code / tomo

   1 '\" t
   2 .\" Copyright (c) 2025 Bruce Hill
   3 .\" All rights reserved.
   4 .\"
   5 .TH Num 3 2025-11-29 "Tomo man-pages"
   6 .SH NAME
   7 Num \- a Tomo type
   8 .SH LIBRARY
   9 Tomo Standard Library
  10 .fi
  11 .SH METHODS
  12 
  13 .TP
  14 .BI Num.1_PI\ :\ Num
  15 The constant $\frac{1}{\pi}$. 
  16 
  17 For more, see:
  18 .BR Tomo-Num.1_PI (3)
  19 
  20 
  21 .TP
  22 .BI Num.2_PI\ :\ Num
  23 The constant $2 \times \pi$. 
  24 
  25 For more, see:
  26 .BR Tomo-Num.2_PI (3)
  27 
  28 
  29 .TP
  30 .BI Num.2_SQRTPI\ :\ Num
  31 The constant $2 \times \sqrt{\pi}$. 
  32 
  33 For more, see:
  34 .BR Tomo-Num.2_SQRTPI (3)
  35 
  36 
  37 .TP
  38 .BI Num.E\ :\ Num
  39 The base of the natural logarithm ($e$). 
  40 
  41 For more, see:
  42 .BR Tomo-Num.E (3)
  43 
  44 
  45 .TP
  46 .BI Num.INF\ :\ Num
  47 Positive infinity. 
  48 
  49 For more, see:
  50 .BR Tomo-Num.INF (3)
  51 
  52 
  53 .TP
  54 .BI Num.LN10\ :\ Num
  55 The natural logarithm of 10. 
  56 
  57 For more, see:
  58 .BR Tomo-Num.LN10 (3)
  59 
  60 
  61 .TP
  62 .BI Num.LN2\ :\ Num
  63 The natural logarithm of 2. 
  64 
  65 For more, see:
  66 .BR Tomo-Num.LN2 (3)
  67 
  68 
  69 .TP
  70 .BI Num.LOG2E\ :\ Num
  71 The base 2 logarithm of $e$ 
  72 
  73 For more, see:
  74 .BR Tomo-Num.LOG2E (3)
  75 
  76 
  77 .TP
  78 .BI Num.PI\ :\ Num
  79 Pi ($\pi$). 
  80 
  81 For more, see:
  82 .BR Tomo-Num.PI (3)
  83 
  84 
  85 .TP
  86 .BI Num.PI_2\ :\ Num
  87 $\frac{\pi}{2}$ 
  88 
  89 For more, see:
  90 .BR Tomo-Num.PI_2 (3)
  91 
  92 
  93 .TP
  94 .BI Num.PI_4\ :\ Num
  95 $\frac{\pi}{4}$ 
  96 
  97 For more, see:
  98 .BR Tomo-Num.PI_4 (3)
  99 
 100 
 101 .TP
 102 .BI Num.SQRT1_2\ :\ Num
 103 $\sqrt{\frac{1}{2}}$ 
 104 
 105 For more, see:
 106 .BR Tomo-Num.SQRT1_2 (3)
 107 
 108 
 109 .TP
 110 .BI Num.SQRT2\ :\ Num
 111 $\sqrt{2}$ 
 112 
 113 For more, see:
 114 .BR Tomo-Num.SQRT2 (3)
 115 
 116 
 117 .TP
 118 .BI Num.TAU\ :\ Num
 119 Tau ($2 \times \pi$) 
 120 
 121 For more, see:
 122 .BR Tomo-Num.TAU (3)
 123 
 124 
 125 .TP
 126 .BI Num.abs\ :\ func(n:\ Num\ ->\ Num)
 127 Calculates the absolute value of a number. 
 128 
 129 For more, see:
 130 .BR Tomo-Num.abs (3)
 131 
 132 
 133 .TP
 134 .BI Num.acos\ :\ func(x:\ Num\ ->\ Num)
 135 Computes the arc cosine of a number. 
 136 
 137 For more, see:
 138 .BR Tomo-Num.acos (3)
 139 
 140 
 141 .TP
 142 .BI Num.acosh\ :\ func(x:\ Num\ ->\ Num)
