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- Minor fixes regarding real numbers, unit and finalness.

1 <html>
2 <head>
3 <meta name="author" content="Christian Schoenebeck">
4 <title>Real Numbers, Units and Finalness</title>
5 <urlpath>Real_Numbers_Units_and_Finalness</urlpath>
6 <meta name="description" content="New NKSP Core Language Features: Support for real numbers, standard measuring units and finalness.">
7 <link rel="stylesheet" href="http://doc.linuxsampler.org/css/preview.css">
8 <script type="text/javascript" src="http://doc.linuxsampler.org/js/preview.js"></script>
9 </head>
10 <body>
11 <p>
12 As you might have seen from our change log, I've been recently working on
13 a bunch of new core features for our <a href="01_nksp.html">NKSP</a>
14 real-time instrument script engine, with the goal to make instrument
15 scripting more intuitive and less error prone, especially from a
16 musician's point of view.
17 </p>
18 <p>
19 The changes are quite substantial, so here is
20 a more detailed description of what's new, how to use those new
21 features, what's the motivation behind them, and also a discourse
22 about some of the associated language design (and implementation) aspects.
23 </p>
24 <note class="important">
25 Features described in this article refer to LinuxSampler version <b>2.1.1.svn16</b> (or higher).
26 So these features are not available in older versions of the sampler.
27 And since these are new development features, they still might be subject to change.
28 </note>
30 <h2 id="64bit">64-Bit Integers</h2>
31 <p>
32 First of all, integers, i.e. integer number literals (as e.g. <code lang="nksp">4294967295</code>), integer
33 variables (like <code lang="nksp">declare $foo := 4294967295</code>), or
34 integer array variables (like <code>declare %bar[3] := ( 1, 2, 3 ) </code>),
35 and all their arithmetics like
36 <code lang="nksp">($foo + 1024) / 24</code> and all built-in functions (as e.g.
37 <code>min()</code>), are now all 64 bit with <a href="01_nksp.html">NKSP</a>.<br>
38 <br>
39 I hear your "<i>Yaaawn</i>" at this point. You might be surprised though about the amount of
40 <a href="https://en.wikipedia.org/wiki/Diff">diff</a> involved
41 and how often people stumbled over undesired 32-bit truncation with their
42 scripts before. So that change alone reduced error-proneness tremendously.
43 But let's get on.
44 </p>
46 <h2 id="real_numbers">Real Numbers</h2>
47 <p>
48 You are finally no longer limited to integer math with <a href="01_nksp.html">NKSP</a>.
49 You can now also use floating point arithmetics which will make calculations,
50 that is mathematical formulas in your scripts much easier than before.
51 Sounds a bit more interesting, doesn't it?<br>
52 </p>
54 <h3 id="real_variables">Variables</h3>
55 <p>
56 We call those floating point numbers
57 <i title="One of the most important classes of numbers in mathematics where each <b>real number</b> represents a continous quantity qualified for reflecting a distance on a line, and hence real numbers are commonly used for the numerical value of measurements of physical quantities like e.g. length, temperature, mass, velocity.">
58 real numbers
59 </i> from now on and you can
60 write them like you probably already expected; in simple dotted notation like
61 <code>2.98</code>. Likewise there are new variable types for real numbers as well.
62 The syntax to declare a real number variable is:
63 </p>
64 <p>
65 <code lang="nksp">
66 declare ~??real-variable-name?? := ??initial-value??
67 </code>
68 </p>
69 <p>
70 Like e.g.:
71 </p>
72 <p>
73 <code lang="nksp">
74 declare ~foo := 3.14159265
75 </code>
76 </p>
77 <p>
78 So it looks pretty much the same as with integer variables, just that you use
79 "~" as prefix in front of the variable name instead of "$" that you would
80 use for integer variables <b>and</b> the values <b>must always</b> contain a dot so that the parser
81 can distinguish them clearly from integer numbers.
82 Moreover there is now also a real number array variable type which you can
83 declare like this:
84 </p>
85 <p>
86 <code lang="nksp">
87 declare ???real-array-variable-name??[??amount-of-elements??] := ( ??initial-values?? )
88 </code>
89 </p>
90 <p>
91 Like e.g.:
92 </p>
93 <p>
94 <code lang="nksp">
95 declare ?foo[4] := ( 0.1, 2.0, 46.238, 104.97 )
96 </code>
97 </p>
98 <p>
99 Once again, the only differences to integer array variables are that you use
100 "?" as prefix in front of the array variable name instead of "%" that you
101 would use for integer array variables, <b>and</b> that you <b>must always</b> use a
102 dot for each value being assigned.
103 And as with integer variables, if you omit to assign initial value(s) for
104 your real number variables or real array variables then they are automatically
105 initialized with zero value(s) (that is <code>0.0</code> actually).
106 </p>
107 <note class="remark">
108 I actually already had plans for implementing floating point support in
109 <i title="NKSP stands for 'is <b>N</b>ot <b>KSP</b>', which denotes its distinction to an existing proprietary language called <i>KSP</i>. NSKP is a script language specifically designed to write real-time capable software extensions to LinuxSampler's sampler engines that can be bundled individually with sounds by sound designers themselves.">NKSP</i>
110 much earlier, but I somehow had the feeling that <i>KSP</i> would add it as well.
111 And I though before "inventing" again some kind of new syntax set for this feature
112 and then having to somehow merge and maintain cross-compatibility between <i>KSP</i> syntax
113 and <i>NKSP</i> syntax, I decided to wait a bit, and it
114 eventually appeared now on <i>KSP</i> side, so it was a good point to finally fill
115 this gap in <i>NKSP</i>.
