Initial Query

Disassemble the following python into a function called foo: 2 0 LOAD_CONST 1 (16) 2 STORE_FAST 2 (PH) 4 4 LOAD_CONST 2 (0) 6 STORE_FAST 3 (extra) 5 8 LOAD_CONST 2 (0) 10 STORE_FAST 4 (col) 6 12 BUILD_LIST 0 14 STORE_FAST 5 (pivots) 8 16 LOAD_CONST 3 (<code object <listcomp> at 0x101093660, file "/private/tmp/a.py", line 8>) 18 LOAD_CONST 4 ('rref.<locals>.<listcomp>') 20 MAKE_FUNCTION 0 22 LOAD_GLOBAL 0 (range) 24 LOAD_FAST 0 (matrix) 26 LOAD_ATTR 1 (shape) 28 LOAD_CONST 2 (0) 30 BINARY_SUBSCR 32 CALL_FUNCTION 1 34 GET_ITER 36 CALL_FUNCTION 1 38 STORE_FAST 6 (used_for_row) 10 40 LOAD_FAST 0 (matrix) 42 LOAD_FAST 2 (PH) 44 BINARY_MODULO 46 STORE_FAST 0 (matrix) 11 >> 48 LOAD_FAST 4 (col) 50 LOAD_FAST 3 (extra) 52 BINARY_ADD 54 LOAD_FAST 0 (matrix) 56 LOAD_ATTR 1 (shape) 58 LOAD_CONST 5 (1) 60 BINARY_SUBSCR 62 LOAD_CONST 5 (1) 64 BINARY_SUBTRACT 66 COMPARE_OP 0 (<) 68 EXTENDED_ARG 2 70 POP_JUMP_IF_FALSE 628 72 LOAD_FAST 4 (col) 74 LOAD_FAST 0 (matrix) 76 LOAD_ATTR 1 (shape) 78 LOAD_CONST 2 (0) 80 BINARY_SUBSCR 82 COMPARE_OP 0 (<) 84 EXTENDED_ARG 2 86 POP_JUMP_IF_FALSE 628 13 88 LOAD_FAST 0 (matrix) 90 LOAD_FAST 4 (col) 92 LOAD_FAST 4 (col) 94 LOAD_FAST 3 (extra) 96 BINARY_ADD 98 BUILD_TUPLE 2 100 BINARY_SUBSCR 102 LOAD_CONST 2 (0) 104 COMPARE_OP 2 (==) 106 EXTENDED_ARG 1 108 POP_JUMP_IF_FALSE 262 14 110 LOAD_GLOBAL 2 (np) 112 LOAD_METHOD 3 (all) 114 LOAD_FAST 0 (matrix) 116 LOAD_CONST 0 (None) 118 LOAD_CONST 0 (None) 120 BUILD_SLICE 2 122 LOAD_FAST 4 (col) 124 BUILD_TUPLE 2 126 BINARY_SUBSCR 128 LOAD_CONST 2 (0) 130 COMPARE_OP 2 (==) 132 CALL_METHOD 1 134 POP_JUMP_IF_FALSE 146 15 136 LOAD_FAST 3 (extra) 138 LOAD_CONST 5 (1) 140 INPLACE_ADD 142 STORE_FAST 3 (extra) 16 144 JUMP_ABSOLUTE 48 17 >> 146 LOAD_GLOBAL 2 (np) 148 LOAD_METHOD 4 (argwhere) 150 LOAD_FAST 0 (matrix) 152 LOAD_CONST 0 (None) 154 LOAD_CONST 0 (None) 156 BUILD_SLICE 2 158 LOAD_FAST 4 (col) 160 LOAD_FAST 3 (extra) 162 BINARY_ADD 164 BUILD_TUPLE 2 166 BINARY_SUBSCR 168 LOAD_CONST 2 (0) 170 COMPARE_OP 3 (!