#C1.txt: Jan. 23, 2014. How to multiply two integers
Help:=proc(): print(` M(a,b), K(a,b) `): end:

M:=proc(a,b) local d,a1,a2,b1,b2:

if a<10 and b<10 then

  RETURN(a*b):

fi:

#If a had 2d digits, let's write as a=10^d*a1+a2 and ditto for b
#where a1 and a2 have d digits

d:=log[10](max(a,b)):

if type(d,integer) then
d:=d+1:
else
 d:=ceil(d):
fi:

if d mod 2=1 then
 d:=(d+1)/2:
else
 d:=d/2:
fi:

a2:=a mod 10^d:  b2:=b mod 10^d:

a1:=(a-a2)/10^d: b1:= (b-b2)/10^d:

# a*b=(10^d*a1 +a2)* (10^d*b1+b2)=
#(10^d)^2*a1*b1+10^d*a1*b2+a2*10^d*b1+a2*b2

M(a1,b1)*100^d+ ( M(a1,b2)+M(a2,b1))*10^d + M(a2,b2):

end:


#Karatsuba's version
K:=proc(a,b) local d,a1,a2,b1,b2:
option remember:

if a<10 and b<10 then

  RETURN(a*b):

fi:

#If a had 2d digits, let's write as a=10^d*a1+a2 and ditto for b
#where a1 and a2 have d digits

d:=log[10](max(a,b)):

if type(d,integer) then
d:=d+1:
else
 d:=ceil(d):
fi:

if d mod 2=1 then
 d:=(d+1)/2:
else
 d:=d/2:
fi:

a2:=a mod 10^d:  b2:=b mod 10^d:

a1:=(a-a2)/10^d: b1:= (b-b2)/10^d:

# a*b=(10^d*a1 +a2)* (10^d*b1+b2)=
#(10^d)^2*a1*b1+10^d*a1*b2+a2*10^d*b1+a2*b2
#(10^d)^2*a1*b1+10^d*(a1*b2+a2*b1)+a2*b2
#a1*b2+a2*b2=(a1+a2)*(b1+b2)-a1*b1-a2*b2:

K(a1,b1)*100^d+ (K(a1+a2,b1+b2)- K(a1,b1)-K(a2,b2))*10^d + K(a2,b2):

end: