diff options
Diffstat (limited to 'libraries/ghc-bignum/src/GHC')
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/BigNat.hs | 1509 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/BigNat.hs-boot | 19 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/BigNat/Check.hs | 456 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/BigNat/FFI.hs | 581 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/BigNat/GMP.hs | 498 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/BigNat/Native.hs | 719 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/Integer.hs | 1169 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/Natural.hs | 557 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/Natural.hs-boot | 23 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/Primitives.hs | 623 | ||||
| -rw-r--r-- | libraries/ghc-bignum/src/GHC/Num/WordArray.hs | 432 |
11 files changed, 6586 insertions, 0 deletions
diff --git a/libraries/ghc-bignum/src/GHC/Num/BigNat.hs b/libraries/ghc-bignum/src/GHC/Num/BigNat.hs new file mode 100644 index 0000000000..5d0a9919f5 --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/BigNat.hs @@ -0,0 +1,1509 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE BlockArguments #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE MultiWayIf #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE KindSignatures #-} +{-# LANGUAGE BinaryLiterals #-} +{-# OPTIONS_GHC -Wno-name-shadowing #-} + +-- | Multi-precision natural +module GHC.Num.BigNat where + +#include "MachDeps.h" +#include "WordSize.h" + +import GHC.Prim +import GHC.Types +import GHC.Classes +import GHC.Magic +import GHC.Num.Primitives +import GHC.Num.WordArray + +#if WORD_SIZE_IN_BITS < 64 +import GHC.IntWord64 +#endif + +#if defined(BIGNUM_CHECK) +import GHC.Num.BigNat.Check + +#elif defined(BIGNUM_NATIVE) +import GHC.Num.BigNat.Native + +#elif defined(BIGNUM_FFI) +import GHC.Num.BigNat.FFI + +#elif defined(BIGNUM_GMP) +import GHC.Num.BigNat.GMP + +#else +#error Undefined BigNat backend. Use a flag to select it (e.g. gmp, native, ffi)` +#endif + +default () + +-- | A BigNat +-- +-- Represented as an array of limbs (Word#) stored in little-endian order (Word# +-- themselves use machine order). +-- +-- Invariant (canonical representation): higher Word# is non-zero. +-- As a consequence, zero is represented with a WordArray# whose size is 0. +type BigNat = WordArray# -- we use a type-alias to make Integer/Natural easier to wire-in + +-- | Check that the BigNat is valid +bigNatCheck# :: BigNat -> Bool# +bigNatCheck# bn + | 0# <- bigNatSize# bn = 1# + | 0## <- bigNatIndex# bn (bigNatSize# bn -# 1#) = 0# + | True = 1# + +-- | Check that the BigNat is valid +bigNatCheck :: BigNat -> Bool +bigNatCheck bn = isTrue# (bigNatCheck# bn) + +-- | Number of words in the BigNat +bigNatSize :: BigNat -> Word +bigNatSize bn = W# (int2Word# (bigNatSize# bn)) + +-- | Number of words in the BigNat +bigNatSize# :: BigNat -> Int# +bigNatSize# ba = wordArraySize# ba + +-- Note [Why Void#?] +-- ~~~~~~~~~~~~~~~~~ +-- +-- We can't have top-level BigNat for now because they are unlifted ByteArray# +-- (see #17521). So we use functions that take an empty argument Void# that +-- will be discarded at compile time. + +data BigNatW = BigNatW BigNat + +{-# NOINLINE bigNatZeroW #-} +bigNatZeroW :: BigNatW +bigNatZeroW = BigNatW (withNewWordArray# 0# (\_ s -> s)) + +{-# NOINLINE bigNatOneW #-} +bigNatOneW :: BigNatW +bigNatOneW = BigNatW (bigNatFromWord# 1##) + +-- | BigNat Zero +bigNatZero :: Void# -> BigNat -- cf Note [Why Void#?] +bigNatZero _ = case bigNatZeroW of + BigNatW w -> w + +-- | BigNat one +bigNatOne :: Void# -> BigNat -- cf Note [Why Void#?] +bigNatOne _ = case bigNatOneW of + BigNatW w -> w + +-- | Indicate if a bigNat is zero +bigNatIsZero :: BigNat -> Bool +bigNatIsZero bn = isTrue# (bigNatIsZero# bn) + +-- | Indicate if a bigNat is zero +bigNatIsZero# :: BigNat -> Bool# +bigNatIsZero# ba = wordArraySize# ba ==# 0# + +-- | Indicate if a bigNat is one +bigNatIsOne :: BigNat -> Bool +bigNatIsOne bn = isTrue# (bigNatIsOne# bn) + +-- | Indicate if a bigNat is one +bigNatIsOne# :: BigNat -> Bool# +bigNatIsOne# ba = + wordArraySize# ba ==# 1# + &&# indexWordArray# ba 0# `eqWord#` 1## + +-- | Indicate if a bigNat is two +bigNatIsTwo :: BigNat -> Bool +bigNatIsTwo bn = isTrue# (bigNatIsTwo# bn) + +-- | Indicate if a bigNat is two +bigNatIsTwo# :: BigNat -> Bool# +bigNatIsTwo# ba = + wordArraySize# ba ==# 1# + &&# indexWordArray# ba 0# `eqWord#` 2## + +-- | Indicate if the value is a power of two and which one +bigNatIsPowerOf2# :: BigNat -> (# () | Word# #) +bigNatIsPowerOf2# a + | bigNatIsZero a = (# () | #) + | True = case wordIsPowerOf2# msw of + (# () | #) -> (# () | #) + (# | c #) -> case checkAllZeroes (imax -# 1#) of + 0# -> (# () | #) + _ -> (# | c `plusWord#` + (int2Word# imax `uncheckedShiftL#` WORD_SIZE_BITS_SHIFT#) #) + where + msw = bigNatIndex# a imax + sz = bigNatSize# a + imax = sz -# 1# + checkAllZeroes i + | isTrue# (i <# 0#) = 1# + | True = case bigNatIndex# a i of + 0## -> checkAllZeroes (i -# 1#) + _ -> 0# + +-- | Return the Word# at the given index +bigNatIndex# :: BigNat -> Int# -> Word# +bigNatIndex# x i = indexWordArray# x i + +-- | Return the Word# at the given index +bigNatIndex :: BigNat -> Int# -> Word +bigNatIndex bn i = W# (bigNatIndex# bn i) + +------------------------------------------------- +-- Conversion +------------------------------------------------- + +-- | Create a BigNat from a Word +bigNatFromWord :: Word -> BigNat +bigNatFromWord (W# w) = bigNatFromWord# w + +-- | Create a BigNat from a Word +bigNatFromWord# :: Word# -> BigNat +bigNatFromWord# 0## = bigNatZero void# +bigNatFromWord# w = wordArrayFromWord# w + +-- | Convert a list of non-zero Words (most-significant first) into a BigNat +bigNatFromWordList :: [Word] -> BigNat +bigNatFromWordList (W# 0##:xs) = bigNatFromWordList xs +bigNatFromWordList xs = bigNatFromWordListUnsafe xs + +-- | Convert a list of non-zero Words (most-significant first) into a BigNat +bigNatFromWordList# :: [Word] -> WordArray# +{-# NOINLINE bigNatFromWordList# #-} +bigNatFromWordList# xs = bigNatFromWordList xs + +-- | Return the absolute value of the Int# in a BigNat +bigNatFromAbsInt# :: Int# -> BigNat +bigNatFromAbsInt# i = bigNatFromWord# (wordFromAbsInt# i) + +-- | Convert a list of non-zero Words (most-significant first) into a BigNat. +-- Don't remove most-significant zero words +bigNatFromWordListUnsafe :: [Word] -> BigNat +bigNatFromWordListUnsafe [] = bigNatZero void# +bigNatFromWordListUnsafe xs = + let + length i [] = i + length i (_:ys) = length (i +# 1#) ys + !lxs = length 0# xs + writeWordList _mwa _i [] s = s + writeWordList mwa i (W# w:ws) s = + case mwaWrite# mwa i w s of + s1 -> writeWordList mwa (i -# 1#) ws s1 + in withNewWordArray# lxs \mwa -> + writeWordList mwa (lxs -# 1#) xs + +-- | Convert a BigNat into a list of non-zero Words (most-significant first) +bigNatToWordList :: BigNat -> [Word] +bigNatToWordList bn = go (bigNatSize# bn) + where + go 0# = [] + go n = bigNatIndex bn (n -# 1#) : go (n -# 1#) + + +-- | Convert two Word# (most-significant first) into a BigNat +bigNatFromWord2# :: Word# -> Word# -> BigNat +bigNatFromWord2# 0## 0## = bigNatZero void# +bigNatFromWord2# 0## n = bigNatFromWord# n +bigNatFromWord2# w1 w2 = wordArrayFromWord2# w1 w2 + +-- | Convert a BigNat into a Word# +bigNatToWord# :: BigNat -> Word# +bigNatToWord# a + | bigNatIsZero a = 0## + | True = bigNatIndex# a 0# + +-- | Convert a BigNat into a Word# if it fits +bigNatToWordMaybe# :: BigNat -> (# Word# | () #) +bigNatToWordMaybe# a + | bigNatIsZero a = (# 0## | #) + | isTrue# (bigNatSize# a ># 1#) = (# | () #) + | True = (# bigNatIndex# a 0# | #) + +-- | Convert a BigNat into a Word +bigNatToWord :: BigNat -> Word +bigNatToWord bn = W# (bigNatToWord# bn) + +-- | Convert a BigNat into a Int# +bigNatToInt# :: BigNat -> Int# +bigNatToInt# a + | bigNatIsZero a = 0# + | True = indexIntArray# a 0# + +-- | Convert a BigNat into a Int +bigNatToInt :: BigNat -> Int +bigNatToInt bn = I# (bigNatToInt# bn) + +#if WORD_SIZE_IN_BITS == 32 + +-- | Convert a Word64# into a BigNat on 32-bit architectures +bigNatFromWord64# :: Word64# -> BigNat +bigNatFromWord64# w64 = bigNatFromWord2# wh# wl# + where + wh# = word64ToWord# (uncheckedShiftRL64# w64 32#) + wl# = word64ToWord# w64 + +-- | Convert a BigNat into a Word64# on 32-bit architectures +bigNatToWord64# :: BigNat -> Word64# +bigNatToWord64# b + | bigNatIsZero b = wordToWord64# 0## + | wl <- wordToWord64# (bigNatToWord# b) + = if isTrue# (bigNatSize# b ># 1#) + then + let wh = wordToWord64# (bigNatIndex# b 1#) + in uncheckedShiftL64# wh 32# `or64#` wl + else wl + +#endif + +-- | Encode (# BigNat mantissa, Int# exponent #) into a Double# +bigNatEncodeDouble# :: BigNat -> Int# -> Double# +bigNatEncodeDouble# a e + | bigNatIsZero a + = word2Double# 0## -- FIXME: isn't it NaN on 0# exponent? + + | True + = inline bignat_encode_double a e + +------------------------------------------------- +-- Predicates +------------------------------------------------- + +-- | Test if a BigNat is greater than a Word +bigNatGtWord# :: BigNat -> Word# -> Bool# +bigNatGtWord# bn w = + notB# (bigNatIsZero# bn) + &&# ( bigNatSize# bn ># 1# + ||# bigNatIndex# bn 0# `gtWord#` w + ) + +-- | Test if a BigNat is equal to a Word +bigNatEqWord# :: BigNat -> Word# -> Bool# +bigNatEqWord# bn w + | 0## <- w + = bigNatIsZero# bn + + | isTrue# (bigNatSize# bn ==# 1#) + = bigNatIndex# bn 0# `eqWord#` w + + | True + = 0# + +-- | Test if a BigNat is greater than a Word +bigNatGtWord :: BigNat -> Word -> Bool +bigNatGtWord bn (W# w) = isTrue# (bigNatGtWord# bn w) + +-- | Test if a BigNat is lower than or equal to a Word +bigNatLeWord# :: BigNat -> Word# -> Bool# +bigNatLeWord# bn w = notB# (bigNatGtWord# bn w) + +-- | Test if a BigNat is lower than or equal to a Word +bigNatLeWord :: BigNat -> Word -> Bool +bigNatLeWord bn (W# w) = isTrue# (bigNatLeWord# bn w) + +-- | Equality test for BigNat +bigNatEq# :: BigNat -> BigNat -> Bool# +bigNatEq# wa wb + | isTrue# (wordArraySize# wa /=# wordArraySize# wb) = 0# + | isTrue# (wordArraySize# wa ==# 0#) = 1# + | True = inline bignat_compare wa wb ==# 0# + +-- | Equality test for BigNat +bigNatEq :: BigNat -> BigNat -> Bool +bigNatEq a b = isTrue# (bigNatEq# a b) + +-- | Inequality test for BigNat +bigNatNe# :: BigNat -> BigNat -> Bool# +bigNatNe# a b = notB# (bigNatEq# a b) + +-- | Equality test for BigNat +bigNatNe :: BigNat -> BigNat -> Bool +bigNatNe a b = isTrue# (bigNatNe# a b) + +-- | Compare a BigNat and a Word# +bigNatCompareWord# :: BigNat -> Word# -> Ordering +bigNatCompareWord# a b + | bigNatIsZero a = cmpW# 0## b + | isTrue# (wordArraySize# a ># 1#) = GT + | True + = cmpW# (indexWordArray# a 1#) b + +-- | Compare a BigNat and a Word +bigNatCompareWord :: BigNat -> Word -> Ordering +bigNatCompareWord a (W# b) = bigNatCompareWord# a b + +-- | Compare two BigNat +bigNatCompare :: BigNat -> BigNat -> Ordering +bigNatCompare a b = + let + szA = wordArraySize# a + szB = wordArraySize# b + in if + | isTrue# (szA ># szB) -> GT + | isTrue# (szA <# szB) -> LT + | isTrue# (szA ==# 0#) -> EQ + | True -> compareInt# (inline bignat_compare a b) 0# + + +-- | Predicate: a < b +bigNatLt :: BigNat -> BigNat -> Bool +bigNatLt a b = bigNatCompare a b == LT + +------------------------------------------------- +-- Addition +------------------------------------------------- + +-- | Add a bigNat and a Word# +bigNatAddWord# :: BigNat -> Word# -> BigNat +bigNatAddWord# a b + | 0## <- b + = a + + | bigNatIsZero a + = bigNatFromWord# b + + | True + = withNewWordArrayTrimed# (wordArraySize# a +# 1#) \mwa s -> + inline bignat_add_word mwa a b s + +-- | Add a bigNat and a Word +bigNatAddWord :: BigNat -> Word -> BigNat +bigNatAddWord a (W# b) = bigNatAddWord# a b + +-- | Add two bigNats +bigNatAdd :: BigNat -> BigNat -> BigNat +bigNatAdd a b + | bigNatIsZero a = b + | bigNatIsZero b = a + | True = + let + !szA = wordArraySize# a + !szB = wordArraySize# b + !szMax = maxI# szA szB + !sz = szMax +# 1# -- for the potential carry + in withNewWordArrayTrimed# sz \mwa s -> + inline bignat_add mwa a b s + +------------------------------------------------- +-- Multiplication +------------------------------------------------- + +-- | Multiply a BigNat by a Word# +bigNatMulWord# :: BigNat -> Word# -> BigNat +bigNatMulWord# a w + | 0## <- w = bigNatZero void# + | 1## <- w = a + | bigNatIsZero a = bigNatZero void# + | bigNatIsOne a = bigNatFromWord# w + | isTrue# (bigNatSize# a ==# 1#) + = case timesWord2# (bigNatIndex# a 0#) w of + (# h, l #) -> bigNatFromWord2# h l + | True = withNewWordArrayTrimed# (bigNatSize# a +# 1#) \mwa s -> + inline bignat_mul_word mwa a w s + +-- | Multiply a BigNAt by a Word +bigNatMulWord :: BigNat -> Word -> BigNat +bigNatMulWord a (W# w) = bigNatMulWord# a w + +-- | Square a BigNat +bigNatSqr :: BigNat -> BigNat +bigNatSqr a = bigNatMul a a + -- This can be replaced by a backend primitive in the future (e.g. to use + -- GMP's mpn_sqr) + +-- | Multiplication (classical algorithm) +bigNatMul :: BigNat -> BigNat -> BigNat +bigNatMul a b + | bigNatSize b > bigNatSize a = bigNatMul b a -- optimize loops + | bigNatIsZero a = a + | bigNatIsZero b = b + | bigNatIsOne a = b + | bigNatIsOne b = a + | True = + let + !szA = wordArraySize# a + !szB = wordArraySize# b + !sz = szA +# szB + in withNewWordArrayTrimed# sz \mwa s-> + inline bignat_mul mwa a b s + + +------------------------------------------------- +-- Subtraction +------------------------------------------------- + +-- | Subtract a Word# from a BigNat +-- +-- The BigNat must be bigger than the Word#. +bigNatSubWordUnsafe# :: BigNat -> Word# -> BigNat +bigNatSubWordUnsafe# x y + | 0## <- y = x + | True = withNewWordArrayTrimed# sz \mwa -> go mwa y 0# + where + !sz = wordArraySize# x + + go mwa carry i s + | isTrue# (i >=# sz) + = s + + | 0## <- carry + = mwaArrayCopy# mwa i x i (sz -# i) s + + | True + = case subWordC# (indexWordArray# x i) carry of + (# l, c #) -> case mwaWrite# mwa i l s of + s1 -> go mwa (int2Word# c) (i +# 1#) s1 + +-- | Subtract a Word# from a BigNat +-- +-- The BigNat must be bigger than the Word#. +bigNatSubWordUnsafe :: BigNat -> Word -> BigNat +bigNatSubWordUnsafe x (W# y) = bigNatSubWordUnsafe# x y + +-- | Subtract a Word# from a BigNat +bigNatSubWord# :: BigNat -> Word# -> (# () | BigNat #) +bigNatSubWord# a b + | 0## <- b = (# | a #) + | bigNatIsZero a = (# () | #) + | True + = withNewWordArrayTrimedMaybe# (bigNatSize# a) \mwa s -> + inline bignat_sub_word mwa a b s + + +-- | Subtract two BigNat (don't check if a >= b) +bigNatSubUnsafe :: BigNat -> BigNat -> BigNat +bigNatSubUnsafe a b + | bigNatIsZero b = a + | True = + let szA = wordArraySize# a + in withNewWordArrayTrimed# szA \mwa s-> + case inline bignat_sub mwa a b s of + (# s', 0# #) -> s' + (# s', _ #) -> case underflow of _ -> s' + +-- | Subtract two BigNat +bigNatSub :: BigNat -> BigNat -> (# () | BigNat #) +bigNatSub a b + | bigNatIsZero b = (# | a #) + | isTrue# (bigNatSize# a <# bigNatSize# b) + = (# () | #) + + | True + = withNewWordArrayTrimedMaybe# (bigNatSize# a) \mwa s -> + inline bignat_sub mwa a b s + + +------------------------------------------------- +-- Division +------------------------------------------------- + +-- | Divide a BigNat by a Word, return the quotient +-- +-- Require: +-- b /= 0 +bigNatQuotWord# :: BigNat -> Word# -> BigNat +bigNatQuotWord# a b + | 1## <- b = a + | 0## <- b = case divByZero of _ -> bigNatZero void# + | True = + let + sz = wordArraySize# a + in withNewWordArrayTrimed# sz \mwq s -> + inline bignat_quot_word mwq a b s + +-- | Divide a BigNat by a Word, return the quotient +-- +-- Require: +-- b /= 0 +bigNatQuotWord :: BigNat -> Word -> BigNat +bigNatQuotWord a (W# b) = bigNatQuotWord# a b + +-- | Divide a BigNat by a Word, return the remainder +-- +-- Require: +-- b /= 0 +bigNatRemWord# :: BigNat -> Word# -> Word# +bigNatRemWord# a b + | 0## <- b = 1## `remWord#` 0## + | 1## <- b = 0## + | bigNatIsZero a = 0## + | True = inline bignat_rem_word a b + +-- | Divide a BigNat by a Word, return the remainder +-- +-- Require: +-- b /= 0 +bigNatRemWord :: BigNat -> Word -> Word +bigNatRemWord a (W# b) = W# (bigNatRemWord# a b) + +-- | QuotRem a BigNat by a Word +-- +-- Require: +-- b /= 0 +bigNatQuotRemWord# :: BigNat -> Word# -> (# BigNat, Word# #) +bigNatQuotRemWord# a b + | 0## <- b = case divByZero of _ -> (# bigNatZero void#, 0## #) + | 1## <- b = (# a, 0## #) + | isTrue# (bigNatSize# a ==# 1#) + , a0 <- indexWordArray# a 0# + = case compareWord# a0 b of + LT -> (# bigNatZero void#, a0 #) + EQ -> (# bigNatOne void#, 0## #) + GT -> case quotRemWord# a0 b of + (# q, r #) -> (# bigNatFromWord# q, r #) + | True = + let + sz = wordArraySize# a + io s = + case newWordArray# sz s of { (# s1, mwq #) -> + case inline bignat_quotrem_word mwq a b s1 of { (# s2, r #) -> + case mwaTrimZeroes# mwq s2 of { s3 -> + case unsafeFreezeByteArray# mwq s3 of { (# s4, wq #) -> + (# s4, (# wq, r #) #) + }}}} + in case runRW# io of + (# _, (# wq,r #) #) -> (# wq, r #) + + +-- | BigNat division returning (quotient,remainder) +bigNatQuotRem# :: BigNat -> BigNat -> (# BigNat,BigNat #) +bigNatQuotRem# a b + | bigNatIsZero b = case divByZero of _ -> (# bigNatZero void#, bigNatZero void# #) + | bigNatIsZero a = (# bigNatZero void#, bigNatZero void# #) + | bigNatIsOne b = (# a , bigNatZero void# #) + | LT <- cmp = (# bigNatZero void#, a #) + | EQ <- cmp = (# bigNatOne void#, bigNatZero void# #) + | isTrue# (szB ==# 1#) = case bigNatQuotRemWord# a (bigNatIndex# b 0#) of + (# q, r #) -> (# q, bigNatFromWord# r #) + + | True = withNewWordArray2Trimed# szQ szR \mwq mwr s -> + inline bignat_quotrem mwq mwr a b s + where + cmp = bigNatCompare a b + szA = wordArraySize# a + szB = wordArraySize# b + szQ = 1# +# szA -# szB + szR = szB + + +-- | BigNat division returning quotient +bigNatQuot :: BigNat -> BigNat -> BigNat +bigNatQuot a b + | bigNatIsZero b = case divByZero of _ -> bigNatZero void# + | bigNatIsZero a = bigNatZero void# + | bigNatIsOne b = a + | LT <- cmp = bigNatZero void# + | EQ <- cmp = bigNatOne void# + | isTrue# (szB ==# 1#) = bigNatQuotWord# a (bigNatIndex# b 0#) + | True = withNewWordArrayTrimed# szQ \mwq s -> + inline bignat_quot mwq a b s + where + cmp = bigNatCompare a b + szA = wordArraySize# a + szB = wordArraySize# b + szQ = 1# +# szA -# szB + +-- | BigNat division returning remainder +bigNatRem :: BigNat -> BigNat -> BigNat +bigNatRem a b + | bigNatIsZero b = case divByZero of _ -> bigNatZero void# + | bigNatIsZero a = bigNatZero void# + | bigNatIsOne b = bigNatZero void# + | LT <- cmp = a + | EQ <- cmp = bigNatZero void# + | isTrue# (szB ==# 1#) = case bigNatRemWord# a (bigNatIndex# b 0#) of + r -> bigNatFromWord# r + | True = withNewWordArrayTrimed# szR \mwr s -> + inline bignat_rem mwr a b s + where + cmp = bigNatCompare a b + szB = wordArraySize# b + szR = szB + +------------------------------------------------- +-- GCD / LCM +------------------------------------------------- + +-- Word#/Int# GCDs shouldn't be here in BigNat. However GMP provides a very fast +-- implementation so we keep this here at least until we get a native Haskell +-- implementation as fast as GMP's one. Note that these functions are used in +-- `base` (e.g. in GHC.Real) + +-- | Greatest common divisor between two Word# +gcdWord# :: Word# -> Word# -> Word# +gcdWord# = bignat_gcd_word_word + +-- | Greatest common divisor between two Word +gcdWord :: Word -> Word -> Word +gcdWord (W# x) (W# y) = W# (gcdWord# x y) + +-- | Greatest common divisor between two Int# +-- +-- __Warning__: result may become negative if (at least) one argument +-- is 'minBound' +gcdInt# :: Int# -> Int# -> Int# +gcdInt# x y = word2Int# (gcdWord# (wordFromAbsInt# x) (wordFromAbsInt# y)) + +-- | Greatest common divisor between two Int +-- +-- __Warning__: result may become negative if (at least) one argument +-- is 'minBound' +gcdInt :: Int -> Int -> Int +gcdInt (I# x) (I# y) = I# (gcdInt# x y) + +-- | Greatest common divisor +bigNatGcd :: BigNat -> BigNat -> BigNat +bigNatGcd a b + | bigNatIsZero a = b + | bigNatIsZero b = a + | bigNatIsOne a = a + | bigNatIsOne b = b + | True + = case (# bigNatSize# a, bigNatSize# b #) of + (# 1#, 1# #) -> bigNatFromWord# (gcdWord# (bigNatIndex# a 0#) + (bigNatIndex# b 0#)) + (# 1#, _ #) -> bigNatFromWord# (bigNatGcdWord# b (bigNatIndex# a 0#)) + (# _ , 1# #) -> bigNatFromWord# (bigNatGcdWord# a (bigNatIndex# b 0#)) + _ -> + let + go wx wy = -- wx > wy + withNewWordArrayTrimed# (wordArraySize# wy) \mwr s -> + bignat_gcd mwr wx wy s + in case bigNatCompare a b of + EQ -> a + LT -> go b a + GT -> go a b + +-- | Greatest common divisor +bigNatGcdWord# :: BigNat -> Word# -> Word# +bigNatGcdWord# a b + | bigNatIsZero a = 0## + | 0## <- b = 0## + | bigNatIsOne a = 1## + | 1## <- b = 1## + | True = case bigNatCompareWord# a b of + EQ -> b + _ -> bignat_gcd_word a b + +-- | Least common multiple +bigNatLcm :: BigNat -> BigNat -> BigNat +bigNatLcm a b + | bigNatIsZero a = bigNatZero void# + | bigNatIsZero b = bigNatZero void# + | bigNatIsOne a = b + | bigNatIsOne b = a + | True + = case (# bigNatSize# a, bigNatSize# b #) of + (# 1#, 1# #) -> bigNatLcmWordWord# (bigNatIndex# a 0#) (bigNatIndex# b 0#) + (# 1#, _ #) -> bigNatLcmWord# b (bigNatIndex# a 0#) + (# _ , 1# #) -> bigNatLcmWord# a (bigNatIndex# b 0#) + _ -> (a `bigNatQuot` (a `bigNatGcd` b)) `bigNatMul` b + -- TODO: use extended GCD to get a's factor directly + +-- | Least common multiple with a Word# +bigNatLcmWord# :: BigNat -> Word# -> BigNat +bigNatLcmWord# a b + | bigNatIsZero a = bigNatZero void# + | 0## <- b = bigNatZero void# + | bigNatIsOne a = bigNatFromWord# b + | 1## <- b = a + | 1# <- bigNatSize# a = bigNatLcmWordWord# (bigNatIndex# a 0#) b + | True + = (a `bigNatQuotWord#` (a `bigNatGcdWord#` b)) `bigNatMulWord#` b + -- TODO: use extended GCD to get a's factor directly + +-- | Least common multiple between two Word# +bigNatLcmWordWord# :: Word# -> Word# -> BigNat +bigNatLcmWordWord# a b + | 0## <- a = bigNatZero void# + | 0## <- b = bigNatZero void# + | 1## <- a = bigNatFromWord# b + | 1## <- b = bigNatFromWord# a + | True = case (a `quotWord#` (a `gcdWord#` b)) `timesWord2#` b of + -- TODO: use extended GCD to get a's factor directly + (# h, l #) -> bigNatFromWord2# h l + + +------------------------------------------------- +-- Bitwise operations +------------------------------------------------- + +-- | Bitwise OR +bigNatOr :: BigNat -> BigNat -> BigNat +bigNatOr a b + | bigNatIsZero a = b + | bigNatIsZero b = a + | True = withNewWordArray# sz \mwa s -> + inline bignat_or mwa a b s + where + !szA = wordArraySize# a + !szB = wordArraySize# b + !sz = maxI# szA szB + +-- | Bitwise OR with Word# +bigNatOrWord# :: BigNat -> Word# -> BigNat +bigNatOrWord# a b + | bigNatIsZero a = bigNatFromWord# b + | 0## <- b = a + | True = + let sz = wordArraySize# a + in withNewWordArray# sz \mwa s -> + case mwaArrayCopy# mwa 1# a 1# (sz -# 1#) s of + s' -> mwaWrite# mwa 0# (indexWordArray# a 0# `or#` b) s' + +-- | Bitwise AND +bigNatAnd :: BigNat -> BigNat -> BigNat +bigNatAnd a b + | bigNatIsZero a = a + | bigNatIsZero b = b + | True = withNewWordArrayTrimed# sz \mwa s -> + inline bignat_and mwa a b s + where + !szA = wordArraySize# a + !szB = wordArraySize# b + !sz = minI# szA szB + +-- | Bitwise ANDNOT +bigNatAndNot :: BigNat -> BigNat -> BigNat +bigNatAndNot a b + | bigNatIsZero a = a + | bigNatIsZero b = a + | True = withNewWordArrayTrimed# szA \mwa s -> + inline bignat_and_not mwa a b s + where + !szA = wordArraySize# a + +-- | Bitwise AND with Word# +bigNatAndWord# :: BigNat -> Word# -> BigNat +bigNatAndWord# a b + | bigNatIsZero a = a + | True = bigNatFromWord# (indexWordArray# a 0# `and#` b) + +-- | Bitwise ANDNOT with Word# +bigNatAndNotWord# :: BigNat -> Word# -> BigNat +bigNatAndNotWord# a b + | bigNatIsZero a = a + | szA <- bigNatSize# a + = withNewWordArray# szA \mwa s -> + -- duplicate higher limbs + case mwaArrayCopy# mwa 1# a 1# (szA -# 1#) s of + s' -> writeWordArray# mwa 