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https://github.com/josecelano/numeval

PHP library for Numerical Evaluation with complete precision, with no rounding errors. No limit is set on the number of digits of values.
https://github.com/josecelano/numeval

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PHP library for Numerical Evaluation with complete precision, with no rounding errors. No limit is set on the number of digits of values.

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README 

        
# NumEval

NumEval evaluates numerical values of mathematical statements with complete precision, with no rounding errors. No limit is set on the number of digits of values so you can calculate huge numbers as well as incredibly small fractions. You can receive resulting fractions with as many decimals as you want.



Notable features include:

-adding, subtracting, multiplying and dividing numbers with as many decimals as you want.

-finding exact results for roots (when they exist).

-trigonometry functions with more precison.

-logarithms with more precision.

-roots with more precision.

-deterministic prime detection. 



for more information visit: http://noob.software/support/#index/app_instructions#3



Evaluation:



    Addition

        add (accepts strings as value)

        add_total (accepts value-remainder array pair)

    Subtraction

        subtract

        subtract_total

    Multiplication

        result

        multiply_total

    Division

        execute_divide (accepts both strings and value-remainder array pair. Set fourth parameter $fast to true when dividing large numbers)

    Is Divisible

        verified_divisible (accepts value with value and remainder)

    Modulus

    Shorten Fraction

        execute_shorten_fraction (shortens fraction. If $truncate_fractions_length is greater than zero will truncate fraction to set length.)

        minimize_fraction (removes additional zeros from numerator and denominator)

    Powers/Roots

        power (accepts value with remainder and power as value with remainder, to get roots use fractional powers)

        execute_power_whole (for taking integer/whole powers accepts value-remainder pair and power as string)

        execute_power (for taking integer/whole roots accepts value-remainder pair and power as string)

        root_fraction (used as subroutine in power when disable_built_in_approximation is set to true, can be quicker to use directly)

        root (for taking integer roots, returns false if exact root is not found, but closest result is stored as $root_closest_result

        factor_root (starts by factoring number and takes roots of factors)

    Logarithms

    Trigonometry Functions

        returns an array of sin, cos, cot, tan, csc, sec. Function trigonometry accepts slope (cartesian coordinates) as input (two dimensional vector of value remainder array), use function trigonometry_radian if you need to use radians as input.

            Trigonometry (precision of these functions is based on square root precision, which can be configured)

                sin

                cos

                cot

                tan

                csc

                sec

            sin (accepts as input term precision, but can also be configured with $sine_precision same applies for cos, arctan and arccot.)

            cos

            arctan

            arccot

    List Rational Roots

        list_rational_roots, returns a list of all rational roots from 'from' value to 'to' value.

    Is Prime

        prime (deterministic) Strength parameter configures strength of the function(default value is 8), pass $closest_known_prime lower than the value being determined as the second parameter for better validation, use $weak=true for a very fast weak test.

        prime_alt (NumEval's old primality test (deterministic))

        prime_p (Pollard's Rho primality test) (deterministic)

    Absolute

    Negative

    Is Negative

    Floor

    Ceil

    Round

    Is Larger

    Common Fraction Value

        whole_common

    Real Fraction Value

        quick_fraction, takes as input a value-remainder array pair and number of decimals for fraction

        real_fraction, takes as input a fraction and number of decimals for fraction

        numeric_whole, takes as input value, remainder and number of decimals

    Change Base (base <= 10)

    Find Perioidic Continued Fraction

        find_continued_fraction (precision parameter must be equal to or larger than limit parameter for precise result)

        square_root_fraction (finds continued fraction for square roots, returns value if periodic continued fraction is found, false otherwise)

    Resolve Periodic Continued Fraction

        resolve_continued_fraction

    List Divisors

        list_divisors (uses prime_factors function)

    Prime Factors

        prime_factors (uses NumEval's prime function and trial division)

        prime_factors_alt (NumEval's new prime factorization method in combination with Pollard's rho)

    ModExp

    ModMult

    ModAdd

    Co-Prime

    GCD

    Is Perfect Power

    Ord

    Factorial

    Parse Value (parsing value from parse function to value-pair



Evaluation_parse



    Parse (parse function in evaluation_parse class, evaluates numerical statement which can be set using the constructor or set_function)



In addition to these functions NumEval comes with Vector, Multidimensional_vector, Matrix, Quadratic_solver, Arithematic. Vector contains functions for two dimensional vectors and Matrix contains functions for nxn dimensional matrices, both written using NumEval. Two dimensional vector functions accept values in form of array of value pairs for example:

array(array('value' => '1', 'remainder' => '1/2'), array('value' => '2', 'remainder' => '0/1'));



Matrix functions accept values in the form of two dimensional arrays:

array(

array(array('value' => '1', 'remainder' => '1/2'), array('value' => '2', 'remainder' => '0/1')),

array(array('value' => '3', 'remainder' => '1/2'), array('value' => '1', 'remainder' => '1/3'))

);



Quadratic_solver solves quadratic equations using numeval.



Arithematic is for delaying resolving roots and powers until the end of arithematic which can be useful for maximum precision.



NumEval is also available as a NuGet package: https://www.nuget.org/packages/NumEval/