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=== 16-bit PRNG ===
by White Flame

See [[Small, fast 8-bit PRNG]] for details of the algorithm.  This should randomly iterate over a full 0000-ffff range, instead of the 0001-ffff range that the more common Galois LFSR covers.

Code is not well tested, though.

<code asm> lda seed
 beq lowZero ; $0000 and $8000 are special values to test for

 ; Do a normal shift
 asl seed
 lda seed+1
 rol
 bcc noEor

doEor:
  ; high byte is in .A
  eor #>magic
  sta seed+1
  lda seed
  eor #<magic
  sta seed
  rts

lowZero:
 lda seed+1
 beq doEor ; High byte is also zero, so apply the EOR
           ; For speed, you could store 'magic' into 'seed' directly
           ; instead of running the EORs

 ; wasn't zero, check for $8000
 asl
 beq noEor ; if $00 is left after the shift, then it was $80
 bcs doEor ; else, do the EOR based on the carry bit as usual

noEor:
 sta seed+1
 rts</code>

All 2048 magic EOR numbers that give a 16-bit PRNG of period 65536:

<code>$002d
$0039
$003f
$0053
$00bd
$00d7
$012f
$013d
$014f
$015d
$0197
$01a1
$01ad
$01bf
$01c7
$0215
$0219
$0225
$022f
$025d
$026d
$0285
$0291
$02a1
$02e5
$031d
$034b
$0369
$0371
$0387
$038d
$039f
$03a3
$03dd
$03f9
$0429
$0457
$0467
$0483
$0489
$0491
$04bf
$04c1
$0533
$0547
$0569
$0587
$05c3
$05dd
$05eb
$0641
$064b
$0653
$068b
$06c3
$076b
$076d
$0779
$0783
$07f1
$080d
$0861
$08bf
$08d5
$08df
$08e3
$08f1
$08fb
$0939
$097d
$098b
$09a5
$09af
$09c3
$09c5
$09e7
$09f3
$0a7d
$0a81
$0abb
$0ac5
$0b01
$0b13
$0b15
$0b51
$0b5d
$0bcd
$0bd3
$0be5
$0c0f
$0c1d
$0c21
$0c69
$0c71
$0c7b
$0c8d
$0c95
$0ca3
$0caf
$0cf3
$0d43
$0d83
$0d8f
$0dd3
$0de5
$0e45
$0e85
$0e9d
$0ea7
$0f05
$0f09
$0f1b
$0f69
$0f77
$0f87
$0f95
$0fb1
$0fcf
$0fdb
$100b
$1043
$104f
$105d
$107f
$1083
$1085
$1097
$111d
$116f
$11c9
$11db
$11f3
$1241
$1253
$1263
$1277
$1281
$128b
$12af
$12c5
$12db
$12ed
$12f3
$133b
$133d
$1375
$1379
$139d
$1409
$141b
$144d
$1487
$1493
$14af
$14c9
$14d1
$14ed
$14f9
$1507
$158f
$15a1
$15ab
$15d5
$15fb
$161f
$1637
$163d
$1643
$1651
$169b
$16ab
$16d9
$16fd
$173f
$1747
$1753
$1799
$17a3
$17a9
$17d7
$186f
$188d
$1893
$18a9
$18bb
$18f9
$18ff
$1923
$1925
$196b
$1975
$1979
$19b3
$19e5
$19fd
$1a07
$1a57
$1a6b
$1a89
$1ae3
$1ae5
$1b09
$1b2b
$1b47
$1b4b
$1baf
$1bbb
$1bbd
$1bc3
$1bd7
$1be1
$1c29
$1c61
$1c85
$1c9d
$1cb5
$1ccb
$1ccd
$1ce9
$1cef
$1cf1
$1d17
$1d3f