0# + (indexWordArray# a 0# `and#` not# b) s' + +-- | Bitwise AND with Int# +bigNatAndInt# :: BigNat -> Int# -> BigNat +bigNatAndInt# a b + | bigNatIsZero a = a + | isTrue# (b >=# 0#) = bigNatAndWord# a (int2Word# b) + | szA <- bigNatSize# a + = withNewWordArray# szA \mwa s -> + -- duplicate higher limbs (because of sign-extension of b) + case mwaArrayCopy# mwa 1# a 1# (szA -# 1#) s of + s' -> writeWordArray# mwa 0# + (indexWordArray# a 0# `and#` int2Word# b) s' + + +-- | Bitwise XOR +bigNatXor :: BigNat -> BigNat -> BigNat +bigNatXor a b + | bigNatIsZero a = b + | bigNatIsZero b = a + | True = withNewWordArrayTrimed# sz \mwa s -> + inline bignat_xor mwa a b s + where + !szA = wordArraySize# a + !szB = wordArraySize# b + !sz = maxI# szA szB + +-- | Bitwise XOR with Word# +bigNatXorWord# :: BigNat -> Word# -> BigNat +bigNatXorWord# a b + | bigNatIsZero a = bigNatFromWord# b + | 0## <- b = a + | True = + let + sz = wordArraySize# a + in withNewWordArray# sz \mwa s -> + case mwaArrayCopy# mwa 1# a 1# (sz -# 1#) s of + s' -> mwaWrite# mwa 0# (indexWordArray# a 0# `xor#` b) s' + +-- | PopCount for BigNat +bigNatPopCount :: BigNat -> Word +bigNatPopCount a = W# (bigNatPopCount# a) + +-- | PopCount for BigNat +bigNatPopCount# :: BigNat -> Word# +bigNatPopCount# a + | bigNatIsZero a = 0## + | True = inline bignat_popcount a + +-- | Bit shift right +bigNatShiftR# :: BigNat -> Word# -> BigNat +bigNatShiftR# a n + | 0## <- n + = a + + | isTrue# (wordArraySize# a ==# 0#) + = a + + | nw <- word2Int# (n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + , isTrue# (nw >=# wordArraySize# a) + = bigNatZero void# + + | True + = let + !szA = wordArraySize# a + !nw = word2Int# (n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + !sz = szA -# nw + in withNewWordArrayTrimed# sz \mwa s -> + inline bignat_shiftr mwa a n s + +-- | Bit shift right (two's complement) +bigNatShiftRNeg# :: BigNat -> Word# -> BigNat +bigNatShiftRNeg# a n + | 0## <- n + = a + + | isTrue# (wordArraySize# a ==# 0#) + = a + + | nw <- word2Int# (n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + , isTrue# (nw >=# wordArraySize# a) + = bigNatZero void# + + | True + = let + !szA = wordArraySize# a + !nw = (word2Int# n -# 1#) `uncheckedIShiftRL#` WORD_SIZE_BITS_SHIFT# + !sz = szA -# nw + in withNewWordArrayTrimed# sz \mwa s -> + inline bignat_shiftr_neg mwa a n s + + +-- | Bit shift right +bigNatShiftR :: BigNat -> Word -> BigNat +bigNatShiftR a (W# n) = bigNatShiftR# a n + +-- | Bit shift left +bigNatShiftL :: BigNat -> Word -> BigNat +bigNatShiftL a (W# n) = bigNatShiftL# a n + +-- | Bit shift left +bigNatShiftL# :: BigNat -> Word# -> BigNat +bigNatShiftL# a n + | 0## <- n + = a + + | isTrue# (wordArraySize# a ==# 0#) + = a + + | True + = let + !szA = wordArraySize# a + !nw = word2Int# (n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + !nb = word2Int# (n `and#` WORD_SIZE_BITS_MASK##) + !sz = szA +# nw +# (nb /=# 0#) + + in withNewWordArrayTrimed# sz \mwa s -> + inline bignat_shiftl mwa a n s + + +-- | BigNat bit test +bigNatTestBit# :: BigNat -> Word# -> Bool# +bigNatTestBit# a n = + let + !sz = wordArraySize# a + !nw = word2Int# (n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + !nb = n `and#` WORD_SIZE_BITS_MASK## + in if + | isTrue# (nw >=# sz) -> 0# + | True -> testBitW# (indexWordArray# a nw) nb + +-- | BigNat bit test +bigNatTestBit :: BigNat -> Word -> Bool +bigNatTestBit a (W# n) = isTrue# (bigNatTestBit# a n) + + +-- | Return a BigNat whose bit `i` is the only one set. +-- +-- Specialized version of `bigNatShiftL (bigNatFromWord# 1##)` +-- +bigNatBit# :: Word# -> BigNat +bigNatBit# i + | 0## <- i = bigNatOne void# + | True = + let + !nw = word2Int# (i `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + !nb = word2Int# (i `and#` WORD_SIZE_BITS_MASK##) + !sz = nw +# 1# + !v = 1## `uncheckedShiftL#` nb + in withNewWordArray# sz \mwa s -> + -- clear the array + case mwaFill# mwa 0## 0## (int2Word# sz) s of + -- set the bit in the most-significant word + s2 -> mwaWrite# mwa (sz -# 1#) v s2 + +-- | Return a BigNat whose bit `i` is the only one set. +-- +-- Specialized version of `bigNatShiftL (bigNatFromWord# 1##)` +-- +bigNatBit :: Word -> BigNat +bigNatBit (W# i) = bigNatBit# i + +-- | BigNat clear bit +bigNatClearBit# :: BigNat -> Word# -> BigNat +bigNatClearBit# a n + -- check the range validity and the current bit value + | isTrue# (bigNatTestBit# a n ==# 0#) = a + | True + = let + !sz = wordArraySize# a + !nw = word2Int# (n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + !nb = word2Int# (n `and#` WORD_SIZE_BITS_MASK##) + !nv = bigNatIndex# a nw `xor#` bitW# nb + in if + | isTrue# (sz ==# 1#) + -> bigNatFromWord# nv + + -- special case, operating on most-significant Word + | 0## <- nv + , isTrue# (nw +# 1# ==# sz) + -> case sz -# (waClzAt a (sz -# 2#) +# 1#) of + 0# -> bigNatZero void# + nsz -> withNewWordArray# nsz \mwa s -> + mwaArrayCopy# mwa 0# a 0# nsz s + + | True -> + withNewWordArray# sz \mwa s -> + case mwaArrayCopy# mwa 0# a 0# sz s of + s' -> writeWordArray# mwa nw nv s' + +-- | BigNat set bit +bigNatSetBit# :: BigNat -> Word# -> BigNat +bigNatSetBit# a n + -- check the current bit value + | isTrue# (bigNatTestBit# a n) = a + | True + = let + !sz = wordArraySize# a + !nw = word2Int# (n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + !nb = word2Int# (n `and#` WORD_SIZE_BITS_MASK##) + d = nw +# 1# -# sz + in if + -- result BigNat will have more limbs + | isTrue# (d ># 0#) + -> withNewWordArray# (nw +# 1#) \mwa s -> + case mwaArrayCopy# mwa 0# a 0# sz s of + s' -> case mwaFill# mwa 0## (int2Word# sz) (int2Word# (d -# 1#)) s' of + s'' -> writeWordArray# mwa nw (bitW# nb) s'' + + | nv <- bigNatIndex# a nw `or#` bitW# nb + -> withNewWordArray# sz \mwa s -> + case mwaArrayCopy# mwa 0# a 0# sz s of + s' -> writeWordArray# mwa nw nv s' + +-- | Reverse the given bit +bigNatComplementBit# :: BigNat -> Word# -> BigNat +bigNatComplementBit# bn i + | isTrue# (bigNatTestBit# bn i) = bigNatClearBit# bn i + | True = bigNatSetBit# bn i + +------------------------------------------------- +-- Log operations +------------------------------------------------- + +-- | Base 2 logarithm +bigNatLog2# :: BigNat -> Word# +bigNatLog2# a + | bigNatIsZero a = 0## + | True = + let i = int2Word# (bigNatSize# a) `minusWord#` 1## + in wordLog2# (bigNatIndex# a (word2Int# i)) + `plusWord#` (i `uncheckedShiftL#` WORD_SIZE_BITS_SHIFT#) + +-- | Base 2 logarithm +bigNatLog2 :: BigNat -> Word +bigNatLog2 a = W# (bigNatLog2# a) + +-- | Logarithm for an arbitrary base +bigNatLogBase# :: BigNat -> BigNat -> Word# +bigNatLogBase# base a + | bigNatIsZero base || bigNatIsOne base + = case unexpectedValue of _ -> 0## + + | 1# <- bigNatSize# base + , 2## <- bigNatIndex# base 0# + = bigNatLog2# a + + -- TODO: optimize log base power of 2 (256, etc.) + + | True + = case go base of (# _, e' #) -> e' + where + go pw = if a `bigNatLt` pw + then (# a, 0## #) + else case go (bigNatSqr pw) of + (# q, e #) -> if q `bigNatLt` pw + then (# q, 2## `timesWord#` e #) + else (# q `bigNatQuot` pw + , (2## `timesWord#` e) `plusWord#` 1## #) + +-- | Logarithm for an arbitrary base +bigNatLogBase :: BigNat -> BigNat -> Word +bigNatLogBase base a = W# (bigNatLogBase# base a) + +-- | Logarithm for an arbitrary base +bigNatLogBaseWord# :: Word# -> BigNat -> Word# +bigNatLogBaseWord# base a + | 0## <- base = case unexpectedValue of _ -> 0## + | 1## <- base = case unexpectedValue of _ -> 0## + | 2## <- base = bigNatLog2# a + -- TODO: optimize log base power of 2 (256, etc.) + | True = bigNatLogBase# (bigNatFromWord# base) a + +-- | Logarithm for an arbitrary base +bigNatLogBaseWord :: Word -> BigNat -> Word +bigNatLogBaseWord (W# base) a = W# (bigNatLogBaseWord# base a) + +------------------------------------------------- +-- Various +------------------------------------------------- + +-- | Compute the number of digits of the BigNat in the given base. +-- +-- `base` must be > 1 +bigNatSizeInBase# :: Word# -> BigNat -> Word# +bigNatSizeInBase# base a + | isTrue# (base `leWord#` 1##) + = case unexpectedValue of _ -> 0## + + | bigNatIsZero a + = 0## + + | True + = bigNatLogBaseWord# base a `plusWord#` 1## + +-- | Compute the number of digits of the BigNat in the given base. +-- +-- `base` must be > 1 +bigNatSizeInBase :: Word -> BigNat -> Word +bigNatSizeInBase (W# w) a = W# (bigNatSizeInBase# w a) + +------------------------------------------------- +-- PowMod +------------------------------------------------- + +-- Word# powMod shouldn't be here in BigNat. However GMP provides a very fast +-- implementation so we keep this here at least until we get a native Haskell +-- implementation as fast as GMP's one. + +powModWord# :: Word# -> Word# -> Word# -> Word# +powModWord# = bignat_powmod_words + + +-- | \"@'bigNatPowModWord#' /b/ /e/ /m/@\" computes base @/b/@ raised to +-- exponent @/e/@ modulo @/m/@. +bigNatPowModWord# :: BigNat -> BigNat -> Word# -> Word# +bigNatPowModWord# !_ !_ 0## = case divByZero of _ -> 0## +bigNatPowModWord# _ _ 1## = 0## +bigNatPowModWord# b e m + | bigNatIsZero e = 1## + | bigNatIsZero b = 0## + | bigNatIsOne b = 1## + | True = bignat_powmod_word b e m + +-- | \"@'bigNatPowMod' /b/ /e/ /m/@\" computes base @/b/@ raised to +-- exponent @/e/@ modulo @/m/@. +bigNatPowMod :: BigNat -> BigNat -> BigNat -> BigNat +bigNatPowMod !b !e !m + | (# m' | #) <- bigNatToWordMaybe# m + = bigNatFromWord# (bigNatPowModWord# b e m') + | bigNatIsZero m = case divByZero of _ -> bigNatZero void# + | bigNatIsOne m = bigNatFromWord# 0## + | bigNatIsZero e = bigNatFromWord# 1## + | bigNatIsZero b = bigNatFromWord# 0## + | bigNatIsOne b = bigNatFromWord# 1## + | True = withNewWordArrayTrimed# (bigNatSize# m) \mwa s -> + inline bignat_powmod mwa b e m s + +-- | Return count of trailing zero bits +-- +-- Return 0 for zero BigNat +bigNatCtz# :: BigNat -> Word# +bigNatCtz# a + | bigNatIsZero a = 0## + | True = go 0# 0## + where + go i c = case indexWordArray# a i of + 0## -> go (i +# 1#) (c `plusWord#` WORD_SIZE_IN_BITS##) + w -> ctz# w `plusWord#` c + +-- | Return count of trailing zero bits +-- +-- Return 0 for zero BigNat +bigNatCtz :: BigNat -> Word +bigNatCtz a = W# (bigNatCtz# a) + + +-- | Return count of trailing zero words +-- +-- Return 0 for zero BigNat +bigNatCtzWord# :: BigNat -> Word# +bigNatCtzWord# a + | bigNatIsZero a = 0## + | True = go 0# 0## + where + go i c = case indexWordArray# a i of + 0## -> go (i +# 1#) (c `plusWord#` 1##) + _ -> c + +-- | Return count of trailing zero words +-- +-- Return 0 for zero BigNat +bigNatCtzWord :: BigNat -> Word +bigNatCtzWord a = W# (bigNatCtzWord# a) + +------------------------------------------------- +-- Export to memory +------------------------------------------------- + +-- | Write a BigNat in base-256 little-endian representation and return the +-- number of bytes written. +-- +-- Use \"@'bigNatSizeInBase' 256# /i/@\" to compute the exact number of bytes +-- written in advance. In case of @/i/ == 0@, the function will write and report +-- zero bytes written. +bigNatToAddrLE# :: BigNat -> Addr# -> State# s -> (# State# s, Word# #) +bigNatToAddrLE# a addr s0 + | isTrue# (sz ==# 0#) = (# s0, 0## #) + | True = case writeMSB s0 of + (# s1, k #) -> case go 0# s1 of + s2 -> (# s2, k `plusWord#` (int2Word# li `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT#) #) + where + !sz = wordArraySize# a + !li = sz -# 1# + + writeMSB = wordToAddrLE# (indexWordArray# a li) + (addr `plusAddr#` (li `uncheckedIShiftL#` WORD_SIZE_BYTES_SHIFT#)) + + go i s + | isTrue# (i <# li) + , off <- i `uncheckedIShiftL#` WORD_SIZE_BYTES_SHIFT# + , w <- indexWordArray# a i + = case wordWriteAddrLE# w (addr `plusAddr#` off) s of + s -> go (i +# 1#) s + + | True + = s + +-- | Write a BigNat in base-256 big-endian representation and return the +-- number of bytes written. +-- +-- Use \"@'bigNatSizeInBase' 256# /i/@\" to compute the exact number of bytes +-- written in advance. In case of @/i/ == 0@, the function will write and report +-- zero bytes written. +bigNatToAddrBE# :: BigNat -> Addr# -> State# s -> (# State# s, Word# #) +bigNatToAddrBE# a addr s0 + | isTrue# (sz ==# 0#) = (# s0, 0## #) + | msw <- indexWordArray# a (sz -# 1#) + = case wordToAddrBE# msw addr s0 of + (# s1, k #) -> case go (sz -# 1#) (addr `plusAddr#` word2Int# k) s1 of + s2 -> (# s2, k `plusWord#` (int2Word# (sz -# 1#) `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT#) #) + where + sz = wordArraySize# a + + go i adr s + | 0# <- i + = s + + | w <- indexWordArray# a (i -# 1#) + = case wordWriteAddrBE# w adr s of + s' -> go (i -# 1#) + (adr `plusAddr#` WORD_SIZE_IN_BYTES# ) s' + + +-- | Write a BigNat in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Use \"@'bigNatSizeInBase' 256# /i/@\" to compute the exact number of bytes +-- written in advance. In case of @/i/ == 0@, the function will write and report +-- zero bytes written. +bigNatToAddr# :: BigNat -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) +bigNatToAddr# a addr 0# s = bigNatToAddrLE# a addr s +bigNatToAddr# a addr _ s = bigNatToAddrBE# a addr s + +-- | Write a BigNat in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Use \"@'bigNatSizeInBase' 256# /i/@\" to compute the exact number of bytes +-- written in advance. In case of @/i/ == 0@, the function will write and report +-- zero bytes written. +bigNatToAddr :: BigNat -> Addr# -> Bool# -> IO Word +bigNatToAddr a addr e = IO \s -> case bigNatToAddr# a addr e s of + (# s', w #) -> (# s', W# w #) + + + +------------------------------------------------- +-- Import from memory +------------------------------------------------- + +-- | Read a BigNat in base-256 little-endian representation from an Addr#. +-- +-- The size is given in bytes. +-- +-- Higher limbs equal to 0 are automatically trimed. +bigNatFromAddrLE# :: Word# -> Addr# -> State# s -> (# State# s, BigNat #) +bigNatFromAddrLE# 0## _ s = (# s, bigNatZero void# #) +bigNatFromAddrLE# sz addr s = + let + !nw = sz `uncheckedShiftRL#` WORD_SIZE_BYTES_SHIFT# + !nb = sz `and#` WORD_SIZE_BYTES_MASK## + + readMSB mwa s + | 0## <- nb + = s + + | off <- word2Int# (nw `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT#) + = case wordFromAddrLE# nb (addr `plusAddr#` off) s of + (# s, w #) -> mwaWrite# mwa (word2Int# nw) w s + + go mwa i s + | isTrue# (i ==# word2Int# nw) + = s + + | off <- i `uncheckedIShiftL#` WORD_SIZE_BYTES_SHIFT# + = case wordFromAddrLE# WORD_SIZE_IN_BYTES## (addr `plusAddr#` off) s of + (# s, w #) -> case mwaWrite# mwa i w s of + s -> go mwa (i +# 1#) s + + in case newWordArray# (word2Int# nw +# (word2Int# nb /=# 0#)) s of + (# s, mwa #) -> case readMSB mwa s of + s -> case go mwa 0# s of + s -> case mwaTrimZeroes# mwa s of + s -> unsafeFreezeByteArray# mwa s + +-- | Read a BigNat in base-256 big-endian representation from an Addr#. +-- +-- The size is given in bytes. +-- +-- Null higher limbs are automatically trimed. +bigNatFromAddrBE# :: Word# -> Addr# -> State# s -> (# State# s, BigNat #) +bigNatFromAddrBE# 0## _ s = (# s, bigNatZero void# #) +bigNatFromAddrBE# sz addr s = + let + !nw = word2Int# (sz `uncheckedShiftRL#` WORD_SIZE_BYTES_SHIFT#) + !nb = sz `and#` WORD_SIZE_BYTES_MASK## + + goMSB mwa s + | 0## <- nb + = s + + | True + = case wordFromAddrBE# nb addr s of + (# s, w #) -> mwaWrite# mwa nw w s + + go mwa i s + | isTrue# (i ==# nw) + = s + + | k <- nw -# 1# -# i + , off <- (k `uncheckedIShiftL#` WORD_SIZE_BYTES_SHIFT#) +# word2Int# nb + = case wordFromAddrBE# WORD_SIZE_IN_BYTES## (addr `plusAddr#` off) s of + (# s, w #) -> case mwaWrite# mwa i w s of + s -> go mwa (i +# 1#) s + + in case newWordArray# (nw +# (word2Int# nb /=# 0#)) s of + (# s, mwa #) -> case goMSB mwa s of + s -> case go mwa 0# s of + s -> case mwaTrimZeroes# mwa s of + s -> unsafeFreezeByteArray# mwa s + +-- | Read a BigNat in base-256 representation from an Addr#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +bigNatFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, BigNat #) +bigNatFromAddr# sz addr 0# s = bigNatFromAddrLE# sz addr s +bigNatFromAddr# sz addr _ s = bigNatFromAddrBE# sz addr s + +------------------------------------------------- +-- Export to ByteArray +------------------------------------------------- + +-- | Write a BigNat in base-256 little-endian representation and return the +-- number of bytes written. +-- +-- Use \"@'bigNatSizeInBase' 256# /i/@\" to compute the exact number of bytes +-- written in advance. In case of @/i/ == 0@, the function will write and report +-- zero bytes written. +bigNatToMutableByteArrayLE# :: BigNat -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) +bigNatToMutableByteArrayLE# a mba moff s0 + | isTrue# (sz ==# 0#) = (# s0, 0## #) + | True = case writeMSB s0 of + (# s1, k #) -> case go 0# s1 of + s2 -> (# s2, k `plusWord#` (int2Word# li `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT#) #) + where + !sz = wordArraySize# a + !li = sz -# 1# + + writeMSB = wordToMutableByteArrayLE# (indexWordArray# a li) + mba (moff `plusWord#` int2Word# (li `uncheckedIShiftL#` WORD_SIZE_BYTES_SHIFT#)) + + go i s + | isTrue# (i <# li) + , off <- int2Word# i `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT# + , w <- indexWordArray# a i + = case wordWriteMutableByteArrayLE# w mba (moff `plusWord#` off) s of + s -> go (i +# 1#) s + + | True + = s + +-- | Write a BigNat in base-256 big-endian representation and return the +-- number of bytes written. +-- +-- Use \"@'bigNatSizeInBase' 256# /i/@\" to compute the exact number of bytes +-- written in advance. In case of @/i/ == 0@, the function will write and report +-- zero bytes written. +bigNatToMutableByteArrayBE# :: BigNat -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) +bigNatToMutableByteArrayBE# a mba moff s0 + | isTrue# (sz ==# 0#) = (# s0, 0## #) + | msw <- indexWordArray# a (sz -# 1#) + = case wordToMutableByteArrayBE# msw mba moff s0 of + (# s1, k #) -> case go (sz -# 1#) k s1 of + s2 -> (# s2, k `plusWord#` (int2Word# (sz -# 1#) `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT#) #) + where + sz = wordArraySize# a + + go i c s + | 0# <- i + = s + + | w <- indexWordArray# a (i -# 1#) + = case wordWriteMutableByteArrayBE# w mba (moff `plusWord#` c) s of + s' -> go (i -# 1#) + (c `plusWord#` WORD_SIZE_IN_BYTES## ) s' + + +-- | Write a BigNat in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Use \"@'bigNatSizeInBase' 256# /i/@\" to compute the exact number of bytes +-- written in advance. In case of @/i/ == 0@, the function will write and report +-- zero bytes written. +bigNatToMutableByteArray# :: BigNat -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) +bigNatToMutableByteArray# a mba off 0# s = bigNatToMutableByteArrayLE# a mba off s +bigNatToMutableByteArray# a mba off _ s = bigNatToMutableByteArrayBE# a mba off s + +------------------------------------------------- +-- Import from ByteArray +------------------------------------------------- + +-- | Read a BigNat in base-256 little-endian representation from a ByteArray#. +-- +-- The size is given in bytes. +-- +-- Null higher limbs are automatically trimed. +bigNatFromByteArrayLE# :: Word# -> ByteArray# -> Word# -> State# s -> (# State# s, BigNat #) +bigNatFromByteArrayLE# 0## _ _ s = (# s, bigNatZero void# #) +bigNatFromByteArrayLE# sz ba moff s = + let + !nw = sz `uncheckedShiftRL#` WORD_SIZE_BYTES_SHIFT# + !nb = sz `and#` WORD_SIZE_BYTES_MASK## + + readMSB mwa s + | 0## <- nb + = s + + | off <- nw `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT# + = case wordFromByteArrayLE# nb ba (moff `plusWord#` off) of + w -> mwaWrite# mwa (word2Int# nw) w s + + go mwa i s + | isTrue# (i `eqWord#` nw) + = s + + | off <- i `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT# + = case wordFromByteArrayLE# WORD_SIZE_IN_BYTES## ba (moff `plusWord#` off) of + w -> case mwaWrite# mwa (word2Int# i) w s of + s -> go mwa (i `plusWord#` 1##) s + + in case newWordArray# (word2Int# nw +# (word2Int# nb /=# 0#)) s of + (# s, mwa #) -> case readMSB mwa s of + s -> case go mwa 0## s of + s -> case mwaTrimZeroes# mwa s of + s -> unsafeFreezeByteArray# mwa s + +-- | Read a BigNat in base-256 big-endian representation from a ByteArray#. +-- +-- The size is given in bytes. +-- +-- Null higher limbs are automatically trimed. +bigNatFromByteArrayBE# :: Word# -> ByteArray# -> Word# -> State# s -> (# State# s, BigNat #) +bigNatFromByteArrayBE# 0## _ _ s = (# s, bigNatZero void# #) +bigNatFromByteArrayBE# sz ba moff s = + let + !nw = sz `uncheckedShiftRL#` WORD_SIZE_BYTES_SHIFT# + !nb = sz `and#` WORD_SIZE_BYTES_MASK## + + goMSB mwa s + | 0## <- nb + = s + + | True + = case wordFromByteArrayBE# nb ba moff of + w -> mwaWrite# mwa (word2Int# nw) w s + + go mwa i s + | isTrue# (i `eqWord#` nw) + = s + + | k <- nw `minusWord#` 1## `minusWord#` i + , off <- (k `uncheckedShiftL#` WORD_SIZE_BYTES_SHIFT#) `plusWord#` nb + = case wordFromByteArrayBE# WORD_SIZE_IN_BYTES## ba (moff `plusWord#` off) of + w -> case mwaWrite# mwa (word2Int# i) w s of + s -> go mwa (i `plusWord#` 1##) s + + in case newWordArray# (word2Int# nw +# (word2Int# nb /=# 0#)) s of + (# s, mwa #) -> case goMSB mwa s of + s -> case go mwa 0## s of + s -> case mwaTrimZeroes# mwa s of + s -> unsafeFreezeByteArray# mwa s + +-- | Read a BigNat in base-256 representation from a ByteArray#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +bigNatFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, BigNat #) +bigNatFromByteArray# sz ba off 0# s = bigNatFromByteArrayLE# sz ba off s +bigNatFromByteArray# sz ba off _ s = bigNatFromByteArrayBE# sz ba off s diff --git a/libraries/ghc-bignum/src/GHC/Num/BigNat.hs-boot b/libraries/ghc-bignum/src/GHC/Num/BigNat.hs-boot new file mode 100644 index 0000000000..5c325d074f --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/BigNat.hs-boot @@ -0,0 +1,19 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} + +module GHC.Num.BigNat where + +import GHC.Num.WordArray +import GHC.Prim + +type BigNat = WordArray# + +bigNatSubUnsafe :: BigNat -> BigNat -> BigNat +bigNatMulWord# :: BigNat -> Word# -> BigNat +bigNatRem :: BigNat -> BigNat -> BigNat +bigNatRemWord# :: BigNat -> Word# -> Word# +bigNatShiftR# :: BigNat -> Word# -> BigNat +bigNatShiftL# :: BigNat -> Word# -> BigNat +bigNatCtz# :: BigNat -> Word# +bigNatCtzWord# :: BigNat -> Word# diff --git a/libraries/ghc-bignum/src/GHC/Num/BigNat/Check.hs b/libraries/ghc-bignum/src/GHC/Num/BigNat/Check.hs new file mode 100644 index 0000000000..aad7d903ff --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/BigNat/Check.hs @@ -0,0 +1,456 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE GHCForeignImportPrim #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE UnliftedFFITypes #-} +{-# LANGUAGE NegativeLiterals #-} +{-# LANGUAGE ForeignFunctionInterface #-} +{-# OPTIONS_GHC -Wno-name-shadowing #-} +{-# OPTIONS_GHC -ddump-simpl -ddump-to-file #-} + +-- | Check Native implementation against another backend +module GHC.Num.BigNat.Check where + +import GHC.Prim +import GHC.Types +import GHC.Num.WordArray +import GHC.Num.Primitives +import qualified GHC.Num.BigNat.Native as Native + +#if defined(BIGNUM_NATIVE) +#error You can't validate Native backed against itself. Choose another backend (e.g. gmp, ffi) + +#elif defined(BIGNUM_FFI) +import qualified GHC.Num.BigNat.FFI as Other + +#elif defined(BIGNUM_GMP) +import qualified GHC.Num.BigNat.GMP as Other + +#else +#error Undefined BigNat backend. Use a flag to select it (e.g. gmp, native, ffi)` +#endif + +default () + +bignat_compare + :: WordArray# + -> WordArray# + -> Int# +bignat_compare a b = + let + gr = Other.bignat_compare a b + nr = Native.bignat_compare a b + in case gr ==# nr of + 0# -> case unexpectedValue of I# x -> x + _ -> gr + +mwaCompare + :: MutableWordArray# s + -> MutableWordArray# s + -> State# s + -> (# State# s, Bool# #) +mwaCompare mwa mwb s = + case mwaSize# mwa s of + (# s, szA #) -> case mwaSize# mwb s of + (# s, szB #) -> case szA ==# szB of + 0# -> (# s, 0# #) + _ -> let + go i s + | isTrue# (i <# 0#) = (# s, 1# #) + | True = + case