From 67e42f9da90822b4bfe18f0020a287141defb63d Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Thu, 14 Jul 2016 14:43:30 -0400
Subject: [PATCH 01/11] Added dynamic prefix selection. Fixes #163.

---
 src/Numeric/Units/Dimensional/SIUnits.hs      | 63 ++++++++++++++++++-
 src/Numeric/Units/Dimensional/UnitNames.hs    |  5 +-
 .../Units/Dimensional/UnitNames/Internal.hs   | 46 +++++++-------
 3 files changed, 87 insertions(+), 27 deletions(-)

diff --git a/src/Numeric/Units/Dimensional/SIUnits.hs b/src/Numeric/Units/Dimensional/SIUnits.hs
index 8535d75c..603f852b 100644
--- a/src/Numeric/Units/Dimensional/SIUnits.hs
+++ b/src/Numeric/Units/Dimensional/SIUnits.hs
@@ -57,19 +57,22 @@ module Numeric.Units.Dimensional.SIUnits
   -- $submultiples
   deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto,
   -- $reified-prefixes
-  Prefix, applyPrefix, siPrefixes
+  Prefix, applyPrefix, applyOptionalPrefix, siPrefixes, appropriatePrefix, withAppropriatePrefix, appropriatePrefix', withAppropriatePrefix'
 )
 where
 
+import Control.Monad (join)
 import Data.Ratio
+import Data.List (sortBy, find)
+import Data.Ord (comparing, Down(..))
 import Numeric.Units.Dimensional
 import Numeric.Units.Dimensional.Quantities
-import Numeric.Units.Dimensional.UnitNames (Prefix, siPrefixes)
+import Numeric.Units.Dimensional.UnitNames (Prefix, siPrefixes, scaleExponent)
 import qualified Numeric.Units.Dimensional.UnitNames as N
 import Numeric.Units.Dimensional.UnitNames.Internal (ucum, ucumMetric)
 import qualified Numeric.Units.Dimensional.UnitNames.Internal as I
 import Numeric.NumType.DK.Integers ( pos3 )
-import Prelude ( Eq(..), ($), Num, Fractional, Floating, otherwise, error)
+import Prelude ( Eq(..), ($), (.), Num, Fractional, Floating, RealFrac(..), Maybe(..), otherwise, error, Ord(..), fst, snd, Int, Bool, fmap, mod, (&&))
 import qualified Prelude
 
 {- $multiples
@@ -109,12 +112,18 @@ yotta = applyMultiple I.yotta
 Then the submultiples.
 -}
 
+-- | Applies a 'Prefix' to a 'Metric' 'Unit', creating a 'NonMetric' unit.
 applyPrefix :: (Fractional a) => Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a
 applyPrefix p u = mkUnitQ n' x u
   where
     n' = N.applyPrefix p (name u)
     x = N.scaleFactor p
 
+-- | Applies an optional 'Prefix' to a 'Metric' 'Unit', creating a 'NonMetric' unit.
+applyOptionalPrefix :: (Fractional a) => Maybe Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a
+applyOptionalPrefix Nothing = weaken
+applyOptionalPrefix (Just p) = applyPrefix p
+
 deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto
   :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
 deci  = applyPrefix I.deci
@@ -135,6 +144,54 @@ list of all prefixes defined by the SI.
 
 -}
 
+-- | Selects the appropriate 'Prefix' to use with a 'Metric' unit when using it to display
+-- a particular 'Quantity', or 'Nothing' if the supplied unit should be used without a prefix.
+--
+-- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- of the quantity, expressed in the prefixed unit, is greater than or equal to one.
+appropriatePrefix :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Maybe Prefix
+appropriatePrefix u q = selectPrefix (<= e)
+  where
+    val = q /~ u
+    e = Prelude.floor $ Prelude.logBase 10 val :: Prelude.Int
+
+-- | Selects the appropriate 'Prefix' to use with a 'Metric' unit when using it to display
+-- a particular 'Quantity', or 'Nothing' if the supplied unit should be used without a prefix.
+--
+-- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- of the quantity, expressed in the prefixed unit, is greater than or equal to one. Only those prefixes
+-- whose 'scaleExponent' is a multiple of @3@ are considered.
+appropriatePrefix' :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Maybe Prefix
+appropriatePrefix' u q = selectPrefix (\x -> x `mod` 3 == 0 && x <= e)
+  where
+    val = q /~ u
+    e = Prelude.floor $ Prelude.logBase 10 val :: Prelude.Int
+
+-- Selects the first prefix in the list of prefix candidates whose scale exponent matches the supplied predicate.
+selectPrefix :: (Int -> Bool) -> Maybe Prefix
+selectPrefix p = join $ fmap snd $ find (p . fst) prefixCandidates
+
+-- This is a list of candidate prefixes and the least scale exponent at which each applies.
+prefixCandidates :: [(Int, Maybe Prefix)]
+prefixCandidates = sortBy (comparing $ Down . fst) $ (0, Nothing) : fmap (\x -> (scaleExponent x, Just x)) siPrefixes
+
+-- | Constructs a version of a 'Metric' unit, by possibly applying a 'Prefix' to it, appropriate
+-- for display of a particular 'Quantity'.
+--
+-- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- of the quantity, expressed in the prefixed unit, is greater than or equal to one.
+withAppropriatePrefix :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Unit 'NonMetric d a
+withAppropriatePrefix u q = applyOptionalPrefix (appropriatePrefix u q) u
+
+-- | Constructs a version of a 'Metric' unit, by possibly applying a 'Prefix' to it, appropriate
+-- for display of a particular 'Quantity'.
+--
+-- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- of the quantity, expressed in the prefixed unit, is greater than or equal to one. Only those prefixes
+-- whose 'scaleExponent' is a multiple of @3@ are considered.
+withAppropriatePrefix' :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Unit 'NonMetric d a
+withAppropriatePrefix' u q = applyOptionalPrefix (appropriatePrefix' u q) u
+
 {- $base-units
 These are the base units from section 4.1. To avoid a
 myriad of one-letter functions that would doubtlessly cause clashes
diff --git a/src/Numeric/Units/Dimensional/UnitNames.hs b/src/Numeric/Units/Dimensional/UnitNames.hs
index b2cf9fd7..a5f894e0 100644
--- a/src/Numeric/Units/Dimensional/UnitNames.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames.hs
@@ -23,7 +23,7 @@ module Numeric.Units.Dimensional.UnitNames
   -- * Standard Names
   baseUnitName, siPrefixes, nOne,
   -- * Inspecting Prefixes
-  prefixName, scaleFactor,
+  prefixName, scaleExponent, scaleFactor,
   -- * Convenience Type Synonyms for Unit Name Transformations
   UnitNameTransformer, UnitNameTransformer2,
   -- * Forgetting Unwanted Phantom Types
@@ -35,3 +35,6 @@ where
 import Numeric.Units.Dimensional.UnitNames.Internal
 import Numeric.Units.Dimensional.Variants
 import Prelude hiding ((*), (/), (^), product)
+
+scaleFactor :: Prefix -> Rational
+scaleFactor p = 10 ^^ (scaleExponent p)
diff --git a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
index 9f8d00dd..0128d4fa 100644
--- a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
@@ -141,12 +141,12 @@ data Prefix = Prefix
                 -- | The name of a metric prefix.
                 prefixName :: PrefixName,
                 -- | The scale factor denoted by a metric prefix.
-                scaleFactor :: Rational
+                scaleExponent :: Int
               }
   deriving (Eq, Data, Typeable, Generic)
 
