I run Lua on a CPU without dedicated floating point HW, depending on SW emulation.
From luaopt.h I can see that some macros are set to double, but it does not clearly state when floats are used and its a little hard to track it.
If my script does simple stuff like:
a=0
a=a+1
for...
Would that involve a floating point operations at any level?
If no that's fine, but what is then the benefit to change macros to long?
(I tried of course but did not work....)
All numeric operations in Lua are performed (according to the default configuration) in floating point. There is no distinction made between floating point and integer, all values are simply numbers.
The actual C type used to store a Lua number is set in luaconf.h, and it is both allowed and even practical to change that to a suitable integral type. You start by changing LUA_NUMBER from double to int, long, or perhaps ptrdiff_t. Then you will find you need to tweak the related macros that control the conversions between strings and numbers. And, of course, you will likely need to eliminate most or all of the base math library since math.sin() and its friends and neighbors are not particularly useful over integers.
The result will be a Lua interpreter where all numbers are integers. The language will still allow you to type 3.14, but it will be stored as 3. Your code will likely not be completely portable to a Lua interpreter built with the standard configuration since a huge amount of Lua code casually assumes that floating point arithmetic is permitted, and remember that your compiled byte code will definitely not be compatible since byte code will store numbers as LUA_NUMBER.
There is LNUM patch (used, for example, by OpenWrt project which relies heavily on Lua for providing Web UI on hardware without FPU) that allows dual integer/floating point representation of numbers in Lua with conversions happening behind the scenes when required. With it most integer computations will be performed without resorting to FPU. Unfortunately, it's only applicable to Lua 5.1; 5.2 is not supported.
Related
Why such code is used in some applications instead of a MOVE?
add 16 to ZERO giving SOME-RESULT
I spotted this in professionally written code at several spots.
Sorce is on this page
Why such code is used in some applications instead of a MOVE?
add 16 to ZERO giving SOME-RESULT
Without seeing more of the code, it appears that it could be a translation of IBM Assembler to COBOL. In particular, the ZAP (Zero and Add Packed) instruction may be literally translated to the above instruction, particularly if SOME-RESULT is COMP-3. Thus, someone checking the translation could see that the ZAP instruction was faithfully translated.
Or, it could be an assembler programmer's idea of a joke.
Having seen the code, I also note the use of
subtract some-data-item from some-data-item
which is used instead of
move zero to some-data-item
This is consistent with operations used with packed decimal fields in IBM Assembly, where there are no other instructions to accomplish "flexible" moves. By flexible, I mean that the packed decimal instructions contain a length field so that specific size MVC instructions need not be used.
This particular style, being unusual, may be related to catching copyright violations.
From my experience, I'm pretty sure I know the reason why the programmer would have done this. It has something to do with the binary representation of the number.
I bet SOME-RESULT is a packed-decimal (or COMP-3) format number. Let's assume the field is defined like this
05 SOME-RESULT PIC S9(5) COMP-3.
This results in a 3-byte field with a hex representation like this
x'00016C'
The decimal number is encoded as a binary encoded decimal (BCD, one decimal digit per half-byte), and the last half-byte holds the sign.
Let's take a look at how the sign is defined:
if it is one of x'C', x'A', x'F', x'E' (café), then the number is positive
if it is one of x'B', x'D', then the number is negative
any of x'0'..'x'9' are not valid signs, so we can distinguish signed packed-decimals from unsigned.
However, a zoned number (PIC 9(5) DISPLAY) - as in the source code - looks like this:
x'F0F0F0F1F6'
As you can see, each decimal digit is an EBCDIC character with the 'zone' part (the first half-byte) always being x'F'.
Now we get closer to your question!
What happens when we use
MOVE 16 TO SOME-RESULT
If you just MOVE a number to such a field, this results in being compiled into a PACK instruction on the machine code level.
PACK SOME-RESULT,=C'16'
A pack instruction takes a zoned number and packs it by picking only the second half-byte of each byte and storing it in the half-bytes of the packed number - with one exception! When it comes to the last byte, it simply flips the two half-bytes and stores them in the last half-byte of the decimal.
This means that the zone of the last byte of the zoned decimal becomes the sign in the packed decimal:
x'00016F'
So now we have an x'F' as the sign – which is a valid positive sign.
However, what happens if use this Cobol instruction instead
ADD 16 TO ZERO GIVING SOME-RESULT
This compiles into multiple machine level instructions
PACK SOME_RESULT,=C'0'
PACK TEMP,=C'16'
AP SOME_RESULT,TEMP
(or similar - the key point is that is needs an AP somewhere)
This makes a slight difference in the result, because the AP (add packed) instruction always sets the resulting sign to either x'C' for a positive or x'D' for a negative result.
