softposit-rkt

2 API

2.2 Posit Types

2.3 Creating Posits

uint32->posit16

uint32->posit32

uint64->posit16

uint64->posit32

double->posit16

double->posit32

2.4 Converting Between Posit Types

posit8->posit16

posit8->posit32

posit16->posit8

posit16->posit32

posit32->posit8

posit32->posit16

2.5 Converting Back from Posits

posit16->uint32

posit32->uint32

posit16->uint64

posit32->uint64

posit16->double

posit32->double

2.6 Posit Operations

posit8-round-to-int

posit16-round-to-int

posit32-round-to-int

2.8 Quire Types

2.9 Creating Quires

posit16->quire16

posit32->quire32

2.10 Quire Operations

quire16-fdp-add

quire16-fdp-sub

quire16-twos-complement

quire32-fdp-add

quire32-fdp-sub

quire32-twos-complement

2.11 Retrieving Values from Quires

quire16->posit16

quire32->posit32

quire16->double

quire32->double

2.12 Generating Random Posits and Quires

random-posit128

2.13 Posit Constants

2.14 Posit Ordinal Functions

ordinal->p8>ordinal

ordinal->p16>ordinal

ordinal->p32>ordinal

8.12

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softposit-rkt🔗ℹ

David Thien

1 Introduction🔗ℹ

This package is a set of racket bindings for the SoftPosit library. More information on posits can be found on Posithub. Posits are an alternative to floating point numbers designed to improve performance and accuracy.

2 API🔗ℹ

(require softposit-rkt)

package: softposit-rkt

2.1 Posits🔗ℹ

Posits themselves are a representation of the projective reals. The different sizes of posits are included this package are _posit8 _posit16 _posit32 _posit64 and _posit128. Note thought that only the 8, 16, and 32 bit posits currently have arithmetic operators implemented.

The posit types in this package are bindings for c types. Note that only the types and type predicates are bound. All other operations with posits should be accessed with the other provided functions.

2.2 Posit Types🔗ℹ

value
_posit8 : ctype?

An 8-bit posit.

value
_posit16 : ctype?

A 16-bit posit.

value
_posit32 : ctype?

A 32-bit posit.

value
_posit64 : ctype?

A 64-bit posit.

value
_posit128 : ctype?

A 128-bit posit.

procedure
(posit8? v) → boolean?
v : any/c

Returns #t if v is a _posit8, #f otherwise.

procedure
(posit16? v) → boolean?
v : any/c

Returns #t if v is a _posit16, #f otherwise.

procedure
(posit32? v) → boolean?
v : any/c

Returns #t if v is a _posit32, #f otherwise.

procedure
(posit64? v) → boolean?
v : any/c

Returns #t if v is a _posit64, #f otherwise.

procedure
(posit128? v) → boolean?
v : any/c

Returns #t if v is a _posit128, #f otherwise.

2.3 Creating Posits🔗ℹ

procedure
(uint32->posit8 n) → posit8?
n : natural?

Creates a new _posit8 that is the closest representable value to n.

procedure
(uint32->posit16 n) → posit16?
n : natural?

Creates a new _posit16 that is the closest representable value to n.

procedure
(uint32->posit32 n) → posit32?
n : natural?

Creates a new _posit32 that is the closest representable value to n.

procedure
(uint64->posit8 n) → posit8?
n : natural?

Creates a new _posit8 that is the closest representable value to n.

procedure
(uint64->posit16 n) → posit16?
n : natural?

Creates a new _posit16 that is the closest representable value to n.

procedure
(uint64->posit32 n) → posit32?
n : natural?

Creates a new _posit32 that is the closest representable value to n.

procedure
(int32->posit8 n) → posit8?
n : integer?

Creates a new _posit8 that is the closest representable value to n.

procedure
(int32->posit16 n) → posit16?
n : integer?

Creates a new _posit16 that is the closest representable value to n.

procedure
(int32->posit32 n) → posit32?
n : integer?

Creates a new _posit32 that is the closest representable value to n.

procedure
(int64->posit8 n) → posit8?
n : integer?

Creates a new _posit8 that is the closest representable value to n.

procedure
(int64->posit16 n) → posit16?
n : integer?

Creates a new _posit16 that is the closest representable value to n.

procedure
(int64->posit32 n) → posit32?
n : integer?

Creates a new _posit32 that is the closest representable value to n.

procedure
(double->posit8 n) → posit8?
n : real?

Creates a new _posit8 that is the closest representable value to n.

procedure
(double->posit16 n) → posit16?
n : real?

Creates a new _posit16 that is the closest representable value to n.

procedure
(double->posit32 n) → posit32?
n : real?

Creates a new _posit32 that is the closest representable value to n.

