Multiply Function [x]

[Thomas Klemm]

(08-03-2018 01:07 PM)wynen Wrote:  The multiplication of the significants could be done by a shift and add algorithm. Wikipedia

Peasant or binary multiplication

Here's a program for the HP-11C:

Code:

LBL A       ; times
STO 0       ; b a
CLx         ; s=0 a
LBL 0       ; while
x<>y        ; a s
x=0         ; a=0?
GTO 2       ; done
RCL 0       ; b a s
STO+ 0      ; b → 2b
x<>y        ; a b s
2           ; 2 a b s
÷           ; a÷2 b s s
ENTER       ; a÷2 a÷2 b s
INT         ; a'=⌊a÷2⌋ a÷2 b s
x=y         ; 2∣a
GTO 1       ; even
R↓          ; a÷2 b s a'
R↓          ; b s a' a÷2
+           ; s'=s+b a'
GTO 0       ; while
LBL 1       ; even
R↑          ; s'=s a'
GTO 0       ; while
LBL 2       ; done
R↓          ; s
RTN         ;

This is a translation of the following Python program:

Code:

def times(a, b):
    s = 0
    while a != 0:
        if a % 2 != 0:
            s += b
        a /= 2
        b += b
    return s

It works for positive integers \(a\) and \(b\) and calculates \(a\times b\).

Cheers
Thomas