readWordArray# mwa i s of + (# s, a #) -> case readWordArray# mwb i s of + (# s, b #) -> case a `eqWord#` b of + 0# -> (# s, 0# #) + _ -> go (i -# 1#) s + in go (szA -# 1#) s + +mwaCompareOp + :: MutableWordArray# s + -> (MutableWordArray# s -> State# s -> State# s) + -> (MutableWordArray# s -> State# s -> State# s) + -> State# s + -> State# s +mwaCompareOp mwa f g s = + case mwaSize# mwa s of { (# s, sz #) -> + case newWordArray# sz s of { (# s, mwb #) -> + case f mwa s of { s -> + case g mwb s of { s -> + case mwaTrimZeroes# mwa s of { s -> + case mwaTrimZeroes# mwb s of { s -> + case mwaCompare mwa mwb s of + (# s, 0# #) -> case unexpectedValue of _ -> s + (# s, _ #) -> s + }}}}}} + +mwaCompareOp2 + :: MutableWordArray# s + -> MutableWordArray# s + -> (MutableWordArray# s -> MutableWordArray# s -> State# s -> State# s) + -> (MutableWordArray# s -> MutableWordArray# s -> State# s -> State# s) + -> State# s + -> State# s +mwaCompareOp2 mwa mwb f g s = + case mwaSize# mwa s of { (# s, szA #) -> + case mwaSize# mwb s of { (# s, szB #) -> + case newWordArray# szA s of { (# s, mwa' #) -> + case newWordArray# szB s of { (# s, mwb' #) -> + case f mwa mwb s of { s -> + case g mwa' mwb' s of { s -> + case mwaTrimZeroes# mwa s of { s -> + case mwaTrimZeroes# mwb s of { s -> + case mwaTrimZeroes# mwa' s of { s -> + case mwaTrimZeroes# mwb' s of { s -> + case mwaCompare mwa mwa' s of { (# s, ba #) -> + case mwaCompare mwb mwb' s of { (# s, bb #) -> + case ba &&# bb of + 0# -> case unexpectedValue of _ -> s + _ -> s + }}}}}}}}}}}} + +mwaCompareOpBool + :: MutableWordArray# s + -> (MutableWordArray# s -> State# s -> (#State# s, Bool# #)) + -> (MutableWordArray# s -> State# s -> (#State# s, Bool# #)) + -> State# s + -> (# State# s, Bool# #) +mwaCompareOpBool mwa f g s = + case mwaSize# mwa s of { (# s, sz #) -> + case newWordArray# sz s of { (# s, mwb #) -> + case f mwa s of { (# s, ra #) -> + case g mwb s of { (# s, rb #) -> + case ra ==# rb of + 0# -> case unexpectedValue of _ -> (# s, ra #) + _ -> case (ra ==# 1#) of -- don't compare MWAs if overflow signaled! + 1# -> (# s, ra #) + _ -> case mwaTrimZeroes# mwa s of { s -> + case mwaTrimZeroes# mwb s of { s -> + case mwaCompare mwa mwb s of + (# s, 0# #) -> case unexpectedValue of _ -> (# s, ra #) + _ -> (# s, ra #) + }}}}}} + +mwaCompareOpWord + :: MutableWordArray# s + -> (MutableWordArray# s -> State# s -> (#State# s, Word# #)) + -> (MutableWordArray# s -> State# s -> (#State# s, Word# #)) + -> State# s + -> (# State# s, Word# #) +mwaCompareOpWord mwa f g s = + case mwaSize# mwa s of { (# s, sz #) -> + case newWordArray# sz s of { (# s, mwb #) -> + case f mwa s of { (# s, ra #) -> + case g mwb s of { (# s, rb #) -> + case mwaTrimZeroes# mwa s of { s -> + case mwaTrimZeroes# mwb s of { s -> + case mwaCompare mwa mwb s of + (# s, b #) -> case b &&# (ra `eqWord#` rb) of + 0# -> case unexpectedValue of _ -> (# s, ra #) + _ -> (# s, ra #) + }}}}}} + +bignat_add + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_add mwa wa wb + = mwaCompareOp mwa + (\m -> Other.bignat_add m wa wb) + (\m -> Native.bignat_add m wa wb) + +bignat_add_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_add_word mwa wa b + = mwaCompareOp mwa + (\m -> Other.bignat_add_word m wa b) + (\m -> Native.bignat_add_word m wa b) + +bignat_mul_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_mul_word mwa wa b + = mwaCompareOp mwa + (\m -> Other.bignat_mul_word m wa b) + (\m -> Native.bignat_mul_word m wa b) + +bignat_sub + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +bignat_sub mwa wa wb + = mwaCompareOpBool mwa + (\m -> Other.bignat_sub m wa wb) + (\m -> Native.bignat_sub m wa wb) + +bignat_sub_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +bignat_sub_word mwa wa b + = mwaCompareOpBool mwa + (\m -> Other.bignat_sub_word m wa b) + (\m -> Native.bignat_sub_word m wa b) + +bignat_mul + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_mul mwa wa wb + = mwaCompareOp mwa + (\m -> Other.bignat_mul m wa wb) + (\m -> Native.bignat_mul m wa wb) + +bignat_popcount :: WordArray# -> Word# +bignat_popcount wa = + let + gr = Other.bignat_popcount wa + nr = Native.bignat_popcount wa + in case gr `eqWord#` nr of + 0# -> 1## `quotWord#` 0## + _ -> gr + +bignat_shiftl + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_shiftl mwa wa n + = mwaCompareOp mwa + (\m -> Other.bignat_shiftl m wa n) + (\m -> Native.bignat_shiftl m wa n) + +bignat_shiftr + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_shiftr mwa wa n + = mwaCompareOp mwa + (\m -> Other.bignat_shiftr m wa n) + (\m -> Native.bignat_shiftr m wa n) + +bignat_shiftr_neg + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_shiftr_neg mwa wa n + = mwaCompareOp mwa + (\m -> Other.bignat_shiftr_neg m wa n) + (\m -> Native.bignat_shiftr_neg m wa n) + +bignat_or + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_or mwa wa wb + = mwaCompareOp mwa + (\m -> Other.bignat_or m wa wb) + (\m -> Native.bignat_or m wa wb) + +bignat_xor + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_xor mwa wa wb + = mwaCompareOp mwa + (\m -> Other.bignat_xor m wa wb) + (\m -> Native.bignat_xor m wa wb) + +bignat_and + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_and mwa wa wb + = mwaCompareOp mwa + (\m -> Other.bignat_and m wa wb) + (\m -> Native.bignat_and m wa wb) + +bignat_and_not + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_and_not mwa wa wb + = mwaCompareOp mwa + (\m -> Other.bignat_and_not m wa wb) + (\m -> Native.bignat_and_not m wa wb) + +bignat_quotrem + :: MutableWordArray# RealWorld + -> MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_quotrem mwq mwr wa wb + = mwaCompareOp2 mwq mwr + (\m1 m2 -> Other.bignat_quotrem m1 m2 wa wb) + (\m1 m2 -> Native.bignat_quotrem m1 m2 wa wb) + +bignat_quot + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_quot mwq wa wb + = mwaCompareOp mwq + (\m -> Other.bignat_quot m wa wb) + (\m -> Native.bignat_quot m wa wb) + +bignat_rem + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_rem mwr wa wb + = mwaCompareOp mwr + (\m -> Other.bignat_rem m wa wb) + (\m -> Native.bignat_rem m wa wb) + +bignat_quotrem_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> (# State# RealWorld, Word# #) +bignat_quotrem_word mwq wa b + = mwaCompareOpWord mwq + (\m -> Other.bignat_quotrem_word m wa b) + (\m -> Native.bignat_quotrem_word m wa b) + +bignat_quot_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_quot_word mwq wa b + = mwaCompareOp mwq + (\m -> Other.bignat_quot_word m wa b) + (\m -> Native.bignat_quot_word m wa b) + +bignat_rem_word + :: WordArray# + -> Word# + -> Word# +bignat_rem_word wa b = + let + gr = Other.bignat_rem_word wa b + nr = Native.bignat_rem_word wa b + in case gr `eqWord#` nr of + 1# -> gr + _ -> case unexpectedValue of + W# e -> e + +bignat_gcd + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_gcd mwr wa wb + = mwaCompareOp mwr + (\m -> Other.bignat_gcd m wa wb) + (\m -> Native.bignat_gcd m wa wb) + +bignat_gcd_word + :: WordArray# + -> Word# + -> Word# +bignat_gcd_word wa b = + let + gr = Other.bignat_gcd_word wa b + nr = Native.bignat_gcd_word wa b + in case gr `eqWord#` nr of + 1# -> gr + _ -> case unexpectedValue of + W# e -> e + +bignat_gcd_word_word + :: Word# + -> Word# + -> Word# +bignat_gcd_word_word a b = + let + gr = Other.bignat_gcd_word_word a b + nr = Native.bignat_gcd_word_word a b + in case gr `eqWord#` nr of + 1# -> gr + _ -> case unexpectedValue of + W# e -> e + +bignat_encode_double :: WordArray# -> Int# -> Double# +bignat_encode_double a e = + let + gr = Other.bignat_encode_double a e + nr = Native.bignat_encode_double a e + in case gr ==## nr of + 1# -> gr + _ -> case unexpectedValue of + _ -> gr + +bignat_powmod_word :: WordArray# -> WordArray# -> Word# -> Word# +bignat_powmod_word b e m = + let + gr = Other.bignat_powmod_word b e m + nr = Native.bignat_powmod_word b e m + in case gr `eqWord#` nr of + 1# -> gr + _ -> case unexpectedValue of + W# e -> e + +bignat_powmod + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_powmod r b e m + = mwaCompareOp r + (\r' -> Other.bignat_powmod r' b e m) + (\r' -> Native.bignat_powmod r' b e m) + +bignat_powmod_words + :: Word# + -> Word# + -> Word# + -> Word# +bignat_powmod_words b e m = + let + gr = Other.bignat_powmod_words b e m + nr = Native.bignat_powmod_words b e m + in case gr `eqWord#` nr of + 1# -> gr + _ -> case unexpectedValue of + W# e -> e diff --git a/libraries/ghc-bignum/src/GHC/Num/BigNat/FFI.hs b/libraries/ghc-bignum/src/GHC/Num/BigNat/FFI.hs new file mode 100644 index 0000000000..3ef2f7046c --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/BigNat/FFI.hs @@ -0,0 +1,581 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE GHCForeignImportPrim #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE UnliftedFFITypes #-} +{-# LANGUAGE NegativeLiterals #-} +{-# LANGUAGE ForeignFunctionInterface #-} + +-- | External BigNat backend that directly call FFI operations. +-- +-- This backend can be useful for specific compilers such as GHCJS or Asterius +-- that replace bignat foreign calls with calls to the native platform bignat +-- library (e.g. JavaScript's BigInt). You can also link an extra object +-- providing the implementation. +module GHC.Num.BigNat.FFI where + +import GHC.Prim +import GHC.Types +import GHC.Num.WordArray +import GHC.Num.Primitives + +default () + +-- | Compare two non-zero BigNat of the same length +-- +-- Return: +-- < 0 ==> LT +-- == 0 ==> EQ +-- > 0 ==> GT +bignat_compare + :: WordArray# + -> WordArray# + -> Int# +bignat_compare = ghc_bignat_compare + +foreign import ccall unsafe ghc_bignat_compare + :: WordArray# + -> WordArray# + -> Int# + +-- | Add two non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: max (size a, size b) + 1 +-- +-- The potential 0 most-significant Word (i.e. the potential carry) will be +-- removed by the caller if it is not already done by the backend. +bignat_add + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_add mwa wa wb s + = ioVoid (ghc_bignat_add mwa wa wb) s + +foreign import ccall unsafe ghc_bignat_add + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> IO () + +-- | Add a non-zero BigNat and a non-zero Word# +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: size a + 1 +-- +-- The potential 0 most-significant Word (i.e. the potential carry) will be +-- removed by the caller if it is not already done by the backend. +bignat_add_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_add_word mwa wa b s = + ioVoid (ghc_bignat_add_word mwa wa b) s + +foreign import ccall unsafe ghc_bignat_add_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> IO () + +-- | Multiply a non-zero BigNat and a non-zero Word# +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: size a + 1 +-- +-- The potential 0 most-significant Word (i.e. the potential carry) will be +-- removed by the caller if it is not already done by the backend. +bignat_mul_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_mul_word mwa wa b s = + ioVoid (ghc_bignat_mul_word mwa wa b) s + +foreign import ccall unsafe ghc_bignat_mul_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> IO () + +-- | Sub two non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: size a +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +-- +-- Return True to indicate overflow. +bignat_sub + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +bignat_sub mwa wa wb s = ioBool (ghc_bignat_sub mwa wa wb) s + +foreign import ccall unsafe ghc_bignat_sub + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> IO Bool + +-- | Sub a non-zero word from a non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: size a +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +-- +-- Return True to indicate overflow. +bignat_sub_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +bignat_sub_word mwa wa b s = ioBool (ghc_bignat_sub_word mwa wa b) s + +foreign import ccall unsafe ghc_bignat_sub_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> IO Bool + +-- | Multiply two non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: size a+size b +-- +-- The potential 0 most-significant Word (i.e. the potential carry) will be +-- removed by the caller if it is not already done by the backend. +bignat_mul + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_mul mwa wa wb s = ioVoid (ghc_bignat_mul mwa wa wb) s + +foreign import ccall unsafe ghc_bignat_mul + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> IO () + +-- | PopCount of a non-zero BigNat +bignat_popcount :: WordArray# -> Word# +bignat_popcount = ghc_bignat_popcount + +foreign import ccall unsafe ghc_bignat_popcount + :: WordArray# + -> Word# + +-- | Left-shift a non-zero BigNat by a non-zero amount of bits +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: size a + required new limbs +-- +-- The potential 0 most-significant Word (i.e. the potential carry) will be +-- removed by the caller if it is not already done by the backend. +bignat_shiftl + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_shiftl mwa wa n s = ioVoid (ghc_bignat_shiftl mwa wa n) s + +foreign import ccall unsafe ghc_bignat_shiftl + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> IO () + +-- | Right-shift a non-zero BigNat by a non-zero amount of bits +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: required limbs +-- +-- The potential 0 most-significant Word (i.e. the potential carry) will be +-- removed by the caller if it is not already done by the backend. +bignat_shiftr + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_shiftr mwa wa n s = ioVoid (ghc_bignat_shiftr mwa wa n) s + +foreign import ccall unsafe ghc_bignat_shiftr + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> IO () + +-- | Right-shift a non-zero BigNat by a non-zero amount of bits by first +-- converting it into its two's complement representation and then again after +-- the arithmetic shift. +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: required limbs +-- +-- The potential 0 most-significant Words (i.e. the potential carry) will be +-- removed by the caller if it is not already done by the backend. +bignat_shiftr_neg + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_shiftr_neg mwa wa n s = ioVoid (ghc_bignat_shiftr_neg mwa wa n) s + +foreign import ccall unsafe ghc_bignat_shiftr_neg + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> IO () + + +-- | OR two non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: max (size a, size b) +bignat_or + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_or #-} +bignat_or mwa wa wb s = ioVoid (ghc_bignat_or mwa wa wb) s + +foreign import ccall unsafe ghc_bignat_or + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | XOR two non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: max (size a, size b) +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_xor + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_xor #-} +bignat_xor mwa wa wb s = ioVoid (ghc_bignat_xor mwa wa wb) s + +foreign import ccall unsafe ghc_bignat_xor + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | AND two non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: min (size a, size b) +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_and + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_and #-} +bignat_and mwa wa wb s = ioVoid (ghc_bignat_and mwa wa wb) s + +foreign import ccall unsafe ghc_bignat_and + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | ANDNOT two non-zero BigNat +-- +-- Result is to be stored in the MutableWordArray#. +-- The latter has size: size a +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_and_not + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_and_not #-} +bignat_and_not mwa wa wb s = ioVoid (ghc_bignat_and_not mwa wa wb) s + +foreign import ccall unsafe ghc_bignat_and_not + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | QuotRem of two non-zero BigNat +-- +-- Result quotient and remainder are to be stored in the MutableWordArray#. +-- The first one (quotient) has size: size(A)-size(B)+1 +-- The second one (remainder) has size: size(b) +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_quotrem + :: MutableWordArray# RealWorld -- ^ Quotient + -> MutableWordArray# RealWorld -- ^ Remainder + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_quotrem mwq mwr wa wb s = + ioVoid (ghc_bignat_quotrem mwq mwr wa wb) s + +foreign import ccall unsafe ghc_bignat_quotrem + :: MutableWordArray# RealWorld + -> MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | Quotient of two non-zero BigNat +-- +-- Result quotient is to be stored in the MutableWordArray#. +-- The latter has size: size(A)-size(B)+1 +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_quot + :: MutableWordArray# RealWorld -- ^ Quotient + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_quot mwq wa wb s = + ioVoid (ghc_bignat_quot mwq wa wb) s + +foreign import ccall unsafe ghc_bignat_quot + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | Remainder of two non-zero BigNat +-- +-- Result remainder is to be stored in the MutableWordArray#. +-- The latter has size: size(B) +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_rem + :: MutableWordArray# RealWorld -- ^ Quotient + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_rem mwr wa wb s = + ioVoid (ghc_bignat_rem mwr wa wb) s + +foreign import ccall unsafe ghc_bignat_rem + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | QuotRem of a non-zero BigNat and a non-zero Word +-- +-- Result quotient is to be stored in the MutableWordArray#. +-- The latter has size: size(A) +-- +-- The remainder is returned. +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_quotrem_word + :: MutableWordArray# RealWorld -- ^ Quotient + -> WordArray# + -> Word# + -> State# RealWorld + -> (# State# RealWorld, Word# #) +bignat_quotrem_word mwq wa b s = + ioWord# (ghc_bignat_quotrem_word mwq wa b) s + +foreign import ccall unsafe ghc_bignat_quotrem_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> IO Word + +-- | Quot of a non-zero BigNat and a non-zero Word +-- +-- Result quotient is to be stored in the MutableWordArray#. +-- The latter has size: size(A) +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_quot_word + :: MutableWordArray# RealWorld -- ^ Quotient + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_quot_word mwq wa b s = + ioVoid (ghc_bignat_quot_word mwq wa b) s + +foreign import ccall unsafe ghc_bignat_quot_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> IO () + +-- | Remainder of a non-zero BigNat and a non-zero Word +-- +-- The remainder is returned. +bignat_rem_word + :: WordArray# + -> Word# + -> Word# +bignat_rem_word = ghc_bignat_rem_word + +foreign import ccall unsafe ghc_bignat_rem_word + :: WordArray# + -> Word# + -> Word# + + +-- | Greatest common divisor (GCD) of two non-zero and non-one BigNat +-- +-- Result GCD is to be stored in the MutableWordArray#. +-- The latter has size: size(B) +-- The first WordArray# is greater than the second WordArray#. +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_gcd + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_gcd mwr wa wb s = + ioVoid (ghc_bignat_gcd mwr wa wb) s + +foreign import ccall unsafe ghc_bignat_gcd + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> IO () + +-- | Greatest common divisor (GCD) of a non-zero/non-one BigNat and a +-- non-zero/non-one Word# +-- +-- Result GCD is returned +bignat_gcd_word + :: WordArray# + -> Word# + -> Word# +bignat_gcd_word = ghc_bignat_gcd_word + +foreign import ccall unsafe ghc_bignat_gcd_word + :: WordArray# + -> Word# + -> Word# + +-- | Greatest common divisor (GCD) of two Word# +-- +-- Result GCD is returned +bignat_gcd_word_word + :: Word# + -> Word# + -> Word# +bignat_gcd_word_word = ghc_bignat_gcd_word_word + +foreign import ccall unsafe ghc_bignat_gcd_word_word + :: Word# + -> Word# + -> Word# + +-- | Encode (# BigNat mantissa, Int# exponent #) into a Double# +bignat_encode_double :: WordArray# -> Int# -> Double# +bignat_encode_double = ghc_bignat_encode_double + +foreign import ccall unsafe ghc_bignat_encode_double + :: WordArray# + -> Int# + -> Double# + +-- | \"@'bignat_powmod_word' /b/ /e/ /m/@\" computes base @/b/@ raised to +-- exponent @/e/@ modulo @/m/@. +-- +-- b > 1 +-- e > 0 +-- m > 1 +bignat_powmod_word :: WordArray# -> WordArray# -> Word# -> Word# +bignat_powmod_word = ghc_bignat_powmod_word + +foreign import ccall unsafe ghc_bignat_powmod_word + :: WordArray# -> WordArray# -> Word# -> Word# + +-- | \"@'bignat_powmod' r /b/ /e/ /m/@\" computes base @/b/@ raised to +-- exponent @/e/@ modulo @/m/@. +-- +-- b > 1 +-- e > 0 +-- m > 1 +-- +-- Result is to be stored in the MutableWordArray# (which size is equal to the +-- one of m). +-- +-- The potential 0 most-significant Words will be removed by the caller if it is +-- not already done by the backend. +bignat_powmod + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_powmod r b e m s = + ioVoid (ghc_bignat_powmod r b e m) s + +foreign import ccall unsafe ghc_bignat_powmod + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> WordArray# + -> IO () + +-- | \"@'bignat_powmod' /b/ /e/ /m/@\" computes base @/b/@ raised to +-- exponent @/e/@ modulo @/m/@. +-- +-- b > 1 +-- e > 0 +-- m > 1 +bignat_powmod_words + :: Word# + -> Word# + -> Word# + -> Word# +bignat_powmod_words = ghc_bignat_powmod_words + +foreign import ccall unsafe ghc_bignat_powmod_words + :: Word# -> Word# -> Word# -> Word# + diff --git a/libraries/ghc-bignum/src/GHC/Num/BigNat/GMP.hs b/libraries/ghc-bignum/src/GHC/Num/BigNat/GMP.hs new file mode 100644 index 0000000000..cb1fe500d9 --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/BigNat/GMP.hs @@ -0,0 +1,498 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE GHCForeignImportPrim #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE UnliftedFFITypes #-} +{-# LANGUAGE NegativeLiterals #-} +{-# LANGUAGE BlockArguments #-} + +-- | Backend based on the GNU GMP library. +-- +-- This has been adapted from the legacy `integer-gmp` package written by +-- Herbert Valerio Riedel. +module GHC.Num.BigNat.GMP where + +#include "MachDeps.h" +#include "WordSize.h" + +import GHC.Num.WordArray +import GHC.Num.Primitives +import GHC.Prim +import GHC.Types + +default () + +---------------------------------------------------------------------------- +-- type definitions + +-- NB: all code assumes GMP_LIMB_BITS == WORD_SIZE_IN_BITS +-- The C99 code in cbits/gmp_wrappers.c will fail to compile if this doesn't hold + +-- | Type representing a GMP Limb +type GmpLimb = Word -- actually, 'CULong' +type GmpLimb# = Word# + +-- | Count of 'GmpLimb's, must be positive (unless specified otherwise). +type GmpSize = Int -- actually, a 'CLong' +type GmpSize# = Int# + +narrowGmpSize# :: Int# -> Int# +#if SIZEOF_LONG == SIZEOF_HSWORD +narrowGmpSize# x = x +#elif (SIZEOF_LONG == 4) && (SIZEOF_HSWORD == 8) +-- On IL32P64 (i.e. Win64), we have to be careful with CLong not being +-- 64bit. This is mostly an issue on values returned from C functions +-- due to sign-extension. +narrowGmpSize# = narrow32Int# +#endif + +narrowCInt# :: Int# -> Int# +narrowCInt# = narrow32Int# + +bignat_compare :: WordArray# -> WordArray# -> Int# +bignat_compare x y = narrowCInt# (c_mpn_cmp x y (wordArraySize# x)) + +bignat_add + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_add #-} +bignat_add mwa wa wb s + -- weird GMP requirement + | isTrue# (wordArraySize# wb ># wordArraySize# wa) + = bignat_add mwa wb wa s + + | True + = do + case ioWord# (c_mpn_add mwa wa (wordArraySize# wa) wb (wordArraySize# wb)) s of + (# s', c #) -> mwaWriteMostSignificant mwa c s' + +bignat_add_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_add_word #-} +bignat_add_word mwa wa b s = do + case ioWord# (c_mpn_add_1 mwa wa (wordArraySize# wa) b) s of + (# s', c #) -> mwaWriteMostSignificant mwa c s' + +bignat_sub + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +{-# INLINE bignat_sub #-} +bignat_sub mwa wa wb s = + case ioWord# (c_mpn_sub mwa wa (wordArraySize# wa) wb (wordArraySize# wb)) s of + (# s', 0## #) -> (# s', 0# #) + (# s', _ #) -> (# s', 1# #) + +bignat_sub_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +{-# INLINE bignat_sub_word #-} +bignat_sub_word mwa wa b s = + case ioWord# (c_mpn_sub_1 mwa wa (wordArraySize# wa) b) s of + (# s', 0## #) -> (# s', 0# #) + (# s', _ #) -> (# s', 1# #) + +bignat_mul + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_mul #-} +bignat_mul mwa wa wb s = do + case ioWord# (c_mpn_mul mwa wa (wordArraySize# wa) wb (wordArraySize# wb)) s of + (# s', _msl #) -> s' -- we don't care about the most-significant + -- limb. The caller shrink the mwa if + -- necessary anyway. + +bignat_mul_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_mul_word #-} +bignat_mul_word mwa wa b s = + case ioWord# (c_mpn_mul_1 mwa wa (wordArraySize# wa) b) s of + (# s', c #) -> mwaWriteMostSignificant mwa c s' + +bignat_popcount :: WordArray# -> Word# +{-# INLINE bignat_popcount #-} +bignat_popcount wa = c_mpn_popcount wa (wordArraySize# wa) + + +bignat_shiftl + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_shiftl #-} +bignat_shiftl mwa wa n s = + case ioWord# (c_mpn_lshift mwa wa (wordArraySize# wa) n) s of + (# s', _msl #) -> s' -- we don't care about the most-significant + -- limb. The caller shrink the mwa if + -- necessary anyway. + +bignat_shiftr + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_shiftr #-} +bignat_shiftr mwa wa n s = + case ioWord# (c_mpn_rshift mwa wa (wordArraySize# wa) n) s of + (# s', _msl #) -> s' -- we don't care about the most-significant + -- limb. The caller shrink the mwa if + -- necessary anyway. + +bignat_or + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_or #-} +bignat_or mwa wa wb s1 + | isTrue# (szA >=# szB) = go wa szA wb szB s1 + | True = go wb szB wa szA s1 + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + -- nx >= ny + go wx nx wy ny s = case ioVoid (c_mpn_ior_n mwa wx wy ny) s of + s' -> mwaArrayCopy# mwa ny wx ny (nx -# ny) s' + +bignat_xor + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_xor #-} +bignat_xor mwa wa wb s1 + | isTrue# (szA >=# szB) = go wa szA wb szB s1 + | True = go wb szB wa szA s1 + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + -- nx >= ny + go wx nx wy ny s = case ioVoid (c_mpn_xor_n mwa wx wy ny) s of + s' -> mwaArrayCopy# mwa ny wx ny (nx -# ny) s' + +bignat_and + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_and #-} +bignat_and mwa wa wb s = ioVoid (c_mpn_and_n mwa wa wb sz) s + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + !sz = minI# szA szB + +bignat_and_not + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +{-# INLINE bignat_and_not #-} +bignat_and_not mwa wa wb s = + case ioVoid (c_mpn_andn_n mwa wa wb n) s of + s' -> mwaArrayCopy# mwa szB wa szB (szA -# szB) s' + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + !n = minI# szA szB + +bignat_quotrem + :: MutableWordArray# RealWorld + -> MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_quotrem mwq mwr wa wb s = + ioVoid (c_mpn_tdiv_qr mwq mwr 0# wa szA wb szB) s + where + szA = wordArraySize# wa + szB = wordArraySize# wb + +bignat_quot + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_quot mwq wa wb s = + ioVoid (c_mpn_tdiv_q mwq wa szA wb szB) s + where + szA = wordArraySize# wa + szB = wordArraySize# wb + +bignat_rem + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_rem mwr wa wb s = + ioVoid (c_mpn_tdiv_r mwr wa szA wb szB) s + where + szA = wordArraySize# wa + szB = wordArraySize# wb + +bignat_quotrem_word + :: MutableWordArray# RealWorld -- ^ Quotient + -> WordArray# + -> Word# + -> State# RealWorld + -> (# State# RealWorld, Word# #) +bignat_quotrem_word mwq wa b s = + ioWord# (c_mpn_divrem_1 mwq 0# wa szA b) s + where + szA = wordArraySize# wa + +bignat_quot_word + :: MutableWordArray# RealWorld -- ^ Quotient + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_quot_word mwq wa b s = + case bignat_quotrem_word mwq wa b s of + (# s', _ #) -> s' + +bignat_rem_word + :: WordArray# + -> Word# + -> Word# +bignat_rem_word wa b = + c_mpn_mod_1 wa (wordArraySize# wa) b + + +bignat_gcd + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_gcd mwr wa wb s = + -- wa > wb + case ioInt# (c_mpn_gcd# mwr wa (wordArraySize# wa) wb (wordArraySize# wb)) s of + (# s', sz #) -> mwaSetSize# mwr (narrowGmpSize# sz) s' + +bignat_gcd_word + :: WordArray# + -> Word# + -> Word# +bignat_gcd_word wa b = c_mpn_gcd_1# wa (wordArraySize# wa) b + +bignat_gcd_word_word + :: Word# + -> Word# + -> Word# +bignat_gcd_word_word = integer_gmp_gcd_word + + +bignat_encode_double :: WordArray# -> Int# -> Double# +bignat_encode_double wa e = c_mpn_get_d wa (wordArraySize# wa) e + +bignat_shiftr_neg + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_shiftr_neg mwa wa n s = + ioVoid (c_mpn_rshift_2c mwa wa (wordArraySize# wa) n) s + +bignat_powmod_word + :: WordArray# + -> WordArray# + -> Word# + -> Word# +bignat_powmod_word b e m = + integer_gmp_powm1# b (wordArraySize# b) e (wordArraySize# e) m + +bignat_powmod_words + :: Word# + -> Word# + -> Word# + -> Word# +bignat_powmod_words = integer_gmp_powm_word + +bignat_powmod + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_powmod r b e m s = + ioVoid (integer_gmp_powm# r b (wordArraySize# b) e (wordArraySize# e) m (wordArraySize# m)) s + + +---------------------------------------------------------------------- +-- FFI ccall imports + +foreign import ccall unsafe "integer_gmp_gcd_word" + integer_gmp_gcd_word :: GmpLimb# -> GmpLimb# -> GmpLimb# + +foreign import ccall unsafe "integer_gmp_mpn_gcd_1" + c_mpn_gcd_1# :: ByteArray# -> GmpSize# -> GmpLimb# -> GmpLimb# + +foreign import ccall unsafe "integer_gmp_mpn_gcd" + c_mpn_gcd# :: MutableByteArray# s -> ByteArray# -> GmpSize# + -> ByteArray# -> GmpSize# -> IO GmpSize + +foreign import ccall unsafe "integer_gmp_gcdext" + integer_gmp_gcdext# :: MutableByteArray# s -> MutableByteArray# s + -> ByteArray# -> GmpSize# + -> ByteArray# -> GmpSize# -> IO GmpSize + +-- mp_limb_t mpn_add_1 (mp_limb_t *rp, const mp_limb_t *s1p, mp_size_t n, +-- mp_limb_t s2limb) +foreign import ccall unsafe "gmp.h __gmpn_add_1" + c_mpn_add_1 :: MutableByteArray# s -> ByteArray# -> GmpSize# -> GmpLimb# + -> IO GmpLimb + +-- mp_limb_t mpn_sub_1 (mp_limb_t *rp, const mp_limb_t *s1p, mp_size_t n, +-- mp_limb_t s2limb) +foreign import ccall unsafe "gmp.h __gmpn_sub_1" + c_mpn_sub_1 :: MutableByteArray# s -> ByteArray# -> GmpSize# -> GmpLimb# + -> IO GmpLimb + +-- mp_limb_t mpn_mul_1 (mp_limb_t *rp, const mp_limb_t *s1p, mp_size_t n, +-- mp_limb_t s2limb) +foreign import ccall unsafe "gmp.h __gmpn_mul_1" + c_mpn_mul_1 :: MutableByteArray# s -> ByteArray# -> GmpSize# -> GmpLimb# + -> IO GmpLimb + +-- mp_limb_t mpn_add (mp_limb_t *rp, const mp_limb_t *s1p, mp_size_t s1n, +-- const mp_limb_t *s2p, mp_size_t s2n) +foreign import ccall unsafe "gmp.h __gmpn_add" + c_mpn_add :: MutableByteArray# s -> ByteArray# -> GmpSize# + -> ByteArray# -> GmpSize# -> IO GmpLimb + +-- mp_limb_t mpn_sub (mp_limb_t *rp, const mp_limb_t *s1p, mp_size_t s1n, +-- const mp_limb_t *s2p, mp_size_t s2n) +foreign import ccall unsafe "gmp.h __gmpn_sub" + c_mpn_sub :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# + -> GmpSize# -> IO GmpLimb + +-- mp_limb_t mpn_mul (mp_limb_t *rp, const mp_limb_t *s1p, mp_size_t s1n, +-- const mp_limb_t *s2p, mp_size_t s2n) +foreign import ccall unsafe "gmp.h __gmpn_mul" + c_mpn_mul :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# + -> GmpSize# -> IO GmpLimb + +-- int mpn_cmp (const mp_limb_t *s1p, const mp_limb_t *s2p, mp_size_t n) +foreign import ccall unsafe "gmp.h __gmpn_cmp" + c_mpn_cmp :: ByteArray# -> ByteArray# -> GmpSize# -> Int# + +-- void mpn_tdiv_qr (mp_limb_t *qp, mp_limb_t *rp, mp_size_t qxn, +-- const mp_limb_t *np, mp_size_t nn, +-- const mp_limb_t *dp, mp_size_t dn) +foreign import ccall unsafe "gmp.h __gmpn_tdiv_qr" + c_mpn_tdiv_qr :: MutableByteArray# s -> MutableByteArray# s -> GmpSize# + -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO () + +foreign import ccall unsafe "integer_gmp_mpn_tdiv_q" + c_mpn_tdiv_q :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# + -> GmpSize# -> IO () + +foreign import ccall unsafe "integer_gmp_mpn_tdiv_r" + c_mpn_tdiv_r :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# + -> GmpSize# -> IO () + +-- mp_limb_t mpn_divrem_1 (mp_limb_t *r1p, mp_size_t qxn, mp_limb_t *s2p, +-- mp_size_t s2n, mp_limb_t s3limb) +foreign import ccall unsafe "gmp.h __gmpn_divrem_1" + c_mpn_divrem_1 :: MutableByteArray# s -> GmpSize# -> ByteArray# -> GmpSize# + -> GmpLimb# -> IO GmpLimb + +-- mp_limb_t mpn_mod_1 (const mp_limb_t *s1p, mp_size_t s1n, mp_limb_t s2limb) +foreign import ccall unsafe "gmp.h __gmpn_mod_1" + c_mpn_mod_1 :: ByteArray# -> GmpSize# -> GmpLimb# -> GmpLimb# + +-- mp_limb_t integer_gmp_mpn_rshift (mp_limb_t rp[], const mp_limb_t sp[], +-- mp_size_t sn, mp_bitcnt_t count) +foreign import ccall unsafe "integer_gmp_mpn_rshift" + c_mpn_rshift :: MutableByteArray# s -> ByteArray# -> GmpSize# -> Word# + -> IO GmpLimb + +-- mp_limb_t integer_gmp_mpn_rshift (mp_limb_t rp[], const mp_limb_t sp[], +-- mp_size_t sn, mp_bitcnt_t count) +foreign import ccall unsafe "integer_gmp_mpn_rshift_2c" + c_mpn_rshift_2c :: MutableByteArray# s -> ByteArray# -> GmpSize# -> Word# + -> IO GmpLimb + +-- mp_limb_t integer_gmp_mpn_lshift (mp_limb_t rp[], const mp_limb_t sp[], +-- mp_size_t sn, mp_bitcnt_t count) +foreign import ccall unsafe "integer_gmp_mpn_lshift" + c_mpn_lshift :: MutableByteArray# s -> ByteArray# -> GmpSize# -> Word# + -> IO GmpLimb + +-- void mpn_and_n (mp_limb_t *rp, const mp_limb_t *s1p, const mp_limb_t *s2p, +-- mp_size_t n) +foreign import ccall unsafe "integer_gmp_mpn_and_n" + c_mpn_and_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# + -> IO () + +-- void mpn_andn_n (mp_limb_t *rp, const mp_limb_t *s1p, const mp_limb_t *s2p, +-- mp_size_t n) +foreign import ccall unsafe "integer_gmp_mpn_andn_n" + c_mpn_andn_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# + -> IO () + +-- void mpn_ior_n (mp_limb_t *rp, const mp_limb_t *s1p, const mp_limb_t *s2p, +-- mp_size_t n) +foreign import ccall unsafe "integer_gmp_mpn_ior_n" + c_mpn_ior_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# + -> IO () + +-- void mpn_xor_n (mp_limb_t *rp, const mp_limb_t *s1p, const mp_limb_t *s2p, +-- mp_size_t n) +foreign import ccall unsafe "integer_gmp_mpn_xor_n" + c_mpn_xor_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# + -> IO () + +-- mp_bitcnt_t mpn_popcount (const mp_limb_t *s1p, mp_size_t n) +foreign import ccall unsafe "gmp.h __gmpn_popcount" + c_mpn_popcount :: ByteArray# -> GmpSize# -> Word# + +-- double integer_gmp_mpn_get_d (const mp_limb_t sp[], const mp_size_t sn) +foreign import ccall unsafe "integer_gmp_mpn_get_d" + c_mpn_get_d :: ByteArray# -> GmpSize# -> Int# -> Double# + +foreign import ccall unsafe "integer_gmp_powm" + integer_gmp_powm# :: MutableByteArray# RealWorld + -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# + -> ByteArray# -> GmpSize# -> IO GmpSize + +foreign import ccall unsafe "integer_gmp_powm_word" + integer_gmp_powm_word :: GmpLimb# -> GmpLimb# -> GmpLimb# -> GmpLimb# + +foreign import ccall unsafe "integer_gmp_powm1" + integer_gmp_powm1# :: ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# + -> GmpLimb# -> GmpLimb# diff --git a/libraries/ghc-bignum/src/GHC/Num/BigNat/Native.hs b/libraries/ghc-bignum/src/GHC/Num/BigNat/Native.hs new file mode 100644 index 0000000000..a25b36eaec --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/BigNat/Native.hs @@ -0,0 +1,719 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE NegativeLiterals #-} +{-# LANGUAGE MultiWayIf #-} +{-# LANGUAGE BinaryLiterals #-} +{-# OPTIONS_GHC -Wno-name-shadowing #-} + +module GHC.Num.BigNat.Native where + +#include "MachDeps.h" +#include "WordSize.h" + +#if defined(BIGNUM_NATIVE) || defined(BIGNUM_CHECK) +import {-# SOURCE #-} GHC.Num.BigNat +import {-# SOURCE #-} GHC.Num.Natural +#else +import GHC.Num.BigNat +import GHC.Num.Natural +#endif +import GHC.Num.WordArray +import GHC.Num.Primitives +import GHC.Prim +import GHC.Types + +default () + +count_words_bits :: Word# -> (# Word#, Word# #) +count_words_bits n = (# nw, nb #) + where + nw = n `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT# + nb = n `and#` WORD_SIZE_BITS_MASK## + +count_words_bits_int :: Word# -> (# Int#, Int# #) +count_words_bits_int n = case count_words_bits n of + (# nw, nb #) -> (# word2Int# nw, word2Int# nb #) + +bignat_compare :: WordArray# -> WordArray# -> Int# +bignat_compare wa wb = go (sz -# 1#) + where + sz = wordArraySize# wa + go i + | isTrue# (i <# 0#) = 0# + | a <- indexWordArray# wa i + , b <- indexWordArray# wb i + = if | isTrue# (a `eqWord#` b) -> go (i -# 1#) + | isTrue# (a `gtWord#` b) -> 1# + | True -> -1# + +bignat_add + :: MutableWordArray# s -- ^ Result + -> WordArray# + -> WordArray# + -> State# s + -> State# s +bignat_add mwa wa wb = addABc 0# 0## + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + !szMin = minI# szA szB + + -- we have four cases: + -- 1) we have a digit in A and in B + a potential carry + -- => perform triple addition + -- => result in (carry,word) + -- 2) we have a digit only in A or B and a carry + -- => perform double addition from a single array + -- => result in (carry,word) + -- 3) we have a digit only in A or B and no carry + -- => perform array copy and shrink the array + -- 4) We only have a potential carry + -- => write the carry or shrink the array + + addABc i carry s + | isTrue# (i <# szMin) = + let + !(# carry', r #) = plusWord3# + (indexWordArray# wa i) + (indexWordArray# wb i) + carry + in case mwaWrite# mwa i r s of + s' -> addABc (i +# 1#) carry' s' + + | isTrue# ((i ==# szA) &&# (i ==# szB)) + = mwaWriteOrShrink mwa carry i s + + | isTrue# (i ==# szA) + = addAoBc wb i carry s + + | True + = addAoBc wa i carry s + + addAoBc wab i carry s + | isTrue# (i ==# wordArraySize# wab) + = mwaWriteOrShrink mwa carry i s + + | 0## <- carry + = -- copy the remaining words and remove the word allocated for the + -- potential carry + case mwaArrayCopy# mwa i wab i (wordArraySize# wab -# i) s of + s' -> mwaShrink# mwa 1# s' + + | True + = let !(# carry', r #) = plusWord2# (indexWordArray# wab i) carry + in case mwaWrite# mwa i r s of + s' -> addAoBc wab (i +# 1#) carry' s' + +bignat_add_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_add_word mwa wa b s = mwaInitArrayPlusWord mwa wa b s + +bignat_sub_word + :: MutableWordArray# RealWorld + -> WordArray# + -> Word# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +bignat_sub_word mwa wa b = go b 0# + where + !sz = wordArraySize# wa + go carry i s + | isTrue# (i >=# sz) + = (# s, carry `neWord#` 0## #) + + | 0## <- carry + = case mwaArrayCopy# mwa i wa i (sz -# i) s of + s' -> (# s', 0# #) + + | True + = case subWordC# (indexWordArray# wa i) carry of + (# 0##, 0# #) + | isTrue# (i ==# sz) -> case mwaShrink# mwa 1# s of + s' -> (# s', 0# #) + + (# l , c #) -> case mwaWrite# mwa i l s of + s1 -> go (int2Word# c) (i +# 1#) s1 + +bignat_mul_word + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> Word# + -> State# RealWorld + -> State# RealWorld +bignat_mul_word mwa wa b = go 0# 0## + where + !szA = wordArraySize# wa + go i carry s + | isTrue# (i ==# szA) = mwaWriteOrShrink mwa carry i s + | True = + let + ai = indexWordArray# wa i + !(# carry', r #) = plusWord12# carry (timesWord2# ai b) + in case mwaWrite# mwa i r s of + s' -> go (i +# 1#) carry' s' + + +bignat_mul + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_mul mwa wa wb s1 = + -- initialize the resulting WordArray + case mwaFill# mwa 0## 0## (int2Word# sz) s1 of + s' -> mulEachB ctzB s' -- loop on b Words + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + !sz = szA +# szB + + !ctzA = word2Int# (bigNatCtzWord# wa) + !ctzB = word2Int# (bigNatCtzWord# wb) + + -- multiply a single bj Word# to the whole wa WordArray + mul bj j i carry s + | isTrue# (i ==# szA) + -- write the carry + = mwaAddInplaceWord# mwa (i +# j) carry s + + | True = let + ai = indexWordArray# wa i + !(# c',r' #) = timesWord2# ai bj + !(# c'',r #) = plusWord2# r' carry + carry' = plusWord# c' c'' + in case mwaAddInplaceWord# mwa (i +# j) r s of + s' -> mul bj j (i +# 1#) carry' s' + + -- for each bj in wb, call `mul bj wa` + mulEachB i s + | isTrue# (i ==# szB) = s + | True = case indexWordArray# wb i of + -- detect bj == 0## and skip the loop + 0## -> mulEachB (i +# 1#) s + bi -> case mul bi i ctzA 0## s of + s' -> mulEachB (i +# 1#) s' + +bignat_sub + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> (# State# RealWorld, Bool# #) +bignat_sub mwa wa wb s = + -- initialize the resulting WordArray + -- Note: we could avoid the copy by subtracting the first non-zero + -- less-significant word of b... + case mwaArrayCopy# mwa 0# wa 0# (wordArraySize# wa) s of + s' -> mwaSubInplaceArray mwa 0# wb s' + +bignat_popcount :: WordArray# -> Word# +bignat_popcount wa = go 0# 0## + where + !sz = wordArraySize# wa + go i c + | isTrue# (i ==# sz) = c + | True = go (i +# 1#) (c `plusWord#` popCnt# (indexWordArray# wa i)) + +bignat_shiftl + :: MutableWordArray# s + -> WordArray# + -> Word# + -> State# s + -> State# s +bignat_shiftl mwa wa n s1 = + -- set the lower words to 0 + case mwaFill# mwa 0## 0## (int2Word# nw) s1 of + s2 -> if + | 0# <- nb -> mwaArrayCopy# mwa nw wa 0# szA s2 + | True -> mwaBitShift 0# 0## s2 + where + !szA = wordArraySize# wa + !(# nw, nb #) = count_words_bits_int n + !sh = WORD_SIZE_IN_BITS# -# nb + + -- Bit granularity (c is the carry from the previous shift) + mwaBitShift i c s + -- write the carry + | isTrue# (i ==# szA) + = mwaWriteOrShrink mwa c (i +# nw) s + + | True = + let + !ai = indexWordArray# wa i + !v = c `or#` (ai `uncheckedShiftL#` nb) + !c' = ai `uncheckedShiftRL#` sh + in case mwaWrite# mwa (i +# nw) v s of + s' -> mwaBitShift (i +# 1#) c' s' + + +bignat_shiftr + :: MutableWordArray# s + -> WordArray# + -> Word# + -> State# s + -> State# s +bignat_shiftr mwa wa n s1 + | isTrue# (nb ==# 0#) = mwaArrayCopy# mwa 0# wa nw sz s1 + | True = mwaBitShift (sz -# 1#) 0## s1 + where + !szA = wordArraySize# wa + !(# nw, nb #) = count_words_bits_int n + !sz = szA -# nw + !sh = WORD_SIZE_IN_BITS# -# nb + + -- Bit granularity (c is the carry from the previous shift) + mwaBitShift i c s + | isTrue# (i <# 0#) = s + | True = + let + !ai = indexWordArray# wa (i +# nw) + !v = c `or#` (ai `uncheckedShiftRL#` nb) + !c' = ai `uncheckedShiftL#` sh + in case mwaWrite# mwa i v s of + s' -> mwaBitShift (i -# 1#) c' s' + +bignat_shiftr_neg + :: MutableWordArray# s + -> WordArray# + -> Word# + -> State# s + -> State# s +bignat_shiftr_neg mwa wa n s1 + -- initialize higher limb + = case mwaWrite# mwa (szA -# 1#) 0## s1 of + s2 -> case bignat_shiftr mwa wa n s2 of + s3 -> if nz_shifted_out + -- round if non-zero bits were shifted out + then mwaAddInplaceWord# mwa 0# 1## s3 + else s3 + where + !szA = wordArraySize# wa + !(# nw, nb #) = count_words_bits_int n + + -- non-zero bits are shifted out? + nz_shifted_out + -- test nb bits + | isTrue# ( + (nb /=# 0#) + &&# (indexWordArray# wa nw `uncheckedShiftL#` + (WORD_SIZE_IN_BITS# -# nb) `neWord#` 0##)) + = True + -- test nw words + | True + = let + go j + | isTrue# (j ==# nw) = False + | isTrue# (indexWordArray# wa j `neWord#` 0##) = True + | True = go (j +# 1#) + in go 0# + + +bignat_or + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_or mwa wa wb s1 + | isTrue# (szA >=# szB) = go wa szA wb szB s1 + | True = go wb szB wa szA s1 + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + -- nx >= ny + go wx nx wy ny s = + case mwaInitArrayBinOp mwa wx wy or# s of + s' -> mwaArrayCopy# mwa ny wx ny (nx -# ny) s' + +bignat_xor + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_xor mwa wa wb s1 + | isTrue# (szA >=# szB) = go wa szA wb szB s1 + | True = go wb szB wa szA s1 + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + -- nx >= ny + go wx nx wy ny s = + case mwaInitArrayBinOp mwa wx wy xor# s of + s' -> mwaArrayCopy# mwa ny wx ny (nx -# ny) s' + +bignat_and + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_and mwa wa wb s = mwaInitArrayBinOp mwa wa wb and# s + +bignat_and_not + :: MutableWordArray# RealWorld -- ^ Result + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_and_not mwa wa wb s = + case mwaInitArrayBinOp mwa wa wb (\x y -> x `and#` not# y) s of + s' -> mwaArrayCopy# mwa szB wa szB (szA -# szB) s' + where + !szA = wordArraySize# wa + !szB = wordArraySize# wb + +bignat_quotrem + :: MutableWordArray# s + -> MutableWordArray# s + -> WordArray# + -> WordArray# + -> State# s + -> State# s +bignat_quotrem mwq mwr uwa uwb s0 = + -- Normalization consists in left-shifting bits in B and A so that the + -- most-significant bit of the most-significant word of B is 1. It makes + -- quotient prediction much more efficient as we only use the two most + -- significant words of A and the most significant word of B to make the + -- prediction. + + -- we will left-shift A and B of "clzb" bits for normalization + let !clzb = clz# (indexWordArray# uwb (wordArraySize# uwb -# 1#)) + + -- we use a single array initially containing A (normalized) and + -- returning the remainder (normalized): mnwa (for "mutable normalized + -- wordarray A") + -- + -- We allocate it here with an additionnal Word compared to A because + -- normalizing can left shift at most (N-1) bits (on N-bit arch). + in case newWordArray# (wordArraySize# uwa +# 1#) s0 of { (# s1, mnwa #) -> + + -- normalized A in mnwa + let normalizeA s = case mwaWrite# mnwa (wordArraySize# uwa) 0## s of -- init potential carry + s -> case bignat_shiftl mnwa uwa clzb s of -- left shift + s -> mwaTrimZeroes# mnwa s -- remove null carry if any + in case normalizeA s1 of { s2 -> + + -- normalize B. We don't do it in a MutableWordArray because it will remain + -- constant during the whole computation. + let !nwb = bigNatShiftL# uwb clzb in + + -- perform quotrem on normalized inputs + case bignat_quotrem_normalized mwq mnwa nwb s2 of { s3 -> + + -- denormalize the remainder now stored in mnwa. We just have to right shift + -- of "clzb" bits. We copy the result into "mwr" array. + let denormalizeR s = case mwaTrimZeroes# mnwa s of + s -> case unsafeFreezeByteArray# mnwa s of + (# s, wr #) -> case mwaSetSize# mwr (wordArraySize# wr) s of + s -> case bignat_shiftr mwr wr clzb s of + s -> mwaTrimZeroes# mwr s + in denormalizeR s3 + }}} + + + +bignat_quot + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_quot mwq wa wb s = + -- allocate a temporary array for the remainder and call quotrem + case newWordArray# (wordArraySize# wb) s of + (# s, mwr #) -> bignat_quotrem mwq mwr wa wb s + +bignat_rem + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_rem mwr wa wb s = + -- allocate a temporary array for the quotient and call quotrem + -- (we could avoid allocating it as it is not used to compute the result but + -- it would require non trivial modification of bignat_quotrem) + case newWordArray# szQ s of + (# s, mwq #) -> bignat_quotrem mwq mwr wa wb s + where + szA = wordArraySize# wa + szB = wordArraySize# wb + szQ = 1# +# szA -# szB + +-- | Perform quotRem on normalized inputs: +-- * highest bit of B is set +-- * A is trimmed +-- * A >= B +-- * B > 1 +bignat_quotrem_normalized + :: MutableWordArray# s + -> MutableWordArray# s + -> WordArray# + -> State# s + -> State# s +bignat_quotrem_normalized mwq mwa b s0 = + + -- n is the size of B + let !n = wordArraySize# b + + -- m+n is the size of A (m >= 0) + in case mwaSize# mwa s0 of { (# s1, szA #) -> + let !m = szA -# n in + + -- Definitions: + -- MSW(x) is the most-significant word of x + -- MSB(x) the most-significant bit of x + + -- We first compute MSW(Q). Thanks to the normalization of B, MSW(Q) can + -- only be 0 or 1 so we only have to perform a prefix comparison to compute + -- MSW(Q). + -- + -- Proof MSW(Q) < 2: + -- * MSB(MSW(B)) = 1 thanks to normalization. + -- * MSW(B) * MSW(Q) <= MSW(A) by definition + -- * suppose MSW(Q) >= 2: + -- MSW(B) * MSW(Q) >= MSW(B) << 1 { MSW(Q) >= 2 } + -- > MAX_WORD_VALUE { MSB(MSW(B)) = 1 } + -- > MSW(A) { MSW(A) <= MAX_WORD_VALUE } + -- contradiction. + -- + -- If A >= (B << m words) + -- then Qm = 1 + -- A := A - (B << m words) + -- else Qm = 0 + -- A unchanged + let computeQm s = case mwaTrimCompare m mwa b s of + (# s, LT #) -> (# s, 0## #) + (# s, _ #) -> (# s, 1## #) + + updateQj j qj qjb s = case mwaWrite# mwq j qj s of -- write Qj + s | 0## <- qj -> s + | True -> case mwaSubInplaceArray mwa j qjb s of -- subtract (qjB << j words) + (# s, _ #) -> s + + -- update the highest word of Q + updateQm s = case computeQm s of + (# s, qm #) -> updateQj m qm b s + + -- the size of Q is szA+szB+1 BEFORE normalization. Normalization may add + -- an additional higher word to A. + -- * If A has an additional limb: + -- * MSW(A) < MSW(B). Because MSB(MSW(A)) can't be set (it would + -- mean that we shifted a whole word, which we didn't) + -- * hence MSW(Q) = 0 but we don't have to write it (and we mustn't) + -- because of the size of Q + -- * If A has no additional limb: + -- * We have to check if MSW(A) >= MSW(B) and to adjust A and MSW(Q) + -- accordingly + -- + -- We detect if A has an additional limb by comparing the size of Q with m + updateQmMaybe s = case mwaSize# mwq s of + (# s, szQ #) | isTrue# (m <# szQ) -> updateQm s + | True -> s + + in case updateQmMaybe s1 of { s2 -> + + + -- main loop: for j from (m-1) downto 0 + -- We estimate a one Word quotient qj: + -- e1e0 <- a(n+j)a(n+j-1) `div` b(n-1) + -- qj | e1 == 0 = e0 + -- | otherwise = maxBound + -- We loop until we find the real quotient: + -- while (A < ((qj*B) << j words)) qj-- + -- We update A and Qj: + -- Qj := qj + -- A := A - (qj*B << j words) + + let bmsw = wordArrayLast# b -- most significant word of B + + estimateQj j s = + case mwaRead# mwa (n +# j) s of + (# s, a1 #) -> case mwaRead# mwa (n +# j -# 1#) s of + (# s, a0 #) -> case quotRemWord3# (# a1, a0 #) bmsw of + (# (# 0##, qj #), _ #) -> (# s, qj #) + (# (# _, _ #), _ #) -> (# s, WORD_MAXBOUND## #) + + -- we perform the qj*B multiplication once and then we subtract B from + -- qj*B as much as needed until (qj'*B << j words) <= A + findRealQj j qj s = findRealQj' j qj (bigNatMulWord# b qj) s + + findRealQj' j qj qjB s = case mwaTrimCompare j mwa qjB s of + (# s, LT #) -> findRealQj' j (qj `minusWord#` 1##) (bigNatSubUnsafe qjB b) s + -- TODO: we could do the sub inplace to + -- reduce allocations + (# s, _ #) -> (# s, qj, qjB #) + + loop j s = case estimateQj j s of + (# s, qj #) -> case findRealQj j qj s of + (# s, qj, qjB #) -> case updateQj j qj qjB s of + s | 0# <- j -> s + | True -> loop (j -# 1#) s + + + in if | 0# <- m -> s2 + | True -> loop (m -# 1#) s2 + }} + +bignat_quotrem_word + :: MutableWordArray# s -- ^ Quotient + -> WordArray# + -> Word# + -> State# s + -> (# State# s, Word# #) +bignat_quotrem_word mwq wa b s = go (sz -# 1#) 0## s + where + sz = wordArraySize# wa + go i r s + | isTrue# (i <# 0#) = (# s, r #) + | True = + let + ai = indexWordArray# wa i + !