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lognat:;Input: H.L needs to be on [1,2];Output: H.L if z flag is set, else if nz, no result;avg speed: 677 t-states dec h dec h jr nz,$+8 inc l \ dec l ret nz ld l,177 ret inc h ret nz ld b,h ld c,l ld e,l ld d,8 add hl,hl add hl,hl add hl,de ex de,hl add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ adc a,a ld h,a \ ld l,b sla h \ jr c,$+3 \ ld l,c add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc rl l ld a,h adc a,b ld l,a ld h,b cp a ret
lognat:;Input: H.L needs to be on (0,128.0);Output: H.L if c flag set; returns nc if input is negative (HL not modified);Error:; The error on the outputs is as follows:; 20592 inputs are exact; 12075 inputs are off by 1/256; 100 inputs are off by 2/256; So all 32767 inputs are within 2/256, with average error being <1/683 which is smaller than 1/256.;Size: 177 bytes;Speed: average speed is less than 1250 t-states ld a,h \ or l \ jr nz,$+5 ld h,80h \ ret dec h dec h jr nz,$+9 inc l \ dec l jr nz,normalizeln-1 ld l,177 ret inc h jr nz,normalizeln ld b,h ld c,l ld e,l ld d,8 add hl,hl add hl,hl add hl,de ex de,hl call HL_Div_DE ld h,a \ ld l,b sla h \ jr c,$+3 \ ld l,c add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc add hl,hl \ jr c,$+3 \ add hl,bc rl l ld a,h adc a,b ld h,b ld l,a scf retHL_Div_DE: add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ jr nc,$+3 \ add hl,de \ adc a,a add hl,hl \ sbc hl,de \ adc a,a \ ret inc hnormalizeln: xor a inc h \ ret m ld d,a \ ld e,a ld a,l jr z,toosmall inc e \ srl h \ rra \ jr nz,$-4 rla \ rl h dec estepin: ld l,a push de call lognat pop de ;now multiply DE by 355, then divide by 2 (rounding) ld b,d \ ld c,e \ ld a,d ex de,hl add hl,hl add hl,hl ;4 add hl,bc ;5 add hl,hl ;10 add hl,bc ;11 add hl,hl ;22 add hl,hl add hl,hl add hl,hl add hl,bc add hl,hl add hl,bc sra h \ rr l adc hl,de scf rettoosmall: dec d dec e \ add a,a \ jr nc,$-2 inc h jp stepin
ln_88:;Input: HL is a fixed point number;Output: ln(H.L)->H.L;Speed: Avg: 340+(325 worst case) call lg_88 ;now signed multiply HL by 355, then divide by 2 (rounding) ld de,0 bit 7,h jr z,$+9 dec e \ xor a \ sub l \ ld l,a sbc a,a \ sub h \ ld h,a ld b,h ld c,l xor a add hl,hl add hl,hl \ rla add hl,bc \ adc a,d add hl,hl \ rla add hl,bc \ adc a,d add hl,hl \ rla add hl,hl \ rla add hl,hl \ rla add hl,hl \ rla add hl,bc \ adc a,d add hl,hl \ rla add hl,bc \ adc a,d sra a \ rr h ld l,h ld h,a inc e ret nz xor a \ sub l \ ld l,a sbc a,a \ sub h \ ld h,a retlg_88:;Input: HL is a fixed point number;Output: lg(H.L)->H.L;Speed: Avg: 340 ld de,lgLUT ld b,0 ld a,h or a ret m ld a,l jr z,$+8 inc b \ srl h \ rra \ jr nz,$-4 or a \ jr nz,$+6 ld hl,8000h \ ret rra \ inc b \ jr nc,$-2;A is the element to look up in the LUT ld l,a ld c,h dec b add hl,hl add hl,de ld e,(hl) inc hl ld d,(hl) ex de,hl add hl,bc retlglut:.dw $F800.dw $F996.dw $FA52.dw $FACF.dw $FB2C.dw $FB76.dw $FBB3.dw $FBE8.dw $FC16.dw $FC3F.dw $FC64.dw $FC86.dw $FCA5.dw $FCC1.dw $FCDC.dw $FCF4.dw $FD0B.dw $FD21.dw $FD36.dw $FD49.dw $FD5C.dw $FD6D.dw $FD7E.dw $FD8E.dw $FD9D.dw $FDAC.dw $FDBA.dw $FDC8.dw $FDD5.dw $FDE2.dw $FDEE.dw $FDFA.dw $FE06.dw $FE11.dw $FE1C.dw $FE26.dw $FE31.dw $FE3B.dw $FE44.dw $FE4E.dw $FE57.dw $FE60.dw $FE69.dw $FE71.dw $FE7A.dw $FE82.dw $FE8A.dw $FE92.dw $FE9A.dw $FEA1.dw $FEA9.dw $FEB0.dw $FEB7.dw $FEBE.dw $FEC5.dw $FECB.dw $FED2.dw $FED8.dw $FEDF.dw $FEE5.dw $FEEB.dw $FEF1.dw $FEF7.dw $FEFD.dw $FF03.dw $FF09.dw $FF0E.dw $FF14.dw $FF19.dw $FF1E.dw $FF24.dw $FF29.dw $FF2E.dw $FF33.dw $FF38.dw $FF3D.dw $FF42.dw $FF47.dw $FF4B.dw $FF50.dw $FF55.dw $FF59.dw $FF5E.dw $FF62.dw $FF67.dw $FF6B.dw $FF6F.dw $FF74.dw $FF78.dw $FF7C.dw $FF80.dw $FF84.dw $FF88.dw $FF8C.dw $FF90.dw $FF94.dw $FF98.dw $FF9B.dw $FF9F.dw $FFA3.dw $FFA7.dw $FFAA.dw $FFAE.dw $FFB2.dw $FFB5.dw $FFB9.dw $FFBC.dw $FFC0.dw $FFC3.dw $FFC6.dw $FFCA.dw $FFCD.dw $FFD0.dw $FFD4.dw $FFD7.dw $FFDA.dw $FFDD.dw $FFE0.dw $FFE4.dw $FFE7.dw $FFEA.dw $FFED.dw $FFF0.dw $FFF3.dw $FFF6.dw $FFF9.dw $FFFC.dw $FFFF
arctan_88:;Input:; D.E;Output: atan(D.E)->D.E push de ld a,d or a jp p,$+5 neg ld d,a dec a jr nz,checkneedinv inc e \ dec e \ jr nz,checkneedinv pop af \ rla \ ld de,201 \ ret nc \ ld de,-201 \ retcheckneedinv: inc a call nz,DEgt1_Inv;0.E is the value to atan ld hl,adjustatan push hl ld a,e cp 46 \ ret c dec a \ cp 42h \ ret c dec a \ cp 4Eh \ ret c dec a \ cp 57h \ ret c dec a \ cp 5Eh \ ret c dec a \ cp 64h \ ret c dec a \ cp 6Ah \ ret c dec a \ cp 6Fh \ ret c sub 6Fh \ ld e,a ld hl,atanlut add hl,de ld a,(hl) retadjustatan: ld e,a pop bc ld a,b or a jp p,$+5 neg jr z,$+9 ld hl,402 or a sbc hl,de ex de,hl rl b ret nc xor a sub e ld e,a sbc a,a sub d ld d,a retDEgt1_Inv:;Works if DE>1 ld hl,256 ld b,8InvLoop: add hl,hl sbc hl,de jr nc,$+3 add hl,de adc a,a djnz InvLoop cpl ld e,a ld d,b retatanlut:.db $6F.db $6F.db $70.db $71.db $72.db $73.db $73.db $74.db $75.db $76.db $77.db $77.db $78.db $79.db $7A.db $7B.db $7B.db $7C.db $7D.db $7E.db $7F.db $7F.db $80.db $81.db $82.db $82.db $83.db $84.db $85.db $85.db $86.db $87.db $88.db $88.db $89.db $8A.db $8B.db $8B.db $8C.db $8D.db $8E.db $8E.db $8F.db $90.db $90.db $91.db $92.db $93.db $93.db $94.db $95.db $95.db $96.db $97.db $97.db $98.db $99.db $9A.db $9A.db $9B.db $9C.db $9C.db $9D.db $9E.db $9E.db $9F.db $A0.db $A0.db $A1.db $A2.db $A2.db $A3.db $A3.db $A4.db $A5.db $A5.db $A6.db $A7.db $A7.db $A8.db $A9.db $A9.db $AA.db $AA.db $AB.db $AC.db $AC.db $AD.db $AD.db $AE.db $AF.db $AF.db $B0.db $B0.db $B1.db $B2.db $B2.db $B3.db $B3.db $B4.db $B5.db $B5.db $B6.db $B6.db $B7.db $B7.db $B8.db $B9.db $B9.db $BA.db $BA.db $BB.db $BB.db $BC.db $BC.db $BD.db $BE.db $BE.db $BF.db $BF.db $C0.db $C0.db $C1.db $C1.db $C2.db $C2.db $C3.db $C3.db $C4.db $C4.db $C5.db $C6.db $C6.db $C7.db $C7.db $C8.db $C8.db $C9
Rand24:;Inputs: seed1,seed2;Outputs:; HLA is the pseudo-random number; seed1,seed2 incremented accordingly;Destroys: BC,DE;Notes:; seed1*243+83 mod 65519 -> seed1; seed2*251+43 mod 65521 -> seed2; Output seed1*seed2 ld hl,(seed1) xor a ld b,h \ ld c,l ld de,83 add hl,hl \ rla ;2 add hl,bc \ adc a,d ;3 add hl,hl \ rla ;6 add hl,bc \ adc a,d ;7 add hl,hl \ rla ;14 add hl,bc \ adc a,d ;15 add hl,hl \ rla ;30 add hl,hl \ rla ;60 add hl,hl \ rla ;120 add hl,bc \ adc a,d ;121 add hl,hl \ rla ;242 