116 </note>
118 <h3 id="type_casting">Type Casting</h3>
119 <p>
120 Like <i>KSP</i> we are (currently) quite strict about your obligation to distinguish
121 clearly between integer numbers and real numbers with <i>NKSP</i>. That means blindly
122 mixing integers and real numbers e.g. in formulas, will currently cause a parser error
123 like in this example:
124 </p>
125 <p>
126 <code>~foo := (~bar + 1.9) / 24 { WRONG! }</code>
127 </p>
128 <p>
129 In this example you would simply use <code>24.0</code> instead of <code>24</code> to
130 fix the parser error:
131 </p>
132 <p>
133 <code>~foo := (~bar + 1.9) / 24.0 { correct }</code>
134 </p>
135 <p>
136 That's because, when you are mixing integer numbers and real numbers in mathematical
137 operations, like the division in the latter example, what was your intended data type that you
138 expected of the result of that division; a real number or an integer result? Because it
139 would not only mean a different data type, it might certainly also mean a completely
140 different result value accordingly.
141 </p>
142 <p>
143 That does not mean you were not allowed to mix real numbers with integers, it is just
144 that you have to make your point clear to the parser what your intention is. For that
145 purpose there are now 2 new built-in functions <code>int_to_real()</code> and
146 <code>real_to_int()</code> which you may use for required type casts (data type conversions).
147 So let's say you have a mathematical formula where you want to mix that formula with
148 a real number variable and an integer variable, then you might e.g. type cast the
149 integer variable like this:
150 </p>
151 <p>
152 <code>~bla := ~foo / int_to_real($bar)</code>
153 </p>
154 <p>
155 And since this is a very common thing to do, we also have 2 short-hand forms of these
156 2 built-in functions in <i>NKSP</i> which are simply <code>real()</code> and <code>int()</code>:
157 </p>
158 <p>
159 <code>~bla := ~foo / real($bar) { same as above, just shorter } </code>
160 </p>
161 <note>
162 The short-hand functions <code>real()</code> and <code>int()</code> only exist in
163 <i>NKSP</i>. They don't exist with <i>KSP</i>.
164 </note>
165 <note class="remark">
166 In future we might certainly lift this data type strictness and do it like many other
167 programming languages handle this: just showing a parser warning (not an error) on mixed
168 integer vs. real number expressions, and at the same time performing always an implied type cast
169 of the respective integer to a real number type automatically by the compiler.
170 </note>
172 <h3>Built-in Functions</h3>
173 <p>
174 What about real numbers and existing built-in functions? When you check our latest reference
175 documentation of <a href="01_nksp_reference.html">NKSP built-in functions</a>,
176 you will notice that most of them accept now both, integers and real numbers as arguments
177 to their function calls. You should be aware though that the precise acceptance of data
178 types and the resulting behaviour change, varies between the individual built-in functions,
179 which is due to the difference in purpose of all those numerous built-in functions.
180 </p>
181 <p>
182 For instance the data type of the result returned by <code>min()</code> and <code>max()</code>
183 function calls depends now on the data type being passed to those functions. That is
184 if you pass real numbers to those 2 functions then you'll get a real number as result;
185 if you pass integers instead then you'll get an integer as result instead.
186 </p>
187 <p>
188 Then there are functions, like e.g. the new math functions <code>sin()</code>, <code>cos()</code>,
189 <code>tan()</code>, <code>sqrt()</code>, which only accept real numbers as arguments (and
190 always return a real number as result). Trying to pass integers will cause a parser error,
191 because those particular functions are not really useful on integers at all.
192 </p>
193 <p>
194 Likewise the previously already existing functions <code>fade_in()</code> and <code>fade_out()</code>
195 accept now both integers and real numbers for their 2nd argument (<code>??duration-us??</code>),
196 but do not allow real numbers for their 1st argument (<code>??note-id??</code>), because for
197 a duration real numbers make sense, whereas for a <code>??note-id??</code>
198 real numbers would not make any sense and such an attempt is usually a result of some
199 programming error, hence you will get a parser error when trying to pass a real number
200 to the 1st argument of those 2 built-in functions.
201 </p>
202 <p>
203 There might also be differences how built-in functions handle mixed usage of integers
204 and real numbers as arguments, simultaniously for the same function call that is.
205 For instance
206 the <code>min()</code> and <code>max()</code> functions are very permissive and allow you to mix
207 an integer argument with a real number argument. In such mixed cases those 2 functions
208 will simply handle the integer argument as if it was a real number and hence the
209 result's data type would be a real number. So this would be Ok:
210 </p>
211 <p>
212 <code>
213 min(0.3, 300) { OK for this function: mixed real and integer arguments }
214 </code>
215 </p>
216 <p>
218 Yet other functions,
219 like the <code>search()</code>
220 function, are very strict regarding data type. So if you are passing an integer array as 1st argument to
221 the <code>search()</code> function then it only accepts an integer (scalar) as
222 2nd argument, and likewise if you are passing a real number array as 1st argument
223 then it only accepts a real number (scalar) as 2nd argument. Attempts passing
224 different types, or in a different way to that function, will cause a parser error.
225 </p>
226 <note>
227 Use common sense! The accepted data types of arguments and correspending
228 result's data type of built-in functions usually match with your intuition,
229 and if it does not for some reason, then
230 you always get a clear parser error message immediately when trying to pass a wrong data
231 type while typing your scripts (e.g. in Gigedit's script editor). And on doubt you can
232 always refer to the <a href="01_nksp_reference.html">reference documentation</a> for
233 details of course.
234 </note>
236 <h3>Comparing for Equalness</h3>
237 <p>
238 If you are also writing <i>KSP</i> scripts, then you probably already knew most of the things that I
239 described above about real numbers. But here comes an important difference that we
240 have when dealing with real numbers in <i>NKSP</i>: real number value comparison for equalness and unequalness.
