Help/Math/SimpleNumber.html

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  38 <p class="p1"><span class="s1"><b>SimpleNumber<span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></b></span><b>one dimensional value</b></p>
  39 <p class="p2"><br></p>
  40 <p class="p1"><b>superclass: Number</b></p>
  41 <p class="p2"><br></p>
  42 <p class="p1">Represents numbers which can be represented by a single one dimensional value.</p>
  43 <p class="p2"><br></p>
  44 <p class="p1">Most of the Unary and Binary operations are also implemented by <a href="../UGens/Algebraic/UnaryOpUGen.html"><span class="s2">UnaryOpUGen</span></a></p>
  45 <p class="p1">and <a href="../UGens/Algebraic/BinaryOpUGen.html"><span class="s2">BinaryOpUGen</span></a>, so you can get more examples by looking at the help for those.</p>
  46 <p class="p2"><br></p>
  47 <p class="p2"><br></p>
  48 <p class="p3"><b>Unary Operations</b></p>
  49 <p class="p2"><br></p>
  50 <p class="p1"><b>neg</b></p>
  51 <p class="p2"><br></p>
  52 <p class="p1">negation</p>
  53 <p class="p2"><br></p>
  54 <p class="p1"><b>bitNot</b></p>
  55 <p class="p2"><br></p>
  56 <p class="p1">ones complement</p>
  57 <p class="p2"><br></p>
  58 <p class="p1"><b>abs</b></p>
  59 <p class="p2"><br></p>
  60 <p class="p1">absolute value.</p>
  61 <p class="p2"><br></p>
  62 <p class="p1"><b>ceil</b></p>
  63 <p class="p2"><br></p>
  64 <p class="p1">next larger integer.</p>
  65 <p class="p2"><br></p>
  66 <p class="p1"><b>floor</b></p>
  67 <p class="p2"><br></p>
  68 <p class="p1">next smaller integer</p>
  69 <p class="p2"><br></p>
  70 <p class="p1"><b>frac</b></p>
  71 <p class="p2"><br></p>
  72 <p class="p1">fractional part.</p>
  73 <p class="p2"><br></p>
  74 <p class="p1"><b>sign</b></p>
  75 <p class="p2"><br></p>
  76 <p class="p1">Answer -1 if negative, +1 if positive or 0 if zero.</p>
  77 <p class="p2"><br></p>
  78 <p class="p1"><b>squared</b></p>
  79 <p class="p2"><br></p>
  80 <p class="p1">The square of the number.</p>
  81 <p class="p2"><br></p>
  82 <p class="p1"><b>cubed</b></p>
  83 <p class="p2"><br></p>
  84 <p class="p1">The cube of the number.</p>
  85 <p class="p2"><br></p>
  86 <p class="p1"><b>sqrt</b></p>
  87 <p class="p2"><br></p>
  88 <p class="p1">The square root of the number.</p>
  89 <p class="p2"><br></p>
  90 <p class="p1"><b>exp</b></p>
  91 <p class="p2"><br></p>
  92 <p class="p1">e to the power of the receiver.</p>
  93 <p class="p2"><br></p>
  94 <p class="p1"><b>reciprocal</b></p>
  95 <p class="p2"><br></p>
  96 <p class="p1">1 / this</p>
  97 <p class="p2"><br></p>
  98 <p class="p1"><b>midicps</b></p>
  99 <p class="p2"><br></p>
 100 <p class="p1">Convert MIDI note to cycles per second</p>
 101 <p class="p2"><br></p>
 102 <p class="p1"><b>cpsmidi</b></p>
 103 <p class="p2"><br></p>
 104 <p class="p1">Convert cycles per second to MIDI note.</p>
 105 <p class="p2"><br></p>
 106 <p class="p1"><b>midiratio</b></p>
 107 <p class="p2"><br></p>
 108 <p class="p1">Convert an interval in semitones to a ratio.</p>
 109 <p class="p2"><br></p>
 110 <p class="p1"><b>ratiomidi</b></p>
 111 <p class="p2"><br></p>
 112 <p class="p1">Convert a ratio to an interval in semitones.</p>
 113 <p class="p2"><br></p>
 114 <p class="p1"><b>ampdb</b></p>
 115 <p class="p2"><br></p>
 116 <p class="p1">Convert a linear amplitude to decibels.</p>
 117 <p class="p2"><br></p>
 118 <p class="p1"><b>dbamp</b></p>
 119 <p class="p2"><br></p>
 120 <p class="p1">Convert a decibels to a linear amplitude.</p>
 121 <p class="p2"><br></p>
 122 <p class="p1"><b>octcps</b></p>
 123 <p class="p2"><br></p>
 124 <p class="p1">Convert decimal octaves to cycles per second.</p>
 125 <p class="p2"><br></p>
 126 <p class="p1"><b>cpsoct</b></p>
 127 <p class="p2"><br></p>
 128 <p class="p1">Convert cycles per second to decimal octaves.</p>
 129 <p class="p2"><br></p>
 130 <p class="p1"><b>log</b></p>
 131 <p class="p2"><br></p>
 132 <p class="p1">Base e logarithm.</p>
 133 <p class="p2"><br></p>
 134 <p class="p1"><b>log2</b></p>
 135 <p class="p2"><br></p>
 136 <p class="p1">Base 2 logarithm.</p>
 137 <p class="p2"><br></p>
 138 <p class="p1"><b>log10</b></p>
 139 <p class="p2"><br></p>
 140 <p class="p1">Base 10 logarithm.</p>
 141 <p class="p2"><br></p>
 142 <p class="p1"><b>sin</b></p>
 143 <p class="p2"><br></p>
 144 <p class="p1">Sine.</p>
 145 <p class="p2"><br></p>
 146 <p class="p1"><b>cos</b></p>
 147 <p class="p2"><br></p>
 148 <p class="p1">Cosine.</p>
 149 <p class="p2"><br></p>
 150 <p class="p1"><b>tan</b></p>
 151 <p class="p2"><br></p>
 152 <p class="p1">Tangent.</p>
 153 <p class="p2"><br></p>
 154 <p class="p1"><b>asin</b></p>
 155 <p class="p2"><br></p>
 156 <p class="p1">Arcsine.</p>
 157 <p class="p2"><br></p>
 158 <p class="p1"><b>acos</b></p>
 159 <p class="p2"><br></p>
 160 <p class="p1">Arccosine.</p>
 161 <p class="p2"><br></p>
 162 <p class="p1"><b>atan</b></p>
 163 <p class="p2"><br></p>
 164 <p class="p1">Arctangent.</p>
 165 <p class="p2"><br></p>
 166 <p class="p1"><b>sinh</b></p>
 167 <p class="p2"><br></p>
 168 <p class="p1">Hyperbolic sine.</p>
 169 <p class="p2"><br></p>
 170 <p class="p1"><b>cosh</b></p>
 171 <p class="p2"><br></p>
 172 <p class="p1">Hyperbolic cosine.</p>
 173 <p class="p2"><br></p>
 174 <p class="p1"><b>tanh</b></p>
 175 <p class="p2"><br></p>
