BUGFIX-66

Bug 38: Broken Broadword Matrix Multiplication

This multiplies two 4x4 matrices (a and b) and adds a third 4x4 matrix (c) to the result.
Each 4x4 matrix has 1-bit elements and is represented in the low 16 bits of a 64-bit integer.
The matrices are row-major: A matrix element at some row and column is at bit row*4+column.
The 16-bit matrix a is expanded from: (msb) ponm_lkji_hgfe_dcba (lsb)
To: pppp_llll_hhhh_dddd_oooo_kkkk_gggg_cccc_nnnn_jjjj_ffff_bbbb_mmmm_iiii_eeee_aaaa
The 16-bit matrix b is expanded from: (msb) ponm_lkji_hgfe_dcba (lsb)
To: ponm_ponm_ponm_ponm_lkji_lkji_lkji_lkji_hgfe_hgfe_hgfe_hgfe_dcba_dcba_dcba_dcba
All 64 elementwise multiplications are performed together by a single 64-bit AND.
Addition is XOR in this implementation, but OR could be used instead.

Fix The Tiny Bug In This Go Code:

func matrixMultiplyAdd(a, b, c uint64) uint64 { a |= a << 16 a |= a << 32 const ( shift1 = 15 mask1 = 0b_0000_0000_0000_0000_1010_1010_1010_1010_0000_0000_0000_0000_1010_1010_1010_1010 ) swap1 := (a>>shift1 ^ a) & mask1 a ^= swap1 a ^= swap1 << shift1 const ( shift2 = 30 mask2 = 0b_0000_0000_0000_0000_0000_0000_0000_0000_1100_1100_1100_1100_1100_1100_1100_1100 ) swap2 := (a>>shift2 ^ a) & mask2 a ^= swap2 a ^= swap2 << shift2 b |= b << 16 b |= b << 32 const ( shift3 = 12 mask3 = 0b_0000_0000_0000_0000_1111_0000_1111_0000_0000_0000_0000_0000_1111_0000_1111_0000 ) swap3 := (b>>shift3 ^ b) & mask3 b ^= swap3 b ^= swap3 << shift3 const ( shift4 = 24 mask4 = 0b_0000_0000_0000_0000_0000_0000_0000_0000_1111_1111_0000_0000_1111_1111_0000_0000 ) swap4 := (b>>shift4 ^ b) & mask4 b ^= swap4 b ^= swap4 << shift4 c ^= a & b c ^= c >> 32 c ^= c >> 16 return c & (1<<8 - 1) }

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