arithmetic-logic.md

Arithmetic / Logic

Reductions over lists of numbers, and operations over sets.

Operations are listed alphabetically.

Operation	Subcommand	Reference
Cartesian Product	cartesian-product	Cartesian product
Divide	divide	Division
Extended GCD	extended-gcd	Extended Euclidean algorithm
Mean	mean	Arithmetic mean
Median	median	Median
MOD	mod	Modulo
Modular Exponentiation	modular-exponentiation	Modular exponentiation
Modular Inverse	modular-inverse	Modular multiplicative inverse
Multiply	multiply	Multiplication
Power Set	power-set	Power set
Set Difference	set-difference	Relative complement
Set Intersection	set-intersection	Intersection
Set Union	set-union	Union
Standard Deviation	standard-deviation	Standard deviation
Subtract	subtract	Subtraction
Sum	sum	Summation
Symmetric Difference	symmetric-difference	Symmetric difference

Number-list operations

divide, mean, median, multiply, standard-deviation, subtract and sum each read a delimited list of numbers and fold it to a single value, sharing these conventions with CyberChef:

• Number parsing. Each item is parsed like a JavaScript BigNumber: decimals (8, .5, -3.2), scientific notation (1e3), the prefixes 0x / 0o / 0b (0x0a is 10), and Infinity / -Infinity. Any item that is not a valid number is silently excluded from the list.
• Arbitrary precision. Addition, subtraction and multiplication are exact. Division, mean and standard deviation are computed to 20 decimal places (rounding half away from zero), just like CyberChef's bignumber.js.
• Empty result. If no valid numbers remain, the result is NaN.
• Delimiter. The --delimiter flag selects how items are separated. The default is Line feed.

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator: Line feed, Space, Comma, Semi-colon, Colon, CRLF.

Set operations

set-union, set-intersection, set-difference and symmetric-difference take two sets; cartesian-product takes two or more; power-set takes one. Sets are separated by the --sample-delimiter (default \n\n) and items within a set by the --item-delimiter (default ,). Both delimiters accept backslash escapes (\n, \t, …). Giving the wrong number of sets is an error.

Flag	Type	Default	Description
--sample-delimiter	string	\n\n	Separator between sets (power-set has no sample delimiter).
--item-delimiter	string	,	Separator between items within a set.

---

Cartesian Product

Returns every combination drawing one item from each of two or more sets. Each combination is formatted as (a,b,…) and the combinations are joined by the item delimiter.

Options

Flag	Type	Default	Description
--sample-delimiter	string	\n\n	Separator between sets.
--item-delimiter	string	,	Separator between items and between combinations.

Simple example

printf '1,2\n\na,b' | cchef cartesian-product

Output:

(1,a),(1,b),(2,a),(2,b)

---

Divide

Divides the list left-to-right (a / b / c / …). Non-numeric items are excluded.

Options

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator (see shared options).

Simple example

cchef divide --delimiter Space -i '0x0a 8 .5'

Output:

2.5

Non-terminating result (20 decimal places)

cchef divide --delimiter Space -i '1 3'

Output:

0.33333333333333333333

---

Mean

Computes the mean (average) of the list. Non-numeric items are excluded.

Options

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator (see shared options).

Simple example

cchef mean --delimiter Space -i '0x0a 8 .5 .5'

Output:

4.75

---

Extended GCD

Runs the extended Euclidean algorithm on two whole numbers, reporting their greatest common divisor together with the Bezout coefficients — the x and y for which a*x + b*y = gcd(a, b).

Either value may be written in decimal or in hexadecimal with an 0x prefix, and there is no limit on their size. Leaving one blank takes that value from the input instead, so a number can be piped in.

Option	Type	Default	Notes
--value-a	string	(empty)	Decimal or 0x hex. Blank takes it from the input.
--value-b	string	(empty)	Decimal or 0x hex. Blank takes it from the input.

Simple example

cchef extended-gcd --value-a 3 --value-b 11

Output:

gcd: 1

Bezout coefficients:
x = 4
y = -1

Complex example

The value left blank comes from the input, so this asks for the divisor of 42 and 35:

cchef extended-gcd --value-b 35 -i 42

Output:

gcd: 7

Bezout coefficients:
x = 1
y = -1

Median

Computes the median of the list, sorting it first and averaging the two middle values for an even-length list. Non-numeric items are excluded.

CyberChef fixed a bug in mid-2026 (PR #2284) where odd-length lists were not sorted before the median was taken. cchef matches the corrected behavior (a true numeric median for all list lengths).

Options

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator (see shared options).

Simple example (odd length)

cchef median --delimiter Space -i '10 1 2'

Output:

2

Even length (mean of the two middle values)

cchef median --delimiter Space -i '10 1 2 5'

Output:

3.5

---

MOD

Reduces every number in a list by a modulus. Numbers are taken from the input using the delimiter, anything that is not a number is ignored, and the results are always reported separated by spaces whatever the input used.

The remainder takes the sign of the number being reduced, not of the modulus, and a number with a fractional part keeps one.

Option	Type	Default	Notes
--modulus	number	2	Cannot be zero.
--delimiter	option	Line feed	Also Space, Comma, Semi-colon, Colon, CRLF.

