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Already sorry in advance for all the bad C jokes that are going to be part of this section \texttt{C} is a compiled, low-level programming language, lacking many features modern high-level programming languages offer, like Object Oriented programming, true Functional Programming, Garbage Collection, complex abstract datatypes and vectors, just to name a few. 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zPgMD^*A+0M?g|(_m)K-5O!`7l5lsnL^a*yDy@rCwT4pJmIfkPhriaUHMp{3SHa)}v zrcy>qj!6_9pvy?~c3gvY+VP@tlo|J~DUlBG(Y>!feF{A7X~ zU}g4u+elqPN3N66^IJKx#eSDqXS(^n%4%m9LnjvxCsQ*79(FJXCjvFKn1VRMe*owH Ba3TNz diff --git a/semester3/spca/spca-summary.tex b/semester3/spca/spca-summary.tex index c9c1598..bc394a6 100644 --- a/semester3/spca/spca-summary.tex +++ b/semester3/spca/spca-summary.tex @@ -54,7 +54,20 @@ % │ Content │ % ╰────────────────────────────────────────────────╯ % ── Intro to C ────────────────────────────────────────────────────── -\input{parts/intro-to-c/start.tex} +\newsection +\section{The C Programming Language} +\input{parts/00_c/00_intro.tex} +% ── Intro to x86 asm ──────────────────────────────────────────────── +\newsection +\section{x86 Assembly} +\input{parts/01_asm/00_intro.tex} + + +% ── Hardware recap ────────────────────────────────────────────────── +\newsection +\section{Hardware} +\input{parts/02_hw/00_intro.tex} + \end{document} From c7618f38a44903ae58566a399647df5e94453eab Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sun, 4 Jan 2026 12:09:01 +0100 Subject: [PATCH 3/6] [SPCA] Start C syntax summary --- semester3/spca/code-examples/.clang-format | 276 ++++++++++++++++++ .../code-examples/00_c/01_syntax/00_intro.c | 16 + .../code-examples/00_c/01_syntax/01_func.c | 37 +++ .../code-examples/00_c/01_syntax/01_func.h | 4 + semester3/spca/parts/00_c/00_intro.tex | 13 +- semester3/spca/parts/00_c/01_syntax.tex | 6 + semester3/spca/spca-summary.pdf | Bin 115261 -> 156730 bytes semester3/spca/spca-summary.tex | 5 +- 8 files changed, 350 insertions(+), 7 deletions(-) create mode 100644 semester3/spca/code-examples/.clang-format create mode 100644 semester3/spca/code-examples/00_c/01_syntax/00_intro.c create mode 100644 semester3/spca/code-examples/00_c/01_syntax/01_func.c create mode 100644 semester3/spca/code-examples/00_c/01_syntax/01_func.h create mode 100644 semester3/spca/parts/00_c/01_syntax.tex diff --git a/semester3/spca/code-examples/.clang-format b/semester3/spca/code-examples/.clang-format new file mode 100644 index 0000000..ea63d60 --- /dev/null +++ b/semester3/spca/code-examples/.clang-format @@ -0,0 +1,276 @@ +# ───────────────────────────────────────────────────────────────────── +# ╭─────────────────────────────────────────────────╮ +# │ clang-format config │ +# ╰─────────────────────────────────────────────────╯ +# ───────────────────────────────────────────────────────────────────── +BasedOnStyle: LLVM +AccessModifierOffset: -2 +AlignAfterOpenBracket: BlockIndent +AlignArrayOfStructures: Left +AlignConsecutiveAssignments: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionPointers: false + PadOperators: true +AlignConsecutiveBitFields: + Enabled: true + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveDeclarations: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveMacros: + Enabled: true + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveShortCaseStatements: + Enabled: true + AcrossEmptyLines: false + AcrossComments: false + AlignCaseArrows: false + AlignCaseColons: false +AlignConsecutiveTableGenBreakingDAGArgColons: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveTableGenCondOperatorColons: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveTableGenDefinitionColons: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionPointers: false + PadOperators: false +AlignEscapedNewlines: Right +AlignOperands: Align +AlignTrailingComments: + Kind: Always + OverEmptyLines: 0 +AllowAllArgumentsOnNextLine: true +AllowAllParametersOfDeclarationOnNextLine: true +AllowBreakBeforeNoexceptSpecifier: Never +AllowShortBlocksOnASingleLine: Never +AllowShortCaseExpressionOnASingleLine: true +AllowShortCaseLabelsOnASingleLine: false +AllowShortCompoundRequirementOnASingleLine: true +AllowShortEnumsOnASingleLine: true +AllowShortFunctionsOnASingleLine: Empty +AllowShortIfStatementsOnASingleLine: Never +AllowShortLambdasOnASingleLine: All +AllowShortLoopsOnASingleLine: false +AlwaysBreakAfterDefinitionReturnType: None +AlwaysBreakBeforeMultilineStrings: false +AttributeMacros: + - __capability +BinPackArguments: false +BinPackParameters: false +BitFieldColonSpacing: Both +BraceWrapping: + AfterCaseLabel: false + AfterClass: false + AfterControlStatement: Never + AfterEnum: false + AfterFunction: false + AfterNamespace: false + AfterObjCDeclaration: false + AfterStruct: true + AfterUnion: false + AfterExternBlock: false + BeforeCatch: false + BeforeElse: false + BeforeLambdaBody: false + BeforeWhile: false + IndentBraces: false + SplitEmptyFunction: true + SplitEmptyRecord: true + SplitEmptyNamespace: true +BreakAdjacentStringLiterals: true +BreakAfterAttributes: Always +BreakAfterJavaFieldAnnotations: false +BreakAfterReturnType: None +BreakArrays: true +BreakBeforeBinaryOperators: All +BreakBeforeBraces: Attach +BreakBeforeConceptDeclarations: Always +BreakBeforeInlineASMColon: OnlyMultiline +BreakBeforeTernaryOperators: true +BreakConstructorInitializers: BeforeColon +BreakFunctionDefinitionParameters: false +BreakInheritanceList: BeforeColon +BreakStringLiterals: true +BreakTemplateDeclarations: MultiLine +ColumnLimit: 100 +CommentPragmas: "^ IWYU pragma:" +CompactNamespaces: false +ConstructorInitializerIndentWidth: 4 +ContinuationIndentWidth: 4 +Cpp11BracedListStyle: true +DerivePointerAlignment: true +DisableFormat: false +EmptyLineAfterAccessModifier: Never +EmptyLineBeforeAccessModifier: Always +ExperimentalAutoDetectBinPacking: false +FixNamespaceComments: true +ForEachMacros: + - foreach + - Q_FOREACH + - BOOST_FOREACH +IfMacros: + - KJ_IF_MAYBE +IncludeBlocks: Preserve +IncludeCategories: + - Regex: ^"(llvm|llvm-c|clang|clang-c)/ + Priority: 2 + SortPriority: 0 + CaseSensitive: false + - Regex: ^(<|"(gtest|gmock|isl|json)/) + Priority: 3 + SortPriority: 0 + CaseSensitive: false + - Regex: .* + Priority: 1 + SortPriority: 0 + CaseSensitive: false +IncludeIsMainRegex: (Test)?$ +IncludeIsMainSourceRegex: "" +IndentAccessModifiers: true +IndentCaseBlocks: true +IndentCaseLabels: true +IndentExternBlock: AfterExternBlock +IndentGotoLabels: true +IndentPPDirectives: BeforeHash +IndentRequiresClause: true +IndentWidth: 4 +IndentWrappedFunctionNames: true +InsertBraces: false +InsertNewlineAtEOF: false +InsertTrailingCommas: None +IntegerLiteralSeparator: + Binary: 0 + BinaryMinDigits: 0 + Decimal: 0 + DecimalMinDigits: 0 + Hex: 0 + HexMinDigits: 0 +JavaScriptQuotes: Leave +JavaScriptWrapImports: true +KeepEmptyLines: + AtEndOfFile: false + AtStartOfBlock: true + AtStartOfFile: true +LambdaBodyIndentation: Signature +LineEnding: DeriveLF +MacroBlockBegin: "" +MacroBlockEnd: "" +MainIncludeChar: Quote +MaxEmptyLinesToKeep: 1 +NamespaceIndentation: None +ObjCBinPackProtocolList: Auto +ObjCBlockIndentWidth: 2 +ObjCBreakBeforeNestedBlockParam: true +ObjCSpaceAfterProperty: false +ObjCSpaceBeforeProtocolList: true +PPIndentWidth: -1 +PackConstructorInitializers: BinPack +PenaltyBreakAssignment: 2 +PenaltyBreakBeforeFirstCallParameter: 19 +PenaltyBreakComment: 300 +PenaltyBreakFirstLessLess: 120 +PenaltyBreakOpenParenthesis: 0 +PenaltyBreakScopeResolution: 500 +PenaltyBreakString: 1000 +PenaltyBreakTemplateDeclaration: 10 +PenaltyExcessCharacter: 1000000 +PenaltyIndentedWhitespace: 0 +PenaltyReturnTypeOnItsOwnLine: 60 +PointerAlignment: Right +QualifierAlignment: Left +ReferenceAlignment: Pointer +ReflowComments: true +RemoveBracesLLVM: true +RemoveParentheses: MultipleParentheses +RemoveSemicolon: false +RequiresClausePosition: OwnLine +RequiresExpressionIndentation: OuterScope +SeparateDefinitionBlocks: Always +ShortNamespaceLines: 1 +SkipMacroDefinitionBody: false +SortIncludes: CaseSensitive +SortJavaStaticImport: Before +SortUsingDeclarations: LexicographicNumeric +SpaceAfterCStyleCast: true +SpaceAfterLogicalNot: false +SpaceAfterTemplateKeyword: true +SpaceAroundPointerQualifiers: Default +SpaceBeforeAssignmentOperators: true +SpaceBeforeCaseColon: false +SpaceBeforeCpp11BracedList: true +SpaceBeforeCtorInitializerColon: true +SpaceBeforeInheritanceColon: true +SpaceBeforeJsonColon: false +SpaceBeforeParens: ControlStatements +SpaceBeforeParensOptions: + AfterControlStatements: true + AfterForeachMacros: true + AfterFunctionDeclarationName: true + AfterFunctionDefinitionName: true + AfterIfMacros: true + AfterOverloadedOperator: false + AfterPlacementOperator: true + AfterRequiresInClause: false + AfterRequiresInExpression: false + BeforeNonEmptyParentheses: false +SpaceBeforeRangeBasedForLoopColon: true +SpaceBeforeSquareBrackets: false +SpaceInEmptyBlock: false +SpacesBeforeTrailingComments: 1 +SpacesInAngles: Never +SpacesInContainerLiterals: true +SpacesInLineCommentPrefix: + Minimum: 1 + Maximum: -1 +SpacesInParens: Custom +SpacesInParensOptions: + ExceptDoubleParentheses: false + InConditionalStatements: true + InCStyleCasts: false + InEmptyParentheses: false + Other: true +SpacesInSquareBrackets: true +Standard: Latest +StatementAttributeLikeMacros: + - Q_EMIT +StatementMacros: + - Q_UNUSED + - QT_REQUIRE_VERSION +TabWidth: 4 +TableGenBreakInsideDAGArg: DontBreak +UseTab: Never +VerilogBreakBetweenInstancePorts: true +WhitespaceSensitiveMacros: + - BOOST_PP_STRINGIZE + - CF_SWIFT_NAME + - NS_SWIFT_NAME + - PP_STRINGIZE + - STRINGIZE diff --git a/semester3/spca/code-examples/00_c/01_syntax/00_intro.c b/semester3/spca/code-examples/00_c/01_syntax/00_intro.c new file mode 100644 index 0000000..f503d99 --- /dev/null +++ b/semester3/spca/code-examples/00_c/01_syntax/00_intro.c @@ -0,0 +1,16 @@ +// This is a line comment +/* this is a block comment */ +#include "01_func.h" // Relative import + +int i = 0; // This allocates an integer on the stack + +int main( int argc, char *argv[] ) { + // This is the function body of a function (here the main function) + // which serves as the entrypoint to the program in C and has arguments + printf( "Argc: %d\n", argc ); // Number of arguments passed, always >= 1 + // (first argument is the executable name) + for ( int i = 0; i < argc; i++ ) // For loop just like any other sane programming language + printf( "Arg %d: %s\n", i, argv[ i ] ); // Outputs the i-th argument from CLI + + get_user_input_int( "Select a number" ); +} diff --git a/semester3/spca/code-examples/00_c/01_syntax/01_func.c b/semester3/spca/code-examples/00_c/01_syntax/01_func.c new file mode 100644 index 0000000..63df54d --- /dev/null +++ b/semester3/spca/code-examples/00_c/01_syntax/01_func.c @@ -0,0 +1,37 @@ +#include "01_func.h" + +int get_user_input_int( char prompt[] ) { + int input_data; + printf( "%s", prompt ); // Always wrap strings like this for printf + scanf( "%d", &input_data ); // Get user input from CLI + + // If statements just like any other language + if ( input_data ) + printf( "Not 0" ); + else + printf( "Input is zero" ); + + switch ( input_data ) { + case 5: + printf( "You win!" ); + break; // Doesn't fall through + case 6: + printf( "You were close" ); // Falls through + default: + printf( "No win" ); // Case for any not covered input + } + + int input_data_copy = input_data; + + while ( input_data > 