From 30d72eb5b83ce53b48cde33de54635350a428168 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 25 May 2023 08:31:36 +0200
Subject: [PATCH] Vortragsfolien und Beispiele 24.5.2023
---
20230523/io-ports-and-interrupts.pdf | 1 +
.../logo-hochschule-bochum-cvh-text-v2.pdf | 1 +
20230523/logo-hochschule-bochum.pdf | 1 +
20230523/parameters-01.c | 15 +
20230523/parameters-01.s | 42 +
20230523/parameters-02.c | 8 +
20230523/parameters-02.s | 28 +
20230523/parameters-03.c | 7 +
20230523/parameters-03.s | 41 +
20230523/parameters-03.s-m32 | 65 +
20230523/parameters-04.c | 7 +
20230523/paramlib-02.c | 7 +
20230523/paramlib-02.h | 3 +
20230523/paramlib-03.c | 10 +
20230523/paramlib-03.h | 4 +
20230523/paramlib-03.s | 55 +
20230523/paramlib-03.s-m32 | 72 +
20230523/paramlib-04.c | 11 +
20230523/paramlib-04.h | 5 +
20230523/paramlib-04.s | 51 +
20230523/pgslides.sty | 1 +
20230523/rtech-20230523.pdf | Bin 0 -> 198178 bytes
20230523/rtech-20230523.tex | 1743 ++++++++
20230523/rtech-20230523.txt | 15 +
20230523/test-arm-01.c | 9 +
20230523/test-arm-01.s-arm | 52 +
20230523/test-arm-01.s-x86 | 30 +
20230523/test-arm-01.s-x86-Os | 30 +
20230523/test-arm-02.c | 8 +
20230523/test-arm-02.s-arm | 37 +
20230523/test-arm-02.s-avr | 40 +
20230523/test-arm-02.s-x86 | 16 +
20230523/test-arm-03.c | 10 +
20230523/test-arm-03.s-x86 | 18 +
20230523/test-arm-04.c | 11 +
20230523/test-arm-04.s-x86 | 19 +
20230523/test-arm-05.c | 12 +
20230523/test-arm-05.s-x86 | 20 +
20230524/buffer-overflow-01.c | 10 +
20230524/buffer-overflow-02.c | 10 +
20230524/io-ports-and-interrupts.pdf | 1 +
.../logo-hochschule-bochum-cvh-text-v2.pdf | 1 +
20230524/logo-hochschule-bochum.pdf | 1 +
20230524/parameters-01-O0-stack-4.s | 56 +
20230524/parameters-01-O0.s | 56 +
20230524/parameters-01.c | 13 +
20230524/parameters-01.s | 36 +
20230524/parameters-02.c | 16 +
20230524/parameters-02.s | 92 +
20230524/pgslides.sty | 1 +
20230524/rtech-20230524.pdf | Bin 0 -> 124227 bytes
20230524/rtech-20230524.tex | 1761 ++++++++
common/io-ports-and-interrupts.eps | 3658 +++++++++++++++++
common/io-ports-and-interrupts.pdf | Bin 0 -> 6074 bytes
common/io-ports-and-interrupts.tex | 43 +
55 files changed, 8260 insertions(+)
create mode 120000 20230523/io-ports-and-interrupts.pdf
create mode 120000 20230523/logo-hochschule-bochum-cvh-text-v2.pdf
create mode 120000 20230523/logo-hochschule-bochum.pdf
create mode 100644 20230523/parameters-01.c
create mode 100644 20230523/parameters-01.s
create mode 100644 20230523/parameters-02.c
create mode 100644 20230523/parameters-02.s
create mode 100644 20230523/parameters-03.c
create mode 100644 20230523/parameters-03.s
create mode 100644 20230523/parameters-03.s-m32
create mode 100644 20230523/parameters-04.c
create mode 100644 20230523/paramlib-02.c
create mode 100644 20230523/paramlib-02.h
create mode 100644 20230523/paramlib-03.c
create mode 100644 20230523/paramlib-03.h
create mode 100644 20230523/paramlib-03.s
create mode 100644 20230523/paramlib-03.s-m32
create mode 100644 20230523/paramlib-04.c
create mode 100644 20230523/paramlib-04.h
create mode 100644 20230523/paramlib-04.s
create mode 120000 20230523/pgslides.sty
create mode 100644 20230523/rtech-20230523.pdf
create mode 100644 20230523/rtech-20230523.tex
create mode 100644 20230523/rtech-20230523.txt
create mode 100644 20230523/test-arm-01.c
create mode 100644 20230523/test-arm-01.s-arm
create mode 100644 20230523/test-arm-01.s-x86
create mode 100644 20230523/test-arm-01.s-x86-Os
create mode 100644 20230523/test-arm-02.c
create mode 100644 20230523/test-arm-02.s-arm
create mode 100644 20230523/test-arm-02.s-avr
create mode 100644 20230523/test-arm-02.s-x86
create mode 100644 20230523/test-arm-03.c
create mode 100644 20230523/test-arm-03.s-x86
create mode 100644 20230523/test-arm-04.c
create mode 100644 20230523/test-arm-04.s-x86
create mode 100644 20230523/test-arm-05.c
create mode 100644 20230523/test-arm-05.s-x86
create mode 100644 20230524/buffer-overflow-01.c
create mode 100644 20230524/buffer-overflow-02.c
create mode 120000 20230524/io-ports-and-interrupts.pdf
create mode 120000 20230524/logo-hochschule-bochum-cvh-text-v2.pdf
create mode 120000 20230524/logo-hochschule-bochum.pdf
create mode 100644 20230524/parameters-01-O0-stack-4.s
create mode 100644 20230524/parameters-01-O0.s
create mode 100644 20230524/parameters-01.c
create mode 100644 20230524/parameters-01.s
create mode 100644 20230524/parameters-02.c
create mode 100644 20230524/parameters-02.s
create mode 120000 20230524/pgslides.sty
create mode 100644 20230524/rtech-20230524.pdf
create mode 100644 20230524/rtech-20230524.tex
create mode 100644 common/io-ports-and-interrupts.eps
create mode 100644 common/io-ports-and-interrupts.pdf
create mode 100644 common/io-ports-and-interrupts.tex
diff --git a/20230523/io-ports-and-interrupts.pdf b/20230523/io-ports-and-interrupts.pdf
new file mode 120000
index 0000000..bcd46f7
--- /dev/null
+++ b/20230523/io-ports-and-interrupts.pdf