 143 Computes the inverse hyperbolic cosine of a number. 
 144 
 145 For more, see:
 146 .BR Tomo-Num.acosh (3)
 147 
 148 
 149 .TP
 150 .BI Num.asin\ :\ func(x:\ Num\ ->\ Num)
 151 Computes the arc sine of a number. 
 152 
 153 For more, see:
 154 .BR Tomo-Num.asin (3)
 155 
 156 
 157 .TP
 158 .BI Num.asinh\ :\ func(x:\ Num\ ->\ Num)
 159 Computes the inverse hyperbolic sine of a number. 
 160 
 161 For more, see:
 162 .BR Tomo-Num.asinh (3)
 163 
 164 
 165 .TP
 166 .BI Num.atan\ :\ func(x:\ Num\ ->\ Num)
 167 Computes the arc tangent of a number. 
 168 
 169 For more, see:
 170 .BR Tomo-Num.atan (3)
 171 
 172 
 173 .TP
 174 .BI Num.atan2\ :\ func(x:\ Num,\ y:\ Num\ ->\ Num)
 175 Computes the arc tangent of the quotient of two numbers. 
 176 
 177 For more, see:
 178 .BR Tomo-Num.atan2 (3)
 179 
 180 
 181 .TP
 182 .BI Num.atanh\ :\ func(x:\ Num\ ->\ Num)
 183 Computes the inverse hyperbolic tangent of a number. 
 184 
 185 For more, see:
 186 .BR Tomo-Num.atanh (3)
 187 
 188 
 189 .TP
 190 .BI Num.cbrt\ :\ func(x:\ Num\ ->\ Num)
 191 Computes the cube root of a number. 
 192 
 193 For more, see:
 194 .BR Tomo-Num.cbrt (3)
 195 
 196 
 197 .TP
 198 .BI Num.ceil\ :\ func(x:\ Num\ ->\ Num)
 199 Rounds a number up to the nearest integer. 
 200 
 201 For more, see:
 202 .BR Tomo-Num.ceil (3)
 203 
 204 
 205 .TP
 206 .BI Num.clamped\ :\ func(x:\ Num,\ low:\ Num,\ high:\ Num\ ->\ Num)
 207 Returns the given number clamped between two values so that it is within that range. 
 208 
 209 For more, see:
 210 .BR Tomo-Num.clamped (3)
 211 
 212 
 213 .TP
 214 .BI Num.copysign\ :\ func(x:\ Num,\ y:\ Num\ ->\ Num)
 215 Copies the sign of one number to another. 
 216 
 217 For more, see:
 218 .BR Tomo-Num.copysign (3)
 219 
 220 
 221 .TP
 222 .BI Num.cos\ :\ func(x:\ Num\ ->\ Num)
 223 Computes the cosine of a number (angle in radians). 
 224 
 225 For more, see:
 226 .BR Tomo-Num.cos (3)
 227 
 228 
 229 .TP
 230 .BI Num.cosh\ :\ func(x:\ Num\ ->\ Num)
 231 Computes the hyperbolic cosine of a number. 
 232 
 233 For more, see:
 234 .BR Tomo-Num.cosh (3)
 235 
 236 
 237 .TP
 238 .BI Num.erf\ :\ func(x:\ Num\ ->\ Num)
 239 Computes the error function of a number. 
 240 
 241 For more, see:
 242 .BR Tomo-Num.erf (3)
 243 
 244 
 245 .TP
 246 .BI Num.erfc\ :\ func(x:\ Num\ ->\ Num)
 247 Computes the complementary error function of a number. 
 248 
 249 For more, see:
 250 .BR Tomo-Num.erfc (3)
 251 
 252 
 253 .TP
 254 .BI Num.exp\ :\ func(x:\ Num\ ->\ Num)
 255 Computes the exponential function $e^x$ for a number. 
 256 
 257 For more, see:
 258 .BR Tomo-Num.exp (3)
 259 
 260 
 261 .TP
 262 .BI Num.exp2\ :\ func(x:\ Num\ ->\ Num)
 263 Computes $2^x$ for a number. 
 264 
 265 For more, see:
 266 .BR Tomo-Num.exp2 (3)
 267 
 268 
 269 .TP
 270 .BI Num.expm1\ :\ func(x:\ Num\ ->\ Num)
 271 Computes $e^x - 1$ for a number. 
 272 
 273 For more, see:
 274 .BR Tomo-Num.expm1 (3)
 275 
 276 
 277 .TP
 278 .BI Num.fdim\ :\ func(x:\ Num,\ y:\ Num\ ->\ Num)
