Changes between Version 7 and Version 8 of PrimBool
 Timestamp:
 Jan 28, 2013 3:36:09 PM (2 years ago)
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PrimBool
v7 v8 51 51 52 52 and in following assembler code: 53 54 53 {{{ 55 54 .Lc1rf: … … 80 79 There are five possible branches to take, although four of them have the same result. This is caused by code duplication introduced by caseofcase transform (see [http://ics.p.lodz.pl/~stolarek/blog/2013/01/takingmagicoutofghcortracingcompilationbytransformation/ this blog post] for a step by step derivation). According to Ben Lippmeier, who submitted the original bug report, mispredicted branches are bad in object code because they stall the pipeline. 81 80 82 == Possible solutions and their consequences ==81 == Workarounds == 83 82 84 Unnecessary branches could be eliminated by introducing primitive logical operators AND, OR and NOT (they will be denoted as `#`, `&&#` and `not#` respectively). These operators would be strict and treat their logical parameters as unboxed integers (`1#` for `True` and `0#` for `False`). Result would be produced by using lowlevel bitwise operations. This means that if logical operators were chained together like in a given example only the final result would have to be inspected and thus only one branch would be necessary. 83 It is possible to work around the issue of code duplication by using GHC primops `tagToEnum#` and `dataToTag#`. These allow to distinguish between `True` and `False` by means of accessing the tag of a data type constructor. This means that `dataToTag#` can convert `True` to `1#` and `False` to `0#`, while `tagToEnum#` does the opposite (see paper [http://research.microsoft.com/enus/um/people/simonpj/papers/ptrtag/index.htm "Faster Laziness Using Dynamic Pointer Tagging"] for more details): 85 84 86 Note (Jan Stolarek): My first thought was that introducing primitve logical operators will require changing `Bool` data type to a primitive unboxed version. This might not be the case. Please treat two solution apporaches as possibly wrong. 87 88 === First approach === 89 90 Treat `Bool` as a boxed version of primitive `Bool#`. `True` would be equivalent of `B# True#`, `False` of `B# False#`: 91 {{{ 92 data Bool = B# True#  B# False# 93 94  B# :: Bool# > Bool 85 {{{ 86 ghci> import GHC.Exts 87 ghci> import GHC.Prim 88 ghci> :set XMagicHash 89 ghci> I# (dataToTag# True) 90 1 91 ghci> I# (dataToTag# False) 92 0 93 ghci> (tagToEnum# 0#) :: Bool 94 False 95 ghci> (tagToEnum# 1#) :: Bool 96 True 97 ghci> 95 98 }}} 96 99 97 Not sure if this can be considered equivalent to what the Haskell Report says about Bool. We need to ensure that `Bool#` is populated only by `True#` and `False#` and that these two are translated to `1#` and `0#` in the Core. It should be **impossible** to write such a function at Haskell level: 100 Having the possibility of converting `Bool` to an unboxed `Int#` allows us to compute results of logical expression by means of logical bitwise operations. The result can be converted back to a `Bool` so this is transparent on the Haskell source level, except for the fact that defined logical binary operators will be strict in both their arguments. 101 102 '''NOTE: Validity of this solution is based on assumption that `True` will always have a tag of `1#`, while `False` will have a tag of `0#`. Changing this invariant in the future would make these primitive logical operators invalid.''' 103 104 === First workaround === 105 106 First workaround assumes converting each result of comparison into an unboxed `Int` and replacing `` with `+#`: 98 107 99 108 {{{ 100 g :: Bool > Int > Int 101 g (B# b) (I# i) = I# (b + i) 109 case (dataToTag# (x <# 0#)) +# (dataToTag# (x >=# width)) +# 110 (dataToTag# (y <# 0#)) +# (dataToTag# (y >=# height)) of 111 0# > E2  note that branch order is reversed 112 _ > E1 102 113 }}} 103 114 104 This approach might require one additional case expression to inspect the value of `Bool` at the Core level. For example:115 This compiles to: 105 116 106 117 {{{ 107 f :: Int > Int > Int 108 f x y = if x > y 109 then x 110 else y 111 }}} 112 113 would compile to: 114 115 {{{ 116 case x of _ { I# xP > 117 case y of _ { I# yP > 118 case ># xP yP of _ { 119 B# bP > case bP of _ { 1# > e1; 0# > e2 } 120 } 121 } 118 case +# 119 (+# 120 (+# (dataToTag# (<# x 0)) (dataToTag# (>=# x width))) 121 (dataToTag# (<# y 0))) 122 (dataToTag# (>=# y height)) 123 of _ { 124 __DEFAULT > E1; 125 0 > E2 122 126 } 123 127 }}} 124 128 125 This would complicate Core a bit but it should be possible to compile such Core to exactly the same result as with normal `Bool`. This code assumes that `>#` has type `Int# > Int# > Bool`, but to truly avoid branching in the Core we need `.