If I store an integer field in int32...will this use more space than int64?
From what I understand the varint will adjust its size with the size of the number being stored.
No, this only impacts the generated code. Any combination of [s|u]int{32|64} uses "varint" encoding, so the size is generally related to the magnitude, at least after noting the difference in negative numbers. In particular, a negative number that doesn't use sint* will be disproportionately large (10 bytes, IIRC), regardless of whether it is 32 or 64.
Related
I want to transfer a serialized protobuf message over TCP and I've tried to use the first field to indicate the total length of the serialized message.
I know that the int32 will change the length after encoding. So, maybe a fixed32 is a good choice.
But at last of the Encoding chapter, I found that I can't depend on it even if I use a fixed32 with field_num #1. Because Field Order said that the order may change.
My question is when do I use fixed value types? Are there any example scenarios?
"My question is when do I use fixed value types?"
When it comes to serializing values, there's always a tradeoff. If we look at the Protobuf-documentation, we see we have a few options when it comes to 32-bit integers:
int32: Uses variable-length encoding. Inefficient for encoding negative numbers – if your field is likely to have negative values, use sint32 instead.
uint32: Uses variable-length encoding.
sint32: Uses variable-length encoding. Signed int value. These more efficiently encode negative numbers than regular int32s.
fixed32: Always four bytes. More efficient than uint32 if values are often greater than 2^28.
sfixed32: Always four bytes.
int32 is a variable-length data-type. Any information that is not specified in the type itself, needs to be expressed somehow. To deserialize a variable-length number, we need to know what the length is. That is contained in the serialized message as well, which requires additional storage space. The same goes for an optional negative sign. The resulting message may be smaller because of this, but may be larger as well.
Say we have a lot of integers between 0 and 255 to encode. It would be cheaper to send this information as a two bytes (one byte with that actual value, and one byte to indicate that we just have one byte), than to send a full 32-bit (4 bytes) integer [fictional values, actual implementation may differ]. On the other hand, if we want to serialize a large value, that can only fit in 4 bytes the result may be larger (4 bytes and an additional byte to indicate that the value is 4 bytes; a total of 5 bytes). In this case it will be more efficient to use a fixed32. We simply know a fixed32 is 4 bytes; we don't need to serialize that fixed32 is a 4-byte number.
And if we look at fixed32 it actually mentions that the tradeoff point is around 2^28 (for unsigned integers).
So some types are good [as in, more efficient in terms of storage space] for large values, some for small values, some for positive/negative values. It all depends on what the actual values represent.
"Are there any example scenarios?"
32-bit hashes (ie: CRC-32), IPv4 addresses/masks. A predictable message sizes could be relevant.
Assume we have some sequence as input. For performance reasons we may want to convert it in homogeneous representation. And in order to transform it into homogeneous representation we are trying to convert it to same type. Here lets consider only 2 types in input - int64 and float64 (in my simple code I will use numpy and python; it is not the matter of this question - one may think only about 64-bit integer and 64-bit floats).
First we may try to cast everything to float64.
So we want something like so as input:
31 1.2 -1234
be converted to float64. If we would have all int64 we may left it unchanged ("already homogeneous"), or if something else was found we would return "not homogeneous". Pretty straightforward.
But here is the problem. Consider a bit modified input:
31000000 1.2 -1234
Idea is clear - we need to check that our "caster" is able to handle large by absolute value int64 properly:
format(np.float64(31000000), '.0f') # just convert to float64 and print
'31000000'
Seems like not a problem at all. So lets go to the deal right away:
im = np.iinfo(np.int64).max # maximum of int64 type
format(np.float64(im), '.0f')
format(np.float64(im-100), '.0f')
'9223372036854775808'
'9223372036854775808'
Now its really undesired - we lose some information which maybe needed. I.e. we want to preserve all the information provided in the input sequence.
So our im and im-100 values cast to the same float64 representation. The reason of this is clear - float64 has only 53 significand of total 64 bits. That is why its precision enough to represent log10(2^53) ~= 15.95 i.e. about all 16-length int64 without any information loss. But int64 type contains up to 19 digits.
So we end up with about [10^16; 10^19] (more precisely [10^log10(53); int64.max]) range in which each int64 may be represented with information loss.