=) 172 CALL_METHOD 1 174 LOAD_METHOD 5 (flatten) 176 CALL_METHOD 0 178 LOAD_CONST 6 (-1) 180 BINARY_SUBSCR 182 STORE_FAST 7 (other) 18 184 LOAD_FAST 7 (other) 186 LOAD_FAST 4 (col) 188 COMPARE_OP 0 (<) 190 POP_JUMP_IF_FALSE 202 19 192 LOAD_FAST 3 (extra) 194 LOAD_CONST 5 (1) 196 INPLACE_ADD 198 STORE_FAST 3 (extra) 20 200 JUMP_ABSOLUTE 48 22 >> 202 LOAD_GLOBAL 6 (list) 204 LOAD_FAST 0 (matrix) 206 LOAD_FAST 7 (other) 208 BINARY_SUBSCR 210 CALL_FUNCTION 1 212 LOAD_GLOBAL 6 (list) 214 LOAD_FAST 0 (matrix) 216 LOAD_FAST 4 (col) 218 BINARY_SUBSCR 220 CALL_FUNCTION 1 222 ROT_TWO 224 LOAD_FAST 0 (matrix) 226 LOAD_FAST 4 (col) 228 STORE_SUBSCR 230 LOAD_FAST 0 (matrix) 232 LOAD_FAST 7 (other) 234 STORE_SUBSCR 23 236 LOAD_FAST 6 (used_for_row) 238 LOAD_FAST 7 (other) 240 BINARY_SUBSCR 242 LOAD_FAST 6 (used_for_row) 244 LOAD_FAST 4 (col) 246 BINARY_SUBSCR 248 ROT_TWO 250 LOAD_FAST 6 (used_for_row) 252 LOAD_FAST 4 (col) 254 STORE_SUBSCR 256 LOAD_FAST 6 (used_for_row) 258 LOAD_FAST 7 (other) 260 STORE_SUBSCR 25 >> 262 LOAD_FAST 5 (pivots) 264 LOAD_METHOD 7 (append) 266 LOAD_FAST 4 (col) 268 LOAD_FAST 3 (extra) 270 BINARY_ADD 272 CALL_METHOD 1 274 POP_TOP 26 276 LOAD_FAST 0 (matrix) 278 LOAD_FAST 4 (col) 280 LOAD_FAST 4 (col) 282 LOAD_FAST 3 (extra) 284 BINARY_ADD 286 BUILD_TUPLE 2 288 BINARY_SUBSCR 290 STORE_FAST 8 (pivot) 27 292 LOAD_FAST 4 (col) 294 LOAD_FAST 3 (extra) 296 BINARY_ADD 298 LOAD_FAST 1 (graphlen) 300 COMPARE_OP 0 (<) 302 EXTENDED_ARG 1 304 POP_JUMP_IF_FALSE 348 28 306 LOAD_GLOBAL 2 (np) 308 LOAD_METHOD 8 (abs) 310 LOAD_FAST 8 (pivot) 312 CALL_METHOD 1 314 LOAD_CONST 5 (1) 316 COMPARE_OP 2 (==) 318 EXTENDED_ARG 1 320 POP_JUMP_IF_TRUE 396 322 LOAD_GLOBAL 2 (np) 324 LOAD_METHOD 8 (abs) 326 LOAD_FAST 8 (pivot) 328 CALL_METHOD 1 330 LOAD_FAST 2 (PH) 332 LOAD_CONST 5 (1) 334 BINARY_SUBTRACT 336 COMPARE_OP 2 (==) 338 EXTENDED_ARG 1 340 POP_JUMP_IF_TRUE 396 342 LOAD_ASSERTION_ERROR 344 RAISE_VARARGS 1 346 JUMP_FORWARD 48 (to 396) 30 >> 348 