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Vwsim-hdl

Vwsim-term

The VWSIM Mathematical Term Language.

Introduction

VWSIM provides a language to express mathematical terms (expressions). Here, the subset of this language available to the user is presented. These expressions can be used when the user is describing netlists using the vwsim-hdl. At simulation time, these terms are evaluated to double-precision floating point numbers.

A term is one of the following:

Quoted constant
Symbol constant
Symbol variable
Function Call

Quoted Constant

A quoted constant is a QUOTE followed by a rational or double-precision floating point number.

Examples:

'1
'3/7
'3.4d0
'7.9d2

Symbol Constant

A symbol constant is a symbolp that has * as the first and last character. The available constants are:

Constant name	Description
pi	Pi
e	Euler's number
h	Planck's constant (Joules * seconds)
h_bar	Planck's Constant divided by two pi
e_C	Charge of an electron (Coulombs)
K_b	Boltzmann's constant (Joules/Kelvin)
deltaV	Size of the Josephson junction (JJ) transition region (Volts)
phi0	Magnetic Flux Quantum (Webers)
Icfact	Ratio of JJ critical current to quasiparticle step height

The constants also include the multipliers *kilo*, *mega*, *giga*, *tera*, *peta*, *milli*, *micro*, *nano*, *pico*, and *femto*. See vwsim-constants for the values of all of the constants.

Symbol Variable

A symbol variable is a symbolp that denotes a variable value that will be looked up at simulation time. The user is allowed to use the $time$ and $hn$ symbol variables.

$time$ is the current simulation time as a floating point number.

$hn$ is the current simulation step size as a floating point number.

Note: it is recommended to use the $time$< function whenever possible. See the description below.

Function Call

A function call is of the form:

(fun-name arg0 arg1 ...)

where each available fun-name and its arity is described below, and each argument is a term.

A note on the use of booleans: the vwsim-term language provides a few functions that deal with booleans ($time$<, f-not, f<, f=, if). Since the evaluation of terms only produces a floating point number, these functions understand the number 0.0d0 to be FALSE and any other value to be TRUE.

Unary Functions

Function	Description
$time$<	Check whether the current simulation time is less than the provided argument. Returns a boolean (see discussion above about booleans).
f-not	Logical not
f0-	Negation
f-abs	Absolute value
f-1/x	Reciprocal
f-sqrt	Square root
f-sin	Sine
f-cos	Cosine
f-tan	Tangent
f-tanh	Hyperbolic tangent
f-exp	Expontential function (e^x)

Binary Functions

Function	Description
f+	Addition
f-	Subtraction
f*	Multiplication
f/	Division
f<	Less than
f=	Equality
f-mod	Modulo

Ternary Functions

Function	Description
if	If the first argument evaluates to 0.0d0 (FALSE), then the third argument is evaluated. Otherwise, the second argument is evaluated.

Some more examples of terms:

(f+ '1 '2)
(f+ '1.2d0 *pi*)
(f* '2 $hn$)
(if (f-not (f< '1 *phi0*)) '4 '5)
(if ($time$< '2/100) '1.0d0 '2.0d0)