Ticket #3376: m4ri_strassen_standard.patch

File m4ri_strassen_standard.patch, 16.6 kB (added by malb, 5 months ago)

a/sage/matrix/matrix_mod2_dense.pxd

old	new
10	10	int width
11	11	int *rowswap
12	12
	13	ctypedef struct permutation:
	14	int *values
	15	int size
13	16
14	17	ctypedef int BIT
15	18
…	…
63	66	# set BIT
64	67	cdef void mzd_write_bit( packedmatrix *m, int row, int col, BIT value)
65	68
	69	cdef void mzd_write_zeroed_bits(packedmatrix *m, int x, int y, int n, word values)
	70
	71	cdef void mzd_clear_bits(packedmatrix *m, int x, int y, int n)
	72
66	73	# get BIT
67	74	cdef BIT mzd_read_bit( packedmatrix *m, int row, int col )
	75
	76	# get BITs (n<=64)
	77	cdef word mzd_read_bits( packedmatrix *m, int row, int col, int n)
	78
68	79
69	80	######################
70	81	# Low-Level Arithmetic
…	…
77	88	cdef void mzd_row_clear_offset(packedmatrix *m, int, int)
78	89
79	90	cdef void mzd_row_add_offset(packedmatrix *m, int, int, int)
	91
	92	cdef permutation mzd_col_block_rotate(packedmatrix M, int ,int, int, int, permutation *)
80	93
81	94	############
82	95	# Arithmetic
…	…
98	111	cdef packedmatrix mzd_addmul_m4rm(packedmatrix , packedmatrix , packedmatrix , int k)
99	112
100	113	# matrix multiplication via Strassen's formula
101		cdef packedmatrix mzd_mul~~_strassen~~(packedmatrix , packedmatrix , packedmatrix , int cutoff)
	114	cdef packedmatrix mzd_mul(packedmatrix , packedmatrix , packedmatrix , int cutoff)
102	115
103	116	# C = C + AB via Strassen's formula
104		cdef packedmatrix mzd_addmul~~_strassen~~(packedmatrix , packedmatrix , packedmatrix , int cutoff)
	117	cdef packedmatrix mzd_addmul(packedmatrix , packedmatrix , packedmatrix , int cutoff)
105	118
106	119	# equality testing
107	120	cdef int mzd_equal(packedmatrix , packedmatrix )
…	…
133	146	cdef object _zero
134	147
135	148
136		cdef Matrix_mod2_dense _multiply_m4rm_c(Matrix_mod2_dense self, Matrix_mod2_dense right, int k)
	149	cpdef Matrix_mod2_dense _multiply_m4rm(Matrix_mod2_dense self, Matrix_mod2_dense right, int k)
	150	cpdef Matrix_mod2_dense _multiply_strassen(Matrix_mod2_dense self, Matrix_mod2_dense right, int cutoff)

a/sage/matrix/matrix_mod2_dense.pyx

old	new
391	391	verbose('matrix multiply of %s x %s matrix by %s x %s matrix'%(
392	392	self._nrows, self._ncols, right._nrows, right._ncols))
393	393
394		cdef int n = self._ncols
395		return self._multiply_m4rm_c(right,0)
	394	return self._multiply_strassen(right, 0)
396	395
397		~~def _multiply_m4rm(Matrix_mod2_dense self, Matrix_mod2_dense right, k=0, transpose=False~~):
	396	cpdef Matrix_mod2_dense _multiply_m4rm(Matrix_mod2_dense self, Matrix_mod2_dense right, int k):
398	397	"""
399	398	Multiply matrices using the 'Method of the Four Russians
400	399	Multiplication' (M4RM) or Konrod's method.
…	…
422	421	[0 0 1 0]
423	422	[1 0 0 1]
424	423	[1 1 0 0]
425		sage: A._multiply_m4rm(B)
	424	sage: A._multiply_m4rm(B, 0)
426	425	[0 0 0 0]
427	426	[1 0 0 1]
428	427	[0 1 0 1]
429	428	[1 1 0 0]
	429
	430	TESTS:
	431	sage: A = random_matrix(GF(2),0,0)
	432	sage: B = random_matrix(GF(2),0,0)
	433	sage: A._multiply_m4rm(B, 0)
	434	[]
	435	sage: A = random_matrix(GF(2),3,0)
	436	sage: B = random_matrix(GF(2),0,3)
	437	sage: A._multiply_m4rm(B, 0)
	438	[0 0 0]
	439	[0 0 0]
	440	[0 0 0]
	441	sage: A = random_matrix(GF(2),0,3)
	442	sage: B = random_matrix(GF(2),3,0)
	443	sage: A._multiply_m4rm(B, 0)
	444	[]
430	445
431	446	ALGORITHM: Uses the 'Method of the Four Russians'
432	447	multiplication as implemented in the M4RI library.
