Long multiplication
From Rosetta Code
You are encouraged to solve this task according to the task description, using any language you may know.
For output, display the result of 2^64 * 2^64. The decimal representation of 2^64 is:
18446744073709551616
The output of 2^64 * 2^64 is 2^128, and that is:
340282366920938463463374607431768211456
Contents |
[edit] Ada
The following implementation uses representation of a long number by an array of 32-bit elements:
type Long_Number is array (Natural range <>) of Unsigned_32;
function "*" (Left, Right : Long_Number) return Long_Number is
Result : Long_Number (0..Left'Length + Right'Length - 1) := (others => 0);
Accum : Unsigned_64;
begin
for I in Left'Range loop
for J in Right'Range loop
Accum := Unsigned_64 (Left (I)) * Unsigned_64 (Right (J));
for K in I + J..Result'Last loop
exit when Accum = 0;
Accum := Accum + Unsigned_64 (Result (K));
Result (K) := Unsigned_32 (Accum and 16#FFFF_FFFF#);
Accum := Accum / 2**32;
end loop;
end loop;
end loop;
for Index in reverse Result'Range loop -- Normalization
if Result (Index) /= 0 then
return Result (0..Index);
end if;
end loop;
return (0 => 0);
end "*";
The task requires conversion into decimal base. For this we also need division to short number with a remainder. Here it is:
procedure Div
( Dividend : in out Long_Number;
Last : in out Natural;
Remainder : out Unsigned_32;
Divisor : Unsigned_32
) is
Div : constant Unsigned_64 := Unsigned_64 (Divisor);
Accum : Unsigned_64 := 0;
Size : Natural := 0;
begin
for Index in reverse Dividend'First..Last loop
Accum := Accum * 2**32 + Unsigned_64 (Dividend (Index));
Dividend (Index) := Unsigned_32 (Accum / Div);
if Size = 0 and then Dividend (Index) /= 0 then
Size := Index;
end if;
Accum := Accum mod Div;
end loop;
Remainder := Unsigned_32 (Accum);
Last := Size;
end Div;
With the above the test program:
with Ada.Strings.Unbounded; use Ada.Strings.Unbounded;
with Ada.Text_IO; use Ada.Text_IO;
with Interfaces; use Interfaces;
procedure Long_Multiplication is
-- Insert definitions above here
procedure Put (Value : Long_Number) is
X : Long_Number := Value;
Last : Natural := X'Last;
Digit : Unsigned_32;
Result : Unbounded_String;
begin
loop
Div (X, Last, Digit, 10);
Append (Result, Character'Val (Digit + Character'Pos ('0')));
exit when Last = 0 and then X (0) = 0;
end loop;
for Index in reverse 1..Length (Result) loop
Put (Element (Result, Index));
end loop;
end Put;
X : Long_Number := (0 => 0, 1 => 0, 2 => 1) * (0 => 0, 1 => 0, 2 => 1);
begin
Put (X);
end Long_Multiplication;
Sample output:
340282366920938463463374607431768211456
[edit] ALGOL 68
The long multiplication for the golden ratio has been included as half the digits cancel and end up as being zero. This is useful for testing.
[edit] Built in or standard distribution routines
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386 ALGOL 68G allows any precision for long long int to be defined when the program is run, e.g. 200 digits.
PRAGMAT precision=200 PRAGMAT
MODE INTEGER = LONG LONG INT;
LONG INT default integer width := 69;
INT width = 69+2;
INT fix w = 1, fix h = 1; # round up #
LONG LONG INT golden ratio w := ENTIER ((long long sqrt(5)-1) / 2 * LENG LENG 10 ** default integer width + fix w),
golden ratio h := ENTIER ((long long sqrt(5)+1) / 2 * LENG LENG 10 ** default integer width + fix h);
test: (
print((
"The approximate golden ratios, width: ", whole(golden ratio w,width), new line,
" length: ", whole(golden ratio h,width), new line,
" product is exactly: ", whole(golden ratio w*golden ratio h,width*2), new line));
INTEGER two to the power of 64 = LONG 2 ** 64;
INTEGER neg two to the power of 64 = -(LONG 2 ** 64);
print(("2 ** 64 * -(2 ** 64) = ", whole(two to the power of 64*neg two to the power of 64,width), new line))
)
Output:
The approximate golden ratios, width: +618033988749894848204586834365638117720309179805762862135448622705261
length: +1618033988749894848204586834365638117720309179805762862135448622705261
product is exactly: +1000000000000000000000000000000000000000000000000000000000000000000001201173450350400438606015942314498798603569682901026716145698077078121
2 ** 64 * -(2 ** 64) = -340282366920938463463374607431768211456
[edit] Implementation example
Works with: ALGOL 68 version Standard - no extensions to language used Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386
MODE DIGIT = INT;
MODE INTEGER = FLEX[0]DIGIT; # an arbitary number of digits #
# "digits" are stored in digit base ten, but 10000 & 2**n (inc hex) can be used #
INT digit base = 1000;
# if possible, then print the digit with one character #
STRING hex digit repr = "0123456789abcdefghijklmnopqrstuvwxyz"[AT 0];
INT digit base digit width = ( digit base <= UPB hex digit repr + 1 | 1 | 1 + ENTIER log(digit base-1) );
INT next digit = -1; # reverse order so digits appear in "normal" order when printed #
PROC raise value error = ([]STRING args)VOID:
( print(("Value Error: ", args, new line)); stop );
PROC raise not implemented error = ([]STRING args)VOID:
( print(("Not implemented Error: ", args, new line)); stop );
PROC raise integer not implemented error = (STRING message)INTEGER:
( raise not implemented error(("INTEGER ", message)); SKIP );
INT half max int = max int OVER 2;
IF digit base > half max int THEN raise value error("INTEGER addition may fail") FI;
INT sqrt max int = ENTIER sqrt(max int);
IF digit base > sqrt max int THEN raise value error("INTEGER multiplication may fail") FI;
# initialise/cast a INTEGER from a LONG LONG INT #
OP INTEGERINIT = (LONG LONG INT number)INTEGER:(
[1 + ENTIER (SHORTEN SHORTEN long long log(ABS number) / log(digit base))]DIGIT out;
LONG LONG INT carry := number;
FOR digit out FROM UPB out BY next digit TO LWB out DO
LONG LONG INT prev carry := carry;
carry %:= digit base; # avoid MOD as it doesn't under handle -ve numbers #
out[digit out] := SHORTEN SHORTEN (prev carry - carry * digit base)
OD;
out
);
# initialise/cast a INTEGER from an LONG INT #
OP INTEGERINIT = (LONG INT number)INTEGER: INTEGERINIT LENG number;
# initialise/cast a INTEGER from an INT #
OP INTEGERINIT = (INT number)INTEGER: INTEGERINIT LENG LENG number;
# remove leading zero "digits" #
OP NORMALISE = ([]DIGIT number)INTEGER: (
INT leading zeros := LWB number - 1;
FOR digit number FROM LWB number TO UPB number
WHILE number[digit number] = 0 DO leading zeros := digit number OD;
IF leading zeros = UPB number THEN 0 ELSE number[leading zeros+1:] FI
);
#####################################################################
Define a standard representation for the INTEGER mode. Note: this is
rather crude because for a large "digit base" the number is represented as
blocks of decimals. It works nicely for powers of ten (10,100,1000,...),
but for most larger bases (greater then 35) the repr will be a surprise.