(# q,r' #) = quotRemWord2# r ai b + in case mwaWrite# mwq i q s of + s' -> go (i -# 1#) r' s' + +bignat_quot_word + :: MutableWordArray# s -- ^ Quotient + -> WordArray# + -> Word# + -> State# s + -> State# s +bignat_quot_word mwq wa b s = go (sz -# 1#) 0## s + where + sz = wordArraySize# wa + go i r s + | isTrue# (i <# 0#) = s + | True = + let + ai = indexWordArray# wa i + !(# q,r' #) = quotRemWord2# r ai b + in case mwaWrite# mwq i q s of + s' -> go (i -# 1#) r' s' + +bignat_rem_word + :: WordArray# + -> Word# + -> Word# +bignat_rem_word wa b = go (sz -# 1#) 0## + where + sz = wordArraySize# wa + go i r + | isTrue# (i <# 0#) = r + | True = + let + ai = indexWordArray# wa i + !(# _,r' #) = quotRemWord2# r ai b + in go (i -# 1#) r' + + +bignat_gcd + :: MutableWordArray# s + -> WordArray# + -> WordArray# + -> State# s + -> State# s +bignat_gcd mwr = go + where + go wmax wmin s + | isTrue# (wordArraySize# wmin ==# 0#) + = mwaInitCopyShrink# mwr wmax s + + | True + = let + wmax' = wmin + !wmin' = bigNatRem wmax wmin + in go wmax' wmin' s + +bignat_gcd_word + :: WordArray# + -> Word# + -> Word# +bignat_gcd_word a b = bignat_gcd_word_word b (bigNatRemWord# a b) + +-- | This operation doesn't really belongs here, but GMP's one is much faster +-- than this simple implementation (basic Euclid algorithm). +-- +-- Ideally we should make an implementation as fast as GMP's one and put it into +-- GHC.Num.Primitives. +bignat_gcd_word_word + :: Word# + -> Word# + -> Word# +bignat_gcd_word_word a 0## = a +bignat_gcd_word_word a b = bignat_gcd_word_word b (a `remWord#` b) + +bignat_encode_double :: WordArray# -> Int# -> Double# +bignat_encode_double wa e0 = go 0.0## e0 0# + where + sz = wordArraySize# wa + go acc e i + | isTrue# (i >=# sz) = acc + | True + = go (acc +## wordEncodeDouble# (indexWordArray# wa i) e) + (e +# WORD_SIZE_IN_BITS#) -- FIXME: we assume that e doesn't overflow... + (i +# 1#) + +bignat_powmod_word :: WordArray# -> WordArray# -> Word# -> Word# +bignat_powmod_word b0 e0 m = go (naturalFromBigNat b0) (naturalFromBigNat e0) (naturalFromWord# 1##) + where + go !b e !r + | isTrue# (e `naturalTestBit#` 0##) + = go b' e' ((r `naturalMul` b) `naturalRem` m') + + | naturalIsZero e + = naturalToWord# r + + | True + = go b' e' r + where + b' = (b `naturalMul` b) `naturalRem` m' + m' = naturalFromWord# m + e' = e `naturalShiftR#` 1## -- slightly faster than "e `div` 2" + +bignat_powmod + :: MutableWordArray# RealWorld + -> WordArray# + -> WordArray# + -> WordArray# + -> State# RealWorld + -> State# RealWorld +bignat_powmod r b0 e0 m s = mwaInitCopyShrink# r r' s + where + !r' = go (naturalFromBigNat b0) + (naturalFromBigNat e0) + (naturalFromWord# 1##) + + go !b e !r + | isTrue# (e `naturalTestBit#` 0##) + = go b' e' ((r `naturalMul` b) `naturalRem` m') + + | naturalIsZero e + = naturalToBigNat r + + | True + = go b' e' r + where + b' = (b `naturalMul` b) `naturalRem` m' + m' = naturalFromBigNat m + e' = e `naturalShiftR#` 1## -- slightly faster than "e `div` 2" + +bignat_powmod_words + :: Word# + -> Word# + -> Word# + -> Word# +bignat_powmod_words b e m = + bignat_powmod_word (wordArrayFromWord# b) + (wordArrayFromWord# e) + m diff --git a/libraries/ghc-bignum/src/GHC/Num/Integer.hs b/libraries/ghc-bignum/src/GHC/Num/Integer.hs new file mode 100644 index 0000000000..b4f6ee0c54 --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/Integer.hs @@ -0,0 +1,1169 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE NegativeLiterals #-} +{-# LANGUAGE BinaryLiterals #-} +{-# LANGUAGE BlockArguments #-} + +-- | +-- Module : GHC.Num.Integer +-- Copyright : (c) Sylvain Henry 2019, +-- (c) Herbert Valerio Riedel 2014 +-- License : BSD3 +-- +-- Maintainer : sylvain@haskus.fr +-- Stability : provisional +-- Portability : non-portable (GHC Extensions) +-- +-- The 'Integer' type. + +module GHC.Num.Integer where + +#include "MachDeps.h" +#include "WordSize.h" + +import GHC.Prim +import GHC.Types +import GHC.Classes +import GHC.Magic +import GHC.Num.Primitives +import GHC.Num.BigNat +import GHC.Num.Natural + +#if WORD_SIZE_IN_BITS < 64 +import GHC.IntWord64 +#endif + +default () + +-- | Arbitrary precision integers. In contrast with fixed-size integral types +-- such as 'Int', the 'Integer' type represents the entire infinite range of +-- integers. +-- +-- Integers are stored in a kind of sign-magnitude form, hence do not expect +-- two's complement form when using bit operations. +-- +-- If the value is small (fit into an 'Int'), 'IS' constructor is used. +-- Otherwise 'IP' and 'IN' constructors are used to store a 'BigNat' +-- representing respectively the positive or the negative value magnitude. +-- +-- Invariant: 'IP' and 'IN' are used iff value doesn't fit in 'IS' +data Integer + = IS !Int# -- ^ iff value in @[minBound::'Int', maxBound::'Int']@ range + | IP !BigNat -- ^ iff value in @]maxBound::'Int', +inf[@ range + | IN !BigNat -- ^ iff value in @]-inf, minBound::'Int'[@ range + + +-- | Check Integer invariants +integerCheck# :: Integer -> Bool# +integerCheck# (IS _) = 1# +integerCheck# (IP bn) = bigNatCheck# bn &&# (bn `bigNatGtWord#` INT_MAXBOUND##) +integerCheck# (IN bn) = bigNatCheck# bn &&# (bn `bigNatGtWord#` ABS_INT_MINBOUND##) + +-- | Check Integer invariants +integerCheck :: Integer -> Bool +integerCheck i = isTrue# (integerCheck# i) + +-- | Integer Zero +integerZero :: Integer +integerZero = IS 0# + +-- | Integer One +integerOne :: Integer +integerOne = IS 1# + +--------------------------------------------------------------------- +-- Conversions +--------------------------------------------------------------------- + +-- | Create a positive Integer from a BigNat +integerFromBigNat :: BigNat -> Integer +integerFromBigNat !bn + | bigNatIsZero bn + = integerZero + + | isTrue# (bn `bigNatLeWord#` INT_MAXBOUND##) + = IS (word2Int# (bigNatIndex# bn 0#)) + + | True + = IP bn + +-- | Create a negative Integer from a BigNat +integerFromBigNatNeg :: BigNat -> Integer +integerFromBigNatNeg !bn + | bigNatIsZero bn + = integerZero + + | 1# <- bigNatSize# bn + , i <- negateInt# (word2Int# (bigNatIndex# bn 0#)) + , isTrue# (i <=# 0#) + = IS i + + | True + = IN bn + +-- | Create an Integer from a sign-bit and a BigNat +integerFromBigNatSign :: Int# -> BigNat -> Integer +integerFromBigNatSign !sign !bn + | 0# <- sign + = integerFromBigNat bn + + | True + = integerFromBigNatNeg bn + +-- | Convert an Integer into a BigNat. +-- +-- Return 0 for negative Integers. +integerToBigNatClamp :: Integer -> BigNat +integerToBigNatClamp (IP x) = x +integerToBigNatClamp (IS x) + | isTrue# (x >=# 0#) = bigNatFromWord# (int2Word# x) +integerToBigNatClamp _ = bigNatZero void# + +-- | Create an Integer from an Int# +integerFromInt# :: Int# -> Integer +integerFromInt# i = IS i + +-- | Create an Integer from an Int +integerFromInt :: Int -> Integer +integerFromInt (I# i) = IS i + +-- | Truncates 'Integer' to least-significant 'Int#' +integerToInt# :: Integer -> Int# +{-# NOINLINE integerToInt# #-} +integerToInt# (IS i) = i +integerToInt# (IP b) = word2Int# (bigNatToWord# b) +integerToInt# (IN b) = negateInt# (word2Int# (bigNatToWord# b)) + +-- | Truncates 'Integer' to least-significant 'Int#' +integerToInt :: Integer -> Int +integerToInt i = I# (integerToInt# i) + +-- | Convert a Word# into an Integer +integerFromWord# :: Word# -> Integer +{-# NOINLINE integerFromWord# #-} +integerFromWord# w + | i <- word2Int# w + , isTrue# (i >=# 0#) + = IS i + + | True + = IP (bigNatFromWord# w) + +-- | Convert a Word into an Integer +integerFromWord :: Word -> Integer +integerFromWord (W# w) = integerFromWord# w + +-- | Create a negative Integer with the given Word magnitude +integerFromWordNeg# :: Word# -> Integer +integerFromWordNeg# w + | isTrue# (w `leWord#` ABS_INT_MINBOUND##) + = IS (negateInt# (word2Int# w)) + + | True + = IN (bigNatFromWord# w) + +-- | Create an Integer from a sign and a Word magnitude +integerFromWordSign# :: Int# -> Word# -> Integer +integerFromWordSign# 0# w = integerFromWord# w +integerFromWordSign# _ w = integerFromWordNeg# w + +-- | Truncate an Integer into a Word +integerToWord# :: Integer -> Word# +{-# NOINLINE integerToWord# #-} +integerToWord# (IS i) = int2Word# i +integerToWord# (IP bn) = bigNatToWord# bn +integerToWord# (IN bn) = int2Word# (negateInt# (word2Int# (bigNatToWord# bn))) + +-- | Truncate an Integer into a Word +integerToWord :: Integer -> Word +integerToWord !i = W# (integerToWord# i) + +-- | Convert a Natural into an Integer +integerFromNatural :: Natural -> Integer +{-# NOINLINE integerFromNatural #-} +integerFromNatural (NS x) = integerFromWord# x +integerFromNatural (NB x) = integerFromBigNat x + +-- | Convert a list of Word into an Integer +integerFromWordList :: Bool -> [Word] -> Integer +integerFromWordList True ws = integerFromBigNatNeg (bigNatFromWordList ws) +integerFromWordList False ws = integerFromBigNat (bigNatFromWordList ws) + +-- | Convert a Integer into a Natural +-- +-- Return 0 for negative Integers. +integerToNaturalClamp :: Integer -> Natural +{-# NOINLINE integerToNaturalClamp #-} +integerToNaturalClamp (IS x) + | isTrue# (x <# 0#) = naturalZero + | True = naturalFromWord# (int2Word# x) +integerToNaturalClamp (IP x) = naturalFromBigNat x +integerToNaturalClamp (IN _) = naturalZero + +-- | Convert a Integer into a Natural +-- +-- Return absolute value +integerToNatural :: Integer -> Natural +{-# NOINLINE integerToNatural #-} +integerToNatural (IS x) = naturalFromWord# (wordFromAbsInt# x) +integerToNatural (IP x) = naturalFromBigNat x +integerToNatural (IN x) = naturalFromBigNat x + +--------------------------------------------------------------------- +-- Predicates +--------------------------------------------------------------------- + +-- | Negative predicate +integerIsNegative# :: Integer -> Bool# +integerIsNegative# (IS i#) = i# <# 0# +integerIsNegative# (IP _) = 0# +integerIsNegative# (IN _) = 1# + +-- | Negative predicate +integerIsNegative :: Integer -> Bool +integerIsNegative !i = isTrue# (integerIsNegative# i) + +-- | Zero predicate +integerIsZero :: Integer -> Bool +integerIsZero (IS 0#) = True +integerIsZero _ = False + +-- | Not-equal predicate. +integerNe :: Integer -> Integer -> Bool +integerNe !x !y = isTrue# (integerNe# x y) + +-- | Equal predicate. +integerEq :: Integer -> Integer -> Bool +integerEq !x !y = isTrue# (integerEq# x y) + +-- | Lower-or-equal predicate. +integerLe :: Integer -> Integer -> Bool +integerLe !x !y = isTrue# (integerLe# x y) + +-- | Lower predicate. +integerLt :: Integer -> Integer -> Bool +integerLt !x !y = isTrue# (integerLt# x y) + +-- | Greater predicate. +integerGt :: Integer -> Integer -> Bool +integerGt !x !y = isTrue# (integerGt# x y) + +-- | Greater-or-equal predicate. +integerGe :: Integer -> Integer -> Bool +integerGe !x !y = isTrue# (integerGe# x y) + +-- | Equal predicate. +integerEq# :: Integer -> Integer -> Bool# +{-# NOINLINE integerEq# #-} +integerEq# (IS x) (IS y) = x ==# y +integerEq# (IN x) (IN y) = bigNatEq# x y +integerEq# (IP x) (IP y) = bigNatEq# x y +integerEq# _ _ = 0# + +-- | Not-equal predicate. +integerNe# :: Integer -> Integer -> Bool# +{-# NOINLINE integerNe# #-} +integerNe# (IS x) (IS y) = x /=# y +integerNe# (IN x) (IN y) = bigNatNe# x y +integerNe# (IP x) (IP y) = bigNatNe# x y +integerNe# _ _ = 1# + +-- | Greater predicate. +integerGt# :: Integer -> Integer -> Bool# +{-# NOINLINE integerGt# #-} +integerGt# (IS x) (IS y) = x ># y +integerGt# x y | GT <- integerCompare x y = 1# +integerGt# _ _ = 0# + +-- | Lower-or-equal predicate. +integerLe# :: Integer -> Integer -> Bool# +{-# NOINLINE integerLe# #-} +integerLe# (IS x) (IS y) = x <=# y +integerLe# x y | GT <- integerCompare x y = 0# +integerLe# _ _ = 1# + +-- | Lower predicate. +integerLt# :: Integer -> Integer -> Bool# +{-# NOINLINE integerLt# #-} +integerLt# (IS x) (IS y) = x <# y +integerLt# x y | LT <- integerCompare x y = 1# +integerLt# _ _ = 0# + +-- | Greater-or-equal predicate. +integerGe# :: Integer -> Integer -> Bool# +{-# NOINLINE integerGe# #-} +integerGe# (IS x) (IS y) = x >=# y +integerGe# x y | LT <- integerCompare x y = 0# +integerGe# _ _ = 1# + +instance Eq Integer where + (==) = integerEq + (/=) = integerNe + +-- | Compare two Integer +integerCompare :: Integer -> Integer -> Ordering +{-# NOINLINE integerCompare #-} +integerCompare (IS x) (IS y) = compareInt# x y +integerCompare (IP x) (IP y) = bigNatCompare x y +integerCompare (IN x) (IN y) = bigNatCompare y x +integerCompare (IS _) (IP _) = LT +integerCompare (IS _) (IN _) = GT +integerCompare (IP _) (IS _) = GT +integerCompare (IN _) (IS _) = LT +integerCompare (IP _) (IN _) = GT +integerCompare (IN _) (IP _) = LT + +instance Ord Integer where + compare = integerCompare + +--------------------------------------------------------------------- +-- Operations +--------------------------------------------------------------------- + +-- | Subtract one 'Integer' from another. +integerSub :: Integer -> Integer -> Integer +{-# NOINLINE integerSub #-} +integerSub !x (IS 0#) = x +integerSub (IS x#) (IS y#) + = case subIntC# x# y# of + (# z#, 0# #) -> IS z# + (# 0#, _ #) -> IN (bigNatFromWord2# 1## 0##) + (# z#, _ #) + | isTrue# (z# ># 0#) + -> IN (bigNatFromWord# ( (int2Word# (negateInt# z#)))) + | True + -> IP (bigNatFromWord# ( (int2Word# z#))) +integerSub (IS x#) (IP y) + | isTrue# (x# >=# 0#) + = integerFromBigNatNeg (bigNatSubWordUnsafe# y (int2Word# x#)) + | True + = IN (bigNatAddWord# y (int2Word# (negateInt# x#))) +integerSub (IS x#) (IN y) + | isTrue# (x# >=# 0#) + = IP (bigNatAddWord# y (int2Word# x#)) + | True + = integerFromBigNat (bigNatSubWordUnsafe# y (int2Word# (negateInt# x#))) +integerSub (IP x) (IP y) + = case bigNatCompare x y of + LT -> integerFromBigNatNeg (bigNatSubUnsafe y x) + EQ -> IS 0# + GT -> integerFromBigNat (bigNatSubUnsafe x y) +integerSub (IP x) (IN y) = IP (bigNatAdd x y) +integerSub (IN x) (IP y) = IN (bigNatAdd x y) +integerSub (IN x) (IN y) + = case bigNatCompare x y of + LT -> integerFromBigNat (bigNatSubUnsafe y x) + EQ -> IS 0# + GT -> integerFromBigNatNeg (bigNatSubUnsafe x y) +integerSub (IP x) (IS y#) + | isTrue# (y# >=# 0#) + = integerFromBigNat (bigNatSubWordUnsafe# x (int2Word# y#)) + | True + = IP (bigNatAddWord# x (int2Word# (negateInt# y#))) +integerSub (IN x) (IS y#) + | isTrue# (y# >=# 0#) + = IN (bigNatAddWord# x (int2Word# y#)) + | True + = integerFromBigNatNeg (bigNatSubWordUnsafe# x (int2Word# (negateInt# y#))) + +-- | Add two 'Integer's +integerAdd :: Integer -> Integer -> Integer +{-# NOINLINE integerAdd #-} +integerAdd !x (IS 0#) = x +integerAdd (IS 0#) y = y +integerAdd (IS x#) (IS y#) + = case addIntC# x# y# of + (# z#, 0# #) -> IS z# + (# 0#, _ #) -> IN (bigNatFromWord2# 1## 0##) -- 2*minBound::Int + (# z#, _ #) + | isTrue# (z# ># 0#) -> IN (bigNatFromWord# ( (int2Word# (negateInt# z#)))) + | True -> IP (bigNatFromWord# ( (int2Word# z#))) +integerAdd y@(IS _) x = integerAdd x y +integerAdd (IP x) (IP y) = IP (bigNatAdd x y) +integerAdd (IN x) (IN y) = IN (bigNatAdd x y) +integerAdd (IP x) (IS y#) -- edge-case: @(maxBound+1) + minBound == 0@ + | isTrue# (y# >=# 0#) = IP (bigNatAddWord# x (int2Word# y#)) + | True = integerFromBigNat (bigNatSubWordUnsafe# x (int2Word# + (negateInt# y#))) +integerAdd (IN x) (IS y#) -- edge-case: @(minBound-1) + maxBound == -2@ + | isTrue# (y# >=# 0#) = integerFromBigNatNeg (bigNatSubWordUnsafe# x (int2Word# y#)) + | True = IN (bigNatAddWord# x (int2Word# (negateInt# y#))) +integerAdd y@(IN _) x@(IP _) = integerAdd x y +integerAdd (IP x) (IN y) + = case bigNatCompare x y of + LT -> integerFromBigNatNeg (bigNatSubUnsafe y x) + EQ -> IS 0# + GT -> integerFromBigNat (bigNatSubUnsafe x y) + +-- | Multiply two 'Integer's +integerMul :: Integer -> Integer -> Integer +{-# NOINLINE integerMul #-} +integerMul !_ (IS 0#) = IS 0# +integerMul (IS 0#) _ = IS 0# +integerMul x (IS 1#) = x +integerMul (IS 1#) y = y +integerMul x (IS -1#) = integerNegate x +integerMul (IS -1#) y = integerNegate y +#if __GLASGOW_HASKELL__ < 809 +integerMul (IS x) (IS y) = case mulIntMayOflo# x y of + 0# -> IS (x *# y) + _ -> case (# isTrue# (x >=# 0#), isTrue# (y >=# 0#) #) of + (# False, False #) -> case timesWord2# (int2Word# (negateInt# x)) + (int2Word# (negateInt# y)) of + (# 0##,l #) -> integerFromWord# l + (# h ,l #) -> IP (bigNatFromWord2# h l) + + (# True, False #) -> case timesWord2# (int2Word# x) + (int2Word# (negateInt# y)) of + (# 0##,l #) -> integerFromWordNeg# l + (# h ,l #) -> IN (bigNatFromWord2# h l) + + (# False, True #) -> case timesWord2# (int2Word# (negateInt# x)) + (int2Word# y) of + (# 0##,l #) -> integerFromWordNeg# l + (# h ,l #) -> IN (bigNatFromWord2# h l) + + (# True, True #) -> case timesWord2# (int2Word# x) + (int2Word# y) of + (# 0##,l #) -> integerFromWord# l + (# h ,l #) -> IP (bigNatFromWord2# h l) +#else +integerMul (IS x) (IS y) = case timesInt2# x y of + (# 0#, _h, l #) -> IS l + (# _ , h, l #) + | isTrue# (h >=# 0#) + -> IP (bigNatFromWord2# (int2Word# h) (int2Word# l)) + | True + -> let + -- two's complement of a two-word negative Int: + -- l' = complement l + 1 + -- h' = complement h + carry + !(# l',c #) = addWordC# (not# (int2Word# l)) 1## + !h' = int2Word# c `plusWord#` not# (int2Word# h) + in IN (bigNatFromWord2# h' l') +#endif +integerMul x@(IS _) y = integerMul y x +integerMul (IP x) (IP y) = IP (bigNatMul x y) +integerMul (IP x) (IN y) = IN (bigNatMul x y) +integerMul (IP x) (IS y) + | isTrue# (y >=# 0#) = IP (bigNatMulWord# x (int2Word# y)) + | True = IN (bigNatMulWord# x (int2Word# (negateInt# y))) +integerMul (IN x) (IN y) = IP (bigNatMul x y) +integerMul (IN x) (IP y) = IN (bigNatMul x y) +integerMul (IN x) (IS y) + | isTrue# (y >=# 0#) = IN (bigNatMulWord# x (int2Word# y)) + | True = IP (bigNatMulWord# x (int2Word# (negateInt# y))) + +-- | Negate 'Integer'. +-- +-- One edge-case issue to take into account is that Int's range is not +-- symmetric around 0. I.e. @minBound+maxBound = -1@ +-- +-- IP is used iff n > maxBound::Int +-- IN is used iff n < minBound::Int +integerNegate :: Integer -> Integer +{-# NOINLINE integerNegate #-} +integerNegate (IN b) = IP b +integerNegate (IS INT_MINBOUND#) = IP (bigNatFromWord# ABS_INT_MINBOUND##) +integerNegate (IS i) = IS (negateInt# i) +integerNegate (IP b) + | isTrue# (bigNatEqWord# b ABS_INT_MINBOUND##) = IS INT_MINBOUND# + | True = IN b + + +-- | Compute absolute value of an 'Integer' +integerAbs :: Integer -> Integer +{-# NOINLINE integerAbs #-} +integerAbs (IN i) = IP i +integerAbs n@(IP _) = n +integerAbs n@(IS i) + | isTrue# (i >=# 0#) = n + | INT_MINBOUND# <- i = IP (bigNatFromWord# ABS_INT_MINBOUND##) + | True = IS (negateInt# i) + + +-- | Return @-1@, @0@, and @1@ depending on whether argument is +-- negative, zero, or positive, respectively +integerSignum :: Integer -> Integer +{-# NOINLINE integerSignum #-} +integerSignum !j = IS (integerSignum# j) + +-- | Return @-1#@, @0#@, and @1#@ depending on whether argument is +-- negative, zero, or positive, respectively +integerSignum# :: Integer -> Int# +{-# NOINLINE integerSignum# #-} +integerSignum# (IN _) = -1# +integerSignum# (IS i#) = sgnI# i# +integerSignum# (IP _ ) = 1# + +-- | Count number of set bits. For negative arguments returns +-- the negated population count of the absolute value. +integerPopCount# :: Integer -> Int# +{-# NOINLINE integerPopCount# #-} +integerPopCount# (IS i) + | isTrue# (i >=# 0#) = word2Int# (popCntI# i) + | True = negateInt# (word2Int# (popCntI# (negateInt# i))) +integerPopCount# (IP bn) = word2Int# (bigNatPopCount# bn) +integerPopCount# (IN bn) = negateInt# (word2Int# (bigNatPopCount# bn)) + +-- | Positive 'Integer' for which only /n/-th bit is set +integerBit# :: Word# -> Integer +{-# NOINLINE integerBit# #-} +integerBit# i + | isTrue# (i `ltWord#` (WORD_SIZE_IN_BITS## `minusWord#` 1##)) + = IS (uncheckedIShiftL# 1# (word2Int# i)) + + | True = IP (bigNatBit# i) + +-- | 'Integer' for which only /n/-th bit is set +integerBit :: Word -> Integer +integerBit (W# i) = integerBit# i + +-- | Test if /n/-th bit is set. +-- +-- Fake 2's complement for negative values (might be slow) +integerTestBit# :: Integer -> Word# -> Bool# +{-# NOINLINE integerTestBit# #-} +integerTestBit# (IS x) i + | isTrue# (i `ltWord#` WORD_SIZE_IN_BITS##) + = testBitI# x i + | True + = x <# 0# +integerTestBit# (IP x) i = bigNatTestBit# x i +integerTestBit# (IN x) i + | isTrue# (iw >=# n) + = 1# + -- if all the limbs j with j < iw are null, then we have to consider the + -- carry of the 2's complement convertion. Otherwise we just have to return + -- the inverse of the bit test + | allZ iw = testBitW# (xi `minusWord#` 1##) ib ==# 0# + | True = testBitW# xi ib ==# 0# + where + !xi = bigNatIndex# x iw + !n = bigNatSize# x + !iw = word2Int# (i `uncheckedShiftRL#` WORD_SIZE_BITS_SHIFT#) + !ib = i `and#` WORD_SIZE_BITS_MASK## + + allZ 0# = True + allZ j | isTrue# (bigNatIndex# x (j -# 1#) `eqWord#` 0##) = allZ (j -# 1#) + | True = False + +-- | Test if /n/-th bit is set. For negative Integers it tests the n-th bit of +-- the negated argument. +-- +-- Fake 2's complement for negative values (might be slow) +integerTestBit :: Integer -> Word -> Bool +integerTestBit !i (W# n) = isTrue# (integerTestBit# i n) + +-- | Shift-right operation +-- +-- Fake 2's complement for negative values (might be slow) +integerShiftR# :: Integer -> Word# -> Integer +{-# NOINLINE integerShiftR# #-} +integerShiftR# !x 0## = x +integerShiftR# (IS i) n = IS (iShiftRA# i (word2Int# n)) + where + iShiftRA# a b + | isTrue# (b >=# WORD_SIZE_IN_BITS#) = (a <# 0#) *# (-1#) + | True = a `uncheckedIShiftRA#` b +integerShiftR# (IP bn) n = integerFromBigNat (bigNatShiftR# bn n) +integerShiftR# (IN bn) n = + case integerFromBigNatNeg (bigNatShiftRNeg# bn n) of + IS 0# -> IS -1# + r -> r + +-- | Shift-right operation +-- +-- Fake 2's complement for negative values (might be slow) +integerShiftR :: Integer -> Word -> Integer +integerShiftR !x (W# w) = integerShiftR# x w + +-- | Shift-left operation +integerShiftL# :: Integer -> Word# -> Integer +{-# NOINLINE integerShiftL# #-} +integerShiftL# !x 0## = x +integerShiftL# (IS 0#) _ = IS 0# +integerShiftL# (IS 1#) n = integerBit# n +integerShiftL# (IS i) n + | isTrue# (i >=# 0#) = integerFromBigNat (bigNatShiftL# (bigNatFromWord# (int2Word# i)) n) + | True = integerFromBigNatNeg (bigNatShiftL# (bigNatFromWord# (int2Word# (negateInt# i))) n) +integerShiftL# (IP bn) n = IP (bigNatShiftL# bn n) +integerShiftL# (IN bn) n = IN (bigNatShiftL# bn n) + +-- | Shift-left operation +-- +-- Remember that bits are stored in sign-magnitude form, hence the behavior of +-- negative Integers is different from negative Int's behavior. +integerShiftL :: Integer -> Word -> Integer +integerShiftL !x (W# w) = integerShiftL# x w + +-- | Bitwise OR operation +-- +-- Fake 2's complement for negative values (might be slow) +integerOr :: Integer -> Integer -> Integer +{-# NOINLINE integerOr #-} +integerOr a b = case a of + IS 0# -> b + IS -1# -> IS -1# + IS x -> case b of + IS 0# -> a + IS -1# -> IS -1# + IS y -> IS (orI# x y) + IP y + | isTrue# (x >=# 0#) -> integerFromBigNat (bigNatOrWord# y (int2Word# x)) + | True -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatAndNot -- use De Morgan's laws + (bigNatFromWord# + (int2Word# (negateInt# x) `minusWord#` 1##)) + y) + 1##) + IN y + | isTrue# (x >=# 0#) -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatAndNotWord# -- use De Morgan's laws + (bigNatSubWordUnsafe# y 1##) + (int2Word# x)) + 1##) + | True -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatAndWord# -- use De Morgan's laws + (bigNatSubWordUnsafe# y 1##) + (int2Word# (negateInt# x) `minusWord#` 1##)) + 1##) + IP x -> case b of + IS _ -> integerOr b a + IP y -> integerFromBigNat (bigNatOr x y) + IN y -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatAndNot -- use De Morgan's laws + (bigNatSubWordUnsafe# y 1##) + x) + 1##) + IN x -> case b of + IS _ -> integerOr b a + IN y -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatAnd -- use De Morgan's laws + (bigNatSubWordUnsafe# x 1##) + (bigNatSubWordUnsafe# y 1##)) + 1##) + IP y -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatAndNot -- use De Morgan's laws + (bigNatSubWordUnsafe# x 1##) + y) + 1##) + + +-- | Bitwise XOR operation +-- +-- Fake 2's complement for negative values (might be slow) +integerXor :: Integer -> Integer -> Integer +{-# NOINLINE integerXor #-} +integerXor a b = case a of + IS 0# -> b + IS -1# -> integerComplement b + IS x -> case b of + IS 0# -> a + IS -1# -> integerComplement a + IS y -> IS (xorI# x y) + IP y + | isTrue# (x >=# 0#) -> integerFromBigNat (bigNatXorWord# y (int2Word# x)) + | True -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatXorWord# + y + (int2Word# (negateInt# x) `minusWord#` 1##)) + 1##) + IN y + | isTrue# (x >=# 0#) -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatXorWord# + (bigNatSubWordUnsafe# y 1##) + (int2Word# x)) + 1##) + | True -> integerFromBigNat + (bigNatXorWord# -- xor (not x) (not y) = xor x y + (bigNatSubWordUnsafe# y 1##) + (int2Word# (negateInt# x) `minusWord#` 1##)) + IP x -> case b of + IS _ -> integerXor b a + IP y -> integerFromBigNat (bigNatXor x y) + IN y -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatXor + x + (bigNatSubWordUnsafe# y 1##)) + 1##) + IN x -> case b of + IS _ -> integerXor b a + IN y -> integerFromBigNat + (bigNatXor -- xor (not x) (not y) = xor x y + (bigNatSubWordUnsafe# x 1##) + (bigNatSubWordUnsafe# y 1##)) + IP y -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatXor + y + (bigNatSubWordUnsafe# x 1##)) + 1##) + + + +-- | Bitwise AND operation +-- +-- Fake 2's complement for negative values (might be slow) +integerAnd :: Integer -> Integer -> Integer +{-# NOINLINE integerAnd #-} +integerAnd a b = case a of + IS 0# -> IS 0# + IS -1# -> b + IS x -> case b of + IS 0# -> IS 0# + IS -1# -> a + IS y -> IS (andI# x y) + IP y -> integerFromBigNat (bigNatAndInt# y x) + IN y + | isTrue# (x >=# 0#) -> integerFromWord# (int2Word# x `andNot#` (indexWordArray# y 0# `minusWord#` 1##)) + | True -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatOrWord# -- use De Morgan's laws + (bigNatSubWordUnsafe# y 1##) + (wordFromAbsInt# x `minusWord#` 1##)) + 1##) + IP x -> case b of + IS _ -> integerAnd b a + IP y -> integerFromBigNat (bigNatAnd x y) + IN y -> integerFromBigNat (bigNatAndNot x (bigNatSubWordUnsafe# y 1##)) + IN x -> case b of + IS _ -> integerAnd b a + IN y -> integerFromBigNatNeg + (bigNatAddWord# + (bigNatOr -- use De Morgan's laws + (bigNatSubWordUnsafe# x 1##) + (bigNatSubWordUnsafe# y 1##)) + 1##) + IP y -> integerFromBigNat (bigNatAndNot y (bigNatSubWordUnsafe# x 1##)) + + + +-- | Binary complement of the +integerComplement :: Integer -> Integer +{-# NOINLINE integerComplement #-} +integerComplement (IS x) = IS (notI# x) +integerComplement (IP x) = IN (bigNatAddWord# x 1##) +integerComplement (IN x) = IP (bigNatSubWordUnsafe# x 1##) + + +-- | Simultaneous 'integerQuot' and 'integerRem'. +-- +-- Divisor must be non-zero otherwise the GHC runtime will terminate +-- with a division-by-zero fault. +integerQuotRem# :: Integer -> Integer -> (# Integer, Integer #) +{-# NOINLINE integerQuotRem# #-} +integerQuotRem# !n (IS 1#) = (# n, IS 0# #) +integerQuotRem# !n (IS -1#) = let !q = integerNegate n in (# q, (IS 0#) #) +integerQuotRem# !_ (IS 0#) = (# divByZero, divByZero #) +integerQuotRem# (IS 0#) _ = (# IS 0#, IS 0# #) +integerQuotRem# (IS n#) (IS d#) = case quotRemInt# n# d# of + (# q#, r# #) -> (# IS q#, IS r# #) +integerQuotRem# (IP n) (IP d) = case bigNatQuotRem# n d of + (# q, r #) -> (# integerFromBigNat q, integerFromBigNat r #) +integerQuotRem# (IP n) (IN d) = case bigNatQuotRem# n d of + (# q, r #) -> (# integerFromBigNatNeg q, integerFromBigNat r #) +integerQuotRem# (IN n) (IN d) = case bigNatQuotRem# n d of + (# q, r #) -> (# integerFromBigNat q, integerFromBigNatNeg r #) +integerQuotRem# (IN n) (IP d) = case bigNatQuotRem# n d of + (# q, r #) -> (# integerFromBigNatNeg q, integerFromBigNatNeg r #) +integerQuotRem# (IP n) (IS d#) + | isTrue# (d# >=# 0#) = case bigNatQuotRemWord# n (int2Word# d#) of + (# q, r# #) -> (# integerFromBigNat q, integerFromWord# r# #) + | True = case bigNatQuotRemWord# n (int2Word# (negateInt# d#)) of + (# q, r# #) -> (# integerFromBigNatNeg q, integerFromWord# r# #) +integerQuotRem# (IN n) (IS d#) + | isTrue# (d# >=# 0#) = case bigNatQuotRemWord# n (int2Word# d#) of + (# q, r# #) -> (# integerFromBigNatNeg q, integerFromWordNeg# r# #) + | True = case bigNatQuotRemWord# n (int2Word# (negateInt# d#)) of + (# q, r# #) -> (# integerFromBigNat q, integerFromWordNeg# r# #) +integerQuotRem# n@(IS _) (IN _) = (# IS 0#, n #) -- since @n < d@ +integerQuotRem# n@(IS n#) (IP d) -- need to account for (IS minBound) + | isTrue# (n# ># 0#) = (# IS 0#, n #) + | isTrue# (bigNatGtWord# d (int2Word# (negateInt# n#))) = (# IS 0#, n #) + | True {- abs(n) == d -} = (# IS -1#, IS 0# #) + +-- | Simultaneous 'integerQuot' and 'integerRem'. +-- +-- Divisor must be non-zero otherwise the GHC runtime will terminate +-- with a division-by-zero fault. +integerQuotRem :: Integer -> Integer -> (Integer, Integer) +integerQuotRem !x !y = case integerQuotRem# x y of + (# q, r #) -> (q, r) + + +integerQuot :: Integer -> Integer -> Integer +{-# NOINLINE integerQuot #-} +integerQuot !n (IS 1#) = n +integerQuot !n (IS -1#) = integerNegate n +integerQuot !_ (IS 0#) = divByZero +integerQuot (IS 0#) _ = IS 0# +integerQuot (IS n#) (IS d#) = IS (quotInt# n# d#) +integerQuot (IP n) (IS d#) + | isTrue# (d# >=# 0#) = integerFromBigNat (bigNatQuotWord# n (int2Word# d#)) + | True = integerFromBigNatNeg (bigNatQuotWord# n + (int2Word# (negateInt# d#))) +integerQuot (IN n) (IS d#) + | isTrue# (d# >=# 0#) = integerFromBigNatNeg (bigNatQuotWord# n (int2Word# d#)) + | True = integerFromBigNat (bigNatQuotWord# n + (int2Word# (negateInt# d#))) +integerQuot (IP n) (IP d) = integerFromBigNat (bigNatQuot n d) +integerQuot (IP n) (IN d) = integerFromBigNatNeg (bigNatQuot n d) +integerQuot (IN n) (IP d) = integerFromBigNatNeg (bigNatQuot n d) +integerQuot (IN n) (IN d) = integerFromBigNat (bigNatQuot n d) +integerQuot n d = case integerQuotRem# n d of (# q, _ #) -> q + +integerRem :: Integer -> Integer -> Integer +{-# NOINLINE integerRem #-} +integerRem !_ (IS 1#) = IS 0# +integerRem _ (IS -1#) = IS 0# +integerRem _ (IS 0#) = IS (remInt# 0# 0#) +integerRem (IS 0#) _ = IS 0# +integerRem (IS n#) (IS d#) = IS (remInt# n# d#) +integerRem (IP n) (IS d#) + = integerFromWord# (bigNatRemWord# n (int2Word# (absI# d#))) +integerRem (IN n) (IS d#) + = integerFromWordNeg# (bigNatRemWord# n (int2Word# (absI# d#))) +integerRem (IP n) (IP d) = integerFromBigNat (bigNatRem n d) +integerRem (IP n) (IN d) = integerFromBigNat (bigNatRem n d) +integerRem (IN n) (IP d) = integerFromBigNatNeg (bigNatRem n d) +integerRem (IN n) (IN d) = integerFromBigNatNeg (bigNatRem n d) +integerRem n d = case integerQuotRem# n d of (# _, r #) -> r + + +-- | Simultaneous 'integerDiv' and 'integerMod'. +-- +-- Divisor must be non-zero otherwise the GHC runtime will terminate +-- with a division-by-zero fault. +integerDivMod# :: Integer -> Integer -> (# Integer, Integer #) +{-# NOINLINE integerDivMod# #-} +integerDivMod# !n !d + | isTrue# (integerSignum# r ==# negateInt# (integerSignum# d)) + = let !q' = integerAdd q (IS -1#) -- TODO: optimize + !r' = integerAdd r d + in (# q', r' #) + | True = qr + where + !qr@(# q, r #) = integerQuotRem# n d + +-- | Simultaneous 'integerDiv' and 'integerMod'. +-- +-- Divisor must be non-zero otherwise the GHC runtime will terminate +-- with a division-by-zero fault. +integerDivMod :: Integer -> Integer -> (Integer, Integer) +integerDivMod !n !d = case integerDivMod# n d of + (# q,r #) -> (q,r) + + +integerDiv :: Integer -> Integer -> Integer +{-# NOINLINE integerDiv #-} +integerDiv !n !d + -- same-sign ops can be handled by more efficient 'integerQuot' + | isTrue# (integerIsNegative# n ==# integerIsNegative# d) = integerQuot n d + | True = case integerDivMod# n d of (# q, _ #) -> q + + +integerMod :: Integer -> Integer -> Integer +{-# NOINLINE integerMod #-} +integerMod !n !d + -- same-sign ops can be handled by more efficient 'integerRem' + | isTrue# (integerIsNegative# n ==# integerIsNegative# d) = integerRem n d + | True = case integerDivMod# n d of (# _, r #) -> r + +-- | Compute greatest common divisor. +integerGcd :: Integer -> Integer -> Integer +{-# NOINLINE integerGcd #-} +integerGcd (IS 0#) !b = integerAbs b +integerGcd a (IS 0#) = integerAbs a +integerGcd (IS 1#) _ = IS 1# +integerGcd (IS -1#) _ = IS 1# +integerGcd _ (IS 1#) = IS 1# +integerGcd _ (IS -1#) = IS 1# +integerGcd (IS a) (IS b) = integerFromWord# (gcdWord# + (int2Word# (absI# a)) + (int2Word# (absI# b))) +integerGcd a@(IS _) b = integerGcd b a +integerGcd (IN a) b = integerGcd (IP a) b +integerGcd (IP a) (IP b) = integerFromBigNat (bigNatGcd a b) +integerGcd (IP a) (IN b) = integerFromBigNat (bigNatGcd a b) +integerGcd (IP a) (IS b) = integerFromWord# (bigNatGcdWord# a (int2Word# (absI# b))) + +-- | Compute least common multiple. +integerLcm :: Integer -> Integer -> Integer +{-# NOINLINE integerLcm #-} +integerLcm (IS 0#) !_ = IS 0# +integerLcm (IS 1#) b = integerAbs b +integerLcm (IS -1#) b = integerAbs b +integerLcm _ (IS 0#) = IS 0# +integerLcm a (IS 1#) = integerAbs a +integerLcm a (IS -1#) = integerAbs a +integerLcm a b = (aa `integerQuot` (aa `integerGcd` ab)) `integerMul` ab + where -- TODO: use extended GCD to get a's factor directly + aa = integerAbs a + ab = integerAbs b + +-- | Square a Integer +integerSqr :: Integer -> Integer +integerSqr !a = integerMul a a + + +-- | Base 2 logarithm (floor) +-- +-- For numbers <= 0, return 0 +integerLog2# :: Integer -> Word# +integerLog2# (IS i) + | isTrue# (i <=# 0#) = 0## + | True = wordLog2# (int2Word# i) +integerLog2# (IN _) = 0## +integerLog2# (IP b) = bigNatLog2# b + +-- | Base 2 logarithm (floor) +-- +-- For numbers <= 0, return 0 +integerLog2 :: Integer -> Word +integerLog2 !i = W# (integerLog2# i) + +-- | Logarithm (floor) for an arbitrary base +-- +-- For numbers <= 0, return 0 +integerLogBaseWord# :: Word# -> Integer -> Word# +integerLogBaseWord# base !i + | integerIsNegative i = 0## + | True = naturalLogBaseWord# base (integerToNatural i) + +-- | Logarithm (floor) for an arbitrary base +-- +-- For numbers <= 0, return 0 +integerLogBaseWord :: Word -> Integer -> Word +integerLogBaseWord (W# base) !i = W# (integerLogBaseWord# base i) + +-- | Logarithm (floor) for an arbitrary base +-- +-- For numbers <= 0, return 0 +integerLogBase# :: Integer -> Integer -> Word# +integerLogBase# !base !i + | integerIsNegative i = 0## + | True = naturalLogBase# (integerToNatural base) + (integerToNatural i) + +-- | Logarithm (floor) for an arbitrary base +-- +-- For numbers <= 0, return 0 +integerLogBase :: Integer -> Integer -> Word +integerLogBase !base !i = W# (integerLogBase# base i) + +-- | Indicate if the value is a power of two and which one +integerIsPowerOf2# :: Integer -> (# () | Word# #) +integerIsPowerOf2# (IS i) + | isTrue# (i <=# 0#) = (# () | #) + | True = wordIsPowerOf2# (int2Word# i) +integerIsPowerOf2# (IN _) = (# () | #) +integerIsPowerOf2# (IP w) = bigNatIsPowerOf2# w + +#if WORD_SIZE_IN_BITS == 32 + +-- | Convert an Int64# into an Integer on 32-bit architectures +integerFromInt64# :: Int64# -> Integer +{-# NOINLINE integerFromInt64# #-} +integerFromInt64# !i + | isTrue# ((i `leInt64#` intToInt64# 0x7FFFFFFF#) + &&# (i `geInt64#` intToInt64# -0x80000000#)) + = IS (int64ToInt# i) + + | isTrue# (i `geInt64#` intToInt64# 0#) + = IP (bigNatFromWord64# (int64ToWord64# i)) + + | True + = IN (bigNatFromWord64# (int64ToWord64# (negateInt64# i))) + +-- | Convert a Word64# into an Integer on 32-bit architectures +integerFromWord64# :: Word64# -> Integer +{-# NOINLINE integerFromWord64# #-} +integerFromWord64# !w + | isTrue# (w `leWord64#` wordToWord64# 0x7FFFFFFF##) + = IS (int64ToInt# (word64ToInt64# w)) + | True + = IP (bigNatFromWord64# w) + +-- | Convert an Integer into an Int64# on 32-bit architectures +integerToInt64# :: Integer -> Int64# +{-# NOINLINE integerToInt64# #-} +integerToInt64# (IS i) = intToInt64# i +integerToInt64# (IP b) = word64ToInt64# (bigNatToWord64# b) +integerToInt64# (IN b) = negateInt64# (word64ToInt64# (bigNatToWord64# b)) + +-- | Convert an Integer into a Word64# on 32-bit architectures +integerToWord64# :: Integer -> Word64# +{-# NOINLINE integerToWord64# #-} +integerToWord64# (IS i) = int64ToWord64# (intToInt64# i) +integerToWord64# (IP b) = bigNatToWord64# b +integerToWord64# (IN b) = int64ToWord64# (negateInt64# (word64ToInt64# (bigNatToWord64# b))) + +#else + +-- | Convert an Int64# into an Integer on 64-bit architectures +integerFromInt64# :: Int# -> Integer +integerFromInt64# !x = IS x + +#endif + +---------------------------------------------------------------------------- +-- Conversions to/from floating point +---------------------------------------------------------------------------- + +-- | Decode a Double# into (# Integer mantissa, Int# exponent #) +integerDecodeDouble# :: Double# -> (# Integer, Int# #) +{-# NOINLINE integerDecodeDouble# #-} +integerDecodeDouble# !x = case decodeDouble_Int64# x of + (# m, e #) -> (# integerFromInt64# m, e #) + +-- | Decode a Double# into (# Integer mantissa, Int# exponent #) +integerDecodeDouble :: Double -> (Integer, Int) +integerDecodeDouble (D# x) = case integerDecodeDouble# x of + (# m, e #) -> (m, I# e) + +-- | Encode (# Integer mantissa, Int# exponent #) into a Double# +integerEncodeDouble# :: Integer -> Int# -> Double# +{-# NOINLINE integerEncodeDouble# #-} +integerEncodeDouble# (IS i) 0# = int2Double# i +integerEncodeDouble# (IS i) e = intEncodeDouble# i e +integerEncodeDouble# (IP b) e = bigNatEncodeDouble# b e +integerEncodeDouble# (IN b) e = negateDouble# (bigNatEncodeDouble# b e) + +-- | Encode (Integer mantissa, Int exponent) into a Double +integerEncodeDouble :: Integer -> Int -> Double +integerEncodeDouble !m (I# e) = D# (integerEncodeDouble# m e) + +-- | Encode an Integer (mantissa) into a Double# +integerToDouble# :: Integer -> Double# +{-# NOINLINE integerToDouble# #-} +integerToDouble# !i = integerEncodeDouble# i 0# + +-- | Encode an Integer (mantissa) into a Float# +integerToFloat# :: Integer -> Float# +{-# NOINLINE integerToFloat# #-} +integerToFloat# !i = integerEncodeFloat# i 0# + +-- | Encode (# Integer mantissa, Int# exponent #) into a Float# +-- +-- TODO: Not sure if it's worth to write 'Float' optimized versions here +integerEncodeFloat# :: Integer -> Int# -> Float# +{-# NOINLINE integerEncodeFloat# #-} +integerEncodeFloat# !m 0# = double2Float# (integerToDouble# m) +integerEncodeFloat# !m e = double2Float# (integerEncodeDouble# m e) + +-- | Compute the number of digits of the Integer (without the sign) in the given base. +-- +-- `base` must be > 1 +integerSizeInBase# :: Word# -> Integer -> Word# +integerSizeInBase# base (IS i) = wordSizeInBase# base (int2Word# (absI# i)) +integerSizeInBase# base (IP n) = bigNatSizeInBase# base n +integerSizeInBase# base (IN n) = bigNatSizeInBase# base n + +-- | Write an 'Integer' (without sign) to @/addr/@ in base-256 representation +-- and return the number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +integerToAddr# :: Integer -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) +integerToAddr# (IS i) = wordToAddr# (int2Word# (absI# i)) +integerToAddr# (IP n) = bigNatToAddr# n +integerToAddr# (IN n) = bigNatToAddr# n + +-- | Write an 'Integer' (without sign) to @/addr/@ in base-256 representation +-- and return the number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +integerToAddr :: Integer -> Addr# -> Bool# -> IO Word +integerToAddr a addr e = IO \s -> case integerToAddr# a addr e s of + (# s', w #) -> (# s', W# w #) + +-- | Read an 'Integer' (without sign) in base-256 representation from an Addr#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +integerFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Integer #) +integerFromAddr# sz addr e s = + case bigNatFromAddr# sz addr e s of + (# s', n #) -> (# s', integerFromBigNat n #) + +-- | Read an 'Integer' (without sign) in base-256 representation from an Addr#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +integerFromAddr :: Word# -> Addr# -> Bool# -> IO Integer +integerFromAddr sz addr e = IO (integerFromAddr# sz addr e) + + + +-- | Write an 'Integer' (without sign) in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +integerToMutableByteArray# :: Integer -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) +integerToMutableByteArray# (IS i) = wordToMutableByteArray# (int2Word# (absI# i)) +integerToMutableByteArray# (IP a) = bigNatToMutableByteArray# a +integerToMutableByteArray# (IN a) = bigNatToMutableByteArray# a + +-- | Write an 'Integer' (without sign) in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +integerToMutableByteArray :: Integer -> MutableByteArray# RealWorld -> Word# -> Bool# -> IO Word +integerToMutableByteArray i mba w e = IO \s -> case integerToMutableByteArray# i mba w e s of + (# s', r #) -> (# s', W# r #) + +-- | Read an 'Integer' (without sign) in base-256 representation from a ByteArray#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +integerFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Integer #) +integerFromByteArray# sz ba off e s = case bigNatFromByteArray# sz ba off e s of + (# s', a #) -> (# s', integerFromBigNat a #) + +-- | Read an 'Integer' (without sign) in base-256 representation from a ByteArray#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +integerFromByteArray :: Word# -> ByteArray# -> Word# -> Bool# -> Integer +integerFromByteArray sz ba off e = case runRW# (integerFromByteArray# sz ba off e) of + (# _, i #) -> i diff --git a/libraries/ghc-bignum/src/GHC/Num/Natural.hs b/libraries/ghc-bignum/src/GHC/Num/Natural.hs new file mode 100644 index 0000000000..1adb02181d --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/Natural.hs @@ -0,0 +1,557 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE BlockArguments #-} + +#include "MachDeps.h" +#include "WordSize.h" + +module GHC.Num.Natural where + +import GHC.Prim +import GHC.Types +import GHC.Classes + +import GHC.Num.BigNat +import GHC.Num.Primitives + +default () + +-- | Natural number +-- +-- Invariant: numbers <= WORD_MAXBOUND use the `NS` constructor +data Natural + = NS !Word# + | NB !BigNat + +instance Eq Natural where + (==) = naturalEq + (/=) = naturalNe + +instance Ord Natural where + compare = naturalCompare + + +-- | Check Natural invariants +naturalCheck# :: Natural -> Bool# +naturalCheck# (NS _) = 1# +naturalCheck# (NB bn) = bigNatCheck# bn &&# bigNatSize# bn ># 1# + +-- | Check Natural invariants +naturalCheck :: Natural -> Bool +naturalCheck !n = isTrue# (naturalCheck# n) + +-- | Zero Natural +naturalZero :: Natural +naturalZero = NS 0## + +-- | One Natural +naturalOne :: Natural +naturalOne = NS 1## + +-- | Test Zero Natural +naturalIsZero :: Natural -> Bool +naturalIsZero (NS 0##) = True +naturalIsZero _ = False + +-- | Test One Natural +naturalIsOne :: Natural -> Bool +naturalIsOne (NS 1##) = True +naturalIsOne _ = False + +-- | Indicate if the value is a power of two and which one +naturalIsPowerOf2# :: Natural -> (# () | Word# #) +naturalIsPowerOf2# (NS w) = wordIsPowerOf2# w +naturalIsPowerOf2# (NB w) = bigNatIsPowerOf2# w + +-- | Create a Natural from a BigNat (respect the invariants) +naturalFromBigNat :: BigNat -> Natural +naturalFromBigNat x = case bigNatSize# x of + 0# -> naturalZero + 1# -> NS (bigNatIndex# x 0#) + _ -> NB x + +-- | Convert a Natural into a BigNat +naturalToBigNat :: Natural -> BigNat +naturalToBigNat (NS w) = bigNatFromWord# w +naturalToBigNat (NB bn) = bn + +-- | Create a Natural from a Word# +naturalFromWord# :: Word# -> Natural +{-# NOINLINE naturalFromWord# #-} +naturalFromWord# x = NS x + +-- | Convert two Word# (most-significant first) into a Natural +naturalFromWord2# :: Word# -> Word# -> Natural +naturalFromWord2# 0## 0## = naturalZero +naturalFromWord2# 0## n = NS n +naturalFromWord2# w1 w2 = NB (bigNatFromWord2# w2 w1) + +-- | Create a Natural from a Word +naturalFromWord :: Word -> Natural +naturalFromWord (W# x) = NS x + +-- | Create a Natural from a list of Word +naturalFromWordList :: [Word] -> Natural +naturalFromWordList xs = naturalFromBigNat (bigNatFromWordList xs) + +-- | Convert the lower bits of a Natural into a Word# +naturalToWord# :: Natural -> Word# +{-# NOINLINE naturalToWord# #-} +naturalToWord# (NS x) = x +naturalToWord# (NB b) = bigNatIndex# b 0# + +-- | Convert the lower bits of a Natural into a Word +naturalToWord :: Natural -> Word +naturalToWord !n = W# (naturalToWord# n) + + +-- | Try downcasting 'Natural' to 'Word' value. +-- Returns '()' if value doesn't fit in 'Word'. +naturalToWordMaybe# :: Natural -> (# Word# | () #) +naturalToWordMaybe# (NS w) = (# w | #) +naturalToWordMaybe# _ = (# | () #) + +-- | Create a Natural from an Int# (unsafe: silently converts negative values +-- into positive ones) +naturalFromIntUnsafe# :: Int# -> Natural +naturalFromIntUnsafe# !i = NS (int2Word# i) + +-- | Create a Natural from an Int (unsafe: silently converts negative values +-- into