2.4 Converting Between Posit Types🔗ℹ

procedure
(posit8->posit16 p) → posit16?
p : posit8?

Converts a _posit8 to a _posit16.

procedure
(posit8->posit32 p) → posit32?
p : posit8?

Converts a _posit8 to a _posit32.

procedure
(posit16->posit8 p) → posit8?
p : posit16?

Converts a _posit16 to a _posit8.

procedure
(posit16->posit32 p) → posit32?
p : posit16?

Converts a _posit16 to a _posit32.

procedure
(posit32->posit8 p) → posit8?
p : posit32?

Converts a _posit32 to a _posit8.

procedure
(posit32->posit16 p) → posit16?
p : posit32?

Converts a _posit32 to a _posit16.

2.5 Converting Back from Posits🔗ℹ

Note that there are multiple bindings exposed which cast back to natural numbers and to integers (e.g. posit16->uint32 and posit16->uint64). Although these will cast back to the same racket type, they are different functions in the underlying C code, so be careful to avoid unexpected behavior when hitting the maximum value for uint32s. It is recommended to always cast to a double to avoid losing decimal accuracy.

procedure
(posit8->uint32 p) → natural?
p : posit8?

Casts a _posit8 to a uint32.

procedure
(posit16->uint32 p) → natural?
p : posit16?

Casts a _posit16 to a uint32.

procedure
(posit32->uint32 p) → natural?
p : posit32?

Casts a _posit32 to a uint32.

procedure
(posit8->uint64 p) → natural?
p : posit8?

Casts a _posit8 to a uint64.

procedure
(posit16->uint64 p) → natural?
p : posit16?

Casts a _posit16 to a uint64.

procedure
(posit32->uint64 p) → natural?
p : posit32?

Casts a _posit32 to a uint64.

procedure
(posit8->int32 p) → integer?
p : posit8?

Casts a _posit8 to a int32.

procedure
(posit16->int32 p) → integer?
p : posit16?

Casts a _posit16 to a int32.

procedure
(posit32->int32 p) → integer?
p : posit32?

Casts a _posit32 to a int32.

procedure
(posit8->int64 p) → integer?
p : posit8?

Casts a _posit8 to a int64.

procedure
(posit16->int64 p) → integer?
p : posit16?

Casts a _posit16 to a int64.

procedure
(posit32->int64 p) → integer?
p : posit32?

Casts a _posit32 to a int64.

procedure
(posit8->double p) → real?
p : posit8?

Casts a _posit8 to a double.

procedure
(posit16->double p) → real?
p : posit16?

Casts a _posit16 to a int64.

procedure
(posit32->double p) → real?
p : posit32?

Casts a _posit32 to a int64.

2.6 Posit Operations🔗ℹ

procedure
(posit8-round-to-int p) → posit8?
p : posit8?

Rounds p to the nearest integer.

procedure
(posit8-add p1 p2) → posit8?
p1 : posit8?
p2 : posit8?

Adds p1 and p2.

procedure
(posit8-sub p1 p2) → posit8?
p1 : posit8?
p2 : posit8?

Subtracts p2 from p1.

procedure
(posit8-mul p1 p2) → posit8?
p1 : posit8?
p2 : posit8?

Multiplies p1 and p2.

procedure
(posit8-div p1 p2) → posit8?
p1 : posit8?
p2 : posit8?

Divides p1 by p2.

procedure
(posit8mulAdd p1 p2 p3) → posit8?
  p1 : posit8?
  p2 : posit8?
  p3 : posit8?

Performs the operation (p1 * p2) + p3 (similar to the fma operator).

procedure
(posit8-sqrt p1) → posit8?
p1 : posit8?

Takes the square root of p1.

procedure
(posit8-neg p1) → posit8?
p1 : posit8?

Negates p1.

procedure
(posit16-neg p1) → posit16?
p1 : posit16?

Negates p1.

procedure
(posit32-neg p1) → posit32?
p1 : posit32?

Negates p1.

procedure
(posit8= p1 p2) → boolean?
p1 : posit8?
p2 : posit8?

Returns #t if the arguments are equal.

procedure
(posit8< p1 p2) → boolean?
p1 : posit8?
p2 : posit8?

Returns #t if p1 is strictly less than p2.

procedure
(posit8<= p1 p2) → boolean?
p1 : posit8?
p2 : posit8?

Returns #t if p1 is less than or equal to p2.

procedure
(posit8> p1 p2) → boolean?
p1 : posit8?
p2 : posit8?

Returns #t if p1 is strictly greater than p2.

procedure
(posit8>= p1 p2) → boolean?
p1 : posit8?
p2 : posit8?

