The ratmath Reference Manual

This is the ratmath Reference Manual, version 1, generated automatically by Declt version 4.0 beta 2 "William Riker" on Sat Dec 03 23:08:36 2022 GMT+0.

Table of Contents


1 Introduction


2 Systems

The main system appears first, followed by any subsystem dependency.


2.1 ratmath

Math utilities for working with rational numbers and intervals.

Author

Jesse Off <>

License

MIT

Version

1

Source

ratmath.asd.

Child Components

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.


3.1 Lisp


3.1.1 ratmath/ratmath.asd

Source

ratmath.asd.

Parent Component

ratmath (system).

ASDF Systems

ratmath.


3.1.2 ratmath/package.lisp

Source

ratmath.asd.

Parent Component

ratmath (system).

Packages

ratmath.


3.1.3 ratmath/fifo.lisp

Dependency

package.lisp (file).

Source

ratmath.asd.

Parent Component

ratmath (system).

Internals

3.1.4 ratmath/pipe.lisp

Dependency

fifo.lisp (file).

Source

ratmath.asd.

Parent Component

ratmath (system).

Public Interface
Internals

3.1.5 ratmath/ratmath.lisp

Dependency

pipe.lisp (file).

Source

ratmath.asd.

Parent Component

ratmath (system).

Public Interface
Internals

4 Packages

Packages are listed by definition order.


4.1 ratmath

Source

package.lisp.

Use List

common-lisp.

Public Interface
Internals

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.


5.1 Public Interface


5.1.1 Macros

Macro: infsup (&rest args)

Returns infimum/supremum intervals. All strings and numbers in tree are converted keeping everything else intact. Exacts are fuzzified according to :tol and :abstol first, and then potentially widened further with :limd and :limn, which performs a rational approximation. Intervals already present in the structure, whether by explicit cons or via a string, will not be fuzzified further by :abstol and :tol, but they may be widened if rational approximation is called out via :limd/:limn args. Exact rationals will only convert to intervals if 1) their numerators/denominators exceed :limn/:limd or 2) an :open t arg is given. When the arg is an exact and rational approximation is called out, a 2nd value, alpha, is returned which is a number from 0-1 representing the location of the original exact in the returned interval.

Package

ratmath.

Source

ratmath.lisp.

Macro: pipe-cons (object pipe)
Package

ratmath.

Source

pipe.lisp.

Macro: pipe-sink-until-condition (pipe &rest conds)

Exposes elements of pipe until one of the condition types in conds is signalled. Returns nil for end of pipe, or 3 values: #1 being the interrupted pipe, #2 being the condition object, and #3 being the particular condition clause type in the original args that matched.

Package

ratmath.

Source

pipe.lisp.

Macro: rat (&rest args)

Performs a rational approximation of an exact number or interval. Takes keyword args :limn and :limd to represent max numerator and max denominator. Also will parse numeric strings into intervals ala parse-interval. Always returns an exact (i.e. not another interval).

Package

ratmath.

Source

ratmath.lisp.

Macro: with-interval-math (&rest body)

Replaces arithmetic calls like *-/+ with interval*-/+ and turns ~##.## symbols into literal rational intervals with implied precision based on the number of digits after the decimal point. (as in parse-interval)

Package

ratmath.

Source

ratmath.lisp.


5.1.2 Ordinary functions

Function: farey-pipe (order &key test-fn from-cf limn)

Returns a farey sequence; 2nd value is an encapsulated reverse sequence

Package

ratmath.

Source

ratmath.lisp.

Function: fractions (arg &key order)

Prints out rational approximations, one per line, with the PPM or PPB error.

Package

ratmath.

Source

ratmath.lisp.

Function: hull (&rest args)

Takes exacts and intervals as arguments and returns an interval enclosure containing the min/max. If the range between min and max is 0, hull will return an exact.

Package

ratmath.

Source

ratmath.lisp.

Function: interval (l u)

Constructs an interval from the given lower/upper bounds

Package

ratmath.

Source

ratmath.lisp.

Function: list-to-pipe (l)

Returns a pipe from a list input argument.

Package

ratmath.

Source

pipe.lisp.

Function: lower (x)

Returns the lower limit of an interval

Package

ratmath.

Source

ratmath.lisp.

Function: napiers-constant-generator ()

Returns an infinite/irrational continued fraction expansion of Euler’s number ’e’

Package

ratmath.

Source

ratmath.lisp.

Function: parse-interval (s)

Turns strings of rationals or floats into rational intervals. Infers interval radius from number specification. e.g. 1.000 implies an interval of [.9995, 1.0005) whereas just 1 implies [.5, 1.5). Exponent notation is also recognized; 1e3 is [500, 1500) whereas 1000 is [999.5, 1000.5). A rational specified as 22/7 is converted as (43/14, 45/14).

Package

ratmath.

Source

ratmath.lisp.

Function: pipe-append (pipe1 pipe2)

Appends two pipes together

Package

ratmath.

Source

pipe.lisp.

Function: pipe-apply (procedure pipe)

Runs procedure on every element as they are exposed, but does not transform the element.

Package

ratmath.

Source

pipe.lisp.

Function: pipe-end-after (test pipe)

Runs test on each element. When it returns t, the pipe is truncated after that element

Package

ratmath.

Source

pipe.lisp.

Function: pipe-end-before (test pipe)

Runs test on each element. When it returns t, the pipe is truncated before that element

Package

ratmath.

Source

pipe.lisp.

Function: pipe-endp (pipe)
Package

ratmath.

Source

pipe.lisp.

Function: pipe-filter (procedure pipe)

If procedure returns t, that particular pipe element is removed from the sequence.

Package

ratmath.

Source

pipe.lisp.

Function: pipe-first (pipe)
Package

ratmath.

Source

pipe.lisp.

Function: pipe-head (pipe &optional n)

Truncates a pipe after n (default: 1) elements

Package

ratmath.

Source

pipe.lisp.

Function: pipe-last (pipe &optional n)
Package

ratmath.

Source

pipe.lisp.

Function: pipe-mapc (procedure pipe)

Runs function on each element. Returns nothing.

Package

ratmath.

Source

pipe.lisp.

Function: pipe-printer (pipe)
Package

ratmath.

Source

pipe.lisp.

Function: pipe-rest (pipe)

Analogous to the rest function except works on a pipe rather than list

Package

ratmath.

Source

pipe.lisp.

Function: pipe-signaler (pipe)

For each condition object in pipe, set up some useful restarts and signal it. If nothing handles it, the default behavior is to ignore. If the use-value restart is invoked, that value will be returned as a pipe datum element.

Package

ratmath.

Source

pipe.lisp.

Function: pipe-sink (pipe)

Exposes elements of pipe forever, ignoring the elements. Similar to pipe-mapc with a no-op procedure. Useful to provoke the pipeline processing of an infinite pipe.

Package

ratmath.

Source

pipe.lisp.

Function: pipe-sink-until (test pipe)

Exposes elements of pipe until test returns t. When that happens, returns the (non-empty) pipe. If the pipe goes empty, returns nil. The test procedure is called with the current element as arg.

Package

ratmath.

Source

pipe.lisp.

Function: pipe-to-list (pipe)

Returns a list from the given pipe input argument. Infinite recursion results if the pipe is infinite.

Package

ratmath.

Source

pipe.lisp.

Function: pipe-transform (procedure pipe)

Runs procedure on each element of pipe; replacing each original element

Package

ratmath.

Source

pipe.lisp.

Function: pipe-uniq (pipe &optional pair-uniq-p carry)

Removes duplicates according to optional predicate func. Only dups in sequence are removed.

Package

ratmath.

Source

pipe.lisp.

Function: rat-pipe (arg &optional mult)

Returns a pipe of best rational approximations for every power-of-mult numerator/denominator. If arg is not a number, assumes it is a continued fraction pipe.

Package

ratmath.

Source

ratmath.lisp.

Function: upper (x)

Returns the upper limit of an interval

Package

ratmath.

Source

ratmath.lisp.

Function: ~ (&rest args)

Converts intervals into an exacts. :random picks a random value within the interval instead of the midpoint. :rat picks the first convergent rational fraction (which may not be the midpoint) :upper or :lower selects the upper or lower limit. :alpha modifies whats considered the midpoint of the interval. :discrete requests to only return one of either the lower or upper interval limit. By default, returns the midpoint. If passed in a list/tree, recursively modifies everything that looks like an interval and leaves everything else intact.

