How to exponentiate really large numbers in Objective-C?

Question

I'm having some trouble calculating the result of an 8-digit number to the power of a 3-digit number programmatically in Objective-C.

Take these numbers, for instance: 16468920^258, which should result in a number that is 1862 digits in length.

I naïvely tried:

unsigned long long result = 1;
for (int i = 0; i < 258; i++)
    result *= 16468920;

…but result outputs 0.

Then I tried:

long double result = powl(16468920, 258);

…but result outputs inf.

After finding out about NSDecimal, I tried this:

NSDecimal result;
NSDecimal number = [[NSDecimalNumber decimalNumberWithString:@"16468920"] decimalValue];
NSDecimalPower(&result, &number, 258, NSRoundPlain);

…but result outputs NaN, so I tried:

NSDecimalNumber *number = [[NSDecimalNumber alloc] initWithInt:16468920];
NSDecimalNumber *result = [number decimalNumberByRaisingToPower:258];

…but this code raises an NSDecimalNumberOverflowException.

Any pointers as to which direction I should be going?

You are going to have to use one of the libraries mentioned here -> http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic because to store that number as a plain binary number would mean God only knows how many bits — borrrden, Jun 25 '13 at 02:34
You need to think about what you can possibly do with this number once you get it. (Roughly 5610 bits, BTW, or 701 bytes.) — Hot Licks, Jun 25 '13 at 02:45

sjs · Accepted Answer · 2013-06-25T02:44:31.667

3

Since Objective-C is a superset of C, you can use a C library such a BN:

int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);

BN_exp() raises a to the p-th power and places the result in r ("r=a^p"). This
function is faster than repeated applications of BN_mul().

See, for example, here for how to get openssl into iOS.

edited Jun 25 '13 at 02:44

answered Jun 25 '13 at 02:38

sjs

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1

Perfect! This seems to have done the trick! I used the port of [OpenSSL for iOS](https://github.com/st3fan/ios-openssl) along with this [Wrapper for OpenSSL's BigNumber math functions](https://github.com/davedelong/CHMath) to output the result as an `NSString`! – gomollon Jun 25 '13 at 03:35

score 0 · Answer 2 · answered Aug 17 '15 at 06:43

You get that issue because your result still bigger that NSDecimalNumber could store.

I recommend you to could use JKBigInteger instead, it is a Objective-C wrapper around LibTomMath C library. And really easy to use and understand.

Hope this could help.

How to exponentiate really large numbers in Objective-C?

2 Answers2