Large numbers

General
1

Here’s a factorial function. This happens to take advantage of Lua’s tail-call elimination:

function factorial(n, a)
    if n == 0 then
        return a
    end
        
    return factorial(n - 1, a * n)
end
    
print(factorial(21, 1))

…except with 21 and above, I don’t see the proper result. Are the numbers too large? Any way to see large numbers in Lua, or does it require a separate library?

Thanks.

2

Codea uses 64 bit math and the largest number is 9,223,372,036,854,775,807.

3

Try this code and you’ll see it go from positive to largest number to negative which is correct.

function setup()
    a=9223372036854775800
    for z=1,20 do
        print(a+z)
    end
end
4

On my TI-89 Titanium calculator, it will do 299! and show a 613 digit number. It will do 449! and give a result of 3.85193051803 e997 . After that it just give you what you entered. The largest integer number on the calculator is 614 digits.

If I use the WolframAlpha app on my iPad, I don’t know the largest factorial it will do.

5

I believe there are Lua libraries available to support large numbers/arbitrary precision, though I’ve never used one (yet).

6

I just remembered that I wrote a factorial program. Enter the factorial and tap the screen. Doing factorial 12345 takes 1.7 seconds and prints 45,151 digits. I’m not sure how large a factorial it will do, but 123456 takes 228 seconds on my iPad Air 3 and prints 574,965 digits. So just going up 1 digit increased the size and time by a lot.

Code removed, updated code shown below.
7

While we’re looking at large numbers, here’s a program that will multiply 2 strings of numbers. This example multiples 2 strings of 1600 digits. There’s no checking, so don’t put anything other than a number in the string. Run in portrait mode for the larger print area.

function setup()
    a="98765432109876543210987654321098765432109876543210"  -- string of 50 digits
    for z=1,5 do
        a=a..a  -- create string of 1600 digits
    end
    b=a
    
    str=mult(a,b)   -- multiply 2 1600 digit numbers
    
    print("a x b = ")
    print(str)
    print("digit size of a "..#a)
    print("digit size of b "..#b)
    print("digit size of a*b "..#str)
end   
    
function mult(str1,str2)
    local r,n1,n2={},{},{} 
    for z=1,#str1 do
        table.insert(n1,tonumber(string.sub(str1,z,z)))
        table.insert(r,0)
    end    
    for z=1,#str2 do
        table.insert(n2,tonumber(string.sub(str2,z,z)))
        table.insert(r,0)
    end
    for x=#n2,1,-1 do
        local carry=0
        for y=#n1,1,-1 do
            local v=r[x+y]+n2[x]*n1[y]+carry
            r[x+y]=v%10
            carry=math.floor(v/10)
        end
        r[x]=carry
    end
    if r[1]==0 then
        table.remove(r,1)
    end
    return(table.concat(r))
end
8

Here’s an updated version of my factorial program. It’s best to run it in portrait mode to show more of the print area.

function setup()
    s=require("socket")
    parameter.text("Factorial","")
    parameter.action("calculate factorial",calc)
end

function calc()
    st=s:gettime()
    output.clear()
    fact=tonumber(Factorial) or 1
    print("Calculating "..fact.."!")
    limit=1000000000000
    local carry,b,a=0,0,{1}
    for s=2,fact do
        carry=0
        for z=#a,1,-1 do
            b=a[z]*s+carry
            if b>limit then
                carry=b//limit
                a[z]=b%limit
            else
                carry=0
                a[z]=b  
            end   
        end
        while carry>0 do
            table.insert(a,1,carry%limit)
            carry=carry//limit
        end
    end
    size=string.len(a[1])
    for z=2,#a do
        str="000000000000"..a[z]
        a[z]=string.sub(str,#str-11)
        size=size+#a[z]
    end 
    print(fact.."! = ",table.concat(a)) 
    print("Number of digits ",size)
    print(s:gettime()-st.." seconds")
    showKeyboard()
    hideKeyboard()
    Factorial=""
end
9

What’s nice around this forum is your creativity. Fun to see you take a posted question and watch you play with it. Codea is built for this type of quick turn-around. Thanks!

10

@brianolive Thats what’s fun with Codea. I try to answer the questions asked, but I also like to throw some examples that I hope will give others something to explore. That’s one way to learn.

11

@dave1707 do not forget that Codea will not handle the print function with too large strings (web pages from ‘data’ in http.request, this here, etc).

Edit: Also added this little info on the Lua article.