Q: What decision in such situation should one made in order to represent int64 and float64 homogeneously.
I see several options for now:
Just convert all int64 range to float64 and "forget" about possible information loss.
Motivation here is "majority of input barely will be > 10^16 int64 values".
EDIT: This clause was misleading. In clear formulation we don't consider such solutions (but left it for completeness).
Do not make such automatic conversions at all. Only if explicitly specified.
I.e. we agree with performance drawbacks. For any int-float arrays. Even with ones as in simplest 1st case.
Calculate threshold for performing conversion to float64 without possible information loss. And use it while making casting decision. If int64 above this threshold found - do not convert (return "not homogeneous").
We've already calculate this threshold. It is log10(2^53) rounded.
Create new type "fint64". This is an exotic decision but I'm considering even this one for completeness.
Motivation here consists of 2 points. First one: it is frequent situation when user wants to store int and float types together. Second - is structure of float64 type. I'm not quite understand why one will need ~308 digits value range if significand consists only of ~16 of them and other ~292 is itself a noise. So we might use one of float64 exponent bits to indicate whether its float or int is stored here. But for int64 it would be definitely drawback to lose 1 bit. Cause would reduce our integer range twice. But we would gain possibility freely store ints along with floats without any additional overhead.
EDIT: While my initial thinking of this was as "exotic" decision in fact it is just a variant of another solution alternative - composite type for our representation (see 5 clause). But need to add here that my 1st composition has definite drawback - losing some range for float64 and for int64. What we rather do - is not to subtract 1 bit but add one bit which represents a flag for int or float type stored in following 64 bits.
As proposed #Brendan one may use composite type consists of "combination of 2 or more primitive types". So using additional primitives we may cover our "problem" range for int64 for example and get homogeneous representation in this "new" type.
EDITs:
Because here question arisen I need to try be very specific: Devised application in question do following thing - convert sequence of int64 or float64 to some homogeneous representation lossless if possible. The solutions are compared by performance (e.g. total excessive RAM needed for representation). That is all. No any other requirements is considered here (cause we should consider a problem in its minimal state - not writing whole application). Correspondingly algo that represents our data in homogeneous state lossless (we are sure we not lost any information) fits into our app.
I've decided to remove words "app" and "user" from question - it was also misleading.
When choosing a data type there are 3 requirements:
if values may have different signs
needed precision
needed range
Of course hardware doesn't provide a lot of types to choose from; so you'll need to select the next largest provided type. For example, if you want to store values ranging from 0 to 500 with 8 bits of precision; then hardware won't provide anything like that and you will need to use either 16-bit integer or 32-bit floating point.
When choosing a homogeneous representation there are 3 requirements:
if values may have different signs; determined from the requirements from all of the original types being represented
needed precision; determined from the requirements from all of the original types being represented
needed range; determined from the requirements from all of the original types being represented
For example, if you have integers from -10 to +10000000000 you need a 35 bit integer type that doesn't exist so you'll use a 64-bit integer, and if you need floating point values from -2 to +2 with 31 bits of precision then you'll need a 33 bit floating point type that doesn't exist so you'll use a 64-bit floating point type; and from the requirements of these two original types you'll know that a homogeneous representation will need a sign flag, a 33 bit significand (with an implied bit), and a 1-bit exponent; which doesn't exist so you'll use a 64-bit floating point type as the homogeneous representation.
However; if you don't know anything about the requirements of the original data types (and only know that whatever the requirements were they led to the selection of a 64-bit integer type and a 64-bit floating point type), then you'll have to assume "worst cases". This leads to needing a homogeneous representation that has a sign flag, 62 bits of precision (plus an implied 1 bit) and an 8 bit exponent. Of course this 71 bit floating point type doesn't exist, so you need to select the next largest type.
Also note that sometimes there is no "next largest type" that hardware supports. When this happens you need to resort to "composed types" - a combination of 2 or more primitive types. This can include anything up to and including "big rational numbers" (numbers represented by 3 big integers in "numerator / divisor * (1 << exponent)" form).