241 </p>
242 <p>
243 In our automated
244 <a href="http://svn.linuxsampler.org/cgi-bin/viewvc.cgi/linuxsampler/trunk/src/scriptvm/tests/NKSPCoreLangTest.cpp?view=markup">NKSP core language test cases</a>
245 you find an example that looks
246 like this (slightly changed here for simplicity):
247 </p>
248 <p>
249 <code>
250 on init
251 declare ~a := 0.165
252 declare ~b := 0.185
253 declare ~x := 0.1
254 declare ~y := 0.25
256 if (~a + ~b = ~x + ~y)
257 message("Test succeeded")
258 else
259 message("Test failed")
260 end if
262 end on
263 </code>
264 </p>
265 <p>
266 When you add the values of those variables from this example in your head, you will see that the actual
267 test in that example theoretically boils down to comparing <code>if (0.35 = 0.35)</code>.
268 Hence this test should always succeed. At least
269 that's what one would expect if one would do the calculations above manually by humans
270 in the real world.
271 In practice though, when this script is executed on a computer, the numbers on both sides would
272 slightly deviate from <code>0.35</code>. These differences to the expected value are
273 actually extremely little, that is very tiny fractions of several digits behind the decimal point,
274 but the final consequence would still be nevertheless different values on both sides and this test "would" hence fail.
275 These small errors are due to the technical way
276 <a href="https://en.wikipedia.org/wiki/Floating-point_arithmetic">floating point numbers are encoded</a>
277 on any modern <i>CPU</i> which causes small calculation errors with these summations for instance.
278 Due to that very well known circumstance of floating point arithmetics on
279 CPUs, it is commonly discouraged with system programming languages like C/C++
280 to directly compare floating point numbers for equalness, nor for unequalness for that exact reason.
281 </p>
282 <p>
283 However the use case for the NKSP language is completely different from
284 system level programming languages like C/C++. We don't need to be so
285 conservative in many aspects those languages need to be. The musical context of
286 <i>NKSP</i> simply has different requirements. Simplicity and high level
287 handling is more important for <i>NKSP</i> than revealing bit by bit
288 of the actual CPU registers bare-bone directly to users of instrument scripts.
289 So I decided to implement
290 real number equal (<code>=</code> operator) and unequal comparison
291 (<code>#</code> operator) to automatically take the expected floating
292 point tolerances of the underlying CPU into account.
293 </p>
294 <p>
295 So in short: the
296 <u>test case example above does <b>not</b> fail with our <i>NKSP</i> implementation</u>!
297 </p>
298 <p>
299 That does not mean you can simply switch off your head when doing
300 real number arithmetics and subsequent comparisons of those calculations.
301 Because with every calculation you do, the total amount of calculation
302 error (caused by the utilized floating point processing hardware) increases,
303 so after a certain amount of subsequent calculations
304 our equal/unequal comparisons would fail as well after a certain point.
305 But most of the time you will have formulas which end up with a very
306 limited amount of floating point calculations before you eventually
307 do your comparisons, so in most cases you should just be fine. But keep
308 this issue in mind when doing e.g. numeric (large amount of subsequent)
309 calculations e.g. in <code>while</code> loops.
310 </p>
311 <p>
312 What about the other comparison operators like <code>&lt;</code>,
313 <code>&gt;</code>, <code>&lt;=</code>, <code>&gt;=</code>? Well,
314 those other comparison operators all behave like with system level
315 programming languages. So these comparison operators currently
316 do <b>not</b> take the mentioned floating point tolerances into
317 account and hence they behave differently than the <code>=</code>
318 and <code>#</code> operators with <i>NKSP</i>.
319 The idea was that those other
320 comparison operators are typically used for what mathematicians
321 call "transitivity". So they are used e.g. for sorting tasks
322 where there should always be a clear determinism of the
323 comparison results, and where execution speed is an issue as well.
324 Because the truth is also that our floating point tolerance
325 aware "equal" / "unequal" comparisons come with the price of
326 requiring execution of additional calculations on the underlying CPU.
327 </p>
329 <note class="remark">
330 You might wonder now, isn't this still sort of a hack? Wouldn't
331 there be a better way to implement real numbers in <i>NKSP</i> so that
332 all calculations would behave exactly as we would expect them from
333 theoretical math? The short answer is both <b>yes</b> and <b>no</b>.<br>
334 <br>
335 <b>Yes</b>, we could implement support for real numbers as so called
336 <a href="https://en.wikipedia.org/wiki/Computer_algebra_system">algebraic system</a>,
337 which would accomplish that real number calculations would always exactly
338 result as you would expect them to do from traditional mathematics,
339 like certain mathematical software applications use to do it
340 (e.g. <a href="https://en.wikipedia.org/wiki/Maple_(software)">Maple</a>).
341 However to achieve that we could no longer utilize hardware acceleration
342 of the CPU's floating point unit, because it is limited to floating point
343 values of fixed precision (e.g. either 32 bit and/or 64 bit).
344 Hence we would need to execute a huge amount of instructions on the CPU
345 instead for every single real number calculation in scripts, so there would
346 be a severe performance penalty.<br>
347 <br>
348 And <b>no</b>, we actually cannot do that in <i>NKSP</i> at all, because this kind of
349 complex real number implementation would require memory allocations at
350 runtime, which in turn would violate a key feature of <i>NKSP</i>
351 scripting: its guaranteed real-time stability and runtime determinism.
352 </note>
354 <h2 id="units">Standard Measuring Units</h2>
355 <p>
356 If you are coming from <i>KSP</i> then you are eventually going to think next
357 "WTF? What is this all about?". But hang with me, no matter how often you
358 wrote instrument scripts before, you will most
359 certainly regularly come into a situation like described next and we
360 have a convenient fix for that.
361 <p>
363 <h3 id="unit_literals">Unit Literals</h3>
364 <p>
365 Let's consider you wanted to pause your script at a certain point for let's say
366 1 second. Ok, you remember from the back of your head that you need to use the
367 built-in <code>wait()</code> function for that, but which value do you need to
368 pass exactly to achieve that 1 second break?
