This question already has answers here:
Is using double faster than float?
(10 answers)
Closed 8 years ago.
I am reading "accelerated C++". I found one sentence which states "sometimes double is faster in execution than float in C++". After reading sentence I got confused about float and double working. Please explain this point to me.
Depends on what the native hardware does.
If the hardware is (or is like) x86 with legacy x87 math, float and double are both extended (for free) to an internal 80-bit format, so both have the same performance (except for cache footprint / memory bandwidth)
If the hardware implements both natively, like most modern ISAs (including x86-64 where SSE2 is the default for scalar FP math), then usually most FPU operations are the same speed for both. Double division and sqrt can be slower than float, as well as of course being significantly slower than multiply or add. (Float being smaller can mean fewer cache misses. And with SIMD, twice as many elements per vector for loops that vectorize).
If the hardware implements only double, then float will be slower if conversion to/from the native double format isn't free as part of float-load and float-store instructions.
If the hardware implements float only, then emulating double with it will cost even more time. In this case, float will be faster.
And if the hardware implements neither, and both have to be implemented in software. In this case, both will be slow, but double will be slightly slower (more load and store operations at the least).
The quote you mention is probably referring to the x86 platform, where the first case was given. But this doesn't hold true in general.
Also beware that x * 3.3 + y for float x,y will trigger promotion to double for both variables. This is not the hardware's fault, and you should avoid it by writing 3.3f to let your compiler make efficient asm that actually keeps numbers as floats if that's what you want.
You can find a complete answer in this article:
What Every Computer Scientist Should Know About Floating-Point Arithmetic
This is a quote from a previous Stack Overflow thread, about how float and double variables affect memory bandwidth:
If a double requires
more storage than a float, then it
will take longer to read the data.
That's the naive answer. On a modern
IA32, it all depends on where the data
is coming from. If it's in L1 cache,
the load is negligible provided the
data comes from a single cache line.
If it spans more than one cache line
there's a small overhead. If it's from
L2, it takes a while longer, if it's
in RAM then it's longer still and
finally, if it's on disk it's a huge
time. So the choice of float or double
is less imporant than the way the data
is used. If you want to do a small
calculation on lots of sequential
data, a small data type is preferable.
Doing a lot of computation on a small
data set would allow you to use bigger
data types with any significant
effect. If you're accessing the data
very randomly, then the choice of data
size is unimportant - data is loaded
in pages / cache lines. So even if you
only want a byte from RAM, you could
get 32 bytes transfered (this is very
dependant on the architecture of the
system). On top of all of this, the
CPU/FPU could be super-scalar (aka
pipelined). So, even though a load may
take several cycles, the CPU/FPU could
be busy doing something else (a
multiply for instance) that hides the
load time to a degree
Short answer is: it depends.
CPU with x87 will crunch floats and doubles equally fast. Vectorized code will run faster with floats, because SSE can crunch 4 floats or 2 doubles in one pass.
Another thing to consider is memory speed. Depending on your algorithm, your CPU could be idling a lot while waiting for the data. Memory intensive code will benefit from using floats, but ALU limited code won't (unless it is vectorized).
I can think of two basic cases when doubles are faster than floats:
Your hardware supports double operations but not float operations, so floats will be emulated by software and therefore be slower.
You really need the precision of doubles. Now, if you use floats anyway you will have to use two floats to reach similar precision to double. The emulation of a true double with floats will be slower than using floats in the first place.
You do not necessarily need doubles but your numeric algorithm converges faster due to the enhanced precision of doubles. Also, doubles might offer enough precision to use a faster but numerically less stable algorithm at all.
For completeness' sake I also give some reasons for the opposite case of floats being faster. You can see for yourself whichs reasons dominate in your case:
Floats are faster than doubles when you don't need double's
precision and you are memory-bandwidth bound and your hardware
doesn't carry a penalty on floats.
They conserve memory-bandwidth because they occupy half the space
per number.
