diff options
| -rw-r--r-- | src/lib/math/bigint/bigint.cpp | 7 | ||||
| -rw-r--r-- | src/lib/math/bigint/bigint.h | 2 | ||||
| -rw-r--r-- | src/lib/math/bigint/divide.cpp | 40 | ||||
| -rw-r--r-- | src/tests/data/bn/divide.vec | 2968 |
4 files changed, 2995 insertions, 22 deletions
diff --git a/src/lib/math/bigint/bigint.cpp b/src/lib/math/bigint/bigint.cpp index a4545e4a1..1a09a92f1 100644 --- a/src/lib/math/bigint/bigint.cpp +++ b/src/lib/math/bigint/bigint.cpp @@ -317,7 +317,7 @@ BigInt BigInt::operator-() const return x; } -void BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws) +size_t BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws) { if(p.is_negative()) throw Invalid_Argument("BigInt::reduce_below mod must be positive"); @@ -332,14 +332,19 @@ void BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws) clear_mem(ws.data(), ws.size()); + size_t reductions = 0; + for(;;) { word borrow = bigint_sub3(ws.data(), data(), p_words + 1, p.data(), p_words); if(borrow) break; + ++reductions; swap_reg(ws); } + + return reductions; } /* diff --git a/src/lib/math/bigint/bigint.h b/src/lib/math/bigint/bigint.h index f0aa04391..9b7af4169 100644 --- a/src/lib/math/bigint/bigint.h +++ b/src/lib/math/bigint/bigint.h @@ -344,7 +344,7 @@ class BOTAN_PUBLIC_API(2,0) BigInt final * mod and performs repeated subtractions. It should not be used if * *this is much larger than mod, instead use modulo operator. */ - void reduce_below(const BigInt& mod, secure_vector<word> &ws); + size_t reduce_below(const BigInt& mod, secure_vector<word> &ws); /** * Zeroize the BigInt. The size of the underlying register is not diff --git a/src/lib/math/bigint/divide.cpp b/src/lib/math/bigint/divide.cpp index 2dfb7405e..ed9a12112 100644 --- a/src/lib/math/bigint/divide.cpp +++ b/src/lib/math/bigint/divide.cpp @@ -154,6 +154,8 @@ BigInt ct_modulo(const BigInt& x, const BigInt& y) /* * Solve x = q * y + r +* +* See Handbook of Applied Cryptography section 14.2.5 */ void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out) { @@ -166,11 +168,12 @@ void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out) BigInt r = x; BigInt q = 0; + secure_vector<word> ws; r.set_sign(BigInt::Positive); y.set_sign(BigInt::Positive); - if(r >= y) + if(r.is_nonzero()) { // Calculate shifts needed to normalize y with high bit set const size_t shifts = BOTAN_MP_WORD_BITS - high_bit(y.word_at(y_words-1)); @@ -180,7 +183,7 @@ void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out) // we know y has not changed size, since we only shifted up to set high bit const size_t t = y_words - 1; - const size_t n = r.sig_words() - 1; // r may have changed size however + const size_t n = std::max(t, r.sig_words() - 1); // r may have