 279 Computes the positive difference between two numbers. 
 280 
 281 For more, see:
 282 .BR Tomo-Num.fdim (3)
 283 
 284 
 285 .TP
 286 .BI Num.floor\ :\ func(x:\ Num\ ->\ Num)
 287 Rounds a number down to the nearest integer. 
 288 
 289 For more, see:
 290 .BR Tomo-Num.floor (3)
 291 
 292 
 293 .TP
 294 .BI Num.hypot\ :\ func(x:\ Num,\ y:\ Num\ ->\ Num)
 295 Computes the Euclidean norm, $\sqrt{x^2 + y^2}$, of two numbers. 
 296 
 297 For more, see:
 298 .BR Tomo-Num.hypot (3)
 299 
 300 
 301 .TP
 302 .BI Num.is_between\ :\ func(x:\ Num,\ low:\ Num,\ high:\ Num\ ->\ Bool)
 303 Determines if a number is between two numbers (inclusive). 
 304 
 305 For more, see:
 306 .BR Tomo-Num.is_between (3)
 307 
 308 
 309 .TP
 310 .BI Num.isfinite\ :\ func(n:\ Num\ ->\ Bool)
 311 Checks if a number is finite. 
 312 
 313 For more, see:
 314 .BR Tomo-Num.isfinite (3)
 315 
 316 
 317 .TP
 318 .BI Num.isinf\ :\ func(n:\ Num\ ->\ Bool)
 319 Checks if a number is infinite. 
 320 
 321 For more, see:
 322 .BR Tomo-Num.isinf (3)
 323 
 324 
 325 .TP
 326 .BI Num.j0\ :\ func(x:\ Num\ ->\ Num)
 327 Computes the Bessel function of the first kind of order 0. 
 328 
 329 For more, see:
 330 .BR Tomo-Num.j0 (3)
 331 
 332 
 333 .TP
 334 .BI Num.j1\ :\ func(x:\ Num\ ->\ Num)
 335 Computes the Bessel function of the first kind of order 1. 
 336 
 337 For more, see:
 338 .BR Tomo-Num.j1 (3)
 339 
 340 
 341 .TP
 342 .BI Num.log\ :\ func(x:\ Num\ ->\ Num)
 343 Computes the natural logarithm (base $e$) of a number. 
 344 
 345 For more, see:
 346 .BR Tomo-Num.log (3)
 347 
 348 
 349 .TP
 350 .BI Num.log10\ :\ func(x:\ Num\ ->\ Num)
 351 Computes the base-10 logarithm of a number. 
 352 
 353 For more, see:
 354 .BR Tomo-Num.log10 (3)
 355 
 356 
 357 .TP
 358 .BI Num.log1p\ :\ func(x:\ Num\ ->\ Num)
 359 Computes $\log(1 + x)$ for a number. 
 360 
 361 For more, see:
 362 .BR Tomo-Num.log1p (3)
 363 
 364 
 365 .TP
 366 .BI Num.log2\ :\ func(x:\ Num\ ->\ Num)
 367 Computes the base-2 logarithm of a number. 
 368 
 369 For more, see:
 370 .BR Tomo-Num.log2 (3)
 371 
 372 
 373 .TP
 374 .BI Num.logb\ :\ func(x:\ Num\ ->\ Num)
 375 Computes the binary exponent (base-2 logarithm) of a number. 
 376 
 377 For more, see:
 378 .BR Tomo-Num.logb (3)
 379 
 380 
 381 .TP
 382 .BI Num.mix\ :\ func(amount:\ Num,\ x:\ Num,\ y:\ Num\ ->\ Num)
 383 Interpolates between two numbers based on a given amount. 
 384 
 385 For more, see:
 386 .BR Tomo-Num.mix (3)
 387 
 388 
 389 .TP
 390 .BI Num.near\ :\ func(x:\ Num,\ y:\ Num,\ ratio:\ Num\ =\ 1e-9,\ min_epsilon:\ Num\ =\ 1e-9\ ->\ Bool)
 391 Checks if two numbers are approximately equal within specified tolerances. If two numbers are within an absolute difference or the ratio between the two is small enough, they are considered near each other. 
