Division

In mathematics, division (÷) is an arithmetic elementary operation.

Multiplication

Multiplication is the mathematical operation of scaling one number by another



Faster slower integer

Example

"Multiplication is far easier and faster for a cpu to do than division"

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Which is fast comparison: Convert.ToInt32(stringValue)==intValue or stringValue==intValue.ToString()

"Integer multiplication is much faster than division"

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Fast Euclidean division in C

"I picked c 1 1 8 for this example simply because it is exact in ieee-754 floating-point representation and typically multiplication is much faster than division"

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Fast way to "improve" the length of a unit length vector

"According to stephen canon modern implementations favor taylor expansion over rational function approximation where division is much slower than multiplication"

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Definitions of sqrt, sin, cos, pow etc. in cmath

"Yes division is usually much slower than multiplication"

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Is divide slower than Multiply?

"Is it possible that the division is six times slower than multiplication and"

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Float Operations Performance C++

"The tostring should be slower than parse since division is generally slower than multiplication"

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Is it more efficient to compare ints and ints or strings and strings

"But i wonder why is division actually slower than multiplication"

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Why is division more expensive than multiplication?

"Division is slower than multiplication due to some reasons"

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Will the compiler optimize division into multiplication

"Both works but division is generally slower than multiplication"

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Calculating prime numbers in python

"Division algorithms are slower than multiplication algorithms in most cases"

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Is Multiplying the Inverse Better or Worse?

"In all other cases division appears to be several times slower than multiplication"

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What has a better performance: multiplication or division?

"Division is per se slower than multiplication however i don t know the details"

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Why is float division slow?

"I found out that integer division is much slower than multiplication unfortunately"

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Optimizing Fixed-Point Sqrt

"And division may be slower than multiplication or may still be fast"

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Do different operators have different amounts of cpu usage?

"Because division is often much slower than multiplication if performance is critical you might keep a table with powers of ten and their reciprocals"

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Java: convert float to double preserving decimal point precision

"Division is about 10 times slower than multiplication"

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Efficient Multiply/Divide of two 128-bit Integers on x86 (no 64-bit)

"Which one is faster is indeed a cpu-specific issue or at least how much faster is cpu specific yes division is typically seen as slower than multiplication"

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Is Multiplying the Inverse Better or Worse?

"The compiler or the jit is likely to convert the first case to the second anyway since multiplication is typically faster than division"

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Differences between mult and div operations on floating point numbers

"On mobile arm cpus i would expect floating point division to be somewhere 10-100 slower than multiplication"

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Log2 not found in my math.h?

"It s just as fast as going the opposite direction if not faster given that division generally takes longer than multiplication"

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Reverse factorial

"If the latter yes floating point multiplication is generally faster than division"

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A good way to do a fast divide in C++?

"Division is inherently a much slower operation than multiplication"

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Floating point division vs floating point multiplication

"But since division is pretty expensive i think that this is even worse than 2 multiplication"

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Euler 11. There must be a better way than this

"So division is always a bit worse than multiplication"

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Polynomial evaluation accuracy, multiplication versus division

"I always thought a multiplication is computationally cheaper than a division"

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NumPy performance: uint8 vs. float and multiplication vs. division?

"Multiplication is way faster than division"

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Speed up Python Loop append

"In many processors integer multiplication is vastly faster than integer division"

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How do computers find modulus?

"According to this author integer multiplication can be 40 times faster than integer division"

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Most efficient way to calculate lexicographic index

"Multiplication and division are a bit trickier but again a few tips;multiplication is the easier of the tasks just remember to multiplying each block of one number with the other and carry the zeros"

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Convert string to a large integer?

"As to why multiplication is faster than division and when the divisor is fixed this is a faster route"

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Why does GCC use multiplication by a strange number in implementing integer division?

"I used multiplication for both operations because multiplication is typically faster than division"

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Rounding floats in processing.org

"Multiplication is usually faster than division"

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SIGABRT error for - https://www.codechef.com/problems/PRIME1

"For the division-to-multiplication case you are assuming that multiplication is faster than division"

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Would C# compiler or Jitter optimize these kinds of arithmetic operations?

"In usual programming practice one wouldn t bother and simply multiplying by the floating-point representation of 180 ï because multiplication is so much faster than division"

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Should I combine multiplication and division steps when working with floating point values?