1 ) { + input_data -= 1; + printf( "Hello World" ); + } + + do { + input_data -= 1; + printf( "Bye World" ); + } while ( input_data_copy > 1 ); + + return 0; +} diff --git a/semester3/spca/code-examples/00_c/01_syntax/01_func.h b/semester3/spca/code-examples/00_c/01_syntax/01_func.h new file mode 100644 index 0000000..f0e9cb1 --- /dev/null +++ b/semester3/spca/code-examples/00_c/01_syntax/01_func.h @@ -0,0 +1,4 @@ +#include // Import from system path + // (like library imports in other languages) + +int get_user_input_int( char prompt[] ); diff --git a/semester3/spca/parts/00_c/00_intro.tex b/semester3/spca/parts/00_c/00_intro.tex index 90e44f4..7e75a14 100644 --- a/semester3/spca/parts/00_c/00_intro.tex +++ b/semester3/spca/parts/00_c/00_intro.tex @@ -1,8 +1,13 @@ I can clearly C why you'd want to use C. Already sorry in advance for all the bad C jokes that are going to be part of this section -\texttt{C} is a compiled, low-level programming language, lacking many features modern high-level programming languages offer, like Object Oriented programming, true Functional Programming, Garbage Collection, complex abstract datatypes and vectors, just to name a few. (It is possible to replicate these, more on this later). +\texttt{C} is a compiled, low-level programming language, lacking many features modern high-level programming languages offer, like Object Oriented programming, +true Functional Programming (like Haskell implements), Garbage Collection, complex abstract datatypes and vectors, just to name a few. +(It is possible to replicate these using Preprocessor macros, more on this later). -On the other hand, it offers the ability to directly integrate assembly code into the \texttt{.c} files, as well as bit level data manipulation and extensive memory management options, again just to name a few. +On the other hand, it offers the ability to directly integrate assembly code into the \texttt{.c} files, +as well as bit level data manipulation and extensive memory management options, again just to name a few. -This of course leads to \texttt{C} performing excellently and there are many programming languages who's compiler doesn't directly produce machine code or assembly, but instead optimized \texttt{C} code that is then compiled into machine code using a \texttt{C} compiler. -This has a number of benefits, most notably that \texttt{C} compilers can produce very efficient assembly, as lots of effort is put into the \texttt{C} compilers by the hardware manufacturers. +This of course leads to \texttt{C} performing excellently and there are many programming languages who's compiler doesn't directly produce machine code or assembly, +but instead optimized \texttt{C} code that is then compiled into machine code using a \texttt{C} compiler. +This has a number of benefits, most notably that \texttt{C} compilers can produce very efficient assembly, +as lots of effort is put into the \texttt{C} compilers by the hardware manufacturers. diff --git a/semester3/spca/parts/00_c/01_syntax.tex b/semester3/spca/parts/00_c/01_syntax.tex new file mode 100644 index 0000000..2193dba --- /dev/null +++ b/semester3/spca/parts/00_c/01_syntax.tex @@ -0,0 +1,6 @@ +\subsection{The Syntax} +\texttt{C} uses a very similar syntax as many other programming languages, like \texttt{Java}, \texttt{JavaScript} and many more\dots +to be precise, it is \textit{them} that use the \texttt{C} syntax, not the other way around. So: +\inputcodewithfilename{c}{code-examples/00_c/01_syntax/}{00_intro.c} +\inputcodewithfilename{c}{code-examples/00_c/01_syntax/}{01_func.h} +\inputcodewithfilename{c}{code-examples/00_c/01_syntax/}{01_func.c} diff --git a/semester3/spca/spca-summary.pdf b/semester3/spca/spca-summary.pdf index e08d2c3a7e8eb3b26024ed2ed5d45df6c28f089a..4101d0b9fe78345eae6c0d53531061d1447a290c 100644 GIT binary patch delta 103178 zcmZU(Q*fYdu&y23wr$(CIq}4{@y51oOsq*Vv2AN&PHba;YuCU2lYMsg$y3!;-FJ6i z^>l|qcZ|U{NWp?