/* Autogenerated: './word_by_word_montgomery' --static n256 64 115792089210356248762697446949407573529996955224135760342422259061068512044369 add opp mul divstep */ /* curve description: n256 */ /* machine_wordsize = 64 (from "64") */ /* requested operations: add, opp, mul, divstep */ /* m = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 (from "115792089210356248762697446949407573529996955224135760342422259061068512044369") */ /* */ /* 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_n256_uint1; typedef signed char fiat_n256_int1; #if defined(__GNUC__) || defined(__clang__) # define FIAT_N256_FIAT_EXTENSION __extension__ # define FIAT_N256_FIAT_INLINE __inline__ #else # define FIAT_N256_FIAT_EXTENSION # define FIAT_N256_FIAT_INLINE #endif FIAT_N256_FIAT_EXTENSION typedef signed __int128 fiat_n256_int128; FIAT_N256_FIAT_EXTENSION typedef unsigned __int128 fiat_n256_uint128; /* The type fiat_n256_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_n256_montgomery_domain_field_element[4]; #if (-1 & 3) != 3 #error "This code only works on a two's complement system" #endif /* * The function fiat_n256_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_n256_addcarryx_u64(uint64_t* out1, fiat_n256_uint1* out2, fiat_n256_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_n256_uint128 x1; uint64_t x2; fiat_n256_uint1 x3; x1 = ((arg1 + (fiat_n256_uint128)arg2) + arg3); x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); x3 = (fiat_n256_uint1)(x1 >> 64); *out1 = x2; *out2 = x3; } /* * The function fiat_n256_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_n256_subborrowx_u64(uint64_t* out1, fiat_n256_uint1* out2, fiat_n256_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_n256_int128 x1; fiat_n256_int1 x2; uint64_t x3; x1 = ((arg2 - (fiat_n256_int128)arg1) - arg3); x2 = (fiat_n256_int1)(x1 >> 64); x3 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); *out1 = x3; *out2 = (fiat_n256_uint1)(0x0 - x2); } /* * The function fiat_n256_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_n256_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) { fiat_n256_uint128 x1; uint64_t x2; uint64_t x3; x1 = ((fiat_n256_uint128)arg1 * arg2); x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff)); x3 = (uint64_t)(x1 >> 64); *out1 = x2; *out2 = x3; } /* * The function fiat_n256_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_n256_cmovznz_u64(uint64_t* out1, fiat_n256_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_n256_uint1 x1; uint64_t x2; uint64_t x3; x1 = (!(!arg1)); x2 = ((fiat_n256_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff)); x3 = ((x2 & arg3) | ((~x2) & arg2)); *out1 = x3; } /* * The function fiat_n256_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 void fiat_n256_add(fiat_n256_montgomery_domain_field_element out1, const fiat_n256_montgomery_domain_field_element arg1, const fiat_n256_montgomery_domain_field_element arg2) { uint64_t x1; fiat_n256_uint1 x2; uint64_t x3; fiat_n256_uint1 