 176 <p class="p1">Hyperbolic tangent.</p>
 177 <p class="p2"><br></p>
 178 <p class="p1"><b>rand</b></p>
 179 <p class="p2"><br></p>
 180 <p class="p1">Random number from zero up to the receiver, exclusive.</p>
 181 <p class="p2"><br></p>
 182 <p class="p1"><b>rand2</b></p>
 183 <p class="p2"><br></p>
 184 <p class="p1">Random number from -this to +this.</p>
 185 <p class="p2"><br></p>
 186 <p class="p1"><b>linrand</b></p>
 187 <p class="p2"><br></p>
 188 <p class="p1">Linearly distributed random number from zero to this.</p>
 189 <p class="p2"><br></p>
 190 <p class="p1"><b>bilinrand</b></p>
 191 <p class="p2"><br></p>
 192 <p class="p1">Bilateral linearly distributed random number from -this to +this.</p>
 193 <p class="p2"><br></p>
 194 <p class="p1"><b>sum3rand</b></p>
 195 <p class="p2"><br></p>
 196 <p class="p1">A random number<span class="Apple-converted-space">  </span>from -this to +this that is the result of summing three uniform random generators</p>
 197 <p class="p1">to yield a bell-like distribution. This was suggested by Larry Polansky as a poor man's gaussian.</p>
 198 <p class="p2"><br></p>
 199 <p class="p1"><b>distort</b></p>
 200 <p class="p2"><br></p>
 201 <p class="p1">a nonlinear distortion function.</p>
 202 <p class="p2"><br></p>
 203 <p class="p1"><b>softclip</b></p>
 204 <p class="p2"><br></p>
 205 <p class="p1">Distortion with a perfectly linear region from -0.5 to +0.5</p>
 206 <p class="p2"><br></p>
 207 <p class="p1"><b>scurve</b></p>
 208 <p class="p2"><br></p>
 209 <p class="p1">Map receiver in the onto an S-curve.</p>
 210 <p class="p2"><br></p>
 211 <p class="p4">((0..100) / 100 ).collect(_.scurve).plot</p>
 212 <p class="p5"><br></p>
 213 <p class="p1"><b>ramp</b></p>
 214 <p class="p2"><br></p>
 215 <p class="p1">Map receiver onto a ramp starting at 0.</p>
 216 <p class="p2"><br></p>
 217 <p class="p4">((-100..100) / 100 ).collect(_.ramp).plot</p>
 218 <p class="p2"><br></p>
 219 <p class="p1"><b>coin</b></p>
 220 <p class="p2"><br></p>
 221 <p class="p1">Answers a Boolean which is the result of a random test whose probability of success in a range from<span class="Apple-converted-space"> </span></p>
 222 <p class="p1">zero to one is <span class="s3">this</span>.</p>
 223 <p class="p2"><br></p>
 224 <p class="p1"><b>even</b></p>
 225 <p class="p2"><br></p>
 226 <p class="p1">Answer if the number is even.</p>
 227 <p class="p2"><br></p>
 228 <p class="p1"><b>odd</b></p>
 229 <p class="p2"><br></p>
 230 <p class="p1">Answer if the number is odd.</p>
 231 <p class="p2"><br></p>
 232 <p class="p1"><b>isPositive</b></p>
 233 <p class="p2"><br></p>
 234 <p class="p1">Answer if the number is &gt;= 0.</p>
 235 <p class="p2"><br></p>
 236 <p class="p1"><b>isNegative</b></p>
 237 <p class="p2"><br></p>
 238 <p class="p1">Answer if the number is &lt; 0.</p>
 239 <p class="p2"><br></p>
 240 <p class="p1"><b>isStrictlyPositive</b></p>
 241 <p class="p2"><br></p>
 242 <p class="p1">Answer if the number is &gt; 0.</p>
 243 <p class="p2"><br></p>
 244 <p class="p1"><b>booleanValue</b></p>
 245 <p class="p2"><br></p>
 246 <p class="p1">return true, if strictly positive ( &gt; 0), otherwise false (see <a href="../Core/Boolean.html"><span class="s2">Boolean</span></a>)</p>
 247 <p class="p2"><br></p>
 248 <p class="p1"><b>isValidUGenInput</b></p>
 249 <p class="p2"><br></p>
 250 <p class="p1">return false if receiver cannot be used in UGen.</p>
 251 <p class="p2"><br></p>
 252 <p class="p1"><b>magnitude</b></p>
 253 <p class="p2"><br></p>
 254 <p class="p1">returns abolute value (see <a href="Polar.html"><span class="s2">Polar</span></a>, <a href="Complex.html"><span class="s2">Complex</span></a>)</p>
 255 <p class="p2"><br></p>
 256 <p class="p1"><b>angle</b></p>
 257 <p class="p2"><br></p>
 258 <p class="p1">returns angle of receiver conceived as <a href="Polar.html"><span class="s2">Polar</span></a> or <a href="Complex.html"><span class="s2">Complex</span></a><span class="s2"> </span>number.</p>
 259 <p class="p2"><br></p>
 260 <p class="p1"><b>wait</b></p>
 261 <p class="p1"><span class="Apple-tab-span">     </span>within a routine, yield the number so that the clock can wait for this many beats.</p>
 262 <p class="p1"><span class="Apple-tab-span">     </span>(see <a href="../Core/Kernel/Routine.html"><span class="s2">Routine</span></a>)</p>
 263 <p class="p2"><span class="Apple-tab-span">     </span></p>
 264 <p class="p6"><span class="s4"><span class="Apple-tab-span">    </span></span>// create a routine by a function fork</p>
 265 <p class="p4"><span class="Apple-tab-span">     </span>(</p>
 266 <p class="p4"><span class="Apple-tab-span">     </span>fork {</p>
 267 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>1.wait;</p>
 268 <p class="p7"><span class="s4"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>"I did wait"<span class="s4">.postln;</span></p>
 269 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>1.0.rand.wait;</p>
 270 <p class="p7"><span class="s4"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>"No you didn't"<span class="s4">.postln;</span></p>
 271 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>2.wait;</p>
 272 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(1..).do { <span class="s2">|i|</span><span class="Apple-converted-space"> </span></p>
