Utilities | Quickutil

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There are 43 utilities.

positivep v1.0

Check if n is positive.

Provides: positivep

math synonyms

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negativep v1.0

Check if n is negative.

Provides: negativep

math synonyms

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non-negative-p v1.0

Check if n is non-negative.

Provides: non-negative-p

math synonyms

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non-positive-p v1.0

Check if n is non-positive.

Provides: non-positive-p

math synonyms

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non-zero-p v1.0

Check if n is non-zero.

Provides: non-zero-p

math synonyms

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digit-count v2.0

Compute the number of digits in the non-negative integer n in base base. By default, the base is 10.

Provides: digit-count

math integers

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range-product v1.0

Compute lower * (lower+1) * ... * (upper-1) * upper.

Provides: range-product

math

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factorial v1.0

Compute the factorial of n, where n! = 1 * 2 * ... * n.

Provides: factorial
Requires: range-product

alexandria math

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binomial-coefficient v1.0

Binomial coefficient of n and k.

Provides: binomial-coefficient
Requires: factorial, range-product

alexandria math

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mulf v1.0

A modifying version of multiplication, similar to incf.

Provides: mulf

math orthogonality

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divf v1.0

A modifying version of division, similar to decf.

Provides: divf

math orthogonality

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half v1.0

Compute half of x.

Provides: half

math

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double v1.0

Compute double x.

Provides: double

math

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square v1.0

Compute the square of x.

Provides: square

math

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cube v1.0

Compute the cube of x.

Provides: cube

math

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digits v1.0

Return a list of the digits of the non-negative integer n in base base. By default, decimal digits are returned.

The order of the digits is such that the kth element of the list refers to the coefficient of base^k. In other words, given the resulting list

(c0 c1 c2 ... ck)

the following identity holds:

n = c0 + c1*base + c2*base^2 + ... + ck*base^k.

Provides: digits

math integers

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nth-digit v1.0

Get the nth digit in a rational number number in base base. If n is positive, it refers to digits to the left of the decimal point, and if negative, to the right. The digits of a negative number match that of its positive counterpart.

Provides: nth-digit

math setters

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bit-vector-integer v1.0

Convert a bit vector bv to a positive integer. The bits of the integer are ordered from most significant to least significant, unless least-significant-first is true.

Provides: bit-vector-integer

math integers sequences bit-vectors

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integer-bit-vector v1.0

Convert a positive integer n to a bit vector. The least significant bits will be first if least-significant-first is true.

Provides: integer-bit-vector

math integers sequences bit-vectors

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primes-below v1.0

Return a sorted list of all primes below an integer n.

Examples:

(primes-below 13) => (2 3 5 7 11)  
(primes-below -1) => NIL

Provides: primes-below

math

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sec v1.0

Compute the secant of a number z.

Provides: sec

math orthogonality

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csc v1.0

Compute the cosecant of a number z.

Provides: csc

math orthogonality

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cot v1.0

Compute the cotangent of a number z.

Provides: cot

math orthogonality

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asec v1.0

Compute the arcsecant of a number z.

Provides: asec

math orthogonality

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acsc v1.0

Compute the arccosecant of a number z.

Provides: acsc

math orthogonality

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acot v1.0

Compute the arccotangent of a number z.

Provides: acot

math orthogonality

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imaginary-i v1.0

The imaginary number i = sqrt(-1).

Provides: imaginary-i, ii

math constants

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exponential-e v1.0

The exponential number e = 2.71828....

Provides: exponential-e, ee

math constants

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map-combinations v1.0

Calls function with each combination of length constructable from the elements of the subsequence of sequence delimited by start and end. start defaults to 0, end to length of sequence, and length to the length of the delimited subsequence. (So unless length is specified there is only a single combination, which has the same elements as the delimited subsequence.) If copy is true (the default) each combination is freshly allocated. If copy is false all combinations are eq to each other, in which case consequences are specified if a combination is modified by function.

Provides: map-combinations
Requires: ensure-function

alexandria sequences math

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map-permutations v1.0

Calls function with each permutation of length constructable from the subsequence of sequence delimited by start and end. start defaults to 0, end to length of the sequence, and length to the length of the delimited subsequence.

Provides: map-permutations
Requires: map-combinations

alexandria sequences math

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map-derangements v1.0

Calls function with each derangement of the subsequence of sequence denoted by the bounding index designators start and end. Derangement is a permutation of the sequence where no element remains in place. sequence is not modified, but individual derangements are eq to each other. Consequences are unspecified if calling function modifies either the derangement or sequence.

Provides: map-derangements

alexandria sequences math

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extremum v1.0

Returns the element of sequence that would appear first if the subsequence bounded by start and end was sorted using predicate and key.

extremum determines the relationship between two elements of sequence by using the predicate function. predicate should return true if and only if the first argument is strictly less than the second one (in some appropriate sense). Two arguments x and y are considered to be equal if (funcall predicate x y) and (funcall predicate y x) are both false.

The arguments to the predicate function are computed from elements of sequence using the key function, if supplied. If key is not supplied or is nil, the sequence element itself is used.

If sequence is empty, nil is returned.

Provides: extremum
Requires: ensure-function

alexandria sequences math

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clamp v1.0

Clamps the number into [min, max] range. Returns min if number is lesser then min and max if number is greater then max, otherwise returns number.

Provides: clamp

alexandria math

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gaussian-random v1.0

Returns two gaussian random double floats as the primary and secondary value, optionally constrained by min and max. Gaussian random numbers form a standard normal distribution around 0.0d0.

Sufficiently positive min or negative max will cause the algorithm used to take a very long time. If min is positive it should be close to zero, and similarly if max is negative it should be close to zero.

Provides: gaussian-random

alexandria math random

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lerp v1.0

Returns the result of linear interpolation between a and b, using the interpolation coefficient v.

Provides: lerp

alexandria math

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mean v1.0

Returns the mean of sample. sample must be a sequence of numbers.

Provides: mean

alexandria math statistics

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median v1.0

Returns median of sample. sample must be a sequence of real numbers.

Provides: median
Requires: copy-sequence

alexandria math statistics

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variance v1.0

Variance of sample. Returns the biased variance if biased is true (the default), and the unbiased estimator of variance if biased is false. sample must be a sequence of numbers.

Provides: variance
Requires: mean

alexandria math statistics

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standard-deviation v1.0

Standard deviation of sample. Returns the biased standard deviation if biased is true (the default), and the square root of the unbiased estimator for variance if biased is false (which is not the same as the unbiased estimator for standard deviation). sample must be a sequence of numbers.

Provides: standard-deviation
Requires: variance

alexandria math statistics

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maxf v1.0

Modify-macro for max. Sets place designated by the first argument to the maximum of its original value and numbers.