"Multiplication is much faster than division"

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What is fastest x86-64 assembly-language divide algorithm for huge numbers?

"I would also suggest to replace terms like a l1 0.3e1 with as multiplication is faster then division"

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How can I improve performance via a high-level approach when implementing long equations in C++

"This because 1 x is simpler than y x and multiplication is faster than division"

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Calculating GFlops

"Multiplication is faster division is more accurate"

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Should I use multiplication or division?

"Multiplication is faster than division see fog s tables"

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What does clang's `-Ofast` option do in practical terms especially for any differences from gcc?

"As hroptatyr mentioned the multiplication is quite fast and it s much faster than division"

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How can I use bit shifting to replace integer division?

"Multiplication is usually significantly faster than division"

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Fast multiplication/division by 2 for floats and doubles (C/C++)

"First of all multiplication is faster than division"

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Is there a preferred way to order floating-point operands?

"Similar to pmg s solution but still faster because multiplication is faster than division -"

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Find the "string length" of an int

"Division is faster for unint8 than multiplication in your case"

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NumPy performance: uint8 vs. float and multiplication vs. division?

"Division is about 20 faster than multiplication"

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Should I use multiplication or division?

"Therefore i conclude that division is faster than multiplication"

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Unexpected apparent performance difference between integer multiplication and division

"Multiplication is faster than division so the second method is faster"

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A good way to do a fast divide in C++?

"Since you re resizing the window make sure to assign the w and h values not as numbers but as products or dynamic numbers multiplication is faster than division but you can also use division"

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Alpha Blending in SDL resets after resizing window

"Also addition is faster than multiplication and multiplication is faster than division"

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Performance Testing for Calculation-Heavy Programs

"Multiplication is faster than division"

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Is multiplication faster than float division?

"On many processors integer multiplication is faster than integer division"

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Efficient (cycles wise) algorithm to compute modulo 25?

Float integer unable

Example

"Here is results of my bench mark division type time uint8 879.5ms uint16 885.284ms int 982.195ms float 654.654ms as well as floating point multiplication is faster than integer multiplication. here is results of my bench mark multiplication type time uint8 166.339ms uint16 524.045ms int 432.041ms float 402.109ms my system spec cpu core i7-7700 ram 64gb visual studio 2015"

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Why float division is faster than integer division in c++?

"Float division is not much slower than integer division but the compiler may be unable to do the same optimizations;for example the compiler can replace integer division between 3 with a multiplication and a binary shift"

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Why is float division slow?

Addition comparison single

Example

"Since most processors can do an addition comparison or multiplication in a single cycle those are all counted as one flop;but division always takes longer"

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What is FLOP/s and is it a good measure of performance?

"Here is such a rational class it could be easily extended to do more than multiplication addition division negation inversion ... notice how the last function can concentrate on the recipe logic delegating the use of fractions to the rational class which in turn is completely ignorant of the recipe-business"

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How can I keep fraction formatting using JavaScript?

Longer pen paper

Example

"How can multiplication function takes longer than division"

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Slow matrix multiplication when using OpenCL enabled OpenCV

"Division takes a lot longer than multiplication - just do it with pen and paper to see"

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Sort several arrays together and return the ranking number in the all-arrays combined score

"Why does division take so much longer than multiplication"

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Multiply by 0.5 rather than divide by 2

Cycles fewer common

Example

"It is common knowledge that division takes many more clock cycles to compute than multiplication"

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Should I use multiplication or division for recurring floats?

"It has to do with the fact that multiplication is itself done by means of binary shifts and additions - far fewer than with division"

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How to use right shift to avoid operator division

"Floating point multiplication usually takes fewer cycles than floating point division"

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Is multiplication faster than float division?

Hardware slower correct

Example

"On many machines particularly those without hardware support for division division is a slower operation than multiplication so this approach can yield a considerable speedup"

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Calculating Reciprocals: n**(-1) or (1/n)?

"You always need to know the magic number here 0xaaaaaaab and the correct operations after the multiplication shifts and or additions in most cases and both is different depending on the number you want to divide by and both take too much cpu time to calculate both on the fly that would be slower than hardware division"

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What's the fastest way to divide an integer by 3?

Modern fast cpus

Example

"Can be fast or it can be awfully slow even if division is done entirely in hardware if it is done using a div instruction this instruction is about 3 to 4 times slower than a multiplication on modern cpus"

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What's the fastest way to divide an integer by 3?