x4; uint64_t x5; fiat_n256_uint1 x6; uint64_t x7; fiat_n256_uint1 x8; uint64_t x9; fiat_n256_uint1 x10; uint64_t x11; fiat_n256_uint1 x12; uint64_t x13; fiat_n256_uint1 x14; uint64_t x15; fiat_n256_uint1 x16; uint64_t x17; fiat_n256_uint1 x18; uint64_t x19; uint64_t x20; uint64_t x21; uint64_t x22; fiat_n256_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); fiat_n256_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); fiat_n256_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); fiat_n256_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); fiat_n256_subborrowx_u64(&x9, &x10, 0x0, x1, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_subborrowx_u64(&x11, &x12, x10, x3, UINT64_C(0xbce6faada7179e84)); fiat_n256_subborrowx_u64(&x13, &x14, x12, x5, UINT64_C(0xffffffffffffffff)); fiat_n256_subborrowx_u64(&x15, &x16, x14, x7, UINT64_C(0xffffffff00000000)); fiat_n256_subborrowx_u64(&x17, &x18, x16, x8, 0x0); fiat_n256_cmovznz_u64(&x19, x18, x9, x1); fiat_n256_cmovznz_u64(&x20, x18, x11, x3); fiat_n256_cmovznz_u64(&x21, x18, x13, x5); fiat_n256_cmovznz_u64(&x22, x18, x15, x7); out1[0] = x19; out1[1] = x20; out1[2] = x21; out1[3] = x22; } /* * The function fiat_n256_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 void fiat_n256_opp(fiat_n256_montgomery_domain_field_element out1, const fiat_n256_montgomery_domain_field_element arg1) { uint64_t x1; fiat_n256_uint1 x2; uint64_t x3; fiat_n256_uint1 x4; uint64_t x5; fiat_n256_uint1 x6; uint64_t x7; fiat_n256_uint1 x8; uint64_t x9; uint64_t x10; fiat_n256_uint1 x11; uint64_t x12; fiat_n256_uint1 x13; uint64_t x14; fiat_n256_uint1 x15; uint64_t x16; fiat_n256_uint1 x17; fiat_n256_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0])); fiat_n256_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1])); fiat_n256_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2])); fiat_n256_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3])); fiat_n256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff)); fiat_n256_addcarryx_u64(&x10, &x11, 0x0, x1, (x9 & UINT64_C(0xf3b9cac2fc632551))); fiat_n256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT64_C(0xbce6faada7179e84))); fiat_n256_addcarryx_u64(&x14, &x15, x13, x5, x9); fiat_n256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000000))); out1[0] = x10; out1[1] = x12; out1[2] = x14; out1[3] = x16; } /* * The function fiat_n256_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 void fiat_n256_mul(fiat_n256_montgomery_domain_field_element out1, const fiat_n256_montgomery_domain_field_element arg1, const fiat_n256_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_n256_uint1 x14; uint64_t x15; fiat_n256_uint1 x16; uint64_t x17; fiat_n256_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; uint64_t x27; uint64_t x28; uint64_t x29; uint64_t x30; fiat_n256_uint1 x31; uint64_t x32; fiat_n256_uint1 x33; uint64_t x34; fiat_n256_uint1 x35; uint64_t x36; uint64_t x37; fiat_n256_uint1 x38; uint64_t