Why do easing/tweening function implementations often have multiple parameters? - animation

Most easing function collections I found in my life have complex function signatures, such as jQuery: function easing (x, t, b, c, d) { ... }. Examples:
https://github.com/kikito/tween.lua/blob/master/tween.lua
http://gizma.com/easing/#l
Why are all these parameters required? Wouldn't it be way easier to just implemente these functions as displayed on http://easings.net/ on a normalized scale, with
one input value between 0 and 1
one output value (usually, but not in special cases such as 'elastic') between 0 and 1
and wrap those to work with arbirtrary start/end times and values, using a function such as:
function wrapEasing(fn, startTime, endTime, now, startValue, endValue) {
var progress = (now - startTime) / (endTime - startTime);
var easedProgress = fn(progress);
return startValue + easedProgress * (endValue - startValue);
}
(This is more of a maths question, I used javascript syntax just as an example -- it applies to all programming languages.)
Yes, I found other examples, too:
https://github.com/CreateJS/TweenJS/blob/master/src/tweenjs/Ease.js
Question is -- why do many people do it the complicated way? Maybe because that would require functional programming?

Related

Removing mutability without losing speed

I have a function like this:
fun randomWalk(numSteps: Int): Int {
var n = 0
repeat(numSteps) { n += (-1 + 2 * Random.nextInt(2)) }
return n.absoluteValue
}
This works fine, except that it uses a mutable variable, and I would like to make everything immutable when possible, for better safety and readability. So I came up with an equivalent version that doesn't use any mutable variables:
fun randomWalk_seq(numSteps: Int): Int =
generateSequence(0) { it + (-1 + 2 * Random.nextInt(2)) }
.elementAt(numSteps)
.absoluteValue
This also works fine and produces the same results, but it takes 3 times longer.
I used the following way to measure it:
#OptIn(ExperimentalTime::class)
fun main() {
val numSamples = 100000
val numSteps = 15708
repeat(5) {
val randomWalkSamples: IntArray
val duration = measureTime {
randomWalkSamples = IntArray(numSamples) { randomWalk(numSteps) }
}
println(duration)
}
}
I know it's a bit hacky (I could have used JMH but this is just a quick test - at least I know that measureTime uses a monotonic clock). The results for the iterative (mutable) version:
2.965358406s
2.560777033s
2.554363661s
2.564279403s
2.608323586s
As expected, the first line shows it took a bit longer on the first run due to the warming up of the JIT, but the next 4 lines have fairly small variation.
After replacing randomWalk with randomWalk_seq:
6.636866719s
6.980840906s
6.993998111s
6.994038706s
7.018054467s
Somewhat surprisingly, I don't see any warmup time - the first line is always lesser duration than the following 4 lines, every time I run this. And also, every time I run it, the duration keeps increasing, with line 5 always being the greatest duration.
Can someone explain the findings, and also is there any way of making this function not use any mutable variables but still have performance that is close to the mutable version?
Your solution is slower for two main reasons: boxing and the complexity of the iterator used by generateSequence()'s Sequence implementation.
Boxing happens because a Sequence uses its types generically, so it cannot use primitive 32-bit Ints directly, but must wrap them in classes and unwrap them when retrieving the items.
You can see the complexity of the iterator by Ctrl+clicking the generateSequence function to view the source code.
#Михаил Нафталь's suggestion is faster because it avoids the complex iterator of the sequence, but it still has boxing.
I tried writing an overload of sumOf that uses IntProgression directly instead of Iterable<T>, so it won't use boxing, and that resulted in equivalent performance to your imperative code with the var. As you can see, it's inline and when put together with the { -1 + 2 * Random.nextInt(2) } lambda suggested by #Михаил Нафталь, then the resulting compiled code will be equivalent to your imperative code.
inline fun IntProgression.sumOf(selector: (Int) -> Int): Int {
var sum: Int = 0.toInt()
for (element in this) {
sum += selector(element)
}
return sum
}
Ultimately, I don't think you're buying yourself much in the way of code clarity by removing a single var in such a small function. I would say the sequence code is arguably harder to read. vars may add to code complexity in complex algorithms, but I don't think they do in such simple algorithms, especially when there's only one of them and it's local to the function.
Equivalent immutable one-liner is:
fun randomWalk2(numSteps: Int) =
(1..numSteps).sumOf { -1 + 2 * Random.nextInt(2) }.absoluteValue
Probably, even more performant would be to replace
with
so that you'll have one multiplication and n additions instead of n multiplications and (2*n-1) additions:
fun randomWalk3(numSteps: Int) =
(-numSteps + 2 * (1..numSteps).sumOf { Random.nextInt(2) }).absoluteValue
Update
As #Tenfour04 noted, there is no specific stdlib implementation for IntProgression.sumOf, so it's resolved to Iterable<T>.sumOf, which will add unnecessary overhead for int boxing.
So, it's better to use IntArray here instead of IntProgression:
fun randomWalk4(numSteps: Int) =
(-numSteps + 2 * IntArray(numSteps).sumOf { Random.nextInt(2) }).absoluteValue
Still encourage you to check this all with JMH
I think:"Removing mutability without losing speed" is wrong title .because
mutability thing comes to deal with the flow that program want to achieve .
you are using var inside function.... and 100% this var will not ever change from outside this function and that is mutability concept.
if we git rid off from var everywhere why we need it in programming ?

