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Questions tagged [arithmetic]

The tag has no usage guidance.

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2answers
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Why does Integer.MIN_VALUE - Integer.MAX_VALUE equals to 1 in Java?

If you run the statement: System .out.println( (Integer.MIN_VALUE)-(Integer .MAX_VALUE )); In java it returns 1 as the answer. Is this because Java just considers those values as 32bit integers ...
2
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2answers
175 views

Is writing arithmetic functions to allow “type coercion” a good idea?

Let's say I want to write a function to compute factorials of nonnegative integers. I could write something like this: fact :: Num a => Int -> a fact n = fromInteger(product [1..n]) (Let's ...
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2answers
145 views

Describe a slope (N/M), approximately as small number of fractions (n/m)

What algorithm can I use to describe a specified gradient (N/M) approximately as the sum of a set of rational fractions { (n1/m1) + (n2/m2) … } ? Design constraints: The algorithm takes as input (N, ...
0
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1answer
279 views

For learning purposes, how should I set about implementing an arbitrary precision library in C or C++?

I know I am reinventing the wheel. But I'm really interested in implementing arbitrary precision numbers (integers, rationals, complex, etc) in C or C++ and their algorithms. Please be patient. My ...
0
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4answers
342 views

Shortening a boolean AND with third operand

I'm trying to calculate the sum of 2 bits using basic binary arithmetic and currently, I'm doing this: function Add(bool a, bool b, bool carry) { return { Result: a ^ b ^ carry, ...
2
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2answers
2k views

Understanding of the Carry Flag Bit

Intel 8085: In my textbook it is said: "Carry Flag - this flag is the carry out from the MSB of the A-register. CY is set after an ADD instruction if carry out was generated from the A-register." I ...
3
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1answer
2k views

Difficulties with Two's complement in Assembly

Everything discussed here will refer to Intel 8085 (8-bit architecture). When using two's complement number "conversion" : 1.) If we take SBI 0F (subtraction) for example; immediate value 0F(hex) or ...
-1
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1answer
68 views

Multiprecision Arithmetic; The Carry Flag

Intel 8085: I'm having big troubles understanding addition or subtraction with more than 16-bit numbers in Intel 8085: 1.) If I execute ADC M instruction then this should happen: (A)<--(A)+((H)(L))...
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4answers
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Why are arbitrary-precision decimals used over rational numbers in practice?

The basic arithmetic a computer chip can do only works on numbers(integers or floating point) of a fixed size. There are many algorithms that could be extended to work on numbers of arbitrary size (...
0
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1answer
79 views

How do two (programming) methods for capping daily rep stack up?

I wrote a supersuccessful answer to a question on an SE site that got (at least) 21 upvotes in a 24-hour period. In theory, I should have gotten 210 rep points, but there is a daily reputation limit ...
0
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1answer
431 views

Combine sequences of numbers with “variable bitlengths” into short unique strings

It is not unlikely that what I want to do is not possible, but it doesn't hurt to ask. Imagine a set of lists, each containing positive integers (in my case, a list always consists of four integers, ...
59
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5answers
16k views

Will a computer attempt to divide by zero?

We all know 0/0 is Undefined and returns an error if I were to put it into a calculator, and if I were to create a program (in C at least) the OS would terminate it when I try to divide by zero. But ...
-1
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1answer
57 views

multiplication with insufficiently long registers [duplicate]

I want to multiply two numbers but since I don’t have long enough registers in the current architecture need to “break them down” into shorter ones and somehow perform the calculation. For example: ...
4
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3answers
1k views

Is order of arguments in an arithmetic expression important to achieve as most exact result as possible (speed is not necessary)?

Actually, in this question I do not ask about particular language or architecture, however I understand there might be some differences. In physics / engineering it is usually better to handle ...
4
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2answers
189 views

What do you get when you cross a multi-precision integer with a floating-point number?

I'm working on adding multi-precision integers to the suite of numeric types in my APL interpreter, but I'm not sure what to do about the odd type-combinations that now arise. I now have the following ...
3
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1answer
4k views

how to enumerate/generate all possible binary trees from N leaves and N-1 nodes?

I am trying to implement the 24 Game in ansi C. This game goes as follows: For a list of four given numbers, try to find a solution involving these four numbers, that, using addition(+), subtraction(-...
1
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2answers
305 views

How do you guard against hidden overflows

consider the following: (i+j)/2 i and j are both 32 bit integers and the result should also be. But in the little equation, there's a hidden overflow, i+j could become larger then a 32 bit integer ...
1
vote
1answer
709 views

Next power of 2 for a number (in search for better “bit-twiddling” way)

I just wonder if there exists better (i.e. faster?) way to get the next power of 2 for a given number than the following one (maybe some better sort of "bit-twiddling" hack is possible?) ... static ...
9
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3answers
582 views

What rationale is used when programming language designers decide what sign the result of modulo operation takes?

Going through Modulo operation (the avenue I entered while exploring the difference between rem and mod) I came across: In mathematics the result of the modulo operation is the remainder of the ...
10
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2answers
4k views

Name of the Countdown Numbers round problem - and algorithmic solutions?

For the non-Brits in the audience, there's a segment of a daytime game-show where contestants have a set of 6 numbers and a randomly generated target number. They have to reach the target number using ...
5
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2answers
5k views

Array Multiplication and Division

I came across a question that (eventually) landed me wondering about array arithmetic. I'm thinking specifically in Ruby, but I think the concepts are language independent. So, addition and ...
5
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2answers
3k views

Performance and other issues with using floating point types in C++

Being interested in C++ performance programming there is one aspect I really have no clue about- and that is the implications of using floating point calculations vs doubles vs normal integer ...
4
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2answers
530 views

Arithmetic Coding vs. Machine Numeric Precision

When subdividing intervals for arithmetic coding, the worst case scenario is that the final interval will have size 2^(1-n), where n is the number of unique symbols you are encoding. This will reach ...
3
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2answers
725 views

Arithmetic Coding Questions

I have been reading up on arithmetic coding and, while I understand how it works, all the guides and instructions I've read start with something like: Set up your intervals based upon the frequency ...
9
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3answers
39k views

Is there something special about the number 65535?

2¹⁶-1 & 2⁵ = 2⁵ (or? obviously ?) A developer asked me today what is bitwise 65535 & 32 i.e. 2¹⁶-1 & 2⁵ = ? I thought at first spontaneously 32 but it seemed to easy whereupon I thought ...
3
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1answer
1k views

Dummy float values to force floating-point operations

It is common to use idioms such as: x/60.0 to force a floating-point division when x is an integer in languages which do not have distinct operators for integer and decimal division. Is this an ...