Of course if the original types (the 64-bit integer type and 64-bit floating point type) were primitive types and your homogeneous representation needs to use a "composed type"; then your "for performance reasons we may want to convert it in homogeneous representation" assumption is likely to be false (it's likely that, for performance reasons, you want to avoid using a homogeneous representation).
In other words:
If you don't know anything about the requirements of the original data types, it's likely that, for performance reasons, you want to avoid using a homogeneous representation.
Now...
Let's rephrase your question as "How to deal with design failures (choosing the wrong types which don't meet requirements)?". There is only one answer, and that is to avoid the design failure. Run-time checks (e.g. throwing an exception if the conversion to the homogeneous representation caused precision loss) serve no purpose other than to notify developers of design failures.
It is actually very basic: use 64 bits floating point. Floating point is an approximation, and you will loose precision for many ints. But there are no uncertainties other than "might this originally have been integral" and "does the original value deviates more than 1.0".
I know of one non-standard floating point representation that would be more powerfull (to be found in the net). That might (or might not) help cover the ints.
The only way to have an exact int mapping, would be to reduce the int range, and guarantee (say) 60 bits ints to be precise, and the remaining range approximated by floating point. Floating point would have to be reduced too, either exponential range as mentioned, or precision (the mantissa).
In Go's constant specification, it is mentioned that:
Numeric constants represent exact values of arbitrary precision and do not overflow.
So I tried
const VeryVeryBigNumber = 1 << 200
and it works. However, the biggest shift count I could try is 511 and using 512 will throw:
shift count too large: 512.
What does 512 represents? I have no intention to use it, I just want to know why is it limited to 511 in my machine (I'm using ubuntu 64 bit and go 1.9.2)?
Thanks
512 is kind of an arbitrary limit. The only thing the spec says is:
Implementation restriction: Although numeric constants have arbitrary
precision in the language, a compiler may implement them using an
internal representation with limited precision. That said, every
implementation must:
Represent integer constants with at least 256 bits.
Unfortunately, the comments around the limits don't give a reason.
At some point, a limit has to be used. I would recommend sticking to the required 256.
Very large integers are often stored as variable-length arrays of digits in memory, as opposed to a straightforward binary representation as is the case with most primitive 'int' or 'long' types, as in Java or C. With this in mind, I would be interested to know algorithm(s) that can compute:
At what count an integer must reach before it becomes more efficient to store it as a BigInteger (or equivalent arbitrary-precision arithmetic construct) with a given radix for the integer's digits;
Which radix would be most efficient to store the digits of this large integer.
I have mentioned 'efficiency'; by this, I mean I am mainly concerned with the amount of space such a BigInteger would consume, though I would also be interested to hear any comments on processing speed or time complexity.
An integer should consume the least space if stored in a raw binary format (unless maybe it is a small integer and data type is way too wide for it - to store 1 in 128 bit long long). Storing differently does not save any memory and is used to make the work with such integers easier.
If byte by byte, this translates into 256'ecimal radix - 256 possible values, as much as the byte can hold.
BigInt is never more efficient than one of the integer types directly supported by hardware. If you can use what's supported directly, use it.
What's supported by hardware most efficiently, likely a power of 2 or, often equivalently, binary.
For example, if I add a short integer and a float data type, will each allocate the same amount of memory? They have different maximum values, but have different data structures as well, so I was not sure.
Also, do mathematical operations take different amounts of time with different data types?
It's hard to answer this exactly without knowing which language/hardware you are using, but in most cases different data types do take up different amounts of memory and data type can affect the speed of mathematical operations. For example, in Java and C#, a short is 16 bits and a float is 32 bits. I would expect floating point math to be slower than integer math in general, although this can be complex as explained in this post.
For other languages (such as C), the size of the basic data types is hardware-dependent, so an int might be 32 bits on some machines and 64 bits on others.
the reason we have datatypes is efficiency. That includes both size and treatment of data(types).
A char datatype has 8 bits (you may also call it 8-bit integer since the numerical values are simply mapped to characters in the ASCII table) = 256 possible values
A 32-bit integer has ... you guessed it 32 bits = 2³² possible values
Mathematical Operations are performed by shifting or comparing those bits..
More bits = more operations = more time
Reference: http://en.wikipedia.org/wiki/Data_type