How to use stans integrate_ode x inputs?

Recently stan has added the integrate_ode method. Unfortunately the only documentation I can find is the stan reference manual (p.191ff). I have a model that would require some driving signal. As I understand the parameter x_r and x_i are supposed to be used for this.
For the sake of a concrete example lets assume I want to implement the example from the documentation with following change:
real[] sho(real t,
real[] y,
real[] theta,
real[] x_r,
int[] x_i) {
real dydt[2];
real input_signal; // Change from here!!!
input_signal <- how_to(t, x_r, x_i);
dydt[1] <- y[2] + input_signal; // Change to here!!!
dydt[2] <- -y[1] - theta[1] * y[2];
return dydt;
}
the input signal is supposed to be a time series that is inputted - let's say I submit input_signal_vector <- sin(t) + rnorm(T, sd=0.1) (which is supposed to be a signal at the time points in ts) and I plan to use for input_signal the closest value in time.
The only way I can imagine is one could concat ts and input_signal_vector in x_r and then a search in this array. But I can not imagine this is the intended use of these parameter. It would also be extremely inefficient.
So if someone could show how such a case is supposed to be solved I would be very grateful.

Pass parameters between method name

I was wondering if you know of any programming language in which we can pass parameters inside method name. I'm guessing this could improve the code readability. I.e.
Lets say I want to multiply to integers in a method. Normally my method declaration would be something like:
function multiply(int a, int b){
return a*b;
}
However, it may be nice to be able to define it this way also:
function multiply (int a) times (int b){
return a*b;
}
This way, we could make a more explicit call in the code by calling:
var c = multiply(4)times(2);
This could have a greater impact on more complicated code and programming syntax.
Do you know if something like this exists?
Of course, there is Smalltalk which is really expressive with its keyword messages...
n := collection size // 2.
head := collection copyFrom: 1 to: n.
Other than that, you will find that in ADA or Python, and probably some others you can prefix each argument with a key (which should match the function parameter names)...

