I've been learning elixir this month, and was in a situation where I wanted to convert a binary object into a list of bits, for pattern matching.
My research led me here, to an article showing a method for doing so. However, I don't fully understand one of the arguments passed to the extract function.
I could just copy and paste the code, but I'd like to understand what's going on under the hood here.
The argument is this: <<b :: size(1), bits :: bitstring>>.
What I understand
I understand that << x >> denotes a binary object x. Logically to me, it looks as though this is similar to performing: [head | tail] = list on a List, to get the first element, and then the remaining ones as a new list called tail.
What I don't understand
However, I'm not familiar with the syntax, and I have never seen :: in elixir, nor have I ever seen a binary object separated by a comma: ,. I also, haven't seen size(x) used in Elixir, and have never encountered a bitstring.
The Bottom Line
If someone, could explain exactly how the syntax for this argument breaks down, or point me towards a resource I would highly appreciate it.
For your convenience, the code from that article:
defmodule Bits do
# this is the public api which allows you to pass any binary representation
def extract(str) when is_binary(str) do
extract(str, [])
end
# this function does the heavy lifting by matching the input binary to
# a single bit and sends the rest of the bits recursively back to itself
defp extract(<<b :: size(1), bits :: bitstring>>, acc) when is_bitstring(bits) do
extract(bits, [b | acc])
end
# this is the terminal condition when we don't have anything more to extract
defp extract(<<>>, acc), do: acc |> Enum.reverse
end
IO.inspect Bits.extract("!!") # => [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]
IO.inspect Bits.extract(<< 99 >>) #=> [0, 1, 1, 0, 0, 0, 1, 1]
Elixir pattern matching seems mind blowingly easy to use for
structured binary data.
Yep. You can thank the erlang inventors.
According to the documentation, <<x :: size(y)>> denotes a bitstring,
whos decimal value is x and is represented by a string of bits that is
y in length.
Let's dumb it down a bit: <<x :: size(y)>> is the integer x inserted into y bits. Examples:
<<1 :: size(1)>> => 1
<<1 :: size(2)>> => 01
<<1 :: size(3)>> => 001
<<2 :: size(3)>> => 010
<<2 :: size(4)>> => 0010
The number of bits in the binary type is divisible by 8, so a binary type has a whole number of bytes (1 byte = 8 bits). The number of bits in a bitstring is not divisible by 8. That's the difference between the binary type and the bitstring type.
I understand that << x >> denotes a binary object x. Logically to me,
it looks as though this is similar to performing: [head | tail] = list
on a List, to get the first element, and then the remaining ones as a
new list called tail.
Yes:
defmodule A do
def show_list([]), do: :ok
def show_list([head|tail]) do
IO.puts head
show_list(tail)
end
def show_binary(<<>>), do: :ok
def show_binary(<<char::binary-size(1), rest::binary>>) do
IO.puts char
show_binary(rest)
end
end
In iex:
iex(6)> A.show_list(["a", "b", "c"])
a
b
c
:ok
iex(7)> "abc" = <<"abc">> = <<"a", "b", "c">> = <<97, 98, 99>>
"abc"
iex(9)> A.show_binary(<<97, 98, 99>>)
a
b
c
:ok
Or you can interpret the integers in the binary as plain old integers:
def show(<<>>), do: :ok
def show(<<ascii_code::integer-size(8), rest::binary>>) do
IO.puts ascii_code
show(rest)
end
In iex:
iex(6)> A.show(<<97, 98, 99>>)
97
98
99
:ok
The utf8 type is super useful because it will grab as many bytes as required to get a whole utf8 character:
def show(<<>>), do: :ok
def show(<<char::utf8, rest::binary>>) do
IO.puts char
show(rest)
end
In iex:
iex(8)> A.show("ۑ")
8364
235
:ok
As you can see, the uft8 type returns the unicode codepoint of the character. To get the character as a string/binary:
def show(<<>>), do: :ok
def show(<<codepoint::utf8, rest::binary>>) do
IO.puts <<codepoint::utf8>>
show(rest)
end
You take the codepoint(an integer) and use it to create the binary/string <<codepoint::utf8>>.
In iex:
iex(1)> A.show("ۑ")
€
ë
:ok
You can't specify a size for the utf8 type, though, so if you want to read multiple utf8 characters, you have to specify multiple segments.
And of course, the segment rest::binary, i.e. a binary type with no size specified, is super useful. It can only appear at the end of a pattern, and rest::binary is like the greedy regex: (.*). The same goes for rest::bitstring.