LOAD_GLOBAL 2 (np) 350 LOAD_METHOD 8 (abs) 352 LOAD_FAST 8 (pivot) 354 CALL_METHOD 1 356 LOAD_CONST 7 (2) 358 COMPARE_OP 2 (==) 360 EXTENDED_ARG 1 362 POP_JUMP_IF_TRUE 388 364 LOAD_GLOBAL 2 (np) 366 LOAD_METHOD 8 (abs) 368 LOAD_FAST 8 (pivot) 370 CALL_METHOD 1 372 LOAD_FAST 2 (PH) 374 LOAD_CONST 7 (2) 376 BINARY_SUBTRACT 378 COMPARE_OP 2 (==) 380 EXTENDED_ARG 1 382 POP_JUMP_IF_TRUE 388 384 LOAD_ASSERTION_ERROR 386 RAISE_VARARGS 1 31 >> 388 LOAD_FAST 8 (pivot) 390 LOAD_CONST 7 (2) 392 INPLACE_FLOOR_DIVIDE 394 STORE_FAST 8 (pivot) 32 >> 396 LOAD_FAST 0 (matrix) 398 LOAD_FAST 4 (col) 400 DUP_TOP_TWO 402 BINARY_SUBSCR 404 LOAD_FAST 8 (pivot) 406 INPLACE_MULTIPLY 408 ROT_THREE 410 STORE_SUBSCR 33 412 LOAD_FAST 0 (matrix) 414 LOAD_FAST 4 (col) 416 DUP_TOP_TWO 418 BINARY_SUBSCR 420 LOAD_FAST 2 (PH) 422 INPLACE_MODULO 424 ROT_THREE 426 STORE_SUBSCR 35 428 LOAD_GLOBAL 2 (np) 430 LOAD_METHOD 4 (argwhere) 432 LOAD_FAST 0 (matrix) 434 LOAD_CONST 0 (None) 436 LOAD_CONST 0 (None) 438 BUILD_SLICE 2 440 LOAD_FAST 4 (col) 442 LOAD_FAST 3 (extra) 444 BINARY_ADD 446 BUILD_TUPLE 2 448 BINARY_SUBSCR 450 CALL_METHOD 1 452 LOAD_METHOD 5 (flatten) 454 CALL_METHOD 0 456 STORE_FAST 9 (others) 37 458 LOAD_FAST 9 (others) 460 GET_ITER >> 462 FOR_ITER 154 (to 618) 464 STORE_FAST 10 (i) 38 466 LOAD_FAST 10 (i) 468 LOAD_FAST 4 (col) 470 COMPARE_OP 2 (==) 472 EXTENDED_ARG 1 474 POP_JUMP_IF_FALSE 480 476 EXTENDED_ARG 1 478 JUMP_ABSOLUTE 462 39 >> 480 LOAD_FAST 6 (used_for_row) 482 LOAD_FAST 10 (i) 484 DUP_TOP_TWO 486 BINARY_SUBSCR 488 LOAD_FAST 6 (used_for_row) 490 LOAD_FAST 4 (col) 492 BINARY_SUBSCR 494 INPLACE_OR 496 ROT_THREE 498 STORE_SUBSCR 40 500 LOAD_FAST 4 (col) 502 LOAD_FAST 1 (graphlen) 504 COMPARE_OP 0 (<) 506 EXTENDED_ARG 2 508 POP_JUMP_IF_FALSE 548 41 510 LOAD_FAST 0 (matrix) 512 LOAD_FAST 10 (i) 514 DUP_TOP_TWO 516 BINARY_SUBSCR 518 LOAD_FAST 0 (matrix) 520 LOAD_FAST 4 (col) 522 BINARY_SUBSCR 524 LOAD_FAST 0 (matrix) 526 LOAD_FAST 10 (i) 528 LOAD_FAST 4 (col) 530 LOAD_FAST 3 (extra) 532 BINARY_ADD 534 BUILD_TUPLE 2 536 BINARY_SUBSCR 538 BINARY_MULTIPLY 540 INPLACE_SUBTRACT 542 ROT_THREE 544 STORE_SUBSCR 546 JUMP_FORWARD 50 (to 598) 43 >> 548 LOAD_FAST 0 (matrix) 550 LOAD_FAST 10 (i) 552 LOAD_FAST 4 (col) 554 LOAD_FAST 3 (extra) 556 BINARY_ADD 558 BUILD_TUPLE 2 560 BINARY_SUBSCR 562 LOAD_CONST 2 (0) 564 COMPARE_OP 3 (!=) 566 EXTENDED_ARG 2 568 POP_JUMP_IF_FALSE 598 44 570 LOAD_FAST 0 (matrix) 572 LOAD_FAST 10 (i) 574 BINARY_SUBSCR 576 LOAD_FAST 0 (matrix) 578 LOAD_FAST 4 (col) 580 BINARY_SUBSCR 582 BINARY_SUBTRACT 584 LOAD_FAST 2 (PH) 586 BINARY_MODULO 588 LOAD_FAST 0 (matrix) 590 LOAD_FAST 10 (i) 592 STORE_SUBSCR 594 EXTENDED_ARG 2 596 JUMP_ABSOLUTE 548 45 >> 598 LOAD_FAST 0 (matrix) 600 LOAD_FAST 10 (i) 602 DUP_TOP_TWO 604 BINARY_SUBSCR 606 LOAD_FAST 2 (PH) 608 INPLACE_MODULO 610 ROT_THREE 612 STORE_SUBSCR 614 EXTENDED_ARG 1 616 JUMP_ABSOLUTE 462 47 >> 618 LOAD_FAST 4 (col) 620 LOAD_CONST 5 (1) 622 INPLACE_ADD 624 STORE_FAST 4 (col) 626 JUMP_ABSOLUTE 48 49 >> 628 LOAD_GLOBAL 2 (np) 630 LOAD_METHOD 9 (array) 632 LOAD_FAST 0 (matrix) 634 CALL_METHOD 1 636 LOAD_FAST 2 (PH) 638 BINARY_MODULO 640 STORE_FAST 0 (matrix) 50 642 LOAD_CONST 8 (<code object <listcomp> at 0x101093b30, file "/private/tmp/a.py", line 50>) 644 LOAD_CONST 4 ('rref.<locals>.<listcomp>') 646 MAKE_FUNCTION 0 648 LOAD_FAST 6 (used_for_row) 650 GET_ITER 652 CALL_FUNCTION 1 654 RETURN_VALUE Disassembly of <code object <listcomp> at 0x101093660, file "/private/tmp/a.py", line 8>: 8 0 BUILD_LIST 0 2 LOAD_FAST 0 (.0) >> 4 FOR_ITER 14 (to 20) 6 STORE_FAST 1 (i) 8 LOAD_GLOBAL 0 (set) 10 LOAD_FAST 1 (i) 12 BUILD_LIST 1 14 CALL_FUNCTION 1 16 LIST_APPEND 2 18 JUMP_ABSOLUTE 4 >> 20 RETURN_VALUE Disassembly of <code object <listcomp> at 0x101093b30, file "/private/tmp/a.py", line 50>: 50 0 BUILD_LIST 0 2 LOAD_FAST 0 (.0) >> 4 FOR_ITER 12 (to 18) 6 STORE_FAST 1 (x) 8 LOAD_GLOBAL 0 (sorted) 10 LOAD_FAST 1 (x) 12 CALL_FUNCTION 1 14 LIST_APPEND 2 16 JUMP_ABSOLUTE 4 >> 18 RETURN_VALUE