add hl,bc \ adc a,d ;243 add hl,de \ adc a,d ;243x+83;now AHL mod 65519; Essentially, we can at least subtract A*65519=A(65536-17), so add A*17 to HL ex de,hl ld l,a ld b,h ld c,l add hl,hl add hl,hl add hl,hl add hl,hl add hl,bc add hl,de ld de,65519 jr nc,$+5 or a \ sbc hl,de or a \ sbc hl,de jr nc,$+3 add hl,de ld (seed1),hl;seed1 done, now we need to do seed2 ld hl,(seed2); seed1*243+83 mod 65519 -> seed1; seed2*251+43 mod 65521 -> seed2; Output seed1*seed2 xor a ld b,h \ ld c,l ld de,43 add hl,hl \ rla ;2 add hl,bc \ adc a,d ;3 add hl,hl \ rla ;6 add hl,bc \ adc a,d ;7 add hl,hl \ rla ;14 add hl,bc \ adc a,d ;15 add hl,hl \ rla ;30 add hl,bc \ adc a,d ;31 add hl,hl \ rla ;62 add hl,hl \ rla ;124 add hl,bc \ adc a,d ;125 add hl,hl \ rla ;250 add hl,bc \ adc a,d ;251 add hl,de \ adc a,d ;251x+83;now AHL mod 65521; Essentially, we can at least subtract A*65521=A(65536-15), so add A*15 to HL ex de,hl ld l,a ld b,h ld c,l add hl,hl add hl,hl add hl,hl add hl,hl sbc hl,bc add hl,de ld de,65521 jr nc,$+5 or a \ sbc hl,de or a \ sbc hl,de jr nc,$+3 add hl,de ld (seed2),hl;now seed1 and seed 2 are computed ld bc,(seed1) ex de,hl call BC_Times_DE ex de,hl ld l,b ld h,0 ld b,h ld c,l add hl,hl add hl,hl add hl,bc add hl,hl add hl,hl add hl,bc add hl,hl add hl,bc ld c,d ld d,e ld e,a ld a,c sbc hl,bc sbc a,b ret nc ld c,43 add hl,bc ret;now do BC_times_DEBC_Times_DE:;BHLA is the result ld a,b or a ld hl,0 ld b,h;1 add a,a jr nc,$+4 ld h,d ld l,e;2 add hl,hl rla jr nc,$+4 add hl,de adc a,b;227+10b-7p add hl,hl rla jr nc,$+4 add hl,de adc a,b add hl,hl rla jr nc,$+4 add hl,de adc a,b add hl,hl rla jr nc,$+4 add hl,de adc a,b add hl,hl rla jr nc,$+4 add hl,de adc a,b add hl,hl rla jr nc,$+4 add hl,de adc a,b add hl,hl rla jr nc,$+4 add hl,de adc a,b;===;AHL is the result of B*DE*256 push hl ld h,b ld l,b ld b,a ld a,c ld c,h;1 add a,a jr nc,$+4 ld h,d ld l,e;2 add hl,hl rla jr nc,$+4 add hl,de adc a,c;227+10b-7p add hl,hl rla jr nc,$+4 add hl,de adc a,c add hl,hl rla jr nc,$+4 add hl,de adc a,c add hl,hl rla jr nc,$+4 add hl,de adc a,c add hl,hl rla jr nc,$+4 add hl,de adc a,c add hl,hl rla jr nc,$+4 add hl,de adc a,c add hl,hl rla jr nc,$+4 add hl,de adc a,c pop de;Now BDE*256+AHL ld c,a ld a,l ld l,h ld h,c add hl,de ret nc inc b;BHLA is the 32-bit result retseed1: .dw 0seed2: .dw 0
rand:;Tested and passes all CAcert tests;Uses a very simple 32-bit LCG and 32-bit LFSR;it has a period of 18,446,744,069,414,584,320;roughly 18.4 quintillion.;291ccseed1_0=$+1 ld hl,12345seed1_1=$+1 ld de,6789 ld b,h ld c,l add hl,hl \ rl e \ rl d add hl,hl \ rl e \ rl d inc l add hl,bc ld (seed1_0),hl ld hl,(seed1_1) adc hl,de ld (seed1_1),hl ex de,hlseed2_0=$+1 ld hl,9876seed2_1=$+1 ld bc,54321 add hl,hl \ rl c \ rl b ld (seed2_1),bc sbc a,a and %11000101 xor l ld l,a ld (seed2_0),hl ex de,hl add hl,bc ret
;#define smc ;uncomment if you are using SMCrand16:;collaboration by Zeda with Runer112;160cc or 148cc if using SMC;26 bytes;cycle: 4,294,901,760 (almost 4.3 billion)#ifdef smcseed1=$+1 ld hl,9999#else ld hl,(seed1)#endif ld b,h ld c,l add hl,hl add hl,hl inc l add hl,bc ld (seed1),hl#ifdef smcseed2=$+1 ld hl,9999#else ld hl,(seed2)#endif add hl,hl sbc a,a and %00101101 xor l ld l,a ld (seed2),hl add hl,bc ret