$1d53
$1d59
$1d5f
$1d65
$1d77
$1d81
$1d87
$1dff
$1e21
$1e3f
$1e5f
$1e71
$1e7b
$1e99
$1e9f
$1ec3
$1ecf
$1ee7
$1ef3
$1f29
$1f3b
$1f57
$1f75
$1f83
$1f9b
$1fb9
$1fbf
$1fc1
$203d
$2051
$208f
$209b
$20b9
$20c7
$2105
$2187
$2195
$21a9
$21b1
$21e1
$2227
$2235
$2241
$2253
$228b
$2293
$22af
$22b1
$2329
$2345
$2357
$236d
$23e3
$240f
$242d
$2439
$244b
$2499
$249f
$24e7
$24ff
$2515
$2557
$255d
$2573
$2579
$259b
$25e5
$2607
$2615
$2623
$263d
$2651
$267f
$2683
$26fb
$2711
$2739
$2759
$2763
$2787
$27a5
$27c5
$27ed
$281d
$2841
$2871
$287b
$28a9
$28c5
$28f5
$290b
$2919
$2943
$2945
$2983
$2989
$299d
$29b9
$29c7
$29d5
$29f1
$2a25
$2a29
$2a31
$2a3b
$2a7f
$2a85
$2aa7
$2acd
$2ad9
$2b09
$2b27
$2b53
$2b7b
$2b7d
$2b99
$2bd1
$2bdb
$2c1f
$2c3b
$2c4f
$2c5d
$2c61
$2c6b
$2c73
$2c79
$2cb9
$2ce3
$2cf7
$2cfb
$2d35
$2d41
$2d65
$2d81
$2ddb
$2de1
$2e0f
$2e47
$2e4b
$2e4d
$2e71
$2ec5
$2ef9
$2eff
$2f3d
$2f43
$2f5b
$2f67
$2fa7
$2fd3
$3017
$3027
$3077
$3081
$30af
$30c3
$30dd
$30ed
$30f5
$3107
$310d
$3129
$3173
$31a7
$31ab
$31cd
$31d9
$322f
$3237
$323d
$3249
$3257
$325b
$3275
$329d
$32b5
$32d9
$32ef
$32f1
$3305
$331b
$3339
$339f
$33a9
$33c5
$33d1
$33f3
$3415
$3425
$349b
$34fd
$3505
$351d
$354b
$3571
$357d
$35a3
$35c9
$35d7
$361b
$3635
$366f
$3699
$36a9
$36c3
$36d1
$36ed
$3707
$370b
$3719
$3743
$37cd
$37e3
$3801
$380d
$381f
$3837
$3849
$385d
$386d
$38c7
$38cb
$38df
$38fb
$3921
$393f
$394d
$3953
$395f
$3965
$3999
$39b7
$39bd
$39c9
$39ff
$3a09
$3a1b
$3a55
$3a65
$3a69
$3a77
$3abd
$3acf
$3af3
$3b29
$3b45
$3b5b
$3b9d
$3bcb
$3bd3
$3bef
$3bf1
$3c47
$3c4b
$3c69
$3c6f
$3c93
$3d07
$3d13
$3d23
$3d31
$3d3d
$3d43
$3d49
$3d67
$3d6b
$3d83
$3d91
$3db3
$3dc1
$3dcd
$3e31
$3e43
$3e45
$3e51
$3e57
$3e8f
$3ed3
$3edf
$3ee9
$3efb
$3f1d
$3f81
$3fa5
$3fc5
$4075
$409d
$40cd
$4109
$413f
$414b
$4153
$4159
$4193
$4199
$41af
$41bb
$41bd
$41e1
$41e7
$41f3
$41ff
$4203
$4211
$424b
$4271
$4281
$42a9
$42cf
$42e1
$42ed
$430b
$4343
$437f
$4383
$43bf
$43ef
$43fb
$440f
$4447
$4477
$4495
$449f
$44a3
$44bb
$44c5
$44e1
$44f9
$450b
$4529
$4537
$4573
$4589
$458f
$459b
$459d
$45b5
$45b9
$45f7
$45fd
$4629
$4645
$465d
$4673
$4691
$46a1
$46cb
$46d5
$46df
$46e9
$46fd
$4721
$477d
$4793
$4799
$47c3
$47c9
$47f9
$481d
$4835
$483f
$4859
$4881
$48a9
$48c3
$48db
$48ff
$490b
$4915
$492f
$4931
$49df
$49e5
$49fb
$4a13
$4a15
$4a2f
$4a6d
$4a75
$4aad
$4ab5
$4acb
$4adf
$4af7
$4afb
$4b21
$4b4d
$4b63
$4b7d
$4bb7
$4bc9
