hash-macros.sas

```/* hash-macros
* Richard A. DeVenezia
* Jan 17, 2004
*
* Macros to (hopefully) simplify coding hash array solutions
*
* mod
* 17JAN2004 - Initial release
* 03JUN2004 - Improved example
* 22OCT2023 - Updated for SESUG 2023 paper "Hashes from the Ashes"
*/```

Sample: problem   usage
Recommended reading: The numerous and educating papers of Paul Dorfman, including
Sugi 26 Paper 128-26, Paul M. Dorfman
QUICK DISK TABLE LOOKUP
VIA HYBRID INDEXING INTO A
DIRECTLY ADDRESSED SAS DATA SET

```%macro hashSize (n=, data=, load = 0.5) ;

/*
* n - an apriori determined n specified by user
* data - let n be number of rows in data
* load - load factor (0,1)
*
* Determine size of array that will contain a hash of N items
* at a given load factor. Find 1st prime > rowcount / load.
*/

/* The 2,262 prime numbers < sqrt(4e8) are minimal factorization candidate set */
/* If the hash size starting point is greater than the 4e8 factorization candidates,
* new candidates will be continued by +2 until target primality achieved
*/

%local pf400m; /* prime factor candidates for data sets with <= 400,000,000 nobs */
%let pf400m =
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179
181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379
383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599
601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823
827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039
1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231
1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447
1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619
1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847
1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053
2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269
2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459
2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689
2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887
2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121
3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347
3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559
3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779
3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007
4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231
4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463
4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691
4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943
4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167
5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417
5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647
5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851
5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101
6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323
6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571
6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823
6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027
7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307
7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549
7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759
7789 7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 7919 7927 7933 7937 7949 7951 7963 7993 8009 8011 8017 8039 8053
8059 8069 8081 8087 8089 8093 8101 8111 8117 8123 8147 8161 8167 8171 8179 8191 8209 8219 8221 8231 8233 8237 8243 8263 8269 8273 8287
8291 8293 8297 8311 8317 8329 8353 8363 8369 8377 8387 8389 8419 8423 8429 8431 8443 8447 8461 8467 8501 8513 8521 8527 8537 8539 8543
8563 8573 8581 8597 8599 8609 8623 8627 8629 8641 8647 8663 8669 8677 8681 8689 8693 8699 8707 8713 8719 8731 8737 8741 8747 8753 8761
8779 8783 8803 8807 8819 8821 8831 8837 8839 8849 8861 8863 8867 8887 8893 8923 8929 8933 8941 8951 8963 8969 8971 8999 9001 9007 9011
9013 9029 9041 9043 9049 9059 9067 9091 9103 9109 9127 9133 9137 9151 9157 9161 9173 9181 9187 9199 9203 9209 9221 9227 9239 9241 9257
9277 9281 9283 9293 9311 9319 9323 9337 9341 9343 9349 9371 9377 9391 9397 9403 9413 9419 9421 9431 9433 9437 9439 9461 9463 9467 9473
9479 9491 9497 9511 9521 9533 9539 9547 9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 9679 9689 9697 9719 9721 9733 9739
9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 9949 9967
9973 10007 10009 10037 10039 10061 10067 10069 10079 10091 10093 10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177 10181
10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 10303 10313 10321 10331 10333 10337 10343 10357 10369 10391
10399 10427 10429 10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 10531 10559 10567 10589 10597 10601 10607 10613
10627 10631 10639 10651 10657 10663 10667 10687 10691 10709 10711 10723 10729 10733 10739 10753 10771 10781 10789 10799 10831 10837
10847 10853 10859 10861 10867 10883 10889 10891 10903 10909 10937 10939 10949 10957 10973 10979 10987 10993 11003 11027 11047 11057
11059 11069 11071 11083 11087 11093 11113 11117 11119 11131 11149 11159 11161 11171 11173 11177 11197 11213 11239 11243 11251 11257
11261 11273 11279 11287 11299 11311 11317 11321 11329 11351 11353 11369 11383 11393 11399 11411 11423 11437 11443 11447 11467 11471