~rLZEPgL83lr=Wt-0%;oZ>YE}6J@48V^ZETb{@%phs^KRfMRCfI zNclr3893^~8|A${KWxz#6nGvIYqZjZWD82o53^WYi2P?t#R7d$Kp`G^5HA~^0C#Iyh}@A-CRbq z(B)C~N=@Q1aGL)J?jmbGl^+uGC(bk7l0z-})foOh&{B>?!=j-6a*6HG)IA^?6c*CJ zNI*v-kg{ZsD;rj_@&n?|Oa{s90VuO9dPq+ck>YtCA!A`ikS!}-DO?RFDQbgIoQd6V z4}M8yl~+Sj)x6Pr`qX>2W_!K*%-EGZQS_%NOr^P$XPIC_0%PYe1q-^L{CLAC%#6H7JJ>&f5Sa}*HuG`y_Km-@1Ngc>X;4b* ze`(;waD!YA$|zBK;v5IbV`eUNjy&HUq3>EU7;=NdN#^tcQ5i*pBf(xS>Rk}_JG<+g z)dl#=Y%oXHE)bd82J5PFDH{EkH8!0@h}qC1NApmHgs_C5(E-dUnvZNV5U9EH2vCd9 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zAt)w_AXqag@Fj8o8ny4#vM&`nO1Y5nP>0dT}FWnOdSy=~RlAS2XFd93c@D-B6 zk_E5N!j+%*1s3DT3U(4-kEGTM(-paP>t12@ZrQ`3P&o z5cm!l)n%f`?_=^Fka|o=(?+2Be`Pd-P<2D;{-_y~3zCEJJAl~&9%$ZPDN#>DOKR~2x57^ ziGQRrGWNn&_Tg0ahn(fsG`qXdrN*K1tNpjxBo*5PfC10U#=*)2OHMAPAP)O~0B?89 Ao&W#< diff --git a/semester3/spca/spca-summary.tex b/semester3/spca/spca-summary.tex index bc394a6..916d125 100644 --- a/semester3/spca/spca-summary.tex +++ b/semester3/spca/spca-summary.tex @@ -1,8 +1,6 @@ \documentclass{article} -\newcommand{\dir}{~/projects/latex} -\input{\dir/include.tex} -\load{recommended} +\input{~/projects/latex/dist/full.tex} \setup{Systems Programming and Computer Architecture} @@ -57,6 +55,7 @@ \newsection \section{The C Programming Language} \input{parts/00_c/00_intro.tex} +\input{parts/00_c/01_syntax.tex} % ── Intro to x86 asm ──────────────────────────────────────────────── From 4550168877fefe4240c2a615afa16216735d07e9 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sun, 4 Jan 2026 13:59:33 +0100 Subject: [PATCH 4/6] [SPCA] Restructre, some notes --- .../00_c/{01_syntax => }/00_intro.c | 2 +- .../00_c/{01_syntax => }/01_func.c | 4 ++-- .../00_c/{01_syntax => }/01_func.h | 0 .../spca/code-examples/00_c/02_pointers.c | 0 .../spca/code-examples/00_c/02_pointers.h | 0 semester3/spca/parts/00_c/00_intro.tex | 10 ++++++---- semester3/spca/parts/00_c/01_syntax.tex | 13 ++++++++++--- semester3/spca/spca-summary.pdf | Bin 156730 -> 316710 bytes semester3/spca/spca-summary.tex | 3 +++ 9 files changed, 22 insertions(+), 10 deletions(-) rename semester3/spca/code-examples/00_c/{01_syntax => }/00_intro.c (88%) rename semester3/spca/code-examples/00_c/{01_syntax => }/01_func.c (92%) rename semester3/spca/code-examples/00_c/{01_syntax => }/01_func.h (100%) create mode 100644 semester3/spca/code-examples/00_c/02_pointers.c create mode 100644 semester3/spca/code-examples/00_c/02_pointers.h diff --git a/semester3/spca/code-examples/00_c/01_syntax/00_intro.c b/semester3/spca/code-examples/00_c/00_intro.c similarity index 88% rename from semester3/spca/code-examples/00_c/01_syntax/00_intro.c rename to semester3/spca/code-examples/00_c/00_intro.c index f503d99..7635eed 100644 --- a/semester3/spca/code-examples/00_c/01_syntax/00_intro.c +++ b/semester3/spca/code-examples/00_c/00_intro.c @@ -12,5 +12,5 @@ int main( int argc, char *argv[] ) { for ( int i = 0; i < argc; i++ ) // For loop just like any other sane programming language printf( "Arg %d: %s\n", i, argv[ i ] ); // Outputs the i-th argument from CLI - get_user_input_int( "Select a number" ); + get_user_input_int( "Select a number" ); // Function calls as in any other language } diff --git a/semester3/spca/code-examples/00_c/01_syntax/01_func.c b/semester3/spca/code-examples/00_c/01_func.c similarity index 92% rename from semester3/spca/code-examples/00_c/01_syntax/01_func.c rename to semester3/spca/code-examples/00_c/01_func.c index 63df54d..374e138 100644 --- a/semester3/spca/code-examples/00_c/01_syntax/01_func.c +++ b/semester3/spca/code-examples/00_c/01_func.c @@ -25,12 +25,12 @@ int get_user_input_int( char prompt[] ) { while ( input_data > 1 ) { input_data -= 1; - printf( "Hello World" ); + printf( "Hello World\n" ); } do { input_data -= 1; - printf( "Bye World" ); + printf( "Bye World\n" ); } while ( input_data_copy > 1 ); return 0; diff --git a/semester3/spca/code-examples/00_c/01_syntax/01_func.h b/semester3/spca/code-examples/00_c/01_func.h similarity index 100% rename from semester3/spca/code-examples/00_c/01_syntax/01_func.h rename to semester3/spca/code-examples/00_c/01_func.h diff --git a/semester3/spca/code-examples/00_c/02_pointers.c b/semester3/spca/code-examples/00_c/02_pointers.c new file mode 100644 index 0000000..e69de29 diff --git a/semester3/spca/code-examples/00_c/02_pointers.h b/semester3/spca/code-examples/00_c/02_pointers.h new file mode 100644 index 0000000..e69de29 diff --git a/semester3/spca/parts/00_c/00_intro.tex b/semester3/spca/parts/00_c/00_intro.tex index 7e75a14..2a4df05 100644 --- a/semester3/spca/parts/00_c/00_intro.tex +++ b/semester3/spca/parts/00_c/00_intro.tex @@ -1,13 +1,15 @@ -I can clearly C why you'd want to use C. Already sorry in advance for all the bad C jokes that are going to be part of this section +\begin{scriptsize} + \textit{I can clearly C why you'd want to use C. Already sorry in advance for all the bad C jokes that are going to be part of this section} +\end{scriptsize} \texttt{C} is a compiled, low-level programming language, lacking many features modern high-level programming languages offer, like Object Oriented programming, true Functional Programming (like Haskell implements), Garbage Collection, complex abstract datatypes and vectors, just to name a few. (It is possible to replicate these using Preprocessor macros, more on this later). -On the other hand, it offers the ability to directly integrate assembly code into the \texttt{.c} files, +On the other hand, it offers low-level hardware access, the ability to directly integrate assembly code into the \texttt{.c} files, as well as bit level data manipulation and extensive memory management options, again just to name a few. -This of course leads to \texttt{C} performing excellently and there are many programming languages who's compiler doesn't directly produce machine code or assembly, +This of course leads to \texttt{C} performing excellently and there are many programming languages whose compiler doesn't directly produce machine code or assembly, but instead optimized \texttt{C} code that is then compiled into machine code using a \texttt{C} compiler. -This has a number of benefits, most notably that \texttt{C} compilers can produce very efficient assembly, +This has a number of benefits, most notably that \texttt{C} compilers can produce very efficient assembly, as lots of effort is put into the \texttt{C} compilers by the hardware manufacturers. diff --git a/semester3/spca/parts/00_c/01_syntax.tex b/semester3/spca/parts/00_c/01_syntax.tex index 2193dba..0db7469 100644 --- a/semester3/spca/parts/00_c/01_syntax.tex +++ b/semester3/spca/parts/00_c/01_syntax.tex @@ -1,6 +1,13 @@ \subsection{The Syntax} \texttt{C} uses a very similar syntax as many other programming languages, like \texttt{Java}, \texttt{JavaScript} and many more\dots to be precise, it is \textit{them} that use the \texttt{C} syntax, not the other way around. So: -\inputcodewithfilename{c}{code-examples/00_c/01_syntax/}{00_intro.c} -\inputcodewithfilename{c}{code-examples/00_c/01_syntax/}{01_func.h} -\inputcodewithfilename{c}{code-examples/00_c/01_syntax/}{01_func.c} +\inputcodewithfilename{c}{code-examples/00_c/}{00_intro.c} + +In \texttt{C} we are referring to the implementation of a function as a \bi{(function) definition} (correspondingly, \textit{variable definition}, if the variable is initialized) +and to the definition of the function signature (or variables, without initializing them) as the \bi{(function) declaration} (or, correspondingly, \textit{variable declaration}). + +\texttt{C} code is usuallt split into the