…	…
452	467	if self._ncols != right._nrows:
453	468	raise ArithmeticError, "left ncols must match right nrows"
454	469
455		~~return self._multiply_m4rm_c(right, 0)~~
456
457		~~cdef Matrix_mod2_dense _multiply_m4rm_c(Matrix_mod2_dense self, Matrix_mod2_dense right, int k):~~
458		~~"""~~
459		~~TESTS:~~
460		~~sage: A = random_matrix(GF(2),0,0)~~
461		~~sage: B = random_matrix(GF(2),0,0)~~
462		~~sage: A._multiply_m4rm(B)~~
463		[]
464		~~sage: A = random_matrix(GF(2),3,0)~~
465		~~sage: B = random_matrix(GF(2),0,3)~~
466		~~sage: A._multiply_m4rm(B)~~
467		~~[0 0 0]~~
468		~~[0 0 0]~~
469		~~[0 0 0]~~
470		~~sage: A = random_matrix(GF(2),0,3)~~
471		~~sage: B = random_matrix(GF(2),3,0)~~
472		~~sage: A._multiply_m4rm(B)~~
473		[]
474		~~"""~~
475	470	if get_verbose() >= 2:
476	471	verbose('m4rm multiply of %s x %s matrix by %s x %s matrix'%(
477	472	self._nrows, self._ncols, right._nrows, right._ncols))
…	…
485	480	ans._entries = mzd_mul_m4rm(ans._entries, self._entries, right._entries, k)
486	481	_sig_off
487	482	return ans
488
489	483
490	484	def _multiply_classical(Matrix_mod2_dense self, Matrix_mod2_dense right):
491	485	r"""
…	…
536	530	A._entries = mzd_mul_naiv(A._entries, self._entries,(<Matrix_mod2_dense>right)._entries)
537	531	return A
538	532
539		~~def _multiply_strassen(self, Matrix_mod2_dense right, cutoff=2048~~):
	533	cpdef Matrix_mod2_dense _multiply_strassen(Matrix_mod2_dense self, Matrix_mod2_dense right, int cutoff):
540	534	"""
541	535	Strassen-Winograd $O(n^{2.807})$ multiplication [Str69].
542	536
…	…
554	548	INPUT:
555	549	right -- a matrix of matching dimensions.
556	550	cutoff -- matrix dimension where M4RM should be used
557		instead of Strassen (default: ~~2048~~)
	551	instead of Strassen (default: let M4RI decide)
558	552
559	553	EXAMPLE:
560	554	sage: A = Matrix(GF(2), 4, 3, [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1] )
…	…
568	562	[0 0 1 0]
569	563	[1 0 0 1]
570	564	[1 1 0 0]
571		sage: A._multiply_strassen(B)
	565	sage: A._multiply_strassen(B, 0)
572	566	[0 0 0 0]
573	567	[1 0 0 1]
574	568	[0 1 0 1]
575	569	[1 1 0 0]
576	570	sage: A = random_matrix(GF(2),2701,3000)
577	571	sage: B = random_matrix(GF(2),3000,3172)
578		sage: A._multiply_strassen(B, ~~cutoff=1024) == A._multiply_m4rm(B~~)
	572	sage: A._multiply_strassen(B, 256) == A._multiply_m4rm(B, 0)
579	573	True
580	574
581	575	TESTS:
582	576	sage: A = random_matrix(GF(2),0,0)
583	577	sage: B = random_matrix(GF(2),0,0)
584		sage: A._multiply_strassen(B)
	578	sage: A._multiply_strassen(B, 0)
585	579	[]
586	580	sage: A = random_matrix(GF(2),3,0)
587	581	sage: B = random_matrix(GF(2),0,3)
588		sage: A._multiply_strassen(B)
	582	sage: A._multiply_strassen(B, 0)
589	583	[0 0 0]
590	584	[0 0 0]
591	585	[0 0 0]
592	586	sage: A = random_matrix(GF(2),0,3)
593	587	sage: B = random_matrix(GF(2),3,0)
594		sage: A._multiply_strassen(B)
	588	sage: A._multiply_strassen(B, 0)
595	589	[]
596	590
597	591	ALGORITHM: Uses Strassen-Winograd matrix multiplication with
…	…
616	610	ans = self.new_matrix(nrows = self.nrows(), ncols = right.ncols())
617	611	if self._nrows == 0 or self._ncols == 0 or right._ncols == 0:
618	612	return ans
	613
619	614	_sig_on
620		ans._entries = mzd_mul~~_strassen~~(ans._entries, self._entries, right._entries, cutoff)