 273 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="s5">"yes I did"</span>.postln;<span class="Apple-converted-space"> </span></p>
 274 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>i.asFloat.rand.wait;<span class="Apple-converted-space"> </span></p>
 275 <p class="p7"><span class="s4"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>"no you didn't"<span class="s4">.postln;<span class="Apple-converted-space"> </span></span></p>
 276 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>i.wait<span class="Apple-converted-space"> </span></p>
 277 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>}</p>
 278 <p class="p4"><span class="Apple-tab-span">     </span>}</p>
 279 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 280 <p class="p5"><br></p>
 281 <p class="p1"><b>waitUntil</b></p>
 282 <p class="p1"><span class="Apple-tab-span">     </span>like wait, only specify a time (measured in beats of the current thread's clock)</p>
 283 <p class="p1"><span class="Apple-tab-span">     </span>(see <a href="../Core/Kernel/Routine.html"><span class="s2">Routine</span></a>)</p>
 284 <p class="p2"><br></p>
 285 <p class="p1"><b>sleep</b></p>
 286 <p class="p1"><span class="Apple-tab-span">     </span>make the current thread sleep, until woken up by re-scheduling. (see <a href="../Core/Kernel/Routine.html"><span class="s2">Routine</span></a>)</p>
 287 <p class="p2"><span class="Apple-tab-span">     </span><span class="s6"><span class="Apple-tab-span">   </span></span></p>
 288 <p class="p2"><br></p>
 289 <p class="p3"><b>Binary Operations</b></p>
 290 <p class="p2"><br></p>
 291 <p class="p1"><b>+ aNumber</b></p>
 292 <p class="p2"><br></p>
 293 <p class="p1">Addition</p>
 294 <p class="p2"><br></p>
 295 <p class="p1"><b>- aNumber</b></p>
 296 <p class="p2"><br></p>
 297 <p class="p1">Subtraction</p>
 298 <p class="p2"><br></p>
 299 <p class="p1"><b>* aNumber</b></p>
 300 <p class="p2"><br></p>
 301 <p class="p1">Multiplication</p>
 302 <p class="p2"><br></p>
 303 <p class="p1"><b>/ aNumber</b></p>
 304 <p class="p2"><br></p>
 305 <p class="p1">Division</p>
 306 <p class="p2"><br></p>
 307 <p class="p1"><b>% aNumber</b></p>
 308 <p class="p2"><br></p>
 309 <p class="p1">Modulo</p>
 310 <p class="p2"><br></p>
 311 <p class="p1"><b>div(aNumber)</b></p>
 312 <p class="p2"><br></p>
 313 <p class="p1">Integer Division</p>
 314 <p class="p2"><br></p>
 315 <p class="p1"><b>** aNumber</b></p>
 316 <p class="p2"><br></p>
 317 <p class="p1">Exponentiation</p>
 318 <p class="p2"><br></p>
 319 <p class="p1"><b>min(aNumber)</b></p>
 320 <p class="p2"><br></p>
 321 <p class="p1">Minimum</p>
 322 <p class="p2"><br></p>
 323 <p class="p1"><b>max(aNumber)</b></p>
 324 <p class="p2"><br></p>
 325 <p class="p1">Maximum</p>
 326 <p class="p2"><br></p>
 327 <p class="p1"><b>&amp; aNumber</b></p>
 328 <p class="p2"><br></p>
 329 <p class="p1">Bitwise And</p>
 330 <p class="p2"><br></p>
 331 <p class="p1"><b>| aNumber</b></p>
 332 <p class="p2"><br></p>
 333 <p class="p1">Bitwise Or</p>
 334 <p class="p2"><br></p>
 335 <p class="p1"><b>bitXor(aNumber)</b></p>
 336 <p class="p2"><br></p>
 337 <p class="p1">Bitwise Exclusive Or</p>
 338 <p class="p2"><br></p>
 339 <p class="p1"><b>bitHammingDistance(aNumber)</b></p>
 340 <p class="p2"><br></p>
 341 <p class="p1">Binary Hamming distance, or the count of bits that are not the same in the two numbers</p>
 342 <p class="p2"><br></p>
 343 <p class="p1"><b>bitTest(aNumber)</b></p>
 344 <p class="p2"><br></p>
 345 <p class="p1">Returns true if bit at index aNumber is set.</p>
 346 <p class="p2"><br></p>
 347 <p class="p1"><b>lcm(aNumber)</b></p>
 348 <p class="p2"><br></p>
 349 <p class="p1">Least common multiple</p>
 350 <p class="p2"><br></p>
 351 <p class="p1"><b>gcd(aNumber)</b></p>
 352 <p class="p2"><br></p>
 353 <p class="p1">Greatest common divisor</p>
 354 <p class="p2"><br></p>
 355 <p class="p1"><b>round(aNumber)</b></p>
 356 <p class="p2"><br></p>
 357 <p class="p1">Round to multiple of aNumber</p>
 358 <p class="p2"><br></p>
 359 <p class="p1"><b>trunc(aNumber)</b></p>
 360 <p class="p2"><br></p>
 361 <p class="p1">Truncate to multiple of aNumber</p>
 362 <p class="p2"><br></p>
 363 <p class="p1"><b>atan2(aNumber)</b></p>
 364 <p class="p2"><br></p>
 365 <p class="p1">Arctangent of (this/aNumber)</p>
 366 <p class="p2"><br></p>
 367 <p class="p1"><b>hypot(aNumber)</b></p>
 368 <p class="p2"><br></p>
 369 <p class="p1">Square root of the sum of the squares.</p>
 370 <p class="p2"><br></p>
 371 <p class="p1"><b>&lt;&lt; aNumber</b></p>
 372 <p class="p2"><br></p>
 373 <p class="p1">Binary shift left.</p>
 374 <p class="p2"><br></p>
 375 <p class="p1"><b>&gt;&gt; aNumber</b></p>
 376 <p class="p2"><br></p>
 377 <p class="p1">Binary shift right.</p>
 378 <p class="p2"><br></p>
 379 <p class="p1"><b>+&gt;&gt; aNumber</b></p>
 380 <p class="p2"><br></p>
 381 <p class="p1">Unsigned binary shift right.</p>
 382 <p class="p2"><br></p>
 383 <p class="p1"><b>fill(aNumber)</b></p>
 384 <p class="p2"><br></p>
 385 <p class="p1"><b>ring1(aNumber)</b></p>
 386 <p class="p2"><br></p>
 387 <p class="p1">(a * b) + a</p>
 388 <p class="p2"><br></p>
 389 <p class="p1"><b>ring2(aNumber)</b></p>
 390 <p class="p2"><br></p>
 391 <p class="p1">((a*b) + a + b)</p>
 392 <p class="p2"><br></p>
 393 <p class="p1"><b>ring3(aNumber)</b></p>
 394 <p class="p2"><br></p>
 395 <p class="p1">(a*a *b)</p>
