# Operator, Function, Number and Command Reference

In the following descriptions, optional values are given in brackets ([]) and values given in angle brackets (<>) are not to be taken literally (you are expected to choose a suitable value). For example “fix[<N>]” can represent “fix” or “fix4”, but not “fixN”.

For each action that changes the stack a synopsis of those changes is given in the form of two lists separated by =>. The list on the left represents the stack before the action is applied, and the list on the right represents the stack after the action was applied. In both of these lists, the x register is given first (on the left). Those registers that are involved in the action are listed explicitly, and the rest are represented by .... In the before picture, the names of the registers involved in the action are simply named. In the after picture, the new values of the registers are described. Those values represented by ... on the right side of => are the same as represented by ... on the left, though they may have moved. For example:

x, y, ... => x+y, ...

This represents addition. In this case the values in the x and y registers are summed and placed into the x register. All other values move to the left one place.

## Arithmetic Operators

The values in the x and y registers are popped from the stack and the sum is placed back on the stack into the x register.

x, y, ... → x+y, ...

-: subtraction

The values in the x and y registers are popped from the stack and the difference is placed back on the stack into the x register.

x, y, ... → x-y, ...

*: multiplication

The values in the x and y registers are popped from the stack and the product is placed back on the stack into the x register.

x, y, ... → x*y, ...

/: true division

The values in the x and y registers are popped from the stack and the quotient is placed back on the stack into the x register. Both values are treated as real numbers and the result is a real number. So

0: 1 2/
500m:
x, y, ... → y/x, ...

//: floor division

The values in the x and y registers are popped from the stack, the quotient is computed and then converted to an integer using the floor operation (it is replaced by the largest integer that is smaller than the quotient), and that is placed back on the stack into the x register. So

0: 1 2//
0:
x, y, ... → y//x, ...

%: modulus

The values in the x and y registers are popped from the stack, the quotient is computed and the remainder is placed back on the stack into the x register. So

0: 14 3%
2:

In this case 2 is the remainder because 3 goes evenly into 14 three times, which leaves a remainder of 2.

x, y, ... → y%x, ...

chs: change sign

The value in the x register is replaced with its negative.

x, ... → −x, ...

recip: reciprocal

The value in the x register is replaced with its reciprocal.

x, ... → 1/x, ...

ceil: round towards positive infinity

The value in the x register is replaced with its value rounded towards infinity (replaced with the smallest integer greater than its value).

x, ... → ceil(x), ...

floor: round towards negative infinity

The value in the x register is replaced with its value rounded towards negative infinity (replaced with the largest integer smaller than its value).

x, ... → floor(x), ...

!: factorial

The value in the x register is replaced with the factorial of its value rounded to the nearest integer.

x, ... → x!, ...

%chg: percent change

The values in the x and y registers are popped from the stack and the percent difference between x and y relative to y is pushed back into the x register.

x, y, ... → 100*(x-y)/y, ...

||: parallel combination

The values in the x and y registers are popped from the stack and replaced with the reciprocal of the sum of their reciprocals. If the values in the x and y registers are both resistances, both elastances, or both inductances, then the result is the resistance, elastance or inductance of the two in parallel. If the values are conductances, capacitances or susceptances, then the result is the conductance, capacitance or susceptance of the two in series.

x, y, ... → 1/(1/x+1/y), ...

## Powers, Roots, Exponentials and Logarithms

**: raise y to the power of x

The values in the x and y registers are popped from the stack and replaced with the value of y raised to the power of x.

x, y, ... → y**x, ...

aliases: pow,ytox

exp: natural exponential

The value in the x register is replaced with its exponential. Supports a complex argument.

x, ... → exp(x), ...

alias: powe

ln: natural logarithm

The value in the x register is replaced with its natural logarithm. Supports a complex argument.

x, ... → ln(x), ...

alias: loge

pow10: raise 10 to the power of x

The value in the x register is replaced with 10 raised to x.

x, ... → 10**x, ...

alias: 10tox

log: base 10 logarithm

The value in the x register is replaced with its common logarithm.

x, ... → log(x), ...

aliases: log10,lg

pow2: raise 2 to the power of x

The value in the x register is replaced with 2 raised to x.

x, ... → 2**x, ...

alias: 2tox

log2: base 2 logarithm

The value in the x register is replaced with its base 2 logarithm.

x, ... → log2(x), ...

alias: lb

sqr: square

The value in the x register is replaced with its square.

x, ... → x**2, ...

sqrt: square root

The value in the x register is replaced with its square root.

x, ... → sqrt(x), ...

alias: rt

cbrt: cube root

The value in the x register is replaced with its cube root.

x, ... → cbrt(x), ...

