Finding magic factors for bitboard based move generation

Tool to find factors for Magic bitboards.

Results

All magics for a given square are equivalent to a magic in the range [0, period] [1].

c is the occupancy of the attack mask for the given square (the "easy" shift).

Tables contain magics for fixed shift and shift c with proven minimal table size (attacks mapped to indexes from in [0, range]), as well as magics with reduced shift c - 1.

The latter include results from Grant Osborne, Peter Österlund, Volker Annuss, Gerd Isenberg, and Richard Pijl. New results in bold.

Rooks

	s	period	c	magic 12	range 12	magic c	range c	magic c - 1
a1	0	2^63	12
b1	1	2^62	11
c1	2	2^63	11
d1	3	2^63	11
e1	4	2^63	11
f1	5	2^63	11
g1	6	2^63	11
h1	7	2^63	12
a2	8	2^55	11
b2	9	2^54	10
c2	10	2^55	10
d2	11	2^55	10
e2	12	2^55	10
f2	13	2^55	10
g2	14	2^55	10
h2	15	2^55	11
a3	16	2^56	11					disproved
b3	17	2^55	10					disproved
c3	18	2^54	10					disproved
d3	19	2^53	10					disproved
e3	20	2^52	10					disproved
f3	21	2^51	10					disproved
g3	22	2^50	10					disproved
h3	23	2^49	11			0x1aad001575729	2038	disproved
a4	24	2^56	11					disproved
b4	25	2^55	10					disproved
c4	26	2^54	10					disproved
d4	27	2^53	10					disproved
e4	28	2^52	10					disproved
f4	29	2^51	10					disproved
g4	30	2^50	10					disproved
h4	31	2^49	11			0x137894006eced	2044	disproved
a5	32	2^56	11					disproved
b5	33	2^55	10					disproved
c5	34	2^54	10					disproved
d5	35	2^53	10					disproved
e5	36	2^52	10					disproved
f5	37	2^51	10					disproved
g5	38	2^50	10					disproved
h5	39	2^49	11			0x4242136fff00	2045	disproved
a6	40	2^56	11					disproved
b6	41	2^55	10					disproved
c6	42	2^54	10					disproved
d6	43	2^53	10					disproved
e6	44	2^52	10					disproved
f6	45	2^51	10					disproved
g6	46	2^50	10					disproved
h6	47	2^49	11			0x6c6c92246ffe	2040	disproved
a7	48	2^56	11					0x48fffe99fecfaa00
b7	49	2^55	10					0x48fffe99fecfaa00
c7	50	2^54	10					0x497fffadff9c2e00
d7	51	2^53	10					0x613fffddffce9200
e7	52	2^52	10					0xffffffe9ffe7ce00
f7	53	2^51	10					0xfffffff5fff3e600
g7	54	2^50	10					0x3ff95e5e6a4c0
h7	55	2^49	11					0x510ffff5f63c96a0
a8	56	2^56	12					0xebffffb9ff9fc526
b8	57	2^55	11					0x61fffeddfeedaeae
c8	58	2^54	11					0x53bfffedffdeb1a2
d8	59	2^53	11					0x127fffb9ffdfb5f6
e8	60	2^52	11					0x411fffddffdbf4d6
f8	61	2^51	11					disproved
g8	62	2^50	10					0x3ffef27eebe74
h8	63	2^49	12					0x7645fffecbfea79e

Bishops

	s	period	c	magic 9	range 9	magic c	range c	magic c - 1
a1	0	2^55	6					0xffedf9fd7cfcffff
b1	1	2^54	5					0xfc0962854a77f576
c1	2	2^55	5
d1	3	2^54	5
e1	4	2^53	5					disproved
f1	5	2^52	5					disproved
g1	6	2^51	5					0xfc0a66c64a7ef576
h1	7	2^50	6					0x7ffdfdfcbd79ffff
a2	8	2^47	5					0xfc0846a64a34fff6
b2	9	2^46	5					0xfc087a874a3cf7f6
c2	10	2^47	5					disproved
d2	11	2^46	5					disproved
e2	12	2^45	5	0x4402000000	62	0x8f24760b248	30	disproved
f2	13	2^44	5	0x21c1007bff	59	0xa21427af62	28	disproved
g2	14	2^43	5	0x1041040040	61	0x52e9060be9	22	0x820a13ffe0
h2	15	2^42	5	0x820820020	61	0x29748305f5	22	0x410509fff0
a3	16	2^55	5					0x73c01af56cf4cffb
b3	17	2^54	5					0x41a01cfad64aaffc
c3	18	2^55	7					disproved
d3	19	2^54	7					disproved
e3	20	2^53	7					disproved
f3	21	2^52	7					disproved
g3	22	2^51	5					0x7c0c028f5b34ff76
h3	23	2^50	5					0xfc0a028e5ab4df76
a4	24	2^54	5					disproved
b4	25	2^53	5					disproved
c4	26	2^52	7					disproved
d4	27	2^55	9					disproved
e4	28	2^54	9					disproved
f4	29	2^53	7					disproved
g4	30	2^52	5					disproved
h4	31	2^51	5					disproved
a5	32	2^53	5					disproved
b5	33	2^52	5					disproved
c5	34	2^51	7					disproved
d5	35	2^50	9	0x20080080080	511	0x20080080080	511	disproved
e5	36	2^55	9					disproved
f5	37	2^54	7					disproved
g5	38	2^53	5					disproved
h5	39	2^52	5					disproved
a6	40	2^52	5					0xdcefd9b54bfcc09f
b6	41	2^51	5					0xf95ffa765afd602b
c6	42	2^50	7					disproved
d6	43	2^42	7	0x8840200040	132	0xa44000800	127	disproved
e6	44	2^47	7					disproved
f6	45	2^55	7					disproved
g6	46	2^54	5					0x43ff9a5cf4ca0c01
h6	47	2^53	5					0x4bffcd8e7c587601
a7	48	2^51	5					0xfc0ff2865334f576
b7	49	2^50	5					0xfc0bf6ce5924f576
c7	50	2^42	5	0x820806000	35	0x50c34179e6	29	disproved
d7	51	2^34	5	0x8403000	60	0x20880000	31	disproved
e7	52	2^39	5	0x100202000	31	0x4f68bcb86d	29	disproved
f7	53	2^47	5					disproved
g7	54	2^55	5					0xc3ffb7dc36ca8c89
h7	55	2^54	5					0xc3ff8a54f4ca2c89
a8	56	2^50	6					0xfffffcfcfd79edff
b8	57	2^42	5	0x820820020	61	0x58c328c2ee	22	0x1ec04eae595
c8	58	2^34	5	0x8208060	35	0x50c3417a	29	disproved
d8	59	2^26	5	0x84030	60	0x208800	31	disproved
e8	60	2^31	5	0x1002020	31	0x4f68bcb9	29	disproved
f8	61	2^39	5	0x40408020	31	0x74486419f	26	disproved
g8	62	2^47	5					0xfc087e8e4bb2f736
h8	63	2^55	6					0x43ff9e4ef4ca2c89

Tools

verify.py <CANDIDATE>

Verifies a magic candidate.

v2/daq

Select BISHOP or ROOK, SQUARE and SHIFT in v2/Makefile, make and run ./daq. Counts all magics with the specified settings.

gpu/test

Select square, piece type and shift in generate.py. make and run ./test to find magic factors with the specified shift or disprove their existence. Works best for bishop squares (with small shifts and small table sizes).

References

1. Disproving the existence of some magics. 2017.
2. No bishop magics with fixed shift 8. 2018.