$4bcf
$4bdd
$4bf3
$4bf9
$4bff
$4c1f
$4c67
$4c73
$4ca7
$4cb9
$4cc7
$4cf7
$4cfd
$4d0f
$4d39
$4d4d
$4d5f
$4d69
$4d71
$4d8b
$4d8d
$4de7
$4deb
$4df3
$4e4b
$4e6f
$4e81
$4e87
$4ea3
$4eaf
$4eb1
$4eeb
$4ef5
$4f25
$4f31
$4f49
$4f57
$4f5b
$4f61
$4f6d
$4f8f
$4fa1
$4fe3
$5003
$500f
$5059
$5081
$50a5
$50b7
$50bb
$50c9
$50d7
$50eb
$5107
$5125
$5149
$515d
$516d
$51a1
$51a7
$51d3
$51df
$520b
$5245
$525d
$5261
$5297
$5309
$5327
$5363
$5377
$53e1
$5457
$545b
$547f
$5483
$54b5
$54b9
$54df
$5527
$552d
$554b
$5593
$55af
$55f5
$5621
$562b
$562d
$5647
$569f
$56c5
$56f5
$5729
$5751
$57ab
$5807
$5825
$583d
$5889
$58b3
$58d3
$58d9
$58df
$592b
$594b
$594d
$5969
$598d
$5993
$599f
$59a3
$59cf
$59d7
$59ff
$5a55
$5a71
$5a7d
$5a99
$5aa5
$5ab7
$5ad7
$5b45
$5b4f
$5b57
$5bab
$5bc7
$5bdf
$5c05
$5c99
$5ca3
$5ca5
$5ceb
$5d07
$5d31
$5d37
$5d3b
$5d7f
$5d91
$5dab
$5dc7
$5df1
$5dfd
$5e0b
$5e19
$5e29
$5e37
$5e57
$5e67
$5eab
$5ed5
$5ee5
$5f55
$5f8d
$5fbd
$6021
$6039
$6063
$6077
$609f
$60dd
$610b
$6119
$613d
$6143
$6167
$617f
$61ad
$61d3
$6213
$6231
$623b
$6261
$626b
$6273
$628f
$6297
$632d
$6333
$6335
$6353
$6365
$637b
$6381
$63ed
$63f5
$6407
$641f
$643b
$6443
$6451
$6497
$649b
$64e9
$64f7
$650f
$652b
$6535
$6539
$653f
$6565
$6593
$65a5
$65e7
$65f3
$6605
$6671
$66a9
$66bb
$66d7
$6707
$6719
$676b
$6779
$67a1
$67bf
$67d9
$67df
$67f7
$6801
$680b
$681f
$6849
$689d
$68cb
$68d3
$68d5
$6917
$6947
$6955
$698d
$69af
$69cf
$69d7
$6a77
$6aa5
$6ae7
$6b01
$6b0d
$6b23
$6b57
$6b6b
$6b8f
$6b9d
$6bab
$6bc7
$6bfb
$6c03
$6c1d
$6c39
$6c6f
$6c81
$6c93
$6ca5
$6ce7
$6d15
$6d3b
$6d43
$6d89
$6d9d
$6db3
$6dbf
$6dc1
$6de5
$6e19
$6e51
$6e5d
$6e67
$6e7f
$6e85
$6e91
$6e97
$6e9b
$6ed9
$6efd
$6f47
$6f8d
$6fc9
$6fdb
$6fff
$7025
$7029
$7057
$705b
$7061
$706b
$706d
$709d
$70b3
$70fd
$7111
$7159
$715f
$716f
$7181
$71c3
$71dd
$71f9
$7205
$721d
$722d
$725f
$7263
$7271
$7299
$72a3
$72af
$72cf
$72dd
$72e1
$7329
$7345
$736d
$7391
$739b
$73ad
$73b9
$7411
$7439
$7469
$747d
$7481
$7487
$7495
$74b7
$74c5
$74d7
$74ed
$7501
$7515
$7523
$7549
$7583
$759b
$75a1
$75a7
$760d
$7619
$763b
$763d
$7643
$7657
$769d
$76c7
$76df
$771b
$771d
$7741
$774b
$7781
$77a5
$77b7
$7809
$7835
$783f
$7899
$78c9
$78d1
$78db
$78dd
$78eb
$7901
$790d
$7979
$797f
$7991
$7997
$79e9
$79ef
$7a01
$7a1f
$7aa7
$7aab
$7ab9
$7af7
$7b05
$7b39
$7b63
$7bb1
$7bbb
$7bf5
$7c37
$7c4f
$7c5d
$7ca1
$7cb5
$7cbf
$7ccb
$7cd3
$7d21
$7d47
$7d59
$7d87
$7da5