369 Would it be <code>wait(1000)</code>
370 or probably <code>wait(1000000)</code>? Of course now you reach out for the
371 reference documentation at this point and eventually find out that it
372 would actually be <code>wait(1000000)</code>. Not very intuitive. And
373 the large amount of zeros required does not help to make your code necessarily
374 more readable either, right?
375 </p>
376 <p>
377 So what about actually writing what we had in mind at first place:
378 </p>
379 <p>
380 <code>
381 wait(1s)
382 </code>
383 </p>
384 <p>
385 It couldn't be much clearer.
386 </p>
387 <p>
388 Or you want a break of 23 milliseconds instead? Then let's just write that!
389 </p>
390 <p>
391 <code>
392 wait(23ms)
393 </code>
394 </p>
395 <p>
396 Now let's consider another example: Say you wanted to reduce volume of some voices by 3.5 decibel.
397 You remember that was something like <code>change_vol(??note??, ??volume??)</code>,
398 but what would <code>??volume??</code> be exactly? Digging out the docs yet again you
399 find out the correct call was <code>change_vol($EVENT_ID, -3500)</code>.<br>
400 <br>
401 We can do better than that:
402 </p>
403 <p>
404 <code>
405 change_vol($EVENT_ID, -3.5dB)
406 </code>
407 </p>
408 <p>
409 You rather want a slight volume increase by just 56 milli dB instead?
410 </p>
411 <p>
412 <code>
413 change_vol($EVENT_ID, +56mdB)
414 </code>
415 </p>
416 <p>
417 Or let's lower the tuning of a note by -24 Cents:
418 </p>
419 <p>
420 <code>
421 change_tune($EVENT_ID, -24c)
422 </code>
423 </p>
424 <p>
425 I'm sure you got the point. We are naturally using standard measuring
426 units in our daily life without noticing their importance, but they actually help us a
427 lot to give some otherwise purely abstract numbers an intuitive meaning to us.
428 Hence it just made sense to add measuring units as core feature of the NKSP
429 language, their built-in functions, variables and whatever you do with them.
430 </p>
432 <h3>Calculating with Units</h3>
433 <p>
434 Having said that, these examples above were just meant as warm up appetizer.
435 Of course you can do much more with this feature than just passing them
436 literally to some built-in function call as we did above so far.
437 You can assign them to variables, too, like:
438 </p>
439 <p>
440 <code>
441 declare ~pitchLfoFrequency := 1.2kHz
442 </code>
443 </p>
444 <p>
445 You can use them in combinations with integers or real numbers, and of course
446 you can do all mathematical calculations and comparisons that you would
447 naturally be able to do in real life. For instance the following example
448 </p>
449 <code>
450 on init
451 declare $a := 1s
452 declare $b := 12ms
453 declare $result := $a - $b
454 message("Result of calculation is " &amp; $result)
455 end on
456 </code>
457 </p>
458 <p>
459 would print the text <code>"Result of calculation is 988ms"</code> to the terminal
460 (notice that <code>$a</code> and <code>$b</code> actually used different units here).<br>
461 <br>
462 Or the following example
463 </p>
464 <code>
465 on init
466 declare ~a := 2.0mdB
467 declare ~b := 3.2mdB
468 message( 4.0 * ( ~a + ~b ) / 2.0 + 0.1mdB )
469 end on
470 </code>
471 </p>
472 <p>
473 would print the text <code>"10.5mdB"</code> to the terminal.<br>
474 <br>
475 Or let's make this little value comparison check:
476 </p>
477 <p>
478 <code>
479 on init
480 declare ~foo := 999ms
481 declare ~bar := 1s
482 if (~foo &lt; ~bar)
483 message("Test succeeded")
484 else
485 message("Test failed")
486 end fi
487 end on
488 </code>
489 </p>
490 <p>
491 which will succeed of course
492 (notice again that <code>~foo</code> and <code>~bar</code> used different units here as well).<br>
493 <br>
494 So as you can see the units are not just eye candy for your code, they
495 are actually interpreted actively by the script engine appropriately such that all your
496 calculations, comparisons and function calls behave as
497 you would expect them to do from your real-life experience.
498 </p>
500 <h3>Unit Components</h3>
501 <p>
502 In the examples above you might have noticed that the units' components
503 were shown in different colors. That's not a glitch of the website,
504 that's intentional and in fact NKSP code on this website is in general,
505 automatically displayed in the same way as with e.g. Gigedit's instrument
506 script editor. So what's the deal?
507 </p>
508 <p>
509 If you take the value <code>6.8mdB</code> as an example, you have in front
510 the <code>??numeric component?? = 6.8</code> of course, followed
511 by the <code>??metric prefix?? = <span class="up">md</span></code> for
512 "milli deci" (which is always simply some kind of multiplication factor)
513 and finally the fundamental <code>??unit type?? = <span class="ut">B</span></code> for "Bel" (which actually gives the number its final meaning).
514 </p>
515 <p>
516 So here's where language design comes into play. From language point of view both
517 the <code>??numeric component??</code> and the optional <code>??metric prefix??</code>
518 are runtime features which may change at any time,
519 whereas the optional <code>??unit type??</code> is always
520 a constant, "sticky", parse-time feature that you may never change at runtime.
521 That means if you define a variable like e.g. <code>declare $foo := 1s</code>
522 that variable <code>$foo</code> is now firmly tied to the unit type "seconds" for your entire script.
523 You may change the variable's numeric component and metric prefix later on at any time like e.g.
524 <code>$foo := 8ms</code>, but you must not change the variable ever to a different
525 unit type later on like <code>$foo := 8Hz</code>. Trying to switch
526 the variable to a different unit type that way will cause a parser error.
527 Changing the fundamental unit type of a variable is not allowed, because it
528 would change the semantical meaning of the variable.
529 </p>
530 <note class="remark">
531 What may look like a lousy limitation of the technical implementation
532 is in fact an intentional language design decision and is actually a feature,
533 called <i>determinism</i>.