There are also platforms that can process more floats than doubles
in parallel.
On Intel, the coprocessor (nowadays integrated) will handle both equally fast, but as some others have noted, doubles result in higher memory bandwidth which can cause bottlenecks. If you're using scalar SSE instructions (default for most compilers on 64-bit), the same applies. So generally, unless you're working on a large set of data, it doesn't matter much.
However, parallel SSE instructions will allow four floats to be handled in one instruction, but only two doubles, so here float can be significantly faster.
In experiments of adding 3.3 for 2000000000 times, results are:
Summation time in s: 2.82 summed value: 6.71089e+07 // float
Summation time in s: 2.78585 summed value: 6.6e+09 // double
Summation time in s: 2.76812 summed value: 6.6e+09 // long double
So double is faster and default in C and C++. It's more portable and the default across all C and C++ library functions. Alos double has significantly higher precision than float.
Even Stroustrup recommends double over float:
"The exact meaning of single-, double-, and extended-precision is implementation-defined. Choosing the right precision for a problem where the choice matters requires significant understanding of floating-point computation. If you don't have that understanding, get advice, take the time to learn, or use double and hope for the best."
Perhaps the only case where you should use float instead of double is on 64bit hardware with a modern gcc. Because float is smaller; double is 8 bytes and float is 4 bytes.
float is usually faster. double offers greater precision. However performance may vary in some cases if special processor extensions such as 3dNow or SSE are used.
There is only one reason 32-bit floats can be slower than 64-bit doubles (or 80-bit 80x87). And that is alignment. Other than that, floats take less memory, generally meaning faster access, better cache performance. It also takes fewer cycles to process 32-bit instructions. And even when (co)-processor has no 32-bit instructions, it can perform them on 64-bit registers with the same speed. It probably possible to create a test case where doubles will be faster than floats, and v.v., but my measurements of real statistics algos didn't show noticeable difference.
Related
This question already has answers here:
Should I use double or float?
(11 answers)
Closed last year.
I'm pretty new to coding, so this might be a stupid question, but why should you ever use a float when a double is more precise and has more bits?
Memory
The biggest reason is memory space. A float takes up 32 bits (4 bytes) while a double takes up 64 bits (8 bytes). This may not seem like a big deal, but some applications deal with a lot of numbers.
Let's say I'm simulating some system with a 3D grid that is a cube of values with a width of 1,000 points. That's 1,000,000,000 data points. If each point is a float value, I need 4 GB of memory. For doubles, I need 8 GB of memory. If I need to store more than one value at each point in the grid, the memory requirements just get bigger.
Grids similar to what I just described can be useful in physical simulations (climate or weather models, certain fluid dynamics simulations, etc). In those types of simulations, adding twice as many points can often be more useful than adding twice the precision at each point.
Speed
Depending on the hardware, the speed of calculation might also be a factor for time-sensitive calculations, but which is better depends on the underlying hardware. (See this answer for more details on that: https://stackoverflow.com/a/4584707/5941564)
If you are developing real-time software for a very specific piece of hardware that handles float faster than doubles, you should favor floats. But, some processors handle doubles faster, so you need to know your hardware before making that kind of performance decision.
I've got the opposite rule of thumb -- I have not needed many algorithms outside some heavy simulations which I compute with Octave that would require doubles over floats (save computing deep zoom Mandelbrot fractals and even those require arbitrary precision arithmetics after a certain point). Surely one needs to understand the constraints of the application and the constraints of the CPU architecture that one is working on.
I would often go even one step further, trying to avoid floating points, when it's possible to use 8-bit or 16-bit integers -- this apparently includes even Machine Learning applications, given that both Intel and Arm architectures have implemented 'neural network' extensions solely operating on 8-bit data and they have already implemented 16-bit float operations on hardware as well.
The smaller memory footprint of floats plays a crucial factor in four ways at least, three of which are related to speed. When the algorithm is memory bound (the number of arithmetic operations is small compared to the number of memory operation and the data does not fit in 1st level cache), float operations will theoretically be about twice as fast as doubles, as one needs to load and save half the memory.