positive ones) +naturalFromIntUnsafe :: Int -> Natural +naturalFromIntUnsafe (I# i) = naturalFromIntUnsafe# i + +-- | Create a Natural from an Int# +-- +-- Throws 'Control.Exception.Underflow' when passed a negative 'Int'. +naturalFromIntThrow# :: Int# -> Natural +naturalFromIntThrow# i + | isTrue# (i <# 0#) = case underflow of _ -> NS 0## + | True = naturalFromIntUnsafe# i + +-- | Create a Natural from an Int +-- +-- Throws 'Control.Exception.Underflow' when passed a negative 'Int'. +naturalFromIntThrow :: Int -> Natural +naturalFromIntThrow (I# i) = naturalFromIntThrow# i + +-- | Create an Int# from a Natural (can overflow the int and give a negative +-- number) +naturalToInt# :: Natural -> Int# +naturalToInt# !n = word2Int# (naturalToWord# n) + +-- | Create an Int# from a Natural (can overflow the int and give a negative +-- number) +naturalToInt :: Natural -> Int +naturalToInt !n = I# (naturalToInt# n) + +-- | Create a Natural from an Int# +-- +-- Underflow exception if Int# is negative +naturalFromInt# :: Int# -> Natural +naturalFromInt# !i + | isTrue# (i >=# 0#) = NS (int2Word# i) + | True = case underflow of _ -> NS 0## + +-- | Create a Natural from an Int +-- +-- Underflow exception if Int# is negative +naturalFromInt :: Int -> Natural +naturalFromInt (I# i) = naturalFromInt# i + +-- | Encode (# Natural mantissa, Int# exponent #) into a Double# +naturalEncodeDouble# :: Natural -> Int# -> Double# +naturalEncodeDouble# (NS w) 0# = word2Double# w +naturalEncodeDouble# (NS w) e = wordEncodeDouble# w e +naturalEncodeDouble# (NB b) e = bigNatEncodeDouble# b e + +-- | Encode a Natural (mantissa) into a Double# +naturalToDouble# :: Natural -> Double# +naturalToDouble# !n = naturalEncodeDouble# n 0# + +-- | Encode an Natural (mantissa) into a Float# +naturalToFloat# :: Natural -> Float# +naturalToFloat# !i = naturalEncodeFloat# i 0# + +-- | Encode (# Natural mantissa, Int# exponent #) into a Float# +-- +-- TODO: Not sure if it's worth to write 'Float' optimized versions here +naturalEncodeFloat# :: Natural -> Int# -> Float# +naturalEncodeFloat# !m 0# = double2Float# (naturalToDouble# m) +naturalEncodeFloat# !m e = double2Float# (naturalEncodeDouble# m e) + +-- | Equality test for Natural +naturalEq# :: Natural -> Natural -> Bool# +naturalEq# (NS x) (NS y) = x `eqWord#` y +naturalEq# (NB x) (NB y) = bigNatEq# x y +naturalEq# _ _ = 0# + +-- | Equality test for Natural +naturalEq :: Natural -> Natural -> Bool +naturalEq !x !y = isTrue# (naturalEq# x y) + +-- | Inequality test for Natural +naturalNe# :: Natural -> Natural -> Bool# +naturalNe# (NS x) (NS y) = x `neWord#` y +naturalNe# (NB x) (NB y) = bigNatNe# x y +naturalNe# _ _ = 1# + +-- | Inequality test for Natural +naturalNe :: Natural -> Natural -> Bool +naturalNe !x !y = isTrue# (naturalNe# x y) + +-- | Compare two Natural +naturalCompare :: Natural -> Natural -> Ordering +naturalCompare (NS x) (NS y) = compare (W# x) (W# y) +naturalCompare (NB x) (NB y) = bigNatCompare x y +naturalCompare (NS _) (NB _) = LT +naturalCompare (NB _) (NS _) = GT + +-- | PopCount for Natural +naturalPopCount# :: Natural -> Word# +naturalPopCount# (NS x) = popCnt# x +naturalPopCount# (NB x) = bigNatPopCount# x + +-- | PopCount for Natural +naturalPopCount :: Natural -> Word +naturalPopCount (NS x) = W# (popCnt# x) +naturalPopCount (NB x) = bigNatPopCount x + +-- | Right shift for Natural +naturalShiftR# :: Natural -> Word# -> Natural +naturalShiftR# (NS x) n = NS (x `shiftRW#` n) +naturalShiftR# (NB x) n = naturalFromBigNat (x `bigNatShiftR#` n) + +-- | Right shift for Natural +naturalShiftR :: Natural -> Word -> Natural +naturalShiftR x (W# n) = naturalShiftR# x n + +-- | Left shift +naturalShiftL# :: Natural -> Word# -> Natural +naturalShiftL# (NS x) n + | isTrue# (clz# x `geWord#` n) = NS (x `uncheckedShiftL#` word2Int# n) + | True = NB (bigNatFromWord# x `bigNatShiftL#` n) +naturalShiftL# (NB x) n = NB (x `bigNatShiftL#` n) + +-- | Left shift +naturalShiftL :: Natural -> Word -> Natural +naturalShiftL !x (W# n) = naturalShiftL# x n + +-- | Add two naturals +naturalAdd :: Natural -> Natural -> Natural +{-# NOINLINE naturalAdd #-} +naturalAdd (NS x) (NB y) = NB (bigNatAddWord# y x) +naturalAdd (NB x) (NS y) = NB (bigNatAddWord# x y) +naturalAdd (NB x) (NB y) = NB (bigNatAdd x y) +naturalAdd (NS x) (NS y) = + case addWordC# x y of + (# l,0# #) -> NS l + (# l,c #) -> NB (bigNatFromWord2# (int2Word# c) l) + +-- | Sub two naturals +naturalSub :: Natural -> Natural -> (# () | Natural #) +{-# NOINLINE naturalSub #-} +naturalSub (NS _) (NB _) = (# () | #) +naturalSub (NB x) (NS y) = (# | naturalFromBigNat (bigNatSubWordUnsafe# x y) #) +naturalSub (NS x) (NS y) = + case subWordC# x y of + (# l,0# #) -> (# | NS l #) + (# _,_ #) -> (# () | #) +naturalSub (NB x) (NB y) = + case bigNatSub x y of + (# () | #) -> (# () | #) + (# | z #) -> (# | naturalFromBigNat z #) + +-- | Sub two naturals +-- +-- Throw an Underflow exception if x < y +naturalSubThrow :: Natural -> Natural -> Natural +naturalSubThrow (NS _) (NB _) = case underflow of _ -> NS 0## +naturalSubThrow (NB x) (NS y) = naturalFromBigNat (bigNatSubWordUnsafe# x y) +naturalSubThrow (NS x) (NS y) = + case subWordC# x y of + (# l,0# #) -> NS l + (# _,_ #) -> case underflow of _ -> NS 0## +naturalSubThrow (NB x) (NB y) = + case bigNatSub x y of + (# () | #) -> case underflow of _ -> NS 0## + (# | z #) -> naturalFromBigNat z + +-- | Sub two naturals +-- +-- Unsafe: don't check that x >= y +-- Undefined results if it happens +naturalSubUnsafe :: Natural -> Natural -> Natural +{-# NOINLINE naturalSubUnsafe #-} +naturalSubUnsafe (NS x) (NS y) = NS (minusWord# x y) +naturalSubUnsafe (NS _) (NB _) = naturalZero +naturalSubUnsafe (NB x) (NS y) = naturalFromBigNat (bigNatSubWordUnsafe# x y) +naturalSubUnsafe (NB x) (NB y) = + case bigNatSub x y of + (# () | #) -> naturalZero + (# | z #) -> naturalFromBigNat z + +-- | Multiplication +naturalMul :: Natural -> Natural -> Natural +{-# NOINLINE naturalMul #-} +naturalMul a b = case a of + NS 0## -> NS 0## + NS 1## -> b + NS x -> case b of + NS 0## -> NS 0## + NS 1## -> a + NS y -> case timesWord2# x y of + (# h,l #) -> naturalFromWord2# h l + NB y -> NB (bigNatMulWord# y x) + NB x -> case b of + NS 0## -> NS 0## + NS 1## -> a + NS y -> NB (bigNatMulWord# x y) + NB y -> NB (bigNatMul x y) + +-- | Square a Natural +naturalSqr :: Natural -> Natural +naturalSqr !a = naturalMul a a + +-- | Signum for Natural +naturalSignum :: Natural -> Natural +naturalSignum (NS 0##) = NS 0## +naturalSignum _ = NS 1## + +-- | Negate for Natural +naturalNegate :: Natural -> Natural +{-# NOINLINE naturalNegate #-} +naturalNegate (NS 0##) = NS 0## +naturalNegate _ = case underflow of _ -> NS 0## + +-- | Return division quotient and remainder +-- +-- Division by zero is handled by BigNat +naturalQuotRem# :: Natural -> Natural -> (# Natural, Natural #) +{-# NOINLINE naturalQuotRem# #-} +naturalQuotRem# (NS n) (NS d) = case quotRemWord# n d of + (# q, r #) -> (# NS q, NS r #) +naturalQuotRem# (NB n) (NS d) = case bigNatQuotRemWord# n d of + (# q, r #) -> (# naturalFromBigNat q, NS r #) +naturalQuotRem# (NS n) (NB d) = case bigNatQuotRem# (bigNatFromWord# n) d of + (# q, r #) -> (# naturalFromBigNat q, naturalFromBigNat r #) +naturalQuotRem# (NB n) (NB d) = case bigNatQuotRem# n d of + (# q, r #) -> (# naturalFromBigNat q, naturalFromBigNat r #) + +-- | Return division quotient and remainder +naturalQuotRem :: Natural -> Natural -> (Natural, Natural) +naturalQuotRem !n !d = case naturalQuotRem# n d of + (# q, r #) -> (q,r) + +-- | Return division quotient +naturalQuot :: Natural -> Natural -> Natural +{-# NOINLINE naturalQuot #-} +naturalQuot (NS n) (NS d) = case quotWord# n d of + q -> NS q +naturalQuot (NB n) (NS d) = case bigNatQuotWord# n d of + q -> naturalFromBigNat q +naturalQuot (NS n) (NB d) = case bigNatQuot (bigNatFromWord# n) d of + q -> naturalFromBigNat q +naturalQuot (NB n) (NB d) = case bigNatQuot n d of + q -> naturalFromBigNat q + +-- | Return division remainder +naturalRem :: Natural -> Natural -> Natural +{-# NOINLINE naturalRem #-} +naturalRem (NS n) (NS d) = case remWord# n d of + r -> NS r +naturalRem (NB n) (NS d) = case bigNatRemWord# n d of + r -> NS r +naturalRem (NS n) (NB d) = case bigNatRem (bigNatFromWord# n) d of + r -> naturalFromBigNat r +naturalRem (NB n) (NB d) = case bigNatRem n d of + r -> naturalFromBigNat r + +naturalAnd :: Natural -> Natural -> Natural +naturalAnd (NS n) (NS m) = NS (n `and#` m) +naturalAnd (NS n) (NB m) = NS (n `and#` bigNatToWord# m) +naturalAnd (NB n) (NS m) = NS (bigNatToWord# n `and#` m) +naturalAnd (NB n) (NB m) = naturalFromBigNat (bigNatAnd n m) + +naturalAndNot :: Natural -> Natural -> Natural +naturalAndNot (NS n) (NS m) = NS (n `and#` not# m) +naturalAndNot (NS n) (NB m) = NS (n `and#` not# (bigNatToWord# m)) +naturalAndNot (NB n) (NS m) = NS (bigNatToWord# n `and#` not# m) +naturalAndNot (NB n) (NB m) = naturalFromBigNat (bigNatAndNot n m) + +naturalOr :: Natural -> Natural -> Natural +naturalOr (NS n) (NS m) = NS (n `or#` m) +naturalOr (NS n) (NB m) = NB (bigNatOrWord# m n) +naturalOr (NB n) (NS m) = NB (bigNatOrWord# n m) +naturalOr (NB n) (NB m) = NB (bigNatOr n m) + +naturalXor :: Natural -> Natural -> Natural +naturalXor (NS n) (NS m) = NS (n `xor#` m) +naturalXor (NS n) (NB m) = NB (bigNatXorWord# m n) +naturalXor (NB n) (NS m) = NB (bigNatXorWord# n m) +naturalXor (NB n) (NB m) = naturalFromBigNat (bigNatXor n m) + +naturalTestBit# :: Natural -> Word# -> Bool# +naturalTestBit# (NS w) i = (i `ltWord#` WORD_SIZE_IN_BITS##) &&# + ((w `and#` (1## `uncheckedShiftL#` word2Int# i)) `neWord#` 0##) +naturalTestBit# (NB bn) i = bigNatTestBit# bn i + +naturalTestBit :: Natural -> Word -> Bool +naturalTestBit !n (W# i) = isTrue# (naturalTestBit# n i) + +naturalBit# :: Word# -> Natural +naturalBit# i + | isTrue# (i `ltWord#` WORD_SIZE_IN_BITS##) = NS (1## `uncheckedShiftL#` word2Int# i) + | True = NB (bigNatBit# i) + +naturalBit :: Word -> Natural +naturalBit (W# i) = naturalBit# i + +-- | Compute greatest common divisor. +naturalGcd :: Natural -> Natural -> Natural +naturalGcd (NS 0##) !y = y +naturalGcd x (NS 0##) = x +naturalGcd (NS 1##) _ = NS 1## +naturalGcd _ (NS 1##) = NS 1## +naturalGcd (NB x) (NB y) = naturalFromBigNat (bigNatGcd x y) +naturalGcd (NB x) (NS y) = NS (bigNatGcdWord# x y) +naturalGcd (NS x) (NB y) = NS (bigNatGcdWord# y x) +naturalGcd (NS x) (NS y) = NS (gcdWord# x y) + +-- | Compute least common multiple. +naturalLcm :: Natural -> Natural -> Natural +naturalLcm (NS 0##) !_ = NS 0## +naturalLcm _ (NS 0##) = NS 0## +naturalLcm (NS 1##) y = y +naturalLcm x (NS 1##) = x +naturalLcm (NS a ) (NS b ) = naturalFromBigNat (bigNatLcmWordWord# a b) +naturalLcm (NB a ) (NS b ) = naturalFromBigNat (bigNatLcmWord# a b) +naturalLcm (NS a ) (NB b ) = naturalFromBigNat (bigNatLcmWord# b a) +naturalLcm (NB a ) (NB b ) = naturalFromBigNat (bigNatLcm a b) + +-- | Base 2 logarithm +naturalLog2# :: Natural -> Word# +naturalLog2# (NS w) = wordLog2# w +naturalLog2# (NB b) = bigNatLog2# b + +-- | Base 2 logarithm +naturalLog2 :: Natural -> Word +naturalLog2 !n = W# (naturalLog2# n) + +-- | Logarithm for an arbitrary base +naturalLogBaseWord# :: Word# -> Natural -> Word# +naturalLogBaseWord# base (NS a) = wordLogBase# base a +naturalLogBaseWord# base (NB a) = bigNatLogBaseWord# base a + +-- | Logarithm for an arbitrary base +naturalLogBaseWord :: Word -> Natural -> Word +naturalLogBaseWord (W# base) !a = W# (naturalLogBaseWord# base a) + +-- | Logarithm for an arbitrary base +naturalLogBase# :: Natural -> Natural -> Word# +naturalLogBase# (NS base) !a = naturalLogBaseWord# base a +naturalLogBase# (NB _ ) (NS _) = 0## +naturalLogBase# (NB base) (NB a) = bigNatLogBase# base a + +-- | Logarithm for an arbitrary base +naturalLogBase :: Natural -> Natural -> Word +naturalLogBase !base !a = W# (naturalLogBase# base a) + +-- | \"@'naturalPowMod' /b/ /e/ /m/@\" computes base @/b/@ raised to +-- exponent @/e/@ modulo @/m/@. +naturalPowMod :: Natural -> Natural -> Natural -> Natural +naturalPowMod !_ !_ (NS 0##) = case divByZero of _ -> naturalZero +naturalPowMod _ _ (NS 1##) = NS 0## +naturalPowMod _ (NS 0##) _ = NS 1## +naturalPowMod (NS 0##) _ _ = NS 0## +naturalPowMod (NS 1##) _ _ = NS 1## +naturalPowMod (NS b) (NS e) (NS m) = NS (powModWord# b e m) +naturalPowMod b e (NS m) = NS (bigNatPowModWord# + (naturalToBigNat b) + (naturalToBigNat e) + m) +naturalPowMod b e (NB m) = naturalFromBigNat + (bigNatPowMod (naturalToBigNat b) + (naturalToBigNat e) + m) + +-- | Compute the number of digits of the Natural in the given base. +-- +-- `base` must be > 1 +naturalSizeInBase# :: Word# -> Natural -> Word# +naturalSizeInBase# base (NS w) = wordSizeInBase# base w +naturalSizeInBase# base (NB n) = bigNatSizeInBase# base n + +-- | Write a 'Natural' to @/addr/@ in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +naturalToAddr# :: Natural -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) +naturalToAddr# (NS i) = wordToAddr# i +naturalToAddr# (NB n) = bigNatToAddr# n + +-- | Write a 'Natural' to @/addr/@ in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +naturalToAddr :: Natural -> Addr# -> Bool# -> IO Word +naturalToAddr a addr e = IO \s -> case naturalToAddr# a addr e s of + (# s', w #) -> (# s', W# w #) + + +-- | Read a Natural in base-256 representation from an Addr#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +naturalFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Natural #) +naturalFromAddr# sz addr e s = + case bigNatFromAddr# sz addr e s of + (# s', n #) -> (# s', naturalFromBigNat n #) + +-- | Read a Natural in base-256 representation from an Addr#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +naturalFromAddr :: Word# -> Addr# -> Bool# -> IO Natural +naturalFromAddr sz addr e = IO (naturalFromAddr# sz addr e) + + +-- | Write a Natural in base-256 representation and return the +-- number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +naturalToMutableByteArray# :: Natural -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) +naturalToMutableByteArray# (NS w) = wordToMutableByteArray# w +naturalToMutableByteArray# (NB a) = bigNatToMutableByteArray# a + +-- | Read a Natural in base-256 representation from a ByteArray#. +-- +-- The size is given in bytes. +-- +-- The endianness is selected with the Bool# parameter: most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- Null higher limbs are automatically trimed. +naturalFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Natural #) +naturalFromByteArray# sz ba off e s = case bigNatFromByteArray# sz ba off e s of + (# s', a #) -> (# s', naturalFromBigNat a #) diff --git a/libraries/ghc-bignum/src/GHC/Num/Natural.hs-boot b/libraries/ghc-bignum/src/GHC/Num/Natural.hs-boot new file mode 100644 index 0000000000..28cf5d1771 --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/Natural.hs-boot @@ -0,0 +1,23 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MagicHash #-} + +module GHC.Num.Natural where + +import {-# SOURCE #-} GHC.Num.BigNat +import GHC.Num.Primitives +import GHC.Prim +import GHC.Types + +data Natural + = NS !Word# + | NB !BigNat + +naturalToWord# :: Natural -> Word# +naturalFromWord# :: Word# -> Natural +naturalToBigNat :: Natural -> BigNat +naturalFromBigNat :: BigNat -> Natural +naturalMul :: Natural -> Natural -> Natural +naturalRem :: Natural -> Natural -> Natural +naturalIsZero :: Natural -> Bool +naturalShiftR# :: Natural -> Word# -> Natural +naturalTestBit# :: Natural -> Word# -> Bool# diff --git a/libraries/ghc-bignum/src/GHC/Num/Primitives.hs b/libraries/ghc-bignum/src/GHC/Num/Primitives.hs new file mode 100644 index 0000000000..2c1a0b6955 --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/Primitives.hs @@ -0,0 +1,623 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE UnliftedFFITypes #-} +{-# LANGUAGE NegativeLiterals #-} +{-# LANGUAGE ExplicitForAll #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE BlockArguments #-} +{-# LANGUAGE BinaryLiterals #-} +{-# OPTIONS_GHC -fexpose-all-unfoldings #-} + +module GHC.Num.Primitives + ( + -- * Bool# + Bool# + , (&&#) + , (||#) + , notB# + -- * Int# + , testBitI# + , minI# + , maxI# + , sgnI# + , absI# + , cmpI# + , intEncodeDouble# + , popCntI# + -- * Word# + , andNot# + , cmpW# + , bitW# + , maxW# + , minW# + , testBitW# + , shiftRW# + , plusWord3# + , plusWord12# + , quotRemWord3# + , wordFromAbsInt# + , wordLog2# + , wordLogBase# + , wordSizeInBase# + , wordIsPowerOf2# + , wordEncodeDouble# + , wordReverseBits# + , wordReverseBits32# + , wordReverseBytes# + -- ** Addr import/export + , wordFromAddr# + , wordFromAddrLE# + , wordFromAddrBE# + , wordToAddr# + , wordToAddrLE# + , wordToAddrBE# + , wordWriteAddrLE# + , wordWriteAddrBE# + -- ** ByteArray import/export + , wordFromByteArray# + , wordFromByteArrayLE# + , wordFromByteArrayBE# + , wordToMutableByteArray# + , wordToMutableByteArrayLE# + , wordToMutableByteArrayBE# + , wordWriteMutableByteArrayLE# + , wordWriteMutableByteArrayBE# + -- * Exception + , underflow + , divByZero + , unexpectedValue + -- * IO + , ioWord# + , ioInt# + , ioVoid + , ioBool + ) +where + +#include "MachDeps.h" +#include "WordSize.h" + +-- Required for WORDS_BIGENDIAN +#include <ghcautoconf.h> + +#if (__GLASGOW_HASKELL__ < 811) +import GHC.Magic +#endif + +import GHC.Prim +import GHC.Types +import GHC.Tuple () -- See Note [Depend on GHC.Tuple] in GHC.Base + +default () + +---------------------------------- +-- Bool# +---------------------------------- + +type Bool# = Int# + +(&&#) :: Bool# -> Bool# -> Bool# +(&&#) = andI# + +(||#) :: Bool# -> Bool# -> Bool# +(||#) = orI# + +notB# :: Bool# -> Bool# +notB# x = x `xorI#` 1# + +infixr 3 &&# +infixr 2 ||# + + +---------------------------------- +-- Int# +---------------------------------- + +-- | Branchless `abs` +absI# :: Int# -> Int# +absI# i# = (i# `xorI#` nsign) -# nsign + where + -- nsign = negateInt# (i# <# 0#) + nsign = uncheckedIShiftRA# i# (WORD_SIZE_IN_BITS# -# 1#) + +-- | Branchless `signum` +sgnI# :: Int# -> Int# +sgnI# x# = (x# ># 0#) -# (x# <# 0#) + +-- | Population count +popCntI# :: Int# -> Word# +popCntI# i = popCnt# (int2Word# i) + +-- | Branchless comparison +cmpI# :: Int# -> Int# -> Int# +cmpI# x# y# = (x# ># y#) -# (x# <# y#) + +testBitI# :: Int# -> Word# -> Bool# +testBitI# x i = ((uncheckedIShiftL# 1# (word2Int# i)) `andI#` x) /=# 0# + +minI# :: Int# -> Int# -> Int# +minI# x y | isTrue# (x <=# y) = x + | True = y + +maxI# :: Int# -> Int# -> Int# +maxI# x y | isTrue# (x >=# y) = x + | True = y + +-- | Encode (# Int# mantissa, Int# exponent #) into a Double#. +-- +-- (provided by GHC's RTS) +foreign import ccall unsafe "__int_encodeDouble" + intEncodeDouble# :: Int# -> Int# -> Double# + +---------------------------------- +-- Word# +---------------------------------- + +andNot# :: Word# -> Word# -> Word# +andNot# x y = x `and#` (not# y) + +cmpW# :: Word# -> Word# -> Ordering +{-# INLINE cmpW# #-} +cmpW# x# y# + | isTrue# (x# `ltWord#` y#) = LT + | isTrue# (x# `eqWord#` y#) = EQ + | True = GT + +-- | Return the absolute value of the Int# in a Word# +wordFromAbsInt# :: Int# -> Word# +wordFromAbsInt# i + | isTrue# (i >=# 0#) = int2Word# i + | True = int2Word# (negateInt# i) + +minW# :: Word# -> Word# -> Word# +minW# x# y# | isTrue# (x# `leWord#` y#) = x# + | True = y# + +maxW# :: Word# -> Word# -> Word# +maxW# x# y# | isTrue# (x# `gtWord#` y#) = x# + | True = y# + +bitW# :: Int# -> Word# +bitW# k = 1## `uncheckedShiftL#` k + +testBitW# :: Word# -> Word# -> Bool# +testBitW# w k = w `and#` (1## `uncheckedShiftL#` word2Int# k) `neWord#` 0## + +-- | Safe right shift for Word# +shiftRW# :: Word# -> Word# -> Word# +shiftRW# a b + | isTrue# (b `geWord#` WORD_SIZE_IN_BITS##) = 0## + | True = a `uncheckedShiftRL#` (word2Int# b) + +-- | (h,l) <- a + (hb,lb) +plusWord12# :: Word# -> (# Word#,Word# #) -> (# Word#,Word# #) +{-# INLINABLE plusWord12# #-} +plusWord12# a0 (# b1,b0 #) = (# m1, m0 #) + where + !(# t, m0 #) = plusWord2# a0 b0 + !m1 = plusWord# t b1 + +-- | Add 3 values together +plusWord3# :: Word# -> Word# -> Word# -> (# Word#, Word# #) +{-# INLINABLE plusWord3# #-} +plusWord3# a b c = (# r1, r0 #) + where + !(# t1, t0 #) = plusWord2# a b + !(# t2, r0 #) = plusWord2# t0 c + !r1 = plusWord# t1 t2 + + +-- | 2-by-1 large division +-- +-- Requires: +-- b0 /= 0 +-- a1 >= b0 (not required, but if not q1=0) +quotRemWord3# :: (# Word#,Word# #) -> Word# -> (# (# Word#,Word# #),Word# #) +quotRemWord3# (# a1,a0 #) b0 = (# (# q1, q0 #), r0 #) + where + !(# q1, r' #) = quotRemWord# a1 b0 + !