534 The price of this limitation of forcing unit types to be a constant parse time
535 feature of variables and expressions comes with the profit of buying substantial
536 error checks at parse time, and that in turn helps you to write more
537 reliable instrument scripts in a shorter amount of time. For instance no
538 matter how complex your mathematical formulas are in your scripts, the parser
539 will always be able to check already at parse-time whether the
540 final, evaluated results of your formulas and overall code that you pass to
541 built-in functions, will finally be of correct unit type expected by the
542 respective function that you are going to call with them as function arguments.
543 Or in other words: the parser is able to check the correct meaning of your formulas at parse-time.
544 So the parser will stop you immediately
545 from doing such and similar mistakes by raising a parser error immediately while you are typing
546 your script code. So you neither
547 have to load the script into the sampler, nor do you have to run and test the
548 code just to spot such kind of mistakes. You will always see them instantly
549 in the code editor while you are typing your code.
550 </note>
551 <p>
552 So getting back and proceed with an early example, this code would be fine:
553 </p>
554 <p>
555 <code>
556 on note
557 declare ~reduction := -3.5dB { correct unit type }
558 change_vol($EVENT_ID, ~reduction)
559 end note
560 </code>
561 </p>
562 <p>
563 That's Ok because the built-in function <code>change_vol()</code>
564 optionally accepts the unit <code>B</code> for its 2nd argument.
565 Whereas the following would immediately raise a parser error:
566 </p>
567 <p>
568 <code>
569 on note
570 declare ~reduction := -3.5kHz { WRONG unit type for change_vol() call! }
571 change_vol($EVENT_ID, ~reduction)
572 end note
573 </code>
574 </p>
575 <p>
576 That's because using the unit type Hertz for changing volume with the
577 built-in function <code>change_vol()</code> does not make any sense,
578 that built-in function expects a unit type suitable for volume changes,
579 not a unit type for frequencies, and hence it is clearly a
580 programming mistake. So getting this error in
581 practice, you may have simply picked a wrong variable by accident for
582 a certain function call for instance and the parser will immediately
583 point you on that undesired circumstance.
584 </p>
585 <p>
586 As another example, you may now also use units with the built-in random number
587 generating function like e.g. <code>random(100Hz, 5kHz)</code>. The function
588 would then return an arbitrary value between <code>100Hz</code> and <code>5kHz</code>
589 each time you call it that way, so that makes sense. But trying e.g. <code>random(100Hz, 5s)</code>
590 would not make any sense and consequently you would immediately get a parser
591 error that you are attempting to pass two different unit types to the <code>random()</code> function,
592 which is not accepted by this particular built-in function.
593 And these kinds of parse-time errors are always detected,
594 no matter whether you are literally passing constant
595 values like in the simple example here, but also through every other means like
596 variables and complex mathematical expressions.