 instance Ord Prefix where
-  compare = comparing scaleFactor
+  compare = comparing scaleExponent
 
 instance NFData Prefix where -- instance is derived from Generic instance
 
@@ -190,27 +190,27 @@ baseUnitNames :: [UnitName 'NonMetric]
 baseUnitNames = [weaken nMeter, nKilogram, weaken nSecond, weaken nAmpere, weaken nKelvin, weaken nMole, weaken nCandela]
 
 deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta :: Prefix
-deka  = prefix "da" "da" "deka" 1e1
-hecto = prefix "h" "h" "hecto"  1e2
-kilo  = prefix "k" "k" "kilo"   1e3
-mega  = prefix "M" "M" "mega"   1e6
-giga  = prefix "G" "G" "giga"   1e9
-tera  = prefix "T" "T" "tera"   1e12
-peta  = prefix "P" "P" "peta"   1e15
-exa   = prefix "E" "E" "exa"    1e18
-zetta = prefix "Z" "Z" "zetta"  1e21
-yotta = prefix "Y" "Y" "yotta"  1e24
+deka  = prefix "da" "da" "deka" 1
+hecto = prefix "h" "h" "hecto"  2
+kilo  = prefix "k" "k" "kilo"   3
+mega  = prefix "M" "M" "mega"   6
+giga  = prefix "G" "G" "giga"   9
+tera  = prefix "T" "T" "tera"   12
+peta  = prefix "P" "P" "peta"   15
+exa   = prefix "E" "E" "exa"    18
+zetta = prefix "Z" "Z" "zetta"  21
+yotta = prefix "Y" "Y" "yotta"  24
 deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto :: Prefix
-deci  = prefix "d" "d" "deci"   1e-1
-centi = prefix "c" "c" "centi"  1e-2
-milli = prefix "m" "m" "milli"  1e-3
-micro = prefix "u" "μ" "micro"  1e-6
-nano  = prefix "n" "n" "nano"   1e-9
-pico  = prefix "p" "p" "pico"   1e-12
-femto = prefix "f" "f" "femto"  1e-15
-atto  = prefix "a" "a" "atto"   1e-18
-zepto = prefix "z" "z" "zepto"  1e-21
-yocto = prefix "y" "y" "yocto"  1e-24
+deci  = prefix "d" "d" "deci"   $ -1
+centi = prefix "c" "c" "centi"  $ -2
+milli = prefix "m" "m" "milli"  $ -3
+micro = prefix "u" "μ" "micro"  $ -6
+nano  = prefix "n" "n" "nano"   $ -9
+pico  = prefix "p" "p" "pico"   $ -12
+femto = prefix "f" "f" "femto"  $ -15
+atto  = prefix "a" "a" "atto"   $ -18
+zepto = prefix "z" "z" "zepto"  $ -21
+yocto = prefix "y" "y" "yocto"  $ -24
 
 -- | A list of all 'Prefix'es defined by the SI.
 siPrefixes :: [Prefix]
@@ -319,7 +319,7 @@ instance HasInterchangeName (UnitName m) where
                                  in InterchangeName { name = n', authority = authority . interchangeName $ n, I.isAtomic = False }
   interchangeName (Weaken n) = interchangeName n
 
-prefix :: String -> String -> String -> Rational -> Prefix
+prefix :: String -> String -> String -> Int -> Prefix
 prefix i a f q = Prefix n q
   where
     n = NameAtom (InterchangeName i UCUM True) a f

From 9799f385b586ddc4528983ca513a84338f33f38d Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Thu, 14 Jul 2016 14:47:34 -0400
Subject: [PATCH 02/11] Changelog.

---
 CHANGELOG.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index ff961030..c0a22fe3 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -37,6 +37,7 @@ vNext
 * Added an `AEq` instance for `Quantity`.
 * Exposed the name of an 'AnyUnit' without promoting it to a 'Unit' first.
 * Exposed a way to convert atomic 'UnitName's back into 'NameAtom's.
+* Added dynamic selection of metric prefixes based on the magnitude of a quantity to be displayed.
 * Added the `btu`, a unit of energy.
 * Added the `gauss`, a unit of magnetic flux density.
 * Added the `angstrom`, a unit of length.