LLM Generation

Query

Output

Below is one acceptable â€œreâ€assemblyâ€ of the bytecode into a Python function named foo. (Note that several choices of variable names and minor details are possible. This version is written so that its controlâ€flow and operations mirror the disassembled code.) Also note that the code assumes that numpy has been imported as â€œnp.â€ ------------------------------------------------------------ # For example, at the top of your module: import numpy as np def foo(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] # Build a â€œused_for_rowâ€ list where each row starts with its own index used_for_row = [set([i]) for i in range(matrix.shape[0])] # Work modulo PH matrix = matrix % PH # The main loop continues while we have room in the matrix. # (The condition corresponds to: (col+extra) < (number_of_columns-1) and col < number_of_rows.) while (col + extra < matrix.shape[1] - 1) and (col < matrix.shape[0]): # If the candidate pivot is zero... if matrix[col, col + extra] == 0: # If the entire column (at index col) is zero, then we â€œskipâ€ one extra column. if np.all(matrix[:, col] == 0): extra += 1 continue else: # Otherwise, search for a nonzero entry in column (col+extra) (using argwhere) # and choose the last such index. other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1] # If that candidate row lies above the current pivot row then skip extra. if other < col: extra += 1 continue # Otherwise swap the current row with the â€œotherâ€ row. matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] # Register the pivot position. pivots.append(col + extra) pivot = matrix[col, col + extra] # Depending on whether we are in the first part of the matrix or not, # check that the pivot has the expected â€œsmallâ€ absolute value. if (col + extra) < graphlen: if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1): raise AssertionError("Pivot (in first block) must be Â±1 modulo PH") else: if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2): raise AssertionError("Pivot (in second block) must be Â±2 modulo PH") # In the second block, we â€œnormalizeâ€ the pivot by integerâ€dividing by 2 pivot //= 2 # Multiply the pivot by itself and reduce modulo PH. # (This evidently normalizes the pivot row.) matrix[col][col + extra] *= pivot matrix[col][col + extra] %= PH # Find all row indices where the current pivot column (col+extra) is nonzero. others = np.argwhere(matrix[:, col + extra]).flatten() for i in others: # Skip the pivot row itself. if i == col: continue # Record that row i now â€œcomes fromâ€ the pivot row. used_for_row[i] |= used_for_row[col] # Do different row operations depending on which â€œblockâ€ we are in. if col < graphlen: # For rows in the first block, subtract a multiple of the pivot row so that # matrix[i, col+extra] becomes zero. matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH elif matrix[i, col + extra] != 0: # In the second block, if the entry is nonzero, subtract the pivot row. matrix[i] = (matrix[i] - matrix[col]) % PH else: # Either way, impose the modulo reduction. matrix[i] %= PH # Move on to the next row. col += 1 # At the end, ensure the matrix is a numpy array modulo PH. matrix = np.array(matrix) % PH # Finally, return the â€œused_for_rowâ€ record for each row, with each set sorted. return [sorted(x) for x in used_for_row] ------------------------------------------------------------ Explanation of key parts: 1. The variable PH is set to 16. The â€œextraâ€ counter allows the algorithm to skip a column if the pivot candidate is 0. 2. The list comprehension builds used_for_row so that each row â€œremembersâ€ its original index. 3. The whileâ€loop continues until (col+extra) is too high to be within the matrixâ€™s columns or we run out of rows. 4. When the candidate pivot is zero, the code either increments extra (if the entire column is zero) or swaps the row with a lower row that has a nonzero entry. 5. Depending on whether the working column is before graphlen or not, the pivot is expected to be Â±1 (mod PH) or Â±2 (mod PH) and normalized accordingly. 6. Then standard elimination is performed on â€œotherâ€ rows (those with nonzero entry in the pivot column) and results are reduced modulo PH. 7. Finally, the function returns the list of â€œused_for_rowâ€ sets, each sorted. This function should capture (in one acceptable form) the behavior described by the disassembled bytecode.

Extract Code

I extracted the following code from that output:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Build a â€œused_for_rowâ€ list where each row starts with its own index
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work modulo PH
    matrix = matrix % PH
    
    # The main loop continues while we have room in the matrix.
    # (The condition corresponds to: (col+extra) < (number_of_columns-1) and col < number_of_rows.)
    while (col + extra < matrix.shape[1] - 1) and (col < matrix.shape[0]):
        # If the candidate pivot is zero...
        if matrix[col, col + extra] == 0:
            # If the entire column (at index col) is zero, then we â€œskipâ€ one extra column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            else:
                # Otherwise, search for a nonzero entry in column (col+extra) (using argwhere)
                # and choose the last such index.
                other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
                # If that candidate row lies above the current pivot row then skip extra.
                if other < col:
                    extra += 1
                    continue
                # Otherwise swap the current row with the â€œotherâ€ row.
                matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
                used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Register the pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Depending on whether we are in the first part of the matrix or not,
        # check that the pivot has the expected â€œsmallâ€ absolute value.
        if (col + extra) < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot (in first block) must be Â±1 modulo PH")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot (in second block) must be Â±2 modulo PH")
            # In the second block, we â€œnormalizeâ€ the pivot by integerâ€dividing by 2
            pivot //= 2
        
        # Multiply the pivot by itself and reduce modulo PH.
        # (This evidently normalizes the pivot row.)
        matrix[col][col + extra] *= pivot
        matrix[col][col + extra] %= PH
        