11483 11489 11491 11497 11503 11519 11527 11549 11551 11579 11587 11593 11597 11617 11621 11633 11657 11677 11681 11689 11699 11701
11717 11719 11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 11833 11839 11863 11867 11887 11897 11903 11909
11923 11927 11933 11939 11941 11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 12049 12071 12073 12097 12101 12107
12109 12113 12119 12143 12149 12157 12161 12163 12197 12203 12211 12227 12239 12241 12251 12253 12263 12269 12277 12281 12289 12301
12323 12329 12343 12347 12373 12377 12379 12391 12401 12409 12413 12421 12433 12437 12451 12457 12473 12479 12487 12491 12497 12503
12511 12517 12527 12539 12541 12547 12553 12569 12577 12583 12589 12601 12611 12613 12619 12637 12641 12647 12653 12659 12671 12689
12697 12703 12713 12721 12739 12743 12757 12763 12781 12791 12799 12809 12821 12823 12829 12841 12853 12889 12893 12899 12907 12911
12917 12919 12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 13007 13009 13033 13037 13043 13049 13063 13093 13099 13103
13109 13121 13127 13147 13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 13259 13267 13291 13297 13309 13313
13327 13331 13337 13339 13367 13381 13397 13399 13411 13417 13421 13441 13451 13457 13463 13469 13477 13487 13499 13513 13523 13537
13553 13567 13577 13591 13597 13613 13619 13627 13633 13649 13669 13679 13681 13687 13691 13693 13697 13709 13711 13721 13723 13729
13751 13757 13759 13763 13781 13789 13799 13807 13829 13831 13841 13859 13873 13877 13879 13883 13901 13903 13907 13913 13921 13931
13933 13963 13967 13997 13999 14009 14011 14029 14033 14051 14057 14071 14081 14083 14087 14107 14143 14149 14153 14159 14173 14177
14197 14207 14221 14243 14249 14251 14281 14293 14303 14321 14323 14327 14341 14347 14369 14387 14389 14401 14407 14411 14419 14423
14431 14437 14447 14449 14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 14557 14561 14563 14591 14593 14621 14627 14629
14633 14639 14653 14657 14669 14683 14699 14713 14717 14723 14731 14737 14741 14747 14753 14759 14767 14771 14779 14783 14797 14813
14821 14827 14831 14843 14851 14867 14869 14879 14887 14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 15017 15031
15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 15137 15139 15149 15161 15173 15187 15193 15199 15217 15227 15233 15241
15259 15263 15269 15271 15277 15287 15289 15299 15307 15313 15319 15329 15331 15349 15359 15361 15373 15377 15383 15391 15401 15413
15427 15439 15443 15451 15461 15467 15473 15493 15497 15511 15527 15541 15551 15559 15569 15581 15583 15601 15607 15619 15629 15641
15643 15647 15649 15661 15667 15671 15679 15683 15727 15731 15733 15737 15739 15749 15761 15767 15773 15787 15791 15797 15803 15809
15817 15823 15859 15877 15881 15887 15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 15991 16001 16007 16033 16057 16061
16063 16067 16069 16073 16087 16091 16097 16103 16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 16249 16253
16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 16381 16411 16417 16421 16427 16433 16447 16451 16453 16477 16481 16487
16493 16519 16529 16547 16553 16561 16567 16573 16603 16607 16619 16631 16633 16649 16651 16657 16661 16673 16691 16693 16699 16703
16729 16741 16747 16759 16763 16787 16811 16823 16829 16831 16843 16871 16879 16883 16889 16901 16903 16921 16927 16931 16937 16943
16963 16979 16981 16987 16993 17011 17021 17027 17029 17033 17041 17047 17053 17077 17093 17099 17107 17117 17123 17137 17159 17167
17183 17189 17191 17203 17207 17209 17231 17239 17257 17291 17293 17299 17317 17321 17327 17333 17341 17351 17359 17377 17383 17387
17389 17393 17401 17417 17419 17431 17443 17449 17467 17471 17477 17483 17489 17491 17497 17509 17519 17539 17551 17569 17573 17579
17581 17597 17599 17609 17623 17627 17657 17659 17669 17681 17683 17707 17713 17729 17737 17747 17749 17761 17783 17789 17791 17807
17827 17837 17839 17851 17863 17881 17891 17903 17909 17911 17921 17923 17929 17939 17957 17959 17971 17977 17981 17987 17989 18013
18041 18043 18047 18049 18059 18061 18077 18089 18097 18119 18121 18127 18131 18133 18143 18149 18169 18181 18191 18199 18211 18217
18223 18229 18233 18251 18253 18257 18269 18287 18289 18301 18307 18311 18313 18329 18341 18353 18367 18371 18379 18397 18401 18413
18427 18433 18439 18443 18451 18457 18461 18481 18493 18503 18517 18521 18523 18539 18541 18553 18583 18587 18593 18617 18637 18661
18671 18679 18691 18701 18713 18719 18731 18743 18749 18757 18773 18787 18793 18797 18803 18839 18859 18869 18899 18911 18913 18917
18919 18947 18959 18973 18979 19001 19009 19013 19031 19037 19051 19069 19073 19079 19081 19087 19121 19139 19141 19157 19163 19181
19183 19207 19211 19213 19219 19231 19237 19249 19259 19267 19273 19289 19301 19309 19319 19333 19373 19379 19381 19387 19391 19403
19417 19421 19423 19427 19429 19433 19441 19447 19457 19463 19469 19471 19477 19483 19489 19501 19507 19531 19541 19543 19553 19559
19571 19577 19583 19597 19603 19609 19661 19681 19687 19697 19699 19709 19717 19727 19739 19751 19753 19759 19763 19777 19793 19801
19813 19819 19841 19843 19853 19861 19867 19889 19891 19913 19919 19927 19937 19949 19961 19963 19973 19979 19991 19993 19997
;
%local ix ixtop ;
%let ixtop = %sysfunc(countw(&pf400m)) ;