@@ -0,0 +1 @@
+../common/io-ports-and-interrupts.pdf
\ No newline at end of file
diff --git a/20230523/logo-hochschule-bochum-cvh-text-v2.pdf b/20230523/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000..4aa99b8
--- /dev/null
+++ b/20230523/logo-hochschule-bochum-cvh-text-v2.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum-cvh-text-v2.pdf
\ No newline at end of file
diff --git a/20230523/logo-hochschule-bochum.pdf b/20230523/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20230523/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20230523/parameters-01.c b/20230523/parameters-01.c
new file mode 100644
index 0000000..ad24b30
--- /dev/null
+++ b/20230523/parameters-01.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+
+typedef char string[42];
+
+void print (string msg)
+{
+ printf ("%s\n", msg);
+}
+
+int main (void)
+{
+ string hello = "Hello, world!";
+ print (hello);
+ return 0;
+}
diff --git a/20230523/parameters-01.s b/20230523/parameters-01.s
new file mode 100644
index 0000000..49a0a7b
--- /dev/null
+++ b/20230523/parameters-01.s
@@ -0,0 +1,42 @@
+ .file "parameters-01.c"
+ .text
+ .globl print
+ .type print, @function
+print:
+.LFB11:
+ .cfi_startproc
+ subq $8, %rsp
+ .cfi_def_cfa_offset 16
+ call puts@PLT
+ addq $8, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE11:
+ .size print, .-print
+ .globl main
+ .type main, @function
+main:
+.LFB12:
+ .cfi_startproc
+ subq $56, %rsp
+ .cfi_def_cfa_offset 64
+ movabsq $8583909746840200520, %rax
+ movabsq $143418749551, %rdx
+ movq %rax, (%rsp)
+ movq %rdx, 8(%rsp)
+ movq $0, 16(%rsp)
+ movq $0, 24(%rsp)
+ movq $0, 32(%rsp)
+ movw $0, 40(%rsp)
+ movq %rsp, %rdi
+ call puts@PLT
+ movl $0, %eax
+ addq $56, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE12:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/parameters-02.c b/20230523/parameters-02.c
new file mode 100644
index 0000000..f87bf30
--- /dev/null
+++ b/20230523/parameters-02.c
@@ -0,0 +1,8 @@
+#include "paramlib-02.h"
+
+int main (void)
+{
+ string hello = "Hello, world!";
+ print (hello);
+ return 0;
+}
diff --git a/20230523/parameters-02.s b/20230523/parameters-02.s
new file mode 100644
index 0000000..02bc062
--- /dev/null
+++ b/20230523/parameters-02.s
@@ -0,0 +1,28 @@
+ .file "parameters-02.c"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB0:
+ .cfi_startproc
+ subq $56, %rsp
+ .cfi_def_cfa_offset 64
+ movabsq $8583909746840200520, %rax
+ movabsq $143418749551, %rdx
+ movq %rax, (%rsp)
+ movq %rdx, 8(%rsp)
+ movq $0, 16(%rsp)
+ movq $0, 24(%rsp)
+ movq $0, 32(%rsp)
+ movw $0, 40(%rsp)
+ movq %rsp, %rdi
+ call print@PLT
+ movl $0, %eax
+ addq $56, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE0:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/parameters-03.c b/20230523/parameters-03.c
new file mode 100644
index 0000000..c3570cc
--- /dev/null
+++ b/20230523/parameters-03.c
@@ -0,0 +1,7 @@
+#include "paramlib-03.h"
+
+int main (void)
+{
+ print ('H', 'e', 'l', 'l', 'o', ',', ' ', 'w', 'o', 'r', 'l', 'd', '!', '\n');
+ return 0;
+}
diff --git a/20230523/parameters-03.s b/20230523/parameters-03.s
new file mode 100644
index 0000000..14c10b0
--- /dev/null
+++ b/20230523/parameters-03.s
@@ -0,0 +1,41 @@
+ .file "parameters-03.c"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB0:
+ .cfi_startproc
+ subq $8, %rsp
+ .cfi_def_cfa_offset 16
+ pushq $10
+ .cfi_def_cfa_offset 24
+ pushq $33
+ .cfi_def_cfa_offset 32
+ pushq $100
+ .cfi_def_cfa_offset 40
+ pushq $108
+ .cfi_def_cfa_offset 48
+ pushq $114
+ .cfi_def_cfa_offset 56
+ pushq $111
+ .cfi_def_cfa_offset 64
+ pushq $119
+ .cfi_def_cfa_offset 72
+ pushq $32
+ .cfi_def_cfa_offset 80
+ movl $44, %r9d
+ movl $111, %r8d
+ movl $108, %ecx
+ movl $108, %edx
+ movl $101, %esi
+ movl $72, %edi
+ call print@PLT
+ movl $0, %eax
+ addq $72, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE0:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/parameters-03.s-m32 b/20230523/parameters-03.s-m32
new file mode 100644
index 0000000..716903d
--- /dev/null
+++ b/20230523/parameters-03.s-m32
@@ -0,0 +1,65 @@
+ .file "parameters-03.c"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB0:
+ .cfi_startproc
+ leal 4(%esp), %ecx
+ .cfi_def_cfa 1, 0
+ andl $-16, %esp
+ pushl -4(%ecx)
+ pushl %ebp
+ .cfi_escape 0x10,0x5,0x2,0x75,0
+ movl %esp, %ebp
+ pushl %ebx
+ pushl %ecx
+ .cfi_escape 0xf,0x3,0x75,0x78,0x6
+ .cfi_escape 0x10,0x3,0x2,0x75,0x7c
+ call __x86.get_pc_thunk.bx
+ addl $_GLOBAL_OFFSET_TABLE_, %ebx
+ subl $8, %esp
+ pushl $10
+ pushl $33
+ pushl $100
+ pushl $108
+ pushl $114
+ pushl $111
+ pushl $119
+ pushl $32
+ pushl $44
+ pushl $111
+ pushl $108
+ pushl $108
+ pushl $101
+ pushl $72
+ call print@PLT
+ addl $64, %esp
+ movl $0, %eax
+ leal -8(%ebp), %esp
+ popl %ecx
+ .cfi_restore 1
+ .cfi_def_cfa 1, 0
+ popl %ebx
+ .cfi_restore 3
+ popl %ebp
+ .cfi_restore 5
+ leal -4(%ecx), %esp
+ .cfi_def_cfa 4, 4
+ ret
+ .cfi_endproc
+.LFE0:
+ .size main, .-main
+ .section .text.__x86.get_pc_thunk.bx,"axG",@progbits,__x86.get_pc_thunk.bx,comdat
+ .globl __x86.get_pc_thunk.bx
+ .hidden __x86.get_pc_thunk.bx
+ .type __x86.get_pc_thunk.bx, @function
+__x86.get_pc_thunk.bx:
+.LFB1:
+ .cfi_startproc
+ movl (%esp), %ebx
+ ret
+ .cfi_endproc
+.LFE1:
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/parameters-04.c b/20230523/parameters-04.c
new file mode 100644
index 0000000..937cc4f
--- /dev/null
+++ b/20230523/parameters-04.c
@@ -0,0 +1,7 @@
+#include "paramlib-04.h"
+
+int main (void)
+{
+ print ("Hä?", 'H', 'e', 'l', 'l', 'o', ',', ' ', 'w', 'o', 'r', 'l', 'd', '!', '\n');
+ return 0;
+}
diff --git a/20230523/paramlib-02.c b/20230523/paramlib-02.c
new file mode 100644
index 0000000..8b13246
--- /dev/null
+++ b/20230523/paramlib-02.c
@@ -0,0 +1,7 @@
+#include <stdio.h>
+#include "paramlib-02.h"
+
+void print (string msg)
+{
+ printf ("%s\n", msg);
+}
diff --git a/20230523/paramlib-02.h b/20230523/paramlib-02.h
new file mode 100644
index 0000000..fcfab1f
--- /dev/null
+++ b/20230523/paramlib-02.h
@@ -0,0 +1,3 @@
+typedef char string[42];
+
+extern void print (string msg);
diff --git a/20230523/paramlib-03.c b/20230523/paramlib-03.c
new file mode 100644
index 0000000..96afc51
--- /dev/null
+++ b/20230523/paramlib-03.c
@@ -0,0 +1,10 @@
+#include <stdio.h>
+
+void print (int h, int e, int l1, int l2, int o1,
+ int comma, int space,
+ int w, int o2, int r, int l3, int d,
+ int bang, int newline)
+{
+ printf ("%c%c%c%c%c%c%c%c%c%c%c%c%c%c",
+ h, e, l1, l2, o1, comma, space, w, o2, r, l3, d, bang, newline);
+}
diff --git a/20230523/paramlib-03.h b/20230523/paramlib-03.h
new file mode 100644
index 0000000..c4eaee9
--- /dev/null
+++ b/20230523/paramlib-03.h
@@ -0,0 +1,4 @@
+extern void print (int h, int e, int l1, int l2, int o1,
+ int comma, int space,
+ int w, int o2, int r, int l3, int d,
+ int bang, int newline);
diff --git a/20230523/paramlib-03.s b/20230523/paramlib-03.s
new file mode 100644
index 0000000..55c50fe
--- /dev/null
+++ b/20230523/paramlib-03.s
@@ -0,0 +1,55 @@
+ .file "paramlib-03.c"
+ .text
+ .section .rodata.str1.1,"aMS",@progbits,1
+.LC0:
+ .string "%c%c%c%c%c%c%c%c%c%c%c%c%c%c"
+ .text
+ .globl print
+ .type print, @function
+print:
+.LFB11:
+ .cfi_startproc
+ subq $16, %rsp
+ .cfi_def_cfa_offset 24
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 32
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 40
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 48
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 56
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 64
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 72
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 80
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 88
+ pushq %r9
+ .cfi_def_cfa_offset 96
+ movl %r8d, %r9d
+ movl %ecx, %r8d
+ movl %edx, %ecx
+ movl %esi, %edx
+ movl %edi, %esi
+ leaq .LC0(%rip), %rdi
+ movl $0, %eax
+ call printf@PLT
+ addq $88, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE11:
+ .size print, .-print
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/paramlib-03.s-m32 b/20230523/paramlib-03.s-m32
new file mode 100644
index 0000000..7d5b641
--- /dev/null
+++ b/20230523/paramlib-03.s-m32
@@ -0,0 +1,72 @@
+ .file "paramlib-03.c"
+ .text
+ .section .rodata.str1.1,"aMS",@progbits,1
+.LC0:
+ .string "%c%c%c%c%c%c%c%c%c%c%c%c%c%c"
+ .text
+ .globl print
+ .type print, @function
+print:
+.LFB11:
+ .cfi_startproc
+ pushl %ebx
+ .cfi_def_cfa_offset 8
+ .cfi_offset 3, -8
+ subl $12, %esp
+ .cfi_def_cfa_offset 20
+ call __x86.get_pc_thunk.bx
+ addl $_GLOBAL_OFFSET_TABLE_, %ebx
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 24
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 28
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 32
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 36
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 40
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 44
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 48
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 52
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 56
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 60
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 64
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 68
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 72
+ pushl 72(%esp)
+ .cfi_def_cfa_offset 76
+ leal .LC0@GOTOFF(%ebx), %eax
+ pushl %eax
+ .cfi_def_cfa_offset 80
+ call printf@PLT
+ addl $72, %esp
+ .cfi_def_cfa_offset 8
+ popl %ebx
+ .cfi_restore 3
+ .cfi_def_cfa_offset 4
+ ret
+ .cfi_endproc
+.LFE11:
+ .size print, .-print
+ .section .text.__x86.get_pc_thunk.bx,"axG",@progbits,__x86.get_pc_thunk.bx,comdat
+ .globl __x86.get_pc_thunk.bx
+ .hidden __x86.get_pc_thunk.bx
+ .type __x86.get_pc_thunk.bx, @function
+__x86.get_pc_thunk.bx:
+.LFB12:
+ .cfi_startproc
+ movl (%esp), %ebx
+ ret
+ .cfi_endproc
+.LFE12:
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/paramlib-04.c b/20230523/paramlib-04.c
new file mode 100644
index 0000000..20b88b0
--- /dev/null
+++ b/20230523/paramlib-04.c
@@ -0,0 +1,11 @@
+#include <stdio.h>
+
+void print (char *Hae,
+ int h, int e, int l1, int l2, int o1,
+ int comma, int space,
+ int w, int o2, int r, int l3, int d,
+ int bang, int newline)
+{
+ printf ("%c%c%c%c%c%c%c%c%c%c%c%c%c%c",
+ h, e, l1, l2, o1, comma, space, w, o2, r, l3, d, bang, newline);
+}
diff --git a/20230523/paramlib-04.h b/20230523/paramlib-04.h
new file mode 100644
index 0000000..b86e321
--- /dev/null
+++ b/20230523/paramlib-04.h
@@ -0,0 +1,5 @@
+extern void print (char *Hae,
+ int h, int e, int l1, int l2, int o1,
+ int comma, int space,
+ int w, int o2, int r, int l3, int d,
+ int bang, int newline);
diff --git a/20230523/paramlib-04.s b/20230523/paramlib-04.s
new file mode 100644
index 0000000..c3ce046
--- /dev/null
+++ b/20230523/paramlib-04.s
@@ -0,0 +1,51 @@
+ .file "paramlib-04.c"
+ .text
+ .section .rodata.str1.1,"aMS",@progbits,1
+.LC0:
+ .string "%c%c%c%c%c%c%c%c%c%c%c%c%c%c"
+ .text
+ .globl print
+ .type print, @function
+print:
+.LFB11:
+ .cfi_startproc
+ subq $16, %rsp
+ .cfi_def_cfa_offset 24
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 32
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 40
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 48
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 56
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 64
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 72
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 80
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 88
+ movl 88(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 96
+ leaq .LC0(%rip), %rdi
+ movl $0, %eax
+ call printf@PLT
+ addq $88, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE11:
+ .size print, .-print
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/pgslides.sty b/20230523/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20230523/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/20230523/rtech-20230523.pdf b/20230523/rtech-20230523.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..f95e0223aa56b6d123607969dbe8c9aaddbc8bad
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diff --git a/20230523/rtech-20230523.tex b/20230523/rtech-20230523.tex
new file mode 100644
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--- /dev/null
+++ b/20230523/rtech-20230523.tex
@@ -0,0 +1,1743 @@
+% rtech-20230523.pdf - Lecture Slides on Computer Technology
+% Copyright (C) 2012, 2013, 2014, 2021, 2022, 2023 Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document. If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document. If not, see <http://creativecommons.org/licenses/>.
+
+% README: Der CPU-Stack
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{pdftricks}
+%\usepackage[obeyfamily=false,mathrm=mathsf,textrm=sffamily]{siunitx}
+%\usepackage{eurosym}
+\usepackage{tikz}
+
+\newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+\newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+
+\lstdefinestyle{asm}{basicstyle=\color{structure},
+ language={},
+ gobble=4}
+
+\begin{psinputs}
+ \usepackage[utf8]{inputenc}
+ \usepackage[german]{babel}
+ \usepackage[T1]{fontenc}
+ \usepackage{helvet}
+ \renewcommand*\familydefault{\sfdefault}
+ \usepackage{pstricks,pst-grad,pst-circ-pg}
+ \newcommand{\invisible}{\tiny\color{white}}
+ \psset{unit=1cm}
+ \psset{logicLabelstyle=\invisible}
+ \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+ \psset{logicSymbolstyle=\logicSymbol}
+ \newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+ \newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+\end{psinputs}
+
+\title{Rechnertechnik}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{23.\ Mai 2022}
+
+\begin{document}
+
+\maketitleframe
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+ \shownosectionnonumber
+
+ \begin{itemize}
+ \item[\textbf{1}] \textbf{Einführung}
+ \item[\textbf{2}] \textbf{Vom Schaltkreis zum Computer}
+ \item[\textbf{3}] \textbf{Assember-Programmierung}
+ \begin{itemize}
+ \item[3.1] Struktur von Assembler-Programmen
+ \item[3.2] Beispiel: Redcode
+ \color{medgreen}
+ \item[3.3] Architekturmerkmale von Prozessore
+ \color{orange}
+ \item[3.4] Der CPU-Stack
+ \color{red}
+ \item[3.5] Computer-Sprachen
+ \end{itemize}
+% \color{gray}
+% \item[\textbf{5}] \textbf{Hardwarenahe Programmierung}
+% \item[\textbf{6}] \textbf{Anwender-Software}
+% \item[\textbf{7}] \textbf{Bus-Systeme}
+% \item[\textbf{8}] \textbf{Pipelining}
+% \item[\textbf{9}] \textbf{Ausblick}
+ \item[\textbf{\dots\hspace{-0.75em}}]
+ \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{2}
+\section{Assembler-Programmierung}
+\setcounter{subsection}{2}
+\subsection{Architekturmerkmale von Prozessoren}
+\subsubsection{Speicherarchitekturen}
+
+\begin{frame}
+
+ \showsubsection
+
+ Oder: Jede Assembler-Sprache ist anders.
