Default
Math context and dialect
Mathematical context and dialect (calc)
mod
Returns the remainder of dividing x by y.
x integer or decimal value
y integer or decimal value
returns decimal remainder of x/y
cc math |type?
; returns contextpow
Returns base raised to the power of exponent.
base integer, decimal, or complex value
exponent integer, decimal, or complex value
returns decimal result of base raised to the power of exponent for integer/decimal inputs, complex result for complex inputs
cc math |type?
; returns contextpow 2 3
; returns 8log2
Returns the binary logarithm (base-2) of x.
x integer or decimal value
returns decimal binary logarithm of x
log2 8
; returns 3log10
Returns the decimal logarithm (base-10) of x.
x integer or decimal value
returns decimal base-10 logarithm of x
log10 100
; returns 2log
Returns the natural logarithm of x.
x integer, decimal, or complex value (must not be zero)
returns decimal natural logarithm of x for integer/decimal input, complex logarithm for complex input
log 1
; returns 0log 2.718281828459045
; returns 1log 0
; correctly causes error:
; Word not found: log. Check spelling or ensure the word is defined in the current context. log complex 0 0
; correctly causes error:
; Word not found: log. Check spelling or ensure the word is defined in the current context. log1p
Returns the natural logarithm of 1 plus its argument x.
x integer or decimal value
returns decimal natural logarithm of (1 + x)
log1p 0
; returns 0logb
Returns the binary exponent of x.
x integer or decimal value
returns decimal binary exponent of x
logb 8
; returns 3sq
Returns the square of x.
x integer or decimal value
returns decimal square of x
sq 4
; returns 16sin
Returns the sine of the radian argument.
x integer, decimal, or complex value in radians
returns decimal sine of x for integer/decimal input, complex sine for complex input
sin 0
; returns 0round\to sin pi 10
; returns 0cos
Returns the cosine of the radian argument.
x integer, decimal, or complex value in radians
returns decimal cosine of x for integer/decimal input, complex cosine for complex input
cos 0
; returns 1tan
Returns the tangent of the radian argument.
x integer, decimal, or complex value in radians
returns decimal tangent of x for integer/decimal input, complex tangent for complex input
tan 0
; returns 0sqrt
Returns the square root of x.
x integer, decimal, or complex value
returns decimal square root of x for integer/decimal input, complex square root for complex input
sqrt 9
; returns 3abs
Returns the absolute value of a number.
x integer, decimal, or complex value
returns absolute value of x (same type as input for integer/decimal, decimal for complex)
abs -5
; returns 5abs 5
; returns 5abs complex 3 4
; returns 5acos
Returns the arccosine (inverse cosine) in radians.
x integer or decimal value between -1 and 1
returns decimal arccosine of x in radians
acos 1
; returns 0acosh
Returns the inverse hyperbolic cosine.
x integer or decimal value >= 1
returns decimal inverse hyperbolic cosine of x
acosh 1
; returns 0asin
Returns the arcsine (inverse sine) in radians.
x integer or decimal value between -1 and 1
returns decimal arcsine of x in radians
asin 0
; returns 0asinh
Returns the inverse hyperbolic sine.
x integer or decimal value
returns decimal inverse hyperbolic sine of x
asinh 0
; returns 0atan
Returns the arctangent (inverse tangent) in radians.
x integer or decimal value
returns decimal arctangent of x in radians
atan 0
; returns 0atan2
Returns the arc tangent of y/x, using the signs of the two to determine the quadrant of the return value.
y integer or decimal value
x integer or decimal value
returns decimal arctangent of y/x in radians, using signs to determine quadrant
atan2 0 1
; returns 0atanh
Returns the inverse hyperbolic tangent.
x integer or decimal value between -1 and 1
returns decimal inverse hyperbolic tangent of x
atanh 0
; returns 0ceil
Returns the least integer value greater than or equal to x.
x integer or decimal value
returns decimal ceiling of x (smallest integer >= x)
ceil 3.1
; returns 4cbrt
Returns the cube root of x.