#####################################################################
OP REPR = (DIGIT d)STRING:
IF digit base > UPB hex digit repr THEN
STRING out := whole(ABS d, -digit base digit width);
# Replace spaces with zeros #
FOR digit out FROM LWB out TO UPB out DO
IF out[digit out] = " " THEN out[digit out] := "0" FI
OD;
out
ELSE # small enough to represent as ASCII (hex) characters #
hex digit repr[ABS d]
FI;
OP REPR = (INTEGER number)STRING:(
STRING sep = ( digit base digit width > 1 | "," | "" );
INT width := digit base digit width + UPB sep;
[width * UPB number - UPB sep]CHAR out;
INT leading zeros := LWB out - 1;
FOR digit TO UPB number DO
INT start := digit * width - width + 1;
out[start:start+digit base digit width-1] := REPR number[digit];
IF digit base digit width /= 1 & digit /= UPB number THEN
out[start+digit base digit width] := ","
FI
OD;
# eliminate leading zeros #
FOR digit out FROM LWB out TO UPB out
WHILE out[digit out] = "0" OR out[digit out] = sep
DO leading zeros := digit out OD;
CHAR sign = ( number[1]<0 | "-" | "+" );
# finally return the semi-normalised result #
IF leading zeros = UPB out THEN "0" ELSE sign + out[leading zeros+1:] FI
);
################################################################
# Finally Define the required INTEGER multiplication OPerator. #
################################################################
OP * = (INTEGER a, b)INTEGER:(
# initialise out to all zeros #
[UPB a + UPB b]INT ab; FOR place ab TO UPB ab DO ab[place ab]:=0 OD;
FOR place a FROM UPB a BY next digit TO LWB a DO
DIGIT carry := 0;
# calculate each digit (whilst removing the carry) #
FOR place b FROM UPB b BY next digit TO LWB b DO
# n.b. result may be 2 digits #
INT result := ab[place a + place b] + a[place a]*b[place b] + carry;
carry := result % digit base; # avoid MOD as it doesn't under handle -ve numbers #
ab[place a + place b] := result - carry * digit base
OD;
ab[place a + LWB b + next digit] +:= carry
OD;
NORMALISE ab
);
# The following standard operators could (potentially) also be defined #
OP - = (INTEGER a)INTEGER: raise integer not implemented error("monadic minus"),
ABS = (INTEGER a)INTEGER: raise integer not implemented error("ABS"),
ODD = (INTEGER a)INTEGER: raise integer not implemented error("ODD"),
BIN = (INTEGER a)INTEGER: raise integer not implemented error("BIN");
OP + = (INTEGER a, b)INTEGER: raise integer not implemented error("addition"),
- = (INTEGER a, b)INTEGER: raise integer not implemented error("subtraction"),
/ = (INTEGER a, b)REAL: ( VOID(raise integer not implemented error("floating point division")); SKIP),
% = (INTEGER a, b)INTEGER: raise integer not implemented error("fixed point division"),
%* = (INTEGER a, b)INTEGER: raise integer not implemented error("modulo division"),
** = (INTEGER a, b)INTEGER: raise integer not implemented error("to the power of");
LONG INT default integer width := long long int width - 2;
INT fix w = -1177584, fix h = -3915074; # floating point error, probably GMP/hardware specific #
INTEGER golden ratio w := INTEGERINIT ENTIER ((long long sqrt(5)-1) / 2 * LENG LENG 10 ** default integer width + fix w),
golden ratio h := INTEGERINIT ENTIER ((long long sqrt(5)+1) / 2 * LENG LENG 10 ** default integer width + fix h);
test: (
print((
"The approximate golden ratios, width: ", REPR golden ratio w, new line,
" length: ", REPR golden ratio h, new line,
" product is exactly: ", REPR (golden ratio w * golden ratio h), new line));
INTEGER two to the power of 64 = INTEGERINIT(LONG 2 ** 64);
INTEGER neg two to the power of 64 = INTEGERINIT(-(LONG 2 ** 64));
print(("2 ** 64 * -(2 ** 64) = ", REPR (two to the power of 64 * neg two to the power of 64), new line))
)
Output:
The approximate golden ratios, width: +618,033,988,749,894,848,204,586,834,365,638,117,720,309,179,805,762,862,135,448,622,705,261
length: +1,618,033,988,749,894,848,204,586,834,365,638,117,720,309,179,805,762,862,135,448,622,705,261
product is exactly: +1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,001,201,173,450,350,400,438,606,015,942,314,498,798,603,569,682,901,026,716,145,698,077,078,121
2 ** 64 * -(2 ** 64) = -340,282,366,920,938,463,463,374,607,431,768,211,456
[edit] Other libraries or implementation specific extensions
As of February 2009 no open source libraries to do this task have been located.