597 </p>
598 <p>
599 The following tables list the unit types and metric prefixes currently supported by <i>NKSP</i>.
600 </p>
601 <p>
602 <table>
603 <tr>
604 <th>Unit Type</th> <th>Description</th> <th>Purpose</th>
605 </tr>
606 <tr>
607 <td><code>s</code></td>
608 <td>short for "seconds"</td>
609 <td>May be used for time durations.</td>
610 </tr>
611 <tr>
612 <td><code>Hz</code></td>
613 <td>short for "Hertz"</td>
614 <td>May be used for frequencies.</td>
615 </tr>
616 <tr>
617 <td><code>B</code></td>
618 <td>short for "Bel"</td>
619 <td>May be used for volume changes and other kinds of relative changes
620 (e.g. depth of envelope generators).</td>
621 </tr>
622 </table>
624 <table>
625 <tr>
626 <th>Metric Prefix</th> <th>Description</th> <th>Equivalent Factor</th>
627 </tr>
628 <tr>
629 <td><code>u</code></td>
630 <td>short for "micro"</td>
631 <td>10<sup>-6</sup>&nbsp;&nbsp;=&nbsp;&nbsp;0.000001</td>
632 </tr>
633 <tr>
634 <td><code>m</code></td>
635 <td>short for "milli"</td>
636 <td>10<sup>-3</sup>&nbsp;&nbsp;=&nbsp;&nbsp;0.001</td>
637 </tr>
638 <tr>
639 <td><code>c</code></td>
640 <td>short for "centi"</td>
641 <td>10<sup>-2</sup>&nbsp;&nbsp;=&nbsp;&nbsp;0.01</td>
642 </tr>
643 <tr>
644 <td><code>d</code></td>
645 <td>short for "deci"</td>
646 <td>10<sup>-1</sup>&nbsp;&nbsp;=&nbsp;&nbsp;0.1</td>
647 </tr>
648 <tr>
649 <td><code>da</code></td>
650 <td>short for "deca"</td>
651 <td>10<sup>1</sup>&nbsp;&nbsp;=&nbsp;&nbsp;10</td>
652 </tr>
653 <tr>
654 <td><code>h</code></td>
655 <td>short for "hecto"</td>
656 <td>10<sup>2</sup>&nbsp;&nbsp;=&nbsp;&nbsp;100</td>
657 </tr>
658 <tr>
659 <td><code>k</code></td>
660 <td>short for "kilo"</td>
661 <td>10<sup>3</sup>&nbsp;&nbsp;=&nbsp;&nbsp;1000</td>
662 </tr>
663 </table>
664 </p>
665 <p>
666 Of course there are much more standard unit types and metric prefixes than
667 those, but currently we only support those listed above. Simply because
668 I found these listed ones to be actually useful for instrument scripts.
669 </p>
670 <note class="important">
671 When changing tuning, which is commonly expected by musicians in "Cents",
672 like e.g.: <code>change_tune($EVENT_ID, -24c)</code>, you might have noticed
673 already from the markup color here, that this is actually not handled as a unit
674 type by the <i>NKSP</i> language and that's why it is not listed as
675 a unit type in the table above. So tuning changes in "Cents" is actually just a value
676 with metric prefix "centi" and without any unit type, since tuning changes
677 in "Cents" is really just a relative multiplication factor for changing the pitch of
678 a note depending on the current base frequency of the note.<br>
679 <br>
680 This might look a bit odd to you, it is semantically however absolutely correct
681 to handle tuning changes in "Cents" that way by the language. You can still also use expressions like
682 "milli Cents", e.g.: <code>change_tune($EVENT_ID, +324mc)</code>, which is also
683 valid since we (currently) allow a combination of up to 2 metric prefixes with <i>NKSP</i>.<br>
684 <br>
685 The obvious advantage of not making "Cents" a dedicated unit type is that we can
686 just use the character "c" in scripts both for tuning changes, as well as for conventional
687 "centi" metric usage like <code>1cs</code> ("one centi second").
688 The downside of this design decision (that is "Cents" being defined as metric prefix) on the other hand
689 means that we loose the previously described parse-time stickyness feature that we
690 would have with "real" unit types, and hence also loose some of the described
691 error detection mechanisms that we have with "real" unit types at parse time.<br>
692 <br>
693 <u>In practice that means:</u> you need to be a bit more cautious when doing calculations
694 with tuning values in "Cents" compared to other tasks like volume changes, because with every
695 calculation you do in your scripts, you might accidentally drop the "Cents" from your unit, which
696 eventually will cause e.g. the <code>change_tune()</code> function to
697 behave completely differently (since a value without any metric prefix
698 will then be interpreted by <code>change_tune()</code> to be a value in "milli cents",
699 exactly like this function did before introduction of units feature in <i>NKSP</i>).
700 </note>
702 <h3 id="unit_conversion">Unit Conversion</h3>
703 <p>
704 Even though you are not allowed to change the unit type of a variable itself
705 by assignment at runtime, that does not mean there was no way to get rid of
706 units or that you were unable to convert values from one unit type to a
707 different unit type. You can do that very easily actually with <i>NKSP</i>,
708 exactly as you learned in school; i.e. by multiplications and divisions.
709 </p>
710 <p>
711 Let's say you have a variable <code>$someFrequency</code> that you
712 use for controlling some LFO's frequency by script, and for some reason you really
713 want to use the same value of that variable (for what reason ever)
714 to change some volume with <code>change_vol()</code>, then all you have
715 to do is dividing the existing unit type away, and multiplying it
716 with the new unit type:
717 </p>
718 <p>
719 <code>
720 on note
721 declare $someFrequency := 100Hz
722 change_vol($EVENT_ID, $someFrequency / 1Hz * 1mdB)
723 end note
724 </code>
725 </p>
726 <p>
727 Which would convert the variable's original value <code>100Hz</code>
728 to <code>100mdB</code> before passing it to the <code>change_vol()</code>
729 function. So this actually did 3 things:
730 </p>
731 <p>
732 <ol>
733 <li>the divsion (by <code>/ 1Hz</code>) dropped the old unit type (Hertz),</li>
734 <li>the multiplication (by <code>* 1mdB</code>) added the new unit type (Bel)</li>
735 <li>and that multiplication also changed the metric prefix (to milli deci) before the result is finally passed to the <code>change_vol()</code> function.</li>
736 </ol>
737 </p>
738 <p>
739 And since <code>change_vol()</code> would now receive the value
740 in correct unit type, this overall solution is hence legal and accepted by the parser without any complaint.
741 And this type of unit conversion does not break any parse-time determinism
742 and error detection features either, since it is not touching the variable's
743 unit type directly (only the temporary value eventually being passed to the <code>change_vol()</code> function here),
744 and so the result of the unit conversion expressions above
745 can always reliably be evaluated by the parser at parse-time.
746 </p>
747 <note class="important">
748 There are some intended limitations when performing unit type conversions though.
749 For instance you are never allowed to multiply some unit type with another unit type
750 in <i>NKSP</i>, neither different unit types like e.g. <code>100Hz * 1B</code>, nor
751 with the same unit type like e.g. <code>4s * 8s</code>. That's because we don't have
752 any practical usage for e.g. "square seconds" or other kinds of mixed unit types
753 in instrument scripts.
754 So trying to create a number or variable with more than one unit type will always
755 raise a parser error. So keep that in mind and use common sense when writing
756 calculations with units. And like always: the parser will always point you on
757 misusage immediately.
758 </note>
760 <h3>Array Variables</h3>
761 <p>
762 And as we are at limitations regarding units:
763 Currently <b>unit types</b> are not accepted for array variables yet. <b>Metric prefixes</b>
764 are allowed though!
765 </p>
766 <p>
767 <code>
768 declare %foo[4] := ( 800, 1m, 14c, 43) { OK - metric prefixes, but no unit types }
769 declare %bar[4] := ( 800s, 1ms, 14kHz, 43mdB) { WRONG - unit types not allowed for arrays yet }
770 </code>
771 </p>
772 <p>
773 Main reason for that current limitation is that unlike with scalar variables,
774 accessing array variables at runtime with an index by yet another (runtime changeable)
775 variable might break the previously described parse-time determinism of unit types.
776 That means if we just take the array variable <code>%bar[]</code> declared above
777 and would access it in our scripts with another variable like:
778 </p>
779 <p>
780 <code>
781 %bar[$someVar]
782 </code>
783 </p>
784 <p>
785 then what would that unit type of that array access be? Notice that the array variable
786 <code>%bar[]</code> was initialized with 3 different unit types for its individual elements.
787 So the unit type of the array access would obviously depend on the precise
788 value of variable <code>$someVar</code>, which most probably will change at runtime and
789 hence the compiler would not know at parse-time yet.