x39; fiat_n256_uint1 x40; uint64_t x41; fiat_n256_uint1 x42; uint64_t x43; fiat_n256_uint1 x44; uint64_t x45; fiat_n256_uint1 x46; uint64_t x47; uint64_t x48; uint64_t x49; uint64_t x50; uint64_t x51; uint64_t x52; uint64_t x53; uint64_t x54; uint64_t x55; fiat_n256_uint1 x56; uint64_t x57; fiat_n256_uint1 x58; uint64_t x59; fiat_n256_uint1 x60; uint64_t x61; uint64_t x62; fiat_n256_uint1 x63; uint64_t x64; fiat_n256_uint1 x65; uint64_t x66; fiat_n256_uint1 x67; uint64_t x68; fiat_n256_uint1 x69; uint64_t x70; fiat_n256_uint1 x71; uint64_t x72; uint64_t x73; uint64_t x74; uint64_t x75; uint64_t x76; uint64_t x77; uint64_t x78; uint64_t x79; uint64_t x80; uint64_t x81; uint64_t x82; fiat_n256_uint1 x83; uint64_t x84; fiat_n256_uint1 x85; uint64_t x86; fiat_n256_uint1 x87; uint64_t x88; uint64_t x89; fiat_n256_uint1 x90; uint64_t x91; fiat_n256_uint1 x92; uint64_t x93; fiat_n256_uint1 x94; uint64_t x95; fiat_n256_uint1 x96; uint64_t x97; fiat_n256_uint1 x98; uint64_t x99; uint64_t x100; uint64_t x101; uint64_t x102; uint64_t x103; uint64_t x104; uint64_t x105; uint64_t x106; uint64_t x107; uint64_t x108; fiat_n256_uint1 x109; uint64_t x110; fiat_n256_uint1 x111; uint64_t x112; fiat_n256_uint1 x113; uint64_t x114; uint64_t x115; fiat_n256_uint1 x116; uint64_t x117; fiat_n256_uint1 x118; uint64_t x119; fiat_n256_uint1 x120; uint64_t x121; fiat_n256_uint1 x122; uint64_t x123; fiat_n256_uint1 x124; uint64_t x125; uint64_t x126; uint64_t 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; fiat_n256_uint1 x136; uint64_t x137; fiat_n256_uint1 x138; uint64_t x139; fiat_n256_uint1 x140; uint64_t x141; uint64_t x142; fiat_n256_uint1 x143; uint64_t x144; fiat_n256_uint1 x145; uint64_t x146; fiat_n256_uint1 x147; uint64_t x148; fiat_n256_uint1 x149; uint64_t x150; fiat_n256_uint1 x151; uint64_t x152; uint64_t x153; uint64_t x154; uint64_t x155; uint64_t x156; uint64_t x157; uint64_t x158; uint64_t x159; uint64_t x160; uint64_t x161; fiat_n256_uint1 x162; uint64_t x163; fiat_n256_uint1 x164; uint64_t x165; fiat_n256_uint1 x166; uint64_t x167; uint64_t x168; fiat_n256_uint1 x169; uint64_t x170; fiat_n256_uint1 x171; uint64_t x172; fiat_n256_uint1 x173; uint64_t x174; fiat_n256_uint1 x175; uint64_t x176; fiat_n256_uint1 x177; uint64_t x178; uint64_t x179; uint64_t x180; uint64_t x181; uint64_t x182; uint64_t x183; uint64_t x184; uint64_t x185; uint64_t x186; uint64_t x187; uint64_t x188; fiat_n256_uint1 x189; uint64_t x190; fiat_n256_uint1 x191; uint64_t x192; fiat_n256_uint1 x193; uint64_t x194; uint64_t x195; fiat_n256_uint1 x196; uint64_t x197; fiat_n256_uint1 x198; uint64_t x199; fiat_n256_uint1 x200; uint64_t x201; fiat_n256_uint1 x202; uint64_t x203; fiat_n256_uint1 x204; uint64_t x205; uint64_t x206; fiat_n256_uint1 x207; uint64_t x208; fiat_n256_uint1 x209; uint64_t x210; fiat_n256_uint1 x211; uint64_t x212; fiat_n256_uint1 x213; uint64_t x214; fiat_n256_uint1 x215; uint64_t x216; uint64_t x217; uint64_t x218; uint64_t x219; x1 = (arg1[1]); x2 = (arg1[2]); x3 = (arg1[3]); x4 = (arg1[0]); fiat_n256_mulx_u64(&x5, &x6, x4, (arg2[3])); fiat_n256_mulx_u64(&x7, &x8, x4, (arg2[2])); fiat_n256_mulx_u64(&x9, &x10, x4, (arg2[1])); fiat_n256_mulx_u64(&x11, &x12, x4, (arg2[0])); fiat_n256_addcarryx_u64(&x13, &x14, 0x0, x12, x9); fiat_n256_addcarryx_u64(&x15, &x16, x14, x10, x7); fiat_n256_addcarryx_u64(&x17, &x18, x16, x8, x5); x19 = (x18 + x6); fiat_n256_mulx_u64(&x20, &x21, x11, UINT64_C(0xccd1c8aaee00bc4f)); fiat_n256_mulx_u64(&x22, &x23, x20, UINT64_C(0xffffffff00000000)); fiat_n256_mulx_u64(&x24, &x25, x20, UINT64_C(0xffffffffffffffff)); fiat_n256_mulx_u64(&x26, &x27, x20, UINT64_C(0xbce6faada7179e84)); fiat_n256_mulx_u64(&x28, &x29, x20, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_addcarryx_u64(&x30, &x31, 0x0, x29, x26); fiat_n256_addcarryx_u64(&x32, &x33, x31, x27, x24); fiat_n256_addcarryx_u64(&x34, &x35, x33, x25, x22); x36 = (x35 + x23); fiat_n256_addcarryx_u64(&x37, &x38, 0x0, x11, x28); fiat_n256_addcarryx_u64(&x39, &x40, x38, x13, x30); fiat_n256_addcarryx_u64(&x41, &x42, x40, x15, x32); fiat_n256_addcarryx_u64(&x43, &x44, x42, x17, x34); fiat_n256_addcarryx_u64(&x45, &x46, x44, x19, x36); fiat_n256_mulx_u64(&x47, &x48, x1, (arg2[3])); fiat_n256_mulx_u64(&x49, &x50, x1, (arg2[2])); fiat_n256_mulx_u64(&x51, &x52, x1, (arg2[1])); fiat_n256_mulx_u64(&x53, &x54, x1, (arg2[0])); fiat_n256_addcarryx_u64(&x55, &x56, 0x0, x54, x51); fiat_n256_addcarryx_u64(&x57, &x58, x56, x52, x49); fiat_n256_addcarryx_u64(&x59, &x60, x58, x50, x47); x61 = (x60 + x48); fiat_n256_addcarryx_u64(&x62, &x63, 0x0, x39, x53); fiat_n256_addcarryx_u64(&x64, &x65, x63, x41, x55); fiat_n256_addcarryx_u64(&x66, &x67, x65, x43, x57); fiat_n256_addcarryx_u64(&x68, &x69, x67, x45, x59); fiat_n256_addcarryx_u64(&x70, &x71, x69, x46, x61); fiat_n256_mulx_u64(&x72, &x73, x62, UINT64_C(0xccd1c8aaee00bc4f)); fiat_n256_mulx_u64(&x74, &x75, x72, UINT64_C(0xffffffff00000000)); fiat_n256_mulx_u64(&x76, &x77, x72, UINT64_C(0xffffffffffffffff)); fiat_n256_mulx_u64(&x78, &x79, x72, UINT64_C(0xbce6faada7179e84)); fiat_n256_mulx_u64(&x80, &x81, x72, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_addcarryx_u64(&x82, &x83, 0x0, x81, x78); fiat_n256_addcarryx_u64(&x84, &x85, x83, x79, x76); fiat_n256_addcarryx_u64(&x86, &x87, x85, x77, x74); x88 = (x87 + x75); fiat_n256_addcarryx_u64(&x89, &x90, 0x0, x62, x80); fiat_n256_addcarryx_u64(&x91, &x92, x90, x64, x82); fiat_n256_addcarryx_u64(&x93, &x94, x92, x66, x84); fiat_n256_addcarryx_u64(&x95, &x96, x94, x68, x86); fiat_n256_addcarryx_u64(&x97, &x98, x96, x70, x88); x99 = ((uint64_t)x98 + x71); fiat_n256_mulx_u64(&x100, &x101, x2, (arg2[3])); fiat_n256_mulx_u64(&x102, &x103, x2, (arg2[2])); fiat_n256_mulx_u64(&x104, &x105, x2, (arg2[1])); fiat_n256_mulx_u64(&x106, &x107, x2, (arg2[0])); fiat_n256_addcarryx_u64(&x108, &x109, 0x0, x107, x104); fiat_n256_addcarryx_u64(&x110, &x111, x109, x105, x102); fiat_n256_addcarryx_u64(&x112, &x113, x111, x103, x100); x114 = (x113 + x101); fiat_n256_addcarryx_u64(&x115, &x116, 0x0, x91, x106); fiat_n256_addcarryx_u64(&x117, &x118, x116, x93, x108); fiat_n256_addcarryx_u64(&x119, &x120, x118, x95, x110); fiat_n256_addcarryx_u64(&x121, &x122, x120, x97, x112); fiat_n256_addcarryx_u64(&x123, &x124, x122, x99, x114); fiat_n256_mulx_u64(&x125, &x126, x115, UINT64_C(0xccd1c8aaee00bc4f)); fiat_n256_mulx_u64(&x127, &x128, x125, UINT64_C(0xffffffff00000000)); fiat_n256_mulx_u64(&x129, &x130, x125, UINT64_C(0xffffffffffffffff)); fiat_n256_mulx_u64(&x131, &x132, x125, UINT64_C(0xbce6faada7179e84)); fiat_n256_mulx_u64(&x133, &x134, x125, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_addcarryx_u64(&x135, &x136, 0x0, x134, x131); fiat_n256_addcarryx_u64(&x137, &x138, x136, x132, x129); fiat_n256_addcarryx_u64(&x139, &x140, x138, x130, x127); x141 = (x140 + x128); fiat_n256_addcarryx_u64(&x142, &x143, 0x0, x115, x133); fiat_n256_addcarryx_u64(&x144, &x145, x143, x117, x135); fiat_n256_addcarryx_u64(&x146, &x147, x145, x119, x137); fiat_n256_addcarryx_u64(&x148, &x149, x147, x121, x139); fiat_n256_addcarryx_u64(&x150, &x151, x149, x123, x141); x152 = ((uint64_t)x151 + x124); fiat_n256_mulx_u64(&x153, &x154, x3, (arg2[3])); fiat_n256_mulx_u64(&x155, &x156, x3, (arg2[2])); fiat_n256_mulx_u64(&x157, &x158, x3, (arg2[1])); fiat_n256_mulx_u64(&x159, &x160, x3, (arg2[0])); fiat_n256_addcarryx_u64(&x161, &x162, 0x0, x160, x157); fiat_n256_addcarryx_u64(&x163, &x164, x162, x158, x155); fiat_n256_addcarryx_u64(&x165, &x166, x164, x156, x153); x167 = (x166 + x154); fiat_n256_addcarryx_u64(&x168, &x169, 0x0, x144, x159); fiat_n256_addcarryx_u64(&x170, &x171, x169, x146, x161); fiat_n256_addcarryx_u64(&x172, &x173, x171, x148, x163); fiat_n256_addcarryx_u64(&x174, &x175, x173, x150, x165); fiat_n256_addcarryx_u64(&x176, &x177, x175, x152, x167); fiat_n256_mulx_u64(&x178, &x179, x168, UINT64_C(0xccd1c8aaee00bc4f)); fiat_n256_mulx_u64(&x180, &x181, x178, UINT64_C(0xffffffff00000000)); fiat_n256_mulx_u64(&x182, &x183, x178, UINT64_C(0xffffffffffffffff)); fiat_n256_mulx_u64(&x184, &x185, x178, UINT64_C(0xbce6faada7179e84)); fiat_n256_mulx_u64(&x186, &x187, x178, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_addcarryx_u64(&x188, &x189, 0x0, x187, x184); fiat_n256_addcarryx_u64(&x190, &x191, x189, x185, x182); fiat_n256_addcarryx_u64(&x192, &x193, x191, x183, x180); x194 = (x193 + x181); fiat_n256_addcarryx_u64(&x195, &x196, 0x0, x168, x186); fiat_n256_addcarryx_u64(&x197, &x198, x196, x170, x188); fiat_n256_addcarryx_u64(&x199, &x200, x198, x172, x190); fiat_n256_addcarryx_u64(&x201, &x202, x200, x174, x192); fiat_n256_addcarryx_u64(&x203, &x204, x202, x176, x194); x205 = ((uint64_t)x204 + x177); fiat_n256_subborrowx_u64(&x206, &x207, 0x0, x197, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_subborrowx_u64(&x208, &x209, x207, x199, UINT64_C(0xbce6faada7179e84)); fiat_n256_subborrowx_u64(&x210, &x211, x209, x201, UINT64_C(0xffffffffffffffff)); fiat_n256_subborrowx_u64(&x212, &x213, x211, x203, UINT64_C(0xffffffff00000000)); fiat_n256_subborrowx_u64(&x214, &x215, x213, x205, 