[edit] AutoHotkey
ahk discussion
MsgBox % x := mul(256,256)
MsgBox % x := mul(x,x)
MsgBox % x := mul(x,x) ; 18446744073709551616
MsgBox % x := mul(x,x) ; 340282366920938463463374607431768211456
mul(b,c) { ; <- b*c
VarSetCapacity(a, n:=StrLen(b)+StrLen(c), 48), NumPut(0,a,n,"char")
Loop % StrLen(c) {
i := StrLen(c)+1-A_Index, cy := 0
Loop % StrLen(b) {
j := StrLen(b)+1-A_Index,
t := SubStr(a,i+j,1) + SubStr(b,j,1) * SubStr(c,i,1) + cy
cy := t // 10
NumPut(mod(t,10)+48,a,i+j-1,"char")
}
NumPut(cy+48,a,i+j-2,"char")
}
Return cy ? a : SubStr(a,2)
}
[edit] AWK
Works with: gawk version 3.1.0
Translation of: Tcl
BEGIN {
DEBUG = 0
n = 2^64
nn = sprintf("%.0f", n)
printf "2^64 * 2^64 = %.0f\n", multiply(nn, nn)
printf "2^64 * 2^64 = %.0f\n", n*n
exit
}
function multiply(x, y, len_x,len_y,ax,ay,j,m,c,i,k,d,v,res,mul,result) {
len_x = split_reverse(x, ax)
len_y = split_reverse(y, ay)
print_array(ax)
print_array(ay)
for (j=1; j<=len_y; j++) {
m = ay[j]
c = 0
i = j - 1
for (k=1; k<=len_x; k++) {
d = ax[k]
i++
v = res[i]
if (v == "") {
append_array(res, 0)
v = 0
}
mul = v + c + d*m
c = int(mul / 10)
v = mul % 10
res[i] = v
}
append_array(res, c)
}
print_array(res)
result = reverse_join(res)
sub(/^0+/, "", result)
return result
}
function split_reverse(x, a, a_x) {
split(x, a_x, //)
return reverse_array(a_x, a)
}
function reverse_array(a,b, len,i) {
len = length_array(a)
for (i in a) {
b[1+len-i] = a[i]
}
return len
}
function length_array(a, len,i) {
len = 0
for (i in a) len++
return len
}
function append_array(a, value, len) {
len = length_array(a)
a[++len] = value
}
function reverse_join(a, len,str,i) {
len = length_array(a)
str = ""
for (i=len; i>=1; i--) {
str = str a[i]
}
return str
}
function print_array(a, len,i) {
if (DEBUG) {
len = length_array(a)
print "length=" len
for (i=1; i<=len; i++) {
printf("%s ", i%10)
}
print ""
for (i=1; i<=len; i++) {
#print i " " a[i]
printf("%s ", a[i])
}
print ""
print "===="
}
}
outputs:
2^64 * 2^64 = 340282366920938463463374607431768211456 2^64 * 2^64 = 340282366920938463463374607431768211456
[edit] Basic
Works with: QBasic
Version 1:
'PROGRAM : BIG MULTIPLICATION VER #1
'LRCVS 01.01.2010
'THIS PROGRAM SIMPLY MAKES A MULTIPLICATION
'WITH ALL THE PARTIAL PRODUCTS.
'............................................................
DECLARE SUB A.INICIO (A$, B$)
DECLARE SUB B.STORE (CAD$, N$)
DECLARE SUB C.PIZARRA ()
DECLARE SUB D.ENCABEZADOS (A$, B$)
DECLARE SUB E.MULTIPLICACION (A$, B$)
DECLARE SUB G.SUMA ()
DECLARE FUNCTION F.INVCAD$ (CAD$)
RANDOMIZE TIMER
CALL A.INICIO(A$, B$)
CALL B.STORE(A$, "A")
CALL B.STORE(B$, "B")
CALL C.PIZARRA
CALL D.ENCABEZADOS(A$, B$)
CALL E.MULTIPLICACION(A$, B$)
CALL G.SUMA
SUB A.INICIO (A$, B$)
CLS
'Note: Number of digits > 1000
INPUT "NUMBER OF DIGITS "; S
CLS
A$ = ""
B$ = ""
FOR N = 1 TO S
A$ = A$ + LTRIM$(STR$(INT(RND * 9)))
NEXT N
FOR N = 1 TO S
B$ = B$ + LTRIM$(STR$(INT(RND * 9)))
NEXT N
END SUB
SUB B.STORE (CAD$, N$)
OPEN "O", #1, N$
FOR M = LEN(CAD$) TO 1 STEP -1
WRITE #1, MID$(CAD$, M, 1)
NEXT M
CLOSE (1)
END SUB
SUB C.PIZARRA
OPEN "A", #3, "R"
WRITE #3, ""
CLOSE (3)
KILL "R"
END SUB
SUB D.ENCABEZADOS (A$, B$)
LT = LEN(A$) + LEN(B$) + 1
L$ = STRING$(LT, " ")
OPEN "A", #3, "R"
MID$(L$, LT - LEN(A$) + 1) = A$
WRITE #3, L$
CLOSE (3)
L$ = STRING$(LT, " ")
OPEN "A", #3, "R"
MID$(L$, LT - LEN(B$) - 1) = "X " + B$
WRITE #3, L$
CLOSE (3)
END SUB
SUB E.MULTIPLICACION (A$, B$)
LT = LEN(A$) + LEN(B$) + 1
L$ = STRING$(LT, " ")
C$ = ""
D$ = ""
E$ = ""
CT1 = 1
ACUM = 0
OPEN "I", #2, "B"
WHILE EOF(2) <> -1
INPUT #2, B$
OPEN "I", #1, "A"
WHILE EOF(1) <> -1
INPUT #1, A$
RP = (VAL(A$) * VAL(B$)) + ACUM
C$ = LTRIM$(STR$(RP))
IF EOF(1) <> -1 THEN D$ = D$ + RIGHT$(C$, 1)
IF EOF(1) = -1 THEN D$ = D$ + F.INVCAD$(C$)
E$ = LEFT$(C$, LEN(C$) - 1)
ACUM = VAL(E$)
WEND
CLOSE (1)
MID$(L$, LT - CT1 - LEN(D$) + 2) = F.INVCAD$(D$)
OPEN "A", #3, "R"
WRITE #3, L$
CLOSE (3)
L$ = STRING$(LT, " ")
ACUM = 0
C$ = ""
D$ = ""
E$ = ""
CT1 = CT1 + 1
WEND
CLOSE (2)
END SUB
FUNCTION F.INVCAD$ (CAD$)
LCAD = LEN(CAD$)
CADTEM$ = ""
FOR CAD = LCAD TO 1 STEP -1
CADTEM$ = CADTEM$ + MID$(CAD$, CAD, 1)
NEXT CAD
F.INVCAD$ = CADTEM$
END FUNCTION
SUB G.SUMA
CF = 0
OPEN "I", #3, "R"
WHILE EOF(3) <> -1
INPUT #3, R$
CF = CF + 1
AN = LEN(R$)
WEND
CF = CF - 2
CLOSE (3)
W$ = ""
ST = 0
ACUS = 0
FOR P = 1 TO AN
K = 0
OPEN "I", #3, "R"
WHILE EOF(3) <> -1
INPUT #3, R$
K = K + 1
IF K > 2 THEN ST = ST + VAL(MID$(R$, AN - P + 1, 1))
IF K > 2 THEN M$ = LTRIM$(STR$(ST + ACUS))
WEND
'COLOR 10: LOCATE CF + 3, AN - P + 1: PRINT RIGHT$(M$, 1); : COLOR 7
W$ = W$ + RIGHT$(M$, 1)
ACUS = VAL(LEFT$(M$, LEN(M$) - 1))
CLOSE (3)
ST = 0
NEXT P
OPEN "A", #3, "R"
WRITE #3, " " + RIGHT$(F.INVCAD(W$), AN - 1)
CLOSE (3)
CLS
PRINT "THE SOLUTION IN THE FILE: R"
END SUB
Version 2:
'PROGRAM: BIG MULTIPLICATION VER # 2
'LRCVS 01/01/2010
'THIS PROGRAM SIMPLY MAKES A BIG MULTIPLICATION
'WITHOUT THE PARTIAL PRODUCTS.