So the difference lies in the sign
x'00016C'
Finally, the question is why would one make this difference? After all, both x'F' and x'C' are valid positive signs. So why care?
There is one situation when this slight difference can cause big problems: When the packed decimal is part of an index key, then we would not get a match, even though the numbers are semantically identical!
Because this situation occurred quite often in older databases like VSAM and DL/I (later: IMS/DB), it became good practice to "normalize" packed decimals if they were part of an index key.
However, some programmers adopted the practice without knowing why, so you may come across code that uses this "normalization" even though the data are not used for index keys.
You might also wonder why a compiler does not optimize out the ADD 16 TO ZERO. I'm pretty sure it once did, but that broke a lot of applications, so this specific optimization was removed again or at least made a non-default option with warnings.
Additional useful info
Note that at least the Enterprise Cobol for z/OS compiler allows you to see exactly the machine code that is produced from your source code if use the LIST compile option (see this example output). I recommend to always compile with options LIST, MAP, OFFSET, XREF because these options enable you find the exact problem in your Cobol source even when you only have a program dump from an abend.
Anyway, good programming practice is not to care about the compiler or the machine code, but about the other programmers who will have to maintain, and thus read and understand the code. Good practice would be to always prefer simple and readable instructions, and to document the reasons (right in the code) when deviating from this rule.
Some programmers like to do things "just because they can". I have a feeling that is what you are seeing here. It makes about as much sense as doing
a := 0 + b
would in go.
How are operators overloaded for numbers? I need this for replacing the standard floating point numbers in Lua with big floats (384 bit floats from Cephes) that I've added as a library without having to change Lua itself. The reason is that sometimes normal Lua doubles get mixed up with the big floats if you don't convert the Lua doubles to big floats first.
Can it be done with just some Lua code, or does Lua have to be changed (not necessarily a problem, but still undesirable)?
Why does Erlang not include arbitrary precision for math functions? I recently had to use math:pow(2,4333), and it throws an error. Why does Erlang not use libraries like GMP? Are there any plans to include it in the standard library? (Haskell uses it, [strike]even Java has bignums[strike]).
Thanks.
Update:
To add more perspective, I understand that it can be done using NIFs. I was solving problems from hackerrank in which the input uses larger numbers. pow/2 can be easily written in Erlang and it worked, but for larger computations, it would be slow.
Java returns double for pow so it does not work for Math.pow(2, 1024) which gives Infinity.
Erlang has bignums for integers but uses 64-bit IEEE standard floating point numbers. So while you can happily compute factorial(10000) with integers by default the math library uses floating point so math:pow(2, 4333) does not work.
How could I handle operations with a number like:
48534588306961133067968196965257961415756656521818848750723547477673457670019632882524164647651492025728980571833579341743988603191694784406703
Nothing that I've tried worked so far... unsigned long, long long, etc...
What you need is a library that provides support for operations on integers of arbitrary length. However, from what I've been able to find out, there are no such libraries written in Objective-C.
You are nevertheless in luck as Objective-C is a superset of C. That makes it possible for you to use C libraries such as those described in the answers to this somewhat dated SO question.
Also, since the Clang compiler supports C++ and combining Objective-C and C++ code, you can probably use something like big int.
Note that none of the built-in types is even close to being big enough to represent numbers with as many digits as your examples. The biggest available integer type is unsigned long long, if you don't need negative numbers, and its size is 8 bytes/64 bits, which gives you a range of 0-18446744073709551615, or 20 digits max.
You could use JKBigInteger instead, it is a Objective-C wrapper around LibTomMath C library. And really easy to use and understand.
In your case:
JKBigInteger *int = [[JKBigInteger alloc] initWithString:#"48534588306961133067968196965257961415756656521818848750723547477673457670019632882524164647651492025728980571833579341743988603191694784406703"];
You can try here : http://gmplib.org/
GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on. GMP has a rich set of functions, and the functions have a regular interface.
As 64 bits support is not expected in the next version it is no longer an option to wait for the possibility to migrate our existing code base to unicode and 64-bit in one go.
However it would be nice if we could already prepare our code for 64-bit when doing our unicode translation. This will minimize impact in the event it will finally appear in version 2020.
Any suggestions how to approach this without introducing to much clutter if it doesn't arrive until 2020?
There's another similar question, but I'll repeat my reply here too, to make sure as many people see this info:
First up, a disclaimer: although I work for Embarcadero. I can't speak for my employer. What I'm about to write is based on my own opinion of how a hypothetical 64-bit Delphi should work, but there may or may not be competing opinions and other foreseen or unforeseen incompatibilities and events that cause alternative design decisions to be made.