 396 <p class="p2"><br></p>
 397 <p class="p1"><b>ring4(aNumber)</b></p>
 398 <p class="p2"><br></p>
 399 <p class="p1">((a*a *b) - (a*b*b))</p>
 400 <p class="p2"><br></p>
 401 <p class="p1"><b>difsqr(aNumber)</b></p>
 402 <p class="p2"><br></p>
 403 <p class="p1">(a*a) - (b*b)</p>
 404 <p class="p2"><br></p>
 405 <p class="p1"><b>sumsqr(aNumber)</b></p>
 406 <p class="p2"><br></p>
 407 <p class="p1">(a*a) + (b*b)</p>
 408 <p class="p2"><br></p>
 409 <p class="p1"><b>sqrdif(aNumber)</b></p>
 410 <p class="p2"><br></p>
 411 <p class="p1">(a - b)**2</p>
 412 <p class="p2"><br></p>
 413 <p class="p1"><b>sqrsum(aNumber)</b></p>
 414 <p class="p2"><br></p>
 415 <p class="p1">(a + b)**2</p>
 416 <p class="p2"><br></p>
 417 <p class="p1"><b>absdif(aNumber)</b></p>
 418 <p class="p2"><br></p>
 419 <p class="p1">(a - b).abs</p>
 420 <p class="p2"><br></p>
 421 <p class="p1"><b>amclip(aNumber)</b></p>
 422 <p class="p2"><br></p>
 423 <p class="p1">0<span class="Apple-converted-space">  </span>when<span class="Apple-converted-space">  </span>b &lt;= 0,<span class="Apple-converted-space">  </span>a*b<span class="Apple-converted-space">  </span>when<span class="Apple-converted-space">  </span>b &gt; 0</p>
 424 <p class="p2"><br></p>
 425 <p class="p1"><b>scaleneg(aNumber)</b></p>
 426 <p class="p2"><br></p>
 427 <p class="p1">a*b when a &lt; 0, otherwise a.</p>
 428 <p class="p2"><br></p>
 429 <p class="p1"><b>clip2(aNumber)</b></p>
 430 <p class="p2"><br></p>
 431 <p class="p1">clips receiver to +/- aNumber</p>
 432 <p class="p2"><br></p>
 433 <p class="p1"><b>excess(aNumber)</b></p>
 434 <p class="p2"><br></p>
 435 <p class="p1">Returns the difference of the receiver and its clipped form: (a - clip2(a,b)).</p>
 436 <p class="p2"><br></p>
 437 <p class="p1"><b>&lt;! aNumber</b></p>
 438 <p class="p2"><br></p>
 439 <p class="p1">Return the receiver. aNumber is ignored.</p>
 440 <p class="p2"><br></p>
 441 <p class="p1"><b>asFraction(denominator, fasterBetter)</b></p>
 442 <p class="p2"><br></p>
 443 <p class="p1">Return an array of denominator and divisor of the nearest and smallest fraction</p>
 444 <p class="p2"><br></p>
 445 <p class="p1"><b>rrand(aNumber)</b></p>
 446 <p class="p2"><br></p>
 447 <p class="p1">Returns a random number in the interval ]a, b[. If both a and b are Integer then the result will be an Integer.</p>
 448 <p class="p2"><br></p>
 449 <p class="p1"><b>exprand(aNumber)</b></p>
 450 <p class="p2"><br></p>
 451 <p class="p1">Returns an exponentially distributed random number in the interval ]a, b[. Always returns a Float.</p>
 452 <p class="p2"><br></p>
 453 <p class="p1"><b>gauss(standardDeviation)</b></p>
 454 <p class="p2"><br></p>
 455 <p class="p1">Returns a gaussian distributed random number. Always returns a Float.</p>
 456 <p class="p2"><span class="Apple-tab-span">     </span></p>
 457 <p class="p4">(0..1000).collect { |num| gauss(0.0, num) }.plot;</p>
 458 <p class="p2"><br></p>
 459 <p class="p2"><br></p>
 460 <p class="p1"><b>nextTimeOnGrid(clock)</b></p>
 461 <p class="p2"><br></p>
 462 <p class="p1">Return the next possible multiple of the clock's beats.</p>
 463 <p class="p2"><br></p>
 464 <p class="p2"><br></p>
 465 <p class="p2"><br></p>
 466 <p class="p3"><b>N-ary Operations</b></p>
 467 <p class="p2"><br></p>
 468 <p class="p2"><br></p>
 469 <p class="p1"><b>degreeToKey(scale, stepsPerOctave)</b></p>
 470 <p class="p2"><br></p>
 471 <p class="p1"><span class="Apple-tab-span">     </span>the value is truncated to an integer and used as an index into an octave repeating table of note values.</p>
 472 <p class="p1"><span class="Apple-tab-span">     </span>Indices wrap around the table and shift octaves as they do</p>
 473 <p class="p1"><span class="Apple-tab-span">     </span>stepsPerOctave is 12 by default</p>
 474 <p class="p2"><span class="Apple-tab-span">     </span></p>
 475 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(</p>
 476 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>l = [0, 1, 5, 9, 11]; <span class="s8">// pentatonic scale</span></p>
 477 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(1, 2..15).collect { <span class="s2">|i|</span> i.degreeToKey(l, 12) }</p>
 478 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 479 <p class="p2"><br></p>
 480 <p class="p2"><br></p>
 481 <p class="p1"><b>keyToDegree(scale, stepsPerOctave)</b></p>
 482 <p class="p2"><br></p>
 483 <p class="p1"><span class="Apple-tab-span">     </span>inverse of degreeToKey.</p>
 484 <p class="p1"><span class="Apple-tab-span">     </span>stepsPerOctave is 12 by default</p>
 485 <p class="p2"><span class="Apple-tab-span">     </span></p>
 486 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(</p>
 487 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>l = [0, 1, 5, 9, 11]; <span class="s8">// pentatonic scale</span></p>
 488 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(60, 61..75).collect { <span class="s2">|i|</span> i.keyToDegree(l, 12) }</p>
 489 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 490 <p class="p4"><span class="Apple-tab-span">     </span>(</p>
 491 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>l = [0, 1, 5, 9, 11]; <span class="s8">// pentatonic scale</span></p>
 492 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(60, 61..75).postln.collect { <span class="s2">|i|</span> i.keyToDegree(l, 12).degreeToKey(l) }</p>