From 3b919c85e223ea27dc8808e33b5cf15c5d976147 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Fri, 15 Jul 2016 09:57:40 -0400
Subject: [PATCH 03/11] Relaxed type of appropriatePrefix to allow its use in
 more complicated scenarios.

---
 src/Numeric/Units/Dimensional/SIUnits.hs | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/src/Numeric/Units/Dimensional/SIUnits.hs b/src/Numeric/Units/Dimensional/SIUnits.hs
index 603f852b..0f18361e 100644
--- a/src/Numeric/Units/Dimensional/SIUnits.hs
+++ b/src/Numeric/Units/Dimensional/SIUnits.hs
@@ -149,7 +149,10 @@ list of all prefixes defined by the SI.
 --
 -- The appropriate prefix is defined to be the largest prefix such that the resulting value
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one.
-appropriatePrefix :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Maybe Prefix
+--
+-- Note that the supplied prefix need not be 'Metric'. This is intended for use to compute a prefix to insert
+-- somewhere in the denominator of a composite (and hence 'NonMetric') unit.
+appropriatePrefix :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Maybe Prefix
 appropriatePrefix u q = selectPrefix (<= e)
   where
     val = q /~ u
@@ -161,7 +164,10 @@ appropriatePrefix u q = selectPrefix (<= e)
 -- The appropriate prefix is defined to be the largest prefix such that the resulting value
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one. Only those prefixes
 -- whose 'scaleExponent' is a multiple of @3@ are considered.
-appropriatePrefix' :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Maybe Prefix
+--
+-- Note that the supplied prefix need not be 'Metric'. This is intended for use to compute a prefix to insert
+-- somewhere in the denominator of a composite (and hence 'NonMetric') unit.
+appropriatePrefix' :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Maybe Prefix
 appropriatePrefix' u q = selectPrefix (\x -> x `mod` 3 == 0 && x <= e)
   where
     val = q /~ u

From b7bc2cc937471c7db869ef3ea55d405f5cbf1bc0 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Mon, 18 Jul 2016 16:12:31 -0400
Subject: [PATCH 04/11] Changed handling when value is smaller than the
 smallest unit to be consistent with what happens when it is larger than the
 largest unit.

---
 src/Numeric/Units/Dimensional/SIUnits.hs | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/Numeric/Units/Dimensional/SIUnits.hs b/src/Numeric/Units/Dimensional/SIUnits.hs
index 0f18361e..ff98dafa 100644
--- a/src/Numeric/Units/Dimensional/SIUnits.hs
+++ b/src/Numeric/Units/Dimensional/SIUnits.hs
@@ -62,9 +62,10 @@ module Numeric.Units.Dimensional.SIUnits
 where
 
 import Control.Monad (join)
-import Data.Ratio
 import Data.List (sortBy, find)
+import Data.Maybe (maybe)
 import Data.Ord (comparing, Down(..))
+import Data.Ratio
 import Numeric.Units.Dimensional
 import Numeric.Units.Dimensional.Quantities
 import Numeric.Units.Dimensional.UnitNames (Prefix, siPrefixes, scaleExponent)
@@ -175,7 +176,7 @@ appropriatePrefix' u q = selectPrefix (\x -> x `mod` 3 == 0 && x <= e)
 
 -- Selects the first prefix in the list of prefix candidates whose scale exponent matches the supplied predicate.
 selectPrefix :: (Int -> Bool) -> Maybe Prefix
-selectPrefix p = join $ fmap snd $ find (p . fst) prefixCandidates
+selectPrefix p = maybe (Just . Prelude.head $ siPrefixes) snd $ find (p . fst) prefixCandidates
 
 -- This is a list of candidate prefixes and the least scale exponent at which each applies.
 prefixCandidates :: [(Int, Maybe Prefix)]

From 173669852ea6d7d291e1ebc4fa0c6e31bfb570b1 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Mon, 25 Jul 2016 21:06:05 -0400
Subject: [PATCH 05/11] Added very important absolute value to unit selection.

---
 src/Numeric/Units/Dimensional/SIUnits.hs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/Numeric/Units/Dimensional/SIUnits.hs b/src/Numeric/Units/Dimensional/SIUnits.hs
index ff98dafa..392372cc 100644
--- a/src/Numeric/Units/Dimensional/SIUnits.hs
+++ b/src/Numeric/Units/Dimensional/SIUnits.hs
@@ -171,7 +171,7 @@ appropriatePrefix u q = selectPrefix (<= e)
 appropriatePrefix' :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Maybe Prefix
 appropriatePrefix' u q = selectPrefix (\x -> x `mod` 3 == 0 && x <= e)
   where
-    val = q /~ u
+    val = abs q /~ u
     e = Prelude.floor $ Prelude.logBase 10 val :: Prelude.Int
 
 -- Selects the first prefix in the list of prefix candidates whose scale exponent matches the supplied predicate.

From badc738e1df9697fde947ccff549761c4ee92200 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Mon, 25 Jul 2016 21:06:40 -0400
Subject: [PATCH 06/11] Removed redundant import.

---
 src/Numeric/Units/Dimensional/SIUnits.hs | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/Numeric/Units/Dimensional/SIUnits.hs b/src/Numeric/Units/Dimensional/SIUnits.hs
index 392372cc..02ca8887 100644
--- a/src/Numeric/Units/Dimensional/SIUnits.hs
+++ b/src/Numeric/Units/Dimensional/SIUnits.hs
@@ -61,7 +61,6 @@ module Numeric.Units.Dimensional.SIUnits
 )
 where
 
-import Control.Monad (join)
 import Data.List (sortBy, find)
 import Data.Maybe (maybe)
 import Data.Ord (comparing, Down(..))

From ea6d3fe5ab07a89a0fb1336163986d144b97da28 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Sun, 7 Aug 2016 14:28:13 -0400
Subject: [PATCH 07/11] Changed Prefix so that emptyPrefix can be a Prefix.