%if %length(&data) %then %do ;
%local dsid ;
%let dsid = %sysfunc(open(&data)) ;
%if &dsid %then %do ;
%let n = %sysfunc (attrn(&dsid, NOBS)) ;
%let dsid=%sysfunc(close(&dsid)) ;
%end ;
%else %do ;
%put ERROR: hash_size could not open &data.  Forcing an error ;
;DATA_NOT_FOUND ;
%end ;
%end ;

%local ip up pr ;

%let pr = %sysfunc (floor(&n/&load)) ;
%let pr = %eval (&pr + 1 - %sysfunc(mod(&pr,2))) ; /* advance to next odd number */

%do %until ( &ip > &up ) ;
%let pr = %eval (&pr + 2) ;

%let up = %sysfunc(ceil(%sysfunc(sqrt(&pr)))) ;

%let ix = 0 ;
%do ip = 2 %to &up %by 2 ;
%let ix = %eval(&ix+1) ;
%if &ix <= &ixtop
%then %let ip = %scan(&pf400m, &ix) ;

%if %sysfunc(mod(&pr,&ip)) = 0 %then %goto failed ;
%end ;
%failed:
%end ;
&pr
%mend hashSize;
```
```%macro declareHash (hash, size, keyAttr=8, policy=LP, allowDuplicates=NO, lpIncrement=1) ;
%let policy = %upcase(&policy) ;
%let allowDuplicates = %upcase (&allowDuplicates) ;

%if (&policy ne LP and &policy ne CL) %then %do ;
%put ERROR: policy=&policy.  Hash collision resolution policy must be LP (Linear Probe) or CL (Coalesced Linking) ;
;UNKNOWN_POLICY ;
%return ;
%end ;

%if (&allowDuplicates ne YES and &allowDuplicates ne NO) %then %do ;
%put ERROR: allowDuplicates=&allowDuplicates.  Allow duplicates must be YES or NO ;
;ALLOW_DUPLICATES_INVALID ;
%return ;
%end ;

%global hash_size_&hash ;
%global hash_policy_&hash ;
%global hash_dups_&hash ;
%global hash_lp_increment_&hash ;
%global hash_add_count_&hash ;

%let hash_size_&hash         = &size ;
%let hash_policy_&hash       = &policy ;
%let hash_dups_&hash         = &allowDuplicates ;
%let hash_lp_increment_&hash = &lpIncrement ;
%let hash_add_count_&hash    = 0 ;

array &hash._keys  [&size] &keyAttr _temporary_ ;

%if &policy eq CL %then %do ;
array &hash._chain [0:&size] _temporary_ ;
retain &hash._chain_addr &size ;
%end ;

retain &hash._max_depth 0 ;
%mend declareHash ;
```
```%macro declareHashKey (hash, key, keyHash=) ;
%global hash_key_&hash ;
%global hash_key_hash_&hash ;
%global hash_dyna_key_&hash ;
%global hash_dyna_key_expr_&hash ;

%let hash_key_&hash = &key ;
%let hash_key_hash_&hash = &keyHash ;

%local p LHS RHS ;
%let p = %index(&key,=) ;
%if &p %then %do ;
%let LHS = %substr(&key,1,&p-1) ;
%let RHS = %substr(&key,&p+1) ;
%end ;