That said:
There are two integer types, NativeInt and NativeUInt, whose size will
float between 32-bit and 64-bit depending on platform. They've been
around for quite a few releases. No other integer types will change size
depending on bitness of the target.
Make sure that any place that relies on casting a pointer value to an
integer or vice versa is using NativeInt or NativeUInt for the integer
type. TComponent.Tag should be NativeInt in later versions of Delphi.
I'd suggest don't use NativeInt or NativeUInt for non-pointer-based values. Try to keep your code semantically the same between 32-bit and 64-bit. If you need 32 bits of range, use Integer; if you need 64 bits, use Int64. That way your code should run the same on both bitnesses. Only if you're casting to and from a Pointer value of some kind, such as a reference or a THandle, should you use NativeInt.
Pointer-like things should follow similar rules to pointers: object
references (obviously), but also things like HWND, THandle, etc.
Don't rely on internal details of strings and dynamic arrays, like
their header data.
Our general policy on API changes for 64-bit should be to keep the
same API between 32-bit and 64-bit where possible, even if it means that
the 64-bit API does not necessarily take advantage of the machine. For
example, TList will probably only handle MaxInt div SizeOf(Pointer)
elements, in order to keep Count, indexes etc. as Integer. Because the
Integer type won't float (i.e. change size depending on bitness), we
don't want to have ripple effects on customer code: any indexes that
round-tripped through an Integer-typed variable, or for-loop index,
would be truncated and potentially cause subtle bugs.
Where APIs are extended for 64-bit, they will most likely be done with
an extra function / method / property to access the extra data, and this
API will also be supported in 32-bit. For example, the Length() standard
routine will probably return values of type Integer for arguments of
type string or dynamic array; if one wants to deal with very large
dynamic arrays, there may be a LongLength() routine as well, whose
implementation in 32-bit is the same as Length(). Length() would throw
an exception in 64-bit if applied to a dynamic array with more than 232
elements.
Related to this, there will probably be improved error checking for
narrowing operations in the language, especially narrowing 64-bit values
to 32-bit locations. This would hit the usability of assigning the
return value of Length to locations of type Integer if Length(),
returned Int64. On the other hand, specifically for compiler-magic
functions like Length(), there may be some advantage of the magic taken,
to e.g. switch the return type based on context. But advantage can't be
similarly taken in non-magic APIs.
Dynamic arrays will probably support 64-bit indexing. Note that Java
arrays are limited to 32-bit indexing, even on 64-bit platforms.
Strings probably will be limited to 32-bit indexing. We have a hard
time coming up with realistic reasons for people wanting 4GB+ strings
that really are strings, and not just managed blobs of data, for which
dynamic arrays may serve just as well.
Perhaps a built-in assembler, but with restrictions, like not being able to freely mix with Delphi code; there are also rules around exceptions and stack frame layout that need to be followed on x64.
First, look at the places where you interact with non-delphi libraries and api-calls,
they might differ. On Win32, libraries with the stdcall calling convenstion are named like _SomeFunction#4 (#4 indicating the size of the parameters, etc). On Win64, there is only one calling convention, and the functions in a dll are no more decorated. If you import functions from dll files, you might need to adjust them.
Keep in mind, in a 64 bit exe you cannot load a 32-bit dll, so, if you depend on 3rd party dll files, you should check for a 64-bit version of those files as well.
Also, look at Integers, if you depend on their max value, for example when you let them overflow and wait for the moment that happens, it will cause trouble if the size of an integer is changed.
Also, when working with streams, and you want to serialize different data, with includes an integer, it will cause trouble, since the size of the integer changed, and your stream will be out of sync.
So, on places where you depend on the size of an integer or pointer, you will need to make adjustments. When serializing sush data, you need to keep in mind this size issue as well, as it might cause data incompatibilities between 32 and 64 bit versions.
Also, the FreePascal compiler with the Lazarus IDE already supports 64-bit. This alternative Object Pascal compiler is not 100% compatible with the Borland/Codegear/Embarcadero dialect of Pascal, so just recompiling with it for 64-bit might not be that simple, but it might help point out problems with 64-bit.
The conversion to 64bit should not be very painful. Start with being intentional about the size of an integer where it matters. Don't use "integer" instead use Int32 for integers sized at 32bits, and Int64 for integers sized at 64bits. In the last bit conversion the definition of Integer went from Int16 to Int32, so your playing it safe by specifying the exact bit depth.
If you have any inline assembly, create a pascal equivalent and create some unit tests to insure that they operate the same way. Perform some timing tests of both and see if the assembly still runs faster enough to keep. If it does, then you will want to make changes to both as they are needed.
Use NativeInt for integers that can contain casted pointers.