Package

ratmath.

Source

ratmath.lisp.

Function: ~= (a b)

Compares either exacts or intervals for possible equality.

Package

ratmath.

Source

ratmath.lisp.


5.1.3 Standalone methods

Method: print-object ((obj convergent) stream)
Source

ratmath.lisp.


5.2 Internals


5.2.1 Macros

Macro: best-convergent-test-fn (&rest args)
Package

ratmath.

Source

ratmath.lisp.

Macro: encapsulate (form)
Package

ratmath.

Source

pipe.lisp.

Macro: expose (procedure)
Package

ratmath.

Source

pipe.lisp.

Macro: fifo-get (f)

Removes and returns object from fifo. If fifo becomes empty, struct is destroyed, i.e. setf nil

Package

ratmath.

Source

fifo.lisp.

Macro: fifo-put (f obj)

Adds obj to fifo, instantiating new fifo struct if necessary. Returns new count of fifo

Package

ratmath.

Source

fifo.lisp.

Macro: interval~ (&rest args)

When the ~ function is encounted within a with-interval-math block, it converts exacts to intervals. Outside of the lexical scope of a with-interval-math block, ~ converts intervals into exacts.

Package

ratmath.

Source

ratmath.lisp.


5.2.2 Ordinary functions

Function: %infsup (x &key limn limd tol abstol open test-fn)
Package

ratmath.

Source

ratmath.lisp.

Function: %rat (x &key limn limd test-fn)
Package

ratmath.

Source

ratmath.lisp.

Function: best-convergent (arg &key limn limd test-fn)

From a rationalized continued-fraction-pipe arg, returns best convergent honoring limits. 2nd value being the next best ignoring limits.

Package

ratmath.

Source

ratmath.lisp.

Function: calc-stern-brocot (n)
Package

ratmath.

Source

ratmath.lisp.

Function: continued-fraction-pipe (f)

Returns a pipe of continued fraction terms from the input rational arg.

Package

ratmath.

Source

ratmath.lisp.

Reader: convergent-a (instance)
Writer: (setf convergent-a) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

a.

Reader: convergent-cf (instance)
Writer: (setf convergent-cf) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

cf.

Function: convergent-denominator (c)
Package

ratmath.

Source

ratmath.lisp.

Function: convergent-equal (a b)
Package

ratmath.

Source

ratmath.lisp.

Function: convergent-fract (c)
Package

ratmath.

Source

ratmath.lisp.

Function: convergent-numerator (c)
Package

ratmath.

Source

ratmath.lisp.

Function: convergent-p (object)
Package

ratmath.

Source

ratmath.lisp.

Function: convergent-q (c)
Package

ratmath.

Source

ratmath.lisp.

Reader: convergent-q-offset (instance)
Writer: (setf convergent-q-offset) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

q-offset.

Reader: convergent-r0 (instance)
Writer: (setf convergent-r0) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

r0.

Reader: convergent-r1 (instance)
Writer: (setf convergent-r1) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

r1.

Reader: convergent-rat (instance)
Writer: (setf convergent-rat) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

rat.

Function: convergent-ratio (c)
Package

ratmath.

Source

ratmath.lisp.

Function: convergent-stern-brocot (c)

From a convergent struct, make a Stern-Brocot struct by calculating the left and right parents

Package

ratmath.

Source

ratmath.lisp.

Function: convergents-pipe (cfs &optional r0 r1 a)

From a continued-fraction-pipe return a pipe of the resultant convergents.

Package

ratmath.

Source

ratmath.lisp.

Function: copy-convergent (instance)
Package

ratmath.

Source

ratmath.lisp.

Function: copy-fifo (instance)
Package

ratmath.

Source

fifo.lisp.

Function: copy-stern-brocot (instance)
Package

ratmath.

Source

ratmath.lisp.

Function: eval-constants (args &optional pure-function-symbolp)
Package

ratmath.

Source

ratmath.lisp.

Function: fifo-count (f)
Package

ratmath.

Source

fifo.lisp.