%let hash_dyna_key_&hash = &LHS ;
%let hash_dyna_key_expr_&hash = &RHS ;

length &hash._key_addr 8 ;
%mend declareHashKey ;
```
```%macro declareHashData (hash, var) ;
%local size ;
%let size = &&hash_size_&hash ;

array &hash._&var (0:&size) _temporary_ ;
%mend declareHashData ;
```
```%macro hashAddKey (hash, rc=) ;
%* PDV variable named in rc will receive -1 if duplicate key
%* found when allowDuplicates = NO ;

%hashAddKey_&&hash_policy_&hash (&hash, rc=&rc)
%mend hashAddKey ;
```
```%macro hashAddKey_CL (hash, rc=) ;
%local size key key_hash count key_addr chain chain_addr keys ;
%local dyna_key dyna_key_expr ;

%let size  = &&hash_size_&hash ;
%let key   = &&hash_key_&hash ;
%let count = &&hash_add_count_&hash ;

%let hash_add_count&hash = %eval ( 1 + &count ) ;

%let key_addr   = &hash._key_addr ;
%let chain      = &hash._chain ;
%let chain_addr = &hash._chain_addr ;
%let keys       = &hash._keys ;
%let end_block  = &hash._addkey_end_block_&count ;

*-------------------- ;
%if %length (&rc) %then
%str(&rc = 0;) ;

%if %length(&dyna_key) ne 0 %then %do ;
&dyna_key = &dyna_key_expr ;
%let key = &dyna_key ;
%end ;

%if %length(&key_hash) = 0 %then
%let key_hash = &key ;

&key_addr = mod ( &key_hash, &size ) + 1 ;

if &chain [ &key_addr ] ne . then do ;

%if &&hash_dups_&hash = YES %then %do ;

%* allowing dup keys, proceed to end of chain ;
do while ( &chain [ &key_addr ] ne 0 ) ;
&key_addr = &chain [ &key_addr ] ;
end ;

%end ;
%else %do ;

%* disallowing duplicate keys ;
%* thus quit code block if key found ;

do while ( 1 ) ;
if ( &key = &keys [ &key_addr ] ) then do ;
%if %length (&rc) %then
%str(&rc = -1;) ;
goto &end_block ;
end ;

%* stop searching if end of chain reached ;
if ( &chain [ &key_addr ] = 0 ) then
leave ;

&key_addr = &chain [ &key_addr ] ;
end ;

%end ;

%* &key_addr is at the end of a chain
%* (where &chain [&key_addr] is 0) ;

%* locate open addr for new end of chain ;
do &chain_addr = &chain_addr by -1
until ( &chain [ &chain_addr ] = . ) ;
if &chain_addr < 1 then &chain_addr = &size ;
end ;

%* point to new end of chain and update key addr ;
&chain [ &key_addr ] = &chain_addr ;
&key_addr = &chain_addr ;
end ;

%* set end of chain marker and set hash validator ;
&chain [ &key_addr ] = 0 ;
&keys [ &key_addr ] = &key ;

&end_block: ;
*-------------------- ;
%mend hashAddKey_CL ;

```
```%macro hashAddKey_LP (hash, rc=) ;
%local size key key_hash increment key_addr keys depth max_depth bound_check ;
%local dyna_key dyna_key_expr ;

%let size          = &&hash_size_&hash ;
%let key           = &&hash_key_&hash ;
%let key_hash      = &&hash_key_hash_&hash ;
%let increment     = &&hash_lp_increment_&hash ;
%let dyna_key      = &&hash_dyna_key_&hash ;
%let dyna_key_expr = &&hash_dyna_key_expr_&hash ;

%let key_addr   = &hash._key_addr ;
%let keys       = &hash._keys ;
%let depth      = &hash._depth ;
%let max_depth  = &hash._max_depth ;

%if &increment = 0 %then %do ;
%put ERROR: Linear probe increment must be non-zero ;
;INVALID_LP_INCREMENT ;
%return ;
%end ;
%else
%if &increment > 0 %then
%let bound_check = if ( &key_addr > &size ) then &key_addr + ( - &size ) ;
%else
%let bound_check = if ( &key_addr <   1   ) then &key_addr + ( + &size ) ;

*-------------------- ;
%if %length (&rc) %then
%str(&rc = 0;) ;