+
+ \bigskip
+
+ \showsubsubsection
+
+ Bezeichnungen
+ \begin{itemize}
+ \item
+ \newterm{Bit\/} = 0 oder 1 -- kleinste Einheit an Information
+ \item
+ \newterm{Byte\/} = Zusammenfassung mehrerer \newterm{Bits}\\
+ zu einer Binärzahl, die ein Zeichen (\newterm{Character\/}) darstellen kann,\\
+ häufig 8 Bits (\newterm{Oktett\/})
+ \item
+ \newterm{Speicherwort\/} = Zusammenfassung mehrerer Bits\\
+ zu der kleinsten adressierbaren Einheit, häufig 1 Byte
+ \item
+ \newterm{RAM\/} = \newterm{Random Access Memory\/} = Hauptspeicher
+ \item
+ \newterm{ROM\/} = \newterm{Read Only Memory\/} = nur lesbarer Speicher
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsection
+
+ Verschiedene Arten von Speicher
+ \begin{itemize}
+ \item
+ \newterm{Prozessor-Register}\\
+ können direkt mit ALU verbunden werden,\\
+ besonders schnell (Flipflops),\\
+ überschaubare Anzahl von Registern
+ \item
+ \newterm{Hauptspeicher}\\
+ kann direkt adressiert und mit Prozessor-Registern abgeglichen werden,\\
+ heute i.\,d.\,R.\ dynamischer Speicher (Kondensatoren)
+ \item
+ \newterm{I/O-Ports}\\
+ sind spezielle Speicheradressen, über die\\
+ mit externen Geräten kommuniziert wird
+ \item
+ \newterm{Massenspeicher}\\
+ liegt auf externem Gerät, wird über I/O-Ports angesprochen,\\
+ Festplatte, Flash-Speicher, \dots
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ \newterm{Von-Neumann-Architektur}\\
+ Es gibt nur 1 Hauptspeicher, in dem sich sowohl die Befehle\\
+ als auch die Daten befinden.
+
+ \begin{onlyenv}<1>
+ \smallskip
+
+ Vorteil: Flexibilität in der Speichernutzung
+
+ Nachteil: Befehle können überschrieben werden.\\
+ $\longrightarrow$ Abstürze und Malware möglich
+ \end{onlyenv}
+
+ \pause
+ \item
+ \newterm{Harvard-Architektur}\\
+ Es gibt 2 Hauptspeicher. In einem befinden sich die Befehle,\\
+ im anderen die Daten.
+
+ \begin{onlyenv}<2>
+ \smallskip
+
+ Vorteil: Befehle können nicht überschrieben werden\\
+ $\longrightarrow$ sicherer als Von-Neumann-Architektur
+
+ Nachteile: Leitungen zum Speicher (Bus) müssen doppelt vorhanden sein,\\
+ freier Befehlsspeicher kann nicht für Daten genutzt werden.
+ \end{onlyenv}
+
+ \pause
+ \item
+ Weitere Kombinationen\\
+ Hauptspeicher und I/O-Ports gemeinsam oder getrennt,\\
+ Hauptspeicher und Prozessorregister gemeinsam oder getrennt
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ Beispiele:
+ \begin{itemize}
+ \item
+ Intel IA-32, AMD64:\\
+ Von-Neumann-Architektur (plus Speicherschutzmechanismen),\\
+ Prozessorregister und I/O-Ports vom Hauptspeicher getrennt
+ \item
+ Atmel AVR (z.\,B.\ ATmega):\\
+ Harvard-Architektur\\
+ (Befehlsspeicher als Flash-Speicher grundsätzlich auch schreibbar),\\
+ Prozessorregister und I/O-Ports in gemeinsamem Adressbereich mit Hauptspeicher
+ \item
+ 6502, Renesas 740-CPU, Renesas-38000-Mikrocontroller:\\
+ Von-Neumann-Architektur,\\
+ I/O-Ports in gemeinsamem Adressbereich mit Hauptspeicher,\\
+ Prozessorregister und Hauptspeicher getrennt
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Registerarchitekturen}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ \vspace*{-\medskipamount}
+
+ \begin{itemize}
+ \item
+ Mehrere Register, einzeln ansprechbar
+ \item
+ \newterm{Akkumulator\/}: Nur 1 Register kann rechnen.
+ \item
+ \newterm{Stack-Architektur\/}: Stapel, "`umgekehrte Polnische Notation"'
+ \end{itemize}
+
+ \pause
+
+ Operationen: typischerweise nur
+ \lstinline{=}, \lstinline{+=}, \lstinline{-=}, \lstinline{*=}, \lstinline{/=}, \dots
+
+ \pause
+ \medskip
+
+ Beispiel: \lstinline{c = a + 2 * b;}
+
+ \pause
+ \medskip
+
+ \begin{minipage}[t]{2cm}
+ C, Java:\smallskip\par
+ \begin{lstlisting}[gobble=6]
+ R = b;
+ R *= 2;
+ R += a;
+ c = R;
+ \end{lstlisting}
+ \end{minipage}\pause
+ \begin{minipage}[t]{4cm}
+ Mehrere Register:\smallskip\par
+ \begin{lstlisting}[style=asm,gobble=6]
+ movl (b), %eax
+ imull $2, %eax, %eax
+ addl (a), %eax
+ movl %eax, (c)
+ \end{lstlisting}
+ \smallskip\par
+ (IA-32-Assembler)
+ \end{minipage}\pause
+ \begin{minipage}[t]{3cm}
+ Akkumulator:\smallskip\par
+ \begin{lstlisting}[style=asm,gobble=6]
+ load (b)
+ mul $2
+ add (a)
+ store (c)
+ \end{lstlisting}
+ \smallskip\par
+ (Pseudo-Assembler)
+ \end{minipage}\pause
+ \begin{minipage}[t]{3cm}
+ Register-Stack:\smallskip\par
+ \begin{lstlisting}[style=asm,gobble=6]
+ push (a)
+ push (b)
+ push $2
+ mul
+ add
+ pop (c)
+ \end{lstlisting}
+ \end{minipage}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ Beispiele:
+ \begin{itemize}
+ \item
+ Intel IA-32, AMD64:\\
+ Mehrere Register, für verschiedene Zwecke spezialisiert (unübersichtlich),\\[\smallskipamount]
+ Fließkommaregister: Stack-Architektur
+ \item
+ Atmel AVR (z.\,B.\ ATmega):\\
+ 32 Register
+ \item
+ 6502, Renesas 740-CPU, Renesas-38000-Mikrocontroller:\\
+ 3 Register: A, X, Y. Nur A kann rechnen $\longrightarrow$ Akkumulator
+ \item
+ Java Virtual Machine (JVM):\\
+ Stack-Architektur
+ \item
+ Redcode:\\
+ Jede Speicherzelle fungiert als Register
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Befehlssätze}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ \newterm{Reduced Instruction Set Computer (RISC)}
+
+ \smallskip
+
+ wenige, wenig mächtige Befehle
+
+ \begin{onlyenv}<1>
+ \textarrow\ Programmierung in Assembler für Menschen unkomfortabel\\
+ \textarrow\ schnelle Abarbeitung der Befehle
+
+ \medskip
+
+ Beispiel: Atmel AVR
+ \begin{itemize}
+ \item
+ Der ``load immediate''-Befehl funktioniert nur
+ für die Register 16 bis 31,\\
+ nicht für die Register 0 bis 15.