Returns #t if p1 is greater than or equal to p2.

procedure
(posit16-round-to-int p) → posit16?
p : posit16?

Rounds p to the nearest integer.

procedure
(posit16-add p1 p2) → posit16?
p1 : posit16?
p2 : posit16?

Adds p1 and p2.

procedure
(posit16-sub p1 p2) → posit16?
p1 : posit16?
p2 : posit16?

Subtracts p2 from p1.

procedure
(posit16-mul p1 p2) → posit16?
p1 : posit16?
p2 : posit16?

Multiplies p1 and p2.

procedure
(posit16-div p1 p2) → posit16?
p1 : posit16?
p2 : posit16?

Divides p1 by p2.

procedure
(posit16mulAdd p1 p2 p3) → posit16?
  p1 : posit16?
  p2 : posit16?
  p3 : posit16?

Performs the operation (p1 * p2) + p3 (similar to the fma operator).

procedure
(posit16-sqrt p1) → posit16?
p1 : posit16?

Takes the square root of p1.

procedure
(posit16= p1 p2) → boolean?
p1 : posit16?
p2 : posit16?

Returns #t if the arguments are equal.

procedure
(posit16< p1 p2) → boolean?
p1 : posit16?
p2 : posit16?

Returns #t if p1 is strictly less than p2.

procedure
(posit16<= p1 p2) → boolean?
p1 : posit16?
p2 : posit16?

Returns #t if p1 is less than or equal to p2.

procedure
(posit16> p1 p2) → boolean?
p1 : posit16?
p2 : posit16?

Returns #t if p1 is strictly greater than p2.

procedure
(posit16>= p1 p2) → boolean?
p1 : posit16?
p2 : posit16?

Returns #t if p1 is greater than or equal to p2.

procedure
(posit32-round-to-int p) → posit32?
p : posit32?

Rounds p to the nearest integer.

procedure
(posit32-add p1 p2) → posit32?
p1 : posit32?
p2 : posit32?

Adds p1 and p2.

procedure
(posit32-sub p1 p2) → posit32?
p1 : posit32?
p2 : posit32?

Subtracts p2 from p1.

procedure
(posit32-mul p1 p2) → posit32?
p1 : posit32?
p2 : posit32?

Multiplies p1 and p2.

procedure
(posit32-div p1 p2) → posit32?
p1 : posit32?
p2 : posit32?

Divides p1 by p2.

procedure
(posit32mulAdd p1 p2 p3) → posit32?
  p1 : posit32?
  p2 : posit32?
  p3 : posit32?

Performs the operation (p1 * p2) + p3 (similar to the fma operator).

procedure
(posit32-sqrt p1) → posit32?
p1 : posit32?

Takes the square root of p1.

procedure
(posit32= p1 p2) → boolean?
p1 : posit32?
p2 : posit32?

Returns #t if the arguments are equal.

procedure
(posit32< p1 p2) → boolean?
p1 : posit32?
p2 : posit32?

Returns #t if p1 is strictly less than p2.

procedure
(posit32<= p1 p2) → boolean?
p1 : posit32?
p2 : posit32?

Returns #t if p1 is less than or equal to p2.

procedure
(posit32> p1 p2) → boolean?
p1 : posit32?
p2 : posit32?

Returns #t if p1 is strictly greater than p2.

procedure
(posit32>= p1 p2) → boolean?
p1 : posit32?
p2 : posit32?

Returns #t if p1 is greater than or equal to p2.

2.7 Quires🔗ℹ

Quires are another feature of the Posit specication. They can be thought of as a large accumulator designed to hold enough bits of information so as to not introduce any rounding error. Note that these accumulators have a fixed number of bits, so only a limited (but very large) number of accumulations can be done on them safely. A _quire8 has 4 times the number of bits as a _posit8, a _quire16 has 8 times the bits as a _posit16, and a _quire32 has 16 times the bits as a _posit32.

2.8 Quire Types🔗ℹ

value
_quire8 : ctype?

An 8-bit quire.

value
_quire16 : ctype?

An 16-bit quire.

value
_quire32 : ctype?

An 32-bit quire.

procedure
(quire8? v) → boolean?
v : any/c

Returns #t if v is a _quire8, #f otherwise.

procedure
(quire16? v) → boolean?
v : any/c

Returns #t if v is a _quire16, #f otherwise.

procedure
(quire32? v) → boolean?
v : any/c

Returns #t if v is a _quire32, #f otherwise.

2.9 Creating Quires🔗ℹ

All quires are initialized to 0.

procedure
(create-quire8) → quire8?

Creates a new _quire8.

procedure
(create-quire16) → quire16?

Creates a new _quire16.

procedure
(create-quire32) → quire32?