%if %length(&dyna_key) ne 0 %then %do ;
&dyna_key = &dyna_key_expr ;
%let key = &dyna_key ;
%end ;

%if %length(&key_hash) = 0 %then
%let key_hash = &key ;

&key_addr = mod ( &key_hash, &size ) + 1 ;

do &depth = 0 by 1 ;

if ( cmiss ( &keys [ &key_addr ] )) then do ;
&keys [ &key_addr ] = &key ;
if ( &depth > &max_depth ) then
&max_depth = &depth ;
leave ;
end ;

%if &&hash_dups_&hash = NO %then %do ;

if ( &keys [ &key_addr ] = &key ) then do ;
%if %length (&rc) %then
%str(&rc = -1 ;) ;
leave ;
end ;

%end ;

&key_addr + ( &increment ) ;
&bound_check ;
end ;
*-------------------- ;
%mend hashAddKey_LP ;
```
```%macro keyArray (hash) ;
&hash._keys
%mend keyArray ;
```
```%macro chainArray (hash) ;
&hash._chain
%mend chainArray ;
```
```%macro dataArray (hash, var) ;
&hash._&var
%mend dataArray ;
```
```%macro hashGetKey (hash) ;
%keyArray(&hash) ( &hash._key_addr )
%mend hashGetKey ;
```
```%macro hashGetData (hash, var) ;
%dataArray(&hash,&var) ( &hash._key_addr )
%mend hashGetData ;
```
```%macro hashSetData (hash, var) ;
%dataArray(&hash,&var) ( &hash._key_addr ) = &var ;
%mend hashSetData ;
```
```%macro hashKey (hash) ;
&&hash_key_&hash
%mend hashKey ;
```
```%macro hashKeyAddr (hash) ;
&hash._key_addr
%mend hashKeyAddr ;
```
```%macro hashFetch (hash, rc=) ;
%* PDV variable named in rc will receive -1 if key not found
%* and will receive 0 if key found ;

%hashFetch_&&hash_policy_&hash (&hash, rc=&rc)
%mend hashFetch ;
```
```%macro hashFetchNext (hash, rc=) ;
%* PDV variable named in rc will receive -1 if key not found
%* and will receive 0 if key found ;

%hashFetchNext_&&hash_policy_&hash (&hash, rc=&rc)
%mend hashFetchNext ;
```
```%macro hashFetch_CL (hash, rc) ;
%local size key key_addr chain keys ;

%let size  = &&hash_size_&hash ;
%let key   = &&hash_key_&hash ;

%let key_addr = &hash._key_addr ;
%let chain    = &hash._chain ;
%let keys     = &hash._keys ;

*-------------------- ;
%if %length (&rc) %then
%str(&rc = -1 ;) ;

&key_addr = mod ( &key, &size ) + 1 ;

if &chain [ &key_addr ] ne . then do ;
do while ( 1 ) ;
if ( &key = &keys [ &key_addr ] ) then do ;
%if %length (&rc) %then
&rc = 0; ;
leave ;
end ;

%* stop searching if end of chain reached ;
if ( &chain [ &key_addr ] = 0 ) then do ;
&key_addr = -1 ;
leave ;
end ;

&key_addr = &chain [ &key_addr ] ;
end ;
end ;
else
&key_addr = -1 ;
*-------------------- ;
%mend hashFetch_CL ;
```
```%macro hashFetchNext_CL (hash, rc) ;
%if &&hash_dups_&hash = NO %then %do ;
%put ERROR: hashFetchNext can only be called for hashes declared with allowDuplicates=YES ;
%put ERROR: hash [&hash] was not declared thus. ;
;CauseError ;
%return ;
%end ;

%local size key key_addr chain ;

%let size  = &&hash_size_&hash ;
%let key   = &&hash_key_&hash ;

%let key_addr = &hash._key_addr ;
%let chain    = &hash._chain ;

*-------------------- ;
%if %length (&rc) %then
&rc = -1; ;

if &key_addr > -1 then do ;

&key_addr = &chain [ &key_addr ] ;

if &chain [ &key_addr ] ne . then do ;
do while ( 1 ) ;
if ( &key = &keys [ &key_addr ] ) then do ;
%if %length (&rc) %then
&rc = 0; ;
leave ;
end ;

%* stop searching if end of chain reached ;
if ( &chain [ &key_addr ] = 0 ) then do ;
&key_addr = -1 ;
leave ;
end ;