"Division may be heavier than multiplication but a commenter pointed out that reciprocals are just as fast as multiplication on modern cpus in which case this isn t correct for your case so if you do have 1 x appearing somewhere inside a loop and more than once you can assist by caching the result inside the loop and then using y"

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Fast 1/X division (reciprocal)

"On modern processors float division is a good order of magnitude slower than float multiplication when measured by reciprocal throughput"

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Fast approximate float division

Precedence higher presedence

Example

"So this is evaluated as note that this behavior is different from most programming languages where unary negation has higher precedence than multiplication and division vb javascript"

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A strange operation problem in SQL Server: -100/-100*10 = 0

"In bnf consider something akin to and oh-by-the-way you probably want to make an additional nonterminal layer to represent the fact that implicit multiplication-by-adjacency is normally considered to have higher precedence than division while explicit multiplication typically is interpreted to have the same precedence"

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Parsing implied versus explicit times operator

"Division has higher precedence than subtraction;this subtraction operator occurs within the second brackets and so has a higher precedence than the multiplication"

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Complex calculation in JavaScript

"Since multiplication is of higher precedence than division"

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Decimal and mathematical operations

"In some of the academic literature implied multiplication is interpreted as having higher precedence than division"

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Which has higher precedence in C -multiplication or division?

"Does multiplication has higher precedence over division or it is other way round"

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Multiplication vs Division in C

"Multiplication has higher precedence than division"

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Macro usage in C?

"Thus python should interpret this like 12 2 i.e 6 since precedence of multiplication is more than division"

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Operator precedence in Python -PEMDAS

"This will be good idea to put factorial as additional case into primary as parentheses have higher order of precedence called earlier than multiplication division etc in term"

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Stroustrup's C++ Book exercise

"It s an exponentation operator with a precedence higher than multiplication or division"

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What does character "^" do in Excel?

"According to bodmas rule --- division come first from multiplication. same in java the precedence of is higher than so division happen first then multiplication"

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What if the meaning of that expression if(x > y / z)

"He line works because of integer division the line works because of modulo;the line works because of operator precedence multiplication has a higher precedence than addition + so it will be done first"

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Why does this loop work?

"I read that multiplication has has higher presedence than division"

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Multiplication and division: weird output in c

Harder remainder bitch

Example

"Multiplication is harder and division remainder is a bitch"

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How do modern processors which are 64 bit usually handle 128 bit / 256 bit encryption?

"Beware of this pitfall when using shifts additions and subtractions to perform multiplication operations;division is a bit harder need to think."

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Assembly 8086 - Implementing any multiplication and division without MUL and DIV instruction

Expensive one sum

Example

"However in general one could expect that a division is a more expensive operation than a multiplication"

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Conditional tests in primality by trial division

"Division is one of a number of operations which as far as computational complexity theory is concerned are no more expensive than multiplication"

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What is the time complexity to divide two numbers?

"In the code we calculate 1.0 sum .. because a division usually is more expensive than a multiplication and thus can gain some efficiency with that"

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How do you turn probabilities that don't sum up to 1 into ones that do?

Constant expensive compiler

Example

"It will be much slower i don t have benchmarks but i would guess at least an order of magnitude maybe more decimal will not benefit from any hardware acceleration and arithmetic on it will require relatively expensive multiplication division by powers of 10 which is far more expensive than multiplication and dividion by powers of 2 to match the exponent before addition subtraction and to bring the exponent back into range after multiplication division"

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When should I use double instead of decimal?

"Usually division is a lot more expensive than multiplication but a smart compiler will often convert division by a compile-time constant to a multiplication anyway"

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What has a better performance: multiplication or division?

"This solution has the disadvantage that if the other factor is not constant the compiler and you can t reasonably avoid the division int_max n to be done at runtime and division is normally more expensive than multiplication"

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Check for int overflow in C++

"Most optimizing c compilers optimize it out to a multiplication operation which is much faster than division it can be done only if the divisor is constant though"

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Print decimal in 8086 emulator

Complexity addition worse

Example

"If you think back to grade school you ll recall that multiplication was harder than addition and division was harder than multiplication"

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Why is multiplying cheaper than dividing?