## Trigonometric Functions

sin: trigonometric sine

The value in the x register is replaced with its sine.

x, ... → sin(x), ...

cos: trigonometric cosine

The value in the x register is replaced with its cosine.

x, ... → cos(x), ...

tan: trigonometric tangent

The value in the x register is replaced with its tangent.

x, ... → tan(x), ...

asin: trigonometric arc sine

The value in the x register is replaced with its arc sine.

x, ... → asin(x), ...

acos: trigonometric arc cosine

The value in the x register is replaced with its arc cosine.

x, ... → acos(x), ...

atan: trigonometric arc tangent

The value in the x register is replaced with its arc tangent.

x, ... → atan(x), ...

Switch the trigonometric mode to radians (functions such as sin, cos, tan, and ptor expect angles to be given in radians; functions such as arg, asin, acos, atan, atan2, and rtop should produce angles in radians).

degs: use degrees

Switch the trigonometric mode to degrees (functions such as sin, cos, tan, and ptor expect angles to be given in degrees; functions such as arg, asin, acos, atan, atan2, and rtop should produce angles in degrees).

## Complex and Vector Functions

abs: magnitude of complex number

The absolute value of the number in the x register is pushed onto the stack if it is real. If the value is complex, the magnitude is pushed onto the stack.

x, ... → abs(x), x, ...

alias: mag

arg: phase of complex number

The argument of the number in the x register is pushed onto the stack if it is complex. If the value is real, zero is pushed onto the stack.

x, ... → arg(x), x, ...

alias: ph

hypot: hypotenuse

The values in the x and y registers are popped from the stack and replaced with the length of the vector from the origin to the point (x, y).

x, y, ... → sqrt(x**2+y**2), ...

alias: len

atan2: two-argument arc tangent

The values in the x and y registers are popped from the stack and replaced with the angle of the vector from the origin to the point.

x, y, ... → atan2(y,x), ...

alias: angle

rtop: convert rectangular to polar coordinates

The values in the x and y registers are popped from the stack and replaced with the length of the vector from the origin to the point (x, y) and with the angle of the vector from the origin to the point (x, y).

x, y, ... → sqrt(x**2+y**2), atan2(y,x), ...

ptor: convert polar to rectangular coordinates

The values in the x and y registers are popped from the stack and interpreted as the length and angle of a vector and are replaced with the coordinates of the end-point of that vector.

x, y, ... → x*cos(y), x*sin(y), ...

## Hyperbolic Functions

sinh: hyperbolic sine

The value in the x register is replaced with its hyperbolic sine.

x, ... → sinh(x), ...

cosh: hyperbolic cosine

The value in the x register is replaced with its hyperbolic cosine.

x, ... → cosh(x), ...

tanh: hyperbolic tangent

The value in the x register is replaced with its hyperbolic tangent.

x, ... → tanh(x), ...

asinh: hyperbolic arc sine

The value in the x register is replaced with its hyperbolic arc sine.

x, ... → asinh(x), ...

acosh: hyperbolic arc cosine

The value in the x register is replaced with its hyperbolic arc cosine.

x, ... → acosh(x), ...

atanh: hyperbolic arc tangent

The value in the x register is replaced with its hyperbolic arc tangent.

x, ... → atanh(x), ...