 392 
 393 For more, see:
 394 .BR Tomo-Num.near (3)
 395 
 396 
 397 .TP
 398 .BI Num.nextafter\ :\ func(x:\ Num,\ y:\ Num\ ->\ Num)
 399 Computes the next representable value after a given number towards a specified direction. 
 400 
 401 For more, see:
 402 .BR Tomo-Num.nextafter (3)
 403 
 404 
 405 .TP
 406 .BI Num.parse\ :\ func(text:\ Text,\ remainder:\ &Text?\ =\ none\ ->\ Num?)
 407 Converts a text representation of a number into a floating-point number. 
 408 
 409 For more, see:
 410 .BR Tomo-Num.parse (3)
 411 
 412 
 413 .TP
 414 .BI Num.percent\ :\ func(n:\ Num,\ precision:\ Num\ =\ 0.01\ ->\ Text)
 415 Convert a number into a percentage text with a percent sign. 
 416 
 417 For more, see:
 418 .BR Tomo-Num.percent (3)
 419 
 420 
 421 .TP
 422 .BI Num.rint\ :\ func(x:\ Num\ ->\ Num)
 423 Rounds a number to the nearest integer, with ties rounded to the nearest even integer. 
 424 
 425 For more, see:
 426 .BR Tomo-Num.rint (3)
 427 
 428 
 429 .TP
 430 .BI Num.round\ :\ func(x:\ Num\ ->\ Num)
 431 Rounds a number to the nearest whole number integer. 
 432 
 433 For more, see:
 434 .BR Tomo-Num.round (3)
 435 
 436 
 437 .TP
 438 .BI Num.significand\ :\ func(x:\ Num\ ->\ Num)
 439 Extracts the significand (or mantissa) of a number. 
 440 
 441 For more, see:
 442 .BR Tomo-Num.significand (3)
 443 
 444 
 445 .TP
 446 .BI Num.sin\ :\ func(x:\ Num\ ->\ Num)
 447 Computes the sine of a number (angle in radians). 
 448 
 449 For more, see:
 450 .BR Tomo-Num.sin (3)
 451 
 452 
 453 .TP
 454 .BI Num.sinh\ :\ func(x:\ Num\ ->\ Num)
 455 Computes the hyperbolic sine of a number. 
 456 
 457 For more, see:
 458 .BR Tomo-Num.sinh (3)
 459 
 460 
 461 .TP
 462 .BI Num.sqrt\ :\ func(x:\ Num\ ->\ Num)
 463 Computes the square root of a number. 
 464 
 465 For more, see:
 466 .BR Tomo-Num.sqrt (3)
 467 
 468 
 469 .TP
 470 .BI Num.tan\ :\ func(x:\ Num\ ->\ Num)
 471 Computes the tangent of a number (angle in radians). 
 472 
 473 For more, see:
 474 .BR Tomo-Num.tan (3)
 475 
 476 
 477 .TP
 478 .BI Num.tanh\ :\ func(x:\ Num\ ->\ Num)
 479 Computes the hyperbolic tangent of a number. 
 480 
 481 For more, see:
 482 .BR Tomo-Num.tanh (3)
 483 
 484 
 485 .TP
 486 .BI Num.tgamma\ :\ func(x:\ Num\ ->\ Num)
 487 Computes the gamma function of a number. 
 488 
 489 For more, see:
 490 .BR Tomo-Num.tgamma (3)
 491 
 492 
 493 .TP
 494 .BI Num.trunc\ :\ func(x:\ Num\ ->\ Num)
 495 Truncates a number to the nearest integer towards zero. 
 496 
 497 For more, see:
 498 .BR Tomo-Num.trunc (3)
 499 
 500 
 501 .TP
 502 .BI Num.with_precision\ :\ func(n:\ Num,\ precision:\ Num\ ->\ Num)
 503 Round a number to the given precision level (specified as \fB10\fR, \fB.1\fR, \fB.001\fR etc). 
 504 
 505 For more, see:
 506 .BR Tomo-Num.with_precision (3)
 507 
 508 
 509 .TP
 510 .BI Num.y0\ :\ func(x:\ Num\ ->\ Num)
 511 Computes the Bessel function of the second kind of order 0. 
 512 
 513 For more, see:
 514 .BR Tomo-Num.y0 (3)
 515 
 516 
 517 .TP
 518 .BI Num.y1\ :\ func(x:\ Num\ ->\ Num)
 519 Computes the Bessel function of the second kind of order 1. 
 520 
 521 For more, see:
 522 .BR Tomo-Num.y1 (3)
 523