Compound Expressions in a Function in Mathematica

I wanted to calculate the power sum S_p(x) = 1^p + 2^p + 3^p + ... + x^p using the code
powersum[x_,p_]:=sum=0;For[i=1,i<x,i++,sum=sum+i^p];sum
but it seems to output 0 every time. Why does it do that?
As written, Mathematica is parsing your expression like this:
powersum[x_,p_]:=sum=0; (*Definition ended here*)
For[i=1,i<x,i++,sum=sum+i^p];
sum
You need to use to wrap your expression in parenthesis to make them all part of the function definition.
powersum[x_,p_]:=(sum=0;For[i=1,i<x,i++,sum=sum+i^p];sum)
Often it is preferable to use Module[]:
powersum[x_,p_]:=Module[{sum},sum=0;For[i=1,i<x,i++,sum=sum+i^p];sum]
or
powersum[x_,p_]:=Module[{sum=0},For[i=1,i<x,i++,sum=sum+i^p];sum]
this is essentially the same as wrapping in () except sum is protected in a local context.
of course for this example you could as well use :
powersum[x_,p_]:=Sum[i^p,{i,1,x-1}]
or
powersum[x_, p_] := Range[x - 1]^p // Total

Best way to write a conversion function

Let's say that I'm writing a function to convert between temperature scales. I want to support at least Celsius, Fahrenheit, and Kelvin. Is it better to pass the source scale and target scale as separate parameters of the function, or some sort of combined parameter?
Example 1 - separate parameters:
function convertTemperature("celsius", "fahrenheit", 22)
Example 2 - combined parameter:
function convertTemperature("c-f", 22)
The code inside the function is probably where it counts. With two parameters, the logic to determine what formula we're going to use is slightly more complicated, but a single parameter doesn't feel right somehow.
Thoughts?
Go with the first option, but rather than allow literal strings (which are error prone), take constant values or an enumeration if your language supports it, like this:
convertTemperature (TempScale.CELSIUS, TempScale.FAHRENHEIT, 22)
Depends on the language.
Generally, I'd use separate arguments with enums.
If it's an object oriented language, then I'd recommend a temperature class, with the temperature stored internally however you like and then functions to output it in whatever units are needed:
temp.celsius(); // returns the temperature of object temp in celsius
When writing such designs, I like to think to myself, "If I needed to add an extra unit, what would design would make it the easiest to do so?" Doing this, I come to the conclusion that enums would be easiest for the following reasons:
1) Adding new values is easy.
2) I avoid doing string comparison
However, how do you write the conversion method? 3p2 is 6. So that means there are 6 different combinations of celsius, Fahrenheit, and kelvin. What if I wanted to add a new temperate format "foo"? That would mean 4p2 which is 12! Two more? 5p2 = 20 combination. Three more? 6p2 = 30 combinations!
You can quickly see how each additional modification requires more and more changes to the code. For this reason I don't do direct conversions! Instead, I do an intermediate conversion. I'd pick one temperature, say Kelvin. And initially, I'd convert to kelvin. I'd then convert kelvin to the desired temperature. Yes, It does result in an extra calculation. However, it makes scalling the code a ton easier. adding adding a new temperature unit will always result in only two new modifications to the code. Easy.
A few things:
I'd use an enumerated type that a syntax checker or compiler can check rather than a string that can be mistyped. In Pseudo-PHP:
define ('kCelsius', 0); define ('kFarenheit', 1); define ('kKelvin', 2);
$a = ConvertTemperature(22, kCelsius, kFarenheit);
Also, it seems more natural to me to place the thing you operate on, in this case the temperature to be converted, first. It gives a logical ordering to your parameters (convert -- what? from? to?) and thus helps with mnemonics.
Your function will be much more robust if you use the first approach. If you need to add another scale, that's one more parameter value to handle. In the second approach, adding another scale means adding as many values as you already had scales on the list, times 2. (For example, to add K to C and F, you'd have to add K-C, K-F, C-K, and C-F.)
A decent way to structure your program would be to first convert whatever comes in to an arbitrarily chosen intermediate scale, and then convert from that intermediate scale to the outgoing scale.
