C++ – Why Does 1 / 0.2 Result in 4 Instead of 5?

You are a victim of branch prediction fail.

What is Branch Prediction?

Consider a railroad junction:

_{Image by Mecanismo, via Wikimedia Commons. Used under the CC-By-SA 3.0 license.}

Now for the sake of argument, suppose this is back in the 1800s - before long-distance or radio communication.

You are a blind operator of a junction and you hear a train coming. You have no idea which way it is supposed to go. You stop the train to ask the driver which direction they want. And then you set the switch appropriately.

Trains are heavy and have a lot of inertia, so they take forever to start up and slow down.

Is there a better way? You guess which direction the train will go!

• If you guessed right, it continues on.
• If you guessed wrong, the driver will stop, back up, and yell at you to flip the switch. Then it can restart down the other path.

If you guess right every time, the train will never have to stop.
If you guess wrong too often, the train will spend a lot of time stopping, backing up, and restarting.

Consider an if-statement: At the processor level, it is a branch instruction:

You are a processor and you see a branch. You have no idea which way it will go. What do you do? You halt execution and wait until the previous instructions are complete. Then you continue down the correct path.

Modern processors are complicated and have long pipelines. This means they take forever to "warm up" and "slow down".

Is there a better way? You guess which direction the branch will go!

• If you guessed right, you continue executing.
• If you guessed wrong, you need to flush the pipeline and roll back to the branch. Then you can restart down the other path.

If you guess right every time, the execution will never have to stop.
If you guess wrong too often, you spend a lot of time stalling, rolling back, and restarting.

This is branch prediction. I admit it's not the best analogy since the train could just signal the direction with a flag. But in computers, the processor doesn't know which direction a branch will go until the last moment.

How would you strategically guess to minimize the number of times that the train must back up and go down the other path? You look at the past history! If the train goes left 99% of the time, then you guess left. If it alternates, then you alternate your guesses. If it goes one way every three times, you guess the same...

In other words, you try to identify a pattern and follow it. This is more or less how branch predictors work.

Most applications have well-behaved branches. Therefore, modern branch predictors will typically achieve >90% hit rates. But when faced with unpredictable branches with no recognizable patterns, branch predictors are virtually useless.

Further reading: "Branch predictor" article on Wikipedia.

As hinted from above, the culprit is this if-statement:

if (data[c] >= 128)
    sum += data[c];

Notice that the data is evenly distributed between 0 and 255. When the data is sorted, roughly the first half of the iterations will not enter the if-statement. After that, they will all enter the if-statement.

This is very friendly to the branch predictor since the branch consecutively goes the same direction many times. Even a simple saturating counter will correctly predict the branch except for the few iterations after it switches direction.

Quick visualization:

T = branch taken
N = branch not taken

data[] = 0, 1, 2, 3, 4, ... 126, 127, 128, 129, 130, ... 250, 251, 252, ...
branch = N  N  N  N  N  ...   N    N    T    T    T  ...   T    T    T  ...

       = NNNNNNNNNNNN ... NNNNNNNTTTTTTTTT ... TTTTTTTTTT  (easy to predict)

However, when the data is completely random, the branch predictor is rendered useless, because it can't predict random data. Thus there will probably be around 50% misprediction (no better than random guessing).

data[] = 226, 185, 125, 158, 198, 144, 217, 79, 202, 118,  14, 150, 177, 182, ...
branch =   T,   T,   N,   T,   T,   T,   T,  N,   T,   N,   N,   T,   T,   T  ...

       = TTNTTTTNTNNTTT ...   (completely random - impossible to predict)

What can be done?

If the compiler isn't able to optimize the branch into a conditional move, you can try some hacks if you are willing to sacrifice readability for performance.

Replace:

if (data[c] >= 128)
    sum += data[c];

with:

int t = (data[c] - 128) >> 31;
sum += ~t & data[c];

This eliminates the branch and replaces it with some bitwise operations.

_{(Note that this hack is not strictly equivalent to the original if-statement. But in this case, it's valid for all the input values of data[].)}

Benchmarks: Core i7 920 @ 3.5 GHz

C++ - Visual Studio 2010 - x64 Release

Java - NetBeans 7.1.1 JDK 7 - x64

Observations:

• With the Branch: There is a huge difference between the sorted and unsorted data.
• With the Hack: There is no difference between sorted and unsorted data.
• In the C++ case, the hack is actually a tad slower than with the branch when the data is sorted.

A general rule of thumb is to avoid data-dependent branching in critical loops (such as in this example).

Update:

• GCC 4.6.1 with -O3 or -ftree-vectorize on x64 is able to generate a conditional move, so there is no difference between the sorted and unsorted data - both are fast. This is called "if-conversion" (to branchless) and is necessary for vectorization but also sometimes good for scalar.

