Namespace: joker.math

v1.0

Contents

• Summary
• Index
• Constants
• Variables
• Functions, Macros, and Special Forms

Summary

Provides floating-point mathematical functions, IEEE-754 helpers, and numeric constants.

Index

• abs
• ceil
• copy-sign
• cos
• cube-root
• dim
• e
• exp
• exp-2
• exp-minus-1
• floor
• hypot
• inf
• inf?
• ln-of-10
• ln-of-2
• log
• log-10
• log-10-of-e
• log-2
• log-2-of-e
• log-binary
• log-plus-1
• max-double
• modf
• nan
• nan?
• next-after
• phi
• pi
• pow
• pow-10
• precision
• round
• round-to-even
• set-precision
• sign-bit
• sin
• smallest-nonzero-double
• sqrt
• sqrt-of-2
• sqrt-of-e
• sqrt-of-phi
• sqrt-of-pi
• trunc

Constants

Constants are variables with :const true in their metadata. Joker currently does not recognize them as special; as such, it allows redefining them or their values.

• e

  Double v1.0

  e

• ln-of-10

  Double v1.0

  Natural logarithm of 10

• ln-of-2

  Double v1.0

  Natural logarithm of 2

• log-10-of-e

  Double v1.0

  Base-10 logarithm of e

• log-2-of-e

  Double v1.0

  Base-2 logarithm of e

• max-double

  Double v1.0

  Largest finite value representable by Double

• phi

  Double v1.0

  Phi

• pi

  Double v1.0

  pi

• smallest-nonzero-double

  Double v1.0

  Smallest positive, non-zero value representable by Double

• sqrt-of-2

  Double v1.0

  Square root of 2

• sqrt-of-e

  Double v1.0

  Square root of e

• sqrt-of-phi

  Double v1.0

  Square root of phi

• sqrt-of-pi

  Double v1.0

  Square root of pi

Variables

(None.)

Functions, Macros, and Special Forms

• abs

  Function v1.0

  (abs x)
  

  Returns the absolute value of x.

• ceil

  Function v1.0

  (ceil x)
  

  Returns the least integer value greater than or equal to x.

• copy-sign

  Function v1.0

  (copy-sign x y)
  

  Returns value with the magnitude of x and the sign of y.

• cos

  Function v1.0

  (cos x)
  

  Returns the cosine of the radian argument x.

• cube-root

  Function v1.0

  (cube-root x)
  

  Returns the cube root of x.

• dim

  Function v1.0

  (dim x y)
  

  Returns the maximum of x-y and 0.

• exp

  Function v1.0

  (exp x)
  

  Returns e**x, the base-e exponential of x.

• exp-2

  Function v1.0

  (exp-2 x)
  

  Returns 2**x, the base-2 exponential of x.

• exp-minus-1

  Function v1.0

  (exp-minus-1 x)
  

  Returns e**x - 1, the base-e exponential of x minus 1.
  
  This is more accurate than (- (exp x) 1.) when x is near zero.

• floor

  Function v1.0

  (floor x)
  

  Returns the greatest integer value less than or equal to x.

• hypot

  Function v1.0

  (hypot p q)
  

  Returns Sqrt(p*p + q*q), taking care to avoid unnecessary overflow and underflow.

• inf

  Function v1.0

  (inf sign)
  

  Returns positive infinity if sign >= 0, negative infinity if sign < 0.

• inf?

  Function v1.0

  (inf? x sign)
  

  Returns whether x is an infinity.
  
  If sign > 0, returns whether x is positive infinity; if < 0, whether negative infinity; if == 0, whether either infinity.

• log

  Function v1.0

  (log x)
  

  Returns the natural logarithm of x.

• log-10

  Function v1.0

  (log-10 x)
  

  Returns the decimal logarithm of x.

• log-2

  Function v1.0

  (log-2 x)
  

  Returns the binary logarithm of x.

• log-binary

  Function v1.0

  (log-binary x)
  

  Returns the binary exponent of x.

• log-plus-1

  Function v1.0

  (log-plus-1 x)
  

  Returns the natural logarithm of 1 plus x.
  
  This is more accurate than (log (+ 1 x)) when x is near zero.

• modf

  Function v1.0

  (modf x)
  

  Returns a vector with the integer and fractional floating-point numbers that sum to x.
  
  Both values have the same sign as x.

• nan

  Function v1.0

  (nan)
  

  Returns an IEEE 754 "not-a-number" value.

• nan?

  Function v1.0

  (nan? x)
  

  Returns whether x is an IEEE 754 "not-a-number" value.

• next-after

  Function v1.0

  (next-after x y)
  

  Returns the next representable Double value after x towards y.

• pow

  Function v1.0

  (pow x y)
  

  Returns x**y, the base-x exponential of y.

• pow-10

  Function v1.0

  (pow-10 x)
  

  Returns 10**x, the base-10 exponential of x.

• precision

  Function v1.0

  (precision f)
  

  Returns the precision of a Number.
  
  The precision excludes any sign or exponent. For a BigInt, it's the
  number of bits needed to represent the number; for a BigFloat, Int,
  or Double, it's the number of bits available in that instance or
  type. E.g. (precision 1) returns either 31 or 63, depending on
  whether the Joker executable is 32-bit or 64-bit (for integers);
  (precision 1.0) returns 53 (as Double is always a float64); and
  (precision 1.0M) returns 53 as well, though prepending or appending
  enough 0 digits will result in a BigFloat with more precision
  reported.
  
  If f is not a supported Number type (such as Ratio), a panic
  results.

• round

  Function v1.0

  (round x)
  

  Returns the integer nearest to x, rounding half away from zero.

• round-to-even

  Function v1.0

  (round-to-even x)
  

  Returns the integer nearest to x, rounding ties to the nearest even integer.

• set-precision

  Function v1.0

  (set-precision prec f)
  

  Returns a copy of a BigFloat with the specified precision.
  
  Calls Go's math/big.(*Float)SetPrec(prec) on a copy of f. prec must
  evaluate to a non-negative integer. Returns the resulting BigFloat.

• sign-bit

  Function v1.0

  (sign-bit x)
  

  Returns whether x is negative or negative zero.

• sin

  Function v1.0

  (sin x)
  

  Returns the sine of the radian argument x.

• sqrt

  Function v1.0

  (sqrt x)
  

  Returns the square root of x.

• trunc

  Function v1.0

  (trunc x)
  

  Returns the integer value of x, rounded toward zero.