A better way would be to have a little library of slopes and intercepts for the various scales, and just look up the numbers for the incoming and outgoing scales and do the calculation in one generic step.
In C# (and probaly Java) it would be best to create a Temperature class that stores temperatures privately as Celcius (or whatever) and which has Celcius, Fahrenheit, and Kelvin properties that do all the conversions for you in their get and set statements?
Depends how many conversions you are going to have. I'd probably choose one parameter, given as an enum: Consider this expanded version of conversion.
enum Conversion
{
CelsiusToFahrenheit,
FahrenheitToCelsius,
KilosToPounds
}
Convert(Conversion conversion, X from);
You now have sane type safety at point of call - one cannot give correctly typed parameters that give an incorrect runtime result. Consider the alternative.
enum Units
{
Pounds,
Kilos,
Celcius,
Farenheight
}
Convert(Unit from, Unit to, X fromAmount);
I can type safely call
Convert(Pounds, Celcius, 5, 10);
But the result is meaningless, and you'll have to fail at runtime. Yes, I know you're only dealing with temperature at the moment, but the general concept still holds (I believe).
I would choose
Example 1 - separate parameters: function convertTemperature("celsius", "fahrenheit", 22)
Otherwise within your function definition you would have to parse "c-f" into "celsius" and "fahrenheit" anyway to get the required conversion scales, which could get messy.
If you're providing something like Google's search box to users, having handy shortcuts like "c-f" is nice for them. Underneath, though, I would convert "c-f" into "celsius" and "fahrenheit" in an outer function before calling convertTemperature() as above.
In this case single parameters looks totally obscure;
Function convert temperature from one scale to another scale.
IMO it's more natural to pass source and target scales as separate parameters. I definitely don't want to try to grasp format of first argument.
I would make an enumeration out of the temperature types and pass in the 2 scale parameters. Something like (in c#):
public void ConvertTemperature(TemperatureTypeEnum SourceTemp,
TemperatureTypeEnum TargetTemp,
decimal Temperature)
{}
I'm always on the lookout for ways to use objects to solve my programming problems. I hope this means that I'm more OO than when I was only using functions to solve problems, but that remains to be seen.
In C#:
interface ITemperature
{
CelciusTemperature ToCelcius();
FarenheitTemperature ToFarenheit();
}
struct FarenheitTemperature : ITemperature
{
public readonly int Value;
public FarenheitTemperature(int value)
{
this.Value = value;
}
public FarenheitTemperature ToFarenheit() { return this; }
public CelciusTemperature ToCelcius()
{
return new CelciusTemperature((this.Value - 32) * 5 / 9);
}
}
struct CelciusTemperature
{
public readonly int Value;
public CelciusTemperature(int value)
{
this.Value = value;
}
public CelciusTemperature ToCelcius() { return this; }
public FarenheitTemperature ToFarenheit()
{
return new FarenheitTemperature(this.Value * 9 / 5 + 32);
}
}
and some tests:
// Freezing
Debug.Assert(new FarenheitTemperature(32).ToCelcius().Equals(new CelciusTemperature(0)));
Debug.Assert(new CelciusTemperature(0).ToFarenheit().Equals(new FarenheitTemperature(32)));
// crossover
Debug.Assert(new FarenheitTemperature(-40).ToCelcius().Equals(new CelciusTemperature(-40)));
Debug.Assert(new CelciusTemperature(-40).ToFarenheit().Equals(new FarenheitTemperature(-40)));
and an example of a bug that this approach avoids:
CelciusTemperature theOutbackInAMidnightOilSong = new CelciusTemperature(45);
FarenheitTemperature x = theOutbackInAMidnightOilSong; // ERROR: Cannot implicitly convert type 'CelciusTemperature' to 'FarenheitTemperature'
Adding Kelvin conversions is left as an exercise.
By the way, it doesn't have to be more work to implement the three-parameter version, as suggested in the question statement.
These are all linear functions, so you can implement something like
float LinearConvert(float in, float scale, float add, bool invert);
where the last bool indicates if you want to do the forward transform or reverse it.
Within your conversion technique, you can have a scale/add pair for X -> Kelvin. When you get a request to convert format X to Y, you can first run X -> Kelvin, then Kelvin -> Y by reversing the Y -> Kelvin process (by flipping the last bool to LinearConvert).
