Verilog-A built-in functions¶

Verilog-A provides useful and frequently used built-in functions which include math, noise, Laplace, limiting and smoothing functions. Comprehensive list of Verilog-A functions with examples are listed below :

Basic Arithmetic & Utility Functions¶

Function	Description
abs(x)	Absolute value
max(x, y)	Maximum of two values
min(x, y)	Minimum of two values
ceil(x)	Smallest integer ≥ x
floor(x)	Largest integer ≤ x
round(x)	Round to nearest integer
pow(x, y)	x raised to power y
sqrt(x)	Square root
sign(x)	Sign of x (−1, 0, +1)
hypot(x,y)	√(x²+y²)

Example of abs():

y = max(abs(x), 1e-6);

Example of hypot(x,y):

real i_comp, q_comp, magnitude;

analog begin
    i_comp = V(in_i);
    q_comp = V(in_q);

    // Calculate magnitude: sqrt(I^2 + Q^2)
    magnitude = hypot(i_comp, q_comp);

    V(out) <+ magnitude;
end

Crucial Convergence Issues at x = 0 for sqrt(x)

In analog simulators (like Spectre or HSPICE), every function must have a continuous derivative to help the simulator converge on a solution. The derivative of sqrt(x) is:

$$\cfrac{d}{dx}\sqrt{x}=\cfrac{1}{2\sqrt{x}}$$

As x approaches 0, the derivative approaches infinity. This often causes the simulator to fail or "hang" because it cannot find a stable slope to follow.

Exponential & Logarithmic Functions¶

Function	Description
exp(x)	eˣ
ln(x)	Natural logarithm
log(x)	Base-10 logarithm
limexp(x)	Limited exponential (numerically safe)

Note

Always prefer limexp() in device models to avoid convergence issues.

Example of limexp():

I(p,n) <+ Is * (limexp(V(p,n)/Vt) - 1);

Trigonometric Functions¶

Function	Description
sin(x)	Sine
cos(x)	Cosine
tan(x)	Tangent
asin(x)	Inverse sine
acos(x)	Inverse cosine
atan(x)	Inverse tangent
atan2(y, x)	Four-quadrant inverse tangent

Example:

V(out) <+ A * sin(2*`M_PI*f*time);

M_PI is a built-in physical constant representing π.

Hyperbolic Functions¶

Function	Description
sinh(x)	Hyperbolic sine
cosh(x)	Hyperbolic cosine
tanh(x)	Hyperbolic tangent
atanh(x)	Inverse hyperbolic tangent
asinh(x)	Inverse hyperbolic sine
acosh(x)	Inverse hyperbolic cosine

Common use: soft limiting, saturation models

Example:

V(out) <+ Vmax * tanh(V(in)/Vmax);

Random & Statistical Functions¶

Function	Description
random()	Uniform random number (0–1)
rdist_normal(mean, sigma)	Gaussian distribution
rdist_uniform(min, max)	Uniform distribution
rdist_poisson(lambda)	Poisson distribution

Example:

offset = rdist_normal(0, sigma_offset);

Used in:

mismatch modeling
Monte-Carlo simulations

Time & Simulation Functions¶

Function	Description
time	Current simulation time
abstime	Absolute time
realtime	Real-time variable

Example:

V(out) <+ sin(2*`M_PI*f*time);

Derivative & Integral Functions¶

Function	Description
ddt(x)	Time derivative (dx/dt)
idt(x, ic)	Time integral with initial condition

Example:

I(p,n) <+ C * ddt(V(p,n));

Transition & Smoothing Functions¶

Function	Description
transition(x, td, tr)	Smooth transition
slew(x, rate)	Slew-rate limiting

Example:

V(out) <+ transition(Vin > Vth, 0, 1n);

Used for:

comparators
DACs
digital-to-analog boundaries

Laplace & Frequency-Domain Functions¶

Function	Description
laplace_zp(input, z[], p[], k)	Zero-pole form
laplace_nd(input, num[], den[])	numerator-denominator form
laplace_zd(input, z[], d[])	zero-denominator form
laplace_np(input, z[], p[], k)	numerator-pole form

More about Laplace functions : Verilog-A Laplace Functions in Detail

Limiting & Protection Functions¶

Function	Description
limit(x, min, max)	Hard limit
clip(x, min, max)	Hard clip

Example:

V(out) <+ limit(Vin, -1.2, 1.2);

Noise Functions¶

Used to model physical noise sources.

white_noise(psd, name)
flicker_noise(psd, exponent, name)

Example:

I(p,n) <+ white_noise(4*P_K*temperature/R, "thermal");

Event and Crossing Functions¶

Used for mixed-signal and event-driven behavior.

cross(expr, direction) – detect zero crossings
timer(t) – periodic event trigger

Example:

@(cross(V(in)-Vth, +1)) begin
    state = 1;
end