xsp32:;Inputs: (seed1), (seed2), and (seed3) are 16-bit seeds. (seed1) and (seed2) can't both be 0.;Outputs: HL is the pseudorandom number;Destroys: A,DE,BC;cycle: 281,474,976,645,120;It would take about 185 years at 15MHz to repeat;min: 258cc (236cc if using SMC);max: 288cc (266cc if using SMC);avg: 273cc (251cc if using SMC);63 bytes (62 bytes if using SMC)#ifdef SMCseed1 = $+1 ld hl,12345seed2 = $+1 ld de,6789#else ld hl,(seed1) ld de,(seed2)#endif;first, XOR it with itself, shifted left 23 bits;low bit of d needs to be shifted in ld a,h rra ld a,l rra jr nc,+_ rl e ccf rr e_: xor d ld d,a;XOR it with itself, shifted right 15 bits ld a,h rla ld a,e rla xor l ld l,a ld a,e rla ld a,d rla jr nc,+_ rr e ccf rl e_: xor h ld h,a;XOR it with itself, shifted left 17 bits;HL<<1 ld (seed1),hl add hl,hl ld a,h xor d ld h,a ld a,l xor e ld l,a ld (seed2),hl ex de,hl#ifdef SMCseed3 = $+1 ld hl,33333#else ld hl,(seed3)#endif inc hl inc h ld (seed3),hl add hl,de ret
xs32:;32-bit xorshift;seed^=seed<<23;seed^=seed>>15;seed^=seed<<17;min: 209cc (193cc if using SMC);max: 239cc (223cc if using SMC);avg: 224cc (208cc if using SMC);53 bytes (52 bytes if using SMC)#ifdef SMCseed1 = $+1 ld hl,12345seed2 = $+1 ld de,6789#else ld hl,(seed1) ld de,(seed2)#endif;first, XOR it with itself, shifted left 23 bits;low bit of d needs to be shifted in ld a,h rra ld a,l rra jr nc,+_ rl e ccf rr e_: xor d ld d,a;XOR it with itself, shifted right 15 bits ld a,h rla ld a,e rla xor l ld l,a ld a,e rla ld a,d rla jr nc,+_ rr e ccf rl e_: xor h ld h,a;XOR it with itself, shifted left 17 bits;HL<<1 ld (seed1),hl add hl,hl ld a,h xor d ld h,a ld a,l xor e ld l,a ld (seed2),hl ret
SqrtHLDE:;input: HLDE;Output: BC;310 bytes;Average is about 1443 t-states push de xor a ld b,a ld e,l ld l,h ld h,a add hl,hl add hl,hl cp h jr nc,$+5 dec h ld a,4 add hl,hl add hl,hl ld c,a sub h jr nc,$+6 cpl ld h,a inc c inc c ld a,c add hl,hl add hl,hl add a,a ld c,a sub h jr nc,$+6 cpl ld h,a inc c inc c ld a,c add hl,hl add hl,hl add a,a ld c,a sub h jr nc,$+6 cpl ld h,a inc c inc c ld a,c ld l,e add hl,hl add hl,hl add a,a ld c,a sub h jr nc,$+6 cpl ld h,a inc c inc c ld a,c add hl,hl add hl,hl add a,a ld c,a sub h jr nc,$+6 cpl ld h,a inc c inc c ld a,c add a,a \ ld c,a add hl,hl add hl,hl jr nc,$+6 sub h \ jp $+6 sub h jr nc,$+6 inc c \ inc c cpl ld h,a ld a,l ld l,h add a,a ld h,a adc hl,hl adc hl,hl sll c \ rl b sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a;iteration 9;now I need to rotate in more bits pop de sla d \ adc hl,hl \ sla d \ adc hl,hl sll c \ rl b sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a sla d \ adc hl,hl \ sla d \ adc hl,hl sll c \ rl b sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a sla d \ adc hl,hl \ sla d \ adc hl,hl sll c \ rl b sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a sla d \ adc hl,hl \ sla d \ adc hl,hl sll c \ rl b sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a sla e \ adc hl,hl \ sla e \ adc hl,hl sll c \ rl b sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a sla e \ adc hl,hl \ sla e \ adc hl,hl sll c \ rl b sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a sll c \ rl b sla e \ adc hl,hl \ sla e \ adc hl,hl jr nc,$+9 or a sbc hl,bc inc c jp $+13 sbc hl,bc jr nc,$+3 add hl,bc sbc a,a \ add a,a \ inc a \ add a,c \ ld c,a sla e \ adc hl,hl \ jr nc,$+4 inc c \ ret sla e \ adc hl,hl \ jr nc,$+8 sbc hl,bc \ or a \ jp $+7 or a \ sbc hl,bc \ ret c scf \ sbc hl,bc \ ret c inc c \ ret
