30-Dec-2022 18:17:44 ubvec_test(): MATLAB/Octave version 4.2.2 Test ubvec() i4vec_print_test(): i4vec_print() prints an I4VEC The I4VEC: 1: 91 2: 92 3: 93 4: 94 ksubset_colex_unrank_test(): ksubset_colex_unrank() unranks K-subsets of an N set, using the colexicographic ordering: The element of rank 5: The element: 1: 5 2: 3 3: 1 ksubset_enum_test(): ksubset_enum() enumerates K-subsets of an N set. K: 0 1 2 3 4 5 N 0: 1 1: 1 1 2: 1 2 1 3: 1 3 3 1 4: 1 4 6 4 1 5: 1 5 10 10 5 1 morse_thue_test(): morse_thue() computes the Morse-Thue numbers. 0110100110 0101101001 0110011010 0110010110 0110100101 1010011001 0110100101 1001101001 0110100110 0101100110 1 nim_sum_test() nim_sum() computes the Nim sum of two integers. I J Nim(I+J) I1, I2, I3 in decimal: 291 624 851 I1, I2, I3 in binary: 11000100100000000000000000000000 00001110010000000000000000000000 11001010110000000000000000000000 I1, I2, I3 in decimal: 646 741 99 I1, I2, I3 in binary: 01100001010000000000000000000000 10100111010000000000000000000000 11000110000000000000000000000000 I1, I2, I3 in decimal: 820 834 118 I1, I2, I3 in binary: 00101100110000000000000000000000 01000010110000000000000000000000 01101110000000000000000000000000 I1, I2, I3 in decimal: 361 975 678 I1, I2, I3 in binary: 10010110100000000000000000000000 11110011110000000000000000000000 01100101010000000000000000000000 I1, I2, I3 in decimal: 490 100 398 I1, I2, I3 in binary: 01010111100000000000000000000000 00100110000000000000000000000000 01110001100000000000000000000000 ubvec_add_test(): ubvec_add() adds unsigned binary vectors representing unsigned integers; I J K = I + J 69 41 Directly: 110 UBVEC_ADD 110 62 18 Directly: 80 UBVEC_ADD 80 10 26 Directly: 36 UBVEC_ADD 36 38 69 Directly: 107 UBVEC_ADD 107 44 92 Directly: 136 UBVEC_ADD 136 27 64 Directly: 91 UBVEC_ADD 91 52 52 Directly: 104 UBVEC_ADD 104 5 60 Directly: 65 UBVEC_ADD 65 50 18 Directly: 68 UBVEC_ADD 68 65 18 Directly: 83 UBVEC_ADD 83 ubvec_and_test() ubvec_and() computes the AND of two unsigned binary vectors representing unsigned integers; I J K = I AND J 30 77 12 74 35 2 75 21 1 83 16 16 36 90 0 55 16 16 69 57 1 94 71 70 10 0 0 30 12 12 ubvec_check_test(): ubvec_check() checks an unsigned binary vector. CHECK? UBVEC value = 0 0: 10011 value = 0 value = 5 5: 10019 value = 0 value = 2 2: 13011 ubvec_complement1_test(): ubvec_complement1() returns the 1's complement of an unsigned binary vector. UBVEC Comp1 01001 10110 01101 10010 00001 11110 00000 11111 01110 10001 ubvec_enum_test(): ubvec_enum() enumerates unsigned binary vectors of N digits N Number 0 1 1 2 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512 10 1024 ubvec_next_test(): ubvec_next() computes the "next" unsigned binary vector. 0000 1000 0100 1100 0010 1010 0110 1110 0001 1001 0101 1101 0011 1011 0111 1111 0000 ubvec_next_gray_test(): ubvec_next_gray() returns the next UBVEC in the Gray code. K UBVEC 0 0 0 0 0 1 0 0 0 1 2 0 0 1 1 3 0 0 1 0 4 0 1 1 0 5 0 1 1 1 6 0 1 0 1 7 0 1 0 0 8 1 1 0 0 9 1 1 0 1 10 1 1 1 1 11 1 1 1 0 12 1 0 1 0 13 1 0 1 1 14 1 0 0 1 15 1 0 0 0 ubvec_next_grlex_test(): ubvec_next_grlex() computes unsigned binary vectors in GRLEX order. 0: 0000 1: 0001 2: 0010 3: 0100 4: 1000 5: 0011 6: 0101 7: 0110 8: 1001 9: 1010 10: 1100 11: 0111 12: 1011 13: 1101 14: 1110 15: 1111 16: 0000 ubvec_or_test(): ubvec_or() computes the OR of two unsigned binary vectors representing unsigned integers; I J K = I OR J 39 1 39 72 15 79 14 90 94 33 89 121 44 84 124 2 27 27 81 27 91 53 53 53 88 55 127 28 16 28 ubvec_print_test(): ubvec_print() prints an unsigned binary vector. UBVEC: 0011101001 ubvec_random_test(): ubvec_random() randomizes an unsigned binary vector. 