changed size however BOTAN_ASSERT_NOMSG(n >= t); @@ -190,38 +193,35 @@ void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out) BigInt shifted_y = y << (BOTAN_MP_WORD_BITS * (n-t)); - while(r >= shifted_y) - { - r -= shifted_y; - q_words[n-t] += 1; - } + // Set q_{n-t} to number of times r > shifted_y + q_words[n-t] = r.reduce_below(shifted_y, ws); + + const word y_t0 = y.word_at(t); + const word y_t1 = y.word_at(t-1); for(size_t j = n; j != t; --j) { const word x_j0 = r.word_at(j); const word x_j1 = r.word_at(j-1); const word x_j2 = r.word_at(j-2); - const word y_t0 = y.word_at(t); - const word y_t1 = y.word_at(t-1); - word qjt = (x_j0 == y_t0) ? MP_WORD_MAX : bigint_divop(x_j0, x_j1, y_t0); + word qjt = bigint_divop(x_j0, x_j1, y_t0); + + qjt = CT::Mask<word>::is_equal(x_j0, y_t0).select(MP_WORD_MAX, qjt); - while(division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2)) - { - qjt -= 1; - } + // Per HAC 14.23, this operation is required at most twice + qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2); + qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2); + BOTAN_DEBUG_ASSERT(division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2) == false); shifted_y >>= BOTAN_MP_WORD_BITS; // Now shifted_y == y << (BOTAN_MP_WORD_BITS * (j-t-1)) r -= qjt * shifted_y; - if(r.is_negative()) - { - // overcorrected - qjt -= 1; - r += shifted_y; - } + // TODO this could be better + qjt -= r.is_negative(); + r += static_cast<word>(r.is_negative()) * shifted_y; q_words[j-t-1] = qjt; } diff --git a/src/tests/data/bn/divide.vec b/src/tests/data/bn/divide.vec index 0a6dd2423..b7195a8e4 100644 --- a/src/tests/data/bn/divide.vec +++ b/src/tests/data/bn/divide.vec @@ -163,3 +163,2971 @@ In1 = 1996953214196350189568 In2 = 13331618315827609940 Output = 149 +In1 = 0xA +In2 = 0xA +Output = 0x1 + +In1 = 0x2020 +In2 = 0xA00 +Output = 0x3 + +In1 = 0xA0A +In2 = 0x1 +Output = 0xA0A + +In1 = 0xA +In2 = 0x1 +Output = 0xA + +In1 = 0xA00 +In2 = 0x100 +Output = 0xA + +In1 = 0xC700 +In2 = 0x100 +Output = 0xC7 + +In1 = 0x6000 +In2 = 0xA +Output = 0x999 + +In1 = 0x2235 +In2 = 0xA00 +Output = 0x3 + +In1 = 0xE00A +In2 = 0xA20 +Output = 0x16 + +In1 = 0x6000 +In2 = 0xEC +Output = 0x68 + +In1 = 0x100 +In2 = 0xC7 +Output = 0x1 + +In1 = 0xE00A +In2 = 0x20 +Output = 0x700 + +In1 = 0xE0E0 +In2 = 0xA20 +Output = 0x16 + +In1 = 0xE00E +In2 = 0x20 +Output = 0x700 + +In1 = 0xE00A +In2 = 0x1A20 +Output = 0x8 + +In1 = 0xE0E0 +In2 = 0x3A20 +Output = 0x3 + +In1 = 0x2C +In2 = 0x7 +Output = 0x6 + +In1 = 0xE0E0 +In2 = 0xE00A +Output = 0x1 + +In1 = 0xE0E0 +In2 = 0x930A +Output = 0x1 + +In1 = 0x6C +In2 = 0x31 +Output = 0x2 + +In1 = 0xFF0A +In2 = 0xA1C +Output = 0x19 + +In1 = 0x203B +In2 = 0x22 +Output = 0xF2 + +In1 = 0xA0A +In2 = 0x101 +Output = 0xA + +In1 = 0xE0 +In2 = 0xA +Output = 0x16 + +In1 = 0xC7C7 +In2 = 0x2020 +Output = 0x6 + +In1 = 0xE00A +In2 = 0xAEA +Output = 0x14 + +In1 = 0x60 +In2 = 0x20 +Output = 0x3 + +In1 = 0x8801 +In2 = 0xA00 +Output = 0xD + +In1 = 0xE00A +In2 = 0xA00 +Output = 0x16 + +In1 = 0xE0A1 +In2 = 0x20E0 +Output = 0x6 + +In1 = 0x4320 +In2 = 0xAE0 +Output = 0x6 + +In1 = 0x100 +In2 = 0x41 +Output = 0x3 + +In1 = 0x6000 +In2 = 0xE +Output = 0x6DB + +In1 = 0xC7C7 +In2 = 0x20A0 +Output = 0x6 + +In1 = 0xEC19 +In2 = 0xA +Output = 0x179C + +In1 = 0x1900 +In2 = 0x232 +Output = 0xB + +In1 = 0xE0A1 +In2 = 0xE0A1 +Output = 0x1 + +In1 = 0xA0A +In2 = 0xA0A +Output = 0x1 + +In1 = 0x20F6 +In2 = 0x20E0 +Output = 0x1 + +In1 = 0x3A00 +In2 = 0x2000 +Output = 0x1 + +In1 = 0xA70E +In2 = 0x6000 +Output = 0x1 + +In1 = 0x6000 +In2 = 0xF +Output = 0x666 + +In1 = 0x400 +In2 = 0x100 +Output = 0x4 + +In1 = 0x22 +In2 = 0x2 +Output = 0x11 + +In1 = 0x2ADF +In2 = 0xEFE +Output = 0x2 + +In1 = 0x20 +In2 = 0xA +Output = 0x3 + +In1 = 0xE0 +In2 = 0x5D +Output = 0x2 + +In1 = 0xFE +In2 = 0x20 +Output = 0x7 + +In1 = 0xE7F5 +In2 = 0x2600 +Output = 0x6 + +In1 = 0xE0 +In2 = 0xA1 +Output = 0x1 + +In1 = 0xE80E +In2 = 0x2020 +Output = 0x7 + +In1 = 0x3522 +In2 = 0xA00 +Output = 0x5 + +In1 = 0x870E +In2 = 0x602D +Output = 0x1 + +In1 = 0x5AD8 +In2 = 0xEFE +Output = 0x6 + +In1 = 0x20F7 +In2 = 0x20E8 +Output = 0x1 + +In1 = 0x5AD8 +In2 = 0x3AFE +Output = 0x1 + +In1 = 0x5AD8 +In2 = 0x3208 +Output = 0x1 + +In1 = 0x3293 +In2 = 0x1F0A +Output = 0x1 + +In1 = 0x400 +In2 = 0x180 +Output = 0x2 + +In1 = 0x4 +In2 = 0x4 +Output = 0x1 + +In1 = 0x262C +In2 = 0x1 +Output = 0x262C + +In1 = 0x8001 +In2 = 0xA00 +Output = 0xC + +In1 = 0x2C01 +In2 = 0x169F +Output = 0x1 + +In1 = 0xA3E0 +In2 = 0xA20 +Output = 0x10 + +In1 = 0x2C +In2 = 0x1 +Output = 0x2C + +In1 = 0xFFFF +In2 = 0xAFF +Output = 0x17 + +In1 = 0xFF03 +In2 = 0x4 +Output = 0x3FC0 + +In1 = 0x3801 +In2 = 0xA +Output = 0x599 + +In1 = 0x32C7 +In2 = 0x1F5A +Output = 0x1 + +In1 = 0x6000 +In2 = 0x90A +Output = 0xA + +In1 = 0x2B01 +In2 = 0xA00 +Output = 0x4 + +In1 = 0xE0C7 +In2 = 0x1E0 +Output = 0x77 + +In1 = 0x8D01 +In2 = 0x4A00 +Output = 0x1 + +In1 = 0xC7FF +In2 = 0x700 +Output = 0x1C + +In1 = 0xE001 +In2 = 0x93 +Output = 0x186 + +In1 = 0x5F +In2 = 0x35 +Output = 0x1 + +In1 = 0xF6DF +In2 = 0xD5FF +Output = 0x1 + +In1 = 0xC760 +In2 = 0x220A +Output = 0x5 + +In1 = 0x4100 +In2 = 0xC3 +Output = 0x55 + +In1 = 0x2C +In2 = 0x3 +Output = 0xE + +In1 = 0xFC02 +In2 = 0x100 +Output = 0xFC + +In1 = 0x89C7 +In2 = 0x1760 +Output = 0x5 + +In1 = 0x1 +In2 = 0x1 +Output = 0x1 + +In1 = 0x100 +In2 = 0x83 +Output = 0x1 + +In1 = 0xFFE0 +In2 = 0x5DD9 +Output = 0x2 + +In1 = 0x3320 +In2 = 0x300 +Output = 0x11 + +In1 = 0x5AD8 +In2 = 0x1E0E +Output = 0x3 + +In1 = 0x6000 +In2 = 0x4F +Output = 0x137 + +In1 = 0xE7F5 +In2 = 0x600 +Output = 0x26 + +In1 = 0xDFFE +In2 = 0x60 +Output = 0x255 + +In1 = 0x89 +In2 = 0x4E +Output = 0x1 + +In1 = 0x3801 +In2 = 0x80A +Output = 0x6 + +In1 = 0xDFE0 +In2 = 0xE0 +Output = 0xFF + +In1 = 0x35D8 +In2 = 0xEFE +Output = 0x3 + +In1 = 0xA3E0 +In2 = 0x2C20 +Output = 0x3 + +In1 = 0x3A0A +In2 = 0xA +Output = 0x5CD + +In1 = 0x8440 +In2 = 0xEFC +Output = 0x8 + +In1 = 0xDE +In2 = 0x10 +Output = 0xD + +In1 = 0x52 +In2 = 0xE +Output = 0x5 + +In1 = 0xFF2B +In2 = 0xFF2B +Output = 0x1 + +In1 = 0xA70E +In2 = 0xA0F7 +Output = 0x1 + +In1 = 0xF8F6 +In2 = 0xC50A +Output = 0x1 + +In1 = 0xFFFF +In2 = 0xEB8 +Output = 0x11 + +In1 = 0x5AFA +In2 = 0x40A +Output = 0x16 + +In1 = 0x3320 +In2 = 0x500 +Output = 0xA + +In1 = 0x6000 +In2 = 0x14F +Output = 0x49 + +In1 = 0xD8 +In2 = 0x8 +Output = 0x1B + +In1 = 0xC7FF +In2 = 0x710 +Output = 0x1C + +In1 = 0xFF2A +In2 = 0xC57 +Output = 0x14 + +In1 = 0x502E +In2 = 0x12C +Output = 0x44 + +In1 = 0x8041 +In2 = 0x4140 +Output = 0x1 + +In1 = 0xD5DF +In2 = 0xD5D5 +Output = 0x1 + +In1 = 0x7F56 +In2 = 0x7EDD +Output = 0x1 + +In1 = 0x20E0 +In2 = 0xAE0 +Output = 0x3 + +In1 = 0xB00 +In2 = 0x4E0 +Output = 0x2 + +In1 = 0x601 +In2 = 0x10 +Output = 0x60 + +In1 = 0x1040 +In2 = 0x4 +Output = 0x410 + +In1 = 0x6B33 +In2 = 0x1 +Output = 0x6B33 + +In1 = 0xE001 +In2 = 0x97 +Output = 0x17B + +In1 = 0x3500 +In2 = 0x4F +Output = 0xAB + +In1 = 0xFED1 +In2 = 0x100 +Output = 0xFE + +In1 = 0x20F2 +In2 = 0x20E8 +Output = 0x1 + +In1 = 0xBA0A +In2 = 0x8 +Output = 0x1741 + +In1 = 0x40D8 +In2 = 0xE35 +Output = 0x4 + +In1 = 0x5E2E +In2 = 0x12C +Output = 0x50 + +In1 = 0x2 +In2 = 0x2 +Output = 0x1 + +In1 = 0x89C7 +In2 = 0x760 +Output = 0x12 + +In1 = 0xFFFF +In2 = 0x400 +Output = 0x3F + +In1 = 0x5BF5 +In2 = 0x600 +Output = 0xF + +In1 = 0x6 +In2 = 0x1 +Output = 0x6 + +In1 = 0x7F56 +In2 = 0x3ADD +Output = 0x2 + +In1 = 0x500 +In2 = 0x180 +Output = 0x3 + +In1 = 0x406 +In2 = 0x12C +Output = 0x3 + +In1 = 0x29DE +In2 = 0xC50 +Output = 0x3 + +In1 = 0xDFE0 +In2 = 0xA0A +Output = 0x16 + +In1 = 0x2800 +In2 = 0x400 +Output = 0xA + +In1 = 0xE0 +In2 = 0x87 +Output = 0x1 + +In1 = 0x3B2C +In2 = 0x1 +Output = 0x3B2C + +In1 = 0x3B2C +In2 = 0xB +Output = 0x561 + +In1 = 0xE0 +In2 = 0xE +Output = 0x10 + +In1 = 0x3B3B +In2 = 0x2C2C +Output = 0x1 + +In1 = 0x2ADF +In2 = 0x2ADF +Output = 0x1 + +In1 = 0xFFFF +In2 = 0x1 +Output = 0xFFFF + +In1 = 0x800A +In2 = 0x1 +Output = 0x800A + +In1 = 0x41 +In2 = 0x41 +Output = 0x1 + +In1 = 0xDB02FCDB00 +In2 = 0xDB02FCDB +Output = 0x100 + +In1 = 0x6B00 +In2 = 0x1 +Output = 0x6B00 + +In1 = 0xE0E0 +In2 = 0xE0 +Output = 0x101 + +In1 = 0xA0 +In2 = 0xB +Output = 0xE + +In1 = 0xA24 +In2 = 0x100 +Output = 0xA + +In1 = 0xE0E0 +In2 = 0xE6 +Output = 0xFA + +In1 = 0x6B2F +In2 = 0x1 +Output = 0x6B2F + +In1 = 0x20 +In2 = 0x1 +Output = 0x20 + +In1 = 0x3B +In2 = 0x2C +Output = 0x1 + +In1 = 0x502 +In2 = 0x101 +Output = 0x4 + +In1 = 0x312F +In2 = 0x1 +Output = 0x312F + +In1 = 0x8001 +In2 = 0x1 +Output = 0x8001 + +In1 = 0xC8 +In2 = 0x8 +Output = 0x19 + +In1 = 0x3A +In2 = 0x20 +Output = 0x1 + +In1 = 0xB +In2 = 0xA +Output = 0x1 + +In1 = 0xA0A +In2 = 0x800 +Output = 0x1 + +In1 = 0x41E400 +In2 = 0x2223 +Output = 0x1EE + +In1 = 0xDB02FC +In2 = 0x1C808 +Output = 0x7A + +In1 = 0xDB022C +In2 = 0x108 +Output = 0xD45F + +In1 = 0xFFFFFF +In2 = 0xFFDA2E +Output = 0x1 + +In1 = 0x80FFFF +In2 = 0x10401 +Output = 0x7F + +In1 = 0xAD802 +In2 = 0xA0108 +Output = 0x1 + +In1 = 0x3B020A +In2 = 0xA8903 +Output = 0x5 + +In1 = 0xE3220 +In2 = 0x30042 +Output = 0x4 + +In1 = 0xE02401 +In2 = 0x1 +Output = 0xE02401 + +In1 = 0x2F0006 +In2 = 0x1 +Output = 0x2F0006 + +In1 = 0xFFE0E000 +In2 = 0xE00E0000 +Output = 0x1 + +In1 = 0x91023120 +In2 = 0x32030002 +Output = 0x2 + +In1 = 0xFFFFFFFF +In2 = 0xFFFFFF02 +Output = 0x1 + +In1 = 0xE02401 +In2 = 0x1001 +Output = 0xE01 + +In1 = 0x41E4FF00 +In2 = 0x2241E423 +Output = 0x1 + +In1 = 0x2F000001 +In2 = 0x1 +Output = 0x2F000001 + +In1 = 0x6BFF00FF +In2 = 0x10000 +Output = 0x6BFF + +In1 = 0x6BFF4F0100 +In2 = 0x2400 +Output = 0x2FFFB15 + +In1 = 0x490601E400 +In2 = 0x1C8E40022 +Output = 0x28 + +In1 = 0xFEFEFE0000 +In2 = 0x4FEFEFE +Output = 0x330A + +In1 = 0xFFFFFF0A31 +In2 = 0x2022E4C760 +Output = 0x7 + +In1 = 0xFFFFFFFFFF +In2 = 0xFFFF02C760 +Output = 0x1 + +In1 = 0xFFFFFF0000 +In2 = 0x2C760 +Output = 0x5C2034 + +In1 = 0xE0BF00 +In2 = 0x101 +Output = 0xDFDF + +In1 = 0x6B00000100 +In2 = 0x2400 +Output = 0x2F8E38E + +In1 = 0x10000FA00 +In2 = 0x2C760 +Output = 0x5C20 + +In1 = 0xFFF7FFFFFF +In2 = 0xF7FF02C760 +Output = 0x1 + +In1 = 0x3BFFFFFFFF +In2 = 0x3BFFFF2C2C +Output = 0x1 + +In1 = 0x41FF000000 +In2 = 0x2C760 +Output = 0x17BFF1 + +In1 = 0x100000000 +In2 = 0xFEFE +Output = 0x10103 + +In1 = 0x6B40FF4F00 +In2 = 0x100000000 +Output = 0x6B + +In1 = 0x4100000000 +In2 = 0xFEFE +Output = 0x4141C4 + +In1 = 0xFFF721FFFF +In2 = 0xF7FF02C760 +Output = 0x1 + +In1 = 0x3F2C07AF00 +In2 = 0x101000000 +Output = 0x3E + +In1 = 0x1B00000000 +In2 = 0x2FC01C808 +Output = 0x9 + +In1 = 0x4000040020 +In2 = 0x1 +Output = 0x4000040020 + +In1 = 0x2F5BF506 +In2 = 0x31 +Output = 0xF76D7D + +In1 = 0x34002C01 +In2 = 0x4100 +Output = 0xCCCD + +In1 = 0xBA +In2 = 0xA +Output = 0x12 + +In1 = 0x22C +In2 = 0x100 +Output = 0x2 + +In1 = 0x6B4B000000 +In2 = 0x24 +Output = 0x2FAF8E38E + +In1 = 0xFFFF06 +In2 = 0xDAFF +Output = 0x12B + +In1 = 0x6B00000100 +In2 = 0x3D00 +Output = 0x1C10C97 + +In1 = 0x47E086 +In2 = 0x474747 +Output = 0x1 + +In1 = 0x2F5BF506 +In2 = 0x6A0031 +Output = 0x72 + +In1 = 0x410641 +In2 = 0x601E4 +Output = 0xA + +In1 = 0x42C0A0700 +In2 = 0x2010000 +Output = 0x214 + +In1 = 0xA4B00 +In2 = 0xDB +Output = 0xC08 + +In1 = 0xBA06 +In2 = 0x2706 +Output = 0x4 + +In1 = 0x5BD80800 +In2 = 0xE0000 +Output = 0x68F + +In1 = 0xE02FF6BFF +In2 = 0x100000000 +Output = 0xE + +In1 = 0x80 +In2 = 0x1 +Output = 0x80 + +In1 = 0x2401009300 +In2 = 0x1FF +Output = 0x1209850C + +In1 = 0x4B00000000 +In2 = 0x6000 +Output = 0xC80000 + +In1 = 0x19 +In2 = 0x2 +Output = 0xC + +In1 = 0xFF +In2 = 0x2B +Output = 0x5 + +In1 = 0xE4902FCDB +In2 = 0xD87A00 +Output = 0x10E4 + +In1 = 0x4B05000000 +In2 = 0x3D06 +Output = 0x13AB713 + +In1 = 0x6C414B000000000000 +In2 = 0xB9036C396BFF0154 +Output = 0x95 + +In1 = 0xFFFFFFFF25FFFF +In2 = 0xFF07F7FF02C760 +Output = 0x1 + +In1 = 0x42C0A07F7E001 +In2 = 0x93FF21FF0000 +Output = 0x7 + +In1 = 0xAC7A0100930000 +In2 = 0x1FFFFFCDB +Output = 0x563D01 + +In1 = 0xFFFFFF80002000 +In2 = 0x7FFD808DA8001 +Output = 0x20 + +In1 = 0x2F000600223A +In2 = 0x222222220101 +Output = 0x1 + +In1 = 0xFD93BE93020022 +In2 = 0x3A0A006B010093 +Output = 0x4 + +In1 = 0x2F0006002001 +In2 = 0x2F0006002001 +Output = 0x1 + +In1 = 0xFFFFFFFFFFFFFF +In2 = 0x4B08FF6B +Output = 0x369676E + +In1 = 0x300000000000 +In2 = 0x4101 +Output = 0xBD08E83B + +In1 = 0xA6B6B2F0001 +In2 = 0x2FC0A003400 +Output = 0x3 + +In1 = 0x2F400610223A +In2 = 0x222222220101 +Output = 0x1 + +In1 = 0x6002027FF0000 +In2 = 0xD5DFD5 +Output = 0x72EB016 + +In1 = 0x80FF53000000 +In2 = 0xAAAA +Output = 0xC17FBDFF + +In1 = 0x44B0000000000 +In2 = 0xFF21FF0000 +Output = 0x44E + +In1 = 0x200A232600 +In2 = 0x200A232600 +Output = 0x1 + +In1 = 0xBA805300000000 +In2 = 0x600041235B +Output = 0x1F154 + +In1 = 0x2F00065300002F00 +In2 = 0x2F000000000005 +Output = 0x100 + +In1 = 0x80FFFF0153000008 +In2 = 0x401 +Output = 0x2037F1C3E3C70E + +In1 = 0x80FFFF01AAAAAAAA +In2 = 0x5300000000000000 +Output = 0x1 + +In1 = 0xFFFFFFFFFFFF00FF +In2 = 0xF90800004B6BFFFF +Output = 0x1 + +In1 = 0x2F4006FFFFFFFF10 +In2 = 0x223A222222220101 +Output = 0x1 + +In1 = 0x80FF100000005300 +In2 = 0xAAAA +Output = 0xC17F597F597F + +In1 = 0x24B0000000009FA +In2 = 0x8000000000087 +Output = 0x49 + +In1 = 0x1B0000010100FB02 +In2 = 0x8FC00FB0208FC01 +Output = 0x3 + +In1 = 0x5BFFFFFFFF0E7804 +In2 = 0x5BFFFFFFFF0E0004 +Output = 0x1 + +In1 = 0x80FFF65300000000 +In2 = 0xAAAA868686 +Output = 0xC1801A + +In1 = 0x8000000000000000 +In2 = 0x100000000000AAAA +Output = 0x7 + +In1 = 0x181818F1F1F1F118 +In2 = 0x18181818181818DF +Output = 0x1 + +In1 = 0x181818F1F1F1F1 +In2 = 0x181818181818DF +Output = 0x1 + +In1 = 0x4FFFFFF0102FF4BFF +In2 = 0x10007012100 +Output = 0x4FFDCFA + 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