 493 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 494 <p class="p5"><span class="Apple-tab-span">     </span></p>
 495 <p class="p1"><b>nearestInList(list)</b></p>
 496 <p class="p2"><br></p>
 497 <p class="p1"><span class="Apple-tab-span">     </span>returns the value in the collection closest to this</p>
 498 <p class="p2"><span class="Apple-tab-span">     </span></p>
 499 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(</p>
 500 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>l = [0, 0.5, 0.9, 1];</p>
 501 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(0, 0.05..1).collect { |i| i.nearestInList(l) }</p>
 502 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 503 <p class="p2"><br></p>
 504 <p class="p2"><br></p>
 505 <p class="p1"><b>nearestInScale(scale, stepsPerOctave)</b></p>
 506 <p class="p2"><br></p>
 507 <p class="p1"><span class="Apple-tab-span">     </span>returns the value in the collection closest to this, assuming an octave repeating table of note values.</p>
 508 <p class="p1"><span class="Apple-tab-span">     </span>stepsPerOctave is 12 by default</p>
 509 <p class="p2"><span class="Apple-tab-span">     </span></p>
 510 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(</p>
 511 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>l = [0, 1, 5, 9, 11]; <span class="s8">// pentatonic scale</span></p>
 512 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(60, 61..76).collect { |i| i.nearestInScale(l, 12) }</p>
 513 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 514 <p class="p2"><span class="Apple-tab-span">     </span></p>
 515 <p class="p1"><b>partition(parts, min)</b></p>
 516 <p class="p2"><br></p>
 517 <p class="p1"><span class="Apple-tab-span">     </span>randomly partition a number into parts of at least min size.</p>
 518 <p class="p2"><br></p>
 519 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>75.partition(8, 3);</p>
 520 <p class="p4"><span class="Apple-tab-span">     </span>75.partition(75, 1);</p>
 521 <p class="p2"><br></p>
 522 <p class="p2"><br></p>
 523 <p class="p1"><b>asTimeString(precision, maxDays = 365, dropDaysIfPossible = true)</b></p>
 524 <p class="p2"><br></p>
 525 <p class="p1"><span class="Apple-tab-span">     </span>returns a string corresponding to the days:hours:minutes:seconds<span class="Apple-converted-space"> </span></p>
 526 <p class="p1"><span class="Apple-tab-span">     </span>based on the receiver as number of seconds.</p>
 527 <p class="p1"><span class="Apple-tab-span">     </span><b>precision</b> is 0.001 (ms) by default</p>
 528 <p class="p1"><span class="Apple-tab-span">     </span>this format is inspired by ISO 8601 time interval display (truncated representation)</p>
 529 <p class="p1"><span class="Apple-tab-span">     </span>returns string "ddd:hh:mm:ss:ttt" where t is milliseconds</p>
 530 <p class="p1"><span class="Apple-tab-span">     </span>see <a href="../Collections/String.html"><span class="s9">String</span></a>:asSecs for complement</p>
 531 <p class="p2"><span class="Apple-tab-span">     </span></p>
 532 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(</p>
 533 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="s2">var</span> start = <span class="s2">Main</span>.elapsedTime;</p>
 534 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>fork { loop { (<span class="s2">Main</span>.elapsedTime - start).asTimeString.postln; 0.05.wait } };</p>
 535 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 536 <p class="p5"><br></p>
 537 <p class="p1"><b>equalWithPrecision(that, precision)</b></p>
 538 <p class="p2"><br></p>
 539 <p class="p1"><span class="Apple-tab-span">     </span>return true if receiver is closer to <b>that</b> than <b>precision</b>. (default for precision: 0.0001)</p>
 540 <p class="p2"><span class="Apple-tab-span">     </span></p>
 541 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>3.1.equalWithPrecision(3.0, 0.05); <span class="s8">// false</span></p>
 542 <p class="p4"><span class="Apple-tab-span">     </span>3.1.equalWithPrecision(3.0, 0.1); <span class="s8">// false</span></p>
 543 <p class="p4"><span class="Apple-tab-span">     </span>3.1.equalWithPrecision(3.0, 0.11); <span class="s8">// true</span></p>
 544 <p class="p5"><br></p>
 545 <p class="p5"><span class="Apple-tab-span">     </span></p>
 546 <p class="p1"><b>quantize(quantum, tolerance, strength)</b></p>
 547 <p class="p2"><b><span class="Apple-tab-span">  </span></b></p>
 548 <p class="p1"><b><span class="Apple-tab-span">  </span></b>round the receiver to the <b>quantum</b> (default: 1.0) allowing for a <b>tolerance</b> (default: 0.05).</p>
 549 <p class="p1"><span class="Apple-tab-span">     </span>How much the value is allowed to differ in the tolerance range is determined by <b>strength</b> (default: 1.0).</p>
 550 <p class="p2"><br></p>
 551 <p class="p4"><span class="Apple-tab-span">     </span>((0..10) / 10).collect { <span class="s2">|num|</span> num.quantize(1, 0.3, 0.5) }.postcs.plot;</p>
 552 <p class="p4"><span class="Apple-tab-span">     </span>((0..10) / 10).collect { <span class="s2">|num|</span> num.quantize(1, 0.6, 0.5) }.postcs.plot;</p>
 553 <p class="p4"><span class="Apple-tab-span">     </span>((0..10) / 10).collect { <span class="s2">|num|</span> num.quantize(1, 1.0, 0.5) }.postcs.plot;</p>