Although the elixir docs don't mention it anywhere, the total number of bits in a segment, where a segment is one of those things:
| | |
v v v
<< 1::size(8), 1::size(16), 1::size(1) >>
is actually unit * size, where each type has a default unit. The default type for a segment is integer, so the type for each segment above defaults to integer. An integer has a default unit of 1 bit, so the total number of bits in the first segment is: 8 * 1 bit = 8 bits. The default unit for the binary type is 8 bits, so a segment like:
<< char::binary-size(6)>>
has a total size of 6 * 8 bits = 48 bits. Equivalently, size(6) is just the number of bytes. You can specify the unit just like you can the size, e.g. <<1::integer-size(2)-unit(3)>>. The total bit size of that segment is: 2 * 3 bits = 6 bits.
However, I'm not familiar with the syntax
Check this out:
def bitstr2bits(bitstr) do
for <<bit::integer-size(1) <- bitstr>>, do: bit
end
In iex:
iex(17)> A.bitstr2bits <<1::integer-size(2), 2::integer-size(2)>>
[0, 1, 1, 0]
Equivalently:
iex(3)> A.bitstr2bits(<<0b01::integer-size(2), 0b10::integer-size(2)>>)
[0, 1, 1, 0]
Elixir tends to abstract away recursion with library functions, so usually you don't have to come up with your own recursive definitions like at your link. However, that link shows one of the standard, basic recursion tricks: adding an accumulator to the function call to gather results that you want the function to return. That function could also be written like this:
def bitstr2bits(<<>>), do: []
def bitstr2bits(<<bit::integer-size(1), rest::bitstring>>) do
[bit | bitstr2bits(rest)]
end
The accumulator function at the link is tail recursive, which means it takes up a constant (small) amount of memory--no matter how many recursive function calls are needed to step through the bitstring. A bitstring with 10 million bits? Requiring 10 million recursive function calls? That would only require a small amount of memory. In the old days, the alternate definition I posted could potentially crash your program because it would take up more and more memory for each recursive function call, and if the bitstring were long enough the amount of memory needed would be too large, and you would get stackoverflow and your program would crash. However, erlang has optimized away the disadvantages of recursive functions that are not tail recursive.
You can read about all these here, short answer:
:: is similar as guard, like a when is_integer(a), in you case size(1) expect a 1 bit binary
, is a separator between matching binaries, like | in [x | []] or like comma in [a, b]
bitstring is a superset over binaries, you can read about it here and here, any binary can be respresented as bitstring
iex> ?h
104
iex> ?e
101
iex> ?l
108
iex> ?o
111
iex> <<104, 101, 108, 108, 111>>
"hello"
iex> [104, 101, 108, 108, 111]
'hello'
but not vice versa
iex> <<1, 2, 3>>
<<1, 2, 3>>
After some research, I realized I overlooked some important information located at: elixir-lang.
According to the documentation, <<x :: size(y)>> denotes a bitstring, whos decimal value is x and is represented by a string of bits that is y in length.
Furthermore, <<binary>> will always attempt to conglomerate values in a left-first direction, into bytes or 8-bits, however, if the number of bits is not divisible by 8, there will by x bytes, followed by a bitstring.
For example:
iex> <<3::size(5), 5::size(6)>> # <<00011, 000101>>
<<24, 5::size(3)>> # automatically shifted to: <<00011000(24) , 101>>
Now, elixir also lets us pattern match binaries, and bitstrings like so:
iex> <<3 :: size(2), b :: bitstring>> = <<61 :: size(6)>> # [11] [1101]
iex> b
<<13 :: size(4)>> # [1101]
So, i completly misunderstood binaries and biststrings, and pattern matching between the two.
Not really the answer to the question stated, but I’d put it here for the sake of formatting. In elixir we usually use Kernel.SpecialForms.for/1 comprehension for bitstring generation.
for << b :: size(1) <- "!!" >>, do: b
#⇒ [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]
for << b :: size(1) <- <<99>> >>, do: b
#⇒ [0, 1, 1, 0, 0, 0, 1, 1]
I wanted to use the bits, in an 8 bit binary to toggle conditions. So
[b1, b2, ...] = extract(<<binary>>)
I then wanted to say:
if b1, do: x....
if b2, do: y...
Is there a better way to do what I'm trying to do, instead of pattern
matching?
First of all, the only terms that evaluate to false in elixir are false and nil (just like in ruby):
iex(18)> x = 1
1
iex(19)> y = 0
0
iex(20)> if x, do: IO.puts "I'm true."
I'm true.
:ok
iex(21)> if y, do: IO.puts "I'm true."
I'm true.
:ok
Although, the fix is easy:
if b1 == 1, do: ...
Extracting the bits into a list is unnecessary because you can just iterate the bitstring:
def check_bits(<<>>), do: :ok
def check_bits(<<bit::integer-size(1), rest::bitstring>>) do
if bit == 1, do: IO.puts "bit is on"
check_bits(rest)
end
In other words, you can treat a bitstring similarly to a list.