source files, ending in \texttt{.c} (where the local functions and variables are declared, as well as all function definitions) +and the header files, ending in \texttt{.h}, where the external declarations are defined. Usually, no definition of functions are in the \texttt{.h} files +\inputcodewithfilename{c}{code-examples/00_c/}{01_func.h} + +\inputcodewithfilename{c}{code-examples/00_c/}{01_func.c} diff --git a/semester3/spca/spca-summary.pdf b/semester3/spca/spca-summary.pdf index 4101d0b9fe78345eae6c0d53531061d1447a290c..00e78cfd7e0335233baa3364f0b3069da5ca1fb1 100644 GIT binary patch literal 316710 zcmce+W3Vkvwl%zM+qP}n#@V)Q+qP|=ZQD58wrv~V^W3*PqQAH|;@&^q8L?L7s?4fb zqsE*g=ggX<3L;{(jCAZ!q_c~|t57Ti3+dFJoeB=4?*D$V%{!_Sao3tes693FyVF4V+CxOpNS|O`!Pr zpq!i?O$=U<*CPii3af1P-`-0j%*_0+dtL-t>v_TH3wOLNqaduU%dO1>w)@G}go?`w^ z>0~x&lmL`xmlvS;Fhju+(Py&guKjQ*P*pqOGeQD7lB%!4FlX55EIr**5)GD!sj z(a-Yyq_n*9{%B1Ph2F_*?6v8)?uTtcUE3Wx`INPWYm~+cdlbo0A~c>JI=zWN$7Lt~ zxREbz&e2?4xPf4DoedyNdcCol=u2Gk?gsq99XopOkVN{@Qhhd0 zkW5v9ob{;Ie2)Z!Nuz6pDvfv#h+I1smUB5t;e-yR@(2Y+|7<=M(*&=*Z^}+KAd&F(aaKjJyX_lM03lN|Rjuon+J41_@{o+}@GJ)ZZ` z%dxs!UYcV|L$*X)1$I7Gb7zk&uh*Yw->Xa8MK$XD?CO6IjzT|Q3NzYG>-ShN0OE_4 zjPE?wnsVYQ@F|dsU>D=pFRBrLpMF=!4_7fIGs>hc>2u((*O;VN+mzVRZX4v7nu;fO zUmc^Q&qI{RfR0VHP~4DWfyo z&zij*tr(@0j>%H+B^R~9T&$=sZL=)PV>b(-+kQ$lf2(lpg_Ugj-iMu4W*4p4&W-9~ zNd{m&@xxDb){?n3+;`V7<$_ldv`WEgiITuIE`k|^0UU3QY)j)Vf1#H~Y7_hqq4mG6 zU;i+3PBw=ByP2zP*lutj_^hbk)-WM4c10BDdP=fyfzj4&WBsC;=PPfphMpr$DKEZW zxluqdS+h5w(bp;}+RI=b#GC-JK@`LfbgSAumSafX6=8}{!zMwZi4dVe#N?sAO-`49bB*W$ z`QslgnWM|g90ggLO*D+LtoiF4AEJvdzn>Lj)hNHU&Ibr6T_>s{@m4xrAdaHVW8HS! 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a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/00_line_integrals.tex +++ b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/00_line_integrals.tex @@ -34,4 +34,26 @@ we have $\displaystyle\int_{\gamma} f(s) \cdot \dx \vec{s} = \int_{\sigma} f(s) \shorttheorem Let $X$ be open set, $f$ conservative vector field. Then $\exists C^1$ function $g$ s.t. $f = \nabla g$. If any two points of $X$ can be joined by a parametrized curve, then $g$ is unique up to a constant: if $\nabla g_1 = f$, then $g - g_1$ is constant on $X$ -\shortremark If $f$ vec. field on $X$, then $g$ is called a \bi{potential} for $f$ +\shortremark Two points $x, y \in X$ can be joined by parametrized curve $\gamma$ if $\gamma(a) = x$ and $\gamma(b) = y$. In that case, $X$ is called \bi{path-connected}. +It is true when $X$ is \textit{convex} (e.g. when $X$ is a disc or a product of intervals). +If $f$ is a vector field on $X$, then $g$ is called a \bi{potential} for $f$ and it is not unique, since we can add a constant to $g$ without changing the gradient.\\ +% +\stepLabelNumber{all} +\shortproposition For a vectorfield to be conservative, a \textit{necessary condition} is that $\displaystyle\frac{\partial f_i}{\partial x_j} = \frac{\partial f_j}{x_i}$ +for any $1 \leq i \neq j \leq n \in \N$\\ +% +\stepLabelNumber{all} +\compactdef{Start Shaped Set} $X \subseteq \R^n$ is star shaped if $\exists x_0 \in X$ s.t. $\forall x \in X$, the line segment from $x$ to $x_0$ is contained in $X$, +and we also say that $X$ is \textit{star shaped around} $x_0$\\ +% +\stepLabelNumber{all} +\shorttheorem Let $X$ start shaped and open, $f$ a $C^1$ vector field fulfilling Proposition \ref{all:4-1-13}. Then $f$ is conservative. + +\drmvspace +\setLabelNumber{all}{20} +\shortdef Let $X \subseteq \R^3$ open and $f$ a $C^1$ vector field. Then the \bi{curl} of $f$ is the conservative vector field +$\text{curl}(f) = \begin{bmatrix} + \partial_y f_3 - \partial_z f_2 \\ + \partial_z f_1 - \partial_x f_3 \\ + \partial_x f_2 - \partial_y f_1 + \end{bmatrix}$ diff --git a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/01_int_in_rn.tex b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/01_int_in_rn.tex