## Decibel Functions

db: convert voltage or current to dB

The value in the x register is replaced with its value in decibels. It is appropriate to apply this form when converting voltage or current to decibels.

x, ... → 20*log(x), ...

aliases: db20,v2db,i2db

adb: convert dB to voltage or current

The value in the x register is converted from decibels and that value is placed back into the x register. It is appropriate to apply this form when converting decibels to voltage or current.

x, ... → 10**(x/20), ...

aliases: db2v,db2i

db10: convert power to dB

The value in the x register is converted from decibels and that value is placed back into the x register. It is appropriate to apply this form when converting power to decibels.

x, ... → 10*log(x), ...

alias: p2db

The value in the x register is converted from decibels and that value is placed back into the x register. It is appropriate to apply this form when converting decibels to voltage or current.

x, ... → 10**(x/10), ...

alias: db2p

vdbm: convert peak voltage to dBm

The value in the x register is expected to be the peak voltage of a sinusoid that is driving a load resistor equal to Rref (a predefined variable). It is replaced with the power delivered to the resistor in decibels relative to 1 milliwatt.

x, ... → 30+10*log10((x**2)/(2*Rref)), ...

alias: v2dbm

dbmv: dBm to peak voltage

The value in the x register is expected to be a power in decibels relative to one milliwatt. It is replaced with the peak voltage of a sinusoid that would be needed to deliver the same power to a load resistor equal to Rref (a predefined variable).

x, ... → sqrt(2*10**(x - 30)/10)*Rref), ...

alias: dbm2v

idbm: peak current to dBm

The value in the x register is expected to be the peak current of a sinusoid that is driving a load resistor equal to Rref (a predefined variable). It is replaced with the power delivered to the resistor in decibels relative to 1 milliwatt.

x, ... → 30+10*log10(((x**2)*Rref/2), ...

alias: i2dbm

dbmi: dBm to peak current

The value in the x register is expected to be a power in decibels relative to one milliwatt. It is replaced with the peak current of a sinusoid that would be needed to deliver the same power to a load resistor equal to Rref (a predefined variable).

x, ... → sqrt(2*10**(x - 30)/10)/Rref), ...

alias: dbm2i

## Constants

pi: the ratio of a circle’s circumference to its diameter

The value of π (3.141592…) is pushed on the stack into the x register.

... → π, ...

alias: π

2pi: the ratio of a circle’s circumference to its radius

2π (6.283185…) is pushed on the stack into the x register.

... → 2π, ...

aliases: tau,τ,2π

rt2: square root of two

√2 (1.4142…) is pushed on the stack into the x register.

... → √2, ...

0C: 0 Celsius in Kelvin

Zero celsius in kelvin (273.15 K) is pushed on the stack into the x register.

... → 0C, ...

j: imaginary unit (square root of −1)

The imaginary unit (square root of -1) is pushed on the stack into the x register.

... → j, ...

j2pi: j2π

2π times the imaginary unit (j6.283185…) is pushed on the stack into the x register.

... → j*2*pi, ...

aliases: jtau,jτ,j2π

k: Boltzmann constant

The Boltzmann constant (R/NA or 1.38064852×10⁻²³ J/K [mks] or 1.38064852×10⁻¹⁶ erg/K [cgs]) is pushed on the stack into the x register.

... → k, ...

h: Planck constant

The Planck constant h (6.626070×10⁻³⁴ J-s [mks] or 6.626070×10⁻²⁷ erg-s [cgs]) is pushed on the stack into the x register.

... → h, ...

q: elementary charge (the charge of an electron)

The elementary charge (the charge of an electron or 1.6021766208×10⁻¹⁹ C [mks] or 4.80320425×10⁻¹⁰ statC [cgs]) is pushed on the stack into the x register.

... → q, ...

c: speed of light in a vacuum

The speed of light in a vacuum (2.99792458×10⁸ m/s) is pushed on the stack into the x register.

... → c, ...

eps0: permittivity of free space

The permittivity of free space (8.854187817×10⁻¹² F/m [mks] or 1/4π [cgs]) is pushed on the stack into the x register.

... → eps0, ...

mu0: permeability of free space

The permeability of free space (4π×10⁻⁷ H/m [mks] or 4π/c² s²/m² [cgs]) is pushed on the stack into the x register.

... → mu0, ...

Z0: Characteristic impedance of free space

The characteristic impedance of free space (376.730313461 Ω) is pushed on the stack into the x register.

... → Z0, ...

hbar: Reduced Planck constant

The reduced Planck constant ħ (1.054571800×10⁻³⁴ J-s [mks] or 1.054571800×10⁻²⁷ erg-s [cgs]) is pushed on the stack into the x register.

... → ħ, ...

alias: ħ

me: rest mass of an electron

The rest mass of an electron (9.10938356×10⁻²⁸ g) is pushed on the stack into the x register.

