Tiling - Tiling - 2022.2 English

Input matrices are processed in distinct blocks. Matrix elements must be rearranged into a specific pattern.

The following table demonstrates how a 16x16 input matrix should be rearranged into a 4x4 tiling pattern.

Note

Indices are quoted assuming a row major matrix. A column major matrix would be the transpose of the table below.

Table 50 Matrix Multiply 4x4 tiling pattern
	Tile Col 0				Tile Col 1				Tile Col 2				Tile Col 3
Tile Row 0	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47
	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63
Tile Row 1	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79
	80	81	82	83	84	85	86	87	88	89	90	91	92	93	94	95
	96	97	98	99	100	101	102	103	104	105	106	107	108	109	110	111
	112	113	114	115	116	117	118	119	120	121	122	123	124	125	126	127
Tile Row 2	128	129	130	131	132	133	134	135	136	137	138	139	140	141	142	143
	144	145	146	147	148	149	150	151	152	153	154	155	156	157	158	159
	160	161	162	163	164	165	166	167	168	169	170	171	172	173	174	175
	176	177	178	179	180	181	182	183	184	185	186	187	188	189	190	191
Tile Row 3	192	193	194	195	196	197	198	199	200	201	202	203	204	205	206	207
	208	209	210	211	212	213	214	215	216	217	218	219	220	221	222	223
	224	225	226	227	228	229	230	231	232	233	234	235	236	237	238	239
	240	241	242	243	244	245	246	247	248	249	250	251	252	253	254	255

This is stored contiguously in memory like:

0, 1, 2, 3, 16, 17, 18, 19, 32, 33, 34, 35, 48, 49, 50, 51, 4, 5, 6, 7, 20, 21, 22, 23, 36, 37, 38, 39, 52, 53, 54, 55, 8, 9, 10, 11, 24, 25, 26, 27, 40, 41, 42, 43, 56, 57, 58, 59, 12, 13, 14, 15, 28, 29, 30, 31, 44, 45, 46, 47, 60, 61, 62, 63, 64, 65, 66, 67, 80, 81, 82, 83, 96, 97, 98, 99, 112, 113, 114, 115, … , 204, 205, 206, 207, 220, 221, 222, 223, 236, 237, 238, 239, 252, 253, 254, 255

The following table demonstrates how a 16x16 input matrix should be rearranged into a 4x2 tiling pattern.

Table 51 Matrix Multiply 4x2 tiling pattern
	Tile Col 0		Tile Col 1		Tile Col 2		Tile Col 3		Tile Col 4		Tile Col 5		Tile Col 6		Tile Col 7
Tile Row 0	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47
	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63
Tile Row 1	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79
	80	81	82	83	84	85	86	87	88	89	90	91	92	93	94	95
	96	97	98	99	100	101	102	103	104	105	106	107	108	109	110	111
	112	113	114	115	116	117	118	119	120	121	122	123	124	125	126	127
Tile Row 2	128	129	130	131	132	133	134	135	136	137	138	139	140	141	142	143
	144	145	146	147	148	149	150	151	152	153	154	155	156	157	158	159
	160	161	162	163	164	165	166	167	168	169	170	171	172	173	174	175
	176	177	178	179	180	181	182	183	184	185	186	187	188	189	190	191
Tile Row 3	192	193	194	195	196	197	198	199	200	201	202	203	204	205	206	207
	208	209	210	211	212	213	214	215	216	217	218	219	220	221	222	223
	224	225	226	227	228	229	230	231	232	233	234	235	236	237	238	239
	240	241	242	243	244	245	246	247	248	249	250	251	252	253	254	255

This is stored contiguously in memory like:

0, 1, 16, 17, 32, 33, 48, 49, 2, 3, 18, 19, 34, 35, 50, 51, …, 206, 207, 222, 223, 238, 239, 254, 255

Multiplying a 16x16 matrix (with 4x4 tiling) with a 16x16 matrix (with 4x2 tiling) will result in a 16x16 matrix with 4x2 tiling.

The following table specifies the tiling scheme used for a given data type combination and the corresponding output data type:

Table 52 Matrix Multiply tiling pattern combination
Input Type Combination		Tiling Scheme		Output Type
A	B	A	B
int16	int16	4x4	4x4	int16
int16	cint16	4x2	2x2	cint16
int16	int32	4x2	2x2	int32
int16	cint32	2x4	4x2	cint32
cint16	int16	4x4	4x2	cint16
cint16	cint16	4x4	4x2	cint16
cint16	int32	4x4	4x2	cint32
cint16	cint32	2x2	2x2	cint32
int32	int16	4x4	4x2	int32
int32	int32	4x4	4x2	int32
int32	cint16	4x4	4x2	cint32
int32	cint32	2x2	2x2	cint32
cint32	int16	2x4	4x2	cint32
cint32	cint16	2x2	2x2	cint32
cint32	int32	2x2	2x2	cint32
cint32	cint32	2x2	2x2	cint32
float	float	4x4	4x2	float
float	cfloat	2x4	4x2	cfloat
cfloat	float	2x4	4x2	cfloat
cfloat	cfloat	4x2	2x2	cfloat

The parameters TP_ADD_TILING_A, TP_ADD_TILING_B, and TP_ADD_DETILING_OUT control the inclusion of an additional pre-processing / post-processing kernel to perform the required data data storage re-ordering. When used with TP_DIM_A_LEADING, TP_DIM_B_LEADING, or TP_DIM_OUT_LEADING, the matrix is also transposed in the tiling kernel.

If the additional kernels are not selected, then the matrix multiply kernels assume incoming data is in the correct format, as specified above.

The tiling imposes a restriction that the matrix dimensions need to be multiples of the tile dimensions. If you require dimensions that do not satisfy these requirements, please pad the matrices up to the closet multiple of the tile dimensions in table Matrix Multiply tiling pattern combination with zeros.