); uint64_t x177; fiat_p256_uint1 x178; fiat_p256_addcarryx_u64(&x177, &x178, x176, x157, x171); uint64_t x179; fiat_p256_uint1 x180; fiat_p256_addcarryx_u64(&x179, &x180, x178, x159, x173); uint64_t x181; fiat_p256_uint1 x182; fiat_p256_addcarryx_u64(&x181, &x182, x180, x161, x165); uint64_t x183; fiat_p256_uint1 x184; fiat_p256_addcarryx_u64(&x183, &x184, x182, x163, x166); uint64_t x185; fiat_p256_uint1 x186; fiat_p256_addcarryx_u64(&x185, &x186, x184, x164, 0x0); uint64_t x187; fiat_p256_uint1 x188; fiat_p256_subborrowx_u64(&x187, &x188, 0x0, x177, UINT64_C(0xffffffffffffffff)); uint64_t x189; fiat_p256_uint1 x190; fiat_p256_subborrowx_u64(&x189, &x190, x188, x179, UINT32_C(0xffffffff)); uint64_t x191; fiat_p256_uint1 x192; fiat_p256_subborrowx_u64(&x191, &x192, x190, x181, 0x0); uint64_t x193; fiat_p256_uint1 x194; fiat_p256_subborrowx_u64(&x193, &x194, x192, x183, UINT64_C(0xffffffff00000001)); uint64_t x195; fiat_p256_uint1 x196; fiat_p256_subborrowx_u64(&x195, &x196, x194, x185, 0x0); uint64_t x197; fiat_p256_cmovznz_u64(&x197, x196, x187, x177); uint64_t x198; fiat_p256_cmovznz_u64(&x198, x196, x189, x179); uint64_t x199; fiat_p256_cmovznz_u64(&x199, x196, x191, x181); uint64_t x200; fiat_p256_cmovznz_u64(&x200, x196, x193, x183); out1[0] = x197; out1[1] = x198; out1[2] = x199; out1[3] = x200; } /* * 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, x9, x5, 0x0); uint64_t x26; fiat_p256_uint1 x27; fiat_p256_addcarryx_u64(&x26, &x27, x13, 0x0, x24); uint64_t x28; fiat_p256_uint1 x29; fiat_p256_addcarryx_u64(&x28, &x29, x15, x26, 0x0); uint64_t x30; fiat_p256_uint1 x31; fiat_p256_addcarryx_u64(&x30, &x31, 0x0, x14, x20); uint64_t x32; fiat_p256_uint1 x33; fiat_p256_addcarryx_u64(&x32, &x33, x31, x28, x22); uint64_t x34; fiat_p256_uint1 x35; fiat_p256_addcarryx_u64(&x34, &x35, x23, x19, 0x0); uint64_t x36; fiat_p256_uint1 x37; fiat_p256_addcarryx_u64(&x36, &x37, x33, x2, x34); uint64_t x38; fiat_p256_uint1 x39; fiat_p256_addcarryx_u64(&x38, &x39, x37, x3, x16); uint64_t x40; fiat_p256_uint1 x41; fiat_p256_addcarryx_u64(&x40, &x41, 0x0, x32, (arg1[2])); uint64_t x42; fiat_p256_uint1 x43; fiat_p256_addcarryx_u64(&x42, &x43, x41, x36, 0x0); uint64_t x44; fiat_p256_uint1 x45; fiat_p256_addcarryx_u64(&x44, &x45, x43, x38, 0x0); uint64_t x46; uint64_t x47; fiat_p256_mulx_u64(&x46, &x47, x40, UINT64_C(0xffffffff00000001)); uint64_t x48; uint64_t x49; fiat_p256_mulx_u64(&x48, &x49, x40, UINT32_C(0xffffffff)); uint64_t x50; uint64_t x51; fiat_p256_mulx_u64(&x50, &x51, x40, UINT64_C(0xffffffffffffffff)); uint64_t x52; fiat_p256_uint1 x53; fiat_p256_addcarryx_u64(&x52, &x53, 0x0, x51, x48); uint64_t x54; fiat_p256_uint1 x55; fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x40, x50); uint64_t