        # Find all row indices where the current pivot column (col+extra) is nonzero.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            # Skip the pivot row itself.
            if i == col:
                continue
            # Record that row i now â€œcomes fromâ€ the pivot row.
            used_for_row[i] |= used_for_row[col]
            # Do different row operations depending on which â€œblockâ€ we are in.
            if col < graphlen:
                # For rows in the first block, subtract a multiple of the pivot row so that
                # matrix[i, col+extra] becomes zero.
                matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH
            elif matrix[i, col + extra] != 0:
                # In the second block, if the entry is nonzero, subtract the pivot row.
                matrix[i] = (matrix[i] - matrix[col]) % PH
            else:
                # Either way, impose the modulo reduction.
                matrix[i] %= PH
        
        # Move on to the next row.
        col += 1
    
    # At the end, ensure the matrix is a numpy array modulo PH.
    matrix = np.array(matrix) % PH
    
    # Finally, return the â€œused_for_rowâ€ record for each row, with each set sorted.
    return [sorted(x) for x in used_for_row]

Run Code Interpreter

Running the following program:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Build a â€œused_for_rowâ€ list where each row starts with its own index
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work modulo PH
    matrix = matrix % PH
    
    # The main loop continues while we have room in the matrix.
    # (The condition corresponds to: (col+extra) < (number_of_columns-1) and col < number_of_rows.)
    while (col + extra < matrix.shape[1] - 1) and (col < matrix.shape[0]):
        # If the candidate pivot is zero...
        if matrix[col, col + extra] == 0:
            # If the entire column (at index col) is zero, then we â€œskipâ€ one extra column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            else:
                # Otherwise, search for a nonzero entry in column (col+extra) (using argwhere)
                # and choose the last such index.
                other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
                # If that candidate row lies above the current pivot row then skip extra.
                if other < col:
                    extra += 1
                    continue
                # Otherwise swap the current row with the â€œotherâ€ row.
                matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
                used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Register the pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Depending on whether we are in the first part of the matrix or not,
        # check that the pivot has the expected â€œsmallâ€ absolute value.
        if (col + extra) < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot (in first block) must be Â±1 modulo PH")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot (in second block) must be Â±2 modulo PH")
            # In the second block, we â€œnormalizeâ€ the pivot by integerâ€dividing by 2
            pivot //= 2
        
        # Multiply the pivot by itself and reduce modulo PH.
        # (This evidently normalizes the pivot row.)
        matrix[col][col + extra] *= pivot
        matrix[col][col + extra] %= PH
        
        # Find all row indices where the current pivot column (col+extra) is nonzero.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            # Skip the pivot row itself.
            if i == col:
                continue
            # Record that row i now â€œcomes fromâ€ the pivot row.
            used_for_row[i] |= used_for_row[col]
            # Do different row operations depending on which â€œblockâ€ we are in.
            if col < graphlen:
                # For rows in the first block, subtract a multiple of the pivot row so that
                # matrix[i, col+extra] becomes zero.
                matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH
            elif matrix[i, col + extra] != 0:
                # In the second block, if the entry is nonzero, subtract the pivot row.
                matrix[i] = (matrix[i] - matrix[col]) % PH
            else:
                # Either way, impose the modulo reduction.
                matrix[i] %= PH
        
        # Move on to the next row.
        col += 1
    
    # At the end, ensure the matrix is a numpy array modulo PH.
    matrix = np.array(matrix) % PH
    
    # Finally, return the â€œused_for_rowâ€ record for each row, with each set sorted.
    return [sorted(x) for x in used_for_row]


arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = foo(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')

And got the output:

Traceback (most recent call last):
  File "/usr/src/app/main.py", line 87, in <module>
    answer = foo(arr, 37)
             ^^^^^^^^^^^^
  File "/usr/src/app/main.py", line 46, in foo
    raise AssertionError("Pivot (in second block) must be Â±2 modulo PH")
AssertionError: Pivot (in second block) must be Â±2 modulo PH