---
 src/Numeric/Units/Dimensional/SIUnits.hs      | 27 ++++++++-----------
 .../Units/Dimensional/UnitNames/Internal.hs   | 18 ++++++++-----
 2 files changed, 22 insertions(+), 23 deletions(-)

diff --git a/src/Numeric/Units/Dimensional/SIUnits.hs b/src/Numeric/Units/Dimensional/SIUnits.hs
index 02ca8887..ea87b86c 100644
--- a/src/Numeric/Units/Dimensional/SIUnits.hs
+++ b/src/Numeric/Units/Dimensional/SIUnits.hs
@@ -57,7 +57,7 @@ module Numeric.Units.Dimensional.SIUnits
   -- $submultiples
   deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto,
   -- $reified-prefixes
-  Prefix, applyPrefix, applyOptionalPrefix, siPrefixes, appropriatePrefix, withAppropriatePrefix, appropriatePrefix', withAppropriatePrefix'
+  Prefix, applyPrefix, siPrefixes, appropriatePrefix, withAppropriatePrefix, appropriatePrefix', withAppropriatePrefix'
 )
 where
 
@@ -72,7 +72,7 @@ import qualified Numeric.Units.Dimensional.UnitNames as N
 import Numeric.Units.Dimensional.UnitNames.Internal (ucum, ucumMetric)
 import qualified Numeric.Units.Dimensional.UnitNames.Internal as I
 import Numeric.NumType.DK.Integers ( pos3 )
-import Prelude ( Eq(..), ($), (.), Num, Fractional, Floating, RealFrac(..), Maybe(..), otherwise, error, Ord(..), fst, snd, Int, Bool, fmap, mod, (&&))
+import Prelude ( Eq(..), ($), (.), Num, Fractional, Floating, RealFrac(..), id, otherwise, error, Ord(..), Int, Bool, mod, (&&))
 import qualified Prelude
 
 {- $multiples
@@ -119,11 +119,6 @@ applyPrefix p u = mkUnitQ n' x u
     n' = N.applyPrefix p (name u)
     x = N.scaleFactor p
 
--- | Applies an optional 'Prefix' to a 'Metric' 'Unit', creating a 'NonMetric' unit.
-applyOptionalPrefix :: (Fractional a) => Maybe Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a
-applyOptionalPrefix Nothing = weaken
-applyOptionalPrefix (Just p) = applyPrefix p
-
 deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto
   :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
 deci  = applyPrefix I.deci
@@ -152,10 +147,10 @@ list of all prefixes defined by the SI.
 --
 -- Note that the supplied prefix need not be 'Metric'. This is intended for use to compute a prefix to insert
 -- somewhere in the denominator of a composite (and hence 'NonMetric') unit.
-appropriatePrefix :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Maybe Prefix
+appropriatePrefix :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Prefix
 appropriatePrefix u q = selectPrefix (<= e)
   where
-    val = q /~ u
+    val = abs q /~ u
     e = Prelude.floor $ Prelude.logBase 10 val :: Prelude.Int
 
 -- | Selects the appropriate 'Prefix' to use with a 'Metric' unit when using it to display
@@ -167,19 +162,19 @@ appropriatePrefix u q = selectPrefix (<= e)
 --
 -- Note that the supplied prefix need not be 'Metric'. This is intended for use to compute a prefix to insert
 -- somewhere in the denominator of a composite (and hence 'NonMetric') unit.
-appropriatePrefix' :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Maybe Prefix
+appropriatePrefix' :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Prefix
 appropriatePrefix' u q = selectPrefix (\x -> x `mod` 3 == 0 && x <= e)
   where
     val = abs q /~ u
     e = Prelude.floor $ Prelude.logBase 10 val :: Prelude.Int
 
 -- Selects the first prefix in the list of prefix candidates whose scale exponent matches the supplied predicate.
-selectPrefix :: (Int -> Bool) -> Maybe Prefix
-selectPrefix p = maybe (Just . Prelude.head $ siPrefixes) snd $ find (p . fst) prefixCandidates
+selectPrefix :: (Int -> Bool) -> Prefix
+selectPrefix p = maybe (Prelude.head siPrefixes) id $ find (p . scaleExponent) prefixCandidates
 
 -- This is a list of candidate prefixes and the least scale exponent at which each applies.
-prefixCandidates :: [(Int, Maybe Prefix)]
-prefixCandidates = sortBy (comparing $ Down . fst) $ (0, Nothing) : fmap (\x -> (scaleExponent x, Just x)) siPrefixes
+prefixCandidates :: [Prefix]
+prefixCandidates = sortBy (comparing $ Down . scaleExponent) siPrefixes
 
 -- | Constructs a version of a 'Metric' unit, by possibly applying a 'Prefix' to it, appropriate
 -- for display of a particular 'Quantity'.
@@ -187,7 +182,7 @@ prefixCandidates = sortBy (comparing $ Down . fst) $ (0, Nothing) : fmap (\x ->
 -- The appropriate prefix is defined to be the largest prefix such that the resulting value
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one.
 withAppropriatePrefix :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Unit 'NonMetric d a
-withAppropriatePrefix u q = applyOptionalPrefix (appropriatePrefix u q) u
+withAppropriatePrefix u q = applyPrefix (appropriatePrefix u q) u
 
 -- | Constructs a version of a 'Metric' unit, by possibly applying a 'Prefix' to it, appropriate
 -- for display of a particular 'Quantity'.
@@ -196,7 +191,7 @@ withAppropriatePrefix u q = applyOptionalPrefix (appropriatePrefix u q) u
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one. Only those prefixes
 -- whose 'scaleExponent' is a multiple of @3@ are considered.
 withAppropriatePrefix' :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Unit 'NonMetric d a
-withAppropriatePrefix' u q = applyOptionalPrefix (appropriatePrefix' u q) u
+withAppropriatePrefix' u q = applyPrefix (appropriatePrefix' u q) u
 