790 </p>
791 <note class="remark">
792 This limitation will most probably be lifted later on by allowing exactly one unit type
793 for an array variable, so that the array would be initialized with exactly the same unit
794 type for all its elements to retain the parse-time determinism that we were talking about.
795 </note>
797 <h2 id="finalness">Finalness</h2>
798 <p>
799 Here comes another new core language feature of <i>NKSP</i> that you certainly don't
800 know from <i>KSP</i> (as it does not exist there), and which definitely requires an
801 elaborate explanation of what it is about: "finalizing" some value.
802 </p>
804 <h3>Default Relativity</h3>
805 <p>
806 When changing synthesis parameters, these are commonly <i>relative</i> changes, depending
807 on other modulation sources. For instance let's say you are using <code>change_vol()</code>
808 in your script to change the volume of voices of a note, then the actual, final volume
809 value being applied to the voices is not just the value that you passed to <code>change_vol()</code>,
810 but rather a combination of that value and values of other modulation sources of volume
811 like a constant gain setting stored with the instrument patch, as well as a continuously
812 changing value coming from an amplitude LFO
813 that you might be using in your instrument patch, and you might most certainly also use
814 an amplitude envelope generator which will also have its impact on the final volume of course.
815 All these individual volume values are multiplied with each other in real-time by the sampler's engine core
816 to eventually calculate the actual, final volume to be applied to the voices, like illustrated in the following
817 schematic figure.
818 </p>
819 <img src="nksp_multi_mods_rel.png" caption="Relative Modulation (Default Behaviour)">
820 <p>
821 This <i>relative</i> handling of synthesis parameters is a good thing, because multiple
822 modulation sources combined make up a vivid sound. However there are situations where this
823 combined behaviour for synthesis parameters is not what you want. Sometimes you want to be
824 able to just say in your script e.g. "Make the volume of those voices exactly -6dB. Period. I mean it!".
825 And that's exactly what the newly introduced "final" operator <code>!</code> does.
826 </p>
828 <h3>Final Operator</h3>
829 <p>
830 <code>
831 on note
832 declare $volume := -6dB
833 change_vol($EVENT_ID, !$volume) { '!' makes value read from variable $volume to become 'final' }
834 end note
835 </code>
836 </p>
837 <p>
838 By prepending an exclamation mark <code>!</code> in front of an expression as shown in the code above,
839 you mark that value of that expression to be "final",
840 wich means the value will bypass the values of all other modulation sources, so the
841 sampler will ignore all other modulation sources that may exist, and
842 will simply use your script's value exclusively for that synthesis parameter,
843 as illustrated in the following figure:
844 </p>
845 <img src="nksp_multi_mods_fin.png" caption="Force 'Finalness' by Script">
846 <p>
847 You can of course revert back at any time to let the sampler process that synthesis parameter
848 relatively again by calling <code>change_vol()</code> and just passing
849 a value for volume without "finalness" (i.e. without <code>!</code> operator) this time.
850 </p>
851 <p>
852 In the previous code example, the "finalness" was applied to the temporary value
853 being passed to the <code>change_vol()</code> function, it did not change
854 the information stored in variable <code>$volume</code> at all though. So this is different
855 from:
856 </p>
857 <p>
858 <code>
859 on note
860 declare $volume := !-6dB { store 'finalness' directly to variable $volume }
861 change_vol($EVENT_ID, $volume)
862 end note
863 </code>
864 </p>
865 <p>
866 In the latter code example the actual "finalness" is stored directly now
867 to the <code>$volume</code> variable instead. Both approaches
868 make sense depending on the actual use case. For instance if you only
869 need "finalness" in rare situations, then you might use the prior
870 solution by using the "final" operator just with the respective function call,
871 whereas in use cases where you would always apply the
872 <code>$volume</code> "finally" and probably need to pass it to several
873 <code>change_vol()</code> function calls at several places in your script,
874 then you might store the "finalness" information directly to the variable instead.
875 </p>
876 <note class="remark">
877 <i>KSP</i> is also using the exclamation mark in front of variable names of string arrays.
878 Our usage of the exclamation mark character for this "finalness" feature
879 does not cause a language conflict with
880 that aspect though, because variable names (i.e. containing exclamation mark) are
881 resolved by the language before our unary <code>!</code> "final" operator is resolved in
882 expressions.
883 </note>
885 <h3>Mixed Finalness</h3>
886 <p>
887 Like with the other new language features described previously above, we also
888 have some potential ambiguities that we need to deal with when applying "finalness".
889 For instance consider this code:
890 </p>
891 <p>
892 <code>
893 on note
894 declare $volume := !-6dB { store 'finalness' directly to variable $volume }
895 change_vol($EVENT_ID, $volume + 2dB) { raises parser warning here ! }
896 end note
897 </code>
898 </p>
899 <p>
900 Should the resulting, expected volume change of <code>-4dB</code> be applied as
901 "final" value or as <i>relative</i> value instead?
902 Because the problem here is that <code>!-6dB</code> obviously means "final",
903 whereas </code>+ 2dB</code> is actually a <i>relative</i> value to be added.
904 </p>
905 <p>
906 In the current version of the sampler the value to be applied in this case would be "final", so you will not get a parser error,
907 however you will get a parser warning to make you aware about this ambiguity.
908 So to fix the example above, that is to to get rid of that parser warning, you can simply add an exclamation
909 mark in front of the other number as well like:
910 </p>
911 <p>
912 <code>
913 on note
914 declare $volume := !-6dB { store 'finalness' directly to variable $volume }
915 change_vol($EVENT_ID, $volume + !2dB) { '!' fixes parser warning }
916 end note
917 </code>
918 </p>
919 <p>
920 Also built-in functions will behave similarly as described above. Certain built-in functions
921 accept <i>finalness</i> for all of their arguments, some functions accept <i>finalness</i> for only certain
922 arguments and some functions won't accept <i>finalness</i> at all. Like with the other new core language
923 features always use common sense and quickly think about whether it would make sense if a
924 certain function would accept <i>finalness</i> for its argument(s). Most of the time your guess will be
925 right, and if not, then the parser will tell you immediately with either an error or warning, and the
926 <a href="01_nksp_reference.html">NKSP built-in functions reference</a> will help you out with
927 details in such rare cases where things might not be clear to you immediately.