+ \item
+ Die meisten Befehle werden in nur 1 Taktzyklus abgearbeitet.
+ \end{itemize}
+
+ \medskip
+
+ Beispiel: Redcode ICWS-86
+ \begin{itemize}
+ \item
+ Es gibt indirekte Adressierung mit Prä-Dekrement,\\
+ aber nicht mit Prä-Inkrement.
+ \item
+ Alle Befehle werden in nur 1 Taktzyklus abgearbeitet.
+ \end{itemize}
+ \end{onlyenv}
+
+ \pause
+ \medskip
+ \item
+ \newterm{Complex Instruction Set Computer (CISC)}
+
+ \smallskip
+
+ Umfangreiche Befehlssätze, mächtige Befehle
+
+ \begin{onlyenv}<2>
+ \textarrow\ komfortable manuelle Programmierung in Assembler\\
+ \textarrow\ längere Abarbeitungszeit der einzelnen Befehle
+
+ \smallskip
+
+ Realisierung: "`Prozessor im Prozessor"' -- \newterm{Mikroprogramme}
+
+ \medskip
+
+ Beispiel: Intel IA-32, AMD64
+ \begin{itemize}
+ \item
+ Es gibt spezielle Befehle für BCD- und String-Operationen.
+ \item
+ Befehle benötigen meistens 2 oder mehr,\\
+ gelegentlich (z.\,B.\ Fließkomma-Operationen) auch über 100 Taktzyklen.
+ \end{itemize}
+ \end{onlyenv}
+
+ \medskip
+ \pause
+ \item
+ \newterm{Very Long Instruction Word (VLIW)\/} und\\
+ \newterm{Explicitly Parallel Instruction Computing (EPIC)}
+
+ \smallskip
+
+ mehrere Befehle gleichzeitig ausführbar
+
+ \begin{onlyenv}<3>
+ \textarrow\ mehr Rechenleistung möglich\\
+ \textarrow\ Programmierung sehr aufwendig
+
+ \medskip
+
+ Beispiel: Intel IA-64
+ \end{onlyenv}
+
+ \pause
+ \medskip
+ \item
+ \newterm{Orthogonaler Befehlssatz}
+
+ \smallskip
+
+ Jeder Befehl ist mit jeder Adressierungsart kombinierbar.
+
+ \medskip
+
+ Beispiel: Redcode
+ \end{itemize}
+ \vspace*{-4cm}
+
+\end{frame}
+
+\subsection{Der CPU-Stack\label{CPU-Stack}}
+\addtocounter{subsubsection}{-1}
+\subsubsection{Was ist ein Stack?}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ \bigskip
+
+\iffalse
+
+ \begin{minipage}[b]{6cm}
+ \begin{center}
+ "`First In -- First Out"'
+
+ \bigskip
+
+ \begin{picture}(6,4)
+ \thicklines
+ \color{structure}
+ \put(0.5,0){\line(1,0){5}}
+
+ \put(3.5,0){\only<1-5>{\line(0,1){1}}}
+ \put(4.5,0){\only<1-4>{\line(0,1){1}}}
+ \put(3.5,1){\only<1-4>{\line(1,0){1}}}
+ \put(4.0,0.5){\only<1-4>{\makebox(0,0){\lstinline{3}}}}
+ \put(3.0,1.5){\only<1>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(3.0,1.5){\only<1>{\makebox(0,0)[b]{\lstinline{push (3)}}}}
+
+ \put(2.5,0){\only<2-6>{\line(0,1){1}}}
+ \put(2.5,1){\only<2-5>{\line(1,0){1}}}
+ \put(3.0,0.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
+ \put(2.0,1.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(2.0,1.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
+
+ \put(1.5,0){\only<3-6>{\line(0,1){1}}}
+ \put(1.5,1){\only<3-6>{\line(1,0){1}}}
+ \put(2.0,0.5){\only<3-6>{\makebox(0,0){\lstinline{137}}}}
+ \put(1.0,1.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(1.0,1.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
+
+ \put(4.55,1.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(5.00,1.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
+
+ \put(3.55,1.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,1.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
+
+ \put(2.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(3.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
+ \end{picture}
+
+ \bigskip
+
+ FIFO = Queue = Reihe
+ \end{center}
+ \end{minipage}\hfill
+
+\fi
+
+ \begin{minipage}[b]{6cm}
+ \begin{center}
+ "`Last In -- First Out"'
+
+ \bigskip
+
+ \begin{picture}(6,4)
+ \thicklines
+ \color{structure}
+ \put(1.5,0){\line(1,0){3}}
+
+ \put(2.5,0){\line(0,1){1}}
+ \put(3.5,0){\line(0,1){1}}
+ \put(2.5,1){\line(1,0){1}}
+ \put(3.0,0.5){\makebox(0,0){\lstinline{3}}}
+ \put(2.0,1.5){\only<1>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(2.0,1.5){\only<1>{\makebox(0,0)[b]{\lstinline{push (3)}}}}
+
+ \put(2.5,1){\only<2-5>{\line(0,1){1}}}
+ \put(3.5,1){\only<2-5>{\line(0,1){1}}}
+ \put(2.5,2){\only<2-5>{\line(1,0){1}}}
+ \put(3.0,1.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
+ \put(2.0,2.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(2.0,2.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
+
+ \put(2.5,2){\only<3-4>{\line(0,1){1}}}
+ \put(3.5,2){\only<3-4>{\line(0,1){1}}}
+ \put(2.5,3){\only<3-4>{\line(1,0){1}}}
+ \put(3.0,2.5){\only<3-4>{\makebox(0,0){\lstinline{137}}}}
+ \put(2.0,3.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(2.0,3.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
+
+ \put(3.55,3.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,3.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
+
+ \put(3.55,2.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,2.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
+
+ \put(3.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
+ \end{picture}
+
+ \bigskip
+
+ LIFO = Stack = Stapel
+ \end{center}
+ \end{minipage}
+
+%
+% \dots
+
+\end{frame}
+\subsubsection{Implementierung}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Speicher, in dem Werte "`gestapelt"' werden: \newterm{Stack}
+
+ \begin{itemize}
+ \item
+ Speicherbereich (ein array) reservieren
+ \item
+ Variable (typischerweise: Prozessorregister) als
+ \newterm{Stack Pointer\/} reservieren \textarrow\ \lstinline{SP}
+ \item
+ Assembler-Befehl \lstinline[style=asm]{push foo}: \quad
+ \lstinline{*SP++ = foo;}
+ \begin{itemize}
+ \item
+ In der Speicherzelle,
+ auf die der Stack Pointer \lstinline{SP} gerade zeigt,\\
+ den Wert \lstinline{foo} speichern.
