A fixed-point number type.

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Nick Patrick <>




A Common Lisp fixed-point numeric type package intended to be similar to the Ada language type. The focus is providing a useful abstraction for known reliable precision in a specific range. This package uses CLOS to encapsulate the underlying type.

If the reader macro is installed (install-reader-macro), then fixed point values can be read without floating point precision issues.

A small utility package (:fixed/real-time) provides a portable fixed-point type representing the internal real time.

Please let me know if you find this useful, or encounter issues.


;; Ordinary power-of-2 fixed point type that supports a resolution of 1/10.
;; This is represented by a 1/16 resolution value.
> (defdelta foo 1/10)

;; Reader macro usage.
> #q foo 1.25
#<FOO 5/4>

;; Fixed point type with precise resolution
;; This is represented by a 1/10 resolution value.
> (defdelta bar 1/10 :small 1/10)

;; Adding range info
> (defdelta foobar 0.01 :small 0.01 :low 0.00 :high 1.00)
> (defparameter fb (make-foobar 0.5))

> fb
#<FOOBAR 0.5>

> (f+ fb (make-foobar 1/2))
#<FOOBAR 1.0>
> (f+ fb (make-foobar 0.51))
;; ERROR: The value 101 is not of type (MOD 101).

> (setf (foobar fb) 0.49)
#<FOOBAR 0.48999998>
> (f+ fb (make-foobar 0.51))
#<FOOBAR 1.0>

;; Base 10 decimal types are simply created like this:
> (fixed:defdecimal milli 3)

;; Using the make-milli function works...but comes with
;; floating point precision issues.
> (make-milli 123456789.001)
#<MILLI 123456782.336>

;; Using the #q reader avoids floating point representation.
> #q milli 123456789.001
#<MILLI 123456789.001>

Fixed-point Reader Macro

A fixed-point reader macro provides a method to input fixed-point literals in decimal form. The reader macro uses the Q format to define a fixed-point spec for the following value.

Install the reader macro as a Q dispatch on # with (install-q-reader).


;; Read in fixed-point literals that can be represented exactly by a Q8 spec.
> #Q8 1.5

> #Q8 0.0078125

;; Read in a fixed-point literal that can be represented exactly by a Q3 spec, and one that can't.
> #Q3 1.5

> #Q3 0.0078125
;; ERROR: 0.0078125 is not a #Q3

Bounds checking can also be performed when the maximum number of useable bits are provided in the Q spec.

;; Read in the most positive Q7.8 value.
> #Q7.8 255.99609375

> #Q7.8 256.0
;; Error: 256.0 is not a #Q7.8

> #Q7.8 -256.0

Decimal fixed-point values can be read as well with #QD and an optional spec value for digits.


> #QD 1.2345678901234567890

> #QD3 1.2345678901234567890
;; ERROR: 1.2345678901234567890 is not a #QD3

> #QD3 1.234
> (float *)


defdelta name delta [:small small-value] [:low low-value] [:high high-value]

=> delta-name

defdecimal name power [:low low-value] [:high high-value]

=> decimal-name


name --- a symbol

delta --- real number

power --- integer

small-value, low-value, and high-value --- optional real numbers


defdelta defines a fixed-point number type named name capable of representing a value with at least the accuracy provided in delta.

If small-value is provided in defdelta, it must be a real value no greater than delta. small-value is used as the minimum resolution scaling factor for the underlying value. When small-value is not provided, it will be chosen automatically and will be no larger than delta.

The small-value can be any real number, but rationals are recommended to avoid unexpected rounding behaviors for some of the operations. If necessary, consider entering a decimal value using the provided #Q reader macro. The following are equivalent.

(defdelta a-fixed-type #qd 0.2 :small #qd 0.2)
(defdelta a-fixed-type 1/5 :small 1/5)

defdecimal defines a fixed-point number type named name capable of representing a base-10 decimal value with up to power number of digits to the right of the decimal. The small-value selected will be (expt 10 (- power)). Note: This declaration is different from the Ada decimal type where you must still define the delta (but as a power-of-10), and you define the number of digits to use in the underlying type.

low-value and high-value are both optional for defdelta or defdecimal, and are used to define the most-negative and most-positive values of the fixed point type.

defdecimal is essentially identical to defdelta when called with an identical delta and small that is a power of 10. The only difference is that values that have a defdecimal defined type will always be printed in decimal form. Values with a defdelta defined type may be printed as rationals.


defdelta and defdecimal create a set of functions and generic methods associated with name.

(make-name value)FunctionReturn a new instance of name with value rounded as necessary with *rounding-method*
(make-name-value value)FunctionReturn a new instance of name with the provided underlying value
(name fp)FunctionReturn the value in the name instance scaled by small
(name-value fp)FunctionReturns the underlying value of an instance of name
(set-name fp value)GenericSet the value of a name instance, rounding as necessary with *rounding-method*
(set-name-value fp value)FunctionSet the underlying integer value of an instance of name
(setf (name fp) value)setfSet the value of fp with rounding as necessary with *rounding-method*
(setf (name-value fp) value)setfSet the underlying value of fp
(small fp) or (small 'name)GenericReturn the small when passed 'name or an instance of name
(delta fp) or (delta 'name)GenericReturn the delta when passed 'name or an instance of name
(size fp) or (size 'name)GenericReturn the number of bits required to store the underlying value of name when it is ranged, otherwise return :INFINITY


+MOST-POSITIVE-NAME+ is defined for each fixed-point type and is either the most positive value, or :POSITIVE-INFINITY if unlimited.

+MOST-NEGATIVE-NAME+ is defined for each fixed-point type and is either the most negative value, or :NEGATIVE-INFINITY if unlimited.

Math Operations

Generic Function Predicates: f= f/= f> f>= f< f<=

Generic Arithmetic Operations: f+ f- f* f/


A utility package that implements a fixed-point type for internal real time.

;; Get the current internal real time as a fixed point
> (defparameter the-time (current-time))
> the-time
#<REAL-TIME 3711125.080>

;; do some stuff

;; calculate deltat
> (f- (current-time) the-time)
#<REAL-TIME 15.616>



Dependencies (1)

  • fiveam

Dependents (0)

    • GitHub
    • Quicklisp