... → me, ...

mp: mass of a proton

The mass of a proton (1.672621898×10⁻²⁴ g) is pushed on the stack into the x register.

... → mp, ...

mn: mass of a neutron

The mass of a neutron (1.674927471×10⁻²⁴ g) is pushed on the stack into the x register.

... → mn, ...

mh: mass of a hydrogen atom

The mass of a hydrogen atom (1.6735328115×10⁻²⁴ g) is pushed on the stack into the x register.

... → mh, ...

amu: unified atomic mass unit

The unified atomic mass unit (1.660539040×10⁻²⁴ g) is pushed on the stack into the x register.

... → amu, ...

G: universal gravitational constant

The universal gravitational constant (6.6746×10⁻¹⁴ m³/g-s²) is pushed on the stack into the x register.

... → G, ...

g: earth gravity

The standard acceleration at sea level due to gravity on earth (9.80665 m/s²)) is pushed on the stack into the x register.

... → g, ...

Rinf: Rydberg constant

The Rydberg constant (10973731 m⁻¹) is pushed on the stack into the x register.

... → Ry, ...

sigma: Stefan-Boltzmann constant

The Stefan-Boltzmann constant (5.670367×10⁻⁸ W/m²K⁴) is pushed on the stack into the x register.

... → sigma, ...

alpha: Fine structure constant

The fine structure constant (7.2973525664e-3) is pushed on the stack into the x register.

... → alpha, ...

R: molar gas constant

The molar gas constant (8.3144598 J/mol-K [mks] or 83.145 Merg/deg-mol [cgs]) is pushed on the stack into the x register.

... → R, ...

Avogadro constant (6.022140857×10²³ mol⁻¹) is pushed on the stack into the x register.

... → NA, ...

mks: use MKS units for constants

Switch the unit system for constants to MKS or SI.

cgs: use ESU CGS units for constants

Switch the unit system for constants to ESU CGS.

## Numbers

«N[.M][S][U]»: a real number

The number is pushed on the stack into the x register. N is the integer portion of the mantissa and M is an optional fractional part. S is a letter that represents an SI scale factor. U the optional units (must not contain special characters). For example, 10MHz represents 10⁷ Hz.

... → num, ...

«N[.M]»e«E[U]»: a real number in scientific notation

The number is pushed on the stack into the x register. N is the integer portion of the mantissa and M is an optional fractional part. E is an integer exponent. U the optional units (must not contain special characters). For example, 2.2e-8F represents 22nF.

... → num, ...

The number is pushed on the stack into the x register. N is an integer in base 16 (use a-f to represent digits greater than 9). For example, 0xFF represents the hexadecimal number FF or the decimal number 255.

... → num, ...

0o«N»: a number in octal

The number is pushed on the stack into the x register. N is an integer in base 8 (it must not contain the digits 8 or 9). For example, 0o77 represents the octal number 77 or the decimal number 63.

... → num, ...

0b«N»: a number in binary

The number is pushed on the stack into the x register. N is an integer in base 2 (it may contain only the digits 0 or 1). For example, 0b1111 represents the octal number 1111 or the decimal number 15.

... → num, ...

'h«N»: a number in Verilog hexadecimal notation

The number is pushed on the stack into the x register. N is an integer in base 16 (use a-f to represent digits greater than 9). For example, ‘hFF represents the hexadecimal number FF or the decimal number 255.

... → num, ...

'd«N»: a number in Verilog decimal

The number is pushed on the stack into the x register. N is an integer in base 10. For example, ‘d99 represents the decimal number 99.

... → num, ...

'o«N»: a number in Verilog octal

The number is pushed on the stack into the x register. N is an integer in base 8 (it must not contain the digits 8 or 9). For example, ‘o77 represents the octal number 77 or the decimal number 63.

... → num, ...

'b«N»: a number in Verilog binary

The number is pushed on the stack into the x register. N is an integer in base 2 (it may contain only the digits 0 or 1). For example, ‘b1111 represents the binary number 1111 or the decimal number 15.

... → num, ...