When the amount of operations is small, but still larger than a few, many floating point algorithms will vectorise -- One can utilise SIMD architecture to put twice as many single precision floating point numbers to a register, executing 4 parallel floating point operations (or more per each starting CPU clock cycle) compared to 2 parallel double precision floating point operations.
Furthermore, the number of floating point numbers placed in registers may play an important role. Some algorithms may need to operate on 64, 128 or 256 different values at the same time -- spilling registers back and forth memory is costly. Some optimisation strategies may need that too (even though Out Of Order -execution could solve the problem automatically).
While modern computer architectures and even many embedded or low-power processors do contain floating point units, it's possible that they are still lacking double precision support completely, or its implementation is inherently much slower.
Finally the size it self plays a role in conserving memory on the 100 million customer devices, even if one as a developer does not care.
Under The most efficient types second here
...and when defining an object to store a floating point number, use the double type, ... The double type is two to three times less efficient than the float type...
Seems like it's contradicting itself?
And I read elsewhere (can't remember where) that computations involving ints are faster than shorts on many machines because they are converted to ints to perform the operations? Is this true? Any links on this?
One can always argue about the quality of the contents on the site you link to. But the two quotes you refer to:
...and when defining an object to store a floating point number, use the double type, ...
and
... The double type is two to three times less efficient than the float type...
Refer to two different things, the first hints that using doubles will give much less problems due to the increased precision, while the other talks about performance. But honestly I wouldn't pay too much attention to that, chance is that if your code performs suboptimal it is due to incorrect choice of algorithm rather than wrong choice of primitive data type.
Here is a quote about performance comparison of single and double precision floats from one of my old teachers: Agner Fog, who has a lot of interesting reads over at his website: http://www.agner.org about software optimizations, if you are really interested in micro optimizations go take a look at it:
In most cases, double precision calculations take no more time than single precision. When the floating point registers are used, there is simply no difference in speed between single and double precision. Long double precision takes only slightly more time. Single precision division, square root and mathematical functions are calculated faster than double precision when the XMM registers are used, while the speed of addition, subtraction, multiplication, etc. is still the same regardless of precision on most processors (when vector operations are not used).
source: http://agner.org/optimize/optimizing_cpp.pdf
While there might be different variations for different compilers, and different processors, the lesson one should learn from it, is that most likely you do not need to worry about optimizations at this level, look at choice of algorithm, even data container, not the primitive data type.
These optimizations are negligible unless you are writing software for space shuttle launches (which recently have not been doing too well). Correct code is far more important than fast code. If you require the precision, using doubles will barely affect the run time.
Things that affect execution time way more than type definitions:
Complexity - The more work there is to do, the more slowly the code will run. Reduce the amount of work needed, or break it up into smaller, faster tasks.
Repetition - Repetition can often be avoided and will inevitably ruin code performance. It comes in many guises-- for example, failing to cache the results of expensive calculations or of remote procedure calls. Every time you recompute, you waste efficiency. They also extend the executable size.
Bad Design - Self explanatory. Think before you code!
I/O - A program whose execution is blocked waiting for input or output (to and from the user, the disk, or a network connection) is bound to perform badly.
There are many more reasons, but these are the biggest. Personally, bad design is where I've seen most of it happen. State machines that could have been stateless, dynamic allocation where static would have been fine, etc. are the real problems.
Depending on the hardware, the actual CPU (or FPU if you like) performance of double is somewhere between half the speed and same speed on modern CPU's [for example add or subtract is probably same speed, multiply or divide may be different for larger type], when compared to float.
On top of that, there are "fewer per cache-line", so if when there is a large number of them, it gets slower still because memory speed is slower. Per cache-line, there are half as many double values -> about half the performance if the application is fully memory bound. It will be much less of a factor in a CPU-bound application.