&key_addr = &chain [ &key_addr ] ;
end ;
end ;
else
&key_addr = -1 ;
end ;
*-------------------- ;
%mend hashFetchNext_CL ;
```
```%macro hashFetch_LP (hash, rc) ;
%local size key increment key_addr keys depth max_depth bound_check ;

%let size          = &&hash_size_&hash ;
%let key           = &&hash_key_&hash ;
%let key_hash      = &&hash_key_hash_&hash ;
%let increment     = &&hash_lp_increment_&hash ;
%let dyna_key      = &&hash_dyna_key_&hash ;
%let dyna_key_expr = &&hash_dyna_key_expr_&hash ;

%let key_addr  = &hash._key_addr ;
%let keys      = &hash._keys ;
%let depth     = &hash._depth ;
%let max_depth = &hash._max_depth ;

%if &increment > 0 %then
%let bound_check = if ( &key_addr > &size ) then &key_addr + ( - &size ) ;
%else
%let bound_check = if ( &key_addr <   1   ) then &key_addr + ( + &size ) ;

*-------------------- ;
%if %length (&rc) %then
%str(&rc = -1 ;)

%if %length(&dyna_key) ne 0 %then %do ;
&dyna_key = &dyna_key_expr ;
%let key = &dyna_key ;
%end ;

%if %length(&key_hash) = 0 %then
%let key_hash = &key ;

&key_addr = mod ( &key_hash, &size ) + 1 ;

if &keys [ &key_addr ] ne . then do ;

&depth = 0 ;

do while ( 1 ) ;
if ( &key = &keys [ &key_addr ] ) then do ;
%if %length (&rc) %then
%str(&rc = 0 ;) ;
leave ;
end ;

%* stop searching if end of probe reached ;
if ( cmiss(&keys [ &key_addr ]) or &depth > &max_depth ) then do ;
&key_addr = -1 ;
leave ;
end ;

&key_addr + ( &increment ) ;
&bound_check ;
&depth + 1 ;
end ;
end ;
else
&key_addr = -1 ;
*-------------------- ;
%mend hashFetch_LP ;
```
```%macro hashFetchNext_LP (hash, rc) ;
%local size key increment key_addr keys depth max_depth bound_check ;

%let size          = &&hash_size_&hash ;
%let key           = &&hash_key_&hash ;
%let key_hash      = &&hash_key_hash_&hash ;
%let increment     = &&hash_lp_increment_&hash ;
%let dyna_key      = &&hash_dyna_key_&hash ;
%let dyna_key_expr = &&hash_dyna_key_expr_&hash ;

%let key_addr  = &hash._key_addr ;
%let keys      = &hash._keys ;
%let depth     = &hash._depth ;
%let max_depth = &hash._max_depth ;

%if &increment > 0 %then
%let bound_check = if ( &key_addr > &size ) then &key_addr + ( - &size ) ;
%else
%let bound_check = if ( &key_addr <   1   ) then &key_addr + ( + &size ) ;

*-------------------- ;
%if %length (&rc) %then
%str(&rc = -1 ;) ;

if ( &key_addr > -1 ) then do ;

do while ( 1 ) ;
&key_addr + ( &increment ) ;
&bound_check ;
&depth + 1 ;

if ( &key = &keys [ &key_addr ] ) then do ;
%if %length (&rc) %then
%str(&rc = 0 ;) ;
leave ;
end ;

%* stop searching if end of probe reached ;
if ( cmiss(&keys [ &key_addr ]) or &depth > &max_depth ) then do ;
&key_addr = -1 ;
leave ;
end ;
end ;

end ;
*-------------------- ;
%mend hashFetchNext_LP ;

