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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.

Also provided is a utility package (:fixed/real-time) providing a portable fixed-point type representing the internal real time.


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


defdecimal name power [:low low-value]



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.

| Operation | Type | Description | | — | — | — | | (make-name value) | Function | Return a new instance of name with value rounded as necessary with *rounding-method* | | (make-name-value value) | Function | Return a new instance of name with the provided underlying value | | (name fp) | Function | Return the value in the name instance scaled by small | | (name-value fp) | Function | Returns the underlying value of an instance of name | | (set-name fp value) | Generic | Set the value of a name instance, rounding as necessary with *rounding-method* | | (set-name-value fp value) | Function | Set the underlying integer value of an instance of name | | (setf (name fp) value) | setf | Set the value of fp with rounding as necessary with *rounding-method* | | (setf (name-value fp) value) | setf | Set the underlying value of fp | | (small fp) or (small ‘name) | Generic | Return the small when passed ’name or an instance of name | | (delta fp) or (delta ‘name) | Generic | Return the delta when passed ’name or an instance of name | | (size fp) or (size 'name) | Generic | Return 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/


;; 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)

;; 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>

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.

e.g. ```lisp

QD 1.2345678901234567890


QD3 1.2345678901234567890

;; ERROR: 1.2345678901234567890 is not a #QD3

QD3 1.234

617/500 (float *) 1.234 ```

Future Work


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>