Reader: fifo-data (instance)
Writer: (setf fifo-data) (instance)
Package

ratmath.

Source

fifo.lisp.

Target Slot

data.

Function: fifo-endp (f)
Package

ratmath.

Source

fifo.lisp.

Function: fifo-head (f)
Package

ratmath.

Source

fifo.lisp.

Reader: fifo-n (instance)
Writer: (setf fifo-n) (instance)
Package

ratmath.

Source

fifo.lisp.

Target Slot

n.

Function: fifo-p (object)
Package

ratmath.

Source

fifo.lisp.

Reader: fifo-tail (instance)
Writer: (setf fifo-tail) (instance)
Package

ratmath.

Source

fifo.lisp.

Target Slot

tail.

Function: functionalp (fn &optional args)
Package

ratmath.

Source

ratmath.lisp.

Function: infsup-limd (arg &key limd limn test-fn open)

Returns an infimum/supremum interval; 2nd value is alpha (>.5 when supremum is closer)

Package

ratmath.

Source

ratmath.lisp.

Function: infsup-tol (x abstol &optional tol)

Returns an infimum/supremum interval given a tolerance.

Package

ratmath.

Source

ratmath.lisp.

Function: interval* (&rest args)
Package

ratmath.

Source

ratmath.lisp.

Function: interval+ (&rest args)
Package

ratmath.

Source

ratmath.lisp.

Function: interval- (&rest args)
Package

ratmath.

Source

ratmath.lisp.

Function: interval/ (&rest args)
Package

ratmath.

Source

ratmath.lisp.

Function: intervalabs (x)
Package

ratmath.

Source

ratmath.lisp.

Function: intervalexp (x)
Package

ratmath.

Source

ratmath.lisp.

Function: intervalexpt (x y)
Package

ratmath.

Source

ratmath.lisp.

Function: intervallog (x &optional n)
Package

ratmath.

Source

ratmath.lisp.

Function: intervalsqrt (x)
Package

ratmath.

Source

ratmath.lisp.

Function: make-convergent (cf r0 r1 a &optional q-offset)
Package

ratmath.

Source

ratmath.lisp.

Function: make-fifo (&key data tail n)
Package

ratmath.

Source

fifo.lisp.

Function: make-semi-convergent (q-offset c)
Package

ratmath.

Source

ratmath.lisp.

Function: make-stern-brocot (left-parent right-parent)
Package

ratmath.

Source

ratmath.lisp.

Function: my- (a b)
Package

ratmath.

Source

ratmath.lisp.

Function: my-min (&rest rest)
Package

ratmath.

Source

ratmath.lisp.

Function: my/ (a b)
Package

ratmath.

Source

ratmath.lisp.

Function: rationalize-continued-fraction-pipe (generator-pipe)

The normal continued-fraction-pipes have each term annotated with a lexical closure that returns the remainder to the terminal value. This value is used to qualify visiting iffy semi-convergents in a denominator/numerator limited rational approximation. With irrational numbers there is no end-value so we can give downpipe logic no insight as to whether an iffy semi-convergent is worthy.

Package

ratmath.

Source

ratmath.lisp.

Function: semi-convergent-closest-to-lim (cv limn limd)

From a specific convergent, check semi-convergents for one below num/denom limits

Package

ratmath.

Source

ratmath.lisp.

Function: semi-convergent-iffy-p (c)

Iffy semi-convergents are the exactly 1/2 CF semi-convergent of even terms.

Package

ratmath.

Source

ratmath.lisp.

Function: semi-convergent-p (c)

Semi-convergents are convergents with a truncated (up to 1/2) CF term

Package

ratmath.

Source

ratmath.lisp.

Function: stern-brocot-denominator (sb)
Package

ratmath.

Source

ratmath.lisp.

Function: stern-brocot-fract (sb)
Package

ratmath.

Source

ratmath.lisp.

Reader: stern-brocot-left-parent (instance)
Writer: (setf stern-brocot-left-parent) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

left-parent.

Function: stern-brocot-numerator (sb)
Package

ratmath.

Source

ratmath.lisp.

Function: stern-brocot-p (object)
Package

ratmath.

Source

ratmath.lisp.

Function: stern-brocot-ratio (sb)
Package

ratmath.