## Number Formats

si[«N»]: use SI notation

Numbers are displayed with a fixed number of digits of precision and the SI scale factors are used to convey the exponent when possible. If an optional whole number N immediately follows si, the precision is set to N digits.

eng[«N»]: use engineering notation

Numbers are displayed with a fixed number of digits of precision and the exponent is given explicitly as an integer. If an optional whole number N immediately follows sci, the precision is set to N digits.

Engineering notation differs from scientific notation in that it allows 1, 2 or 3 digits to precede the decimal point in the mantissa and the exponent is always a multiple of 3.

sci[«N»]: use scientific notation

Numbers are displayed with a fixed number of digits of precision and the exponent is given explicitly as an integer. If an optional whole number N immediately follows sci, the precision is set to N digits.

Scientific notation differs from engineering notation in that it allows only 1 digit to precede the decimal point in the mantissa and the exponent is not constrained to be a multiple of 3.

fix[«N»]: use fixed notation

Numbers are displayed with a fixed number of digits to the right of the decimal point. If an optional whole number N immediately follows fix, the number of digits to the right of the decimal point is set to N.

Numbers are displayed in base 16 (a-f are used to represent digits greater than 9) with a fixed number of digits. If an optional whole number N immediately follows hex, the number of digits displayed is set to N.

oct[«N»]: use octal notation

Numbers are displayed in base 8 with a fixed number of digits. If an optional whole number N immediately follows oct, the number of digits displayed is set to N.

bin[«N»]: use binary notation

Numbers are displayed in base 2 with a fixed number of digits. If an optional whole number N immediately follows bin, the number of digits displayed is set to N.

Numbers are displayed in base 16 in Verilog format (a-f are used to represent digits greater than 9) with a fixed number of digits. If an optional whole number N immediately follows vhex, the number of digits displayed is set to N.

vdec[«N»]: use Verilog decimal notation

Numbers are displayed in base 10 in Verilog format with a fixed number of digits. If an optional whole number N immediately follows vdec, the number of digits displayed is set to N.

voct[«N»]: use Verilog octal notation

Numbers are displayed in base 8 in Verilog format with a fixed number of digits. If an optional whole number N immediately follows voct, the number of digits displayed is set to N.

vbin[«N»]: use Verilog binary notation

Numbers are displayed in base 2 in Verilog format with a fixed number of digits. If an optional whole number N immediately follows vbin, the number of digits displayed is set to N.

## Variable Commands

=«name»: store value into a variable

Store the value in the x register into a variable with the given name.

... → ...

«name»: recall value of a variable

Place the value of the variable with the given name into the x register.

... → value of «name», ...

vars: print variables

List all defined variables and their values.

## Stack Commands

swap: swap x and y

The values in the x and y registers are swapped.

x, y, ... → y, x, ...

dup: duplicate x

The value in the x register is pushed onto the stack again.

x, ... → x, x, ...

alias: enter

The value in the x register is pulled from the stack and discarded.

x, ... → ...

alias: clrx

lastx: recall previous value of x

The previous value of the x register is pushed onto the stack.

... → lastx, ...

stack: print stack

Print all the values stored on the stack.

clstack: clear stack

Remove all values from the stack.

... →

## Miscellaneous Commands

rand: random number between 0 and 1

A number between 0 and 1 is chosen at random and its value is pushed on the stack into x register.

... → rand, ...

`«text»`: print text

Print “text” (the contents of the back-quotes) to the terminal. Generally used in scripts to report and annotate results. Any instances of \$N or \${N} are replaced by the value of register N, where 0 represents the x register, 1 represents the y register, etc. Any instances of \$Var or \${Var} are replaced by the value of the variable Var.

"«units»": set the units of the x register

The units given are applied to the value in the x register. The actual value is unchanged.

x, ... → x "units", ...

>«units»: convert value to given units

The value in the x is popped from the stack, converted to the desired units, and pushed back on to the stack.

x, ... → x converted to specified units, ...

(...)«name»: a user-defined function or macro.

A function is defined with the name «name» where … is a list of commands. When «name» is entered as a command, it is replaced by the list of commands.

quit: quit (:q or ^D also works)

alias: :q

help: print a summary of the available features

?[«topic»]: detailed help on a particular topic

A topic, in the form of a symbol or name, may follow the question mark, in which case a detailed description will be printed for that topic. If no topic is given, a list of available topics is listed.