T && X is equivalent to "if( T) then run X"
T || X is equivalent to "if(!T) then run X"
I don’t exploit this too much in C/C++ because it’s hard to read (and therefore hard to keep track of it to make sure it’s bug free) and most often I’m interested in the output value so I have to watch out for the side effects. However this is common in Bash scripts
Domination Property
In languages that expressions evaluates to a value, sometimes if-statements can be replaced by short-circuit evaluation because short-circuit evaluation exploits the domination property of AND and OR logic operations:
When you FIRST run into the dominant value for the binary operation (0 for AND) and (1 for OR), evaluate no further (i.e. skip the rest) because rest won’t change the overall result away from the dominant value.
So in this use case (emulating if-then statements), what the latter expression X evaluates to or what the combined logic value is irrelevant. We are merely tricking the short-circuit mechanism to trip (short) to NOT evaluate based on what the earlier expression turned out. Action is the ‘norm’. Conditional inaction is the essence of this idiom.
The dual of domination property is idempotent, which is easier to reason because if pre-condition (say T) forces overall expression to boil down to the expression we want to conditionally execute (say X), we are stuck evaluating X if condition T is met.
\newcommand{\Hquad}{\hspace{0.5em}}
\begin{alignat*}{2}
1 \Hquad & \mathrm{AND} & \Hquad X = X \\
0 \Hquad & \mathrm{OR} & \Hquad X = X
\end{alignat*}
These 2 possibilities (domination and idempotency) partitions to space (choices) of possibilities (i.e. cover all possible combinations), in other words there are no other scenarios than described. So the precondition T decides whether you run X or not, which is the equivalent of an if-then statement.
Operator (function) view of logic domination [Functional programming perspective]
By grouping the first value and the binary logic operator with a pair of parenthesis, in dominance view
(0 AND) is also called the ‘clear’ operator
(1 OR) is also called the ‘set’ operator
but this view is not too interesting for our case because we are not interested in what the conditional expression and the overall expression evaluates to, which is signified by ‘clear’ and ‘set’.
On the other hand, (1 AND) and (0 OR) are pass-through (idempotent) operators which passes the evaluation to the latter expression X.
\newcommand{\Hquad}{\hspace{0.5em}}
\begin{alignat*}{2}
(1 \Hquad & \mathrm{AND}) \Hquad & \circ & \Hquad X = X \\
(0 \Hquad & \mathrm{OR}) \Hquad & \circ & \Hquad X = X
\end{alignat*}
Sean Eron Anderson (Stanford CS graphics lab)’s bit twiddling pages often shows a bunch of neat bit tricks, but it’s more like a recipe book than a unified way to summarize the common concepts behind them. Here’s my attempt. This page will get updated as I got the time and more useful insights collected.
Concept: Two ways to get two’s complement
This is the basics of most bit hacks below. Sometimes the definition itself is a bit trick on its own.
You can generalize it to an arbitrary number by subtracting -1 more under the bar on the left hand side and you will get +1 more on the right hand side. Every extra -1 under the bar (bit flips) shows up as +1 outside the bar (bit flips).
This matches the observation that complement schemes (one’s or two’s) both have increasing magnitude move in opposite directions for positive and negative numbers. Look at this table:
Unsigned
Binary
Two’s Complement
7
111
-1
6
110
-2
5
101
-3
4
100
-4
3
011
3
2
010
2
1
001
1
0
000
0
A very important observation that’d be used over and over blow is that in two’s complement, -1 is always a mask of all binary ‘1’s regardless of the word width.
This rule can also read as: magnitude offsets goes in opposite directions
Note that this is NOT distributing bit-flip to two addition/subtraction despite it resembles it with an important distinction that the sign of n changed without turning into (n-1). If it were to distribute, you’ll get (n-2) on the left-hand-side instead of the (n-1) term because the -1 would have been counted twice under distribution.
Bit flips simply doesn’t distribute over the 4 basic (algebraic field) operations. The two’s complement offset is done once and only once when you change the overall representation no matter how many components you break it down into. It’s merely done to shift over the -0 in one’s complement so there’s an extra space for an extra negative number which its positive counterpart is not representable without starting a new digit.
Note to self: the INT_MIN is just the sign bit of ‘1’ followed by all zeros after.