928 </p>
930 <h3>Implied Finalness</h3>
931 <p>
932 Here comes the point where the feature circle of this article closes: the unit type "Bel" used
933 in the examples for the "final" operator above is somewhat special, since the unit type "Bel" is
934 in general used for <i>relative</i> quantities like i.e. volume changes. Tuning changes (i.e. in "Cents") are
935 also relative quantities.
936 </p>
937 <p>
938 However other unit types like "seconds" or "Hertz" are <i>absolute</i>
939 quantities. That means if you are using unit types "Hertz" or "seconds" in your scripts, then their
940 values are automatically applied as <i>implied</i> "final" values, as if you were using the <code>!</code>
941 operator for them in your code. The parser will raise a parser warning though to point you on that
942 circumstance.
943 </p>
944 <p>
945 The following table outlines this issue for the currently supported unit types.
946 </p>
947 <p>
948 <table>
949 <tr>
950 <th>Unit&nbsp;Type</th> <th>Relative</th> <th>Final</th> <th>Reason</th>
951 </tr>
952 <tr>
953 <td>None</td>
954 <td>Yes, by default.</td>
955 <td>Yes, if <code>!</code> is used.</td>
956 <td>If no unit type is used (which includes if <b>only</b> a metric prefix is used like e.g. <code>change_tune($EVENT_ID, -23c)</code>) then such values can be used both for relative, as well as for 'final' changes.</td>
957 </tr>
958 <tr>
959 <td><code>s</code></td>
960 <td>No, never.</td>
961 <td>Yes, always.</td>
962 <td>This unit type is naturally for absolute values only, which implies its value to be always 'final'.</td>
963 </tr>
964 <tr>
965 <td><code>Hz</code></td>
966 <td>No, never.</td>
967 <td>Yes, always.</td>
968 <td>This unit type is naturally for absolute values only, which implies its value to be always 'final'.</td>
969 </tr>
970 <tr>
971 <td><code>B</code></td>
972 <td>Yes, by default.</td>
973 <td>Yes, if <code>!</code> is used.</td>
974 <td>This unit type is naturally for relative changes. So this unit type can be used both for relative, as well as for 'final' changes.</td>
975 </tr>
976 </table>
977 </p>
978 <note class="remark">
979 Since unit types like <i>seconds</i> and <i>Hertz</i> are naturally always used for absolute values
980 in real life,
981 it might be considerable to drop the mentioned parser warnings which currently occur
982 if those units are used in scripts without having used the <code>!</code> operator.
983 </note>
985 <h3>Array Variables</h3>
986 <p>
987 As with unit types, the same current restriction applies to "finalness" in conjunction with
988 array variables at the moment: you may currently <b>not</b> apply "finalness" to the elements of array variables yet.
989 </p>
990 <p>
991 <code>
992 declare %foo[3] := ( !-6dB, -8dB, !2dB ) { WRONG - finalness not allowed for arrays (yet) ! }
993 </code>
994 </p>
995 <p>
996 The reason is also exactly the same, because <i>finalness</i> is a parse-time required information
997 and an array access by using yet another variable like e.g. <code>%foo[$someVar]</code> might
998 break that parse-time awareness of "finalness" for the compiler.
999 </p>
1000 <note class="remark">
1001 Likewise we might certainly lift that restriction later on by
1002 allowing <i>finalness</i> to be applied to arrays by initializing <b>all</b> members of an array to be all "final".
1003 </note>
1005 <h2>Backward Compatibility</h2>
1006 <p>
1007 You might be asking, what do all those new features mean to your existing instrument scripts,
1008 do they break your old scripts?
1009 </p>
1010 <p>
1011 The clear and short answer is:&nbsp;&nbsp;&nbsp;<b>No</b>, of course <u>they do <b>not</b> break your existing scripts</u>!
1012 </p>
1013 <p>
1014 Our goal was always to preserve constant behaviour for existing sounds,
1015 so that even ancient sound files in GigaSampler v1 format still would sound
1016 exactly as you heard them originally for the 1st time many, many years ago
1017 (probably with GigaSampler at that time).
1018 And that means the same policy applies to instrument scripts as well of course.
1019 </p>
1020 <p>
1021 You can also arbitrarily mix your existing instrument scripts by just partly using the new
1022 features described in this article at some sections of your scripts, while
1023 at the same time preserving your old code at other code sections. So these features
1024 are designed that they won't break anything existing, and that they always
1025 collaborate correctly in an arbitrary, mixed way with old <i>NKSP</i> code.
1026 </p>
1028 <h2>Status Quo</h2>
1029 <p>
1030 That's it!&nbsp;&nbsp;For now ...
1031 </p>
1032 <p>
1033 This is the current development state regarding these new <a href="01_nksp.html">NKSP</a>
1034 core language features. It might not be the final word though. I am aware certain
1035 aspects that I decided can be argued about (or maybe even entire features).
1036 And that's actually one of the reasons why I decided to write this (even for my habits)
1037 quite long and detailed article, which also explained the reasons for individual language design
1038 decisions that I took.
1039 </p>
1040 <p>
1041 You can however share your thoughts and arguments about these new features with us
1042 on the <a href="https://sourceforge.net/projects/linuxsampler/lists/linuxsampler-devel">mailing list</a>
1043 of course!
1044 </p>
1045 <note class="important">
1046 Keep in mind, the earlier you come up with suggestions for changes, the higher the chance
1047 that it might actually become changed and vice versa!&nbsp;&nbsp;&nbsp;(See "Backward Compatibility" above)
1048 </note>
1049 </body>
1050 </html>

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