Math library

This page groups the public words from the files imported by ff/lib/math/math.ffp.

pred.ffp

Source: ff/lib/math/pred.ffp
Import: .import <math/pred>

Word	Stack effect	Description
negitive?	n -- flag	Tests whether a number is negative.
positive?	n -- flag	Tests whether a number is positive.
divisor?	n d -- flag	Tests whether d divides n evenly.
even?	n -- flag	Tests whether a number is even.
odd?	n -- flag	Tests whether a number is odd.

arith.ffp

Source: ff/lib/math/arith.ffp
Import: .import <math/arith>

Word	Stack effect	Description
sgn	x -- sgn(x)	Returns the sign of a number.
abs	x -- |x|	Returns the absolute value.
sqr	x -- x²	Squares a number.
min	a b -- min	Returns the smaller of two values.
max	a b -- max	Returns the larger of two values.
clamp	lo hi x -- x'	Constrains a value to an inclusive range.
divrem	a b -- q r	Returns quotient and remainder together.

num.ffp

Source: ff/lib/math/num.ffp
Import: .import <math/num>

Word	Stack effect	Description
!	n -- n!	Computes factorial.
nck	n k -- C(n,k)	Computes a binomial coefficient.
^^	a b -- a↑↑b	Applies Knuth up-arrow tetration.
^^^	a b -- a↑↑↑b	Applies the next higher Knuth hyper-operator.

atan.ffp

Source: ff/lib/math/atan.ffp
Import: .import <math/atan>

Word	Stack effect	Description
iatan	x -- ⌊atan(x)⌋₀	Integer arctangent with zero decimal places.
natan	n x -- ⌊10ⁿ*atan(x)⌋₀	Fixed-point arctangent at decimal precision n.
qatan	u v -- ⌊atan(u/v)⌋₀	Integer arctangent of a rational input.
atan-inv	n x -- ⌊10ⁿ*atan(1/x)⌋₀	Fixed-point arctangent of the reciprocal input.

atanh.ffp

Source: ff/lib/math/atanh.ffp
Import: .import <math/atanh>

Word	Stack effect	Description
iatanh	x -- ⌊atanh(x)⌋₀	Integer inverse hyperbolic tangent with zero decimal places.
natanh	n x -- ⌊10ⁿ*atanh(x)⌋₀	Fixed-point inverse hyperbolic tangent at decimal precision n.
qatanh	u v -- ⌊atanh(u/v)⌋₀	Integer inverse hyperbolic tangent of a rational input.
atanh-inv	n x -- ⌊10ⁿ*atanh(1/x)⌋₀	Fixed-point inverse hyperbolic tangent of the reciprocal input.

sqrt.ffp

Source: ff/lib/math/sqrt.ffp
Import: .import <math/sqrt>

Word	Stack effect	Description
isqrt	x -- ⌊sqrt(x)⌋	Returns the integer square root of a non-negative input.
isqrtrem	x -- ⌊sqrt(x)⌋ x-⌊sqrt(x)⌋²	Returns the integer square root and leftover remainder.
nsqrt	n x -- ⌊10ⁿ*sqrt(x)⌋	Returns a fixed-point square root with n decimal digits.

cbrt.ffp

Source: ff/lib/math/cbrt.ffp
Import: .import <math/cbrt>

Word	Stack effect	Description
icbrt	x -- ⌊cbrt(x)⌋₀	Returns the integer cube root, truncated toward zero.

gcd.ffp

Source: ff/lib/math/gcd.ffp
Import: .import <math/gcd>

Word	Stack effect	Description
gcd	a b -- gcd	Computes the greatest common divisor.
lcm	a b -- lcm	Computes the least common multiple.

ack.ffp

Source: ff/lib/math/ack.ffp
Import: .import <math/ack>

Word	Stack effect	Description
ack	m n -- ack(m,n)	Computes the Ackermann function, with fast paths for small m.

primes.ffp

Source: ff/lib/math/primes.ffp
Import: .import <math/primes>

Word	Stack effect	Description
maybe_prime?	n -- flag	Probabilistic Miller-Rabin primality screen.
prime?	n -- flag	Exact primality test using the screen plus trial division.
next-prime	n -- p	Returns the smallest prime greater than or equal to n.
th-prime	n -- p	Returns the nth prime by repeated search.

log.ffp

Source: ff/lib/math/log.ffp
Import: .import <math/log>

Word	Stack effect	Description
nln2	n -- ⌊10ⁿ*ln(2)⌋	Computes a fixed-point approximation of ln(2).
ilb	x -- ⌊log2(x)⌋	Returns the integer base-2 logarithm.
ilog	x -- ⌊log10(x)⌋	Returns the integer base-10 logarithm.
iln	x -- ⌊ln(x)⌋	Returns an integer natural logarithm approximation.

exp.ffp

Source: ff/lib/math/exp.ffp
Import: .import <math/exp>

Word	Stack effect	Description
iexp	x -- ⌊eˣ⌋	Computes a floored integer exponential using a fixed fast path.
nexp	n x -- ⌊10ⁿ*eˣ⌋	Computes a fixed-point exponential at decimal precision n.
ncosh	n x -- ⌊cosh(x)*10ⁿ⌋	Computes fixed-point hyperbolic cosine.
nsinh	n x -- ⌊sinh(x)*10ⁿ⌋	Computes fixed-point hyperbolic sine.
icosh	x -- ⌊cosh(x)⌋	Integer hyperbolic cosine wrapper around ncosh.
isinh	x -- ⌊sinh(x)⌋	Integer hyperbolic sine wrapper around nsinh.

pi.ffp

Source: ff/lib/math/pi.ffp
Import: .import <math/pi>

Word	Stack effect	Description
npi	n -- ⌊10ⁿ*π⌋	Computes pi to n decimal places in fixed-point form.
tau	n -- ⌊10ⁿ*2*π⌋	Computes tau to n decimal places in fixed-point form.
half_pi	n -- ⌊10ⁿ*π/2⌋	Computes pi/2 to n decimal places in fixed-point form.

trig.ffp

Source: ff/lib/math/trig.ffp
Import: .import <math/trig>

This file is currently a placeholder and does not define public words yet.

prn.ffp

Source: ff/lib/math/prn.ffp
Import: .import <math/prn>

Word	Stack effect	Description
nputn	n x -- {prints x with n fractional digits}	Prints a fixed-point decimal with zero-padded fractional digits.
qputn	p q -- {prints reduced p/q}	Prints a reduced rational number as p/q.