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karatsuba64

Zeda
Apr 16th, 2016
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Z80 Assembler 6.14 KB | None | 0 0
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  1. Karatsuba64:
  2. ;Input: (word64_1),(word64_2)
  3. ;Output: (outp128)
  4. ;best   =1776+3*best(mul32)     =5292cc
  5. ;worst  =2243+3*worst(mul32)    =11165cc
  6. ;avg    =2009.5+3*avg(mul32)    =10011.8699cc
  7.  
  8.     ld hl,(word64_1) \ ld (word32_1),hl
  9.     ld hl,(word64_1+2) \ ld (word32_1+2),hl
  10.     ld hl,(word64_2) \ ld (word32_2),hl
  11.     ld hl,(word64_2+2) \ ld (word32_2+2),hl
  12.     call KaratsubaMul32
  13.     ld hl,(outp64) \ ld (outp128),hl
  14.     ld hl,(outp64+2) \ ld (outp128+2),hl
  15.     ld hl,(outp64+4) \ ld (outp128+4),hl
  16.     ld hl,(outp64+6) \ ld (outp128+6),hl
  17.  
  18.     ld hl,(word64_1+4) \ ld (word32_1),hl
  19.     ld hl,(word64_1+6) \ ld (word32_1+2),hl
  20.     ld hl,(word64_2+4) \ ld (word32_2),hl
  21.     ld hl,(word64_2+6) \ ld (word32_2+2),hl
  22.     call KaratsubaMul32
  23.     ld hl,(outp64) \ ld (outp128+8),hl
  24.     ld hl,(outp64+2) \ ld (outp128+10),hl
  25.     ld hl,(outp64+4) \ ld (outp128+12),hl
  26.     ld hl,(outp64+6) \ ld (outp128+14),hl
  27.  
  28. ;512+2*Karatsuba
  29.     xor a
  30.  
  31.     ld hl,(word64_1)
  32.     ld de,(word64_1+4)
  33.     add hl,de
  34.     ld (word32_1),hl
  35.     ld hl,(word64_1+2)
  36.     ld de,(word64_1+6)
  37.     adc hl,de
  38.     ld (word32_1+2),hl
  39.     rla
  40.  
  41.     ld hl,(word64_2)
  42.     ld de,(word64_2+4)
  43.     add hl,de
  44.     ld (word32_2),hl
  45.     ld hl,(word64_2+2)
  46.     ld de,(word64_2+6)
  47.     adc hl,de
  48.     ld (word32_2+2),hl
  49.     push af
  50.     call KaratsubaMul32
  51. ;790+3*Karatsuba
  52.     pop af
  53.     ld c,a
  54.     ld a,0
  55.     jr nc,Addmore_2
  56.     ld a,c
  57.     ld bc,(word64_1)
  58.     ld hl,(word64_1+4)
  59.     add hl,bc
  60.     ex de,hl
  61.     ld bc,(word64_1+2)
  62.     ld hl,(word64_1+6)
  63.     adc hl,bc
  64.     ex de,hl
  65.     ld bc,(outp64+4)
  66.     add hl,bc
  67.     ld (outp64+4),hl
  68.     ex de,hl
  69.     ld bc,(outp64+6)
  70.     adc hl,bc
  71.     ld (outp64+6),hl
  72.     ld c,a
  73.     ld a,0
  74.     adc a,c
  75. Addmore_2:
  76.     rr c
  77.     jr nc,label_2
  78.     ld bc,(word64_2)
  79.     ld hl,(word64_2+4)
  80.     add hl,bc
  81.     ex de,hl
  82.     ld bc,(word64_2+2)
  83.     ld hl,(word64_2+6)
  84.     adc hl,bc
  85.     ex de,hl
  86.     ld bc,(outp64+4)
  87.     add hl,bc
  88.     ld (outp64+4),hl
  89.     ex de,hl
  90.     ld bc,(outp64+6)
  91.     adc hl,bc
  92.     ld (outp64+6),hl
  93. label_2:
  94.     ld d,0 \ adc a,d
  95.  