Substring Evaluation

Testing if the previous output contains the string All tests passed: False

Initial Query

LLM Generation

Query

Output

Below is one acceptable â€œreconstructionâ€ of the original byteâ€code as a function called foo. (Note that the exact source isnâ€™t uniquely determined by the byteâ€‘code so the following is one highâ€“level equivalent version that uses NumPy; you may need to adjust naming or details to suit your application.) â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ # For example: import numpy as np def foo(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] # Create a â€œused_for_rowâ€ list so that each row i initially â€œcontainsâ€ the set {i} used_for_row = [set([i]) for i in range(matrix.shape[0])] # Work with the entries modulo PH. matrix = matrix % PH # Loop while there are still columns available. while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]: # If our pivot candidate is zero, then check if the entire column is zero. if matrix[col, col + extra] == 0: # If so, simply skip (i.e. increment extra) for this column. if np.all(matrix[:, col] == 0): extra += 1 continue # Otherwise, search for a nonzero entry in the same â€œpivotâ€columnâ€ # (selecting the last such index from np.argwhere). other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1] # If the found row is â€œaboveâ€ the current row, then skip this column. if other < col: extra += 1 continue # Otherwise, swap the current row and the row â€œother.â€ # (Here we cast the row slices to lists so that assignment works as expected.) matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] # Record pivot position. pivots.append(col + extra) pivot = matrix[col, col + extra] # Normalize the pivot. In the first â€œgraphlenâ€ columns a valid pivot must be congruent (in absolute value) # to 1 modulo PH; in later columns it must be â‰¡2 (or PHâ€“2) so that later we divide by 2. if col + extra < graphlen: if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1): raise AssertionError("Pivot value not 1 or -1 in first graphlen columns") else: if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2): raise AssertionError("Pivot value not 2 or -2 in later columns") pivot //= 2 # Multiply the pivot entry by itself (this â€œnormalizesâ€ that entry) # and ensure that the first entry in the row is reduced modulo PH. matrix[col, col + extra] *= pivot matrix[col, col] %= PH # Now eliminate nonzero entries in the current pivot column. others = np.argwhere(matrix[:, col + extra]).flatten() for i in others: if i == col: continue # Merge the sets of rows that contributed to the pivot. used_for_row[i] |= used_for_row[col] # In the â€œgraphlenâ€ part of the matrix, use the pivot column entry to cancel. if col < graphlen: matrix[i] = (matrix[i] - matrix[i, col] * np.array(matrix[col])) % PH # Otherwise, if the entry is nonzero then subtract and reduce modulo PH. elif matrix[i, col + extra] != 0: matrix[i] = (np.array(matrix[i]) - matrix[i, col]) % PH matrix[i] %= PH col += 1 # Finally, convert the result to a NumPy array (again reducing modulo PH) matrix = np.array(matrix) % PH # Return the â€œused_for_rowâ€ list with each set converted to a sorted list. return [sorted(x) for x in used_for_row] â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ Explanatory notes: 1. The constant PH is set to 16. 2. The variable extra allows the algorithm to â€œskipâ€ columns that do not yield a good pivot. 3. The list used_for_row starts with each row i â€œmarkedâ€ by {i} then is updated every time rows are swapped or combined. 4. The loop stops when col+extra reaches matrix.shape[1]â€“1 (so that there is a â€œrightâ€“hand sideâ€) or when there are no more rows. 5. Two listâ€“comprehensions appear (one for used_for_row and one in the return statement) which match the disassembled listâ€“comps. This is one valid reconstruction of the given disassembled python byteâ€“code.

Extract Code

I extracted the following code from that output:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Create a â€œused_for_rowâ€ list so that each row i initially â€œcontainsâ€ the set {i}
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work with the entries modulo PH.
    matrix = matrix % PH

    # Loop while there are still columns available.
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # If our pivot candidate is zero, then check if the entire column is zero.
        if matrix[col, col + extra] == 0:
            # If so, simply skip (i.e. increment extra) for this column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            # Otherwise, search for a nonzero entry in the same â€œpivotâ€columnâ€
            # (selecting the last such index from np.argwhere).
            other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
            # If the found row is â€œaboveâ€ the current row, then skip this column.
            if other < col:
                extra += 1
                continue
            # Otherwise, swap the current row and the row â€œother.â€
            # (Here we cast the row slices to lists so that assignment works as expected.)
            matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
            used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Record pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Normalize the pivot. In the first â€œgraphlenâ€ columns a valid pivot must be congruent (in absolute value)
        # to 1 modulo PH; in later columns it must be â‰¡2 (or PHâ€“2) so that later we divide by 2.
        if col + extra < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot value not 1 or -1 in first graphlen columns")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot value not 2 or -2 in later columns")
            pivot //= 2
        
