rounded-hw: Directed rounding for built-in floating types

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Please see the README on GitHub at https://github.com/minoki/haskell-floating-point/tree/master/rounded-hw#readme

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Properties

Versions	0.1.0.0, 0.2.0, 0.2.0, 0.3.0, 0.4.0
Change log	ChangeLog.md
Dependencies	array, base (>=4.12 && <5), deepseq, fp-ieee (>=0.1 && <0.2), long-double, primitive, tagged, vector [details]
License	BSD-3-Clause
Copyright	2020 ARATA Mizuki
Author	ARATA Mizuki
Maintainer	minorinoki@gmail.com
Category	Numeric, Math
Home page	https://github.com/minoki/haskell-floating-point#readme
Bug tracker	https://github.com/minoki/haskell-floating-point/issues
Source repo	head: git clone https://github.com/minoki/haskell-floating-point
Uploaded	by aratamizuki at 2020-12-27T13:43:43Z

Modules

[Index] [Quick Jump]

Numeric
- Rounded
  - Numeric.Rounded.Hardware

Flags

Manual Flags

Name	Description	Default
avx512	Use AVX512 EVEX encoding	Disabled
c99	Restrict use of platform-dependent features (e.g. SSE2) and only use C99 features	Disabled
float128	Support Float128	Disabled
ghc-prim	Use GHC's "foreign import prim" on the supported platform	Enabled
pure-hs	Disable FFI	Disabled
x87-long-double	Support x87 "long double"	Enabled

Use -f <flag> to enable a flag, or -f -<flag> to disable that flag. More info

Downloads

rounded-hw-0.2.0.tar.gz [browse] (Cabal source package)
Package description (as included in the package)

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aratamizuki

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Readme for rounded-hw-0.2.0

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rounded-hw: Rounding control for built-in floating-point types

This package provides directed rounding and interval arithmetic for built-in floating-point types (i.e. Float, Double). Unlike rounded, this package does not depend on an external C library.

In addition to Float and Double, LongDouble from long-double package is supported on x86. There is also support for Float128 from float128 package under a package flag.

API overview

Controlling the rounding direction

The type RoundingMode represents the four rounding directions.

The type Rounded (r :: RoundingMode) a is a wrapper for a, with instances honoring the rounding direction given by r.

module Numeric.Rounded.Hardware where

data RoundingMode
  = ToNearest     -- ^ Round to the nearest value (IEEE754 roundTiesToEven)
  | TowardNegInf  -- ^ Round downward (IEEE754 roundTowardNegative)
  | TowardInf     -- ^ Round upward (IEEE754 roundTowardPositive)
  | TowardZero    -- ^ Round toward zero (IEEE754 roundTowardZero)

newtype Rounded (r :: RoundingMode) a = Rounded { getRounded :: a }

instance ... => Num (Rounded r a)
instance ... => Fractional (Rounded r a)
instance ... => Real (Rounded r a)
instance ... => RealFrac (Rounded r a)

Interval arithmetic

This library also provides basic interval types. See Numeric.Rounded.Hardware.Interval and Numeric.Rounded.Hardware.Interval.NonEmpty.

Usage

{-# LANGUAGE DataKinds #-}
{-# LANGUAGE HexFloatLiterals #-}
import Numeric
import Numeric.Rounded.Hardware

main = do
  putStrLn $ showHFloat (1 + 0x1p-100 :: Double) "" -- -> 0x1p0
  putStrLn $ showHFloat (1 + 0x1p-100 :: Rounded TowardInf Double) "" -- -> 0x1.0000000000001p0

Backends

There are several options to control the rounding direction.

Pure Haskell (via Rational)
- Very slow, but does not depend on FFI and therefore can be used on non-native backends.
- This implementation is always available via a newtype in Numeric.Rounded.Hardware.Backend.ViaRational.
C FFI
- One of the technologies below is used:
  - C99 (fesetround)
  - SSE2 (_mm_setcsr)
  - AVX512 EVEX encoding (_mm_*_round_*)
  - x87 Control Word (for x87 long double)
  - AArch64 FPCR
- On x86_64, foreign import prim is used to provide faster interval addition/subtraction.

By default, C FFI is used and an appropriate technology is detected. To disable use of C FFI, set pure-hs flag when building.

The name of the backend used can be obtained with Numeric.Rounded.Hardware.Backend.backendName.

>>> backendName (Proxy :: Proxy Double)
"FastFFI+SSE2"