 554 <p class="p2"><br></p>
 555 <p class="p2"><br></p>
 556 <p class="p1"><b>linlin(inMin, inMax, outMin, outMax, clip)</b></p>
 557 <p class="p5"><br></p>
 558 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from an assumed linear input range (inMin..inMax)</p>
 559 <p class="p1"><span class="Apple-tab-span">     </span>to a linear output range (outMin..outMax). If the input exceeds the assumed input range.<span class="Apple-converted-space"> </span></p>
 560 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 561 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).</p>
 562 <p class="p2"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span></p>
 563 <p class="p4"><span class="Apple-tab-span">     </span>(0..10).collect { <span class="s2">|num|</span> num.linlin(0, 10, -4.3, 100) };<span class="Apple-converted-space"> </span></p>
 564 <p class="p4"><span class="Apple-tab-span">     </span>(0..10).linlin(0, 10, -4.3, 100); <span class="s8">// equivalent.</span></p>
 565 <p class="p5"><br></p>
 566 <p class="p2"><br></p>
 567 <p class="p1"><b>linexp(inMin, inMax, outMin, outMax, clip)</b></p>
 568 <p class="p5"><br></p>
 569 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from an assumed linear input range (inMin..inMax)</p>
 570 <p class="p1"><span class="Apple-tab-span">     </span>to an exponential output range (outMin..outMax).</p>
 571 <p class="p1"><span class="Apple-tab-span">     </span>The output range must not include zero.<span class="Apple-converted-space"> </span></p>
 572 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 573 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).</p>
 574 <p class="p2"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span></p>
 575 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(0..10).collect { <span class="s2">|num|</span> num.linexp(0, 10, 4.3, 100) };<span class="Apple-converted-space"> </span></p>
 576 <p class="p4"><span class="Apple-tab-span">     </span>(0..10).linexp(0, 10, 4.3, 100); <span class="s8">// equivalent.</span></p>
 577 <p class="p2"><b><span class="Apple-tab-span">  </span></b></p>
 578 <p class="p1"><b>explin(inMin, inMax, outMin, outMax, clip)</b></p>
 579 <p class="p5"><br></p>
 580 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from an assumed exponential input range (inMin..inMax)</p>
 581 <p class="p1"><span class="Apple-tab-span">     </span>to a linear output range (outMin..outMax). If the input exceeds the assumed input range.</p>
 582 <p class="p1"><span class="Apple-tab-span">     </span>The input range must not include zero.<span class="Apple-converted-space"> </span></p>
 583 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 584 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).<span class="s6"><span class="Apple-tab-span">      </span></span></p>
 585 <p class="p5"><br></p>
 586 <p class="p4"><span class="Apple-tab-span">     </span>(1..10).collect { <span class="s2">|num|</span> num.explin(0.1, 10, -4.3, 100) };<span class="Apple-converted-space"> </span></p>
 587 <p class="p4"><span class="Apple-tab-span">     </span>(1..10).explin(0.1, 10, -4.3, 100); <span class="s8">// equivalent.</span></p>
 588 <p class="p8"><span class="Apple-tab-span">     </span></p>
 589 <p class="p5"><br></p>
 590 <p class="p1"><b>expexp(inMin, inMax, outMin, outMax, clip)</b></p>
 591 <p class="p5"><br></p>
 592 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from an assumed exponential input range (inMin..inMax)</p>
 593 <p class="p1"><span class="Apple-tab-span">     </span>to an exponential output range (outMin..outMax). If the input exceeds the assumed input range.</p>
 594 <p class="p1"><span class="Apple-tab-span">     </span>Both input range and output range must not include zero.<span class="Apple-converted-space"> </span></p>
 595 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 596 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).</p>
 597 <p class="p2"><br></p>
 598 <p class="p4"><span class="Apple-tab-span">     </span>(1..10).collect { <span class="s2">|num|</span> num.expexp(0.1, 10, 4.3, 100) };<span class="Apple-converted-space"> </span></p>
 599 <p class="p4"><span class="Apple-tab-span">     </span>(1..10).expexp(0.1, 10, 4.3, 100); <span class="s8">// equivalent.</span></p>
 600 <p class="p8"><span class="Apple-tab-span">     </span></p>
 601 <p class="p1"><b>lincurve(inMin, inMax, outMin, outMax, curve, clip)</b></p>
 602 <p class="p5"><br></p>
 603 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from an assumed linear input range (inMin..inMax)</p>
 604 <p class="p1"><span class="Apple-tab-span">     </span>to an exponential curve output range (outMin..outMax). A <b>curve</b> is like the curve parameter in <a href="../Control/Env.html"><span class="s10">Env</span></a></p>
 605 <p class="p1"><span class="Apple-tab-span">     </span>Unlike with linexp, the output range may include zero.<span class="Apple-converted-space"> </span></p>
 606 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 607 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).</p>
 608 <p class="p2"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span></p>
 609 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(0..10).collect { <span class="s11">|num|</span> num.lincurve(0, 10, -4.3, 100, -3) };<span class="Apple-converted-space"> </span></p>
