Programmers - algorithms and examples of procedures for quick calculations on asemblere: multiplication and division of 3-byte numbers

<b>Programmers</b> - algorithms and examples of procedures for
quick calculations on asemblere: multiplication and division of 3-byte numbers

Quick calculations in assembler

music by COOPER
(C) GreenFort
_

Yes, many problems with this math, and in fact necessary, and 
you just everywhere. That vector makes itself know, scoring in 
his toy and even the calculation of luminaries in the 
firmament. Anyway, there are always situations where speed 
PZUshnogo calculator is not enough.  We offer you a series of 
articles on mathematical operations. It is understood that a 
person reading these lines have already mastered the basics of 
programming in assembler. 

 Let's start with a simple:

 1. DIVISION.

 The principle of the procedure division is based
on long division, the only difference only in the number 
system: it is binary. 

1.1 Пример_простейшей_процедуры_деления:

INPUT: C = Dividend, Divisor B =
OUTPUT: L = result, A = balance


  ; L = C / B:
DIVIS XOR A; reset the current OS
  ; Tatka
DIVIS2 LD L, # 01; counter (shift 8 times)
D1 RL C; read the current discharge
 RLA; drive bits
 CP B; a result of the current

  ; Discharge
 JR C, ZER; transition if the current

  ; Bit = 0
 SUB B; tek.razryad = 1, de-

  ; Drive
 SLI L; entry level = 1
 JR NC, D1; transition, if the counter is not

  ; Overwhelmed
 RET; output
 ZER SLA L; entry level = 0
 JR NC, D1; transition, if the counter is not

  ; Overwhelmed
 RET; output

L - is used as the counter and stores
result.

   A - remainder of the division of C sequentially read bits in 
the register A. 

   B - remains unchanged after division.

 Protsedurku can, incidentally, to reveal.

If you need more precision of the case, then you can continue 
to divide. 

 Example:
 LD C, that share will
 LD B, in that share will

 CALL DIVIS; primary division
 ; C = 0, A-residue
 LD H, L; preservation result
 CALL DIVIS2; secondary division
 ; Without zeroing the balance

he findings in HL:

H = integer part of result

   L = fractional part of result

 The accuracy: + - (1 / 256), ie two
decimal places are provided.



1.2 Protsedurka_deleniya_3-h_baytovyh_chisel

 At the entrance: A, H, L - three bytes of the dividend
 B, D, E - three bytes of the divisor
 At the exit: A, H, L - result

; A, H, L = (A, H, L) / (B, D, E)
DIVISIO
 LD C, A; byte divisible

  ; Store in C
 XOR A; zeroing drive
 EXX; rezryadov
 LD HL, # 01; counter (24) and
 LD B, H; three-byte keeper
 EXX; result
DIV1SLA L; sample discharge
 RL H
 RL C
 RLA
 CP B; drive more

  ; Divider?
JR C, DIV2; if less, the results
  ; Tat 0)
 JR NZ, DIV3; if more
And the result = 1 drive decreases
 EX AF, AF '; preservation A
 LD A, C; similar test
 CP D; younger of the two bytes for JR C, DIV22; kopitelya and 
divider  JR NZ, DIV32

 LD A, H
 CP E
 JR C, DIV22
DIV32 EX AF, AF '; drive = divisor
DIV3EX AF, AF '
 LD A, L; drive-divider
 LD L, H; (lower 2 digits)
 LD H, C
 AND A
 SBC HL, DE
 LD C, H
 LD H, L
 LD L, A
 JR NC, DIV33
 EX AF, AF '; drive-divider
 SUB B; MSB in
 DEC A; overflow junior
DIV34 EXX; NeuStar vrezultat
 SLI L; current bit = 1
 RL H
 RL B
 EXX
 JP NC, DIV1; counter has not yet con
  ; Creased
 JP DIVEXIT; counter overflowed

  ; The end of the division
DIV22 EX AF, AF '; entry in the result = 0
DIV2EXX
 SLA L
 RL H
 RL B
 EXX
 JP NC, DIV1; counter has not yet con
  ; Creased
DIVEXIT EXX; counter overflowed
 PUSH HL; end division
 LD A, B
 EXX
 POP HL
 RET
DIV33 EX AF, AF '; drive-divider
 SUB B; MSB without
 JP DIV34; overflow junior


  Then, quite convenient to use the result for the addition or 
subtraction: 

Addition of the result with a 3-byte number


  .

   CALL DIVISIO

   LD B ,1-th byte, which adds

   LD DE, 2 and 3 bytes, which adds

   ADD HL, DE

   ADC A, B

  .

 2. MULTIPLICATION.


  Multiplication, and division as based on
Multiplication of a column.

 2.1 Простейшая_процедурка_умножения.

Example:

; HL = B * C
 LD HL, # 0; training results at
 LD E, B; koef.tekuschego discharge
 LD D, H
 LD B, # 08; counter
MCYCSRL C; second sample discharge
  ; Second factor
 JP NC, NOADD; bit = 0 (DE * 0 = 0)
 ADD HL, DE; bit = 1 (DE * 1 = DE)
NOADD SLA E; replacement ratio times RL D; series on track. 
discharge  DJNZ MCYC; Cycle 8

 RET; output

 Of course, immediately apparent that
this construction can be opened.

2.2 Umnozhenie_3-h_baytovyh_chisel.

; A, H, L = A, H, L * B, D, E

MULTI EXX
 LD HL, FLAG; dumping transport
 RES 0, (HL)

   LD B, 24; counter
 LD HL, # 0, the result (C, H, L)
 LD C, H
PF2 EXX
 SRL B; sample discharge
 RR D; second factor
 RR E
 JR NC, PF3; bit = 0, the transition to

  ; Select the next level
 EX AF, AF '; addition to the response
 PUSH HL; current koef.razryada
 EXX
 POP DE
 ADD HL, DE
 ADC A, C
 JP NC, NOFLAG

  And the result does not fit into the three bytes!
 LD A, (FLAG); handler overflow OR 1; of
 LD (FLAG), A
 RET
NOFLAG LD C, A
 EXX
 EX AF, AF '
-PF3 SLA L; move to the next
 RL H; current coefficients. (AHL * 2)
 RLA
 EXX
 DJNZ PF2; cycle at 24
 LD A, C
 RET; output
FLAGDB 0



 1 in the variable FLAG in case of overflow the result, 
although very often the program all thought and the need is not 
there. All possible subsequent operations (addition, 
subtraction) with the answer, such as in division.


 If you will understand, then we think you will not
easily will be able to remake
procedures and a greater number of bytes
to improve the accuracy of calculations.
 We remind you that protsedurki for 3-byte numbers you can use 
as for counting integers and fractional.


To be continued.