Source

ratmath.lisp.

Reader: stern-brocot-right-parent (instance)
Writer: (setf stern-brocot-right-parent) (instance)
Package

ratmath.

Source

ratmath.lisp.

Target Slot

right-parent.

Function: truncate-within-interval (cf1 cf2)

Takes 2 continued-fraction-pipes and returns one that stops at the simplest rational inbetween

Package

ratmath.

Source

ratmath.lisp.


5.2.3 Structures

Structure: convergent

Represents a (semi-)convergent in the rational approximation of a continued fraction.

Package

ratmath.

Source

ratmath.lisp.

Direct superclasses

structure-object.

Direct methods

print-object.

Direct slots
Slot: cf
Readers

convergent-cf.

Writers

(setf convergent-cf).

Slot: r0
Readers

convergent-r0.

Writers

(setf convergent-r0).

Slot: r1
Readers

convergent-r1.

Writers

(setf convergent-r1).

Slot: q-offset
Type

integer

Initform

0

Readers

convergent-q-offset.

Writers

(setf convergent-q-offset).

Slot: a
Readers

convergent-a.

Writers

(setf convergent-a).

Slot: rat
Readers

convergent-rat.

Writers

(setf convergent-rat).

Structure: fifo
Package

ratmath.

Source

fifo.lisp.

Direct superclasses

structure-object.

Direct slots
Slot: data
Type

list

Readers

fifo-data.

Writers

(setf fifo-data).

Slot: tail
Type

list

Readers

fifo-tail.

Writers

(setf fifo-tail).

Slot: n
Type

fixnum

Initform

0

Readers

fifo-n.

Writers

(setf fifo-n).

Structure: stern-brocot

Stern-Brocot left/right parent used to address a node in the Stern-Brocot fraction tree.

Package

ratmath.

Source

ratmath.lisp.

Direct superclasses

structure-object.

Direct slots
Slot: left-parent
Readers

stern-brocot-left-parent.

Writers

(setf stern-brocot-left-parent).

Slot: right-parent
Readers

stern-brocot-right-parent.

Writers

(setf stern-brocot-right-parent).


Appendix A Indexes


A.1 Concepts


A.2 Functions

Jump to:   %   (   ~  
B   C   E   F   H   I   L   M   N   P   R   S   T   U   W  
Index Entry  Section

%
%infsup: Private ordinary functions
%rat: Private ordinary functions

(
(setf convergent-a): Private ordinary functions
(setf convergent-cf): Private ordinary functions
(setf convergent-q-offset): Private ordinary functions
(setf convergent-r0): Private ordinary functions
(setf convergent-r1): Private ordinary functions
(setf convergent-rat): Private ordinary functions
(setf fifo-data): Private ordinary functions
(setf fifo-n): Private ordinary functions
(setf fifo-tail): Private ordinary functions
(setf stern-brocot-left-parent): Private ordinary functions
(setf stern-brocot-right-parent): Private ordinary functions

~
~: Public ordinary functions
~=: Public ordinary functions

B
best-convergent: Private ordinary functions
best-convergent-test-fn: Private macros

C
calc-stern-brocot: Private ordinary functions
continued-fraction-pipe: Private ordinary functions
convergent-a: Private ordinary functions
convergent-cf: Private ordinary functions
convergent-denominator: Private ordinary functions
convergent-equal: Private ordinary functions
convergent-fract: Private ordinary functions
convergent-numerator: Private ordinary functions
convergent-p: Private ordinary functions
convergent-q: Private ordinary functions
convergent-q-offset: Private ordinary functions
convergent-r0: Private ordinary functions
convergent-r1: Private ordinary functions
convergent-rat: Private ordinary functions
convergent-ratio: Private ordinary functions
convergent-stern-brocot: Private ordinary functions
convergents-pipe: Private ordinary functions
copy-convergent: Private ordinary functions
copy-fifo: Private ordinary functions
copy-stern-brocot: Private ordinary functions

E
encapsulate: Private macros
eval-constants: Private ordinary functions
expose: Private macros