Or, instead of performing the logic in the body of the function to determine whether the bit is 1, you can use pattern matching in the head of the function:
def check_bits(<<>>), do: :ok
def check_bits(<< 1::integer-size(1), rest::bitstring >>) do
IO.puts "The bit is 1."
check_bits(rest)
end
def check_bits(<< 0::integer-size(1), rest::bitstring >>) do
IO.puts "The bit is 0."
check_bits(rest)
end
Instead of using a variable, bit, for the match like here:
bit::integer-size(1)
...you use a literal value, 1:
1::integer-size(1)
The only thing that can match a literal value is the literal value itself. As a result, the pattern:
<< 1::integer-size(1), rest::bitstring >>
will only match a bitstring where the first bit, integer-size(1), is 1. The literal matching employed there is similar to doing the following with a list:
def list_contains_4([4|_tail]) do
IO.puts "found a 4"
true #end the recursion and return true
end
def list_contains_4([head|tail]) do
IO.puts "#{head} is not a 4"
list_contains_4(tail)
end
def list_contains_4([]), do: false
The first function clause tries to match the literal 4 at the head of the list. If the head of the list is not 4, there's no match; so elixir moves on to the next function clause, and in the next function clause the variable head will match anything in the list.
Using pattern matching in the head of a function rather than performing logic in the body of a function is considered more stylish and efficient in erlang.
I'd like to have my code take code written in another document, read it, and then use it as though it was written in the code. Say we have the following:
MODULE samplemod
CONTAINS
FUNCTION sillysum(boudary,function) RESULT(counter)
IMPLICIT NONE
REAL(KIND=8) :: boundary, counter
REAL(KIND=8), DIMENSION(:) :: function
INTEGER :: m
counter = 0.d0
DO m = 1, my_mesh%me
counter = function(m) + externalfunction
END DO
END FUNCTION sillysum
END MODULE samplemod
PROGRAM sampleprogram
USE samplemod
REAL(KIND=8), DIMENSION(:) :: function1
ALLOCATE(function1(100))
DO m=1, 100
function1(i) = i
END DO
WRITE(*,*) sillysum(100,function1)
END PROGRAM sampleprogram
Where in some external file (say 'externfunct.txt') one has written m**2. How can the Fortran code read the external function m**2, SIN(m), or even 0 and have that replace externalfunction. Here's a simpler example:
REAL(KIND=8) :: x = 2
CHARACTER(LEN=*) :: strng = "external"
WRITE(*,*) "Hello world, 2 + ", strng, " = ", 2 + external
Where in a txt file I have written I have written SIN(x).
I think there are two different approaches for this (* in fact, there seems a "third" approach also, see EDIT); one is to use a shared library, and the other is to use a parser for math expressions. The first approach is described in a Rossetastone page (Call a function in a shared library) and an SO page (Fortran dynamic libraries, load at runtime?), for example. For the second approach, you can find 3rd-party libraries by searching with "math parser" or "Fortran math parser" etc. Here, I have tried this one because it seems pretty simple (only one module and no installation). If we write a simple test program like this
program test
use interpreter, only: init, evaluate, dp => realkind
implicit none
integer, parameter :: mxvars = 10 !! consider 10 variables at most here
character(10) :: symbols( mxvars )
real(dp) :: values( mxvars ), answer
character(1000) :: funcstr !! a user-defined math expression
character(5) :: stat
!> Define variable names.
symbols( 1 ) = "x"
symbols( 2 ) = "a"
symbols( 3 ) = "b"
symbols( 4 ) = "c"
symbols( 5 ) = "foo"
!> Get a math expression.
print *, "Please input a math expression:"
read(*, "(a)") funcstr !! e.g., a * x + b
!> Init the evaluator.
call init( funcstr, symbols, stat )
if ( stat /= "ok" ) stop "stat /= ok"
!> Set values for the variables.
values( : ) = 0
values( 1 ) = 2.0_dp ! x
values( 2 ) = 10.0_dp ! a
values( 3 ) = 7.0_dp ! b
!> Evaluate.
answer = evaluate( values )
print *, "function value = ", answer
end program
and compile it as (*1)
$ gfortran -ffree-line-length-none interpreter.f90 mytest.f90
we can test various expressions as follows:
$ ./a.out
Please input a math expression:
a * x + b
function value = 27.000000000000000
$ ./a.out
Please input a math expression:
sin( a * x ) + cos( b ) + foo
function value = 1.6668475050709324
The usage of other libraries also seems very similar. Because the performance of each library may be rather different, it may be useful to try several different libraries for comparison.
(*1) The module has some lines with sind, cosd, and tand, but they are not supported by gfortran. So, to compile, I have commented them out and replaced them by stop, i.e.,
stop "sind not supported..."
! pdata(st) = sind(pdata(st))
(I guess sind(x) means sin( x * pi / 180 ), so it may be OK to define it as such.)