sDiv2416: xor d push af xor d ld b, a jp p, divdPos xor a sub l ld l, a ld a, 0 sbc a, h ld h, a ld a, 0 sbc a, b ld b, adivdPos: bit 7, d jr z, divrPos xor a sub e ld e, a ld a, 0 sbc a, d ld d, a ld a, bdivrPos: push hl pop ix ld hl, 0 ld b, 24divLoop: add ix, ix rla adc hl, hl sbc hl, de jr nc, $ + 4 add hl, de ; jp nc, xxxx ; it works because the carry can not be set and "inc ix" is 2 bytes .db $D2 inc ix djnz divLoop push ix pop hl ld b, a pop af ld a, b ret p xor a sub l ld l, a ld a, 0 sbc a, h ld h, a ld a, 0 sbc a, b ret
fastLDIR:;copy BC bytes from HL to DE;Cost:; 27cc for having to call; 110cc for setting up the loop, worst case; 10cc * ceiling(BC/n) ;n=2^k for some k, see the line below "ldirloop:"; 16cc * BC;costs roughly 152-BC*(5-10/n) more than a simple LDIR (worst case);for n=4, BC>=61 saves;for n=8, BC>=41 saves;for n=16, BC>=35 saves * default, see the "ldirloop" to change;for n=32, BC>=33 saves;for n=64, BC>=32 saves push hl push af xor a sub c and 15 ;change to n-1 add a,a ld hl,ldirloop add a,l ld l,a jr nc,$+3 ;these aren't needed if the ldirloop doesn't cross a 256 byte boundary. Can save 12cc on the above timings and 3 bytes. inc h ; pop af ex (sp),hl retldirloop:;n=16, (number of LDI instructions, use qty of 4,8,16,32,64) ldi ldi ldi ldi ldi ldi ldi ldi ldi ldi ldi ldi ldi ldi ldi_ldirloop_end: ldi jp pe,ldirloop ret
xor a sub c and c
smc = 1 ;use 1 if the code is in RAM, since it is faster. If it is in an app, use 0 and define a 2-byte RAM location for the seed.lehmer:;;Input:;; (seed) has the seed value of the RNG;;Output:;; (seed) is updated, HL is the result;;Destroys:;; A,DE,BC;;Timing:;; if seed>0 231cc or 232cc, condition dependent;; if seed=0 91cc;; if smc=1 subtract 6cc;;Size: 44 bytes;;Notes:;; Uses the Lehmer RNG used by the Sinclair ZX81;; 75x mod 65537 -> x#IF smc == 0 ld hl,(seed)#ELSEseed = $+1 ld hl,0#ENDIF;multiply by 75 ld c,l ld b,h xor a adc hl,hl \ jr z,special \ ld d,a \ rla add hl,hl \ rla add hl,hl \ rla \ add hl,bc \ adc a,d add hl,hl \ rla add hl,hl \ rla \ add hl,bc \ adc a,d add hl,hl \ rla \ add hl,bc;modulo 65537, see note below on how this works ld e,a sbc hl,de ;No need to reset the c flag since it is already jr nc,$+3 inc hl ld (seed),hl retspecial:;In the case that HL=0, this should be interpreted as 65536 = -1 mod 65537, so return -75 mod 65537 = -74 mod 65536 in HL ld hl,-74 ld (seed),hl ret ;mod by 2^16 + 1 (a prime);current form is A*2^16+HL;need:; (A*2^16+HL) mod (2^16+1);add 0 as +1-1; (A*(2^16+1-1)+HL) mod (2^16+1);distribute; (A*(2^16+1)-A+HL) mod (2^16+1);A*(2^16+1) mod 2^16+1 = 0, so remove; (-A+HL) mod (2^16+1);Oh hey, that's easy! :P;I use this trick everywhere, you should, too.
