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Unstable Flonums:   May Change Without Warning
flonum->bit-field
bit-field->flonum
flonum->ordinal
ordinal->flonum
flonums-between
flstep
flnext
flprev
-max.0
-min.0
+  min.0
+  max.0
6.2

Unstable Flonums: May Change Without Warning

Neil Toronto <[email protected]>

This library is unstable; compatibility will not be maintained. See Unstable: May Change Without Warning for more information.

 (require unstable/flonum) package: unstable-flonum-lib

You should almost certainly use math/flonum instead of this module, which is more complete and can be used in Typed Racket code.

procedure

(flonum->bit-field x)  (integer-in 0 (- (expt 2 64) 1))

  x : flonum?
Returns the bits comprising x as an integer. A convenient shortcut for composing integer-bytes->integer with real->floating-point-bytes.

Examples:

> (number->string (flonum->bit-field -inf.0) 16)

"fff0000000000000"

> (number->string (flonum->bit-field +inf.0) 16)

"7ff0000000000000"

> (number->string (flonum->bit-field -0.0) 16)

"8000000000000000"

> (number->string (flonum->bit-field 0.0) 16)

"0"

> (number->string (flonum->bit-field -1.0) 16)

"bff0000000000000"

> (number->string (flonum->bit-field 1.0) 16)

"3ff0000000000000"

> (number->string (flonum->bit-field +nan.0) 16)

"7ff8000000000000"

procedure

(bit-field->flonum i)  flonum?

  i : (integer-in 0 (- (expt 2 64) 1))
The inverse of flonum->bit-field.

procedure

(flonum->ordinal x)

  (integer-in (- (- (expt 2 63) 1)) (- (expt 2 63) 1))
  x : flonum?
Returns the signed ordinal index of x in a total order over flonums.

When inputs are not +nan.0, this function is monotone and symmetric; i.e. if (fl<= x y) then (<= (flonum->ordinal x) (flonum->ordinal y)), and (= (flonum->ordinal (- x)) (- (flonum->ordinal x))).

Examples:

> (flonum->ordinal -inf.0)

-9218868437227405312

> (flonum->ordinal +inf.0)

9218868437227405312

> (flonum->ordinal -0.0)

0

> (flonum->ordinal 0.0)

0

> (flonum->ordinal -1.0)

-4607182418800017408

> (flonum->ordinal 1.0)

4607182418800017408

> (flonum->ordinal +nan.0)

9221120237041090560

These properties mean that flonum->ordinal does not distinguish -0.0 and 0.0.

The following plot demonstrates how the density of floating-point numbers decreases with magnitude:

Example:

> (parameterize ([y-axis-ticks? #f])
    (plot (list (function (compose flonum->ordinal exact->inexact) 1/4 8)
                (y-axis 1/2) (y-axis 1) (y-axis 2) (y-axis 4))))

image

procedure

(ordinal->flonum i)  flonum?

  i : (integer-in (- (- (expt 2 63) 1)) (- (expt 2 63) 1))
The inverse of flonum->ordinal.

procedure

(flonums-between x y)  exact-integer?

  x : flonum?
  y : flonum?
Returns the number of flonums between x and y, excluding one endpoint. Equivalent to (- (flonum->ordinal y) (flonum->ordinal x)).

Examples:

> (flonums-between 0.0 1.0)

4607182418800017408

> (flonums-between 1.0 2.0)

4503599627370496

> (flonums-between 2.0 3.0)

2251799813685248

> (flonums-between 1.0 +inf.0)

4611686018427387904

procedure

(flstep x n)  flonum?

  x : flonum?
  n : exact-integer?
Returns the flonum n flonums away from x, according to flonum->ordinal. If x is +nan.0, returns +nan.0.

Examples:

> (flstep 0.0 1)

4.9406564584125e-324

> (flstep (flstep 0.0 1) -1)

0.0

> (flstep 0.0 -1)

-4.9406564584125e-324

> (flstep +inf.0 1)

+inf.0

> (flstep +inf.0 -1)

1.7976931348623157e+308

> (flstep -inf.0 -1)

-inf.0

> (flstep -inf.0 1)

-1.7976931348623157e+308

> (flstep +nan.0 1000)

+nan.0

procedure

(flnext x)  flonum?

  x : flonum?
Equivalent to (flstep x 1).

procedure

(flprev x)  flonum?

  x : flonum?
Equivalent to (flstep x -1).

value

-max.0 : flonum?

value

-min.0 : flonum?

value

+min.0 : flonum?

value

+max.0 : flonum?

The rational flonums with maximum and minimum magnitude.

Examples:

> (list -max.0 +max.0 -min.0 +min.0)

'(-1.7976931348623157e+308

  1.7976931348623157e+308

  -4.9406564584125e-324

  4.9406564584125e-324)

> (plot (function sqrt 0 (* 20 +min.0)))

image