0x0); fiat_n256_cmovznz_u64(&x216, x215, x206, x197); fiat_n256_cmovznz_u64(&x217, x215, x208, x199); fiat_n256_cmovznz_u64(&x218, x215, x210, x201); fiat_n256_cmovznz_u64(&x219, x215, x212, x203); out1[0] = x216; out1[1] = x217; out1[2] = x218; out1[3] = x219; } /* * The function fiat_n256_divstep computes a divstep. * * Preconditions: * 0 ≤ eval arg4 < m * 0 ≤ eval arg5 < m * Postconditions: * out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1) * twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2) * twos_complement_eval out3 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then ⌊(twos_complement_eval arg3 - twos_complement_eval arg2) / 2⌋ else ⌊(twos_complement_eval arg3 + (twos_complement_eval arg3 mod 2) * twos_complement_eval arg2) / 2⌋) * eval (from_montgomery out4) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (2 * eval (from_montgomery arg5)) mod m else (2 * eval (from_montgomery arg4)) mod m) * eval (from_montgomery out5) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (eval (from_montgomery arg4) - eval (from_montgomery arg4)) mod m else (eval (from_montgomery arg5) + (twos_complement_eval arg3 mod 2) * eval (from_montgomery arg4)) mod m) * 0 ≤ eval out5 < m * 0 ≤ eval out5 < m * 0 ≤ eval out2 < m * 0 ≤ eval out3 < m * * Input Bounds: * arg1: [0x0 ~> 0xffffffffffffffff] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [0x0 ~> 0xffffffffffffffff] * out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ static void fiat_n256_divstep(uint64_t* out1, uint64_t out2[5], uint64_t out3[5], uint64_t out4[4], uint64_t out5[4], uint64_t arg1, const uint64_t arg2[5], const uint64_t arg3[5], const uint64_t arg4[4], const uint64_t arg5[4]) { uint64_t x1; fiat_n256_uint1 x2; fiat_n256_uint1 x3; uint64_t x4; fiat_n256_uint1 x5; uint64_t x6; uint64_t x7; uint64_t x8; uint64_t x9; uint64_t x10; uint64_t x11; uint64_t x12; fiat_n256_uint1 x13; uint64_t x14; fiat_n256_uint1 x15; uint64_t x16; fiat_n256_uint1 x17; uint64_t x18; fiat_n256_uint1 x19; uint64_t x20; fiat_n256_uint1 x21; uint64_t x22; uint64_t x23; uint64_t x24; uint64_t x25; uint64_t x26; uint64_t x27; uint64_t x28; uint64_t x29; uint64_t x30; uint64_t x31; fiat_n256_uint1 x32; uint64_t x33; fiat_n256_uint1 x34; uint64_t x35; fiat_n256_uint1 x36; uint64_t x37; fiat_n256_uint1 x38; uint64_t x39; fiat_n256_uint1 x40; uint64_t x41; fiat_n256_uint1 x42; uint64_t x43; fiat_n256_uint1 x44; uint64_t x45; fiat_n256_uint1 x46; uint64_t x47; fiat_n256_uint1 x48; uint64_t x49; uint64_t x50; uint64_t x51; uint64_t x52; uint64_t x53; fiat_n256_uint1 x54; uint64_t x55; fiat_n256_uint1 x56; uint64_t x57; fiat_n256_uint1 x58; uint64_t x59; fiat_n256_uint1 x60; uint64_t x61; uint64_t x62; fiat_n256_uint1 x63; uint64_t x64; fiat_n256_uint1 x65; uint64_t x66; fiat_n256_uint1 x67; uint64_t x68; fiat_n256_uint1 x69; uint64_t x70; uint64_t