Similarly, if you use SSE or similar SIMD technologies, the double will take up twice as much space, so the number of actual calculation with be half as many "per instruction", and typically, the CPU will allow the same number of instructions per cycle for both float and double - except for some operations that take longer for double. Again, leading to about half the performance.
So, yes, I think the page in the link is confusing and mixing up the ideal performance setup between double and float. That is, from a pure performance perspective. It is often much easier to get noticeable calculation errors when using float - which can be a pain to track down - so starting with double and switching to float if it's deemed necessary because you have identified it as a performance issue (either from experience or measurements).
And yes, there are several architectures where only one size integer exists - or only two sizes, such as 8-bit char and 32-bit int, and 16-bit short would be simulated by performing the 32-bit math, and then dropping the top part of the value. For example MIPS has only got 32-bit operations, but can store and load 16-bit values to memory. It doesn't necessarily make it slower, but it certainly means that it's "not faster".
I'm still a beginner at programming and I always have more questions than our book or internet searches can answer (unless I missed something). So I apologize in advance if this was answered but I couldn't find it.
I understand that float has a smaller range than double making it less precise, and from what I understand, long double is even more precise(?). So my question is why would you want to use a variable that is less precise in the first place? Does it have something to do with different platforms, different OS versions, different compilers? Or are there specific moments in programming where its strategically more advantageous to use a float over a double/long double?
Thanks everyone!
In nearly all processors, "smaller" floating point numbers take the same or less clock-cycles in execution. Sometimes the difference isn't very big (or nothing), other times it can be literally twice the number of cycles for double vs. float.
Of course, memory foot-print, which is affecting cache-usage, will also be a factor. float takes half the size of double, and long double is bigger yet.
Edit: Another side-effect of smaller size is that the processor's SIMD extensions (3DNow!, SSE, AVX in x86, and similar extensions are available in several other architectures) may either only work with float, or can take twice as many float vs. double (and as far as I know, no SIMD instructions are available for long double in any processor). So this may improve performance if float is used vs. double, by processing twice as much data in one go. End edit.
So, assuming 6-7 digits of precision is good enough for what you need, and the range of +/-10+/-38 is sufficient, then float should be used. If you need either more digits in the number, or a bigger range, move to double, and if that's not good enough, use long double. But for most things, double should be perfectly adequate.
Obviously, the importance of using "the right size" becomes more important when you have either lots of calculations, or lots of data to work with - if there are 5 variables, and you just use each a couple of times in a program that does a million other things, who cares? If you are doing fluid dynamics calculations for how well a Formula 1 car is doing at 200 mph, then you probably have several tens of million datapoints to calculate, and every data point needs to be calculated dozens of times per second of the cars travel, then using up just a few clockcycles extra in each calculation will make the whole simulation take noticeably longer.
There are two costs to using float, the obvious one of its limited range and precision, and, less obviously, the more difficult analysis those limitations impose.
It is often relatively easy to determine that double is sufficient, even in cases where it would take significant numerical analysis effort to show that float is sufficient. That saves development cost, and risk of incorrect results if the more difficult analysis is not done correctly.
Float's biggest advantage on many processors is its reduced memory footprint. That translates into more numbers per cache line, and more memory bandwidth in terms of numbers transferred per second. Any gain in compute performance is usually relatively slight - indeed, popular processors do all floating point arithmetic in one format that is wider than double.
It seems best to use double unless two conditions are met - there are enough numbers for their memory footprint to be a significant performance issue, and the developers can show that float is precise enough.
You might be interested in seeing the answer posted here Should I use double or float?
But it boils down to memory footprint vs the amount of precision you need for a given situation. In a physics engine, you might care more about precision, so it would make more sense to use a double or long double.
Bottom line:
You should only use as much precision as you need for a given algorithm
The basic principle here would be don't use more than you need.
The first consideration is memory use, you probably realized that already, if you are making only one double no big deal, but what if you create a billion than you just used twice as much memory space as you had too.