 {- $base-units
 These are the base units from section 4.1. To avoid a
diff --git a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
index 0128d4fa..f0a7a996 100644
--- a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
@@ -139,7 +139,7 @@ type PrefixName = NameAtom 'PrefixAtom
 data Prefix = Prefix
               {
                 -- | The name of a metric prefix.
-                prefixName :: PrefixName,
+                prefixName :: Maybe PrefixName,
                 -- | The scale factor denoted by a metric prefix.
                 scaleExponent :: Int
               }
@@ -150,9 +150,6 @@ instance Ord Prefix where
 
 instance NFData Prefix where -- instance is derived from Generic instance
 
-instance HasInterchangeName Prefix where
-  interchangeName = interchangeName . prefixName
-
 -- | The name of the unit of dimensionless values.
 nOne :: UnitName 'NonMetric
 nOne = One
@@ -189,6 +186,11 @@ baseUnitName d = let powers = asList $ dimension d
 baseUnitNames :: [UnitName 'NonMetric]
 baseUnitNames = [weaken nMeter, nKilogram, weaken nSecond, weaken nAmpere, weaken nKelvin, weaken nMole, weaken nCandela]
 
+-- | This is the SI 'Prefix' that is no prefix at all, and that consequently doesn't alter the value of the base unit to
+-- which it is applied.
+emptyPrefix :: Prefix
+emptyPrefix = Prefix Nothing 0
+
 deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta :: Prefix
 deka  = prefix "da" "da" "deka" 1
 hecto = prefix "h" "h" "hecto"  2
@@ -214,11 +216,13 @@ yocto = prefix "y" "y" "yocto"  $ -24
 
 -- | A list of all 'Prefix'es defined by the SI.
 siPrefixes :: [Prefix]
-siPrefixes = [yocto, zepto, atto, femto, pico, nano, micro, milli, centi, deci, deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta]
+siPrefixes = [yocto, zepto, atto, femto, pico, nano, micro, milli, centi, deci, emptyPrefix, deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta]
 
 -- | Forms a 'UnitName' from a 'Metric' name by applying a metric prefix.
 applyPrefix :: Prefix -> UnitName 'Metric -> UnitName 'NonMetric
-applyPrefix = Prefixed . prefixName
+applyPrefix p = case prefixName p of
+                  Just n -> Prefixed n
+                  Nothing -> Weaken
 
 {-
 We will reuse the operators and function names from the Prelude.
@@ -322,7 +326,7 @@ instance HasInterchangeName (UnitName m) where
 prefix :: String -> String -> String -> Int -> Prefix
 prefix i a f q = Prefix n q
   where
-    n = NameAtom (InterchangeName i UCUM True) a f
+    n = Just $ NameAtom (InterchangeName i UCUM True) a f
 
 ucumMetric :: String -> String -> String -> UnitName 'Metric
 ucumMetric i a f = MetricAtomic $ NameAtom (InterchangeName i UCUM True) a f

From 23635e32462d1e7c3023e2eca512ed9c57d06522 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Sun, 7 Aug 2016 15:24:11 -0400
Subject: [PATCH 08/11] Implemented PrefixSets to allow more choice in dynamic
 prefix selection.

---
 src/Numeric/Units/Dimensional/SIUnits.hs      | 42 +++++++------------
 src/Numeric/Units/Dimensional/UnitNames.hs    |  4 +-
 .../Units/Dimensional/UnitNames/Internal.hs   | 32 ++++++++++++--
 3 files changed, 46 insertions(+), 32 deletions(-)

diff --git a/src/Numeric/Units/Dimensional/SIUnits.hs b/src/Numeric/Units/Dimensional/SIUnits.hs
index ea87b86c..e4236960 100644
--- a/src/Numeric/Units/Dimensional/SIUnits.hs
+++ b/src/Numeric/Units/Dimensional/SIUnits.hs
@@ -61,18 +61,15 @@ module Numeric.Units.Dimensional.SIUnits
 )
 where
 
-import Data.List (sortBy, find)
-import Data.Maybe (maybe)
-import Data.Ord (comparing, Down(..))
 import Data.Ratio
 import Numeric.Units.Dimensional
 import Numeric.Units.Dimensional.Quantities
-import Numeric.Units.Dimensional.UnitNames (Prefix, siPrefixes, scaleExponent)
+import Numeric.Units.Dimensional.UnitNames (Prefix, PrefixSet, siPrefixes, selectPrefix)
 import qualified Numeric.Units.Dimensional.UnitNames as N
 import Numeric.Units.Dimensional.UnitNames.Internal (ucum, ucumMetric)
 import qualified Numeric.Units.Dimensional.UnitNames.Internal as I
 import Numeric.NumType.DK.Integers ( pos3 )
-import Prelude ( Eq(..), ($), (.), Num, Fractional, Floating, RealFrac(..), id, otherwise, error, Ord(..), Int, Bool, mod, (&&))
+import Prelude ( Eq(..), ($), Num, Fractional, Floating, RealFrac(..), otherwise, error)
 import qualified Prelude
 
 {- $multiples
@@ -142,56 +139,45 @@ list of all prefixes defined by the SI.
 -- | Selects the appropriate 'Prefix' to use with a 'Metric' unit when using it to display
 -- a particular 'Quantity', or 'Nothing' if the supplied unit should be used without a prefix.
 --
--- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- The appropriate prefix is defined to be the largest SI prefix such that the resulting value
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one.
 --
--- Note that the supplied prefix need not be 'Metric'. This is intended for use to compute a prefix to insert
+-- Note that the supplied unit need not be 'Metric'. This is intended for use to compute a prefix to insert
 -- somewhere in the denominator of a composite (and hence 'NonMetric') unit.
 appropriatePrefix :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Prefix
-appropriatePrefix u q = selectPrefix (<= e)
-  where
-    val = abs q /~ u
-    e = Prelude.floor $ Prelude.logBase 10 val :: Prelude.Int
+appropriatePrefix = appropriatePrefix' siPrefixes
 