x71; uint64_t x72; uint64_t x73; fiat_n256_uint1 x74; uint64_t x75; uint64_t x76; uint64_t x77; uint64_t x78; uint64_t x79; uint64_t x80; fiat_n256_uint1 x81; uint64_t x82; fiat_n256_uint1 x83; uint64_t x84; fiat_n256_uint1 x85; uint64_t x86; fiat_n256_uint1 x87; uint64_t x88; fiat_n256_uint1 x89; uint64_t x90; uint64_t x91; uint64_t x92; uint64_t x93; uint64_t x94; fiat_n256_uint1 x95; uint64_t x96; fiat_n256_uint1 x97; uint64_t x98; fiat_n256_uint1 x99; uint64_t x100; fiat_n256_uint1 x101; uint64_t x102; fiat_n256_uint1 x103; uint64_t x104; fiat_n256_uint1 x105; uint64_t x106; fiat_n256_uint1 x107; uint64_t x108; fiat_n256_uint1 x109; uint64_t x110; fiat_n256_uint1 x111; uint64_t x112; fiat_n256_uint1 x113; uint64_t x114; uint64_t x115; uint64_t x116; uint64_t x117; uint64_t x118; uint64_t x119; uint64_t x120; uint64_t x121; uint64_t x122; uint64_t x123; uint64_t x124; uint64_t x125; uint64_t x126; fiat_n256_addcarryx_u64(&x1, &x2, 0x0, (~arg1), 0x1); x3 = (fiat_n256_uint1)((fiat_n256_uint1)(x1 >> 63) & (fiat_n256_uint1)((arg3[0]) & 0x1)); fiat_n256_addcarryx_u64(&x4, &x5, 0x0, (~arg1), 0x1); fiat_n256_cmovznz_u64(&x6, x3, arg1, x4); fiat_n256_cmovznz_u64(&x7, x3, (arg2[0]), (arg3[0])); fiat_n256_cmovznz_u64(&x8, x3, (arg2[1]), (arg3[1])); fiat_n256_cmovznz_u64(&x9, x3, (arg2[2]), (arg3[2])); fiat_n256_cmovznz_u64(&x10, x3, (arg2[3]), (arg3[3])); fiat_n256_cmovznz_u64(&x11, x3, (arg2[4]), (arg3[4])); fiat_n256_addcarryx_u64(&x12, &x13, 0x0, 0x1, (~(arg2[0]))); fiat_n256_addcarryx_u64(&x14, &x15, x13, 0x0, (~(arg2[1]))); fiat_n256_addcarryx_u64(&x16, &x17, x15, 0x0, (~(arg2[2]))); fiat_n256_addcarryx_u64(&x18, &x19, x17, 0x0, (~(arg2[3]))); fiat_n256_addcarryx_u64(&x20, &x21, x19, 0x0, (~(arg2[4]))); fiat_n256_cmovznz_u64(&x22, x3, (arg3[0]), x12); fiat_n256_cmovznz_u64(&x23, x3, (arg3[1]), x14); fiat_n256_cmovznz_u64(&x24, x3, (arg3[2]), x16); fiat_n256_cmovznz_u64(&x25, x3, (arg3[3]), x18); fiat_n256_cmovznz_u64(&x26, x3, (arg3[4]), x20); fiat_n256_cmovznz_u64(&x27, x3, (arg4[0]), (arg5[0])); fiat_n256_cmovznz_u64(&x28, x3, (arg4[1]), (arg5[1])); fiat_n256_cmovznz_u64(&x29, x3, (arg4[2]), (arg5[2])); fiat_n256_cmovznz_u64(&x30, x3, (arg4[3]), (arg5[3])); fiat_n256_addcarryx_u64(&x31, &x32, 0x0, x27, x27); fiat_n256_addcarryx_u64(&x33, &x34, x32, x28, x28); fiat_n256_addcarryx_u64(&x35, &x36, x34, x29, x29); fiat_n256_addcarryx_u64(&x37, &x38, x36, x30, x30); fiat_n256_subborrowx_u64(&x39, &x40, 0x0, x31, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_subborrowx_u64(&x41, &x42, x40, x33, UINT64_C(0xbce6faada7179e84)); fiat_n256_subborrowx_u64(&x43, &x44, x42, x35, UINT64_C(0xffffffffffffffff)); fiat_n256_subborrowx_u64(&x45, &x46, x44, x37, UINT64_C(0xffffffff00000000)); fiat_n256_subborrowx_u64(&x47, &x48, x46, x38, 0x0); x49 = (arg4[3]); x50 = (arg4[2]); x51 = (arg4[1]); x52 = (arg4[0]); fiat_n256_subborrowx_u64(&x53, &x54, 0x0, 0x0, x52); fiat_n256_subborrowx_u64(&x55, &x56, x54, 0x0, x51); fiat_n256_subborrowx_u64(&x57, &x58, x56, 