"Formally it means division cannot have a complexity worse than multiplication"

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Complexity of division

"Division has worse latency than multiplication or addition by a factor of 2 to 4 on modern x86 cpus and worse throughput by a factor of 6 to 40"

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Floating point division vs floating point multiplication

"If you do it cleverly you only do addition not even multiplication;and division has larger complexity than addition"

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Why is Sieve of Eratosthenes more efficient than the simple "dumb" algorithm?

Time line for-loop

Example

"In addition the for-loop itself is taking much more time than the multiplication or the division ops"

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Why is dividing giving similar times to multiplicating?

"Following advise i received multiplication is cheaper than division i revised one code line and interestingly enough 71.2 dropped to 1.7 but the if statement just below shot up to 64.8 â i just don t get it"

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Performance optimizing critical code in iOS app

"I have heard division takes more time then multiplication but beyond that i could not determine whether writing this in one line or multiple assignment lines was more efficient"

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Java Optimizing arithmetic and Assignment Operators for large input

Expensive costly cost

Example

"Yes mod is more expensive than multiplication as mod is implemented through division"

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Is MOD operation more CPU intensive than multiplication?

"Knowing that a division is much more costly than a multiplication"

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Speeding up the code using numpy

"Division is always much more expensive than multiplication"

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Efficient Multiply/Divide of two 128-bit Integers on x86 (no 64-bit)

"Division is much more expensive than multiplication"

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Trick to divide a constant (power of two) by an integer

"Division is a lot more expensive than multiplication"

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Implementing matrix vector multiplication in assembly

"Is division more expensive than multiplication in c++"

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Is division more expensive than multiplication in C++?

"Division is more expensive than multiplication"

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Is MOD operation more CPU intensive than multiplication?

"The reason for doing so is to reduce hardware cost as division is more expensive than multiplication"

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Generating lookup table for arctan computation

"Recently someone suggested to me that division is always more expensive than multiplication"

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Benefits of multiplication rather than division

"Multiplication is less expensive than division so"

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How to normalize a NumPy array to within a certain range?

Others

Example

Division is inherently iterative unlike multiplication where you can make wide hardware that does the partial products and partial additions in parallel

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How can x86 bsr/bsf have fixed latency, not data dependent? Doesn't it loop over bits like the pseudocode shows?

Easiest way is to simply recognize that division is nothing more than the multiplication of the dividend y and the inverse of the divisor x

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Fast approximate float division

On simple low-cost processors typically bitwise operations are substantially faster than division several times faster than multiplication and sometimes significantly faster than addition

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What is the idea behind ^= 32, that converts lowercase letters to upper and vice versa?

T is not very important as long as alpha is small otherwise you will run into some rather weird nyquist issues aliasing etc and if you are working on a processor where multiplication is cheaper than division or fixed-point issues are important precalculate omega

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Exponential Moving Average Sampled at Varying Times

From what i read on the net multiplication is usually easier to compute than division

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What do single-cycle multiplication and hardware division mean?

In particular this means jit does not replace integer division with multiplication

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Why is if (variable1 % variable2 == 0) inefficient?

Like multiplication and division modulo arithmetic has a higher precedence than addition

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JavaFX GridPane Program

Note this multiplication was chosen over this because double multiplication is about 3.6x faster than double division on the cpu that i m dealing with

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Proper/best type for storing latitude and longitude

A division costs more than a multiplication

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Efficiently using 1-D pyfftw on small slices of a 3-D numpy array

Multiplication takes less time then division so you can try this

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How to check if given number is divisible of 15 in fastest way?

Let s assume that i have code like this as far as i know division is heavier than multiplication so as an the optimization i changed the code as follows however since value is an integer i have to cast it but as far as i know a type cast is also considered a heavy action

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Question about optimization of division code with type cast

Division is slower than multiplication is generally - and definitely using regular expression matching is going to be slower than multiplication is..

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JavaScript Math.round: Doesnt round object to 1 decimal

On most processors division is slower than multiplication for the same data types

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Is divide slower than Multiply?

Hardware integer division is always slower than multiplication and the gap in the relative latencies of these instructions continues to widen

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Fast Division and Modular operation for non two power numbers

On some machines division is much slower than multiplication but on most machines j multiplies and j divides will run a lot faster than 2 n-2 multiplication and one division

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Why am I getting errors using the Lambda function?