 -- | Selects the appropriate 'Prefix' to use with a 'Metric' unit when using it to display
 -- a particular 'Quantity', or 'Nothing' if the supplied unit should be used without a prefix.
 --
--- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- The appropriate prefix is defined to be the largest prefix in the supplied 'PrefixSet' such that the resulting value
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one. Only those prefixes
 -- whose 'scaleExponent' is a multiple of @3@ are considered.
 --
--- Note that the supplied prefix need not be 'Metric'. This is intended for use to compute a prefix to insert
+-- Note that the supplied unit need not be 'Metric'. This is intended for use to compute a prefix to insert
 -- somewhere in the denominator of a composite (and hence 'NonMetric') unit.
-appropriatePrefix' :: (Floating a, RealFrac a) => Unit m d a -> Quantity d a -> Prefix
-appropriatePrefix' u q = selectPrefix (\x -> x `mod` 3 == 0 && x <= e)
+appropriatePrefix' :: (Floating a, RealFrac a) => PrefixSet -> Unit m d a -> Quantity d a -> Prefix
+appropriatePrefix' ps u q = selectPrefix ps e
   where
     val = abs q /~ u
     e = Prelude.floor $ Prelude.logBase 10 val :: Prelude.Int
 
--- Selects the first prefix in the list of prefix candidates whose scale exponent matches the supplied predicate.
-selectPrefix :: (Int -> Bool) -> Prefix
-selectPrefix p = maybe (Prelude.head siPrefixes) id $ find (p . scaleExponent) prefixCandidates
-
--- This is a list of candidate prefixes and the least scale exponent at which each applies.
-prefixCandidates :: [Prefix]
-prefixCandidates = sortBy (comparing $ Down . scaleExponent) siPrefixes
-
 -- | Constructs a version of a 'Metric' unit, by possibly applying a 'Prefix' to it, appropriate
 -- for display of a particular 'Quantity'.
 --
--- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- The appropriate prefix is defined to be the largest SI prefix such that the resulting value
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one.
 withAppropriatePrefix :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Unit 'NonMetric d a
-withAppropriatePrefix u q = applyPrefix (appropriatePrefix u q) u
+withAppropriatePrefix = withAppropriatePrefix' siPrefixes
 
 -- | Constructs a version of a 'Metric' unit, by possibly applying a 'Prefix' to it, appropriate
 -- for display of a particular 'Quantity'.
 --
--- The appropriate prefix is defined to be the largest prefix such that the resulting value
+-- The appropriate prefix is defined to be the largest prefix in the supplied 'PrefixSet' such that the resulting value
 -- of the quantity, expressed in the prefixed unit, is greater than or equal to one. Only those prefixes
 -- whose 'scaleExponent' is a multiple of @3@ are considered.
-withAppropriatePrefix' :: (Floating a, RealFrac a) => Unit 'Metric d a -> Quantity d a -> Unit 'NonMetric d a
-withAppropriatePrefix' u q = applyPrefix (appropriatePrefix' u q) u
+withAppropriatePrefix' :: (Floating a, RealFrac a) => PrefixSet -> Unit 'Metric d a -> Quantity d a -> Unit 'NonMetric d a
+withAppropriatePrefix' ps u q = applyPrefix (appropriatePrefix' ps u q) u
 
 {- $base-units
 These are the base units from section 4.1. To avoid a
diff --git a/src/Numeric/Units/Dimensional/UnitNames.hs b/src/Numeric/Units/Dimensional/UnitNames.hs
index a5f894e0..de5c5e93 100644
--- a/src/Numeric/Units/Dimensional/UnitNames.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames.hs
@@ -21,9 +21,11 @@ module Numeric.Units.Dimensional.UnitNames
   -- * Construction of Unit Names
   atom, applyPrefix, (*), (/), (^), product, reduce, grouped,
   -- * Standard Names
-  baseUnitName, siPrefixes, nOne,
+  baseUnitName, nOne,
   -- * Inspecting Prefixes
   prefixName, scaleExponent, scaleFactor,
+  -- * Sets of Prefixes
+  PrefixSet, prefixSet, unPrefixSet, selectPrefix, siPrefixes, majorSiPrefixes,
   -- * Convenience Type Synonyms for Unit Name Transformations
   UnitNameTransformer, UnitNameTransformer2,
   -- * Forgetting Unwanted Phantom Types
diff --git a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
index f0a7a996..044c5cf8 100644
--- a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
@@ -25,6 +25,9 @@ import Data.Foldable (toList)
 #else
 import Data.Foldable (Foldable, toList)
 #endif
+import Data.Function (on)
+import Data.List (sortBy, nubBy, find)
+import Data.Maybe (fromMaybe)
 import Data.Ord
 import GHC.Generics hiding (Prefix)
 import Numeric.Units.Dimensional.Dimensions.TermLevel (Dimension', asList, HasDimension(..))
@@ -214,9 +217,32 @@ atto  = prefix "a" "a" "atto"   $ -18
 zepto = prefix "z" "z" "zepto"  $ -21
 yocto = prefix "y" "y" "yocto"  $ -24
 