'HERE SEE ONLY THE SOLUTION.
'...............................................................
CLS
PRINT "WAIT"
NA = 2000 'NUMBER OF ELEMENTS OF THE MULTIPLY.
NB = 2000 'NUMBER OF ELEMENTS OF THE MULTIPLIER.
'Solution = 4000 Exacts digits
'......................................................
OPEN "X" + ".MLT" FOR BINARY AS #1
CLOSE (1)
KILL "*.MLT"
'.....................................................
'CREATING THE MULTIPLY >>> A
'CREATING THE MULTIPLIER >>> B
FOR N = 1 TO 2
IF N = 1 THEN F$ = "A" + ".MLT": NN = NA
IF N = 2 THEN F$ = "B" + ".MLT": NN = NB
OPEN F$ FOR BINARY AS #1
FOR N2 = 1 TO NN
RANDOMIZE TIMER
X$ = LTRIM$(STR$(INT(RND * 10)))
SEEK #1, N2: PUT #1, N2, X$
NEXT N2
SEEK #1, N2
CLOSE (1)
NEXT N
'.....................................................
OPEN "A" + ".MLT" FOR BINARY AS #1
FOR K = 0 TO 9
NUM$ = "": Z$ = "": ACU = 0: GG = NA
C$ = LTRIM$(STR$(K))
OPEN C$ + ".MLT" FOR BINARY AS #2
'OPEN "A" + ".MLT" FOR BINARY AS #1
FOR N = 1 TO NA
SEEK #1, GG: GET #1, GG, X$
NUM$ = X$
Z$ = LTRIM$(STR$(ACU + (VAL(X$) * VAL(C$))))
L = LEN(Z$)
ACU = 0
IF L = 1 THEN NUM$ = Z$: PUT #2, N, NUM$
IF L > 1 THEN ACU = VAL(LEFT$(Z$, LEN(Z$) - 1)): NUM$ = RIGHT$(Z$, 1): PUT #2, N, NUM$
SEEK #2, N: PUT #2, N, NUM$
GG = GG - 1
NEXT N
IF L > 1 THEN ACU = VAL(LEFT$(Z$, LEN(Z$) - 1)): NUM$ = LTRIM$(STR$(ACU)): XX$ = XX$ + NUM$: PUT #2, N, NUM$
'CLOSE (1)
CLOSE (2)
NEXT K
CLOSE (1)
'......................................................
ACU = 0
LT5 = 1
LT6 = LT5
OPEN "B" + ".MLT" FOR BINARY AS #1
OPEN "D" + ".MLT" FOR BINARY AS #3
FOR JB = NB TO 1 STEP -1
SEEK #1, JB
GET #1, JB, X$
OPEN X$ + ".MLT" FOR BINARY AS #2: LF = LOF(2): CLOSE (2)
OPEN X$ + ".MLT" FOR BINARY AS #2
FOR KB = 1 TO LF
SEEK #2, KB
GET #2, , NUM$
SEEK #3, LT5
GET #3, LT5, PR$
T$ = ""
T$ = LTRIM$(STR$(ACU + VAL(NUM$) + VAL(PR$)))
PR$ = RIGHT$(T$, 1)
ACU = 0
IF LEN(T$) > 1 THEN ACU = VAL(LEFT$(T$, LEN(T$) - 1))
SEEK #3, LT5: PUT #3, LT5, PR$
LT5 = LT5 + 1
NEXT KB
IF ACU <> 0 THEN PR$ = LTRIM$(STR$(ACU)): PUT #3, LT5, PR$
CLOSE (2)
LT6 = LT6 + 1
LT5 = LT6
ACU = 0
NEXT JB
CLOSE (3)
CLOSE (1)
OPEN "D" + ".MLT" FOR BINARY AS #3: LD = LOF(3): CLOSE (3)
ER = 1
OPEN "D" + ".MLT" FOR BINARY AS #3
OPEN "R" + ".MLT" FOR BINARY AS #4
FOR N = LD TO 1 STEP -1
SEEK #3, N: GET #3, N, PR$
SEEK #4, ER: PUT #4, ER, PR$
ER = ER + 1
NEXT N
CLOSE (4)
CLOSE (3)
KILL "D.MLT"
FOR N = 0 TO 9
C$ = LTRIM$(STR$(N))
KILL C$ + ".MLT"
NEXT N
PRINT "END"
PRINT "THE SOLUTION IN THE FILE: R.MLT"
[edit] C
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define X(V,L,I) ( ((I)<(L)) ? (V[(L)-(I)-1]-'0') : 0)
#define MIN(A,B) ( ((A)<(B)) ? (A) : (B) )
char *longmult(const char *a, const char *b)
{
int n, m, T;
char *r = NULL;
int i, j, k;
int *C, *R;
n = strlen(a);
m = strlen(b);
T = n+m+2;
r = malloc(T+1);
R = malloc(T*sizeof(int));
C = malloc((n+1)*(m+1)*sizeof(int));
memset(r, '0', T);
memset(C, 0, (n+1)*(m+1)*sizeof(int));
r[T] = 0;
for(i=0; i<(m+1); i++)
{
C[i*(n+1)] = (X(b,m,i) * X(a,n,0));
for(j=1; j<(n+1); j++)
{
C[i*(n+1)+j] = (X(b,m,i) * X(a,n,j) + C[i*(n+1)+j-1] / 10);
}
}
for(k=0; k < T; k++)
{
R[k] = 0;
for(j=0; j < MIN(k,m+1) ; j++)
{
i = k-j-1;
if ( (i>n) || (i<0) ) { continue; }
R[k] += (C[j*(n+1)+i]%10);
}
R[k] += ((k-1)<0 ) ? 0 : (R[k-1]/10);
}
for(k=T; k>0; k--) r[k-1] = R[T-k+1]%10 + '0';
free(C); free(R);
return r;
}
/* using */
const char *n1 = "18446744073709551616";
int main()
{
char *res;
int lz;
/* printf("%s * %s = 340282366920938463463374607431768211456\n", n1, n1); */
res = longmult(n1,n1);
for(lz=0; (lz < strlen(res)) && (res[lz]=='0') ;lz++) ;
printf("%s * %s = %s\n", n1, n1, res+lz);
free(res);
return 0;
}
The code does not handle negative intergers, nor there are proper error checks. It is more or less the implementation of the way a human being multiplies two integers. The numbers are stored as strings.