$7da9
$7dc5
$7dd7
$7e1d
$7e2b
$7e4b
$7e59
$7e65
$7e8b
$7e93
$7eaf
$7ebb
$7ec5
$7ed1
$7eed
$7f0b
$7f2f
$7f31
$7f45
$7f75
$7fb3
$7fc7
$7fd3
$8013
$8015
$806d
$8085
$80f7
$8117
$812b
$81b7
$8211
$821b
$8241
$8255
$828b
$8293
$829f
$82bb
$82c9
$82f3
$82ff
$8307
$8329
$8357
$835d
$8361
$8379
$8385
$83bf
$83c1
$83df
$83f1
$8411
$841b
$8433
$844d
$846f
$84af
$84cf
$84d1
$84dd
$84f9
$850d
$8513
$8529
$8537
$8561
$856d
$8579
$857f
$8585
$85c7
$85d9
$85e9
$85fb
$860b
$8619
$8625
$8637
$86ab
$86c1
$86d9
$86f1
$86f7
$870f
$871d
$8721
$8733
$8741
$8753
$87af
$87b1
$87c5
$8833
$885f
$8863
$88c9
$892f
$8931
$895d
$8979
$897f
$899b
$89a7
$89ad
$89ef
$89fb
$8a45
$8a61
$8a67
$8a73
$8a75
$8a9d
$8ae5
$8b35
$8b59
$8b63
$8b81
$8bb7
$8bd1
$8bdb
$8c0d
$8c23
$8c91
$8c97
$8c9d
$8ccb
$8cef
$8d27
$8d95
$8da3
$8da5
$8dbd
$8dc9
$8de7
$8e21
$8e47
$8e69
$8eb1
$8f57
$8f89
$8fd3
$8fd9
$8fe5
$8fef
$9003
$900f
$901b
$9027
$9047
$908d
$90a5
$90e7
$911f
$9143
$916b
$9179
$919b
$91a1
$9231
$9251
$926d
$9279
$9283
$9289
$92a7
$92fd
$9305
$9317
$9327
$9335
$934d
$9355
$939f
$93c5
$93db
$93eb
$93f3
$9401
$943b
$9473
$9489
$9491
$94a7
$94c1
$9505
$951b
$952b
$9539
$9547
$9571
$958b
$958d
$95a9
$95c3
$95d1
$962d
$9635
$965f
$9677
$967d
$96b7
$96db
$96f9
$970d
$9715
$971f
$9761
$97a1
$97ab
$97b9
$97e3
$97e9
$97fd
$980b
$9823
$982f
$9843
$990f
$992b
$9941
$9947
$998b
$998d
$99c3
$99ff
$9a0f
$9a1d
$9a35
$9a6f
$9ad7
$9b31
$9b37
$9b5b
$9b6d
$9b79
$9b7f
$9bcb
$9bdf
$9bef
$9bfd
$9c53
$9c65
$9c69
$9c8d
$9ca3
$9cc5
$9d19
$9d45
$9d49
$9d8f
$9df7
$9e07
$9e4f
$9e57
$9e61
$9e83
$9e91
$9ea7
$9eb9
$9ec7
$9edf
$9ef1
$9f05
$9f11
$9f21
$9f4d
$9f65
$9f7b
$9f93
$9f99
$9fa5
$9fb7
$a011
$a02d
$a033
$a06f
$a07b
$a095
$a0c3
$a0cf
$a0f5
$a107
$a10d
$a125
$a129
$a137
$a145
$a185
$a1d9
$a1fd
$a23b
$a283
$a289
$a291
$a2bf
$a2c1
$a2fd
$a31b
$a321
$a32b
$a333
$a353
$a365
$a3cf
$a449
$a44f
$a467
$a479
$a485
$a4bf
$a4c1
$a4cb
$a4e5
$a4e9
$a4fd
$a505
$a517
$a527
$a52b
$a535
$a555
$a559
$a581
$a5b1
$a5b7
$a5bb
$a5dd
$a62d
$a639
$a64b
$a663
$a671
$a67d
$a6a5
$a6b7
$a6c5
$a71f
$a767
$a797
$a7b3
$a7b9
$a7bf
$a83b
$a8d5
$a8df
$a8fd
$a903
$a933
$a935
$a94b
$a94d
$a953
$a98b
$a9af
$a9b1
$a9e7
$aa77
$aa9f
$aabd
$aac3
$aad1
$aaf5
$ab19
$ab1f
$ab51
$ab57
$ab75
$aba7
$abad
$abb5
$abd3
$abd5
$ac1d
$ac27
$ac5f
$ac69
$ac8d
$acb1
$accf
$ad13
$ad31
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