Concept: XOR can be used for bit flips or check for bit changes
Concept: Top bit holds the sign
Sounds simple, but if you keep in mind that (x<0) is really asking to see if the top bit is 1, you can check if two numbers has opposite signs without bit shifting it down by simply XOR-ing them (anything below the top bit are ignored) and use (x^y)<0 to check for the resulting top bit is 1, which signals that the sign bits are different.
Concept: Sign extensions (the top/sign bit gets drag-copied when right shifted)
When you right shift (in signed integers), the top (sign) bit gets drag-copied (sign extended) by the number of bits you right shifted. (Obviously for signed integers, right shifts are zero-filled)
Can exploit this to
drag the top (sign) bit all the way down to the bottom (so you either get all 1s or 0s) to provide a conditional mask based on the sign (see below)
1??????? \gg 7 \textnormal{ (i.e. type bit width - 1)} = 11111111_2 = -1_{10} \\
0??????? \gg 7 \textnormal{ (i.e. type bit width - 1)} = 00000000_2 = +0_{10} \\
Signed extensions also means a negative number will stay negative and a positive number will stay positive if you right shift
Sign extension behavior is not guaranteed by 1987 ANSI C, but it’s standard on pretty much anything more modern than that. Just make sure anything that uses this behavior are inlined (so the implementation can be easily swapped out), well documented/commented, and platform checks/switches are in place, and there’s a way to quickly check with the slower but platform independent implementation.
Concept: Getting a bit mask of a 1s (if true) and all 0s (if false)
The ability to convert a logic evaluation (condition) that gives
is the basis of many branchless ‘drop/keep this if that’ operations.
This can also be achieved by
putting a minus sign in front, such as -(cond) that will convert a (+1, 0) into (-1, 0), or
more efficiently exploiting sign extensions by dragging the top bit to the bottom (by right shifting by the type’s bit length-1)
computing absolute using the two’s complement’s definition of flip all bits and add 1: drag out a mask that shows that sign, which happens to be a do nothing if all 0s and flip all bits if all 1s in an xor, while the mask of all 1s, which is -1, when subtracted, becomes +1 needed to finish the two’s complement (and that’s subtract by 0 for already positive value).
Concept: sets all binary digits below it to a stream of 1s
When you count binary numbers up, you must exhaust all the lower digits by filling them with all 1s before you get to advance to (set) a new digit on the left of them. For example,
This can be exploited to create bit-masks that preserves all digits on the left of the first ‘1’ seen from the right (LSB), ‘0’ at that lowest (LSB) set bit (aka ‘1’), and all ‘1’s below it.
Binary digits are are the (1 or 0) coefficients of a linear combination of powers of 2. Having a loner ‘1’ (aka everything else is 0) means the number is a power of 2.
Being the lone ‘1’ bit in the number means every bit above it must be zero. Any ‘1’s above the right-most ‘1’ means it’s not the loner, hence not a power of 2.
If you subtract 1 from the power-of-2 number, only all bits below (not including) the line ‘1’ bit becomes 1, and that ‘1’ bit position become zero, and as mentioned before, all bits above it are 0s by definition since the ‘1’ we are working on is a loner.
Since the digits in and are mutually exclusive (see example below)
The xor approach does not work because the upper bits are invariant, so we cannot detect the presence of the upper set bits (upper ‘1’s). It unconditionally gives the same bit pattern (mask) marking the lowest first set bit and everything below it 1s and 0s for everything else above it. Which can be exploited to simplify counting the consecutive trailing zeros (from the right) by turning it into counting the contiguous 1s in this invariant pattern, or add 1 to it and binary search the position of the set bit and subtract 1 because the said bit was made into the invariant (xor) pattern as well so +1 move onto the next upper binary digit.
The or approach detects the presence of the upper set bits but it’s a pain to mask out the invariant lower 1s, which curiously you can do by XOR-ing with the invariant pattern generated by ]latex]2^n \textnormal{ xor } 2^n-1[/latex] or you can do AND-NOT-ing
Which and happens to already does the job by keeping the top bits (which non-zero value detects their presence) yet unconditionally clear the lowest set bit and everything below it.
The gut of is x & (x-1) maneuver is that it clears the bit from the lowest set bit and everything down below
clearLowestSetBitAndEverythingBelow(x): x & (x-1)
This is used by Brian W. Kernighan to count number of set bits by knocking them one off at a time starting from below. Of course the worst case scenario is when the 1s are so dense that the algorithm must go through every bit without jumping past the zeros.