[edit] Using GMP (GNU Multi Precision library)
Library: GMP
#include <stdio.h>
#include <gmp.h>
int main()
{
mpz_t z1, z2, zr;
mpz_init(z2); mpz_init(zr);
mpz_init_set_str(z1, "18446744073709551616", 10);
mpz_set(z2, z1);
mpz_mul(zr, z1, z2);
mpz_out_str(stdout, 10, zr);
printf("\n");
return 0;
}
[edit] C#
System.Numerics.BigInteger was added with C# 4.
Works with: C# version 4+
using System;
using System.Numerics;
class Program {
static void Main() {
BigInteger pow2_64 = BigInteger.Pow(2, 64);
BigInteger result = BigInteger.Multiply(pow2_64, pow2_64);
Console.WriteLine(result);
}
}
Output:
340282366920938463463374607431768211456
[edit] Common Lisp
(defun number->digits (number)
(do ((digits '())) ((zerop number) digits)
(multiple-value-bind (quotient remainder) (floor number 10)
(setf number quotient)
(push remainder digits))))
(defun digits->number (digits)
(reduce #'(lambda (n d) (+ (* 10 n) d)) digits :initial-value 0))
(defun long-multiply (a b)
(labels ((first-digit (list)
"0 if list is empty, else first element of list."
(if (endp list) 0
(first list)))
(long-add (digitses &optional (carry 0) (sum '()))
"Do long addition on the list of lists of digits. Each
list of digits in digitses should begin with the least
significant digit. This is the opposite of the digit
list returned by number->digits which places the most
significant digit first. The digits returned by
long-add do have the most significant bit first."
(if (every 'endp digitses)
(nconc (digits carry) sum)
(let ((column-sum (reduce '+ (mapcar #'first-digit digitses)
:initial-value carry)))
(multiple-value-bind (carry column-digit)
(floor column-sum 10)
(long-add (mapcar 'rest digitses)
carry (list* column-digit sum)))))))
;; get the digits of a and b (least significant bit first), and
;; compute the zero padded rows. Then, add these rows (using
;; long-add) and convert the digits back to a number.
(do ((a (nreverse (digits a)))
(b (nreverse (digits b)))
(prefix '() (list* 0 prefix))
(rows '()))
((endp b) (digits->number (long-add rows)))
(let* ((bi (pop b))
(row (mapcar #'(lambda (ai) (* ai bi)) a)))
(push (append prefix row) rows)))))
> (long-multiply (expt 2 64) (expt 2 64)) 340282366920938463463374607431768211456
[edit] D
Tested with dmd v2.047. D standard library has a growing module for multi-precision:
import std.stdio, std.bigint;
void main() {
// auto x = BigInt(2) ^^ 64 * BigInt(2) ^^ 64; // not possible yet
auto x = (BigInt(1) << 64) * (BigInt(1) << 64);
// writeln(x); // not possible yet
const(char)[] result;
x.toString((const(char)[] s){ result = s; }, "d");
writeln(result);
}
Long multiplication, from the JavaScript version:
import std.stdio, std.algorithm, std.conv, std.range, std.string;
string longMult(string x, string y) {
auto digits1 = array(map!"a - '0'"(retro(x)));
auto digits2 = array(map!"a - '0'"(retro(y)));
int[] res;
foreach (i, d1; digits1)
foreach (j, d2; digits2) {
int idx = i + j;
if (res.length <= idx)
res.length += 1;
res[idx] = d1 * d2 + res[idx];
if (res[idx] > 9) {
if (res.length <= idx + 1)
res.length += 1;
res[idx + 1] = res[idx] / 10 + res[idx + 1];
res[idx] -= res[idx] / 10 * 10;
}
}
// return join(map!"to!string(a)"(retro(res)), ""); // not possible yet
return join(array(map!"to!string(a)"(retro(res))), "");
}
void main() {
string two64 = "18446744073709551616";
writeln(longMult(two64, two64));
}
[edit] Fortran
Works with: Fortran version 95 and later
module LongMoltiplication
implicit none
type longnum
integer, dimension(:), pointer :: num
end type longnum
interface operator (*)
module procedure longmolt_ll
end interface
contains
subroutine longmolt_s2l(istring, num)
character(len=*), intent(in) :: istring
type(longnum), intent(out) :: num
integer :: i, l
l = len(istring)
allocate(num%num(l))
forall(i=1:l) num%num(l-i+1) = iachar(istring(i:i)) - 48
end subroutine longmolt_s2l
! this one performs the moltiplication
function longmolt_ll(a, b) result(c)
type(longnum) :: c
type(longnum), intent(in) :: a, b
integer, dimension(:,:), allocatable :: t
integer :: ntlen, i, j
ntlen = size(a%num) + size(b%num) + 1
allocate(c%num(ntlen))
c%num = 0
allocate(t(size(b%num), ntlen))
t = 0
forall(i=1:size(b%num), j=1:size(a%num)) t(i, j+i-1) = b%num(i) * a%num(j)
do j=2, ntlen
forall(i=1:size(b%num)) t(i, j) = t(i, j) + t(i, j-1)/10
end do
forall(j=1:ntlen) c%num(j) = sum(mod(t(:,j), 10))
do j=2, ntlen
c%num(j) = c%num(j) + c%num(j-1)/10
end do
c%num = mod(c%num, 10)
deallocate(t)
end function longmolt_ll
subroutine longmolt_print(num)
type(longnum), intent(in) :: num
integer :: i, j
do j=size(num%num), 2, -1
if ( num%num(j) /= 0 ) exit
end do
do i=j, 1, -1
write(*,"(I1)", advance="no") num%num(i)
end do
end subroutine longmolt_print
end module LongMoltiplication
program Test
use LongMoltiplication
type(longnum) :: a, b, r
call longmolt_s2l("18446744073709551616", a)
call longmolt_s2l("18446744073709551616", b)
r = a * b
call longmolt_print(r)
write(*,*)
end program Test
[edit] Haskell
digits :: Integer -> [Integer]
digits = map (fromIntegral.digitToInt) . show
lZZ = inits $ repeat 0
table f = map . flip (map . f)
polymul = ((map sum . transpose . zipWith (++) lZZ) .) . table (*)
longmult = (foldl1 ((+) . (10 *)) .) . (. digits) . polymul . digits
Output:
*Main> (2^64) `longmult` (2^64)
340282366920938463463374607431768211456
[edit] Icon and Unicon
Icon and Unicon support large integers.