># :: Int# > Int# > Bool#` so that we get a primitive value that doesn't need to be inspected using case expression but can be directly used by primitive logical operators. 126 127 === Second approach === 129 Similarly we can convert logical && into multiplication. 128 130 129 Second approach assumes creating type `Bool#` that is independent of type `Bool`. Boxing and unboxing would have to be done explicitly via additional functions: 131 === Second workaround === 132 133 The above workaround is a bit clumsy: `dataToTag#`s make the code verbose and it may not be very obvious what the code is doing. Hence the second workaround, that defines an alternative logical `or` operator: 130 134 131 135 {{{ 132 data Bool = True  False  no changes here 133 134 bBox :: Bool# > Bool 135 bBox 1# = True 136 bBox 0# = False 137 138 bUnbox :: Bool > Bool# 139 bUnbox True = 1# 140 bUnbox False = 0# 136 (#) :: Bool > Bool > Bool 137 (#) x y = let xW = int2Word# (dataToTag# x) 138 yW = int2Word# (dataToTag# y) 139 zI = word2Int# (yW `or#` xW) 140 in tagToEnum# zI 141 141 }}} 142 142 143 `Bool#` could not be implemented as an ADT because it is unlifted and unboxed, while ADT value constructors need to be boxed and lifted (see comments in [[GhcFile(compiler/types/TyCon.lhs)]]). There would need to be some magical way of ensuring that `Bool#` is populated only by `#0` and `1#` and that these values cannot be mixed with unboxed integers. Perhaps this could be done by preventing programmer from explicitly creating values of that type (can this be done?) and allow her only to use values returned from functions. 143 This operator is defined in terms of primops `dataToTag#`, `tagToEnum#` and a bitwise or primop `or#`. Since the last one operates only on `Word`s we need to use `int2Word#` and `word2Int#` for conversion between these data types. Luckily, GHC does a good job of removing unnecessary conversions between data types. This means that: 144 144 145 Another problem with this approach is that it would introduce primitive logical operations # and &&# with type `Int# > Int# > Int#`  it is questionable whether anyone would want such operations available to the programmer. I think it is desirable to have primitive logical operators of type `Bool# > Bool# > Bool#`. 145 {{{ 146 case (x <# 0#) # (x >=# width) # (y <# 0#) # (y >=# height) of 147 True > E1 148 False > E2 149 }}} 150 151 compiles to: 152 153 {{{ 154 case tagToEnum# 155 (word2Int# 156 (or# 157 (int2Word# (dataToTag# (>=# y height))) 158 (or# 159 (int2Word# (dataToTag# (<# y 0))) 160 (or# 161 (int2Word# (dataToTag# (>=# x width))) 162 (int2Word# (dataToTag# (<# x 0))))))) 163 of _ { 164 False > E2; 165 True > E1 166 } 167 }}} 168 169 Primitive logical operators `&&#` and `not#` can be defined in a similar matter. 170 171 == Solutions == 172 173 It seems that the best solution to the problem would be implementing second of the above workarounds as a separate primop. Alternatively we can implement primitive bitwise `or`, `and` and `xor` that work on `Int`s instead of `Word`s and define new logical operators using bitwise operators in one of the libraries. 146 174 147 175 == Places of interest in the source code == 148 176 149 The file [[GhcFile(prelude/primops.txt.pp)]] defines !PrimOps and their type signatures. An example definition looks like this: 150 151 {{{ 152 primop IntGtOp ">#" Compare Int# > Int# > Bool 153 with fixity = infix 4 154 }}} 155 156 Existing definitions should remain unchanged or the code using them would break and that is a Very Bad Thing. This would require creating new !PrimOps: 157 158 {{{ 159 primop IntGtOpB ".>#" Compare Int# > Int# > Bool# 160 with fixity = infix 4 161 }}} 162 163 The tricky part here is `Compare`. This a value constructor of `PrimOpInfo` data type defined in [[GhcFile(prelude/PrimOp.lhs)]]: 164 165 {{{ 166 data PrimOpInfo 167 = Dyadic OccName  string :: T > T > T 168 Type 169  Monadic OccName  string :: T > T 170 Type 171  Compare OccName  string :: T > T > Bool 172 Type 173  GenPrimOp OccName  string :: \/a1..an . T1 > .. > Tk > T 174 [TyVar] 175 [Type] 176 Type 177 }}} 178 179 We would need new `PrimOpInfo` value to denote !PrimOps of type `T > T > Bool#`. Appropriate functions like `primOpSig` and `getPrimOpResultInfo` would have to be adjusted accordingly. 177 The file [[GhcFile(prelude/primops.txt.pp)]] defines !PrimOps and their type signatures.