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"