index bd650bb..8c1131e 100644 --- a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/01_int_in_rn.tex +++ b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/integration/01_int_in_rn.tex @@ -1,2 +1,38 @@ \newsectionNoPB \subsection{Riemann integral in Vector Space} +The integral of a continuous function $f: X \rightarrow \R$ with $X \subseteq \R^n$ bounded and closed, is denoted $\int_X f(x) \dx x$ with properties: +\rmvspace +\begin{enumerate}[label=(\arabic*), noitemsep] + \item \bi{(Compatibility)} If $n = 1$ and $X = [a, b]$, integral is the indefinite integral as per Analysis I + \item \bi{(Linearity)} If $f$, $g$ are continuous on $X$ and $a, b \in \R$, then $\displaystyle \int_X (a f(x) + b g(x)) \dx x = a \int_X f(x) \dx x + b \int_X g(x) \dx x$ + \item \bi{(Positivity)} If $f \leq g$, then so is the integral and if $f \geq 0$, so is the integral and if $Y \subseteq X$, then int. over $Y$ is $\leq$ over $X$ + \item \bi{(Upper bound \& Triangle Inequality)} $\displaystyle \left| \int_{X} f(x) \dx x \right| \leq \int_{X} |f(x)|\dx x$ and + $\displaystyle \left| \int_{X} (f(x) + g(x)) \dx x \right| \leq \int_{X} |f(x)| \dx x \int_X |g(x)|$ + \item \bi{(Volume)} The integral of $f$ is the volume of $\{ (x, y) \in X \times \R : 0 \leq y \leq f(x) \} \subseteq \R^{n + 1}$. + If $X$ is a bounded rectangle, e.g. $X = [a_1, b_1] \times \ldots \times [a_n, b_n] \subseteq \R^n$ and $f = 1$, then $\int_{X} \dx x = (b_n - a_n) \dots (b_1 - a_1)$. + We write $\text{Vol}(X)$ or $\text{Vol}_n(X)$ + \item \bi{(Multiple integral)} \textit{(Fubini)} If $n_1, n_2 \in \Z$ s.t. $n = n_1 + n_2$, + then for $x_1 \in \R^{n_1}$, let $Y_{x_1} = \{ x_2 \in \R^{n_2} : (x_1, x_2) \in X \} \subseteq \R^{n_2}$. + Let $X_1$ be the set of $x_1 \in \R^n$ such that $Y_{x_1}$ is not empty. Then $X_1$ and $Y_{x_1}$ are compact.\\ + If $\displaystyle g(x_1) = \int_{Y_{x_1}} f(x_1, x_2) \dx x_2$ is continuous on $X_1$, then + \dnrmvspace + \begin{align*} + \int_{X} f(x_1, x_2) \dx x = \int_{X_1} g(x_1) \dx x = \int_{X_1} g(x_1) \dx x_1 = \int_{X_1} \left( \int_{Y_{x_1}} f(x_1, x_2) \dx x_2 \right) \dx x_1 + \end{align*} + + \rmvspace + Exchanging the role of $x_1$ and $x_2$ we have (with $Z_{x_2} = \{ x_1 : (x_1, x_2) \in X \}$) if integral over $x_1$ is continuous. + \rmvspace + \begin{align*} + \int_{X} f(x_1, x_2) \dx x = \int_{X_2} \left( \int_{Z_{x_2}} f(x_1, x_2) \dx x_1 \right) \dx x_2 + \end{align*} + \drmvspace + \item \bi{(Domain additivity)} If $X_1$ and $X_2$ are compact and $f$ continuous on $X = X_1 \cup X_2$, then (for $Y = X_1 \cap X_2$) + \rmvspace + \begin{align*} + \int_X f(x) \dx x + \int_Y f(x) \dx x = \int_{X_1} f(x) \dx x + \int_{X_2} f(x) \dx x + \end{align*} + + \rmvspace + In particular, if $Y$ empty (or size is ``negligible''), then $\int_{X} f(x) \dx x = \int_{X_1} f(x) \dx x + \int_{X_2} f(x) \dx x$ +\end{enumerate} From 756e1582834b1c37cea6f7468de3737314839dd1 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Mon, 5 Jan 2026 11:42:00 +0100 Subject: [PATCH 6/6] [Analysis] Theory summary complete --- .../analysis-ii-cheat-sheet.pdf | Bin 322977 -> 329908 bytes .../vectors/integration/00_line_integrals.tex | 1 + .../vectors/integration/01_int_in_rn.tex | 62 ++++++++++-------- .../vectors/integration/02_improper_int.tex | 9 +++ .../03_change_of_variable_formula.tex | 7 ++ .../vectors/integration/04_green_formula.tex | 20 ++++++ semester3/numcs/numcs-summary.pdf | Bin 1434262 -> 1433977 bytes 7 files changed, 73 insertions(+), 26 deletions(-) diff --git a/semester3/analysis-ii/cheat-sheet-jh/analysis-ii-cheat-sheet.pdf b/semester3/analysis-ii/cheat-sheet-jh/analysis-ii-cheat-sheet.pdf index cc10e693208ab3f5be93eb96765b64c32a1df745..c0d51aba7b25d08e09f728aa7cfd0e976bf29126 100644 GIT binary patch delta 98848 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