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This library is a relatively small (<500 cloc) mathematical expression evaluator library written in Nim.

The implementation is a simple recursive-descent evaluator.

It only depends on the stdlib (mostly on the math module), and works on all official Nim backends including JavaScript and in the VM

There's a lot of predefined math functions and some constants, and of course you can define custom ones.

Most of the library usage can be shown in this code example:

import mathexpr
# Create a new evaluator instance
# All custom variables and math functions are bound to this evaluator
# so you could have different evaluators with different vars/functions
let e = newEvaluator()

echo e.eval("((4 - 2^3 + 1) * -sqrt(3*3+4*4)) / 2") # 7.5
# Add some variables to our Evaluator object
e.addVars({"a": 5.0})
echo e.eval("+5^+3+1.1 + a") # 131.1
# Variables with the same name overwrite the old ones
e.addVars({"a": 1.0, "b": 2.0})
echo e.eval("a + b") # 3

# Define our custom function which returns
# 25 multiplied by all arguments it got
proc myFunc(args: seq[float]): float =
  result = 25
  for arg in args:
    result *= arg

e.addFunc("work", myFunc)
echo e.eval("work(1, 2, 3) + 5") # 25*1*2*3 + 5 = 155

# Define a custom function which only accepts two arguments
proc test(a: seq[float]): float =
  a[0] + a[1]

e.addFunc("test", test, 2)
echo e.eval("test(1, 5)") # 6

# In some places parentheses and commas are optional:
echo e.eval("work(1 2 3) + 5") # 155
echo e.eval("sqrt 100 + 5") # 15

eval can return NaN or Inf for some inputs, such as 0/0, or 1/0, see src/tests.nim for more info

What is supported?

Supported operators include +, -, /, *, %, ^, <, >, <=, >=, ==, !=

Implemented mathematical functions:

• abs(x) - the absolute value of x
• acos(x) or arccos(x) - the arccosine (in radians) of x
• asin(x) or arcsin(x) - the arcsine (in radians) of x
• atan(x) or arctan(x) or arctg(x) - the arctangent (in radians) of x
• atan2(x, y) or arctan2(x, y) - the arctangent of the quotient from provided x and y
• ceil(x) - the smallest integer greater than or equal to x
• cos(x) - the cosine of x
• cosh(x) - the hyperbolic cosine of x
• deg(x) - converts x in radians to degrees
• exp(x) - the exponential function of x
• sgn(x) - the sign of x
• sqrt(x) - the square root of x
• sum(x, y, z, ...) - sum of all passed arguments
• fac(x) - the factorial of x
• floor(x) - the largest integer not greater than x
• ln(x) - the natural log of x
• log(x) or log10(x) - the common logarithm (base 10) of x
• log2(x) - the binary logarithm (base 2) of x
• max(x, y, z, ...) - biggest argument from any number of arguments
• min(x, y, z, ...) - smallest argument from any number of arguments
• ncr(x, y) or binom(x, y) - the the number of ways a sample of y elements can be obtained from a larger set of x distinguishable objects where order does not matter and repetitions are not allowed
• npr(x, y) - the number of ways of obtaining an ordered subset of y elements from a set of x elements
• rad(x) - converts x in degrees to radians
• pow(x, y) - the x to the y power
• sin(x) - the sine of x
• sinh(x) - the hyperbolic sine of x
• tg(x) or tan(x) - the tangent of x
• tanh(x) - the hyperbolic tangent of x

Predefined constants

• pi - The circle constant (Ludolph's number)
• tau - The circle constant, equals to 2 * pi
• e - Euler's number

Operators in more detail

Following table shows order of evaluation of various operators, lower the precedence - sooner it shall be evaluated.

Precedence	Operator
1	Exponentiation ^
2	Unary + and -
3	Multiplication/division *, /, %
4	Addition/substraction +, -
5	Less than/Greater than comparison <, <=, >, >=
6	Exact comparison ==, !=

Notes on comparison:

• Comparison operators return a float value, 0.0 for false and 1.0 for true
• Every number in mathexpr is a float. Comparing floats exactly is a bit problematic due to precision, so difference less than 0.0001 makes 2 numbers equal by mathexpr's standards.