--- | A list of all 'Prefix'es defined by the SI.
-siPrefixes :: [Prefix]
-siPrefixes = [yocto, zepto, atto, femto, pico, nano, micro, milli, centi, deci, emptyPrefix, deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta]
+-- | A set of 'Prefix'es which necessarily includes the 'emptyPrefix'.
+newtype PrefixSet = PrefixSet { unPrefixSet :: [Prefix] }
+  deriving (Eq, Data)
+
+-- | Constructs a 'PrefixSet' from a list of 'Prefix'es by ensuring that the 'emptyPrefix' is present,
+-- removing duplicates, and sorting the prefixes.
+prefixSet :: [Prefix] -> PrefixSet
+prefixSet = PrefixSet . sortBy (comparing $ Down . scaleExponent) . nubBy ((==) `on` scaleExponent) . (emptyPrefix :)
+
+-- | Chooses a 'Prefix' from a 'PrefixSet', given a scale exponent. The resulting prefix will be that in the prefix set
+-- whose 'scaleExponent' is least, while still greater than the supplied scale exponent. If no prefix in the set has a 
+-- 'scaleExponent' greater than the supplied scale exponent, then the member with the least 'scaleExponent' will be returned.
+selectPrefix :: PrefixSet -> Int -> Prefix
+selectPrefix ps e = fromMaybe (Prelude.head ps') $ find ((<= e) . scaleExponent) ps'
+  where
+    ps' = unPrefixSet ps
+
+-- | The set of all 'Prefix'es defined by the SI.
+siPrefixes :: PrefixSet
+siPrefixes = prefixSet [yocto, zepto, atto, femto, pico, nano, micro, milli, centi, deci, deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta]
+
+-- | The set of all major 'Prefix'es defined by the SI.
+--
+-- A major prefix is one whose scale exponent is a multiple of three.
+majorSiPrefixes :: PrefixSet
+majorSiPrefixes = prefixSet [yocto, zepto, atto, femto, pico, nano, micro, milli, kilo, mega, giga, tera, peta, exa, zetta, yotta]
 
 -- | Forms a 'UnitName' from a 'Metric' name by applying a metric prefix.
 applyPrefix :: Prefix -> UnitName 'Metric -> UnitName 'NonMetric

From 5a2f4437ed23955ee5face8c266b4cf0d16fbecf Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Sun, 7 Aug 2016 16:58:45 -0400
Subject: [PATCH 09/11] Added filtering of PrefixSets. Added explicit Typeable
 instance for old versions of GHC.

---
 src/Numeric/Units/Dimensional/UnitNames.hs          |  2 +-
 src/Numeric/Units/Dimensional/UnitNames/Internal.hs | 10 ++++++++--
 2 files changed, 9 insertions(+), 3 deletions(-)

diff --git a/src/Numeric/Units/Dimensional/UnitNames.hs b/src/Numeric/Units/Dimensional/UnitNames.hs
index de5c5e93..a7d7b671 100644
--- a/src/Numeric/Units/Dimensional/UnitNames.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames.hs
@@ -25,7 +25,7 @@ module Numeric.Units.Dimensional.UnitNames
   -- * Inspecting Prefixes
   prefixName, scaleExponent, scaleFactor,
   -- * Sets of Prefixes
-  PrefixSet, prefixSet, unPrefixSet, selectPrefix, siPrefixes, majorSiPrefixes,
+  PrefixSet, prefixSet, unPrefixSet, filterPrefixSet, selectPrefix, siPrefixes, majorSiPrefixes,
   -- * Convenience Type Synonyms for Unit Name Transformations
   UnitNameTransformer, UnitNameTransformer2,
   -- * Forgetting Unwanted Phantom Types
diff --git a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
index 044c5cf8..7aa52124 100644
--- a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
@@ -219,13 +219,19 @@ yocto = prefix "y" "y" "yocto"  $ -24
 
 -- | A set of 'Prefix'es which necessarily includes the 'emptyPrefix'.
 newtype PrefixSet = PrefixSet { unPrefixSet :: [Prefix] }
-  deriving (Eq, Data)
+  deriving (Eq, Data, Typeable)
 
 -- | Constructs a 'PrefixSet' from a list of 'Prefix'es by ensuring that the 'emptyPrefix' is present,
 -- removing duplicates, and sorting the prefixes.
 prefixSet :: [Prefix] -> PrefixSet
 prefixSet = PrefixSet . sortBy (comparing $ Down . scaleExponent) . nubBy ((==) `on` scaleExponent) . (emptyPrefix :)
 
+-- | Filters a 'PrefixSet', retaining only those 'Prefix'es which match a supplied predicate.
+--
+-- The 'emptyPrefix' is always retained, as it must be a member of every 'PrefixSet'.
+filterPrefixSet :: (Prefix -> Bool) -> PrefixSet -> PrefixSet
+filterPrefixSet p = prefixSet . filter p . unPrefixSet
+
 -- | Chooses a 'Prefix' from a 'PrefixSet', given a scale exponent. The resulting prefix will be that in the prefix set
 -- whose 'scaleExponent' is least, while still greater than the supplied scale exponent. If no prefix in the set has a 
 -- 'scaleExponent' greater than the supplied scale exponent, then the member with the least 'scaleExponent' will be returned.
@@ -242,7 +248,7 @@ siPrefixes = prefixSet [yocto, zepto, atto, femto, pico, nano, micro, milli, cen
 --
 -- A major prefix is one whose scale exponent is a multiple of three.
 majorSiPrefixes :: PrefixSet
-majorSiPrefixes = prefixSet [yocto, zepto, atto, femto, pico, nano, micro, milli, kilo, mega, giga, tera, peta, exa, zetta, yotta]
+majorSiPrefixes = filterPrefixSet ((== 0) . (`mod` 3) . scaleExponent) siPrefixes
 
 -- | Forms a 'UnitName' from a 'Metric' name by applying a metric prefix.
 applyPrefix :: Prefix -> UnitName 'Metric -> UnitName 'NonMetric

From 87ee280b1c0bdf90f395d27f41c644d45a4ccf61 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Fri, 7 Oct 2016 15:42:44 -0400
Subject: [PATCH 10/11] Added equality for units.