Simple example

cchef mod --modulus 3 --delimiter Space -i "15 4 7"

Output:

0 1 1

Complex example

A different delimiter, with values that are not numbers ignored:

cchef mod --modulus 5 --delimiter Comma -i "15,8,23"

Output:

0 3 3

Modular Exponentiation

Raises a base to an exponent, modulo a modulus — the base^exponent mod modulus behind Diffie-Hellman and RSA. The squaring loop keeps intermediate values small, so a crypto-sized exponent costs nothing.

Any of the three may be decimal, optionally signed, or 0x hex. The modulus is required and must not be zero. Either the base or the exponent may be left blank to take it from the input, but not both: with both blank there is one value for two slots, and the operation refuses rather than guessing.

Option	Type	Default	Notes
--base	string	(empty)	Decimal or 0x hex. Blank takes it from the input.
--modulus	string	1	Must not be zero.
--exponent	string	(empty)	Decimal or 0x hex. Blank takes it from the input.

Note. Reduction follows CyberChef, which uses JavaScript's remainder operator: the result takes the sign of the base, so a negative base gives a negative residue rather than the one in [0, modulus). A negative exponent returns 1 rather than a modular inverse, because the loop runs only while the exponent is above zero.

Simple example

cchef modular-exponentiation --base 2 --modulus 1000 --exponent 10

Output:

24

Complex example

Hex arguments, and taking the base from the input:

cchef modular-exponentiation --base 0x10 --modulus 1000 --exponent 0x2

Output:

256

cchef modular-exponentiation --modulus 1000000007 --exponent 65537 -i 123456789

Output:

560583526

Modular Inverse

Finds the number that multiplies with a to give one, modulo m — the x for which a*x = 1 (mod m). There is one only when a and m share no factor; otherwise the operation says so.

As with Extended GCD, either value may be decimal or 0x hex, and leaving one blank takes it from the input.

Option	Type	Default	Notes
--value-a	string	(empty)	Decimal or 0x hex. Blank takes it from the input.
--modulus-m	string	(empty)	Must be greater than zero.

Simple example

cchef modular-inverse --value-a 3 --modulus-m 11

Output:

4

Multiply

Multiplies the list together (a * b * c * …). Non-numeric items are excluded.

Options

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator (see shared options).

Simple example

cchef multiply --delimiter Space -i '0x0a 8 .5'

Output:

40

---

Power Set

Returns every subset of a single set (its power set). Each subset is joined by the item delimiter, subsets are ordered by their length, and each is followed by a newline (so the first line — the empty subset — is blank). Empty items are ignored.

Options

Flag	Type	Default	Description
--item-delimiter	string	,	Separator between items.

Simple example

cchef power-set -i 'a,b,c'

Output:

c
b
a
b,c
a,c
a,b
a,b,c

---

Set Difference

Returns the items of the first set that are not in the second (the relative complement). Duplicates in the first set are removed; order is preserved.

Options

Flag	Type	Default	Description
--sample-delimiter	string	\n\n	Separator between the two sets.
--item-delimiter	string	,	Separator between items.

Simple example

printf '1,2,3,4\n\n3,4' | cchef set-difference

Output:

1,2

---

Set Intersection

Returns the items present in both sets, in the order they appear in the first set. Duplicates in the first set are removed.

Options

Flag	Type	Default	Description
--sample-delimiter	string	\n\n	Separator between the two sets.
--item-delimiter	string	,	Separator between items.

Simple example

printf '1,2,3\n\n2,3,4' | cchef set-intersection

Output:

2,3

---

Set Union

Returns the items that appear in either set, deduplicated. Matching CyberChef's implementation (a JavaScript object used as a hash set), integer-like items are emitted first in ascending numeric order, then the remaining items in the order first seen.

Options

Flag	Type	Default	Description
--sample-delimiter	string	\n\n	Separator between the two sets.
--item-delimiter	string	,	Separator between items.

Simple example

printf '1,2,3\n\n3,4,5' | cchef set-union

Output:

1,2,3,4,5

Integer ordering quirk

printf '3,1,2\n\n5,4' | cchef set-union

Output:

1,2,3,4,5

---

Standard Deviation

Computes the population standard deviation of the list. Non-numeric items are excluded. The result is computed to 20 decimal places.

Options

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator (see shared options).

Simple example

cchef standard-deviation --delimiter Space -i '0x0a 8 .5'

Output:

4.08928138212843238213

---

Subtract

Subtracts the list left-to-right (a - b - c - …). Non-numeric items are excluded.

Options

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator (see shared options).

Simple example

cchef subtract --delimiter Comma -i '321,123,test'

Output:

198

---

Sum

Adds the list together. Non-numeric items are excluded.

Options

Flag	Type	Default	Description
--delimiter	option	Line feed	Item separator (see shared options).

Simple example

The default delimiter is a line feed, so a newline-separated list works with no flags:

printf '10\n8\n0.5' | cchef sum

Output:

18.5

Mixed radices on one line

cchef sum --delimiter Space -i '0x0a 8 .5'

Output:

18.5

---

Symmetric Difference

Returns the items that appear in exactly one of the two sets (the first set's extras followed by the second set's extras). Unlike the other set operations, it preserves duplicates within each side.

Options

Flag	Type	Default	Description
--sample-delimiter	string	\n\n	Separator between the two sets.
--item-delimiter	string	,	Separator between items.

Simple example

printf 'a,b,c\n\nb,c,d' | cchef symmetric-difference

Output:

a,d