Arithmetic functions

ABS — absolute value

ABS(IN: ANY_NUM): ANY_NUM — same type out as in. Returns |IN|. Operates on signed integers (SINT, INT, DINT, LINT) and on REAL / LREAL. Does NOT take unsigned types — they’re already non-negative.

iAbs := ABS(-3);          (* → 3 *)
rAbs := ABS(-2.5);        (* → 2.5 *)
diMag := ABS(diSigned);

SQRT, LN, LOG, EXP

Function	Signature	Notes
`SQRT`	`(REAL): REAL`	Square root. Negative input → NaN
`LN`	`(REAL): REAL`	Natural log (base e). 0 → -∞, <0 → NaN
`LOG`	`(REAL): REAL`	Common log (base 10). Same caveats
`EXP`	`(REAL): REAL`	`e^IN`. Overflow at ~88 → +∞

rRoot := SQRT(2.0);            (* → 1.4142… *)
rNatLog := LN(2.71828);        (* → ~1.0 *)
rLog10  := LOG(100.0);         (* → 2.0 *)
rExp    := EXP(1.0);           (* → e ≈ 2.71828 *)

LREAL versions exist when more precision is needed: SQRT_LREAL, LN_LREAL, etc. — naming is implementation- specific in matiec, look up via library.read_block.

Trigonometric: SIN, COS, TAN

SIN(REAL): REAL etc. All angles in radians. If you have degrees, convert with rRad := rDeg * 3.14159 / 180.0;.

rSin := SIN(0.0);              (* → 0.0 *)
rCos := COS(3.14159);          (* → -1.0 *)
rTan := TAN(0.7854);           (* → ~1.0 (π/4) *)

TAN of (π/2 + n·π) is mathematically infinite; in IEEE-754 it’s a very large finite number (not ±∞).

Inverse trig: ASIN, ACOS, ATAN

ASIN(REAL): REAL returns angle in radians; domain [-1.0, 1.0]. ACOS(REAL): REAL returns angle in radians; domain [-1.0, 1.0]. ATAN(REAL): REAL returns angle in radians; domain unrestricted.

Out-of-domain ASIN/ACOS returns NaN — same caveat as SQRT.

For two-argument arc-tangent (atan2-style, returns full quadrant), the IEC standard library has no ATAN2. matiec exposes a non-standard extension via ATAN2_REAL; portability- critical code should compute the quadrant by hand from SIN and COS.

Type families

The standard treats most of these as (ANY_REAL): ANY_REAL generic — matiec accepts both REAL and LREAL and returns the matching type. Mixing REAL and LREAL in one expression needs REAL_TO_LREAL or LREAL_TO_REAL (type-conversion).

IEC reference

IEC 61131-3 third edition (2013), Annex F.2.2 — “Numerical functions” Tables F.4–F.6.

matiec conformance

matiec implements all standard arithmetic functions per the spec. Trig precision is the underlying C library’s (libm) precision — typically a few ULP for normal inputs.

The LREAL-suffixed versions (SIN_LREAL, SQRT_LREAL, …) are matiec’s way to disambiguate when the standard’s generic (ANY_REAL): ANY_REAL typing isn’t enough.