Creates a new _quire32.

procedure
(posit8->quire8 p) → quire8?
p : posit8?

Creates a quire8 with the value of q.

procedure
(posit16->quire16 p) → quire16?
p : posit16?

Creates a quire16 with the value of q.

procedure
(posit32->quire32 p) → quire32?
p : posit32?

Creates a quire32 with the value of q.

procedure
(double>quire8 n) → quire8?
n : real?

Creates a quire8 with the value of n after n is converted to a posit8.

procedure
(double>quire16 n) → quire16?
n : real?

Creates a quire16 with the value of n after n is converted to a posit16.

procedure
(double>quire32 n) → quire32?
n : real?

Creates a quire32 with the value of n after n is converted to a posit32.

2.10 Quire Operations🔗ℹ

Note that there is currently no twos-complement for _quire8s.

procedure
(quire8-fdp-add q p1 p2) → quire8?
  q : quire8?
  p1 : posit8?
  p2 : posit8?

Returns the result of adding p1 times p2 to q.

procedure
(quire8-fdp-sub q p1 p2) → quire8?
  q : quire8?
  p1 : posit8?
  p2 : posit8?

Returns the result of subtracting p1 times p2 from q.

procedure
(quire16-fdp-add q p1 p2) → quire16?
  q : quire16?
  p1 : posit16?
  p2 : posit16?

Returns the result of adding p1 times p2 to q.

procedure
(quire16-fdp-sub q p1 p2) → quire16?
  q : quire16?
  p1 : posit16?
  p2 : posit16?

Returns the result of subtracting p1 times p2 from q.

procedure
(quire16-twos-complement q) → quire16?
q : quire16?

Returns the twos complement of q.

procedure
(quire32-fdp-add q p1 p2) → quire32?
  q : quire32?
  p1 : posit32?
  p2 : posit32?

Returns the result of adding p1 times p2 to q.

procedure
(quire32-fdp-sub q p1 p2) → quire32?
  q : quire32?
  p1 : posit32?
  p2 : posit32?

Returns the result of subtracting p1 times p2 from q.

procedure
(quire32-twos-complement q) → quire32?
q : quire32?

Returns the twos complement of q.

2.11 Retrieving Values from Quires🔗ℹ

procedure
(quire8->posit8 q) → posit8?
q : quire8?

Casts q to a _posit8.

procedure
(quire16->posit16 q) → posit16?
q : quire16?

Casts q to a _posit16.

procedure
(quire32->posit32 q) → posit32?
q : quire32?

Casts q to a _posit32.

procedure
(quire8->double q) → real?
q : quire8?

Casts q to a double.

procedure
(quire16->double q) → real?
q : quire16?

Casts q to a double.

procedure
(quire32->double q) → real?
q : quire32?

Casts q to a double.

2.12 Generating Random Posits and Quires🔗ℹ

Also included is functionality to generate random posits and quires.

procedure
(random-posit8) → posit8?

Generates a random posit8.

procedure
(random-posit16) → posit16?

Generates a random posit16.

procedure
(random-posit32) → posit32?

Generates a random posit32.

procedure
(random-posit64) → posit64?

Generates a random posit64.

procedure
(random-posit128) → posit128?

Generates a random posit128.

procedure
(random-quire8) → quire8?

Generates a random quire8.

procedure
(random-quire16) → quire16?

Generates a random quire16.

procedure
(random-quire32) → quire32?

Generates a random quire32.

2.13 Posit Constants🔗ℹ

procedure
(posit8-nar) → posit8?

Returns the "not a real" value for posit8s.

procedure
(posit16-nar) → posit16?

Returns the "not a real" value for posit16s.

procedure
(posit32-nar) → posit32?

Returns the "not a real" value for posit32s.

procedure
(posit64-nar) → posit64?

Returns the "not a real" value for posit64s.

procedure
(posit128-nar) → posit128?

Returns the "not a real" value for posit128s.

2.14 Posit Ordinal Functions🔗ℹ

These functions convert to and from the ordinal representation of a posit. NaR returns 0.

procedure
(p8->ordinal p) → natural?
p : posit8?

Returns the ordinal of p.

procedure
(p16->ordinal p) → natural?
p : posit16?

Returns the ordinal of p.

procedure
(p32->ordinal p) → natural?
p : posit32?

Returns the ordinal of p.

procedure
(ordinal->p8>ordinal n) → posit8?
n : natural?

Returns the posit8 of the ordinal n.

procedure
(ordinal->p16>ordinal n) → posit16?
n : natural?

Returns the posit16 of the ordinal n.

procedure
(ordinal->p32>ordinal n) → posit32?
n : natural?

Returns the posit32 of the ordinal n.

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