	615	ans._entries = mzd_mul(ans._entries, self._entries, right._entries, cutoff)
621	616	_sig_off
622	617	return ans
623	618
…	…
1007	1002	[0 1 1]
1008	1003	[0 0 0]
1009	1004	sage: A.swap_columns(0,1); A
	1005	[1 0 0]
	1006	[1 0 1]
	1007	[0 0 0]
1010	1008	"""
1011	1009	mzd_col_swap(self._entries, col1, col2)
1012	1010
…	…
1394	1392	gdImagePng(im, out)
1395	1393	gdImageDestroy(im)
1396	1394	fclose(out)
	1395
	1396
	1397
	1398
	1399	# This is basically test code, do not call it will break Sage's
	1400	# assumptions about matrices (malb).
	1401
	1402	def _read_bits(Matrix_mod2_dense A, int x, int y, int n):
	1403	return mzd_read_bits(A._entries, x, y, n)
	1404
	1405	def _write_zeroed_bits(Matrix_mod2_dense A, int x, int y, int n, unsigned long values):
	1406	"""
	1407	EXAMPLE:
	1408	sage: A = matrix(GF(2),4,66)
	1409	sage: sage.matrix.matrix_mod2_dense._write_zeroed_bits(A,0,0,4,13)
	1410	sage: print A.str()
	1411	[1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1412	[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1413	[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1414	[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1415	sage: ZZ(sage.matrix.matrix_mod2_dense._read_bits(A,0,0,4))
	1416	13
	1417
	1418	sage: sage.matrix.matrix_mod2_dense._write_zeroed_bits(A,1,1,4,13)
	1419	sage: print A.str()
	1420	[1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1421	[0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1422	[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1423	[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1424	sage: ZZ(sage.matrix.matrix_mod2_dense._read_bits(A,1,1,4))
	1425	13
	1426
	1427	sage: sage.matrix.matrix_mod2_dense._write_zeroed_bits(A,2,0,64,2^63 + 2^62 + 1)
	1428	sage: print A.str()
	1429	[1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1430	[0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1431	[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 0 0 0 0 0 0 0 0 0 0 1 0 0]
	1432	[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1433	sage: ZZ(sage.matrix.matrix_mod2_dense._read_bits(A,2,0,64))
	1434	13835058055282163713
	1435
	1436	sage: sage.matrix.matrix_mod2_dense._write_zeroed_bits(A,3,1,64,2^63 + 2^62 + 1)
	1437	sage: print A.str()
	1438	[1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1439	[0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
	1440	[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 0 0 0 0 0 0 0 0 0 0 1 0 0]
	1441	[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 0 0 0 0 0 0 0 0 0 0 1 0]
	1442	sage: ZZ(sage.matrix.matrix_mod2_dense._read_bits(A,3,1,64))
	1443	13835058055282163713
	1444	"""
	1445	mzd_write_zeroed_bits(A._entries, x, y, n, values)
	1446
	1447	def _clear_bits(Matrix_mod2_dense A, int x, int y, int n):
	1448	"""
	1449	EXAMPLE:
	1450	sage: A = matrix(GF(2),3,66)
	1451	sage: for i in range(A.nrows()):
	1452	... for j in range(A.ncols()):
	1453	... A[i,j] = 1
	1454
	1455	sage: print A.str()
	1456	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	1457	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	1458	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	1459
	1460	sage: sage.matrix.matrix_mod2_dense._clear_bits(A,0,0,3)
	1461	sage: sage.matrix.matrix_mod2_dense._clear_bits(A,1,1,3)
	1462	sage: print A.str()