01011 11011 11001 11001 01011 ubvec_rank_gray_test(): ubvec_rank_gray() ranks a UBVEC in the Gray ordering. UBVEC Rank 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 3 0 0 0 1 1 2 0 0 1 0 0 7 0 0 1 0 1 6 0 0 1 1 0 4 0 0 1 1 1 5 0 1 0 0 0 15 0 1 0 0 1 14 0 1 0 1 0 12 0 1 0 1 1 13 0 1 1 0 0 8 0 1 1 0 1 9 0 1 1 1 0 11 0 1 1 1 1 10 1 0 0 0 0 31 1 0 0 0 1 30 1 0 0 1 0 28 1 0 0 1 1 29 1 0 1 0 0 24 1 0 1 0 1 25 1 0 1 1 0 27 1 0 1 1 1 26 1 1 0 0 0 16 1 1 0 0 1 17 1 1 0 1 0 19 1 1 0 1 1 18 1 1 1 0 0 23 1 1 1 0 1 22 1 1 1 1 0 20 1 1 1 1 1 21 ubvec_reverse_test(): ubvec_reverse() reverses an unsigned binary vector. UBVEC Reversed 01011 11010 00010 01000 10000 00001 01011 11010 01100 00110 ubvec_to_ui4_test(): ubvec_to_ui4() converts an unsigned binary vector to an unsigned integer; UI4 --> UBVEC --> UI4 0 0000000000 0 1 0000000001 1 2 0000000010 2 3 0000000011 3 4 0000000100 4 5 0000000101 5 6 0000000110 6 7 0000000111 7 8 0000001000 8 9 0000001001 9 10 0000001010 10 ubvec_unrank_gray_test(): ubvec_unrank_gray() unranks a UBVEC. Rank UBVEC 0 0 0 0 0 0 1 0 0 0 0 1 2 0 0 0 1 1 3 0 0 0 1 0 4 0 0 1 1 0 5 0 0 1 1 1 6 0 0 1 0 1 7 0 0 1 0 0 8 0 1 1 0 0 9 0 1 1 0 1 10 0 1 1 1 1 11 0 1 1 1 0 12 0 1 0 1 0 13 0 1 0 1 1 14 0 1 0 0 1 15 0 1 0 0 0 16 1 1 0 0 0 17 1 1 0 0 1 18 1 1 0 1 1 19 1 1 0 1 0 20 1 1 1 1 0 21 1 1 1 1 1 22 1 1 1 0 1 23 1 1 1 0 0 24 1 0 1 0 0 25 1 0 1 0 1 26 1 0 1 1 1 27 1 0 1 1 0 28 1 0 0 1 0 29 1 0 0 1 1 30 1 0 0 0 1 31 1 0 0 0 0 ubvec_unrank_grlex_test(): ubvec_unrank_grlex() returns the UBVEC of given rank in the graded lexicographical ordering. -- -------- 0 0 0 0 0 -- -------- 1 0 0 0 1 2 0 0 1 0 3 0 1 0 0 4 1 0 0 0 -- -------- 5 0 0 1 1 6 0 1 0 1 7 0 1 1 0 8 1 0 0 1 9 1 0 1 0 10 1 1 0 0 -- -------- 11 0 1 1 1 12 1 0 1 1 13 1 1 0 1 14 1 1 1 0 -- -------- 15 1 1 1 1 ubvec_xor_test(): ubvec_xor() exclusive-ors unsigned binary vectors representing unsigned integers; I J K = I XOR J 80 99 51 43 13 38 9 40 33 43 51 24 81 25 72 85 98 55 16 42 58 46 48 30 90 65 27 45 90 119 ui4_rank_gray_test(): ui4_rank_gray() ranks a UI4 in the Gray ordering. UI4 Rank (binary) 0 0 0 0 0 0 0 1 1 0 0 0 0 1 2 3 0 0 0 1 0 3 2 0 0 0 1 1 4 7 0 0 1 0 0 5 6 0 0 1 0 1 6 4 0 0 1 1 0 7 5 0 0 1 1 1 8 15 0 1 0 0 0 9 14 0 1 0 0 1 10 12 0 1 0 1 0 11 13 0 1 0 1 1 12 8 0 1 1 0 0 13 9 0 1 1 0 1 14 11 0 1 1 1 0 15 10 0 1 1 1 1 16 31 1 0 0 0 0 17 30 1 0 0 0 1 18 28 1 0 0 1 0 19 29 1 0 0 1 1 20 24 1 0 1 0 0 21 25 1 0 1 0 1 22 27 1 0 1 1 0 23 26 1 0 1 1 1 24 16 1 1 0 0 0 25 17 1 1 0 0 1 26 19 1 1 0 1 0 27 18 1 1 0 1 1 28 23 1 1 1 0 0 29 22 1 1 1 0 1 30 20 1 1 1 1 0 31 21 1 1 1 1 1 ui4_to_ubvec_test(): ui4_to_ubvec() converts an unsigned integer to an unsigned binary vector; I --> BVEC 0 0000000000 1 0000000001 2 0000000010 3 0000000011 4 0000000100 5 0000000101 6 0000000110 7 0000000111 8 0000001000 9 0000001001 10 0000001010 ui4_unrank_gray_test(): ui4_unrank_gray() unranks a Gray code. Rank I (binary) 0 0 0 0 0 0 0 1 1 0 0 0 0 1 2 3 0 0 0 1 1 3 2 0 0 0 1 0 4 6 0 0 1 1 0 5 7 0 0 1 1 1 6 5 0 0 1 0 1 7 4 0 0 1 0 0 8 12 0 1 1 0 0 9 13 0 1 1 0 1 10 15 0 1 1 1 1 11 14 0 1 1 1 0 12 10 0 1 0 1 0 13 11 0 1 0 1 1 14 9 0 1 0 0 1 15 8 0 1 0 0 0 16 24 1 1 0 0 0 17 25 1 1 0 0 1 18 27 1 1 0 1 1 19 26 1 1 0 1 0 20 30 1 1 1 1 0 21 31 1 1 1 1 1 22 29 1 1 1 0 1 23 28 1 1 1 0 0 24 20 1 0 1 0 0 25 21 1 0 1 0 1 26 23 1 0 1 1 1 27 22 1 0 1 1 0 28 18 1 0 0 1 0 29 19 1 0 0 1 1 30 17 1 0 0 0 1 31 16 1 0 0 0 0 ubvec_test(): Normal end of execution. 30-Dec-2022 18:17:44