However a special case escaped us, which is x=0. 0x0000 & 0xFFFF is 0, but 0 isn’t a power of 2 unless you consider the minus infinity power which is the territory of floating point anyway. This can be easily patched by making the result unconditionally false if x=0 in the first place.
isPowerOfTwo(x): x && ((x & (x-1))==0)
Note the logical && which means x is first tested for its non-zeroness (by boiling any non-zero value down to +1) and it also enables the efficient short-circuit evaluation which if x is false, which means the result is unconditionally false under &&, the rest are irrelevant so it’s not evaluated.
Concept: Look up table
This is unconditionally the O(1) way because you have a mask of every bit in the type ready and you could index by it. However the penalty is that a load operation could be expensive if not everything can fit in the register file.
breakpoint(): Python’s version of MATLAB’s keyboard() command
callable(): Like MATLAB’s isfunction() but it really checks if there’s a __call__ method
getattr()/hasattr(): MATLAB’s getfield()/isfield(). The 3rd parameter of getfield() is a shortcut to spit out a default if there’s no such field/attribute, which MATLAB doesn’t have
globals()/locals(): more convenient than MATLAB because the whole workspace (current variables) are accessed as a dictionary in Python by calling locals() and globals()
id(): memory address of the item where the variable (reference) is pointing to. Think of it as &x in C.
isinstance(): MATLAB’s isa()
next(): Python favors not actually computing the values until needed so instead it offers a generator (forward iterable) function that spits out one value at each time you kick it with next() and you can’t go back.
chr()/ord(): analogous to MATLAB’s char()/double() cast for characters
Python’s exponentiation is **, not ^ like most other languages (C does not have exponentiation symbol, and ^ was used for xor)
print(…, flush=false) allows a courtesy flush
repr(): MATLAB’s version of disp(), also overloadable standard interface
slice(): MATLAB’s equivalent of colon() special interface
Context Manager
@contextlib.contextmanager decorators basically splits a set-try-yield-finally boilerplate function into 3 parts: __enter__ (everything above yield), BODY (where the yield goes to) and __exit__ (everything below yield), since a with-as statement is a rigidly defined try-finally block, roughly like this:
with EXPR as f:
BODY(using f)
__enter__: f=EVAL(EXPR)
try:
# f isn't evaluated till yield
yield f # Goes to BODY
finally:
__exit__: cleanup(f)
Python uses garbage collectors, so onCleanup() might often work, but it’s not guaranteed to. So any code based on that should not be in production
Answer: Context Manager, a glorified try-catch (more specifically try-finally) block with a rigid structure. It’s a pain in the butt and not fun to deal with if you want to deviate from the native ContextManager that came with the resource opener
‘switch’-case is back as ‘match’-case (the advanced uses are different)
New Python finally supports it, ‘switch’ in C is called ‘match‘ in Python and there are many handy and intuitive syntax just like in MATLAB! Horray!
If you try to do anything fancy with mutables in the cases, be careful about the side effects!
Pass by Variable (Copy-on-Write) like MATLAB
Variables are by large references in Python. Everything including integers are some sort of classes (which are in turn dictionaries with special treatment to certain key names). The garbage collector scans for the last guy using that part of memory not referencing it anymore before cleaning it.
Python even have one ‘None’ for the entire universe with a gazillion things going on pointing to the same memory address where None is stored (that’s why None is idoimatically checked by ‘is’ keyword which checks the address for speed instead of ‘==’ which actually verify the contents for speed). If you look up the reference count (see garbage collector) for commonly used numbers like 1s and 0s, there are thousands of ‘users’ of it!
With C++, it’s a mixture. Complex objects are usually passed by reference for performance reasons but simple structs and data types can be passed as variables (C/C++’s nomenclature calls the non-reference/pointers variables though technically references/pointers are just the same integers identified as addresses) that gets cloned and destroyed when they move across function (stack) boundaries.
In MATLAB, they want it industrial strength, so that’d rather not allow anything insidious/non-transparent to happen in your code by keeping it all pass-by-variable, that is everything is supposed to be treated as different copies as it crosses function boundaries. For performance reason, they figured if you passed a big matrix just for the function to read, MATLAB doesn’t really have to clone that so under the hood you can peak the same matrix that belong to the caller. Once your function changes the contents (they are pretending that it’s a separate copy so of course you can), MATLAB painfully makes a whole copy of it (copy-on-write) which you then have to lug the 2nd (modified) copy around when it travels past function boundaries.
