From 807ac03a6efa9fb722656383075f7a9a389922bb Mon Sep 17 00:00:00 2001 From: yenru0 Date: Thu, 13 Nov 2025 10:10:10 +0900 Subject: [PATCH] complement in 11.13 --- notes/8.md | 34 +++++++++++++++++++++++++++++++++- notes/9.md | 28 ++++++++++++++++++++++++++++ pdf/L9.pdf | Bin 0 -> 713664 bytes 3 files changed, 61 insertions(+), 1 deletion(-) create mode 100644 notes/9.md create mode 100644 pdf/L9.pdf diff --git a/notes/8.md b/notes/8.md index 4096325..e86d7bb 100644 --- a/notes/8.md +++ b/notes/8.md @@ -64,4 +64,36 @@ Analysis of Reaching Definition Effect of an Instruction -`IN[b]` and `OUT[b]` \ No newline at end of file +`IN[b]` and `OUT[b]` + +Meet Operator + +`IN[b] = union(OUT[p1]...OUT[pn])` + +```c +// init +OUT[entry] = {} + + + +``` + +## Liveness Analysis + +Liveness is the concept the variable is used in the future. It helps **eliminating dead code**. + +Transfer function + +* `USE[b]` set of variables used in `b` +* `DEF[b]` set of variables defined in `b` + +so transfer function `f_b` for a basic block b: +```IN[b] = USE[b] + (OUT[b] - DEF[b])``` + +for reaching defintion + +```OUT[b] = union(INs)``` + +For supporting cyclic graphs, repeated computation is needed. + + diff --git a/notes/9.md b/notes/9.md new file mode 100644 index 0000000..33c5358 --- /dev/null +++ b/notes/9.md @@ -0,0 +1,28 @@ +# Control Flow Analysis + +Dominator + +for a given CFG **a node `x` dominates a node `y`** if every path from the Entry block to `y` contains `x`. + +* Each BB dominates itself +* If `x dom y` and `y dom z` then `x dom z` +* If `x dom z` and `y dom z` then either `x dom y` or `y dom x` + +Dominator Tree +* initial node is a root +* `x dom y` means that "`y` is a child of `x`" + + +Natural Loops + +How to Find Natural Loop?: Introduction Backedge + +Important concepts in a loop +* Header and Loop BB +* Back Edges +* Exit Edges +* Preheader (Preloop) + +Loop-Invariant Computation + + diff --git a/pdf/L9.pdf b/pdf/L9.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b8a706ab65c3627dcc2c31bf99a3c52fd8b1e1c7 GIT binary patch literal 713664 zcmdqJbyQu;vNwto+zAB90)p$p-Q696+X5Eu?iwTnCjo*x!QCOj65L%v0t5{nG<*x# zd!OW-ea`pZxcA*L-sKPGT(hgYt7~>w|7uoOQ7Vf|G6I>n(2yzXAb)7cKmZHC-oy$G znV+9o-O~ZYEN1LtY-4Z1tZZxnat5$MidC8AjqNOGKz6hMW;GWlS5p^tClE;0-rfZO z-7YANuW_NdYCR2MGdnYD)CkqJ89V0YiP9S3!dnaCiv@+oCPr=yE)!f+B#nlPq z#495qcK^)Y3}nOmN6X?MXO{=Ql%4F&!8RZO8$0{GJOl;x0n7>@7h^MstnQvZj9C*5 zatApnJAuqWP9Qr|h%_KY?04c26huP?*_qwT`L2cE1b#1QW-)tLI~M>uC$k*b%vl$3 z-y%esceMdPj)x1^{e|_uNdPP7{jUdk1K1wQ*m&+AvfsT`RloyZ0QQIK><=XD4Og0l$j>j+=iGKV-5)-k8fDvt1SBZ13s>d4G`EDdFKFrRHMn0)pI2sc``AIfUGC z1Md5POlV1aI~PcyBoJ`V6|*EOgweb4K+3e0Osqhrcf~TckmbY!xE~Ot05YRY)j%$~ z%#c~mtPb*Uc_0vdxQIPmWbQbJ%ri5vv8cU=E~HHs01qb%fP@SuyRn&iGK;A(i-X+2rXa||fwcRuk{<@{3}E?HMt3d# 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