https://github.com/npatrick04/fixed.git

```
git clone 'https://github.com/npatrick04/fixed.git'
```

(ql:quickload :fixed)

★3

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][: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*.

| 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.

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
> 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>

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)`

.

e.g.

```
;; Read in fixed-point literals that can be represented exactly by a Q8 spec.
> #Q8 1.5
3/2
> #Q8 0.0078125
1/128
;; Read in a fixed-point literal that can be represented exactly by a Q3 spec, and one that can't.
> #Q3 1.5
3/2
> #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
65535/256
> #Q7.8 256.0
;; Error: 256.0 is not a #Q7.8
> #Q7.8 -256.0
-256
```

Decimal fixed-point values can be read as well with `#QD`

and an optional spec value for digits.

e.g. ```lisp

## QD 1.2345678901234567890

1234567890123456789/1000000000000000000

## QD3 1.2345678901234567890

;; ERROR: 1.2345678901234567890 is not a #QD3

## QD3 1.234

617/500 (float *) 1.234 ```

- Fixed-point reader macro improvements
- Read into a superclass of defined delta types
- Determine if the second return value from rounding operations is in the best form.

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
> the-time
#<REAL-TIME 3711125.080>
;; do some stuff
;; calculate deltat
> (f- (current-time) the-time)
#<REAL-TIME 15.616>

MIT