L_To_Dec:;;Unrolled;;Converts the 8-bit register L to binary coded decimal;;Digits stored in LA (A has the lower 2 digits, L the upper).;;Inputs: L is the 8-bit unsigned int to convert;;Output: A has the lower 2 digits (in BCD form), L has the upper;;Destroys: H,F;;141cc ;;27 bytes ld h,0 add hl,hl add hl,hl add hl,hl add hl,hl ld a,h \ daa \ rl l adc a,a \ daa \ rl l adc a,a \ daa \ rl l adc a,a \ daa \ rl l adc a,a \ daa \ rl l ret
setXXOP2: ld hl,OP2 jr setXXsetXXOP1: ld hl,OP1setXX:;;Inputs: A is the unsigned int;; HL is where to write the TI float;;Destroys:All;;291cc+38b (or 144cc if A=0);;average: b=29/255;;295.3215686cc;;59 bytes ld c,0 ld (hl),c \ inc hl ld (hl),81h inc hl \ ld (hl),c ld d,h \ ld e,l inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c or a \ ret z ;If A is zero, exit early. +138cc ld l,a ;\ ld h,c ; | add hl,hl ; |Start converting A to BCD add hl,hl ; | add hl,hl ; | add hl,hl ; | ld a,h \ daa \ rl l ; |Finish converting A to BCD adc a,a \ daa \ rl l ; |Number is in LA adc a,a \ daa \ rl l ; | adc a,a \ daa \ rl l ; | adc a,a \ daa ;/ +124cc ex de,hl ld (hl),a and $F0 ret nz ;+29cc rld ;\ Rotate up 1 digit dec hl ; | ld (hl),80h ; | ret ; /
setXXXOP1: ld hl,OP1setXXX:;;Inputs: A is the unsigned int;; HL is where to write the TI float;;Destroys:All;;423cc+13a+63b (or 233cc if A=0);;average: a=99/255, b=29/255;;435.2117647cc average;;64 bytes ld bc,$0700 ld (hl),c inc hl ld (hl),83h ld d,h ld e,l inc hl \ ld (hl),c \ djnz $-2 or a \ ret z ;If A is zero, exit early. +227cc ld l,a ;\ ld h,c ; | add hl,hl ; |Start converting A to BCD add hl,hl ; | add hl,hl ; | add hl,hl ; | ld a,h \ daa \ rl l ; |Finish converting A to BCD adc a,a \ daa \ rl l ; |Number is in LA adc a,a \ daa \ rl l ; | adc a,a \ daa \ rl l ; | adc a,a \ daa \ rl l ;/ +132cc ex de,hl jr nz,$+6 \ ld e,a \ xor a \ ld (hl),81h ;+(21+4/85)cc inc hl ld (hl),e inc hl ld (hl),a ld a,e and $F0 ret nz ;+48cc rld ;\ Rotate up 1 digit dec hl ; | rld ; | dec hl ; | dec (hl) ; |Decrement exponent ret ; /+63(29/255)cc
setXXX:;;Inputs: A is the unsigned int;; HL is where to write the TI float;;Destroys:All;;334cc+13a+63b (or 144cc if A=0);;average: a=99/255, b=29/255;;346.2117647cc average;;75 bytes ld c,0 ld (hl),c inc hl ld (hl),83h ld d,h ld e,l inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c inc hl \ ld (hl),c or a \ ret z ;If A is zero, exit early. +227cc ld l,a ;\ ld h,c ; | add hl,hl ; |Start converting A to BCD add hl,hl ; | add hl,hl ; | add hl,hl ; | ld a,h \ daa \ rl l ; |Finish converting A to BCD adc a,a \ daa \ rl l ; |Number is in LA adc a,a \ daa \ rl l ; | adc a,a \ daa \ rl l ; | adc a,a \ daa \ rl l ;/ +132cc ex de,hl jr nz,$+6 \ ld e,a \ xor a \ ld (hl),81h ;+(21+4/85)cc inc hl ld (hl),e inc hl ld (hl),a ld a,e and $F0 ret nz ;+48cc rld ;\ Rotate up 1 digit dec hl ; | rld ; | dec hl ; | dec (hl) ; |Decrement exponent ret ; /+63(29/255)cc
setXXX_signed:;;Inputs: A is the signed int;; HL is where to write the TI float ld c,0 ld (hl),c add a,a jr c,$+6 neg ld (hl),80h inc hl ld (hl),81h ld d,h ld e,l inc hl \ ld (hl),c \ djnz $-2 or a \ ret z ld l,a ;\ ld h,c ; | add hl,hl ; |Start converting A to BCD add hl,hl ; | add hl,hl ; | add hl,hl ; | ld a,h \ daa \ rl l ; |Finish converting A to BCD adc a,a \ daa \ rl l ; |Number is in cA adc a,a \ daa \ rl l ; |(c is carry) adc a,a \ daa ;/ ex de,hl jr nc,$+15 ld (hl),82h inc hl inc hl ld (hl),a xor a rld or $10 dec hl ld (hl),a ret inc hl ld (hl),a and $F0 ret nz rld ;\ Rotate up 1 digit dec hl ; | ld (hl),80h ; | ret ; /