This technique gives you something like 4 lines of real code in your convert function, and one piece of data for every type you need to convert between.
Similar to what #Rob #wcm and #David explained...
public class Temperature
{
private double celcius;
public static Temperature FromFarenheit(double farenheit)
{
return new Temperature { Farhenheit = farenheit };
}
public static Temperature FromCelcius(double celcius)
{
return new Temperature { Celcius = celcius };
}
public static Temperature FromKelvin(double kelvin)
{
return new Temperature { Kelvin = kelvin };
}
private double kelvinToCelcius(double kelvin)
{
return 1; // insert formula here
}
private double celciusToKelvin(double celcius)
{
return 1; // insert formula here
}
private double farhenheitToCelcius(double farhenheit)
{
return 1; // insert formula here
}
private double celciusToFarenheit(double kelvin)
{
return 1; // insert formula here
}
public double Kelvin
{
get { return celciusToKelvin(celcius); }
set { celcius = kelvinToCelcius(value); }
}
public double Celcius
{
get { return celcius; }
set { celcius = value; }
}
public double Farhenheit
{
get { return celciusToFarenheit(celcius); }
set { celcius = farhenheitToCelcius(value); }
}
}
I think I'd go whole hog one direction or another. You could write a mini-language that does any sort of conversion like units does:
$ units 'tempF(-40)' tempC
-40
Or use individual functions like the recent Convert::Temperature Perl module does:
use Convert::Temperature;
my $c = new Convert::Temperature();
my $res = $c->from_fahr_to_cel('59');
But that brings up an important point---does the language you are using already have conversion functions? If so, what coding convention do they use? So if the language is C, it would be best to follow the example of the atoi and strtod library functions (untested):
double fahrtocel(double tempF){
return ((tempF-32)*(5/9));
}
double celtofahr(double tempC){
return ((9/5)*tempC + 32);
}
In writing this post, I ran across a very interesting post on using emacs to convert dates. The take-away for this topic is that it uses the one function-per-conversion style. Also, conversions can be very obscure. I tend to do date calculations using SQL because it seems unlikely there are many bugs in that code. In the future, I'm going to look into using emacs.
Here is my take on this (using PHP):
function Temperature($value, $input, $output)
{
$value = floatval($value);
if (isset($input, $output) === true)
{
switch ($input)
{
case 'K': $value = $value - 273.15; break; // Kelvin
case 'F': $value = ($value - 32) * (5 / 9); break; // Fahrenheit
case 'R': $value = ($value - 491.67) * (5 / 9); break; // Rankine
}
switch ($output)
{
case 'K': $value = $value + 273.15; break; // Kelvin
case 'F': $value = $value * (9 / 5) + 32; break; // Fahrenheit
case 'R': $value = ($value + 273.15) * (9 / 5); break; // Rankine
}
}
return $value;
}
Basically the $input value is converted to the standard Celsius scale and then converted back again to the $output scale - one function to rule them all. =)
My vote is two parameters for conversion types, one for the value (as in your first example). I would use enums instead of string literals, however.
Use enums, if your language allows it, for the unit specifications.
I'd say the code inside would be easier with two. I'd have a table with pre-add, multiplty, and post-add, and run the value through the item for one unit, and then through the item for the other unit in reverse. Basically converting the input temperature to a common base value inside, and then out to the other unit. This entire function would be table-driven.
I wish there was some way to accept multiple answers. Based on everyone's recommendations, I think I will stick with the multiple parameters, changing the strings to enums/constants, and moving the value to be converted to the first position in the parameter list. Inside the function, I'll use Kelvin as a common middle ground.
Previously I had written individual functions for each conversion and the overall convertTemperature() function was merely a wrapper with nested switch statements. I'm writing in both classic ASP and PHP, but I wanted to leave the question open to any language.

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