0x0, x50); fiat_n256_subborrowx_u64(&x59, &x60, x58, 0x0, x49); fiat_n256_cmovznz_u64(&x61, x60, 0x0, UINT64_C(0xffffffffffffffff)); fiat_n256_addcarryx_u64(&x62, &x63, 0x0, x53, (x61 & UINT64_C(0xf3b9cac2fc632551))); fiat_n256_addcarryx_u64(&x64, &x65, x63, x55, (x61 & UINT64_C(0xbce6faada7179e84))); fiat_n256_addcarryx_u64(&x66, &x67, x65, x57, x61); fiat_n256_addcarryx_u64(&x68, &x69, x67, x59, (x61 & UINT64_C(0xffffffff00000000))); fiat_n256_cmovznz_u64(&x70, x3, (arg5[0]), x62); fiat_n256_cmovznz_u64(&x71, x3, (arg5[1]), x64); fiat_n256_cmovznz_u64(&x72, x3, (arg5[2]), x66); fiat_n256_cmovznz_u64(&x73, x3, (arg5[3]), x68); x74 = (fiat_n256_uint1)(x22 & 0x1); fiat_n256_cmovznz_u64(&x75, x74, 0x0, x7); fiat_n256_cmovznz_u64(&x76, x74, 0x0, x8); fiat_n256_cmovznz_u64(&x77, x74, 0x0, x9); fiat_n256_cmovznz_u64(&x78, x74, 0x0, x10); fiat_n256_cmovznz_u64(&x79, x74, 0x0, x11); fiat_n256_addcarryx_u64(&x80, &x81, 0x0, x22, x75); fiat_n256_addcarryx_u64(&x82, &x83, x81, x23, x76); fiat_n256_addcarryx_u64(&x84, &x85, x83, x24, x77); fiat_n256_addcarryx_u64(&x86, &x87, x85, x25, x78); fiat_n256_addcarryx_u64(&x88, &x89, x87, x26, x79); fiat_n256_cmovznz_u64(&x90, x74, 0x0, x27); fiat_n256_cmovznz_u64(&x91, x74, 0x0, x28); fiat_n256_cmovznz_u64(&x92, x74, 0x0, x29); fiat_n256_cmovznz_u64(&x93, x74, 0x0, x30); fiat_n256_addcarryx_u64(&x94, &x95, 0x0, x70, x90); fiat_n256_addcarryx_u64(&x96, &x97, x95, x71, x91); fiat_n256_addcarryx_u64(&x98, &x99, x97, x72, x92); fiat_n256_addcarryx_u64(&x100, &x101, x99, x73, x93); fiat_n256_subborrowx_u64(&x102, &x103, 0x0, x94, UINT64_C(0xf3b9cac2fc632551)); fiat_n256_subborrowx_u64(&x104, &x105, x103, x96, UINT64_C(0xbce6faada7179e84)); fiat_n256_subborrowx_u64(&x106, &x107, x105, x98, UINT64_C(0xffffffffffffffff)); fiat_n256_subborrowx_u64(&x108, &x109, x107, x100, UINT64_C(0xffffffff00000000)); fiat_n256_subborrowx_u64(&x110, &x111, x109, x101, 0x0); fiat_n256_addcarryx_u64(&x112, &x113, 0x0, x6, 0x1); x114 = ((x80 >> 1) | ((x82 << 63) & UINT64_C(0xffffffffffffffff))); x115 = ((x82 >> 1) | ((x84 << 63) & UINT64_C(0xffffffffffffffff))); x116 = ((x84 >> 1) | ((x86 << 63) & UINT64_C(0xffffffffffffffff))); x117 = ((x86 >> 1) | ((x88 << 63) & UINT64_C(0xffffffffffffffff))); x118 = ((x88 & UINT64_C(0x8000000000000000)) | (x88 >> 1)); fiat_n256_cmovznz_u64(&x119, x48, x39, x31); fiat_n256_cmovznz_u64(&x120, x48, x41, x33); fiat_n256_cmovznz_u64(&x121, x48, x43, x35); fiat_n256_cmovznz_u64(&x122, x48, x45, x37); fiat_n256_cmovznz_u64(&x123, x111, x102, x94); fiat_n256_cmovznz_u64(&x124, x111, x104, x96); fiat_n256_cmovznz_u64(&x125, x111, x106, x98); fiat_n256_cmovznz_u64(&x126, x111, x108, x100); *out1 = x112; out2[0] = x7; out2[1] = x8; out2[2] = x9; out2[3] = x10; out2[4] = x11; out3[0] = x114; out3[1] = x115; out3[2] = x116; out3[3] = x117; out3[4] = x118; out4[0] = x119; out4[1] = x120; out4[2] = x121; out4[3] = x122; out5[0] = x123; out5[1] = x124; out5[2] = x125; out5[3] = x126; }