Next is processor utilization, I believe on many processors if you use smaller data types it can do a form of threading where it does multiple operations at once.
So an extension to this part of the answer is SSE instructions basically this allows you to used packed data to do multiple floating point operations at once, which in an idealized case can double the speed of your program.
Lastly is readability, when someone is reading your code if you use a float they will immediately realize that you are not going over a certain number. IMO sometimes the right precision number will just flow better in the code.
A float uses less memory than a double, so if you don't need your number to be the size of a double, you might as well use a float since it will take up less memory.
Just like you wouldn't use a bus to drive yourself and a friend to the beach... you would be far better off going in a 2 seater car.
The same applies for a double over a long double... only reserve as much memory as you are going to need. Otherwise with more complex code you run the risk of using too much memory and having processes slow down or crash.
We have a measurement data processing application and currently all data is held as C++ float which means 32bit/4byte on our x86/Windows platform. (32bit Windows Application).
Since precision is becoming an issue, there have been discussions to move to another datatype. The options currently discussed are switching to double (8byte) or implementing a fixed decimal type on top of __int64 (8byte).
The reason the fixed-decimal solution using __int64 as underlying type is even discussed is that someone claimed that double performance is (still) significantly worse than processing floats and that we might see significant performance benefits using a native integer type to store our numbers. (Note that we really would be fine with fixed decimal precision, although the code would obviously become more complex.)
Obviously we need to benchmark in the end, but I would like to ask whether the statement that doubles are worse holds any truth looking at modern processors? I guess for large arrays doubles may mess up cache hits more that floats, but otherwise I really fail to see how they could differ in performance?
It depends on what you do. Additions, subtractions and multiplies on double are just as fast as on float on current x86 and POWER architecture processors. Divisions, square roots and transcendental functions (exp, log, sin, cos, etc.) are usually notably slower with double arguments, since their runtime is dependent on the desired accuracy.
If you go fixed point, multiplies and divisions need to be implemented with long integer multiply / divide instructions which are usually slower than arithmetic on doubles (since processors aren't optimized as much for it). Even more so if you're running in 32 bit mode where a long 64 bit multiply with 128 bit results needs to be synthesized from several 32-bit long multiplies!
Cache utilization is a red herring here. 64-bit integers and doubles are the same size - if you need more than 32 bits, you're gonna eat that penalty no matter what.
Look it up. Both and Intel publish the instruction latencies for their CPUs in freely available PDF documents on their websites.
However, for the most part, performance won't be significantly different, or a couple of reasons:
when using the x87 FPU instead of SSE, all floating point operations are calculated at 80 bits precision internally, and then rounded off, which means that the actual computation is equally expensive for all floating-point types. The only cost is really memory-related then (in terms of CPU cache and memory bandwidth usage, and that's only an issue in float vs double, but irrelevant if you're comparing to int64)
with or without SSE, nearly all floating-point operations are pipelined. When using SSE, the double instructions may (I haven't looked this up) have a higher latency than their float equivalents, but the throughput is the same, so it should be possible to achieve similar performance with doubles.
It's also not a given that a fixed-point datatype would actually be faster either. It might, but the overhead of keeping this datatype consistent after some operations might outweigh the savings. Floating-point operations are fairly cheap on a modern CPU. They have a bit of latency, but as mentioned before, they're generally pipelined, potentially hiding this cost.
So my advice:
Write some quick tests. It shouldn't be that hard to write a program that performs a number of floating-point ops, and then measure how much slower the double version is relative to the float one.
Look it up in the manuals, and see for yourself if there's any significant performance difference between float and double computations
I've trouble the understand the rationale "as double as slower than float we'll use 64 bits int". Guessing performance has always been an black art needing much of experience, on today hardware it is even worse considering the number of factors to take into account. Even measuring is difficult. I know of several cases where micro-benchmarks lent to one solution but in context measurement showed that another was better.