x integer or decimal value
returns decimal cube root of x
cbrt 8
; returns 2copysign
Returns a value with the magnitude of x and the sign of y.
x integer or decimal value
y integer or decimal value
returns decimal with magnitude of x and sign of y
copysign 1 -2
; returns -1dim
Returns the maximum of x-y or 0.
x integer or decimal value
y integer or decimal value
returns decimal max(x-y, 0)
dim 5 3
; returns 2dim 3 5
; returns 0round\ o
Rounds a decimal to the specified number of decimal places.
x decimal value to round
digits integer number of decimal places to round to
returns decimal rounded to specified number of decimal places
round\to 3.14159 2
; returns 3.14round
Rounds a decimal to the nearest integer.
x decimal value
returns decimal rounded to nearest integer
round 3.7
; returns 4round 3.2
; returns 3roundtoeven
Returns the nearest integer, rounding ties to even.
x integer or decimal value
returns decimal rounded to nearest integer, with ties rounded to even
roundtoeven 3.5
; returns 4roundtoeven 2.5
; returns 2erf
Returns the error function of value.
x integer or decimal value
returns decimal error function value of x
erf 0
; returns 0erfc
Returns the complementary error function of value.
x integer or decimal value
returns decimal complementary error function value of x
erfc 0
; returns 1erfcinv
Returns the inverse of erfc(x) function.
x integer or decimal value between 0 and 2
returns decimal inverse complementary error function value of x
erfcinv 1
; returns 0erfinv
Returns the inverse error function of value.
x integer or decimal value between -1 and 1
returns decimal inverse error function value of x
erfinv 0
; returns 0exp
Returns e**x, the base-e exponential of x.
x integer, decimal, or complex value
returns decimal e^x for integer/decimal input, complex e^z for complex input
exp 0
; returns 1exp 1
; returns 2.718281828459045exp2
Returns 2**x, the base-2 exponential of x.
x integer or decimal value
returns decimal 2^x
exp2 3
; returns 8expm1
Returns e**x - 1, the base-e exponential of x minus 1. It is more accurate than exp(x) - 1 when x is near zero.
x integer or decimal value
returns decimal e^x - 1
expm1 0
; returns 0fma
Returns x * y + z, computed with only one rounding. (That is, FMA returns the fused multiply-add of x, y, and z.)
x integer or decimal value
y integer or decimal value
z integer or decimal value
returns decimal (x * y) + z computed with only one rounding
fma 2 3 4
; returns 10j0
Returns the order-zero Bessel function of the first kind.
x integer or decimal value
returns decimal order-zero Bessel function of the first kind
j0 0
; returns 1j1
Returns the order-one Bessel function of the first kind.
x integer or decimal value
returns decimal order-one Bessel function of the first kind
j1 0
; returns 0y0
Returns the order-zero Bessel function of the second kind.
x integer or decimal value
returns decimal order-zero Bessel function of the second kind
y0 1
; returns 0.08825696421567697y1
Returns the order-one Bessel function of the second kind.
x integer or decimal value
returns decimal order-one Bessel function of the second kind
y1 1
; returns -0.7812128213002887yn
Returns the order-n Bessel function of the second kind.
n integer order
x integer or decimal value
returns decimal order-n Bessel function of the second kind
yn 2 1
; returns -1.6506826068162543jn
Returns the order-n Bessel function of the first kind.
n integer order
x integer or decimal value
returns decimal order-n Bessel function of the first kind
jn 2 1
; returns 0.11490348493190049trunc
Returns the integer value of input.
x integer or decimal value
returns decimal integer value of x (truncated toward zero)
trunc 3.7
; returns 3pi
Returns the mathematical constant π (pi).
none
returns decimal value of π (pi)
round\to pi 5
; returns 3.14159deg->rad
Converts degrees to radians.
degrees integer or decimal value in degrees
returns decimal value in radians
deg->rad 180
; returns 3.141592653589793is-near
Returns true if two decimals are close.