[edit] Icon
procedure main()
write(2^64*2^64)
end
[edit] Unicon
This Icon solution works in Unicon.
[edit] J
Solution:
digits =: ,.&.":
polymult =: +//.@(*/)
buildDecimal=: (+ 10x&*)/@|.
longmult=: buildDecimal@polymult&digits/
Example:
longmult ,~ 2x^64
340282366920938463463374607431768211456
Alternatives:
The above may of course be accomplished without the verb definitions:
(+ 10x&*)/@|.@(+//.@(*/)&(,.&.":))/ ,~2x^64
340282366920938463463374607431768211456
Or using the primitive dyad #. instead of (+ 10x&*)/@|. :
(10x&#.)@(+//.@(*/)&(,.&.":))/ ,~2x^64
340282366920938463463374607431768211456
Writing directly:
(2x^64)*(2x^64)
340282366920938463463374607431768211456
Explaining the component verbs:
-
digits
,.&.": 123
1 2 3
-
polymult(polynomial multiplication): ref. [1]
1 2 3 (+//.@(*/)) 1 2 3
1 4 10 12 9
-
buildDecimal(building the decimal result):
(+ 10x&*)/|. 1 4 10 12 9
15129
[edit] Java
This is a straight-forward implementation of Long multiplication. It works with numbers of any length since it uses BigInteger.
import java.math.BigInteger;
public class LongMult {
public static void main(String[] args) {
BigInteger TwoPow64 = new BigInteger("18446744073709551616");
System.out.println(mult(TwoPow64, TwoPow64));
}
public static BigInteger mult(BigInteger a, BigInteger b){
return a.multiply(b);
}
}
Output:
340282366920938463463374607431768211456
[edit] JavaScript
function mult(num1,num2){
var a1 = num1.split("").reverse();
var a2 = num2.split("").reverse();
var aResult = new Array;
for ( iterNum1 = 0; iterNum1 < a1.length; iterNum1++ ) {
for ( iterNum2 = 0; iterNum2 < a2.length; iterNum2++ ) {
idxIter = iterNum1 + iterNum2; // Get the current array position.
aResult[idxIter] = a1[iterNum1] * a2[iterNum2] + ( idxIter >= aResult.length ? 0 : aResult[idxIter] );
if ( aResult[idxIter] > 9 ) { // Carrying
aResult[idxIter + 1] = Math.floor( aResult[idxIter] / 10 ) + ( idxIter + 1 >= aResult.length ? 0 : aResult[idxIter + 1] );
aResult[idxIter] -= Math.floor( aResult[idxIter] / 10 ) * 10;
}
}
}
return aResult.reverse().join("");
}
[edit] Mathematica
We define the long multiplication function:
LongMultiplication[a_,b_]:=Module[{d1,d2},
d1=IntegerDigits[a]//Reverse;
d2=IntegerDigits[b]//Reverse;
Sum[d1[[i]]d2[[j]]*10^(i+j-2),{i,1,Length[d1]},{j,1,Length[d2]}]
]
Example:
n1 = 2^64;
n2 = 2^64;
LongMultiplication[n1, n2]
gives back:
340282366920938463463374607431768211456
To check the speed difference between built-in multiplication (which is already arbitrary precision) we multiply two big numbers (2^8000 has 2409 digits!) and divide their timings:
n1=2^8000;
n2=2^8000;
Timing[LongMultiplication[n1,n2]][[1]]
Timing[n1 n2][[1]]
Floor[%%/%]
gives back:
72.9686
7.*10^-6
10424088
So our custom function takes about 73 second, the built-in function a couple of millionths of a second, so the long multiplication is about 10.5 million times slower! Mathematica uses Karatsuba multiplication for large integers, which is several magnitudes faster for really big numbers. Making it able to multiply 
in about a second; the final result has 9542426 digits; result omitted for obvious reasons.
[edit] Perl
#!/usr/bin/perl -w
use strict;