  96. ;(outp64) - (outp128) - (outp128+8)
  97.     ld hl,(outp64)
  98.     ld bc,(outp128)
  99.     sbc hl,bc
  100.     ld (outp64),hl
  101.  
  102.     ld hl,(outp64+2)
  103.     ld bc,(outp128+2)
  104.     sbc hl,bc
  105.     ld (outp64+2),hl
  106.  
  107.     ld hl,(outp64+4)
  108.     ld bc,(outp128+4)
  109.     sbc hl,bc
  110.     ld (outp64+4),hl
  111.  
  112.     ld hl,(outp64+6)
  113.     ld bc,(outp128+6)
  114.     sbc hl,bc
  115.     ld (outp64+6),hl
  116.     sbc a,d
  117.  
  118.     ld hl,(outp64)
  119.     ld bc,(outp128+8)
  120.     sbc hl,bc
  121.     ld (outp64),hl
  122.  
  123.     ld hl,(outp64+2)
  124.     ld bc,(outp128+10)
  125.     sbc hl,bc
  126.     ld (outp64+2),hl
  127.  
  128.     ld hl,(outp64+4)
  129.     ld bc,(outp128+12)
  130.     sbc hl,bc
  131.     ld (outp64+4),hl
  132.  
  133.     ld hl,(outp64+6)
  134.     ld bc,(outp128+14)
  135.     sbc hl,bc
  136.     ld (outp64+6),hl
  137.     sbc a,d
  138.  
  139. ;(outp64) + (outp128+4)
  140.     ld hl,(outp64)
  141.     ld bc,(outp128+4)
  142.     add hl,bc
  143.     ld (outp128+4),hl
  144.  
  145.     ld hl,(outp64+2)
  146.     ld bc,(outp128+6)
  147.     adc hl,bc
  148.     ld (outp128+6),hl
  149.  
  150.     ld hl,(outp64+4)
  151.     ld bc,(outp128+8)
  152.     adc hl,bc
  153.     ld (outp128+8),hl
  154.  
  155.     ld hl,(outp64+6)
  156.     ld bc,(outp128+10)
  157.     adc hl,bc
  158.     ld (outp128+10),hl
  159.    
  160.     ld hl,(outp128+12)
  161.     ld e,a
  162.     adc hl,de
  163.     ld (outp128+12),hl
  164.     ret nc
  165.     ld hl,(outp128+14)
  166.     inc hl
  167.     ld (outp128+14),hl
  168.     ret
  169. .echo "  Karatsuba64:",$-Karatsuba64
  170. KaratsubaMul32:
  171. ;Input: (word32_1), (word32_2)
  172. ;Output: (outp64)
  173. ;worst: 925+3*worst(Mul)    2974cc
  174. ;best : 785+3*best(Mul)     1172cc
  175. ;avg  : 855+3*avg(Mul)      2667.4566cc
  176. ;Previous best optimized: 3666 t-states worst case, 2880 lower bound
  177. ;has a bug. For example, in pi*e, multiplying the upper 32 bits of each ends in A189, but should be a288
  178.  
  179.     ld bc,(word32_1)
  180.     ld de,(word32_2)
  181.     call BC_Times_DE
  182.     ld c,h
  183.     ld h,l
  184.     ld l,a
  185.     ld (outp),hl
  186.     ld (outp+2),bc
  187.  
  188.  
  189.     ld bc,(word32_1+2)
  190.     ld de,(word32_2+2)
  191.     call BC_Times_DE
  192.     ld c,h
  193.     ld h,l
  194.     ld l,a
  195.     ld (outp+4),hl
  196.     ld (outp+6),bc
  197.  
  198.     xor a
  199.     ld hl,(word32_1)
  200.     ld bc,(word32_1+2)
  201.     add hl,bc
  202.     rla
  203.     ex de,hl
  204.  
  205.     ld hl,(word32_2)
  206.     ld bc,(word32_2+2)
  207.     add hl,bc
  208.     ld b,h
  209.     ld c,l
  210.    