First note that two of the factors which have been given to explain the claimed slower double performance than float are not pertinent here: bandwidth needed will the be same for double as for 64 bits int and SSE2 vectorization would give an advantage to double...
Then consider than using integer computation will increase the pressure on the integer registers and computation units when apparently the floating point one will stay still. (I've already seen cases where doing integer computation in double was a win attributed to the added computation units available)
So I doubt that rolling your own fixed point arithmetic would be advantageous over using double (but I could be showed wrong by measures).
Implementing 64 fixed points isn't really fun. Especially for more complex functions like Sqrt or logarithm. Integers will probably still a bit faster for simple operations like additions. And you'll need to deal with integer overflows. And you need to be careful when implementing rounding, else errors can easily accumulate.
We're implementing fixed points in a C# project because we need determinism which floatingpoint on .net doesn't guarantee. And it's relatively painful. Some formula contained x^3 bang int overflow. Unless you have really compelling reasons not to, use float or double instead of fixedpoint.
SIMD instructions from SSE2 complicate the comparison further, since they allow operation on several floating point numbers(4 floats or 2 doubles) at the same time. I'd use double and try to take advantage of these instructions. So double will probably be significantly slower than floats, but comparing with ints is difficult and I'd prefer float/double over fixedpoint is most scenarios.
It's always best to measure instead of guess. Yes, on many architectures, calculations on doubles process twice the data as calculations on floats (and long doubles are slower still). However, as other answers, and comments on this answer, have pointed out, the x86 architecture doesn't follow the same rules as, say, ARM processors, SPARC processors, etc. On x86 floats, doubles and long doubles are all converted to long doubles for computation. I should have known this, because the conversion causes x86 results to be more accurate than SPARC and Sun went through a lot of trouble to get the less accurate results for Java, sparking some debate (note, that page is from 1998, things have since changed).
Additionally, calculations on doubles are built in to the CPU where calculations on a fixed decimal datatype would be written in software and potentially slower.
You should be able to find a decent fixed sized decimal library and compare.
With various SIMD instruction sets you can perform 4 single precision floating point operations at the same cost as one, essentially you pack 4 floats into a single 128 bit register. When switching to doubles you can only pack 2 doubles into these registers and hence you can only do two operations at the same time.
As many people have said, a 64bit int is probably not worth it if double is an option. At least when SSE is available. This might be different on micro controllers of various kinds but I guess that is not your application. If you need additional precision in long sums of floats, you should keep in mind that this operation is sometimes problematic with floats and doubles and would be more exact on integers.
What are the advantages and disadvantages of using one instead of the other in C++?
If you want to know the true answer, you should read What Every Computer Scientist Should Know About Floating-Point Arithmetic.
In short, although double allows for higher precision in its representation, for certain calculations it would produce larger errors. The "right" choice is: use as much precision as you need but not more and choose the right algorithm.
Many compilers do extended floating point math in "non-strict" mode anyway (i.e. use a wider floating point type available in hardware, e.g. 80-bits and 128-bits floating), this should be taken into account as well. In practice, you can hardly see any difference in speed -- they are natives to hardware anyway.
Unless you have some specific reason to do otherwise, use double.
Perhaps surprisingly, it is double and not float that is the "normal" floating-point type in C (and C++). The standard math functions such as sin and log take doubles as arguments, and return doubles. A normal floating-point literal, as when you write 3.14 in your program, has the type double. Not float.
On typical modern computers, doubles can be just as fast as floats, or even faster, so performance is usually not a factor to consider, even for large calculations. (And those would have to be large calculations, or performance shouldn't even enter your mind. My new i7 desktop computer can do six billion multiplications of doubles in one second.)
This question is impossible to answer since there is no context to the question. Here are some things that can affect the choice:
Compiler implementation of floats, doubles and long doubles. The C++ standard states:
There are three floating point types: float, double, and long double. The type double provides at least as much precision as float, and the type long double provides at least as much precision as double.
So, all three can be the same size in memory.