x56; fiat_p256_uint1 x57; fiat_p256_addcarryx_u64(&x56, &x57, x55, x42, x52); uint64_t x58; fiat_p256_uint1 x59; fiat_p256_addcarryx_u64(&x58, &x59, x53, x49, 0x0); uint64_t x60; fiat_p256_uint1 x61; fiat_p256_addcarryx_u64(&x60, &x61, x57, x44, x58); uint64_t x62; fiat_p256_uint1 x63; fiat_p256_addcarryx_u64(&x62, &x63, x39, 0x0, x17); uint64_t x64; fiat_p256_uint1 x65; fiat_p256_addcarryx_u64(&x64, &x65, x45, x62, 0x0); uint64_t x66; fiat_p256_uint1 x67; fiat_p256_addcarryx_u64(&x66, &x67, x61, x64, x46); uint64_t x68; fiat_p256_uint1 x69; fiat_p256_addcarryx_u64(&x68, &x69, 0x0, x56, (arg1[3])); uint64_t x70; fiat_p256_uint1 x71; fiat_p256_addcarryx_u64(&x70, &x71, x69, x60, 0x0); uint64_t x72; fiat_p256_uint1 x73; fiat_p256_addcarryx_u64(&x72, &x73, x71, x66, 0x0); uint64_t x74; uint64_t x75; fiat_p256_mulx_u64(&x74, &x75, x68, UINT64_C(0xffffffff00000001)); uint64_t x76; uint64_t x77; fiat_p256_mulx_u64(&x76, &x77, x68, UINT32_C(0xffffffff)); uint64_t x78; uint64_t x79; fiat_p256_mulx_u64(&x78, &x79, x68, UINT64_C(0xffffffffffffffff)); uint64_t x80; fiat_p256_uint1 x81; fiat_p256_addcarryx_u64(&x80, &x81, 0x0, x79, x76); uint64_t x82; fiat_p256_uint1 x83; fiat_p256_addcarryx_u64(&x82, &x83, 0x0, x68, x78); uint64_t x84; fiat_p256_uint1 x85; fiat_p256_addcarryx_u64(&x84, &x85, x83, x70, x80); uint64_t x86; fiat_p256_uint1 x87; fiat_p256_addcarryx_u64(&x86, &x87, x81, x77, 0x0); uint64_t x88; fiat_p256_uint1 x89; fiat_p256_addcarryx_u64(&x88, &x89, x85, x72, x86); uint64_t x90; fiat_p256_uint1 x91; fiat_p256_addcarryx_u64(&x90, &x91, x67, 0x0, x47); uint64_t x92; fiat_p256_uint1 x93; fiat_p256_addcarryx_u64(&x92, &x93, x73, x90, 0x0); uint64_t x94; fiat_p256_uint1 x95; fiat_p256_addcarryx_u64(&x94, &x95, x89, x92, x74); uint64_t x96; fiat_p256_uint1 x97; fiat_p256_addcarryx_u64(&x96, &x97, x95, 0x0, x75); uint64_t x98; fiat_p256_uint1 x99; fiat_p256_subborrowx_u64(&x98, &x99, 0x0, x84, UINT64_C(0xffffffffffffffff)); uint64_t x100; fiat_p256_uint1 x101; fiat_p256_subborrowx_u64(&x100, &x101, x99, x88, UINT32_C(0xffffffff)); uint64_t x102; fiat_p256_uint1 x103; fiat_p256_subborrowx_u64(&x102, &x103, x101, x94, 0x0); uint64_t x104; fiat_p256_uint1 x105; fiat_p256_subborrowx_u64(&x104, &x105, x103, x96, UINT64_C(0xffffffff00000001)); uint64_t x106; fiat_p256_uint1 x107; fiat_p256_subborrowx_u64(&x106, &x107, x105, 0x0, 0x0); uint64_t x108; fiat_p256_cmovznz_u64(&x108, x107, x98, x84); uint64_t x109; fiat_p256_cmovznz_u64(&x109, x107, x100, x88); uint64_t x110; fiat_p256_cmovznz_u64(&x110, x107, x102, x94); uint64_t x111; fiat_p256_cmovznz_u64(&x111, x107, x104, x96); out1[0] = x108; out1[1] = x109; out1[2] = x110; out1[3] = x111; } /* * 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; }