# This should probably be done in a loop rather than be recursive.
sub add_with_carry
{
my $resultref = shift;
my $addend = shift;
my $addendpos = shift;
push @$resultref, (0) while (scalar @$resultref < $addendpos + 1);
my $addend_result = $addend + $resultref->[$addendpos];
my @addend_digits = reverse split //, $addend_result;
$resultref->[$addendpos] = shift @addend_digits;
my $carry_digit = shift @addend_digits;
&add_with_carry($resultref, $carry_digit, $addendpos + 1)
if( defined $carry_digit )
}
sub longhand_multiplication
{
my @multiplicand = reverse split //, shift;
my @multiplier = reverse split //, shift;
my @result = ();
my $multiplicand_offset = 0;
foreach my $multiplicand_digit (@multiplicand)
{
my $multiplier_offset = $multiplicand_offset;
foreach my $multiplier_digit (@multiplier)
{
my $multiplication_result = $multiplicand_digit * $multiplier_digit;
my @result_digit_addend_list = reverse split //, $multiplication_result;
my $addend_offset = $multiplier_offset;
foreach my $result_digit_addend (@result_digit_addend_list)
{
&add_with_carry(\@result, $result_digit_addend, $addend_offset++)
}
++$multiplier_offset;
}
++$multiplicand_offset;
}
@result = reverse @result;
return join '', @result;
}
my $sixtyfour = "18446744073709551616";
my $onetwentyeight = &longhand_multiplication($sixtyfour, $sixtyfour);
print "$onetwentyeight\n";
[edit] PicoLisp
: (* (** 2 64) (** 2 64))
-> 340282366920938463463374607431768211456
[edit] PL/I
/* Multiply a by b, giving c. */
multiply: procedure (a, b, c);
declare (a, b, c) (*) fixed decimal (1);
declare (d, e, f) (hbound(a,1)) fixed decimal (1);
declare pr (-hbound(a,1) : hbound(a,1)) fixed decimal (1);
declare p fixed decimal (2), (carry, s) fixed decimal (1);
declare neg bit (1) aligned;
declare (i, j, n, offset) fixed binary (31);
n = hbound(a,1);
d = a;
e = b;
s = a(1) + b(1);
neg = (s = 9);
if a(1) = 9 then call complement (d);
if b(1) = 9 then call complement (e);
pr = 0;
offset = 0; carry = 0;
do i = n to 1 by -1;
do j = n to 1 by -1;
p = d(i) * e(j) + pr(j-offset) + carry;
if p > 9 then do; carry = p/10; p = mod(p, 10); end; else carry = 0;
pr(j-offset) = p;
end;
offset = offset + 1;
end;
do i = hbound(a,1) to 1 by -1;
c(i) = pr(i);
end;
do i = -hbound(a,1) to 1;
if pr(i) ^= 0 then signal fixedoverflow;
end;
if neg then call complement (c);
end multiply;
complement: procedure (a);
declare a(*) fixed decimal (1);
declare i fixed binary (31), carry fixed decimal (1);
declare s fixed decimal (2);
carry = 1;
do i = hbound(a,1) to 1 by -1;
s = 9 - a(i) + carry;
if s > 9 then do; s = s - 10; carry = 1; end; else carry = 0;
a(i) = s;
end;
end complement;
Calling sequence:
a = 0; b = 0; c = 0;
a(60) = 1;
do i = 1 to 64; /* Generate 2**64 */
call add (a, a, b);
put skip;
call output (b);
a = b;
end;
call multiply (a, b, c);
put skip;
call output (c);
Final output:
18446744073709551616
340282366920938463463374607431768211456
[edit] PureBasic
Works with: PureBasic version 4.41
Using Decimal.pbi by Stargåte allows for calculation with long numbers, this is useful since version 4.41 of PureBasic mostly only supporter data types native to x86/x64/PPC etc processors.
XIncludeFile "decimal.pbi"
Define.Decimal *a, *b
*a=PowerDecimal(IntegerToDecimal(2),IntegerToDecimal(64))
*b=TimesDecimal(*a,*a,#NoDecimal)
Print("2^64*2^64 = "+DecimalToString(*b))
Outputs
2^64*2^64 = 340282366920938463463374607431768211456
[edit] Python
(Note that Python comes with arbitrary length integers).
#!/usr/bin/env python
print 2**64*2**64
Works with: Python version 3.0
Translation of: Perl
#!/usr/bin/env python
def add_with_carry(result, addend, addendpos):
while True:
while len(result) < addendpos + 1:
result.append(0)
addend_result = str(int(addend) + int(result[addendpos]))
addend_digits = list(addend_result)
result[addendpos] = addend_digits.pop()
if not addend_digits:
break
addend = addend_digits.pop()
addendpos += 1
def longhand_multiplication(multiplicand, multiplier):
result = []
for multiplicand_offset, multiplicand_digit in enumerate(reversed(multiplicand)):
for multiplier_offset, multiplier_digit in enumerate(reversed(multiplier), start=multiplicand_offset):
multiplication_result = str(int(multiplicand_digit) * int(multiplier_digit))
for addend_offset, result_digit_addend in enumerate(reversed(multiplication_result), start=multiplier_offset):
add_with_carry(result, result_digit_addend, addend_offset)
result.reverse()
return ''.join(result)
if __name__ == "__main__":
sixtyfour = "18446744073709551616"
onetwentyeight = longhand_multiplication(sixtyfour, sixtyfour)
print(onetwentyeight)
Shorter version: Translation of: Haskell
#!/usr/bin/env python
def digits(x):
return [int(c) for c in str(x)]
def mult_table(xs, ys):
return [[x * y for x in xs] for y in ys]
def polymul(xs, ys):
return map(lambda *vs: sum(filter(None, vs)),
*[[0] * i + zs for i, zs in enumerate(mult_table(xs, ys))])
def longmult(x, y):
result = 0
for v in polymul(digits(x), digits(y)):
result = result * 10 + v
return result
if __name__ == "__main__":
print longmult(2**64, 2**64)
[edit] R
[edit] Using GMP
Library: gmp
library(gmp)
a <- as.bigz("18446744073709551616")
mul.bigz(a,a)
"340282366920938463463374607431768211456"
[edit] A native implementation
This code is more verbose than necessary, for ease of understanding.
longmult <- function(xstr, ystr)
{
#get the number described in each string
getnumeric <- function(xstr) as.numeric(unlist(strsplit(xstr, "")))
x <- getnumeric(xstr)
y <- getnumeric(ystr)
#multiply each pair of digits together
mat <- apply(x %o% y, 1, as.character)
#loop over columns, then rows, adding zeroes to end of each number in the matrix to get the correct positioning
ncols <- ncol(mat)
cols <- seq_len(ncols)
for(j in cols)
{
zeroes <- paste(rep("0", ncols-j), collapse="")
mat[,j] <- paste(mat[,j], zeroes, sep="")
}
nrows <- nrow(mat)
rows <- seq_len(nrows)
for(i in rows)
{
zeroes <- paste(rep("0", nrows-i), collapse="")
mat[i,] <- paste(mat[i,], zeroes, sep="")
}
#add zeroes to the start of the each number, so they are all the same length
len <- max(nchar(mat))
strcolumns <- formatC(cbind(as.vector(mat)), width=len)
strcolumns <- gsub(" ", "0", strcolumns)
#line up all the numbers below each other
strmat <- matrix(unlist(strsplit(strcolumns, "")), byrow=TRUE, ncol=len)
#convert to numeric and add them
mat2 <- apply(strmat, 2, as.numeric)
sum1 <- colSums(mat2)
#repeat the process on each of the totals, until each total is a single digit
repeat
{
ntotals <- length(sum1)
totals <- seq_len(ntotals)
for(i in totals)
{
zeroes <- paste(rep("0", ntotals-i), collapse="")
sum1[i] <- paste(sum1[i], zeroes, sep="")
}
len2 <- max(nchar(sum1))
strcolumns2 <- formatC(cbind(as.vector(sum1)), width=len2)
strcolumns2 <- gsub(" ", "0", strcolumns2)
strmat2 <- matrix(unlist(strsplit(strcolumns2, "")), byrow=TRUE, ncol=len2)
mat3 <- apply(strmat2, 2, as.numeric)
sum1 <- colSums(mat3)
if(all(sum1 < 10)) break
}
#Concatenate the digits together
ans <- paste(sum1, collapse="")
ans
}
a <- "18446744073709551616"
longmult(a, a)
"340282366920938463463374607431768211456"
[edit] REXX
/* long multiply */
numeric digits 100
say 2**64*2**64
[edit] Ruby
Translation of: Tcl
def longmult(x,y)
digits = reverse_split_number(x)
result = [0]
j = 0
reverse_split_number(y).each do |m|
c = 0
i = j
digits.each do |d|
v = result[i]
result << 0 if v.zero?
