Why are double preferred over float? [closed]

问题:

In most of the code I see around, double is favourite against float, even when a high precision is not needed.

Since there are performance penalties when using double types (CPU/GPU/memory/bus/cache/...), what is the reason of this double overuse?

Example: in computational fluid dynamics all the software I worked with uses doubles. In this case a high precision is useless (because of the errors due to the approximations in the mathematical model), and there is a huge amount of data to be moved around, which could be cut in half using floats.

The fact that today's computers are powerful is meaningless, because they are used to solve more and more complex problems.

回答1:

In my opinion the answers so far don't really get the right point across, so here's my crack at it.

The short answer is C++ developers use doubles over floats:

• To avoid premature optimization when they don't understand the performance trade-offs well ("they have higher precision, why not?" Is the thought process)
• Habit
• Culture
• To match library function signatures
• To match simple-to-write floating point literals (you can write 0.0 instead of 0.0f)

It's true double may be as fast as a float for a single computation because most FPUs have a wider internal representation than either the 32-bit float or 64-bit double represent.

However that's only a small piece of the picture. Now-days operational optimizations don't mean anything if you're bottle necked on cache/memory bandwidth.

Here is why some developers seeking to optimize their code should look into using 32-bit floats over 64-bit doubles:

• They fit in half the memory. Which is like having all your caches be twice as large. (big win!!!)
• If you really care about performance you'll use SSE instructions. SSE instructions that operate on floating point values have different instructions for 32-bit and 64-bit floating point representations. The 32-bit versions can fit 4 values in the 128-bit register operands, but the 64-bit versions can only fit 2 values. In this scenario you can likely double your FLOPS by using floats over double because each instruction operates on twice as much data.

In general, there is a real lack of knowledge of how floating point numbers really work in the majority of developers I've encountered. So I'm not really surprised most developers blindly use double.

回答2:

Among others:

• The savings are hardly ever worth it (number-crunching is not typical).
• Rounding errors accumulate, so better go to higher precision than needed from the start (experts may know it is precise enough anyway, and there are calculations which can be done exactly).
• Common floating operations using the fpu internally often work on double or higher precision anyway.
• C and C++ can implicitly convert from float to double, the other way needs an explicit cast.
• Variadic and no-prototype functions always get double, not float. (second one is only in ancient C and actively discouraged)
• You may commonly do an operation with more than needed precision, but seldom with less, so libraries generally favor higher precision too.

But in the end, YMMV: Measure, test, and decide for yourself and your specific situation.

BTW: There's even more for performance fanatics: Use the IEEE half precision type. Little hardware or compiler support for it exists, but it cuts your bandwidth requirements in half yet again.

回答3:

double is, in some ways, the "natural" floating point type in the C language, which also influences C++. Consider that:

• an unadorned, ordinary floating-point constant like 13.9 has type double. To make it float, we have to add an extra suffix f or F.
• default argument promotion in C converts float function arguments^* to double: this takes place when no declaration exists for an argument, such as when a function is declared as variadic (e.g. printf) or no declaration exists (old style C, not permitted in C++).
• The %f conversion specifier of printf takes a double argument, not float. There is no dedicated way to print float-s; a float argument default-promotes to double and so matches %f.

On modern hardware, float and double are usually mapped, respectively, to 32 bit and 64 bit IEEE 754 types. The hardware works with the 64 bit values "natively": the floating-point registers are 64 bits wide, and the operations are built around the more precise type (or internally may be even more precise than that). Since double is mapped to that type, it is the "natural" floating-point type.

The precision of float is poor for any serious numerical work, and the reduced range could be a problem also. The IEEE 32 bit type has only 23 bits of mantissa (8 bits are consumed by the exponent field and one bit for the sign). The float type is useful for saving storage in large arrays of floating-point values provided that the loss of precision and range isn't a problem in the given application. For example, 32 bit floating-point values are sometimes used in audio for representing samples.

It is true that the use of a 64 bit type over 32 bit type doubles the raw memory bandwidth. However, that only affects programs which with a large arrays of data, which are accessed in a pattern that shows poor locality. The superior precision of the 64 bit floating-point type trumps issues of optimization. Quality of numerical results is more important than shaving cycles off the running time, in accordance with the principle of "get it right first, then make it fast".

---

* Note, however, that there is no general automatic promotion from float expressions to double; the only promotion of that kind is integral promotion: char, short and bitfields going to int.

回答4:

This is mostly hardware dependent, but consider that the most common CPU (x86/x87 based) have internal FPU that operate on 80bits floating point precision (which exceeds both floats and doubles).

If you have to store in memory some intermediate calculations, double is the good average from internal precision and external space. Performance is more or less the same, on single values. It may be affected by the memory bandwidth on large numeric pipes (since they will have double length).

Consider that floats have a precision that approximate 6 decimal digits. On a N-cubed complexity problem (like a matrix inversion or transformation), you lose two or three more in mul and div, remaining with just 3 meaningful digits. On a 1920 pixel wide display they are simply not enough (you need at least 5 to match a pixel properly).

This roughly makes double to be preferable.

回答5:

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 the risk of incorrect results if the analysis is not done correctly.

Also any performance gain by using float is usually relatively slighter than using double,that is because most of the popular processors do all floating point arithmetic in one format that is even wider than double.

回答6:

I think higher precision is the only reason. Actually most people don't think a lot about it, they just use double.

I think if float precision is good enough for particular task there is no reason to use double.