Python takes this idea a lot further by having anything that’s exactly the same (including None or string literals) to point to the same object until you ask to change the contents, then it makes a new copy for you to change and point to the new copy specifically for the variable name you are referencing with.
Answer: The way Python prevents variables passed as parameters passed into a function from getting modified is to separate variables into mutable (lists, dicts, sets), and immutable (tuples, frozendict is a package right now, frozenset, numerics, strings) types. Anything immutable going past the function boundary gets their own local copy.
Classes Boundaries
MATLAB and C++ has stringent access control, but not in Python. There’s not even const correctness. Just signal your intention with variable naming schemes like all caps and __ prefixes.
C++ do not separate helper functions and class (non-instance) methods. What C++ called static members are really just glorified free functions and global variables tucked under the namespace that happened to be in the class (classes started off as namespace for structs then people add features like overloading and dispatch mechanisms). partitioning the global workspace. Whether a scoped helper function call a scoped variable that happened in the same namespace is nothing special to C++
Python does separate these two concepts though. Class method in Python (decorated by @classmethod), on the other hand, are equivalent to C++’s static methods which they are not allowed to touch anything instance-specific, but they can access anything class-specific. Helper functions, which is called ‘Static Method‘ (decorated by @staticmethod) in Python cannot even touch anything specific to the class.
Variable arguments
C++ doesn’t generally do variable arguments because it defeats polymorphism that uses a function signatures (which is a list of your argument types) to figure out which function to dispatch.
MATLAB uses cell to pack variable arguments. The common idioms are varargin{:} and [varargout{1:nargout}]. To accommodate variable arguments, MATLAB have to give up polymorphism but they still have a little bit of it left: they do dispatch based on the first argument type and it’s very useful in avoiding a lot of stupid switching by detecting data types: just use a consistent function name interface and have each data type implement its own method with the same name.
In Python, there’s no such thing as multiple outputs (return variables) on Python: you output a list and it always gets unpacked (just like MATLAB’s deal() function) when you type a list out on left hand side. If the left hand side is a singleton, it will get the full list that’s still packed. If you write out the elements (which makes the left hand side a list), the returned list will have elements assigned to the left hand side depending on your syntax.
This is often a point of agony deciding on output format when I develop MATLAB code. Apparently TMW wondered the same thing too because their own factory code is all over the place on this too. Most of the time it’s not a good idea to have a context-dependent (depending on how many outputs the user supplied) even if you can technically do that by detecting nargout in MATLAB.
Answer: My recommendation is to make sure the simple, most common case got priority, and stuff the juicy side info in packaged data structures (such as array or cells/monads/lists) and stick to a fixed output format whether you are in Python or MATLAB
Late Binding in Lambda / Anonymous Functions: Capture it!
This often throw people off in Python. MATLAB uses early binding, which means when you created that anonymous function (aka lambda), the free variables (parameters that are not running, aka the input arguments to the lambda/anonymous-function) captured the snapshot of the local workspace at the moment the lambda/anonymous-function was created!
Python on the other hand, uses the same approach as C++: late binding. This means you have to explicitly capture (make a snapshot copy) the free variables if you want to associate it with the values when the anonymous function (lambda) was created, not to wait until the lambda was actually called/used to look for what values to use in the free variables.
P = 612
# P was not captured, thus late binding
f = lambda x : print{f'input/running:{x}, param/free:{P}')
# P was captured as p, thus early binding
g = lambda x, p=P: print{f'input/running:{x}, param/free:{p}')
P = 721
f(8964) # shows "input/running: 8964, param/free: 721"
g(8964) # shows "input/running: 8964, param/free: 612"
[This is probably common knowledge that are repeated in many different places, but I want to arrange it in the perspective that helps my other article to explain how this influence the idea of ContextManager in Python and why ContextManager is still a clumsy way and there is a much neater way to do tackle this classic cleanup problem]
In C, there’s no built-in exception handling. Yet the goal for cleanups is for all manually checked and handled conditions (‘exceptions’) to land exactly in the same graveyard where the resources stands a chance to be released before the program ends. This screams goto (or longjump which is a non-local goto that can march outside the current function) and indeed it’s the only legit use of the goto statement I know that doesn’t make the code more error prone and confusing by littering the end of all your loops with if(error){break;}.
With this feedback approach, all hell breaks loose if you later add another layer and forget to add this. The mistake will break the feedback chain and the code continues to run in the layer after the end of the the while loop you forgot to place the check in, which is an insidious bug if the unwanted execution are benign under most situations.