x integer or decimal value
y integer or decimal value
returns integer 1 if values are very close, 0 otherwise
is-near 0.0000000000001 0
; returns 1is-near 0.1 0
; returns 0near-zero
Returns true if a decimal is close to zero.
x integer or decimal value
returns integer 1 if value is very close to zero, 0 otherwise
near-zero 0.0000000000001
; returns 1near-zero 0.1
; returns 0is-prime
Returns true if the integer is a prime number.
n integer value to check
returns integer 1 if n is prime, 0 otherwise
to-eyr
Converts math dialect to Eyr dialect.
block block containing math expressions
returns block converted to Eyr dialect
to-eyr { 1 + 2 * 3 } |type?
; returns blockcalc
Evaluates expressions in math dialect.
block block containing math expressions with proper operator precedence and parentheses support
returns result of evaluating the math expressions following standard mathematical order of operations
calc { 1 + 2 * 3 }
; returns 7calc { 2 + 3 * 4 }
; returns 14calc { 10 - 6 / 2 }
; returns 7calc { 2 * 3 + 4 }
; returns 10calc { 8 / 2 - 1 }
; returns 3calc { ( 1 + 2 ) * 3 }
; returns 9calc { 2 * ( 3 + 4 ) }
; returns 14calc { ( 10 - 6 ) / 2 }
; returns 2calc { ( 2 + 3 ) * ( 4 - 1 ) }
; returns 15calc { 2 + ( 3 * ( 4 + 1 ) ) }
; returns 17calc { ( ( 2 + 3 ) * 4 ) - 1 }
; returns 19gcd
Returns the greatest common divisor of two integers using Euclidean algorithm.
a integer value
b integer value
returns integer greatest common divisor of a and b
gcd 48 18
; returns 6gcd 17 13
; returns 1gcd 100 25
; returns 25gcd 0 5
; returns 5gcd 7 0
; returns 7Validation
validation dialect for Rye values
validate
Validates and transforms data according to specified rules, returning a dictionary with converted values or an error.
data Dictionary, Context, or List to validate
rules Block containing validation rules
returns validated Dictionary/Context/List with converted values or error if validation fails
validate>ctx
Validates and transforms data according to specified rules, returning a context object for easy field access.
data Dictionary to validate
rules Block containing validation rules
returns validated Context with converted values or error if validation fails
validate>ctx dict { a: 1 } { a: optional 0 } |-> 'a
; returns 1EYR Dialect
Stack based evaluator / dialect
eyr
Evaluates Rye block as Eyr (postfix) stack based code.
block Block of code to evaluate in EYR (postfix) mode
returns result of evaluating the block as postfix stack-based code
eyr { 1 2 }
; returns 3eyr { 5 3 }
; returns 2eyr { 4 2 }
; returns 8eyr { 6 2 }
; returns 3eyr { 1 2 3 }
; returns 3rye0
Evaluates Rye block as Rye0 dialect.
block Block of code to evaluate in RYE0 dialect
returns result of evaluating the block in RYE0 dialect
rye00
Evaluates Rye block as Rye00 dialect (builtins and integers only).
block Block of code to evaluate in RYE00 dialect (builtins and integers only)
returns result of evaluating the block in RYE00 dialect (minimal feature set)
eyr\full
Evaluates Rye block as Eyr (postfix) stack based code.
block Block of code to evaluate in EYR mode returning full stack as block
returns block containing all values from the EYR evaluation stack
eyr\loop
Evaluates Rye block in loop as Eyr code (postfix stack based) N times.
count Integer number of times to loop
block Block of EYR code to execute in each iteration
returns result of the final EYR evaluation
to-eyr
Evaluates Rye block as Eyr (postfix) stack based code.
block Rye block to compile/convert to EYR format
returns block containing the EYR-compiled version of the input block
to-eyr { 1 + 2 } |type?
; returns blockto-eyr { 5 * 3 } |length? |> 0
; returns true