 610 <p class="p4"><span class="Apple-tab-span">     </span>(0..10).lincurve(0, 10, -4.3, 100, -3); <span class="s8">// equivalent.</span></p>
 611 <p class="p9"><span class="s8"><span class="Apple-tab-span">    </span></span>// different curves:</p>
 612 <p class="p4"><span class="Apple-tab-span">     </span>(</p>
 613 <p class="p4"><span class="Apple-tab-span">     </span>(-4..4).do { <span class="s12">|val|</span></p>
 614 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(0..100).collect(<span class="s12">_</span>.lincurve(0, 100, 0, 1, val)).plot</p>
 615 <p class="p4"><span class="Apple-tab-span">     </span>}</p>
 616 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 617 <p class="p8"><span class="Apple-tab-span">     </span></p>
 618 <p class="p8"><span class="Apple-tab-span">     </span></p>
 619 <p class="p1"><b>curvelin(inMin, inMax, outMin, outMax, curve, clip)</b></p>
 620 <p class="p5"><br></p>
 621 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from an assumed curve-exponential input range (inMin..inMax)</p>
 622 <p class="p1"><span class="Apple-tab-span">     </span>to a linear output range (outMin..outMax). If the input exceeds the assumed input range.</p>
 623 <p class="p1"><span class="Apple-tab-span">     </span>A<b> curve</b> is<span class="Apple-converted-space">  </span>like the curve parameter in <a href="../Control/Env.html"><span class="s10">Env</span></a><span class="s10">.</span></p>
 624 <p class="p1"><span class="Apple-tab-span">     </span>Unlike with explin, the input range may include zero.<span class="Apple-converted-space"> </span></p>
 625 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 626 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).<span class="s6"><span class="Apple-tab-span">      </span></span></p>
 627 <p class="p5"><br></p>
 628 <p class="p4"><span class="Apple-tab-span">     </span>(1..10).collect { <span class="s11">|num|</span> num.curvelin(0, 10, -4.3, 100, -3) };<span class="Apple-converted-space"> </span></p>
 629 <p class="p4"><span class="Apple-tab-span">     </span>(1..10).curvelin(0, 10, -4.3, 100, -3); <span class="s8">// equivalent.</span></p>
 630 <p class="p9"><span class="s8"><span class="Apple-tab-span">    </span></span>// different curves:</p>
 631 <p class="p4"><span class="Apple-tab-span">     </span>(</p>
 632 <p class="p4"><span class="Apple-tab-span">     </span>(-4..4).do { <span class="s13">|val|</span></p>
 633 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(0..100).collect(<span class="s13">_</span>.curvelin(0, 100, 0, 1, val)).plot</p>
 634 <p class="p4"><span class="Apple-tab-span">     </span>}</p>
 635 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 636 <p class="p8"><br></p>
 637 <p class="p8"><span class="Apple-tab-span">     </span></p>
 638 <p class="p1"><b>bilin(inCenter, inMin, inMax, outCenter, outMin, outMax, clip)</b></p>
 639 <p class="p5"><br></p>
 640 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from two assumed linear input ranges (inMin..inCenter) and (inCenter..inMax)</p>
 641 <p class="p1"><span class="Apple-tab-span">     </span>to two linear output ranges (outMin..outCenter) and (outCenter..outMax).</p>
 642 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 643 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).</p>
 644 <p class="p2"><br></p>
 645 <p class="p2"><br></p>
 646 <p class="p4"><span class="s7"><span class="Apple-tab-span">    </span></span>(</p>
 647 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>var center = 0.5, ctlCenter;</p>
 648 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>w = <span class="s2">Window</span>("bilin", Rect(100, 100, 200, 100)).front;</p>
 649 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>a = <span class="s2">Slider</span>(w, <span class="s2">Rect</span>(20, 20, 150, 20)).value_(0.5);</p>
 650 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>b = <span class="s2">Slider</span>(w, <span class="s2">Rect</span>(20, 45, 150, 20)).value_(0.5);</p>
 651 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>b.action = { center = b.value };</p>
 652 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>a.mouseDownAction = { ctlCenter = a.value };</p>
 653 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>a.action = {<span class="Apple-converted-space"> </span></p>
 654 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>b.value = a.value.bilin(ctlCenter, 0, 1, center, 0, 1);</p>
 655 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>};</p>
 656 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 657 <p class="p2"><br></p>
 658 <p class="p1"><b>biexp(inCenter, inMin, inMax, outCenter, outMin, outMax, clip)</b></p>
 659 <p class="p5"><br></p>
 660 <p class="p1"><span class="s6"><span class="Apple-tab-span">    </span></span>map the receiver from two assumed exponential input ranges (inMin..inCenter) and (inCenter..inMax)</p>
 661 <p class="p1"><span class="Apple-tab-span">     </span>to two linear output ranges (outMin..outCenter) and (outCenter..outMax).</p>
 662 <p class="p1"><span class="Apple-tab-span">     </span>The input range must not include zero.<span class="Apple-converted-space"> </span></p>
 663 <p class="p1"><span class="Apple-tab-span">     </span>If the input exceeds the input range, the following behaviours are specified by the <b>clip</b> argument:<span class="Apple-converted-space"> </span></p>