ConvOP1:;;Output: HL is the 16-bit result. ld de,OP1ConvFloat:;;Input: DE points to the float.;;Output: HL is the 16-bit result.;;Errors: DataType if the float is negative or complex;; Domain if the integer exceeds 16 bits.;;Timings: Assume no errors were called.;; Input is on:;; (0,1) => 59cc Average=59;; 0 or [1,10) => 120cc or 129cc =124.5;; [10,100) => 176cc or 177cc =176.5;; [100,1000) => 309cc, 310cc, 318cc, or 319cc. =314;; [1000,10000) => 376cc to 378cc =377;; [10000,65536) => 514cc to 516cc, or 523cc to 525cc =519.5;;Average case: 496.577178955078125cc;;vs 959.656982421875cc;;87 bytes ld a,(de) or a jr nz,ErrDataType inc de ld hl,0 ld a,(de) inc de sub 80h ret c jr z,final cp 5 jp c,enterloopErrDomain:;Throws a domain error. bcall(_ErrDomain)ErrDataType:;Throws a data type error. bcall(_ErrDataType)loop: ld a,b ld b,h ld c,l add hl,hl add hl,bc add hl,hl add hl,hl add hl,hl add hl,bc add hl,hl add hl,hlenterloop: ld b,a ex de,hl ld a,(hl) \ and $F0 \ rra \ ld c,a \ rra \ rra \ sub c \ add a,(hl) inc hl ex de,hl add a,l ld l,a jr nc,$+3 inc h dec b ret z djnz loop ld b,h ld c,l xor a;check overflow in this mul by 10! add hl,hl \ adc a,a add hl,hl \ adc a,a add hl,bc \ adc a,0 add hl,hl \ adc a,a jr nz,ErrDomainfinal: ld a,(de) rrca rrca rrca rrca and 15 add a,l ld l,a ret nc inc h ret nz jr ErrDomain
ConvOP1:;;Output: HL is the 16-bit result. ld de,OP1ConvFloat:;;Input: DE points to the float.;;Output: HL is the 16-bit result.;; Input is on:;; (0,1) => 57cc Average=57;; 0 or [1,10) => 117cc or 126cc =121.5;; [10,100) => 174cc or 175cc =174.5;; [100,1000) => 276cc, 277cc, 285cc, or 286cc. =281;; [1000,10000) => 374cc to 376cc =375;; [10000,65536) => 481cc to483cc, or 490cc to 492cc =486.5;;Average case: 467.88153076171875cc ld hl,0 ld a,(de) or a ret z inc de ld a,(de) inc de sub 80h ret c jr z,final cp 5 jp c,enterloop retloop: ld a,b ld b,h ld c,l add hl,hl add hl,bc add hl,hl add hl,hl add hl,hl add hl,bc add hl,hl add hl,hlenterloop: ld b,a ex de,hl ld a,(hl) \ and $F0 \ rra \ ld c,a \ rra \ rra \ sub c \ add a,(hl) inc hl ex de,hl add a,l ld l,a jr nc,$+3 inc h dec b ret z djnz loop ld b,h ld c,l add hl,hl add hl,hl add hl,bc add hl,hlfinal: ld a,(de) rrca rrca rrca rrca and 15 add a,l ld l,a ret nc inc h ret
ConvOP1: ld hl,OP1convFloat:;;Inputs: HL points to the TI Float.;;Outputs: The float is converted to a 16-bit integer held in DE, or LSB in A.;;avg: 436.723938;; 0-digit : 30cc (0,1);; 1-digit : 92cc or 100cc 0 or [1,10);; 2-digit : 134cc [10,100);; 3-digit : 257cc or 265cc [100,1000);; 4-digit : 329cc or 330cc [1000,10000);; 5-digit : 453cc or 454cc or 461cc or 462cc [10000,65536);;95 bytes ld a,(hl) or a jr nz,err_datatype ld de,0 inc hl ld a,(hl) sub 80h ld b,a ;ugh, gotta keep A as the LSB, but we need to get B to be the exponent ld a,e ; ret c inc hl ld a,(hl) jr z,lastdigit2; ld a,(hl) ;\ I feel particularly proud of this code, so feel free to use it ^~^ and $F0 ; |It converts a byte of BCD to an 8-bit int. rra ; |The catch is, I only have A and C to use, and (hl) is the BCD ld c,a ; |number. rra ; |If you come up with faster, please let me know and post it in rra ; |the optimized routines thread on popular TI forums. sub a,c ; |Algo: Multiply upper digit by -6, add the original byte. add a,(hl) ;/ Result is upper_digit*(-6+16)+lower_digit ld e,a dec b ret z dec b jr z,lastdigit inc hl ex de,hl ld a,b sla l add hl,hl ld b,h ld c,l add hl,hl add hl,bc add hl,hl add hl,hl add hl,hl add hl,bc ex de,hl ld b,a ld a,(hl) ;\ I feel particularly proud of this code, so feel free to use it ^~^ and $F0 ; |It converts a byte of BCD to an 8-bit int. rra ; |The catch is, I only