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

[ bsd3, library, math, numeric ] [ Propose Tags ]

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Dependencies array, base (>=4.12 && <5), deepseq, integer-logarithms, long-double, primitive, tagged, vector [details]
License BSD-3-Clause
Copyright 2020 ARATA Mizuki
Author ARATA Mizuki
Category Numeric, Math
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Uploaded by aratamizuki at 2020-06-22T17:15:06Z
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Use AVX512 EVEX encoding


Restrict use of platform-dependent features (e.g. SSE2) and only use C99 features


Support Float128


Use GHC's "foreign import prim" on the supported platform


Disable FFI


Support x87 "long double"


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


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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.


{-# 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


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)