        # Multiply the pivot entry by itself (this â€œnormalizesâ€ that entry)
        # and ensure that the first entry in the row is reduced modulo PH.
        matrix[col, col + extra] *= pivot
        matrix[col, col] %= PH

        # Now eliminate nonzero entries in the current pivot column.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            if i == col:
                continue
            # Merge the sets of rows that contributed to the pivot.
            used_for_row[i] |= used_for_row[col]
            # In the â€œgraphlenâ€ part of the matrix, use the pivot column entry to cancel.
            if col < graphlen:
                matrix[i] = (matrix[i] - matrix[i, col] * np.array(matrix[col])) % PH
            # Otherwise, if the entry is nonzero then subtract and reduce modulo PH.
            elif matrix[i, col + extra] != 0:
                matrix[i] = (np.array(matrix[i]) - matrix[i, col]) % PH
                matrix[i] %= PH

        col += 1

    # Finally, convert the result to a NumPy array (again reducing modulo PH)
    matrix = np.array(matrix) % PH
    # Return the â€œused_for_rowâ€ list with each set converted to a sorted list.
    return [sorted(x) for x in used_for_row]

Run Code Interpreter

Running the following program:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Create a â€œused_for_rowâ€ list so that each row i initially â€œcontainsâ€ the set {i}
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work with the entries modulo PH.
    matrix = matrix % PH

    # Loop while there are still columns available.
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # If our pivot candidate is zero, then check if the entire column is zero.
        if matrix[col, col + extra] == 0:
            # If so, simply skip (i.e. increment extra) for this column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            # Otherwise, search for a nonzero entry in the same â€œpivotâ€columnâ€
            # (selecting the last such index from np.argwhere).
            other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
            # If the found row is â€œaboveâ€ the current row, then skip this column.
            if other < col:
                extra += 1
                continue
            # Otherwise, swap the current row and the row â€œother.â€
            # (Here we cast the row slices to lists so that assignment works as expected.)
            matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
            used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Record pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Normalize the pivot. In the first â€œgraphlenâ€ columns a valid pivot must be congruent (in absolute value)
        # to 1 modulo PH; in later columns it must be â‰¡2 (or PHâ€“2) so that later we divide by 2.
        if col + extra < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot value not 1 or -1 in first graphlen columns")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot value not 2 or -2 in later columns")
            pivot //= 2
        
        # Multiply the pivot entry by itself (this â€œnormalizesâ€ that entry)
        # and ensure that the first entry in the row is reduced modulo PH.
        matrix[col, col + extra] *= pivot
        matrix[col, col] %= PH

        # Now eliminate nonzero entries in the current pivot column.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            if i == col:
                continue
            # Merge the sets of rows that contributed to the pivot.
            used_for_row[i] |= used_for_row[col]
            # In the â€œgraphlenâ€ part of the matrix, use the pivot column entry to cancel.
            if col < graphlen:
                matrix[i] = (matrix[i] - matrix[i, col] * np.array(matrix[col])) % PH
            # Otherwise, if the entry is nonzero then subtract and reduce modulo PH.
            elif matrix[i, col + extra] != 0:
                matrix[i] = (np.array(matrix[i]) - matrix[i, col]) % PH
                matrix[i] %= PH

        col += 1

    # Finally, convert the result to a NumPy array (again reducing modulo PH)
    matrix = np.array(matrix) % PH
    # Return the â€œused_for_rowâ€ list with each set converted to a sorted list.
    return [sorted(x) for x in used_for_row]


arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = foo(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')

And got the output:

Traceback (most recent call last):
  File "/usr/src/app/main.py", line 78, in <module>
    answer = foo(arr, 37)
             ^^^^^^^^^^^^
  File "/usr/src/app/main.py", line 45, in foo
    raise AssertionError("Pivot value not 2 or -2 in later columns")
AssertionError: Pivot value not 2 or -2 in later columns

Substring Evaluation

Testing if the previous output contains the string All tests passed: False