---
 CHANGELOG.md                              |  1 +
 src/Numeric/Units/Dimensional/Internal.hs | 16 ++++++++++++++--
 2 files changed, 15 insertions(+), 2 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index ddea373c..b35ef72c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -39,6 +39,7 @@ vNext
   from RealFloat and IEEE for inspecting floating point quantities.
 * Added an `AEq` instance for `Quantity`.
 * Added `Eq1` and `Ord1` instances for `Quantity`.
+* Added `Eq` and `Eq1` instances for `Unit`.
 * Exposed the name of an 'AnyUnit' without promoting it to a 'Unit' first.
 * Exposed a way to convert atomic 'UnitName's back into 'NameAtom's.
 * Added dynamic selection of metric prefixes based on the magnitude of a quantity to be displayed.
diff --git a/src/Numeric/Units/Dimensional/Internal.hs b/src/Numeric/Units/Dimensional/Internal.hs
index a3ea17ef..20b6214c 100644
--- a/src/Numeric/Units/Dimensional/Internal.hs
+++ b/src/Numeric/Units/Dimensional/Internal.hs
@@ -50,8 +50,8 @@ import qualified Data.Vector.Generic as G
 import qualified Data.Vector.Unboxed.Base as U
 import Prelude
   ( Show, Eq(..), Ord, Bounded(..), Num, Fractional, Functor, Real(..)
-  , String, Maybe(..), Double
-  , (.), ($), (++), (+), (/)
+  , String, Maybe(..), Double, Bool(..)
+  , (.), ($), (++), (+), (/), (&&)
   , show, otherwise, undefined, error, fmap, realToFrac
   )
 import qualified Prelude as P
@@ -131,6 +131,18 @@ instance Ord1 (SQuantity s d) where
   liftCompare = coerce
 #endif
 
+instance (Eq a) => Eq (Unit m d a) where
+  (==) = areEqualUnitsBy (==)
+
+#if MIN_VERSION_base(4,9,0)
+instance Eq1 (Unit m d) where
+  liftEq = areEqualUnitsBy
+#endif
+
+-- define this here so that it is usable even when we are not conditionally compiling a Eq1 instance to define the Eq instance
+areEqualUnitsBy :: (a -> b -> Bool) -> Unit m d a -> Unit m d b -> Bool
+areEqualUnitsBy f (Unit n1 e1 x1) (Unit n2 e2 x2) = n1 == n2 && areExactlyEqual e1 e2 && f x1 x2
+
 instance HasInterchangeName (Unit m d a) where
   interchangeName (Unit n _ _) = interchangeName n
 

From 925819d524ec0e7cc420618069ec927603582215 Mon Sep 17 00:00:00 2001
From: Douglas McClean <douglas.mcclean@gmail.com>
Date: Fri, 7 Oct 2016 15:43:06 -0400
Subject: [PATCH 11/11] Added tests for appropriate prefix selection.

---
 .../Units/Dimensional/UnitNames/Internal.hs    |  9 ++++++---
 tests/Numeric/Units/Dimensional/SIUnitsSpec.hs | 18 ++++++++++++++++++
 2 files changed, 24 insertions(+), 3 deletions(-)
 create mode 100644 tests/Numeric/Units/Dimensional/SIUnitsSpec.hs

diff --git a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
index 7aa52124..f0b883e0 100644
--- a/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
+++ b/src/Numeric/Units/Dimensional/UnitNames/Internal.hs
@@ -26,8 +26,7 @@ import Data.Foldable (toList)
 import Data.Foldable (Foldable, toList)
 #endif
 import Data.Function (on)
-import Data.List (sortBy, nubBy, find)
-import Data.Maybe (fromMaybe)
+import Data.List (sortBy, nubBy)
 import Data.Ord
 import GHC.Generics hiding (Prefix)
 import Numeric.Units.Dimensional.Dimensions.TermLevel (Dimension', asList, HasDimension(..))
@@ -236,8 +235,12 @@ filterPrefixSet p = prefixSet . filter p . unPrefixSet
 -- whose 'scaleExponent' is least, while still greater than the supplied scale exponent. If no prefix in the set has a 
 -- 'scaleExponent' greater than the supplied scale exponent, then the member with the least 'scaleExponent' will be returned.
 selectPrefix :: PrefixSet -> Int -> Prefix
-selectPrefix ps e = fromMaybe (Prelude.head ps') $ find ((<= e) . scaleExponent) ps'
+selectPrefix ps e = go ((<= e) . scaleExponent) ps'
   where
+    go _ (x:[]) = x
+    go f (x:xs) | f x = x
+                | otherwise = go f xs
+    go _ _ = emptyPrefix
     ps' = unPrefixSet ps
 
 -- | The set of all 'Prefix'es defined by the SI.
diff --git a/tests/Numeric/Units/Dimensional/SIUnitsSpec.hs b/tests/Numeric/Units/Dimensional/SIUnitsSpec.hs
new file mode 100644
index 00000000..90ac7376
--- /dev/null
+++ b/tests/Numeric/Units/Dimensional/SIUnitsSpec.hs
@@ -0,0 +1,18 @@
+module Numeric.Units.Dimensional.SIUnitsSpec where
+
+import Numeric.Units.Dimensional.Prelude
+import Test.Hspec
+
+spec :: Spec
+spec = do
+         describe "Dynamic prefix selection" $ do
+           it "selects no prefix when appropriate" $ do
+             withAppropriatePrefix meter ((1.3 :: Double) *~ meter) `shouldBe` weaken meter
+           it "selects kilo as a prefix when appropriate" $ do
+             withAppropriatePrefix newton ((-1742.1 :: Double) *~ newton) `shouldBe` kilo newton
+           it "selects yotta as a prefix when appropriate" $ do
+             withAppropriatePrefix gram ((875 :: Double) *~ yotta gram) `shouldBe` yotta gram
+           it "selects atto as a prefix when appropriate" $ do
+             withAppropriatePrefix second ((85.4 :: Double) *~ atto second) `shouldBe` atto second
+           it "selects yocto as a prefix when appropriate" $ do
+             withAppropriatePrefix watt ((1e-7 :: Double) *~ yocto watt) `shouldBe` yocto watt