The reason to do this is because even though there is an integer division instruction div idiv in the instruction set it s typically very slow several times slower than multiplication

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How does the GCC implementation of modulo (%) work, and why does it not use the div instruction?

I was always taught that division is slower than multiplication but i have no real proof of thisâ has anyone got an opinion on this before i start benchmarking and running test

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JavaScript Performance - Divide or Multiply? / vs *

Removing division operations by passing through the inverse into the shader is another useful tip as division is typically slower than multiplication

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Optimization of HLSL shaders

Division is generally on the order of 10x slower than multiplication on most processor families

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Is division more expensive than multiplication in C++?

Integer division is about an order of magnitude slower than multiplication on current cpus.

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Fast way to check if long integer is a cube (in Java)

Your friend has a point a division actual division not just writing in c is slower than a multiplication

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1,000,000,000 calculations per microsecond?

Integer division is slower than floating point division but using floating point multiplication on integer causes two conversions;the conversions aren t too bad so in total the floating point multiplication is still faster

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1,000,000,000 calculations per microsecond?

It can get a bit more complex with multiplication division but the main downside is performance

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How does a 32bit computer work with large bit numbers? Ex. 512bit integers

I know that most of us grew up with the idea that division is sloooooow and must be avoided;however division unlike multiplication will not overflow

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Check if a spelled number is in a range in C++

The intuition is that division is a more costly affair than multiplication

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Fast lookup from floating point index into array

Every now and then in code it comes up that i need to divide several numbers by the same value since multiplication is faster than division i will often write this as i m wondering if i m really saving any time by doing this

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If I need to divide several numbers by the same value, is it better that I calculate the inverse first?

Note that for signed number the pencil and paper method for multiplication add and shift and division may not work properly;for example the correct method for signed multiplication is booth algorithm

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Assembly imul and idiv

Division and square roots for huge number of bits are not much more complex than multiplication

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Big O complexity of the basic arithmetic operations

0 but most of the time n 10 seems enough and spare one division which was more expensive;i simply use multiplication and it seems to make it much faster almost 4x here at least on the 1..100000000 range

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What's the best way to get the length of the decimal representation of an int in C++?

Division though is an iterative process in logic the implementations you see on educational sites verilog vhdl are simply doing the same thing we did with log division in grade school but like multiplication it is much simpler than grade school you pull down bits from the numerator in the long division until the number being checked against the denominator is equal to or larger basically the number can either go in only zero times or one times into the next number under test unlike decimal where it can be between 0 to 9 times

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Which is harder: a modern Casio calculator in Assembler or division of real numbers in Verilog?

So multiplication is nothing more than n number of shifts and adds which can be implemented in one clock cycle with a massive number of gates

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Which is harder: a modern Casio calculator in Assembler or division of real numbers in Verilog?

Division by 5.0 is more accurate than multiplication by an approximate 0.2

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How to use double to be more secure and precise?

In follow-up to phuclv comment i checked the code generated by jit 1 the results are as follows for variable 5000 division by constant for variable variable because division always takes longer than multiplication the last code snippet is less performant

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Why is if (variable1 % variable2 == 0) inefficient?

Change the half to 0.5 and you should be golden for the math part also multiplication is faster so use the math part instead of division when possible

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C++ printing a function's result?

Iirc floating-point multiplication is much less expensive than division so this might be faster than both

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Efficiency of floating point division and checking values beforehand if eq

This can be a major clock-cycle saver since multiplication is often much faster than a division operation

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Is shifting bits faster than multiplying and dividing in Java? .NET?

As a rule of thumb multiplication is faster than division on all cpus

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Reading assembly comparing multiplication vs division

I wonder why everybody missed that multiplication is much faster than division

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How to check if an integer is a power of 3?

Here s one idea which uses one multiplication and one shift so it ll be faster than a division on most systems

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Optimizing Division by Unknown Denominator Without Using Division Operator

From the performance side float multiplication is faster than division but i don t think that in the gui code it can create significant difference

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In a simple float operation, is there any difference between multiplication and division?

In a 64 bit application this code will be a lot faster than in a 32 bit application in a 32 bit application multiplying two 64 bit numbers take 3 multiplication and 3 additions on 32 bit values - however it might be still faster than a division on a 32 bit machine

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What's the fastest way to divide an integer by 3?