have A and C to use, and (hl) is the BCD ld c,a ; |number. rra ; |If you come up with faster, please let me know and post it in rra ; |the optimized routines thread on popular TI forums. sub a,c ; |Algo: Multiply upper digit by -6, add the original byte. add a,(hl) ;/ Result is upper_digit*(-6+16)+lower_digit. Ha, repost.; inc hl ; add a,e ld e,a jr nc,$+3 inc d dec b ret z dec b jr nz,err_domainlastdigit: inc hl ld a,(hl) ld h,d ld l,e add hl,hl add hl,hl add hl,de add hl,hl jr c,err_domain ex de,hllastdigit2: rrca rrca rrca rrca and 15 add a,e ld e,a ret nc inc d ret nzerr_domain: bcall(_ErrDomain) err_datatype: bcall(_ErrDataType)
mul16:;Inputs:; BC,DE are unsigned integers;Output:; HL:DE is the 32-bit product;Destroys:; A,B,C;min: 359cc;max: 717cc;avg: 596.34375cc;92 bytes ld a,c call DE_Times_A push hl push af ld a,b call DE_Times_A+2 pop bc pop de;AHL; BDE ld c,d add hl,bc adc a,0;AHLE ld d,l ld l,h ld h,a;HLDE retDE_Times_A:;Input: DE,A;Output: A:HL is the product, C=0, B,DE unaffected, z flag set if result is zero, c flag set if A is input as 1, else nc.;A:128~255 219+6{0,10}+{0,19} avg=258.5 *1/2;A:64~127 203+5{0,10}+{0,19} avg=237.5 *1/4;A:32~63 187+4{0,10}+{0,19} avg=216.5 *1/8;A:16~31 171+3{0,10}+{0,19} avg=195.5 *1/16;A:8~15 155+2{0,10}+{0,19} avg=174.5 *1/32;A:4~7 139+{0,10}+{0,19} avg=153.5 *1/64;A:2~3 123+{0,19} avg=132.5 *1/128;A:1 107cc avg=107 *1/256;A:0 119cc avg=119 *1/256;overall avg: 237.671875cc ld c,0 ld h,d ld l,e rla \ jr c,mul_07 rla \ jr c,mul_06 rla \ jr c,mul_05 rla \ jr c,mul_04 rla \ jr c,mul_03 rla \ jr c,mul_02 rla \ jr c,mul_01 rla ret c ld h,a ld l,a retmul_07: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_06: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_05: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_04: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_03: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_02: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_01: add hl,hl \ rla \ ret nc \ add hl,de \ adc a,c ret
DE_Times_A:;Input: DE,A;Output: A:HL is the product, C=0, B,DE unaffected, z flag set if result is zero, c flag set if A is input as 1, else nc.;A:128~255 219+6{0,10}+{0,19} avg=258.5 *1/2;A:64~127 203+5{0,10}+{0,19} avg=237.5 *1/4;A:32~63 187+4{0,10}+{0,19} avg=216.5 *1/8;A:16~31 171+3{0,10}+{0,19} avg=195.5 *1/16;A:8~15 155+2{0,10}+{0,19} avg=174.5 *1/32;A:4~7 139+{0,10}+{0,19} avg=153.5 *1/64;A:2~3 123+{0,19} avg=132.5 *1/128;A:1 107cc avg=107 *1/256;A:0 119cc avg=119 *1/256;overall avg: 237.671875cc ld c,0 ld h,d ld l,e rla \ jr c,mul_07 rla \ jr c,mul_06 rla \ jr c,mul_05 rla \ jr c,mul_04 rla \ jr c,mul_03 rla \ jr c,mul_02 rla \ jr c,mul_01 rla ret c ld h,a ld l,a retmul_07: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_06: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_05: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_04: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_03: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_02: add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,cmul_01: add hl,hl \ rla \ ret nc \ add hl,de \ adc a,c ret
; divide HL by C (HL is signed, C is not); output: HL = quotient, A = remainderdivHLbyCs: bit 7,h push af jr z,divHLbyCsStart ld a,h \ cpl \ ld h,a ld a,l \ cpl \ ld l,a inc hldivHLbyCsStart: xor a ld b,16divHLbyCsLoop: add hl,hl rla cp c jp c,divHLbyCsNext sub c inc ldivHLbyCsNext: djnz divHLbyCLoop ld b,a pop af ld a,b ret z ld a,h \ cpl \ ld h,a ld a,l \ cpl \ ld l,a inc hl ret
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Topic: ASM Optimized routines (Read 108250 times)