(# q0, r0 #) = quotRemWord2# r' a0 b0 + + + +-- | Encode (# Word# mantissa, Int# exponent #) into a Double#. +-- +-- (provided by GHC's RTS) +foreign import ccall unsafe "__word_encodeDouble" + wordEncodeDouble# :: Word# -> Int# -> Double# + +-- | Compute base-2 log of 'Word#' +-- +-- This is internally implemented as count-leading-zeros machine instruction. +wordLog2# :: Word# -> Word# +wordLog2# w = (WORD_SIZE_IN_BITS## `minusWord#` 1##) `minusWord#` (clz# w) + +-- | Logarithm for an arbitrary base +wordLogBase# :: Word# -> Word# -> Word# +wordLogBase# base a + | isTrue# (base `leWord#` 1##) + = case unexpectedValue of _ -> 0## + + | 2## <- base + = wordLog2# a + + | True + = case go base of (# _, e' #) -> e' + where + goSqr pw = case timesWord2# pw pw of + (# 0##, l #) -> go l + (# _ , _ #) -> (# a, 0## #) + go pw = if isTrue# (a `ltWord#` pw) + then (# a, 0## #) + else case goSqr pw of + (# q, e #) -> if isTrue# (q `ltWord#` pw) + then (# q, 2## `timesWord#` e #) + else (# q `quotWord#` pw + , 2## `timesWord#` e `plusWord#` 1## #) + +wordSizeInBase# :: Word# -> Word# -> Word# +wordSizeInBase# _ 0## = 0## +wordSizeInBase# base w = 1## `plusWord#` wordLogBase# base w + +-- | Indicate if the value is a power of two and which one +wordIsPowerOf2# :: Word# -> (# () | Word# #) +wordIsPowerOf2# w + | isTrue# (popCnt# w `neWord#` 1##) = (# () | #) + | True = (# | ctz# w #) + +-- | Reverse bytes in a Word# +wordReverseBytes# :: Word# -> Word# +wordReverseBytes# x0 = r + where +#if WORD_SIZE_IN_BITS == 64 + x1 = ((x0 `and#` 0x00FF00FF00FF00FF##) `uncheckedShiftL#` 8#) `or#` ((x0 `and#` 0xFF00FF00FF00FF00##) `uncheckedShiftRL#` 8#) + x2 = ((x1 `and#` 0x0000FFFF0000FFFF##) `uncheckedShiftL#` 16#) `or#` ((x1 `and#` 0xFFFF0000FFFF0000##) `uncheckedShiftRL#` 16#) + r = ((x2 `and#` 0x00000000FFFFFFFF##) `uncheckedShiftL#` 32#) `or#` ((x2 `and#` 0xFFFFFFFF00000000##) `uncheckedShiftRL#` 32#) +#else + x1 = ((x0 `and#` 0x00FF00FF##) `uncheckedShiftL#` 8#) `or#` ((x0 `and#` 0xFF00FF00##) `uncheckedShiftRL#` 8#) + r = ((x1 `and#` 0x0000FFFF##) `uncheckedShiftL#` 16#) `or#` ((x1 `and#` 0xFFFF0000##) `uncheckedShiftRL#` 16#) +#endif + + +-- | Reverse bits in a Word# +wordReverseBits# :: Word# -> Word# +wordReverseBits# x0 = r + where +#if WORD_SIZE_IN_BITS == 64 + x1 = ((x0 `and#` 0x5555555555555555##) `uncheckedShiftL#` 1#) `or#` ((x0 `and#` 0xAAAAAAAAAAAAAAAA##) `uncheckedShiftRL#` 1#) + x2 = ((x1 `and#` 0x3333333333333333##) `uncheckedShiftL#` 2#) `or#` ((x1 `and#` 0xCCCCCCCCCCCCCCCC##) `uncheckedShiftRL#` 2#) + x3 = ((x2 `and#` 0x0F0F0F0F0F0F0F0F##) `uncheckedShiftL#` 4#) `or#` ((x2 `and#` 0xF0F0F0F0F0F0F0F0##) `uncheckedShiftRL#` 4#) + x4 = ((x3 `and#` 0x00FF00FF00FF00FF##) `uncheckedShiftL#` 8#) `or#` ((x3 `and#` 0xFF00FF00FF00FF00##) `uncheckedShiftRL#` 8#) + x5 = ((x4 `and#` 0x0000FFFF0000FFFF##) `uncheckedShiftL#` 16#) `or#` ((x4 `and#` 0xFFFF0000FFFF0000##) `uncheckedShiftRL#` 16#) + r = ((x5 `and#` 0x00000000FFFFFFFF##) `uncheckedShiftL#` 32#) `or#` ((x5 `and#` 0xFFFFFFFF00000000##) `uncheckedShiftRL#` 32#) +#else + x1 = ((x0 `and#` 0x55555555##) `uncheckedShiftL#` 1#) `or#` ((x0 `and#` 0xAAAAAAAA##) `uncheckedShiftRL#` 1#) + x2 = ((x1 `and#` 0x33333333##) `uncheckedShiftL#` 2#) `or#` ((x1 `and#` 0xCCCCCCCC##) `uncheckedShiftRL#` 2#) + x3 = ((x2 `and#` 0x0F0F0F0F##) `uncheckedShiftL#` 4#) `or#` ((x2 `and#` 0xF0F0F0F0##) `uncheckedShiftRL#` 4#) + x4 = ((x3 `and#` 0x00FF00FF##) `uncheckedShiftL#` 8#) `or#` ((x3 `and#` 0xFF00FF00##) `uncheckedShiftRL#` 8#) + r = ((x4 `and#` 0x0000FFFF##) `uncheckedShiftL#` 16#) `or#` ((x4 `and#` 0xFFFF0000##) `uncheckedShiftRL#` 16#) +#endif + +-- | Reverse bits in the Word32 subwords composing a Word# +wordReverseBits32# :: Word# -> Word# +#if WORD_SIZE_IN_BITS == 64 +wordReverseBits32# x0 = r + where + x1 = ((x0 `and#` 0x5555555555555555##) `uncheckedShiftL#` 1#) `or#` ((x0 `and#` 0xAAAAAAAAAAAAAAAA##) `uncheckedShiftRL#` 1#) + x2 = ((x1 `and#` 0x3333333333333333##) `uncheckedShiftL#` 2#) `or#` ((x1 `and#` 0xCCCCCCCCCCCCCCCC##) `uncheckedShiftRL#` 2#) + x3 = ((x2 `and#` 0x0F0F0F0F0F0F0F0F##) `uncheckedShiftL#` 4#) `or#` ((x2 `and#` 0xF0F0F0F0F0F0F0F0##) `uncheckedShiftRL#` 4#) + x4 = ((x3 `and#` 0x00FF00FF00FF00FF##) `uncheckedShiftL#` 8#) `or#` ((x3 `and#` 0xFF00FF00FF00FF00##) `uncheckedShiftRL#` 8#) + r = ((x4 `and#` 0x0000FFFF0000FFFF##) `uncheckedShiftL#` 16#) `or#` ((x4 `and#` 0xFFFF0000FFFF0000##) `uncheckedShiftRL#` 16#) +#else +wordReverseBits32# x0 = wordReverseBits# x0 +#endif + + +-- | Write a Word to @/addr/@ in base-256 little-endian representation and +-- return the number of bytes written. +wordToAddrLE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) +wordToAddrLE# x addr = go x 0# + where + go w c s + | 0## <- w + = (# s, int2Word# c #) + + | True + = case writeWord8OffAddr# addr c (w `and#` 0xFF##) s of + s' -> go (w `uncheckedShiftRL#` 8#) (c +# 1#) s' + +-- | Write a Word to @/addr/@ in base-256 big-endian representation and +-- return the number of bytes written. +wordToAddrBE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) +wordToAddrBE# w addr = go 0# (WORD_SIZE_IN_BITS# -# clz) + where + !clz = word2Int# (clz# w `and#` (not# 0b0111##)) -- keep complete bytes + + go c sh s + | 0# <- sh + = (# s, int2Word# c #) + + | True + , w' <- (w `uncheckedShiftRL#` (sh -# 8#)) `and#` 0xFF## + = case writeWord8OffAddr# addr c w' s of + s' -> go (c +# 1#) (sh -# 8#) s' + +-- | Write a Word to @/addr/@ in base-256 representation and +-- return the number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +wordToAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) +wordToAddr# a addr 0# s = wordToAddrLE# a addr s +wordToAddr# a addr _ s = wordToAddrBE# a addr s + + +-- | Read a Word from @/addr/@ in base-256 little-endian representation. +-- +-- @'n' is the number of bytes to read. +wordFromAddrLE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) +wordFromAddrLE# n addr s + -- Optimize when we read a full word + | WORD_SIZE_IN_BYTES## <- n + = case readWordOffAddr# addr 0# s of +#if defined(WORDS_BIGENDIAN) + (# s', w #) -> (# s', wordReverseBytes# w #) +#else + (# s', w #) -> (# s', w #) +#endif + +wordFromAddrLE# n addr s0 = go 0## 0# s0 + where + go w c s + | isTrue# (c ==# word2Int# n) + = (# s, w #) + + | True + = case readWord8OffAddr# addr c s of + (# s', b #) -> go (w `or#` (b `uncheckedShiftL#` (c `uncheckedIShiftL#` 3#))) + (c +# 1#) + s' + +-- | Read a Word from @/addr/@ in base-256 big-endian representation. +-- +-- @'n' is the number of bytes to read. +wordFromAddrBE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) +wordFromAddrBE# n addr s + -- Optimize when we read a full word + | WORD_SIZE_IN_BYTES## <- n + = case readWordOffAddr# addr 0# s of +#if defined(WORDS_BIGENDIAN) + (# s', w #) -> (# s', w #) +#else + (# s', w #) -> (# s', wordReverseBytes# w #) +#endif + +wordFromAddrBE# n addr s0 = go 0## 0# s0 + where + go w c s + | isTrue# (c ==# word2Int# n) + = (# s, w #) + + | True + = case readWord8OffAddr# addr c s of + (# s', b #) -> go ((w `uncheckedShiftL#` 8#) `or#` b) + (c +# 1#) + s' + +-- | Read a Word from @/addr/@ in base-256 representation. +-- +-- @'n' is the number of bytes to read. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +wordFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) +wordFromAddr# a addr 0# s = wordFromAddrLE# a addr s +wordFromAddr# a addr _ s = wordFromAddrBE# a addr s + + + +-- | Write a full word with little-endian encoding +wordWriteAddrLE# :: Word# -> Addr# -> State# s -> State# s +wordWriteAddrLE# w addr = writeWordOffAddr# addr 0# +#if defined(WORDS_BIGENDIAN) + (wordReverseBytes# w) +#else + w +#endif + +-- | Write a full word with little-endian encoding +wordWriteAddrBE# :: Word# -> Addr# -> State# s -> State# s +wordWriteAddrBE# w addr = writeWordOffAddr# addr 0# +#if defined(WORDS_BIGENDIAN) + w +#else + (wordReverseBytes# w) +#endif + +-- | Write a Word to @/MutableByteArray/@ in base-256 little-endian +-- representation and return the number of bytes written. +-- +-- The offset is in bytes. +wordToMutableByteArrayLE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) +wordToMutableByteArrayLE# x mba off = go x 0# + where + go w c s + | 0## <- w + = (# s, int2Word# c #) + + | True + = case writeWord8Array# mba (word2Int# off +# c) (w `and#` 0xFF##) s of + s' -> go (w `uncheckedShiftRL#` 8#) (c +# 1#) s' + +-- | Write a Word to @/MutableByteArray/@ in base-256 big-endian representation and +-- return the number of bytes written. +-- +-- The offset is in bytes. +wordToMutableByteArrayBE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) +wordToMutableByteArrayBE# w mba off = go 0# (WORD_SIZE_IN_BITS# -# clz) + where + !clz = word2Int# (clz# w `and#` (not# 0b0111##)) -- keep complete bytes + + go c sh s + | 0# <- sh + = (# s, int2Word# c #) + + | True + , w' <- (w `uncheckedShiftRL#` (sh -# 8#)) `and#` 0xFF## + = case writeWord8Array# mba (word2Int# off +# c) w' s of + s' -> go (c +# 1#) (sh -# 8#) s' + +-- | Write a Word to @/MutableByteArray/@ in base-256 representation and +-- return the number of bytes written. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +-- +-- The offset is in bytes. +wordToMutableByteArray# :: Word# -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) +wordToMutableByteArray# a mba off 0# s = wordToMutableByteArrayLE# a mba off s +wordToMutableByteArray# a mba off _ s = wordToMutableByteArrayBE# a mba off s + +-- | Write a full word with little-endian encoding +wordWriteMutableByteArrayLE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> State# s +wordWriteMutableByteArrayLE# w mba off = writeWord8ArrayAsWord# mba (word2Int# off) +#if defined(WORDS_BIGENDIAN) + (wordReverseBytes# w) +#else + w +#endif + +-- | Write a full word with little-endian encoding +wordWriteMutableByteArrayBE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> State# s +wordWriteMutableByteArrayBE# w mba off = writeWord8ArrayAsWord# mba (word2Int# off) +#if defined(WORDS_BIGENDIAN) + w +#else + (wordReverseBytes# w) +#endif + +-- | Read a Word from @/ByteArray/@ in base-256 little-endian representation. +-- +-- @'n' is the number of bytes to read. +wordFromByteArrayLE# :: Word# -> ByteArray# -> Word# -> Word# +wordFromByteArrayLE# n ba off = + case n of + -- Optimize when we read a full word + WORD_SIZE_IN_BYTES## -> case indexWord8ArrayAsWord# ba (word2Int# off) of +#if defined(WORDS_BIGENDIAN) + w -> wordReverseBytes# w +#else + w -> w +#endif + + _ -> let + go w c + | isTrue# (c ==# word2Int# n) + = w + + | True + = case indexWord8Array# ba (word2Int# off +# c) of + b -> go (w `or#` (b `uncheckedShiftL#` (c `uncheckedIShiftL#` 3#))) + (c +# 1#) + in go 0## 0# + +-- | Read a Word from @/ByteArray/@ in base-256 big-endian representation. +-- +-- @'n' is the number of bytes to read. +wordFromByteArrayBE# :: Word# -> ByteArray# -> Word# -> Word# +wordFromByteArrayBE# n ba off + -- Optimize when we read a full word + | WORD_SIZE_IN_BYTES## <- n + = case indexWord8ArrayAsWord# ba (word2Int# off) of +#if defined(WORDS_BIGENDIAN) + w -> w +#else + w -> wordReverseBytes# w +#endif + +wordFromByteArrayBE# n ba off = go 0## 0# + where + go w c + | isTrue# (c ==# word2Int# n) + = w + + | True + = case indexWord8Array# ba (word2Int# off +# c) of + b -> go ((w `uncheckedShiftL#` 8#) `or#` b) (c +# 1#) + +-- | Read a Word from @/ByteArray/@ in base-256 representation. +-- +-- @'n' is the number of bytes to read. +-- +-- The endianness is selected with the Bool# parameter: write most significant +-- byte first (big-endian) if @1#@ or least significant byte first +-- (little-endian) if @0#@. +wordFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> Word# +wordFromByteArray# a ba off 0# = wordFromByteArrayLE# a ba off +wordFromByteArray# a ba off _ = wordFromByteArrayBE# a ba off + +---------------------------------- +-- IO +---------------------------------- + +ioVoid :: IO a -> State# RealWorld -> State# RealWorld +ioVoid (IO io) s = case io s of + (# s', _ #) -> s' + +ioWord# :: IO Word -> State# RealWorld -> (# State# RealWorld, Word# #) +ioWord# (IO io) s = case io s of + (# s', W# w #) -> (# s', w #) + +ioInt# :: IO Int -> State# RealWorld -> (# State# RealWorld, Int# #) +ioInt# (IO io) s = case io s of + (# s', I# i #) -> (# s', i #) + +ioBool :: IO Bool -> State# RealWorld -> (# State# RealWorld, Bool# #) +ioBool (IO io) s = case io s of + (# s', False #) -> (# s', 0# #) + (# s', True #) -> (# s', 1# #) + + +---------------------------------- +-- Exception +---------------------------------- + +#if (__GLASGOW_HASKELL__ >= 811) + +underflow :: a +underflow = raiseUnderflow# void# + +divByZero :: a +divByZero = raiseDivZero# void# + +unexpectedValue :: a +unexpectedValue = raiseOverflow# void# + +#else + +-- Before GHC 8.11 we use the exception trick taken from #14664 +exception :: a +exception = runRW# \s -> + case atomicLoop s of + (# _, a #) -> a + where + atomicLoop s = atomically# atomicLoop s + +underflow :: a +underflow = exception + +divByZero :: a +divByZero = exception + +unexpectedValue :: a +unexpectedValue = exception + +#endif diff --git a/libraries/ghc-bignum/src/GHC/Num/WordArray.hs b/libraries/ghc-bignum/src/GHC/Num/WordArray.hs new file mode 100644 index 0000000000..78c450b55e --- /dev/null +++ b/libraries/ghc-bignum/src/GHC/Num/WordArray.hs @@ -0,0 +1,432 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE BlockArguments #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE MultiWayIf #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE KindSignatures #-} +{-# OPTIONS_GHC -Wno-name-shadowing #-} + +module GHC.Num.WordArray where + +import GHC.Prim +import GHC.Magic +import GHC.Types +import GHC.Num.Primitives + +#include "MachDeps.h" +#include "WordSize.h" + +default () + +-- | Unlifted array of Word +type WordArray# = ByteArray# +type MutableWordArray# = MutableByteArray# + +data WordArray = WordArray WordArray# +data MutableWordArray s = MutableWordArray (MutableWordArray# s) + +-- | Convert limb count into byte count +wordsToBytes# :: Int# -> Int# +wordsToBytes# i = i `uncheckedIShiftL#` WORD_SIZE_BYTES_SHIFT# + +-- | Convert byte count into limb count +bytesToWords# :: Int# -> Int# +bytesToWords# i = i `uncheckedIShiftRL#` WORD_SIZE_BYTES_SHIFT# + + +-- | Create a new WordArray# of the given size (*in Word#*) and apply the +-- action to it before returning it frozen +withNewWordArray# + :: Int# -- ^ Size in Word + -> (MutableWordArray# RealWorld -> State# RealWorld -> State# RealWorld) + -> WordArray# +withNewWordArray# sz act = case runRW# io of (# _, a #) -> a + where + io s = + case newWordArray# sz s of { (# s, mwa #) -> + case act mwa s of { s -> + unsafeFreezeByteArray# mwa s + }} + +-- | Create two new WordArray# of the given sizes (*in Word#*) and apply the +-- action to them before returning them frozen +withNewWordArray2# + :: Int# -- ^ Size in Word + -> Int# -- ^ Ditto + -> (MutableWordArray# RealWorld + -> MutableWordArray# RealWorld + -> State# RealWorld + -> State# RealWorld) + -> (# WordArray#, WordArray# #) +withNewWordArray2# sz1 sz2 act = case runRW# io of (# _, a #) -> a + where + io s = + case newWordArray# sz1 s of { (# s, mwa1 #) -> + case newWordArray# sz2 s of { (# s, mwa2 #) -> + case act mwa1 mwa2 s of { s -> + case unsafeFreezeByteArray# mwa1 s of { (# s, wa1 #) -> + case unsafeFreezeByteArray# mwa2 s of { (# s, wa2 #) -> + (# s, (# wa1, wa2 #) #) + }}}}} + +-- | Create a new WordArray# +newWordArray# :: Int# -> State# s -> (# State# s, MutableWordArray# s #) +newWordArray# sz s = newByteArray# (wordsToBytes# sz) s + +-- | Create a new WordArray# of the given size (*in Word#*), apply the action to +-- it, trim its most significant zeroes, then return it frozen +withNewWordArrayTrimed# + :: Int# -- ^ Size in Word + -> (MutableWordArray# RealWorld -> State# RealWorld -> State# RealWorld) + -> WordArray# +withNewWordArrayTrimed# sz act = withNewWordArray# sz \mwa s -> + case act mwa s of + s' -> mwaTrimZeroes# mwa s' + +-- | Create two new WordArray# of the given sizes (*in Word#*), apply the action +-- to them, trim their most significant zeroes, then return them frozen +withNewWordArray2Trimed# + :: Int# -- ^ Size in Word + -> Int# -- ^ Ditto + -> (MutableWordArray# RealWorld + -> MutableWordArray# RealWorld + -> State# RealWorld + -> State# RealWorld) + -> (# WordArray#, WordArray# #) +withNewWordArray2Trimed# sz1 sz2 act = withNewWordArray2# sz1 sz2 \mwa1 mwa2 s -> + case act mwa1 mwa2 s of + s' -> case mwaTrimZeroes# mwa1 s' of + s'' -> mwaTrimZeroes# mwa2 s'' + +-- | Create a new WordArray# of the given size (*in Word#*), apply the action to +-- it. If the action returns true#, trim its most significant zeroes, then +-- return it frozen. Otherwise, return (). +withNewWordArrayTrimedMaybe# + :: Int# -- ^ Size in Word + -> (MutableWordArray# RealWorld -> State# RealWorld -> (# State# RealWorld, Bool# #)) + -> (# () | WordArray# #) +withNewWordArrayTrimedMaybe# sz act = case runRW# io of (# _, a #) -> a + where + io s = + case newWordArray# sz s of + (# s, mwa #) -> case act mwa s of + (# s, 0# #) -> (# s, (# () | #) #) + (# s, _ #) -> case mwaTrimZeroes# mwa s of + s -> case unsafeFreezeByteArray# mwa s of + (# s, ba #) -> (# s, (# | ba #) #) + +-- | Create a WordArray# from two Word# +-- +-- `byteArrayFromWord2# msw lsw = lsw:msw` +wordArrayFromWord2# :: Word# -> Word# -> WordArray# +wordArrayFromWord2# msw lsw = + withNewWordArray# 2# \mwa s -> + case mwaWrite# mwa 0# lsw s of + s -> mwaWrite# mwa 1# msw s + +-- | Create a WordArray# from one Word# +wordArrayFromWord# :: Word# -> WordArray# +wordArrayFromWord# w = + withNewWordArray# 1# \mwa s -> + mwaWrite# mwa 0# w s + +-- | Word array size +wordArraySize# :: WordArray# -> Int# +wordArraySize# ba = bytesToWords# (sizeofByteArray# ba) + + +-- | Equality test for WordArray# + +-- | Get size in Words +mwaSize# :: MutableWordArray# s-> State# s -> (# State# s, Int# #) +mwaSize# mba s = case getSizeofMutableByteArray# mba s of + (# s2, sz #) -> (# s2, bytesToWords# sz #) + +-- | Get the last Word (must be non empty!) +wordArrayLast# :: WordArray# -> Word# +wordArrayLast# a = indexWordArray# a (wordArraySize# a -# 1#) + +-- | Copy Words from a WordArray +-- +-- Don't do anything if the number of words to copy is <= 0 +mwaArrayCopy# :: MutableByteArray# s -> Int# -> WordArray# -> Int# -> Int# -> State# s -> State# s +mwaArrayCopy# dst dstIdx src srcIdx n s + | isTrue# (n <=# 0#) = s + | True = copyByteArray# + src (wordsToBytes# srcIdx) + dst (wordsToBytes# dstIdx) + (wordsToBytes# n) s + +-- | Shrink last words of a WordArray +mwaShrink# :: MutableByteArray# s -> Int# -> State# s -> State# s +mwaShrink# _mwa 0# s = s +mwaShrink# mwa i s = + case mwaSize# mwa s of + (# s, n #) -> shrinkMutableByteArray# mwa (wordsToBytes# (n -# i)) s + +-- | Set size +mwaSetSize# :: MutableByteArray# s -> Int# -> State# s -> State# s +mwaSetSize# mwa n s = shrinkMutableByteArray# mwa (wordsToBytes# n) s + +-- | Copy the WordArray into the MWA and shrink the size of MWA to the one of +-- the WordArray +mwaInitCopyShrink# :: MutableByteArray# s -> WordArray# -> State# s -> State# s +mwaInitCopyShrink# mwa wa s = + case mwaArrayCopy# mwa 0# wa 0# (wordArraySize# wa) s of + s -> mwaSetSize# mwa (wordArraySize# wa) s + +-- | Trim ending zeroes +mwaTrimZeroes# :: MutableByteArray# s -> State# s -> State# s +mwaTrimZeroes# mwa s1 = + case mwaClz mwa s1 of + (# s2, 0# #) -> s2 + (# s2, c #) -> mwaShrink# mwa c s2 + +-- | Count leading zero Words +mwaClz :: MutableWordArray# s -> State# s -> (# State# s, Int# #) +mwaClz mwa s1 = case mwaSize# mwa s1 of + (# s2,sz #) -> mwaClzAt mwa (sz -# 1#) s2 + +-- | Count leading zero Words starting at given position +mwaClzAt :: MutableWordArray# s -> Int# -> State# s -> (# State# s, Int# #) +mwaClzAt mwa = go 0# + where + go c i s + | isTrue# (i <# 0#) = (# s, c #) + | True = case readWordArray# mwa i s of + (# s', 0## #) -> go (c +# 1#) (i -# 1#) s' + (# s', _ #) -> (# s', c #) + +-- | Count leading zero Words starting at given position +waClzAt :: WordArray# -> Int# -> Int# +waClzAt wa = go 0# + where + go c i + | isTrue# (i <# 0#) + = c + + | 0## <- indexWordArray# wa i + = go (c +# 1#) (i -# 1#) + + | True + = c + +-- | Compare the most signiciant limbs of a and b. The comparison stops (i.e. +-- returns EQ) when there isn't enough lims in a or b to perform another +-- comparison. +wordArrayCompareMSWords :: WordArray# -> WordArray# -> Ordering +wordArrayCompareMSWords wa wb + | 0# <- szA + , 0# <- szB + = EQ + + | 0# <- szA + = LT + + | 0# <- szB + = GT + + | True + = go (szA -# 1#) (szB -# 1#) + where + szA = wordArraySize# wa + szB = wordArraySize# wb + + go i j + | isTrue# (i <# 0#) = EQ + | isTrue# (j <# 0#) = EQ + | True = + let + a = indexWordArray# wa i + b = indexWordArray# wb j + in if | isTrue# (a `gtWord#` b) -> GT + | isTrue# (b `gtWord#` a) -> LT + | True -> go (i -# 1#) (j -# 1#) + + +-- | Compute MutableWordArray <- WordArray + Word +-- +-- The MutableWordArray may not be initialized and will be erased anyway. +-- +-- Input: Size(MutableWordArray) = Size(WordArray) + 1 +-- Output: Size(MutableWordArray) = Size(WordArray) [+ 1] +mwaInitArrayPlusWord :: MutableWordArray# s -> WordArray# -> Word# -> State# s -> State#s +mwaInitArrayPlusWord mwa wa = go 0# + where + sz = wordArraySize# wa + go i carry s + | isTrue# (i ># sz) = s + | isTrue# (i ==# sz) = mwaWriteOrShrink mwa carry i s + | 0## <- carry = -- copy higher remaining words and shrink the mwa + case mwaArrayCopy# mwa i wa i (sz -# i) s of + s2 -> mwaShrink# mwa 1# s2 + | True = let !(# l,c #) = addWordC# (indexWordArray# wa i) carry + in case mwaWrite# mwa i l s of + s2 -> go (i +# 1#) (int2Word# c) s2 + +-- | Write the most-significant Word: +-- * if it is 0: shrink the array of 1 Word +-- * otherwise: write it +mwaWriteOrShrink :: MutableWordArray# s -> Word# -> Int# -> State# s -> State# s +mwaWriteOrShrink mwa 0## _i s = mwaShrink# mwa 1# s +mwaWriteOrShrink mwa w i s = mwaWrite# mwa i w s + +-- | Compute the index of the most-significant Word and write it. +mwaWriteMostSignificant :: MutableWordArray# s -> Word# -> State# s -> State# s +mwaWriteMostSignificant mwa w s = + case mwaSize# mwa s of + (# s', sz #) -> mwaWriteOrShrink mwa w (sz -# 1#) s' + +-- | MutableWordArray <- zipWith op wa1 wa2 +-- +-- Required output: Size(MutableWordArray) = min Size(wa1) Size(wa2) +mwaInitArrayBinOp :: MutableWordArray# s -> WordArray# -> WordArray# -> (Word# -> Word# -> Word#) -> State# s -> State#s +mwaInitArrayBinOp mwa wa wb op s = go 0# s + where + !sz = minI# (wordArraySize# wa) (wordArraySize# wb) + go i s' + | isTrue# (i ==# sz) = s' + | True = + case indexWordArray# wa i `op` indexWordArray# wb i of + v -> case mwaWrite# mwa i v s' of + s'' -> go (i +# 1#) s'' + +-- | Write an element of the MutableWordArray +mwaWrite# :: MutableWordArray# s -> Int# -> Word# -> State# s -> State# s +mwaWrite# = writeWordArray# + +-- | Fill some part of a MutableWordArray with the given Word# +mwaFill# :: MutableWordArray# s -> Word# -> Word# -> Word# -> State# s -> State# s +mwaFill# _ _ _ 0## s = s +mwaFill# mwa v off n s = case mwaWrite# mwa (word2Int# off) v s of + s' -> mwaFill# mwa v (off `plusWord#` 1##) (n `minusWord#` 1##) s' + +-- | Add Word# inplace (a the specified offset) in the mwa with carry propagation. +mwaAddInplaceWord# :: MutableWordArray# d -> Int# -> Word# -> State# d -> State# d +mwaAddInplaceWord# _ _ 0## s = s +mwaAddInplaceWord# mwa i y s = case readWordArray# mwa i s of + (# s1, x #) -> let !(# h,l #) = plusWord2# x y + in case mwaWrite# mwa i l s1 of + s2 -> mwaAddInplaceWord# mwa (i +# 1#) h s2 + +-- | Sub Word# inplace (at the specified offset) in the mwa with carry +-- propagation. +-- +-- Return True# on overflow +mwaSubInplaceWord# + :: MutableWordArray# d + -> Int# + -> Word# + -> State# d + -> (# State# d, Bool# #) +mwaSubInplaceWord# mwa ii iw s1 = case mwaSize# mwa s1 of + (# is, sz #) -> + let + go _ 0## s = (# s, 0# #) -- no overflow + go i y s + | isTrue# (i >=# sz) = (# s, 1# #) -- overflow + | True = case readWordArray# mwa i s of + (# s1, x #) -> let !(# l,h #) = subWordC# x y + in case mwaWrite# mwa i l s1 of + s2 -> go (i +# 1#) (int2Word# h) s2 + in go ii iw is + + +-- | Trim `a` of `k` less significant limbs and then compare the result with `b` +-- +-- "mwa" doesn't need to be trimmed +mwaTrimCompare :: Int# -> MutableWordArray# s -> WordArray# -> State# s -> (# State# s, Ordering #) +mwaTrimCompare k mwa wb s1 + | (# s, szA #) <- mwaSize# mwa s1 + , szB <- wordArraySize# wb + = + let + go i s + | isTrue# (i <# 0#) = (# s, EQ #) + | True = case readWordArray# mwa (i +# k) s of + (# s2, ai #) -> + let bi = if isTrue# (i >=# szB) + then 0## + else indexWordArray# wb i + in if | isTrue# (ai `gtWord#` bi) -> (# s2, GT #) + | isTrue# (bi `gtWord#` ai) -> (# s2, LT #) + | True -> go (i -# 1#) s2 + + szTrimA = szA -# k + + in if | isTrue# (szTrimA <# szB) -> (# s, LT #) + | True -> go (szA -# k -# 1#) s + + +-- | Sub array inplace (at the specified offset) in the mwa with carry propagation. +-- +-- We don't trim the resulting array! +-- +-- Return True# on overflow. +mwaSubInplaceArray :: MutableWordArray# d -> Int# -> WordArray# -> State# d -> (# State# d, Bool# #) +mwaSubInplaceArray mwa off wb = go (wordArraySize# wb -# 1#) + where + go i s + | isTrue# (i <# 0#) = (# s, 0# #) -- no overflow + | True + = case mwaSubInplaceWord# mwa (off +# i) (indexWordArray# wb i) s of + (# s2, 0# #) -> go (i -# 1#) s2 + (# s2, _ #) -> (# s2, 1# #) -- overflow + +-- | Add array inplace (a the specified offset) in the mwa with carry propagation. +-- +-- Upper bound of the result mutable aray is not checked against overflow. +mwaAddInplaceArray :: MutableWordArray# d -> Int# -> WordArray# -> State# d -> State# d +mwaAddInplaceArray mwa off wb = go 0# 0## + where + !maxi = wordArraySize# wb + go i c s + | isTrue# (i ==# maxi) = mwaAddInplaceWord# mwa (i +# off) c s + | True + = case readWordArray# mwa (i +# off) s of + (# s, v #) -> case plusWord3# v (indexWordArray# wb i) c of + (# c', v' #) -> case writeWordArray# mwa (i +# off) v' s of + s -> go (i +# 1#) c' s + +-- | Sub array inplace (at the specified offset) in the mwa with carry propagation. +-- +-- We don't trim the resulting array! +-- +-- Return True# on overflow. +mwaSubInplaceMutableArray :: MutableWordArray# d -> Int# -> MutableWordArray# d -> State# d -> (# State# d, Bool# #) +mwaSubInplaceMutableArray mwa off mwb s0 = + case mwaSize# mwb s0 of + (# s1, szB #) -> go (szB -# 1#) s1 + where + go i s + | isTrue# (i <# 0#) = (# s, 0# #) -- no overflow + | True + = case readWordArray# mwb i s of + (# s1, bi #) -> case mwaSubInplaceWord# mwa (off +# i) bi s1 of + (# s2, 0# #) -> go (i -# 1#) s2 + (# s2, _ #) -> (# s2, 1# #) -- overflow + +-- | Sub an array inplace and then trim zeroes +-- +-- Don't check overflow. The caller must ensure that a>=b +mwaSubInplaceArrayTrim :: MutableWordArray# d -> Int# -> WordArray# -> State# d -> State# d +mwaSubInplaceArrayTrim mwa off wb s = + case mwaSubInplaceArray mwa off wb s of + (# s', _ #) -> mwaTrimZeroes# mwa s' + + +-- | Read an indexed Word in the MutableWordArray. If the index is out-of-bound, +-- return zero. +mwaReadOrZero :: MutableWordArray# s -> Int# -> State# s -> (# State# s, Word# #) +mwaReadOrZero mwa i s = case mwaSize# mwa s of + (# s2, sz #) + | isTrue# (i >=# sz) -> (# s2, 0## #) + | isTrue# (i <# 0#) -> (# s2, 0## #) + | True -> readWordArray# mwa i s2 + +mwaRead# :: MutableWordArray# s -> Int# -> State# s -> (# State# s, Word# #) +mwaRead# = readWordArray# |