  211.     push af
  212.     call BC_Times_DE
  213.     ld e,h
  214.     ld d,b
  215.     ld h,l
  216.     ld l,a
  217. ;DEHL
  218.  
  219.     pop af
  220.     push hl
  221.     ld c,a
  222.     ld a,0
  223.     jr nc,Addmore_1
  224. ;(ax+b)(cx+d) = acx^2+axd+bcx+bd
  225. ;c flag is c
  226. ;
  227. ;x=2^16
  228. ;a,c are 0 or 1
  229. ;  If a = 1, add c to A (A is the overflow thing), add (word32_2)+(word32_2+2) to DE
  230. ;  If c = 1, add b to DE
  231.     ld a,c
  232.     ld bc,(word32_1)
  233.     ld hl,(word32_1+2)
  234.     add hl,bc
  235.     add hl,de
  236.     ex de,hl
  237.     ld c,a
  238.     ld a,0
  239.     adc a,c
  240. Addmore_1:
  241.     rr c
  242.     jr nc,label_1
  243. ;if bit 7 is set, A =2, else A=0
  244.     ld bc,(word32_2)
  245.     ld hl,(word32_2+2)
  246.     add hl,bc
  247.     add hl,de
  248.     ex de,hl
  249.     adc a,0
  250. label_1:
  251.     pop hl
  252.  
  253.  
  254. ;ADEHL - (outp) - (outp+4)
  255.     ld bc,(outp)
  256. ;   or a
  257.     sbc hl,bc
  258.     ex de,hl
  259. ;HLDE
  260.     ld bc,(outp+2)
  261.     sbc hl,bc \ sbc a,0
  262.     ex de,hl
  263. ;DEHL
  264.     ld bc,(outp+4)
  265.     sbc hl,bc
  266.     ex de,hl
  267. ;HLDE
  268.     ld bc,(outp+6)
  269.     sbc hl,bc \ sbc a,0
  270.     ex de,hl
  271. ;DEHL + (outp+2)
  272.     ld bc,(outp+2)
  273.     add hl,bc
  274.     ld (outp+2),hl
  275.     ex de,hl
  276. ;HLDE
  277.  
  278.     ld bc,(outp+4)
  279.     ld de,(outp+6)
  280.     adc hl,bc
  281.     ld (outp+4),hl
  282.     ld h,0 \ ld l,a
  283.     adc hl,de
  284.     ld (outp+6),hl
  285.     ret
  286. .echo "  Karatsuba32:",$-KaratsubaMul32
  287. BCM:
  288. BC_Times_DE:
  289. ;BC*DE->BHLA
  290. ;out: E=0, A,D are destroyed
  291. ;Assuming B=0, C=0      129cc
  292. ;Assuming B!=0,C=0      329cc~410cc, avg 373cc-3.5
  293. ;         B=0, C!=0
  294. ;Assuming B!=0,C!=0     529cc~683cc, avg 609.5cc-3.5cc
  295. ;Overall average: 79187439/131072=604.15221405029296875cc
  296.  
  297.  
  298.     ld a,b
  299.     ld hl,0
  300.     ld b,h
  301.     or a
  302.     jr z,+_
  303.             add a,a \ jr nc,$+5 \ ld h,d \ ld l,e
  304.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
  305.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
  306.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
  307.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
  308.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
  309.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
  310.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
  311. _:
  312.     push hl
  313.     ld h,b
  314.     ld l,b
  315.     ld b,a
  316.     ld a,c
  317.     ld c,b
  318.     or a
  319.     jr z,+_
  320.             add a,a \ jr nc,$+5 \ ld h,d \ ld l,e
  321.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
  322.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
  323.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
  324.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
  325.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
  326.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
  327.     add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
  328. _:
  329.     pop de
  330.     ld c,a
  331.     ld a,l
  332.     ld l,h
  333.     ld h,c
  334.     add hl,de
  335.     ret nc
  336.     inc b
  337.     ret
  338. .echo "  Base Mult  :",$-BCM
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