%put NOTE: Hash array macros have been compiled. ;```

Sample code - A problem

```/** /

*
* From a SESUG 2003 coffee table discussion.
*
* Environment:
* Each transaction has an id (tid), a prior transaction id (pid) and an amount
* Each id is a unique 15 digit character string
* A transaction can be the prior transaction of only one transaction
* A path in the transaction data is the set of transactions x,y,z,... such that
* x.tid = y.pid and y.tid = z.pid and ...
* Some transactions are in paths of length 1
*
* Task:
* Find M path totals amongst N transactions
*
* Fake data construction:
* Set N to the number of transactions
* Create M (a random number of) paths in the transaction data
* ;

options mprint notes ;

%* number of transactions ;

%let N = %sysevalf (0+1E6) ;

%* probability of transaction having a first backlink and
%* probability of transaction in a path having a backlink ;

%let pt = 0.65 ;
%let pm = 0.65 ;

%* make fake data ;

data transactions (keep=tid pid amount) ;

array ids (&N,2) _temporary_ ;

retain seed 1 ;

* id is a 15 digit number ;
id = 1e14 ;

do row = 1 to hbound (ids) ;

* for simplicity, new id is always greater than previous id
* if id was random a hash would be needed to ensure the id was not a repeat ;

id + 1e7*ranuni(seed) ;
id + 1 ;

ids ( row, 1 ) = id ;

* generate a random backlink trail ;

prow = row ;
p = &pt ;

do while ( ranuni(seed) < p ) ;

p = &pm ;

prow = int ( prow * ranuni(seed) ) ;

if prow = 0 then leave ;

if ids [ prow,1 ] > 0 then do;      * untagged ;
ids [ prow,1 ] = -ids [ prow,1 ]; * tag as being in a trail ;
ids [  row,2 ] = prow;            * store backlink ;
end ;
else
leave;                            * tagged, scram ;
end ;
end ;

* output the simulated transactions ;

do row = 1 to hbound(ids) ;
id = abs ( ids [ row, 1 ] ) ;
tid = put (id, z15.) ;

prow = ids [ row, 2 ] ;
if prow then do ;
id = abs ( ids [ prow, 1 ] ) ;
pid = put (id, z15.) ;
end ;
else
pid = '' ;

amount = int (100*ranuni(seed)) - 30;  * -30 to 69 ;
output ;
end ;

run ;

* disorder the transactions ;

proc sort ;
by amount ;
run ;

/**/```

Sample code - Solve the problem

Finding and summing ~650,000 paths amongst 1,000,000 transactions. In 2003 took about 4 seconds on my then potato system.

```/** /

%global hash_size ;

%let hash_size = %hashSize (load=0.75, data=transactions) ;

data trail_sums (keep=t_id ntids total_amount rename=(t_id=tid)) ;

%* two hashes will allow forward lookup given only backlinks ;
%* different hashing policies only for testing purposes ;

%declareHash (start, &hash_size, policy=CL)
%declareHashKey  (start, tid)
%declareHashData (start, amount)

%declareHash (next, &hash_size, policy=LP)
%declareHashKey  (next, pid)
%declareHashData (next, tid)
%declareHashData (next, amount)

do until (endOfTransactions) ;
set transactions
( keep=tid pid amount
rename=(tid=t_id pid=p_id)
)
end=endOfTransactions ;

%* transform key variables from character to numeric ;

tid = input (t_id, 15.) ;
pid = input (p_id, 15.) ;

if p_id = '' then do ;
%hashAddKey (start, rc=rc)

if (rc < 0) then do ;
put "ERROR: " tid= "is not unique" ;
stop ;
end ;

%hashSetData (start, amount)
end ;
else do ;
%* hash pid to allow forward lookup ;

%hashAddKey (next, rc=rc)

if (rc < 0) then do ;
put "ERROR: " pid= "is not unique" ;
stop ;
end ;

%hashSetData (next, tid)
%hashSetData (next, amount)
end ;
end ;

%*----- ;

* summarize by trail ;

do key_addr = 1 to &hash_size ;

tid = %keyArray (start)(key_addr) ;

* keyArray(tid)(key_addr) = . means no tid was ever hashed to key_addr ;
* but every tid was hashed, so . means there is
* no tid that corresponds to key_addr and thus key_addr can be skipped ;

if tid eq . then continue ;

* sum amount while following the trail ;

total_amount = %dataArray (start,amount)(key_addr) ;
ntids = 1 ;

do until (tid=.) ;
* check if tid is also pid ;
pid = tid ;
%hashFetch (next, rc=rc)
if rc < 0 then leave ;

total_amount + %hashGetData (next, amount) ;
ntids + 1 ;
tid = %hashGetData (next, tid) ;
end ;

output ;

end ;

stop ;

format tid pid z15. ;
run ;

options source ;

proc sort data=trail_sums ;
by descending ntids descending total_amount tid ;
run ;

ods html path="%sysfunc(pathname(WORK))" file="trail_sums.html" style=sasweb ;

proc print label data=trail_sums (obs=100) ;
label
tid='Most recent tid of trail'
ntids='Number of transactions in trail'
;
run ;
ods html close ;

dm log 'top;find "ERROR:"' log ;
/**/```