I am writing an app that , among other things will be able to multiply or divide very large numbers by number 19 - Those large numbers could possibly span hundreds of digits . Do you know of a library I could use for that? Thanks in advance. I have tried using NSDecimalNumber but its not able to produce results past 38 digits.
If licensing is not an issue GMP is good.
Related
I want to generate a 16 bit unsigned integer (uint16_t) which could represent following:
First 2 digits representing some version like 1, 2, 3 etc.
Next 3 digits representing another number may be 123, 345, 071 etc.
And last 11 digits representing a number T234, T566 etc.
How can we do this using objective C. I would like to parse this data later on to get these components back. Please advise.
I think you are misunderstanding just what uint16_t means. It doesn't mean a 16 digit decimal number (which would be any number between 0 and 9,999,999,999,999,999). It means an unsigned number that can be expressed using 16 bits. The range of such a value is 0 to 65535 in decimal. If you really wanted to store the numbers you are talking about you would need 52 bits. You would also be making things very difficult for yourself, since you wouldn't easily be able to extract the first two decimal digits from that 52 bit sequence; You'd have to treat the number as a decimal value then modulus 100 it, you couldn't just say it's bits 1 to 8.
There is a scheme called Binary Coded Decimal that could help you. You would take a 64 bit value (uint64_t) and you'd say that within this value the bits 1-7 are the version (which could be a value up to 127), bits 8-17 are the second number (which could be a value up to 1023) and bits 18-63 could be your third number (those 46 bits would be able to store a number up to 70,368,744,177,663.
All this is technically possible, but you are really going to be making things hard for yourself. It looks like you are storing a version, minor version and build number and most people do that using strings, not decimals
FedEx Ground's tracking numbers have different digits: 12, 15, 20, 22.
12-digits tracking numbers use mod 11 algorithm.
Others use mod 10 algorithm.
But recently I got some 20-digits FedEx Smartpost tracking numbers which can't identified by both algorithms.
So, how can I identify these tracking numbers?
Sample tracking numbers:
7489999873402038xxxx
6129270107532465xxxx
I figured this out.
see:
http://images.fedex.com/us/software/pdf/FedEx_SmartPost_Job_Aid_v2600_06222012.pdf
https://www.pdffiller.com/en/project/10655396.htm
22 digits tracking numbers remove 2 digits application identifiers (91 or 92).
We need add application identifiers to the tracking numbers before mod 10 algorithm.
The 20 digit codes need either 91 (old) or 92 (new) before the code. Pre-pend those and apply a standard mod-10 algorithm used by the IMpb standard.
I'm working on some 65802 code (don't ask :P) and I need to separate a 16-bit value into two 8-bit bytes to store it in memory. How would I go about this?
EDIT:
Also, how would I take two similar bytes and combine them into one 16-bit value?
EDIT:
To clarify, many of the solutions available on the internet are not possible with the programming language I'm using (a version of MS-BASIC). I can't take modulo, and I can't left or rightshift. I've figured out that I can put the two bytes together by multiplying the high byte by 256 and adding it to the low byte, but how would I reverse the process?
http://projecteuler.net/problem=20
I've written code to figure out this problem, however, it seems to be accurate in some cases, and inaccurate in others. When I try solving the problem to 10 (answer is given in question, 27) I get 27, the correct answer. However, when I try solving the question given (100) I get 64, the incorrect answer, as the answer is something else.
Here's my code:
function factorial(num)
if num>=1 then
return num*factorial(num-1)
else
return 1
end
end
function getSumDigits(str)
str=string.format("%18.0f",str):gsub(" ","")
local sum=0
for i=1,#str do
sum=sum+tonumber(str:sub(i,i))
end
return sum
end
print(getSumDigits(tostring(factorial(100))))
64
Since Lua converts large numbers into scientific notation, I had to convert it back to standard notation. I don't think this is a problem, though it might be.
Is there any explanation to this?
Unfortunately, the correct solution is more difficult. The main problem here is that Lua uses 64bit floating point variables, which means this applies.
Long story told short: The number of significant digits in a 64bit float is much too small to store a number like 100!. Lua's floats can store a maximum of 52 mantissa bits, so any number greater than 2^52 will inevitably suffer from rounding errors, which gives you a little over 15 decimal digits. To store 100!, you'll need at least 158 decimal digits.
The number calculated by your factorial() function is reasonably close to the real value of 100! (i.e. the relative error is small), but you need the exact value to get the right solution.
What you need to do is implement your own algorithms for dealing with large numbers. I actually solved that problem in Lua by storing each number as a table, where each entry stores one digit of a decimal number. The complete solution takes a little more than 50 lines of code, so it's not too difficult and a nice exercise.
I am preparing for a quiz in my computer science class, but I am not sure how to find the correct answers. The questions come in 4 varieties, such as--
Assume the following system:
Auxiliary memory containing 4 gigabytes,
Memory block equivalent to 4 kilobytes,
Word size equivalent to 4 bytes.
How many words are in a block,
expressed as 2^_? (write the
exponent)
What is the number of bits needed to
represent the address of a word in
the auxiliary memory of this system?
What is the number of bits needed to
represent the address of a byte in a
block of this system?
If a file contains 32 megabytes, how
many blocks are contained in the
file, expressed as 2^_?
Any ideas how to find the solutions? The teacher hasn't given us any examples with solutions so I haven't been able to figure out how to do this by working backwards or anything and I haven't found any good resources online.
Any thoughts?
Questions like these basically boil down to working with exponents and knowing how the different pieces fit together. For example, from your sample questions, we would do:
How many words are in a block, expressed as 2^_? (write the exponent)
From your description we know that a word is 4 bytes (2^2 bytes) and that a block is 4 kilobytes (2^12 bytes). To find the number of words in one block we simply divide the size of a block by the size of a word (2^12 / 2^2) which tells us that there are 2^10 words per block.
What is the number of bits needed to represent the address of a word in the auxiliary memory of this system?
This type of question is essentially an extension of the previous one. First you need to find the number of words contained in the memory. And from that you can get the number of bits required to represent a word in the memory. So we are told that memory contains 4 gigabytes (2^32 bytes) and that the word is 4 bytes (2^2 bytes); therefore the number words in memory is 2^32/2^2 = 2^30 words. From this we can deduce that 30 bits are required to represent a word in memory because each bit can represent two locations and we need 2^30 locations.
Since this is tagged as homework I will leave the remaining questions as exercises :)
Work backwards. This is actually pretty simple mathematics. (Ignore the word "auxilliary".)
How much is a kilobyte? How much is 4 kilobytes? Try putting in some numbers in 2^x, say x == 4. How much is 2^4 words? 2^8?
If you have 4GB of memory, what is the highest address? How large numbers can you express with 8 bits? 16 bits? Hint: 4GB is an even power of 2. Which?
This is really the same question as 2, but with different input parameters.
How many kilobytes is a megabyte? Express 32 megabytes in kilobytes. Division will be useful.