Usine provides a comprehensive set of mathematical modules for arithmetic, logic, trigonometry, bitwise operations, rounding, and unit conversions. Most modules work equally on single values and arrays.
| Category | Modules | Description |
|---|---|---|
| Arithmetic | 26 | Basic operations (+, -, *, /), power, sqrt, log, exp, abs, sign, mod, distance, random, variable assignment |
| Trigonometry | 12 | Sin, cos, tan, arcsin, arccos, arctan, arctan2, triangle wave, degree/radian conversion, PI and 2PI constants |
| Logical | 13 | AND, OR, NOT, XOR, comparisons (=, <, >, <=, >=, !=), same-value with epsilon, multi-compare |
| Bitwise | 14 | AND, OR, NOT, XOR, SHL, SHR, CRC32, and conversions between bitwise, integer, string, and bit-array |
| Rounding | 4 | Round, ceil, truncate, and fractional part |
| Conversion | 11 | dB/coeff, frequency/linear/MIDI note, pitch/coeff, exponential/power scale, round frequency |
Basic math operations, logarithms, powers, distance calculations, random generators, and variable assignment.
| Module | Description |
|---|---|
| Math + | Addition: A + B |
| Math - | Subtraction: A - B |
| Math * | Multiplication: A * B |
| Math / | Division: A / B |
| Math ABS | Absolute value |
| Math SIGN | Sign: 1 if positive, -1 if negative |
| Math - X | Negation: -X |
| Math 1 - X | Complement: 1 - X |
| Math 1 / X | Inverse: 1 / X |
| Math X + 1 | Increment: X + 1 |
| Math X - 1 | Decrement: X - 1 |
| Math 2 * X - 1 | Bipolar: 2X - 1 |
| Math (X + 1) / 2 | Unipolar: (X + 1) / 2 |
| Math A * X + B | Linear: A * X + B |
| Math SQR | Square: X * X |
| Math SQRT | Square root |
| Math POWER | Power: A^B (A > 0) |
| Math Int POWER | Integer power: A^B (B integer) |
| Math EXP | Exponential |
| Math LN | Natural logarithm |
| Math LOG10 | Base-10 logarithm |
| Math MOD | Integer modulo |
| Math FMOD | Float modulo |
| Math FMOD Circular | Float modulo with positive output [0..B] |
| Math Int DIV | Integer division |
| Math MIN | Minimum of two values |
| Math MAX | Maximum of two values |
| Math HYPOT | Hypotenuse: sqrt(X^2 + Y^2) |
| Math ODD | Returns 1 if odd, 0 if even |
| Math DELTA | Variation: current - previous |
| Math RANDOM | Random value [0..1] |
| Math RANDOM Block | Array of random values (block-size length) |
| Math Constant | Constant value output |
| Math Variable | Conditional assignment: output = input when affect = 1 |
| Math Multiple Variable | Multiple variable assignment with separate affect triggers |
| Math Formula | Formula parser: expressions like A * Log(B) + Sqrt(C) with 50+ operators |
| Math Quadratic Distance 2D | 2D Euclidean distance (supports arrays) |
| Math Quadratic Distance 3D | 3D Euclidean distance (supports arrays) |
Trigonometric functions, angle conversions, and constants.
| Module | Description |
|---|---|
| Trigonometric SIN | Sine |
| Trigonometric COS | Cosine |
| Trigonometric TAN | Tangent |
| Trigonometric ARCSIN | Arc sine |
| Trigonometric ARCCOS | Arc cosine |
| Trigonometric ARCTAN | Arc tangent |
| Trigonometric ARCTAN2 | Arc tangent with quadrant correction: arctan(Y/X) |
| Trigonometric TRIANGLE | Triangle wave function |
| Trigonometric Degree to Radian | Convert degrees to radians |
| Trigonometric Radian to Degree | Convert radians to degrees |
| Trigonometric PI | Constant: PI (3.14159...) |
| Trigonometric 2PI | Constant: 2*PI (6.28318...) |
Boolean logic and comparison operators. All support optional "null flow if false" output.
| Module | Description |
|---|---|
| Logical AND | A AND B |
| Logical OR | A OR B |
| Logical NOT | NOT A (inverts 0/1) |
| Logical XOR | A XOR B |
| Logical EQUAL | A = B |
| Logical Diff | A != B |
| Logical INFERIOR | A < B |
| Logical INFERIOR OR EQUAL | A <= B |
| Logical SUPERIOR | A > B |
| Logical SUPERIOR OR EQUAL | A >= B |
| Logical Same Value | Floating-point equality with epsilon tolerance |
| Logical Not Same Value | Floating-point inequality with epsilon tolerance |
| Logical Multi Compare | Multi-range comparator with between/equal index outputs |
Bitwise logic operations and format conversions between bitwise, integer, string, and bit-array.
| Module | Description |
|---|---|
| Bitwise AND | Bitwise AND |
| Bitwise OR | Bitwise OR |
| Bitwise NOT | Bitwise NOT (inversion) |
| Bitwise XOR | Bitwise XOR |
| Bitwise SHL | Shift left |
| Bitwise SHR | Shift right |
| Bitwise CRC32 | CRC32 checksum |
| Bitwise Constant | Constant bitwise value |
| Bitwise Integer to Bitwise | Integer to bitwise conversion |
| Bitwise to Integer | Bitwise to integer conversion |
| Bitwise String to Bitwise | Binary string to bitwise conversion |
| Bitwise to String | Bitwise to binary/hex string conversion |
| Bitwise Bit Array to Bitwise | 0/1 array to bitwise conversion |
| Bitwise to Bit Array | Bitwise to 0/1 array conversion |
Round, truncate, and extract fractional parts.
| Module | Description |
|---|---|
| Rounding ROUND | Standard rounding (round-to-even) |
| Rounding CEIL | Round up (toward positive infinity) |
| Rounding TRUNC | Truncate decimal part |
| Rounding FRAC | Extract fractional part |
Unit conversions for audio (dB, frequency, MIDI notes, pitch) and curve scaling.
| Module | Description |
|---|---|
| Conversion dB to Multiplication Coeff | dB to linear coefficient: 10^(dB/20) |
| Conversion Multiplication Coeff to dB | Linear coefficient to dB: 20*log10(coeff) |
| Conversion Frequency to Linear | Frequency to linear [0..1] |
| Conversion Linear to Frequency | Linear [0..1] to frequency |
| Conversion Frequency to MIDI Note | Frequency to MIDI note number (with scale/root options) |
| Conversion MIDI Note to Frequency | MIDI note number to frequency |
| Conversion Multiplication Coeff to Pitch | Coefficient to pitch: 12*log2(coeff) |
| Conversion Pitch to Multiplication Coeff | Pitch to coefficient: 2^(pitch/12) |
| Conversion Round Frequency | Round frequency to nearest well-tempered note |
| Conversion Exponential Scale | Exponential scale factor |
| Conversion Power Scale | Power scale factor |
version 7.0.250121
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