I do not want to know when or if to use shift operators in my code i am interested in why multiplication is faster than shifting bits to the left whereas division is not

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Differences in division and multiplication vs bit shifting

The double_unit stuff is how random actually does it internally because multiplication is faster than division see floating point division vs floating point multiplication

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Using a random long to generate random doubles

Even simpler and probably even faster because multiplication is faster than division is dav s answer which is the most natural algorithm.

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Reverse factorial

Floating point multiplication is faster than division so if speed is relevant

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Source code to round floating point number

But the research i ve done so far all points to multiplication being faster than division

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Unexpected apparent performance difference between integer multiplication and division

If the numbers are huge dividing x by b might be betterâ division is usually slower than multiplication but getting out of the huge-number domain early might help more than avoiding division

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Computes the logarithm of a number x relative to a base b.n other words

That is before you factor in the extra multiplication and extra cast;on older µarchs 32 bit integer division often has lower latency numbers listed than double division but older µarchs 32 bit integer division varied more division used to be more serial with for floats round divisors being faster yet for integer division integer division s small results that are faster

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Stop double division before decimals (low precision, fast division; getting only the 'quotient')

If a remains the same and b is changing say if your code is in a loop and your code s clear that a does not change between two iterations for instance because your code s a const variable then the original version can execute faster because multiplication is cheaper than division assuming the compiler moves the computation of 1 .

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Reason for peculiar ordering of division and multiplication in C++

Usually simple operations like addition subtraction and multiplication are very fast;division is a bit slower

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How do I measure the FLOPS my C# app uses?

Math.h defines m_log2e to the value of log e if you define _use_math_defines before inclusion of math.h even though usual approach is to do log n log 2 i would advise to use multiplication instead as division is always slower especially for floats and more so on mobile cpus

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Log2 not found in my math.h?

I am pretty sure it is not possible to compute polynomial division more efficient than multiplication and as you can see in the following table this algorithm is only 3 times slower than a single multiplication

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Best algorithm for series expansion of Rational function

For division things are a little more complicated than multiplication see

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Big Integer arithmetic

Well if it is a single calculation you wil hardly notice any difference but if you talk about millions of transaction then definitely division is costlier than multiplication

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What has a better performance: multiplication or division?

For multiplication the technique described at is a reasonably easy thing to implement and is better than serial addition;division is more complex in general but a good place to start is

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64 bit arithmetic with 16 bit word length(store 64 bit number across 4 words)

Or is there something about multiplication that is more convenient than division in programming

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Calculating Reciprocals: n**(-1) or (1/n)?

In fact if the intent is to divide by 22 10 or some other real value that isn t necessarily exactly representable in binary floating-point then half the times the multiplication is more accurate than the division because it happens by coincidence that the relative error for 1 x is less than the relative error for x

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Should I use multiplication or division for recurring floats?

The multiplication should perform somewhat better than division

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Wrap value into range [min,max] without division

If you are sure that a floating point multiplication is better than a floating point division then

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Rearranging an equation

If multiplication are o n 2 this is slower than long division for large numbers o n 2 vs o n 2 log n

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Numeric division using BCD format

Know that division is far slower than multiplication and square roots are even more expensive think distance magnitude

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Coding a physics simulation using iterative functions and time steps

There are methods of division that are faster than basic long division but still they are slower than multiplication

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Why is division more expensive than multiplication?

When tried with only multiplication division try without sum assignment operations;edit as you can see multiplication is not necessarily the faster operation here

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Why is dividing giving similar times to multiplicating?

Division isn t going to have a big performance impact in your application;floating-point division is generally especially slow so while floating-point multiplication is also relatively slow it s probably faster than floating-point division

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Should I use multiplication or division?

It is well known that integer division is slow operation typically several times slower than integer multiplication

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Fast integer division in Java

I haven t benchmarked any of this code but just by examining the code you can see that using integers division by 2 is shorter than multiplication by 2

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Should I use multiplication or division?

Obviously after the multiplication has overflowed the division isn t going to undo that overflow;because the multiplication overflows 32 bit integers

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Why is 24 * 60 * 60 * 1000 * 1000 divided by 24 * 60 * 60 * 1000 not equal to 1000 in Java?

Both operations are done down at the floating point unit fpu level and even in the world of integral alus the division circuit is a far busier place than a multiplication circuit

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Why is float division slow?

The cpu operation for float division is much more complicated than multiplication

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Why is multiplying cheaper than dividing?

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