src/GHC/Integer/Logarithms/Internals.hs

    {-# LANGUAGE NoImplicitPrelude #-}
    {-# LANGUAGE MagicHash #-}
    {-# LANGUAGE UnboxedTuples #-}
    {-# LANGUAGE CPP #-}

    {-# OPTIONS_HADDOCK hide #-}

    #include "MachDeps.h"

    #if WORD_SIZE_IN_BITS == 32
    # define WSHIFT 5
    # define MMASK 31
    #elif WORD_SIZE_IN_BITS == 64
    # define WSHIFT 6
    # define MMASK 63
    #else
    # error unsupported WORD_SIZE_IN_BITS
    #endif

    -- | Fast 'Integer' logarithms to base 2.  'integerLog2#' and
    -- 'wordLog2#' are of general usefulness, the others are only needed
    -- for a fast implementation of 'fromRational'.  Since they are needed
    -- in "GHC.Float", we must expose this module, but it should not show
    -- up in the docs.
    --
    -- See https://ghc.haskell.org/trac/ghc/ticket/5122
    -- for the origin of the code in this module
    module GHC.Integer.Logarithms.Internals
        ( wordLog2#
        , integerLog2IsPowerOf2#
        , integerLog2#
        , roundingMode#
        ) where

    import GHC.Integer.Type
    import GHC.Integer.Logarithms

    import GHC.Types
    import GHC.Prim

    default ()

    -- | Extended version of 'integerLog2#'
    --
    -- Assumption: Integer is strictly positive
    --
    -- First component of result is @log2 n@, second is @0#@ iff /n/ is a
    -- power of two.
    integerLog2IsPowerOf2# :: Integer -> (# Int#, Int# #)
    -- The power of 2 test is n&(n-1) == 0, thus powers of 2
    -- are indicated bythe second component being zero.
    integerLog2IsPowerOf2# (S# i#) = case int2Word# i# of
          w -> (# wordLog2# w, word2Int# (w `and#` (w `minusWord#` 1##)) #)
    integerLog2IsPowerOf2# (Jn# _) = (# -1#, -1# #)
    -- Find the log2 as above, test whether that word is a power
    -- of 2, if so, check whether only zero bits follow.
    integerLog2IsPowerOf2# (Jp# bn) = check (s -# 1#)
      where
        s = sizeofBigNat# bn
        check :: Int# -> (# Int#, Int# #)
        check i = case indexBigNat# bn i of
                    0## -> check (i -# 1#)
                    w   -> (# wordLog2# w +# (uncheckedIShiftL# i WSHIFT#)
                            , case w `and#` (w `minusWord#` 1##) of
                                0## -> test (i -# 1#)
                                _   -> 1# #)
        test :: Int# -> Int#
        test i = if isTrue# (i <# 0#)
                    then 0#
                    else case indexBigNat# bn i of
                            0## -> test (i -# 1#)
                            _   -> 1#

    -- Assumption: Integer and Int# are strictly positive, Int# is less
    -- than logBase 2 of Integer, otherwise havoc ensues.
    -- Used only for the numerator in fromRational when the denominator
    -- is a power of 2.
    -- The Int# argument is log2 n minus the number of bits in the mantissa
    -- of the target type, i.e. the index of the first non-integral bit in
    -- the quotient.
    --
    -- 0# means round down (towards zero)
    -- 1# means we have a half-integer, round to even
    -- 2# means round up (away from zero)
    roundingMode# :: Integer -> Int# -> Int#
    roundingMode# (S# i#) t =
        case int2Word# i# `and#` ((uncheckedShiftL# 2## t) `minusWord#` 1##) of
          k -> case uncheckedShiftL# 1## t of
                c -> if isTrue# (c `gtWord#` k)
                        then 0#
                        else if isTrue# (c `ltWord#` k)
                                then 2#
                                else 1#

    roundingMode# (Jn# bn) t = roundingMode# (Jp# bn) t -- dummy
    roundingMode# (Jp# bn) t =
        case word2Int# (int2Word# t `and#` MMASK##) of
          j ->      -- index of relevant bit in word
            case uncheckedIShiftRA# t WSHIFT# of
              k ->  -- index of relevant word
                case indexBigNat# bn k `and#`
                        ((uncheckedShiftL# 2## j) `minusWord#` 1##) of
                  r ->
                    case uncheckedShiftL# 1## j of
                      c -> if isTrue# (c `gtWord#` r)
                            then 0#
                            else if isTrue# (c `ltWord#` r)

                                    then 2#
                                    else test (k -# 1#)
      where
        test i = if isTrue# (i <# 0#)
                    then 1#
                    else case indexBigNat# bn i of
                            0## -> test (i -# 1#)
                            _   -> 2#