c, v = (v + c + d*m).divmod(10)
result[i] = v
i += 1
end
result[i] += c
j += 1
end
# calculate the answer from the result array of digits
result.reverse.inject(0) {|sum, n| 10*sum + n}
end
def reverse_split_number(m)
digits = []
while m > 0
m, v = m.divmod 10
digits << v
end
digits
end
n=2**64
printf " %d * %d = %d\n", n, n, n*n
printf "longmult(%d, %d) = %d\n", n, n, longmult(n,n)
18446744073709551616 * 18446744073709551616 = 340282366920938463463374607431768211456 longmult(18446744073709551616, 18446744073709551616) = 340282366920938463463374607431768211456
[edit] Scala
This implementation does not rely on an arbitrary precision numeric type. Instead, only single digits are ever multiplied or added, and all partial results are kept as string.
def addNums(x: String, y: String) = {
val padSize = x.length max y.length
val paddedX = "0" * (padSize - x.length) + x
val paddedY = "0" * (padSize - y.length) + y
val (sum, carry) = (paddedX zip paddedY).foldRight(("", 0)) {
case ((dx, dy), (acc, carry)) =>
val sum = dx.asDigit + dy.asDigit + carry
((sum % 10).toString + acc, sum / 10)
}
if (carry != 0) carry.toString + sum else sum
}
def multByDigit(num: String, digit: Int) = {
val (mult, carry) = num.foldRight(("", 0)) {
case (d, (acc, carry)) =>
val mult = d.asDigit * digit + carry
((mult % 10).toString + acc, mult / 10)
}
if (carry != 0) carry.toString + mult else mult
}
def mult(x: String, y: String) =
y.foldLeft("")((acc, digit) => addNums(acc + "0", multByDigit(x, digit.asDigit)))
Sample:
scala> mult("18446744073709551616", "18446744073709551616")
res25: java.lang.String = 340282366920938463463374607431768211456
Works with: Scala version 2.8 Scala 2.8 introduces `scanLeft` and `scanRight` which can be used to simplify this further:
def adjustResult(result: IndexedSeq[Int]) = (
result
.map(_ % 10) // remove carry from each digit
.tail // drop the seed carry
.reverse // put most significant digits on the left
.dropWhile(_ == 0) // remove leading zeroes
.mkString
)
def addNums(x: String, y: String) = {
val padSize = (x.length max y.length) + 1 // We want to keep a zero to the left, to catch the carry
val paddedX = "0" * (padSize - x.length) + x
val paddedY = "0" * (padSize - y.length) + y
adjustResult((paddedX zip paddedY).scanRight(0) {
case ((dx, dy), last) => dx.asDigit + dy.asDigit + last / 10
})
}
def multByDigit(num: String, digit: Int) = adjustResult(("0"+num).scanRight(0)(_.asDigit * digit + _ / 10))
def mult(x: String, y: String) =
y.foldLeft("")((acc, digit) => addNums(acc + "0", multByDigit(x, digit.asDigit)))
[edit] Seed7
$ include "seed7_05.s7i";
include "bigint.s7i";
const proc: main is func
begin
writeln(2_**64 * 2_**64);
end func;
Output:
340282366920938463463374607431768211456
[edit] Slate
(2 raisedTo: 64) * (2 raisedTo: 64).
[edit] Smalltalk
(2 raisedTo: 64) * (2 raisedTo: 64).
[edit] Tcl
Works with: Tcl version 8.5
Tcl 8.5 supports arbitrary-precision integers, which improves math operations on large integers. It is easy to define our own by following rules for long multiplication; we can then check this against the built-in's result:
package require Tcl 8.5
proc longmult {x y} {
set digits [lreverse [split $x ""]]
set result {0}
set j -2
foreach m [lreverse [split $y ""]] {
set c 0
set i [incr j]
foreach d $digits {
set v [lindex $result [incr i]]
if {$v eq ""} {
lappend result 0
set v 0
}
regexp (.)(.)$ 0[expr {$v + $c + $d*$m}] -> c v
lset result $i $v
}
lappend result $c
}
# Reconvert digit list into a decimal number
set result [string trimleft [join [lreverse $result] ""] 0]
if {$result == ""} then {return 0} else {return $result}
}
puts [set n [expr {2**64}]]
puts [longmult $n $n]
puts [expr {$n * $n}]
outputs
18446744073709551616 340282366920938463463374607431768211456 340282366920938463463374607431768211456
[edit] Ursala
Natural numbers of unlimited size are a built in type, and arithmetic operations on them are available as library functions. However, since the task calls for explicitly implementing long multiplication, here is an implementation using nothing but language primitives. The numbers are represented as lists of booleans, LSB first. The compiler already knows how to parse and display them in decimal.
successor = ~&a^?\1! ~&ah?/~&NfatPRC ~&NNXatPC
sum = ~&B^?a\~&Y@a ~&B?abh/successor@alh2fabt2RC ~&Yabh2Ofabt2RC
product = ~&alrB^& sum@NfalrtPXPRCarh2alPNQX
x = 18446744073709551616
#show+
y = %nP product@iiX x
output:
340282366920938463463374607431768211456
Categories: Programming Tasks | Arbitrary precision | Arithmetic operations | Ada | ALGOL 68 | AutoHotkey | AWK | Basic | C | GMP | C sharp | Common Lisp | D | Fortran | Haskell | Icon | Unicon | J | Java | JavaScript | Mathematica | Perl | PicoLisp | PL/I | PureBasic | Python | R | Gmp | REXX | Ruby | Scala | Seed7 | Slate | Smalltalk | Tcl | Ursala