+ \item
+ Danach den Stack Pointer inkrementieren (um 1 erhöhen).
+ \end{itemize}
+ \item
+ Assembler-Befehl \lstinline[style=asm]{pop bar}: \quad
+ \lstinline{bar = *--SP;}
+ \begin{itemize}
+ \item
+ Zuerst den Stack Pointer dekrementieren (um 1 erniedrigen).
+ \item
+ Danach aus der Speicherzelle,\\
+ auf die der Stack Pointer \lstinline{SP} gerade zeigt,\\
+ einen Wert lesen und in der Variablen \lstinline{bar} speichern.
+ \end{itemize}
+ \end{itemize}
+
+ \pause
+ \medskip
+ Speziell: Unterprogramme
+
+\end{frame}
+
+\subsubsection{Unterprogramme}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{minipage}[t]{4.5cm}
+ Parameter:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \item
+ CPU-Stack
+ \end{itemize}
+
+ \smallskip
+
+ Rückgabewert:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \end{itemize}
+ \end{minipage}%
+ \begin{minipage}[t]{5cm}
+ Aufruf:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{push IP}\\
+ \lstinline[style=asm]{jmp foo}
+ {\color{red}\boldmath $\longleftarrow$ mov \#foo IP}\\
+ \textarrow\ \lstinline[style=asm]{call foo}
+ \end{itemize}
+ Rücksprung:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{pop IP}\\
+ \textarrow\ \lstinline[style=asm]{ret}
+ \end{itemize}
+ \end{minipage}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{minipage}[t]{4.5cm}
+ Parameter:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \item
+ CPU-Stack
+ \end{itemize}
+
+ \smallskip
+
+ Rückgabewert:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \end{itemize}
+ \end{minipage}%
+ \begin{minipage}[t]{5cm}
+ Aufruf:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{push IP}\\
+ \lstinline[style=asm]{jmp foo}
+ {\color{red}\boldmath $\longleftarrow$ mov \#foo IP}\\
+ \textarrow\ \lstinline[style=asm]{call foo}
+ \end{itemize}
+ Rücksprung:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{pop IP}\\
+ \textarrow\ \lstinline[style=asm]{ret}
+ \end{itemize}
+ \end{minipage}
+
+ \bigskip
+
+ \subsubsection{Lokale Variable}
+ \showsubsubsection
+
+ \dots\ speichert man oft ebenfalls auf dem Stack.
+
+ \smallskip
+
+ Speicherplatz reservieren: Stack-Pointer modifizieren
+
+ \medskip
+
+ \newterm{Buffer Overflow\/}:\\
+ Über die Grenzen einer lokalen Variablen hinausschreiben,\\
+ dabei Rücksprungadresse überschreiben \textarrow\ Absturz
+
+\end{frame}
+
+\subsubsection{Register sichern}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Ein Unterprogramm verändert Registerinhalte.
