Open
Description
This should be built as a library (in our /libraries directory) that uses a parsing framework such as Chumsky that takes a string at runtime and calculates its result, including units and dimensional analysis.
This would make a great solo contribution for somebody interested in developing a robust solution for this problem without needing to learn any of Graphite's code base. It would also make a good university team/solo "capstone" project, which our organization can serve as an "industry sponsor" for.
Here's the spec:
Operators
- Infix operators:
- Addition:
+ - Subtraction:
- - Multiplication:
* - Division:
/ - Modulo:
% - Exponentiation:
^ - Equals:
== - Not Equals:
!= - Less Than or Equal To:
<=,≤ - Greater Than or Equal To:
>=,≥ - Less Than:
< - Greater Than:
> - Or:
|| - And:
&&
- Addition:
- Prefix operators:
- Unary Plus:
+ - Unary Minus:
- - Square root:
√ - Not:
!
- Unary Plus:
- Postfix operators:
- Factorial:
!
- Factorial:
- Grouping operators:
- Parentheses:
(and)
- Parentheses:
- Logical operators:
- Equality:
==,!=,>=,<=,<,>,||,&&, and!logical operators to the spec.
- Equality:
Constants
- Infinity:
inf,INF,infinity,INFINITY,∞ - Imaginary unit:
i,I - Pi:
pi,PI,π - Tau:
tau,TAU,τ - Euler's Number:
e - Golden Ratio:
phi,PHI,φ - Earth's gravitational acceleration:
G
Variables
- Single-letter variables (examples:
x,y,z) - Multi-letter variables (examples:
theta,alpha,beta,gamma) - Non-Latin letters and symbols (examples:
λ,あ,א,👍)
Functions
- Trig:
-
sin(),cos(),tan() -
csc(),sec(),cot()
-
- Inverse trig (aliases:
ar-andarc-prefixes):-
asin(),acos(),atan(),atan2() -
acsc(),asec(),acot()
-
- Hyperbolic:
-
sinh(),cosh(),tanh() -
csch(),sech(),coth()
-
- Inverse hyperbolic (aliases:
ar-andarc-prefixes):-
asinh(),acosh(),atanh() -
acsch(),asech(),acoth()
-
- Logarithm:
- Natural log:
ln() - Logarithm base 10:
log() - Logarithm base 2:
log2() - Logarithm base N:
logN()(alias:log_N())- Examples:
log5(),log3.25(),log_8()
- Examples:
- Logarithm with variable base:
log(x, b)
- Natural log:
- Exponential:
- e^x:
exp() - 2^x:
exp2()
- e^x:
- Roots:
- Square root:
sqrt()(alias:root(),root2(),root_2()) - Cube root:
cbrt()(alias:root3(),root_3()) - Nth root:
rootN()(alias:root_N())- Examples:
root3(),root5.237(),root_27.72()
- Examples:
- Root with variable degree:
root(n, x)- Example:
root(27, 3)is equivalent tocbrt(27)
- Example:
- Square root:
- Geometry:
- Hypotenuse equation sqrt(a^2 + b^2):
hypot()
- Hypotenuse equation sqrt(a^2 + b^2):
- Mapping:
- Absolute value:
abs()(magnitude of a real or complex number) - Floor:
floor() - Ceiling:
ceil() - Round:
round() - Clamp:
clamp(x, min, max) - Lerp:
lerp(a, b, t) - Truncate:
trunc() - Fractional part:
frac() - Sign:
sign()
- Absolute value:
- Logical
- Is NaN:
isnan()(returns 1 if the operand is NaN, 0 otherwise) - Equality:
eq()(returns 1 if both operands and units are equal, 0 otherwise) - Greater than:
greater()(returns 1 if the left operand is greater than the right operand and units are equal, 0 otherwise) - Greater-or-equal:
greatereq()(returns 1 if the left operand is greater than or equal to the right operand and units are equal, 0 otherwise) - Less than:
lesser()(returns 1 if the left operand is less than the right operand and units are equal, 0 otherwise) - Less-or-equal:
lessereq()(returns 1 if the left operand is less than or equal to the right operand and units are equal, 0 otherwise) - Not:
not()(returns 1 if the operand is zero, 0 otherwise) - And:
and()(returns 1 if both operands are non-zero, 0 otherwise) - Or:
or()(returns 1 if either operand is non-zero, 0 otherwise) - Xor:
xor()(returns 1 if exactly one operand is non-zero, 0 otherwise) - If:
if(cond, a, b)(returnsaifcondis non-zero,botherwise)- A potential alternative to nonzeroness in these logical functions could be using
trueandfalseas units with either no value, a value of 0, or a value of 1
- A potential alternative to nonzeroness in these logical functions could be using
- Is NaN:
- Complex numbers:
- Real part:
real() - Imaginary part:
imag() - Angle:
arg()(alias:angle())
- Real part:
Number representations
- Integers (examples:
0,42,-42) - Decimals (examples:
0.5,3.14159,-2.71828) - Scientific notation (examples:
1e-6,2.5E3) - Imaginary numbers (examples:
3i,-2.5i,1.5e-3i,2.5e3 + 2.1e-2i) - Units (examples:
5m,5 m,3.5kg,3.5 kg,2.5m/s^2,2.5 m/s^2)
Units
- In addition to the unit abbreviations, full unit names can be used in either singular or plural form
- Math expressions perform dimensional analysis
- The scalar part is simplified while the unit part is kept as a fraction if it cannot be simplified
- Units should only be combined if they are mixed with other units in either the numerator or denominator, defaulting to the unit that would best avoid loss of precision
- Example:
5m + 3m -> 8m - Example:
5ft + 3ft -> 8ft - Example:
5m + 3ft -> 5.9144m(meters are chosen because 1ft = 0.3048m exactly, while its inverse can't be represented exactly)
- Example:
- Values can always be requested for conversion to a specific unit in the API
Unit list
- Unitless
- Pixels:
px
- Length:
- Meter
mand its prefixes thou,pc,pt,in/",ft/',yd,mi,nmi
- Meter
- Area:
- length^2
acre,are,hectare
- Volume:
- length^3, area * length
- Paper sizes:
A0,A1,A2,A3,A4,A5,A6,A7,A8,A9,A10 floz,cup,pint,qt,galland its prefixes
- Mass:
- Kilogram
kgand its prefixes gr,oz,lb,ton,tonne
- Kilogram
- Time:
- Second
sand its prefixes min,hr,day
- Second
- Angle:
- Degrees:
deg/° - Radians:
rad(unitless is not an angle) - Turns:
turn
- Degrees:
- Velocity:
- length / time
m/s,km/h,mph,knot
- Acceleration:
- velocity / time, length / time^2
m/s^2,ft/s^2,g
- Angular velocity:
- angle / time
deg/s,rad/s,rpm,rps
- Angular acceleration:
- angular velocity / time, angle / time^2
deg/s^2,rad/s^2
- Illumination
- TODO: Research and lay out what these are, like candela, nits, etc.
Unit metric prefixes
- Nano (
n) - Micro (
µ,u) - Milli (
m) - Centi (
c) - Deci (
d) - Deca (
da) - Hecto (
h) - Kilo (
k) - Mega (
M) - Giga (
G) - Tera (
T)
Implicit multiplication
- Automatically handle multiplication without explicit
*operator- Between numbers and variables/constants (examples:
3x,2pi) - Between numbers and functions (example:
4sin(90deg)) - Between adjacent variables/constants (examples:
xy,pi r^2)
- Between numbers and variables/constants (examples:
API features
- Parsing/construction separate from evaluation so the same expression can be run repeatedly with different variables without wasted performance
- Setting the result of one expression to a variable for use in subsequent expressions
- Custom supplied units, unit symbols, functions, and constants
- Syntax highlighting
- Initial library implementation (Add math-parser library #2033)
- Add more features as described in the spec above, such as
abs()and others
Sub-issues
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Type
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Status
Ongoing Projects