[EDIT]
A "third" approach may be to call the built-in eval() function in interpreted languages like Python or Julia via system(), e.g., this SO page. Although this also has a lot of weak points (and it is probably much easier to use such languages directly), calling eval() from Fortran might be useful for some specific purposes.
I get the following error when trying to compile:
call qplot (Z, B, m + 1)
1
Error: Type mismatch in argument 'x' at (1); passed REAL(8) to REAL(4)
Everything seems to be in double precision so I can't help but think it is a Dislin error, especially considering that it appears with reference to a Dislin statement. What am I doing wrong? My code is the following:
program test
use dislin
integer :: i
integer, parameter :: n = 2
integer, parameter :: m = 5000
real (kind = 8) :: X(n + 1), Z(0:m), B(0:m)
X(1) = 1.D0
X(2) = 0.D0
X(3) = 2.D0
do i = 0, m
Z(i) = -1.D0 + (2.D0*i) / m
B(i) = f(Z(i))
end do
call qplot (Z, B, m + 1)
read(*,*)
contains
real (kind = 8) function f(t)
implicit none
real (kind = 8), intent(in) :: t
real (kind = 8), parameter :: pi = Atan(1.D0)*4.D0
f = cos(pi*t)
end function f
end program
From the DISLIN manual I read that qplot requires (single precision) floats:
QPLOT connects data points with lines.
The call is: CALL QPLOT (XRAY, YRAY, N) level 0, 1
or: void qplot (const float *xray, const float *yray, int n);
XRAY, YRAY are arrays that contain X- and Y-coordinates.
N is the number of data points.
So you need to convert Z and B to real:
call qplot (real(Z), real(B), m + 1)
Instead of using fixed numbers for the kind of numbers (which vary between compilers), please consider using the ISO_Fortran_env module and the pre-defined constants REAL32 and REAL64.
The qplot routine requires a default real. You can convert your data
call qplot(real(Z), real(B), m + 1)
I second the remark with kind = 8, it is very ugly, if you insist on 8 at least declare a constant
integer, parameter :: rp = 8
and use
real(rp) ::
As the first two answers explain, the standard versions of the dislin routines require single precision arguments. I find it most convenient to use these since I may have single or double arguments, using the real technique to convert the type of double variables. It seems unlikely that the lost precision will be perceptible on a graph. However, if you wish to work exclusively in double precision, there is an alternative set of routines. They have the same names, but take double precision arguments. To obtain them, link in the library "dislin_d".
As a beginner in Z3, I am wondering if there is a way to make Z3Py work with a predefined Python function. Following is a small example which explains my question.
from z3 import *
def f(x):
if x > 0:
print " > 0"
return 1
else:
print " <= 0"
return 0
a=Int('a')
s=Solver()
s.insert(f(a) == 0)
t = s.check()
print t
print a
m = s.model()
print m
f(x) is a function defined in python. When x <= 0, f(x) returns 0. I add a constraint s.insert(f(a) == 0) and hope that Z3 can find a appropriate value for variable "a" (e.g. -3). But these codes are not working correctly. How should I change it?
(Please note that I need f(x) defined outside Z3, and then is called by Z3. )
What I am trying to do is calling a predefined function provided by a graph library without translating it to Z3. I am using the NetworkX library, and some codes are given as following:
import networkx as nx
G1=nx.Graph()
G1.add_edge(0,1)
G2=nx.Graph()
G2.add_edge(0,1)
G2.add_edge(1,2)
print(nx.is_isomorphic(G1, G2))
#False
I need Z3 to help me find a vertex in G2 such that after removing this vertex, G2 is isomorphic to G1. e.g.
G2.remove_node(0)
print(nx.is_isomorphic(G1, G2))
#True
I think this will be tough if f is a general function (e.g., what if it's recursive?), although if you assume it has some structure (e.g., if then else), you might be able to write a simple translator. The issue is that Z3's functions are mathematical in nature and not directly equivalent to Python functions (see http://en.wikipedia.org/wiki/Uninterpreted_function ). If possible for your purpose, I would propose to go the opposite direction: define your function f in terms of Z3 constructs, then evaluate it within your program (e.g., using this method: Z3/Python getting python values from model ). If that won't work for you, please include some additional details on how you need to use the function. Here's a minimal example (rise4fun link: http://rise4fun.com/Z3Py/pslw ):
def f(x):
return If(x > 0, 1, 0)
a=Int('a')
s=Solver()
P = (f(a) == 0)
s.add(P)
t = s.check()
print t
print a
m = s.model()
print m
res = simplify(f(m[a])) # evaluate f at the assignment to a found by Z3
print "is_int_value(res):", is_int_value(res)
print res.as_long() == 0 # Python 0
print f(1)
print simplify(f(1)) # Z3 value of 1, need to convert as above