  (Or somewhat fast: for the already-sorted case, cmov can be slower especially if GCC puts it on the critical path instead of just add, especially on Intel before Broadwell where cmov has 2-cycle latency: gcc optimization flag -O3 makes code slower than -O2)

• VC++ 2010 is unable to generate conditional moves for this branch even under /Ox.

• Intel C++ Compiler (ICC) 11 does something miraculous. It interchanges the two loops, thereby hoisting the unpredictable branch to the outer loop. Not only is it immune to the mispredictions, it's also twice as fast as whatever VC++ and GCC can generate! In other words, ICC took advantage of the test-loop to defeat the benchmark...

• If you give the Intel compiler the branchless code, it just outright vectorizes it... and is just as fast as with the branch (with the loop interchange).

• Clang also vectorizes the if() version, as will GCC 5 and later with -O3, even though it takes quite a few instructions to sign-extend to the 64-bit sum on x86 without SSE4 or AVX2. (-march=x86-64-v2 or v3). See Why is processing an unsorted array the same speed as processing a sorted array with modern x86-64 clang?

This goes to show that even mature modern compilers can vary wildly in their ability to optimize code...

static_cast

static_cast is the first cast you should attempt to use. It does things like implicit conversions between types (such as int to float, or pointer to void*), and it can also call explicit conversion functions (or implicit ones). In many cases, explicitly stating static_cast isn't necessary, but it's important to note that the T(something) syntax is equivalent to (T)something and should be avoided (more on that later). A T(something, something_else) is safe, however, and guaranteed to call the constructor.

static_cast can also cast through inheritance hierarchies. It is unnecessary when casting upwards (towards a base class), but when casting downwards it can be used as long as it doesn't cast through virtual inheritance. It does not do checking, however, and it is undefined behavior to static_cast down a hierarchy to a type that isn't actually the type of the object.

const_cast

const_cast can be used to remove or add const to a variable; no other C++ cast is capable of removing it (not even reinterpret_cast). It is important to note that modifying a formerly const value is only undefined if the original variable is const; if you use it to take the const off a reference to something that wasn't declared with const, it is safe. This can be useful when overloading member functions based on const, for instance. It can also be used to add const to an object, such as to call a member function overload.

const_cast also works similarly on volatile, though that's less common.

dynamic_cast

dynamic_cast is exclusively used for handling polymorphism. You can cast a pointer or reference to any polymorphic type to any other class type (a polymorphic type has at least one virtual function, declared or inherited). You can use it for more than just casting downwards – you can cast sideways or even up another chain. The dynamic_cast will seek out the desired object and return it if possible. If it can't, it will return nullptr in the case of a pointer, or throw std::bad_cast in the case of a reference.

dynamic_cast has some limitations, though. It doesn't work if there are multiple objects of the same type in the inheritance hierarchy (the so-called 'dreaded diamond') and you aren't using virtual inheritance. It also can only go through public inheritance - it will always fail to travel through protected or private inheritance. This is rarely an issue, however, as such forms of inheritance are rare.

reinterpret_cast

reinterpret_cast is the most dangerous cast, and should be used very sparingly. It turns one type directly into another — such as casting the value from one pointer to another, or storing a pointer in an int, or all sorts of other nasty things. Largely, the only guarantee you get with reinterpret_cast is that normally if you cast the result back to the original type, you will get the exact same value (but not if the intermediate type is smaller than the original type). There are a number of conversions that reinterpret_cast cannot do, too. It's often abused for particularly weird conversions and bit manipulations, like turning a raw data stream into actual data, or storing data in the low bits of a pointer to aligned data. For those cases, see std::bit_cast.

C-Style Cast and Function-Style Cast

C-style cast and function-style cast are casts using (type)object or type(object), respectively, and are functionally equivalent. They are defined as the first of the following which succeeds:

• const_cast
• static_cast (though ignoring access restrictions)
• static_cast (see above), then const_cast
• reinterpret_cast
• reinterpret_cast, then const_cast

It can therefore be used as a replacement for other casts in some instances, but can be extremely dangerous because of the ability to devolve into a reinterpret_cast, and the latter should be preferred when explicit casting is needed, unless you are sure static_cast will succeed or reinterpret_cast will fail. Even then, consider the longer, more explicit option.

C-style casts also ignore access control when performing a static_cast, which means that they have the ability to perform an operation that no other cast can. This is mostly a kludge, though, and in my mind is just another reason to avoid C-style casts.

std::bit_cast [C++20]

std::bit_cast copies the bits and bytes of the source object (its representation) directly into a new object of the target type. It's a standards-compliant way to do type punning. If you find yourself writing *reinterpret_cast<SomeType*>(&x), you probably should use std::bit_cast<SomeType>(x) instead.

std::bit_cast is declared in <bit>. The objects must be the same size and be trivially copyable. If you can't yet use C++20, use memcpy to copy the source value into a variable of the desired type.