Classic 8bit * 8bit Unsigned
Input: H = Multiplier, E = Multiplicand, L = 0, D = 0
Output: HL = Product
sla h ; optimised 1st iteration jr nc,$+3 ld l,e add hl,hl ; unroll 7 times jr nc,$+3 ; ... add hl,de ; ...
Classic 16bit * 8bit Unsigned
Input: A = Multiplier, DE = Multiplicand, HL = 0, C = 0
Output: A:HL = Product
add a,a ; optimised 1st iteration jr nc,$+4 ld h,d ld l,e add hl,hl ; unroll 7 times rla ; ... jr nc,$+4 ; ... add hl,de ; ... adc a,c ; ...
Fast 8bit * 8bit Unsigned (using log / antilog tables)
The original routine was written by Jeff Frohwein for the Nintendo Gameboy. You can find it on Devrs.com.
Because of the usage of log / antilog tables this routine is less accurate, but very fast. It takes advantage of the fact that if you take the log of two numbers, add the results and then take the antilog of the total you have done the equivalent of multiplying the two numbers:
x^a * x^b = x^(a+b) a * b = x^(logx(a) + logx(b))
Input: B = Multiplier, C = Multiplicant
Output: DE = Product
FastMult: ld l,c ld h,&82 ld d,(hl) ; d = 32 * log_2(c) ld l,b ld a,(hl) ; a = 32 * log_2(b) add a,d ld l,a ld a,0 adc a,0 ld h,a ; hl = d + a add hl,hl set 2,h ; hl = hl + $0400 set 7,h ; hl = hl + &8000 ld e,(hl) inc hl ld d,(hl) ; de = 2^((hl)/32) ret ; 32*Log_2(x) Table ; ; FOR A=0 TO 255 ; C=4 ; B=2 ; FOR Z=1 TO 10 ; IF (2^C) > A THEN C=C-B ELSE C=C+B ; B=B/2 ; NEXT Z ; PRINT INT(C*32);","; ; NEXT A ORG &8200 logtable: db 0 , 0 , 32 , 50 , 64 , 74 , 82 , 89 , 96 , 101 , 106 , 110 , 114 , 118 , 121 db 125 , 128 , 130 , 133 , 135 , 138 , 140 , 142 , 144 , 146 , 148 , 150 , 152 db 153 , 155 , 157 , 158 , 160 , 161 , 162 , 164 , 165 , 166 , 167 , 169 , 170 db 171 , 172 , 173 , 174 , 175 , 176 , 177 , 178 , 179 , 180 , 181 , 182 , 183 db 184 , 185 , 185 , 186 , 187 , 188 , 189 , 189 , 190 , 191 , 192 , 192 , 193 db 194 , 194 , 195 , 196 , 196 , 197 , 198 , 198 , 199 , 199 , 200 , 201 , 201 db 202 , 202 , 203 , 204 , 204 , 205 , 205 , 206 , 206 , 207 , 207 , 208 , 208 db 209 , 209 , 210 , 210 , 211 , 211 , 212 , 212 , 213 , 213 , 213 , 214 , 214 db 215 , 215 , 216 , 216 , 217 , 217 , 217 , 218 , 218 , 219 , 219 , 219 , 220 db 220 , 221 , 221 , 221 , 222 , 222 , 222 , 223 , 223 , 224 , 224 , 224 , 225 db 225 , 225 , 226 , 226 , 226 , 227 , 227 , 227 , 228 , 228 , 228 , 229 , 229 db 229 , 230 , 230 , 230 , 231 , 231 , 231 , 231 , 232 , 232 , 232 , 233 , 233 db 233 , 234 , 234 , 234 , 234 , 235 , 235 , 235 , 236 , 236 , 236 , 236 , 237 db 237 , 237 , 237 , 238 , 238 , 238 , 238 , 239 , 239 , 239 , 239 , 240 , 240 db 240 , 241 , 241 , 241 , 241 , 241 , 242 , 242 , 242 , 242 , 243 , 243 , 243 db 243 , 244 , 244 , 244 , 244 , 245 , 245 , 245 , 245 , 245 , 246 , 246 , 246 db 246 , 247 , 247 , 247 , 247 , 247 , 248 , 248 , 248 , 248 , 249 , 249 , 249 db 249 , 249 , 250 , 250 , 250 , 250 , 250 , 251 , 251 , 251 , 251 , 251 , 252 db 252 , 252 , 252 , 252 , 253 , 253 , 253 , 253 , 253 , 253 , 254 , 254 , 254 db 254 , 254 , 255 , 255 , 255 , 255 , 255 ; AntiLog 2^(x/32) Table ; ; FOR A=0 to 510 ; PRINT INT(2^(A/32)+.5);","; ; NEXT A ORG &8400 antilog: dw 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 2 dw 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 dw 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 4 , 4 dw 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 5 , 5 , 5 , 5 , 5 , 5 , 5 , 5 , 5 , 6 dw 6 , 6 , 6 , 6 , 6 , 6 , 6 , 7 , 7 , 7 , 7 , 7 , 7 , 7 , 8 , 8 , 8 , 8 , 8 , 9 dw 9 , 9 , 9 , 9 , 10 , 10 , 10 , 10 , 10 , 11 , 11 , 11 , 11 , 12 , 12 , 12 , 12 dw 13 , 13 , 13 , 13 , 14 , 14 , 14 , 15 , 15 , 15 , 16 , 16 , 16 , 17 , 17 , 17 dw 18 , 18 , 19 , 19 , 19 , 20 , 20 , 21 , 21 , 22 , 22 , 23 , 23 , 24 , 24 , 25 dw 25 , 26 , 26 , 27 , 27 , 28 , 29 , 29 , 30 , 31 , 31 , 32 , 33 , 33 , 34 , 35 dw 36 , 36 , 37 , 38 , 39 , 40 , 41 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 dw 50 , 52 , 53 , 54 , 55 , 56 , 57 , 59 , 60 , 61 , 63 , 64 , 65 , 67 , 68 , 70 dw 71 , 73 , 74 , 76 , 78 , 79 , 81 , 83 , 85 , 87 , 89 , 91 , 92 , 95 , 97 , 99 dw 101 , 103 , 105 , 108 , 110 , 112 , 115 , 117 , 120 , 123 , 125 , 128 , 131 dw 134 , 137 , 140 , 143 , 146 , 149 , 152 , 156 , 159 , 162 , 166 , 170 , 173 dw 177 , 181 , 185 , 189 , 193 , 197 , 202 , 206 , 211 , 215 , 220 , 225 , 230 dw 235 , 240 , 245 , 251 , 256 , 262 , 267 , 273 , 279 , 285 , 292 , 298 , 304 dw 311 , 318 , 325 , 332 , 339 , 347 , 354 , 362 , 370 , 378 , 386 , 395 , 403 dw 412 , 421 , 431 , 440 , 450 , 459 , 470 , 480 , 490 , 501 , 512 , 523 , 535 dw 546 , 558 , 571 , 583 , 596 , 609 , 622 , 636 , 650 , 664 , 679 , 693 , 709 dw 724 , 740 , 756 , 773 , 790 , 807 , 825 , 843 , 861 , 880 , 899 , 919 , 939 dw 960 , 981 , 1002 , 1024 , 1046 , 1069 , 1093 , 1117 , 1141 , 1166 , 1192 dw 1218 , 1244 , 1272 , 1300 , 1328 , 1357 , 1387 , 1417 , 1448 , 1480 , 1512 dw 1545 , 1579 , 1614 , 1649 , 1685 , 1722 , 1760 , 1798 , 1838 , 1878 , 1919 dw 1961 , 2004 , 2048 , 2093 , 2139 , 2186 , 2233 , 2282 , 2332 , 2383 , 2435 dw 2489 , 2543 , 2599 , 2656 , 2714 , 2774 , 2834 , 2896 , 2960 , 3025 , 3091 dw 3158 , 3228 , 3298 , 3371 , 3444 , 3520 , 3597 , 3676 , 3756 , 3838 , 3922 dw 4008 , 4096 , 4186 , 4277 , 4371 , 4467 , 4565 , 4664 , 4767 , 4871 , 4978 dw 5087 , 5198 , 5312 , 5428 , 5547 , 5668 , 5793 , 5919 , 6049 , 6182 , 6317 dw 6455 , 6597 , 6741 , 6889 , 7039 , 7194 , 7351 , 7512 , 7677 , 7845 , 8016 dw 8192 , 8371 , 8555 , 8742 , 8933 , 9129 , 9329 , 9533 , 9742 , 9955 , 10173 dw 10396 , 10624 , 10856 , 11094 , 11337 , 11585 , 11839 , 12098 , 12363 , 12634 dw 12910 , 13193 , 13482 , 13777 , 14079 , 14387 , 14702 , 15024 , 15353 , 15689 dw 16033 , 16384 , 16743 , 17109 , 17484 , 17867 , 18258 , 18658 , 19066 , 19484 dw 19911 , 20347 , 20792 , 21247 , 21713 , 22188 , 22674 , 23170 , 23678 , 24196 dw 24726 , 25268 , 25821 , 26386 , 26964 , 27554 , 28158 , 28774 , 29404 , 30048 dw 30706 , 31379 , 32066 , 32768 , 33485 , 34219 , 34968 , 35734 , 36516 , 37316 dw 38133 , 38968 , 39821 , 40693 , 41584 , 42495 , 43425 , 44376 , 45348 , 46341 dw 47356 , 48393 , 49452 , 50535 , 51642 , 52772 , 53928 , 55109 , 56316 , 57549 dw 58809 , 60097 , 61413 , 62757
Faster, accurate 8bit * 8bit Unsigned
I'm currently working on a new routine, based on a routine by Kirk Meyer [1] which uses nibble multiplication tables.
I have a working, tested version which uses 16K of tables and can perform multiplication in 20μs.
The code to produce the tables is below:
.maketabs ld hl,hltab1 .makelp1 ld a,l rla and #1e add restab / 256 ld (hl),a inc l jr nz,makelp1 inc h .makelp2 ld a,l rra:rra:rra and #1e jr z,usez add restab2 - restab / 256 - 2 .usez add restab / 256 ld (hl),a inc l jr nz,makelp2 inc h ; restab .makelp3 ld a,(hl) inc h ld d,(hl) inc h add l ld (hl),a inc h ld a,0 adc d ld (hl),a dec h:dec h:dec h inc l jr nz,makelp3 inc h inc h ld a,h cp restab2 / 256 - 2 jr nz,makelp3 ld b,h ld c,l inc b inc b ld h,restab / 256 + 2 .makelp4 ld e,(hl) inc h ld d,(hl) dec h ex de,hl add hl,hl:add hl,hl:add hl,hl:add hl,hl ex de,hl ld a,e ld (bc),a inc b ld a,d ld (bc),a dec b inc l inc c jr nz,makelp4 inc h inc h inc b inc b ld a,h cp restab2 / 256 jr nz,makelp4 ret ds -$ and #ff .hltab1 ds 256 .hltab2 ds 256 .restab ds 512 * 16 .restab2 ds 512 * 15
The code to perform the multiplication (DE = L * C):
ld h,hltab1 / 256 ; 2 ld b,(hl) ; 4 inc h ; 5 ld h,(hl) ; 7 ld l,c ; 8 ld a,(bc) ; 10 add (hl) ; 12 ld e,a ; 13 inc b ; 14 inc h ; 15 ld a,(bc) ; 17 adc (hl) ; 19 ld d,a ; 20
16K is a lot of memory to use for tables, but I'm working on a way to reduce this to 8K while maintaining similar performance (around 26μs). The idea is rather than using tables for the low and high nibbles, use tables for alternate bits. So there would be 16 tables for the values #00, #01, #04, #05, #10, #11, #14, #15, #40, #41, #44, #45, #50, #51, #54, #55. The values can be shifted by 1 (rather than 4) to give values for the alternate bits using a simple ADD HL,HL.
Executioner 03:58, 8 May 2007 (CEST)
16bit * 16bit Unsigned
Input: BC = Multiplier, DE = Multiplicand
Output: A,HL = Product
ld ix,0 ld hl,0 .mul24b1: ld a,c or b jr z,mul24b3 srl b rr c jr nc,mul24b2 add ix,de ld a,h adc l ld h,a .mul24b2: sla e rl d rl l jr mul24b1: .mul24b3: ld a,h db #dd:ld e,l db #dd:ld d,h ex de,hl ret