Presence of an FPU. Not all CPUs have FPUs and sometimes the floating point types are emulated and sometimes the floating point types are just not supported.
FPU Architecture. The IA32's FPU is 80bit internally - 32 bit and 64 bit floats are expanded to 80bit on load and reduced on store. There's also SIMD which can do four 32bit floats or two 64bit floats in parallel. Use of SIMD is not defined in the standard so it would require a compiler that does more complex analysis to determine if SIMD can be used, or requires the use of special functions (libraries or intrinsics). The upshot of the 80bit internal format is that you can get slightly different results depending on how often the data is saved to RAM (thus, losing precision). For this reason, compilers don't optimise floating point code particularly well.
Memory bandwidth. If a double requires more storage than a float, then it will take longer to read the data. That's the naive answer. On a modern IA32, it all depends on where the data is coming from. If it's in L1 cache, the load is negligible provided the data comes from a single cache line. If it spans more than one cache line there's a small overhead. If it's from L2, it takes a while longer, if it's in RAM then it's longer still and finally, if it's on disk it's a huge time. So the choice of float or double is less important than the way the data is used. If you want to do a small calculation on lots of sequential data, a small data type is preferable. Doing a lot of computation on a small data set would allow you to use bigger data types with any significant effect. If you're accessing the data very randomly, then the choice of data size is unimportant - data is loaded in pages / cache lines. So even if you only want a byte from RAM, you could get 32 bytes transferred (this is very dependant on the architecture of the system). On top of all of this, the CPU/FPU could be super-scalar (aka pipelined). So, even though a load may take several cycles, the CPU/FPU could be busy doing something else (a multiply for instance) that hides the load time to a degree.
The standard does not enforce any particular format for floating point values.
If you have a specification, then that will guide you to the optimal choice. Otherwise, it's down to experience as to what to use.
Double is more precise but is coded on 8 bytes. float is only 4 bytes, so less room and less precision.
You should be very careful if you have double and float in your application. I had a bug due to that in the past. One part of the code was using float while the rest of the code was using double. Copying double to float and then float to double can cause precision error that can have big impact. In my case, it was a chemical factory... hopefully it didn't have dramatic consequences :)
I think that it is because of this kind of bug that the Ariane 6 rocket has exploded a few years ago!!!
Think carefully about the type to be used for a variable
I personnaly go for double all the time until I see some bottlenecks. Then I consider moving to float or optimizing some other part
This depends on how the compiler implements double. It's legal for double and float to be the same type (and it is on some systems).
That being said, if they are indeed different, the main issue is precision. A double has a much higher precision due to it's difference in size. If the numbers you are using will commonly exceed the value of a float, then use a double.
Several other people have mentioned performance isssues. That would be exactly last on my list of considerations. Correctness should be your #1 consideration.
I think regardless of the differences (which as everyone points out, floats take up less space and are in general faster)... does anyone ever suffer performance issues using double? I say use double... and if later on you decide "wow, this is really slow"... find your performance bottleneck (which is probably not the fact you used double). THEN, if it's still too slow for you, see where you can sacrifice some precision and use float.
Use whichever precision is required to achieve the appropriate results. If you then find that your code isn't performing as well as you'd like (you used profiling correct?) take a look at:
Intel 64 and IA-32 Architectures Optimization Reference Manual
Software Optimization for the AMD64 Processor
It depends highly on the CPU the most obvious trade-offs are between precision and memory. With GBs of RAM, memory is not much of an issue, so it's generally better to use doubles.
As for performance, it depends highly on the CPU. floats will usually get better performance than doubles on a 32 bit machine. On 64 bit, doubles are sometimes faster, since it is (usually) the native size. Still, what will matter much more than your choice of data types is whether or not you can take advantage of SIMD instructions on your processor.
double has higher precision, whereas floats take up less memory and are faster. In general you should use float unless you have a case where it isn't accurate enough.
The main difference between float and double is precision. Wikipedia has more info about
Single precision (float) and Double precision.