F
farey-pipe: Public ordinary functions
fifo-count: Private ordinary functions
fifo-data: Private ordinary functions
fifo-endp: Private ordinary functions
fifo-get: Private macros
fifo-head: Private ordinary functions
fifo-n: Private ordinary functions
fifo-p: Private ordinary functions
fifo-put: Private macros
fifo-tail: Private ordinary functions
fractions: Public ordinary functions
Function, %infsup: Private ordinary functions
Function, %rat: Private ordinary functions
Function, (setf convergent-a): Private ordinary functions
Function, (setf convergent-cf): Private ordinary functions
Function, (setf convergent-q-offset): Private ordinary functions
Function, (setf convergent-r0): Private ordinary functions
Function, (setf convergent-r1): Private ordinary functions
Function, (setf convergent-rat): Private ordinary functions
Function, (setf fifo-data): Private ordinary functions
Function, (setf fifo-n): Private ordinary functions
Function, (setf fifo-tail): Private ordinary functions
Function, (setf stern-brocot-left-parent): Private ordinary functions
Function, (setf stern-brocot-right-parent): Private ordinary functions
Function, best-convergent: Private ordinary functions
Function, calc-stern-brocot: Private ordinary functions
Function, continued-fraction-pipe: Private ordinary functions
Function, convergent-a: Private ordinary functions
Function, convergent-cf: Private ordinary functions
Function, convergent-denominator: Private ordinary functions
Function, convergent-equal: Private ordinary functions
Function, convergent-fract: Private ordinary functions
Function, convergent-numerator: Private ordinary functions
Function, convergent-p: Private ordinary functions
Function, convergent-q: Private ordinary functions
Function, convergent-q-offset: Private ordinary functions
Function, convergent-r0: Private ordinary functions
Function, convergent-r1: Private ordinary functions
Function, convergent-rat: Private ordinary functions
Function, convergent-ratio: Private ordinary functions
Function, convergent-stern-brocot: Private ordinary functions
Function, convergents-pipe: Private ordinary functions
Function, copy-convergent: Private ordinary functions
Function, copy-fifo: Private ordinary functions
Function, copy-stern-brocot: Private ordinary functions
Function, eval-constants: Private ordinary functions
Function, farey-pipe: Public ordinary functions
Function, fifo-count: Private ordinary functions
Function, fifo-data: Private ordinary functions
Function, fifo-endp: Private ordinary functions
Function, fifo-head: Private ordinary functions
Function, fifo-n: Private ordinary functions
Function, fifo-p: Private ordinary functions
Function, fifo-tail: Private ordinary functions
Function, fractions: Public ordinary functions
Function, functionalp: Private ordinary functions
Function, hull: Public ordinary functions
Function, infsup-limd: Private ordinary functions
Function, infsup-tol: Private ordinary functions
Function, interval: Public ordinary functions
Function, interval*: Private ordinary functions
Function, interval+: Private ordinary functions
Function, interval-: Private ordinary functions
Function, interval/: Private ordinary functions
Function, intervalabs: Private ordinary functions
Function, intervalexp: Private ordinary functions
Function, intervalexpt: Private ordinary functions
Function, intervallog: Private ordinary functions
Function, intervalsqrt: Private ordinary functions
Function, list-to-pipe: Public ordinary functions
Function, lower: Public ordinary functions
Function, make-convergent: Private ordinary functions
Function, make-fifo: Private ordinary functions
Function, make-semi-convergent: Private ordinary functions
Function, make-stern-brocot: Private ordinary functions
Function, my-: Private ordinary functions
Function, my-min: Private ordinary functions
Function, my/: Private ordinary functions
Function, napiers-constant-generator: Public ordinary functions
Function, parse-interval: Public ordinary functions
Function, pipe-append: Public ordinary functions
Function, pipe-apply: Public ordinary functions
Function, pipe-end-after: Public ordinary functions
Function, pipe-end-before: Public ordinary functions
Function, pipe-endp: Public ordinary functions
Function, pipe-filter: Public ordinary functions
Function, pipe-first: Public ordinary functions
Function, pipe-head: Public ordinary functions
Function, pipe-last: Public ordinary functions
Function, pipe-mapc: Public ordinary functions
Function, pipe-printer: Public ordinary functions
Function, pipe-rest: Public ordinary functions
Function, pipe-signaler: Public ordinary functions
Function, pipe-sink: Public ordinary functions
Function, pipe-sink-until: Public ordinary functions
Function, pipe-to-list: Public ordinary functions
Function, pipe-transform: Public ordinary functions
Function, pipe-uniq: Public ordinary functions
Function, rat-pipe: Public ordinary functions
Function, rationalize-continued-fraction-pipe: Private ordinary functions
Function, semi-convergent-closest-to-lim: Private ordinary functions
Function, semi-convergent-iffy-p: Private ordinary functions
Function, semi-convergent-p: Private ordinary functions
Function, stern-brocot-denominator: Private ordinary functions
Function, stern-brocot-fract: Private ordinary functions
Function, stern-brocot-left-parent: Private ordinary functions
Function, stern-brocot-numerator: Private ordinary functions
Function, stern-brocot-p: Private ordinary functions
Function, stern-brocot-ratio: Private ordinary functions
Function, stern-brocot-right-parent: Private ordinary functions
Function, truncate-within-interval: Private ordinary functions
Function, upper: Public ordinary functions
Function, ~: Public ordinary functions
Function, ~=: Public ordinary functions
functionalp: Private ordinary functions