The break clause will also become meaningless (and compiler invalid) if you convert your loops to non-loops or when you work in the top layer which is likely not inside a loop (even if you are in a bare metal embedded system with a while(0) loop, you don’t want to break that either).
break is a black-list approach which denies the rest of the code in the loop from running when the first error struck. Without break, you can do the reverse (the white-list approach) and put all code after the first check in if(!error) check blocks to authorize their execution instead
One hack to use break statement at the top-layer (no-loop) is to wrap the top layer with a do{BLOCK}while(false); loop which runs once, but the intention is not intuitive from the code so I wouldn’t do this to other programmers who don’t know the idiom without making a TRY-CATCH-FINALLY macro.
// Messy approach without do-while loop wrapper hack in top layer
// Convention: error=0 (false) means success
// The error code matches the check# it fails in this example
int error = 0;
if( int* f = grab_resource_and_spit_zero_if_fail() )
{
// This is hell of messy if you are not in a loop
// that can take advantage of break-statement
//
// If you don't use breaks (which require it to be in a loop),
// you have to explicitly surround all code in if(!error) blocks
...
// Approach 1: Nesting
// Upside: Visually draws out what the logic relation is
// when you're doing checks all over the place
// It's hard to get it conceptually wrong
// (i.e. can debug blindly with mere semantics)
// Downside: more checks means more nests
// you either have excessive indentation
// or have fun tracking brackets
if( !is_fail_1() )
{
...
if( !is_fail_2() )
{
...
if( !is_fail_3() )
{
(you get the idea)
...
} else { error=3; }
} else { error=2; }
} else { error=1; }
// Approach 2: Linear approach
// Idea: Surround everything under if(!error) check.
// Error code will stick to the first error as
// any non-zero error will short-circuit the
// checks after it so the original error code stays
// Upside: No nesting. Easy to follow to recipe consistently
// WARNING: Thou shalt not be tempted to modify error code
// in if(!error) blocks!
// Downside: If you violate the cardinal rule above, unintended
// chunks of code in if(!error) blocks might run and
// it's hard to debug/discover
if(!error)
{
...
}
// this idiom is a branchless way to do
// if(!error){ if(is_fail_13){error=13;} }
// The error==0 should be placed in front to
// take advantage of the short-circuit evaluation
// to avoid actually running the check if there's
// pre-existing error
error = (error>0)*error + (error==0 && !is_fail_13())*13
if(!error)
{
...
}
error = (error>0)*error + (error==0 && !is_fail_14())*14
if(!error)
{
...
}
error = (error>0)*error + (error==0 && !is_fail_15())*15
if(!error)
{
...
}
// Now you are in the first loop so you are allowed to use break
for(...)
{
...
(is_fails 16 .. 41)
...
if( is_fail_42() )
{
error = 42;
break;
}
..
while(...)
{
...
(deep down in the nest)
...
(is_fails 43 .. 101)
...
if( is_fail_102() )
{
error = 102;
break;
}
...
}
if(error) { break; }
...
}
if(error) { break; }
...
clean_the_f_up(f);
}
// goto approach
if( int* f = grab_resource_and_spit_zero_if_fail() )
{
...
(is_fails #1 .. 18)
...
for(...)
{
...
(is_fails 19 .. 41)
...
if( is_fail_41() )
{
goto graveyard;
}
...
while(...)
{
...
(deep down in the nest)
...
(is_fails 43 .. 101)
...
if( is_fail_102() )
{
goto graveyard;
}
...
}
...
}
...
graveyard:
clean_the_f_up(f);
}
By jumping to the graveyard, we don’t need to litter the code with a long chain of error message/signal feedback and/or guard all chunks of code with if(!error) blocks, which is messy because it’s basically re-inventing a lightweight custom exception handling infrastructure that propagates the fault back to the top and give the intermediate layers a chance to intercept it.
As long as you are not using the goto approach to do complicated maneuvers and keep it simple: all faults go to the same bucket, no ifs-and-buts or detours (i.e. no code elsewhere/in-between can intercept the flow), it isn’t spaghetii code: there are no complicated code flow graphs, just every branch pointing to the same destination in one step. You don’t need to feel guilty about using the goto approach if your error handling flow is like this:
which its positive counterpart 
is not representable without starting a new digit.
sets all binary digits below it to a stream of 1s
and 