 664 <p class="p1"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><b>nil</b> (don't clip), <b>\max</b> (clip ceiling), <b>\min</b>, (clip floor), <b>\minmax</b> (clip both - this is default).<span class="Apple-tab-span">       </span></p>
 665 <p class="p2"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span></p>
 666 <p class="p6"><span class="s14"><span class="Apple-tab-span">   </span></span>// doesn't properly work yet.</p>
 667 <p class="p4"><span class="Apple-tab-span">     </span>(</p>
 668 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="s2">var</span> center = 0.5, ctlCenter;</p>
 669 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>w = <span class="s2">Window</span>(<span class="s5">"biexp"</span>, <span class="s2">Rect</span>(100, 100, 200, 100)).front;</p>
 670 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>a = <span class="s2">Slider</span>(w, <span class="s2">Rect</span>(20, 20, 150, 20)).value_(0.5);</p>
 671 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>b = <span class="s2">Slider</span>(w, <span class="s2">Rect</span>(20, 45, 150, 20)).value_(0.5);</p>
 672 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>b.action = { center = b.value };</p>
 673 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>a.mouseDownAction = { ctlCenter = a.value + 0.05 };</p>
 674 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>a.action = {</p>
 675 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>b.value = (a.value + 0.1).biexp(ctlCenter, 0.1, 1.1, center, 0, 1);</p>
 676 <p class="p4"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>};</p>
 677 <p class="p4"><span class="Apple-tab-span">     </span>)</p>
 678 <p class="p5"><span class="Apple-tab-span">     </span></p>
 679 <p class="p1"><b>lcurve(a, m, n, tau)</b></p>
 680 <p class="p2"><br></p>
 681 <p class="p1"><span class="Apple-tab-span">     </span>map the receiver onto an L-curve, using the formula: a * (m * exp(x) * rTau + 1) / (n * exp(x) * rTau + 1).</p>
 682 <p class="p1"><span class="Apple-tab-span">     </span>This is used for smoothing values and limiting them to a range. Defalt values: <b>a = 1; m = 0; tau = 1</b>.</p>
 683 <p class="p5"><span class="Apple-tab-span">     </span></p>
 684 <p class="p4"><span class="Apple-tab-span">     </span>(0..1000).normalize(-10, 10).collect { <span class="s2">|num|</span> num.lcurve }.plot;<span class="s7"><span class="Apple-tab-span">    </span></span></p>
 685 <p class="p2"><span class="Apple-tab-span">     </span></p>
 686 <p class="p5"><br></p>
 687 <p class="p1"><b>gaussCurve(a, b, c)</b></p>
 688 <p class="p2"><br></p>
 689 <p class="p1"><span class="Apple-tab-span">     </span>map the receiver onto a gauss function, using the formula: a * (exp(squared(this - b) / (-2.0 * squared(c))))<span class="Apple-tab-span">       </span>Defalt values: <b>a = 1; b = 0; c = 1</b></p>
 690 <p class="p5"><span class="Apple-tab-span">     </span></p>
 691 <p class="p4"><span class="Apple-tab-span">     </span>(0..1000).normalize(-10, 10).collect { <span class="s2">|num|</span> num.gaussCurve }.plot;</p>
 692 <p class="p5"><span class="Apple-tab-span">     </span></p>
 693 <p class="p5"><span class="Apple-tab-span">     </span></p>
 694 <p class="p1"><b>series(second, last)</b></p>
 695 <p class="p2"><br></p>
 696 <p class="p1"><span class="Apple-tab-span">     </span>return an artithmetic series from <b>this</b> over <b>second</b> to <b>last</b>. This is used in the shortcuts:</p>
 697 <p class="p1"><span class="Apple-tab-span">     </span>(0..100) or (1, 3 .. 17). if <b>second</b> is nil, it is one magnitude step towards last (1 or -1).</p>
 698 <p class="p5"><span class="Apple-tab-span">     </span></p>
 699 <p class="p4"><span class="Apple-tab-span">     </span>series(5, 7, 10);</p>
 700 <p class="p4"><span class="Apple-tab-span">     </span>series(5, nil, 10);</p>
 701 <p class="p4"><span class="Apple-tab-span">     </span>(5, 7 .. 10)<span class="Apple-tab-span">        </span></p>
 702 <p class="p5"><span class="Apple-tab-span">     </span></p>
 703 <p class="p5"><span class="Apple-tab-span">     </span></p>
 704 <p class="p1"><b>seriesIter(second, last)</b></p>
 705 <p class="p2"><br></p>
 706 <p class="p1"><span class="Apple-tab-span">     </span>return a <a href="../Core/Kernel/Routine.html"><span class="s2">Routine</span></a> that iterates over the numbers from <b>this</b> to <b>last</b>.<span class="Apple-converted-space"> </span></p>
 707 <p class="p1"><span class="Apple-tab-span">     </span>Since this is a lazy operation, <b>last</b> may be <b>inf</b>, generating an endless series<span class="Apple-converted-space"> </span></p>
 708 <p class="p10"><span class="s4"><span class="Apple-tab-span">   </span>(see also: <a href="../Language/ListComprehensions.html"><span class="s7">ListComprehensions</span></a>)</span></p>
 709 <p class="p5"><span class="Apple-tab-span">     </span></p>
 710 <p class="p4"><span class="Apple-tab-span">     </span>r = seriesIter(0, 5);</p>
 711 <p class="p4"><span class="Apple-tab-span">     </span>r.nextN(8);<span class="Apple-tab-span"> </span></p>
 712 <p class="p4"><span class="Apple-tab-span">     </span>r.nextN(8);<span class="Apple-tab-span"> </span></p>
 713 <p class="p5"><br></p>
 714 </body>
 715 </html>