H
hull: Public ordinary functions

I
infsup: Public macros
infsup-limd: Private ordinary functions
infsup-tol: Private ordinary functions
interval: Public ordinary functions
interval*: Private ordinary functions
interval+: Private ordinary functions
interval-: Private ordinary functions
interval/: Private ordinary functions
intervalabs: Private ordinary functions
intervalexp: Private ordinary functions
intervalexpt: Private ordinary functions
intervallog: Private ordinary functions
intervalsqrt: Private ordinary functions
interval~: Private macros

L
list-to-pipe: Public ordinary functions
lower: Public ordinary functions

M
Macro, best-convergent-test-fn: Private macros
Macro, encapsulate: Private macros
Macro, expose: Private macros
Macro, fifo-get: Private macros
Macro, fifo-put: Private macros
Macro, infsup: Public macros
Macro, interval~: Private macros
Macro, pipe-cons: Public macros
Macro, pipe-sink-until-condition: Public macros
Macro, rat: Public macros
Macro, with-interval-math: Public macros
make-convergent: Private ordinary functions
make-fifo: Private ordinary functions
make-semi-convergent: Private ordinary functions
make-stern-brocot: Private ordinary functions
Method, print-object: Public standalone methods
my-: Private ordinary functions
my-min: Private ordinary functions
my/: Private ordinary functions

N
napiers-constant-generator: Public ordinary functions

P
parse-interval: Public ordinary functions
pipe-append: Public ordinary functions
pipe-apply: Public ordinary functions
pipe-cons: Public macros
pipe-end-after: Public ordinary functions
pipe-end-before: Public ordinary functions
pipe-endp: Public ordinary functions
pipe-filter: Public ordinary functions
pipe-first: Public ordinary functions
pipe-head: Public ordinary functions
pipe-last: Public ordinary functions
pipe-mapc: Public ordinary functions
pipe-printer: Public ordinary functions
pipe-rest: Public ordinary functions
pipe-signaler: Public ordinary functions
pipe-sink: Public ordinary functions
pipe-sink-until: Public ordinary functions
pipe-sink-until-condition: Public macros
pipe-to-list: Public ordinary functions
pipe-transform: Public ordinary functions
pipe-uniq: Public ordinary functions
print-object: Public standalone methods

R
rat: Public macros
rat-pipe: Public ordinary functions
rationalize-continued-fraction-pipe: Private ordinary functions

S
semi-convergent-closest-to-lim: Private ordinary functions
semi-convergent-iffy-p: Private ordinary functions
semi-convergent-p: Private ordinary functions
stern-brocot-denominator: Private ordinary functions
stern-brocot-fract: Private ordinary functions
stern-brocot-left-parent: Private ordinary functions
stern-brocot-numerator: Private ordinary functions
stern-brocot-p: Private ordinary functions
stern-brocot-ratio: Private ordinary functions
stern-brocot-right-parent: Private ordinary functions

T
truncate-within-interval: Private ordinary functions

U
upper: Public ordinary functions

W
with-interval-math: Public macros