lyng/docs/math.md

Operators

Precedence

Same as in C++.

Priority	Operations
Highest 0	power, not, calls, indexing, dot,...
1	% * /
2	+ -
3	bit shifts << >>
4	<=> (1)
5	<= >= < >
6	== !=
7	bitwise and &
8	bitwise xor ^
9	bitwise or |
10	&&
11 lowest	||

Bitwise operators

available only for Int values. For mixed Int/Real numeric expressions, bitwise operators are not defined.

Bitwise NOT ~x

unary operator that inverts all bits of a 64‑bit signed integer (Int). It follows two's‑complement rules, so ~x is numerically equal to -(x + 1). Examples: ~0 == -1, ~1 == -2, ~(-1) == 0.

Examples:

5 & 3    // -> 1
5 | 3    // -> 7
5 ^ 3    // -> 6
~0       // -> -1
1 << 3   // -> 8
8 >> 3   // -> 1

Notes:

• Shifts operate on 64-bit signed integers (Int is 64-bit). Right shift >> is arithmetic (sign-propagating).
• Shift count is masked to the range 0..63, similar to the JVM/Kotlin behavior (e.g., 1 << 65 equals 1 << 1).

(1)

Shuttle operator: a <=> b returns 0 if a == b, negative Int if a < b and positive Int otherwise. It is necessary to override shuttle operator to make a class comparable.

Operators

+ - * / % : if both operand is Int, calculates as int. Otherwise, as real:

// integer division:
3 / 2
>>> 1

but:

3 / 2.0
>>> 1.5

Round and range

The following functions return its argument if it is Int, or transformed Real otherwise.

name	description
floor(x)	Computes the largest integer value not greater than x
ceil(x)	Computes the least integer value value not less than x
round(x)	Rounds x
x.roundToInt()	shortcut to round(x).toInt()

Lyng math functions

name	meaning
sin(x)	sine
cos(x)	cosine
tan(x)	tangent
asin(x)	sin^{-1}(x)
acos(x)	cos^{-1}(x)
atan(x)	tg^{-1}(x)
sinh(x)	hyperbolic sine
cosh(x)	hyperbolic cosine
tanh(x)	hyperbolic tangent
asinh(x)	sinh^{-1}(x)
acosh(x)	cosh^{-1}(x)
atanh(x)	tgh^{-1}(x)
ln(x)	ln(x), log_e(x)
exp(x)	e^x
log10(x)	log_{10}(x)
pow(x, y)	{x^y}
sqrt(x)	\sqrt {x}
abs(x)	absolute value of x. Int if x is Int, Real otherwise

For example:

assert( sin(π/2) == 1.0)
assert( cos(π/2) < 0.000001)
assert( abs(ln(exp(1))) - 1 < 0.00001)

// abs() keeps the argument type:
assert( abs(-1) is Int)
assert( abs(-2.21) == 2.21 )
>>> void

Scientific constant

name	meaning
Math.PI: Real or π	3.1415926...