	1463	[0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	1464	[1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	1465	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	1466
	1467	sage: sage.matrix.matrix_mod2_dense._clear_bits(A,0,0,64)
	1468	sage: sage.matrix.matrix_mod2_dense._clear_bits(A,1,1,64)
	1469	sage: print A.str()
	1470	[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]
	1471	[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 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
	1472	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	1473	"""
	1474	mzd_clear_bits(A._entries, x, y, n)
	1475
	1476
	1477	def _addmul(Matrix_mod2_dense C, Matrix_mod2_dense A, Matrix_mod2_dense B, int cutoff):
	1478	"""
	1479	EXAMPLE:
	1480	sage: def check_addmul(m,k,n, cutoff):
	1481	... A = random_matrix(GF(2),m, k)
	1482	... B = random_matrix(GF(2),k, n)
	1483	... C = random_matrix(GF(2),m, n)
	1484	... D1 = C + A*B
	1485	... D2 = sage.matrix.matrix_mod2_dense._addmul(C,A,B, cutoff=cutoff)
	1486	... if D1 != D2:
	1487	... return False
	1488	... else:
	1489	... return True
	1490
	1491	sage: check_addmul(1000,1000,1000, 256)
	1492	True
	1493	sage: check_addmul(1000,10,20, 64)
	1494	True
	1495	sage: check_addmul(1710,1290,1000, 256)
	1496	True
	1497	sage: check_addmul(1290, 1710, 200, 64)
	1498	True
	1499	sage: check_addmul(1290, 1710, 2000, 256)
	1500	True
	1501	sage: check_addmul(1290, 1290, 2000, 64)
	1502	True
	1503	"""
	1504	cdef Matrix_mod2_dense D = <Matrix_mod2_dense>C.copy()
	1505	mzd_addmul(D._entries, A._entries, B._entries, cutoff)
	1506	return D
	1507
	1508	def _col_block_rotate(Matrix_mod2_dense A, int zs, int ze, int de):
	1509	"""
	1510	EXAMPLE:
	1511	sage: A = matrix(GF(2), 10, 128)
	1512	sage: for i in range(10):
	1513	... A[i,i+10] = 1
	1514	... for j in range(20,A.ncols()):
	1515	... A[i,j] = 1
	1516	...
	1517
	1518	sage: sage.matrix.matrix_mod2_dense._col_block_rotate(A, 0, 10, A.ncols())
	1519	sage: A.submatrix(0,0,10,10)
	1520	[1 0 0 0 0 0 0 0 0 0]
	1521	[0 1 0 0 0 0 0 0 0 0]
	1522	[0 0 1 0 0 0 0 0 0 0]
	1523	[0 0 0 1 0 0 0 0 0 0]
	1524	[0 0 0 0 1 0 0 0 0 0]
	1525	[0 0 0 0 0 1 0 0 0 0]
	1526	[0 0 0 0 0 0 1 0 0 0]
	1527	[0 0 0 0 0 0 0 1 0 0]
	1528	[0 0 0 0 0 0 0 0 1 0]
	1529	[0 0 0 0 0 0 0 0 0 1]
	1530
	1531	sage: A.submatrix(0,10,10,10)
	1532	[1 1 1 1 1 1 1 1 1 1]
	1533	[1 1 1 1 1 1 1 1 1 1]
	1534	[1 1 1 1 1 1 1 1 1 1]
	1535	[1 1 1 1 1 1 1 1 1 1]
	1536	[1 1 1 1 1 1 1 1 1 1]
	1537	[1 1 1 1 1 1 1 1 1 1]
	1538	[1 1 1 1 1 1 1 1 1 1]
	1539	[1 1 1 1 1 1 1 1 1 1]
	1540	[1 1 1 1 1 1 1 1 1 1]
	1541	[1 1 1 1 1 1 1 1 1 1]
	1542
	1543	sage: A.submatrix(0,100,10,28)
	1544	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1545	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1546	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1547	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1548	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1549	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1550	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1551	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1552	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1553	[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
	1554	"""
	1555	mzd_col_block_rotate(A._entries, zs, ze, de, 1, NULL)

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