+ \begin{itemize}
+ \item
+ im Hauptprogramm nötigenfalls vor Aufruf sichern
+ \item
+ im Unterprogramm vor Benutzung sichern
+ \item
+ Kombinationen (manche Register so, manche so)
+ \end{itemize}
+
+\end{frame}
+
+\subsection{Computer-Sprachen}
+\subsubsection{Maschinensprache}
+
+\iffalse
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ \strut\hfill
+ \begin{minipage}{6.5cm}
+ \vspace*{-1.7cm}
+ \small
+ Computer
+ \begin{itemize}\itemsep0pt
+ \item Rechenwerk (ALU)
+ \item Speicher: Register,\\
+ adressierbarer Hauptspeicher
+ \item Takt: Befehle abarbeiten
+ \item Peripherie: Kommunikation\\
+ mit der Außenwelt
+ \arrowitem in Maschinensprache programmierbar
+ \end{itemize}
+ \end{minipage}\hspace*{-0.5cm}
+
+ In jedem Takt:
+ \begin{itemize}
+ \item
+ dort aus dem Hauptspeicher lesen, wohin das Register \lstinline{IP} zeigt\\
+ \textarrow\ \newterm{Befehl\/} (\newterm{Instruction\/} -- \lstinline{IP} = \newterm{Instruction Pointer\/})
+ \item
+ den \newterm{Befehl\/} an den \newterm{Funktion\/}-Eingang der \newterm{ALU\/} legen
+ \item
+ auf ähnliche Weise weitere Daten an den \newterm{Akkumulator\/}-\\
+ und den \newterm{Daten\/}-Eingang der \newterm{ALU\/} legen
+ \item
+ auf ähnliche Weise den \newterm{Ergebnis\/}-Ausgang der \newterm{ALU}\\
+ in den Hauptspeicher schreiben
+ \textarrow\ Befehl ausgeführt
+ \item
+ Register \lstinline{IP} hochzählen
+ \textarrow\ nächster Befehl
+ \arrowitem
+ Maschinensprache
+ \end{itemize}
+
+\end{frame}
+
+\fi
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\\
+ arithmetische Befehle\\
+ unbedingte und bedingte Sprungbefehle
+ \arrowitem
+ Der Computer kann "`alles"' -- \newterm{Turing-Vollständigkeit}
+ \bigskip
+ \item
+ Maschinensprache = Zahlen \textarrow\ für Menschen schwer handhabbar
+ \arrowitem
+ Namen für die Befehle: \newterm{Mnemonics}
+ \arrowitem
+ \newterm{Assembler\/}-Sprache
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{\strut{\protect\color{gray}Maschinensprache \protect\textarrow\ }Assembler}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ Beispiel: Intel-x86-16-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{mov}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{inc}, \lstinline{dec},
+ \lstinline{xor}, \lstinline{cmp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{jmp}, \lstinline{jz}, \lstinline{jae}, \dots
+ \item
+ Register\hfill
+ \lstinline{ax}, \lstinline{bx}, \dots
+ \end{itemize}
+
+% \begin{onlyenv}<1>
+% \begin{center}
+%% \includegraphics[width=10cm]{programm-screenshot.png}
+% \vspace*{-0.5cm}
+% \end{center}
+% \end{onlyenv}
+% \begin{onlyenv}<2->
+
+ \bigskip
+
+ Beispiel: Atmel-AVR-8-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{ldi}, \lstinline{lds}, \lstinline{sti}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{subi},
+ \lstinline{eor}, \lstinline{cp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{rjmp}, \lstinline{brsh}, \lstinline{brlo}, \dots
+ \item
+ Register\hfill
+ \lstinline{r0}, \lstinline{r1}, \dots
+ \end{itemize}
+
+ \bigskip
+
+ \textarrow\ für jeden Prozessor anders
+
+% \end{onlyenv}
+
+\end{frame}
+
+\subsubsection{\strut{\protect\color{gray}Maschinensprache \protect\textarrow\ Assembler \protect\textarrow\ }Hochsprachen}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ Beispiel: Intel-x86-16-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{mov}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{inc}, \lstinline{dec},
+ \lstinline{xor}, \lstinline{cmp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{jmp}, \lstinline{jz}, \lstinline{jae}, \dots
+ \item
+ Register\hfill
+ \lstinline{ax}, \lstinline{bx}, \dots
+ \end{itemize}
+
+ \bigskip
+
+ Beispiel: Atmel-AVR-8-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{ldi}, \lstinline{lds}, \lstinline{sti}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{subi},
+ \lstinline{eor}, \lstinline{cp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{rjmp}, \lstinline{brsh}, \lstinline{brlo}, \dots
+ \item
+ Register\hfill
+ \lstinline{r0}, \lstinline{r1}, \dots
+ \end{itemize}
+
+ \bigskip
+
+ \textarrow\ für jeden Prozessor anders
+
+ \bigskip
+
+ Hochsprache \textarrow\ für jeden Prozessor gleich
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ Compiler-Sprachen
+ \begin{itemize}
+ \item
+ \newterm{Compiler\/} übersetzt Hochsprachen-\newterm{Quelltext\/} in die Assembler-Sprache
+ \item
+ \newterm{Assembler\/} übersetzt Assembler-Quelltext in die Maschinensprache
+ \item
+ Compiler und Assembler sind Programme,\\
+ geschrieben in Maschinensprache, Assembler oder einer Hochsprache
+ \item
+ Beispiele: Fortran, Algol, Pascal, Ada, C, C++, \dots
+ \end{itemize}
+
+ \pause
+ \medskip
+ Interpreter- oder Skript-Sprachen
+ \begin{itemize}
+ \item
+ \newterm{Interpreter\/} liest Hochsprachen-\newterm{Quelltext\/} und führt ihn sofort aus
+ \item
+ Der Interpreter ist ein Programm,\\
+ geschrieben in Maschinensprache, Assembler oder einer Hochsprache
+ \item
+ Beispiele: Unix-Shell, BASIC, Perl, Python, \dots
+ \end{itemize}
+
+ \pause
+ \medskip
+ Kombinationen
+ \begin{itemize}
+ \item
+ \newterm{Compiler\/} erzeugt \newterm{Zwischencode\/} für eine \newterm{virtuelle Maschine}
+ \item
+ \newterm{Interpreter\/} liest Hochsprachen-\newterm{Zwischencode\/} und führt ihn sofort aus
+ \item
+ Die virtuelle Maschine ist ein Programm,
+ geschrieben in Maschinensprache, Assembler, einer Hoch- oder Skript-Sprache
+ \item
+ Beispiele: UCSD-Pascal, Java, \dots
+ \end{itemize}
+ \medskip
+
+\end{frame}
+
+\section{Hardwarenahe Programmierung}
+\subsection{Bit-Operationen}
+\subsubsection{Zahlensysteme}
+
+\begin{frame}[fragile]
+
+ \showsection
+ \vspace*{-\smallskipamount}
+ \showsubsection
+ \vspace*{-\medskipamount}
+ \showsubsubsection
+
+ \begin{tabular}{rlrl}
+ Basis & Name & Beispiel & Anwendung \\[\smallskipamount]
+ 2 & Binärsystem & 1\,0000\,0011 & Bit-Operationen \\
+ 8 & Oktalsystem & \lstinline,0403, & Dateizugriffsrechte (Unix) \\
+ 10 & Dezimalsystem & \lstinline,259, & Alltag \\
+ 16 & Hexadezimalsystem & \lstinline,0x103, & Bit-Operationen \\
+ 256 & (keiner gebräuchlich) & 0.0.1.3 & IP-Adressen (IPv4)
+ \end{tabular}
+
+ \bigskip
+
+ \begin{itemize}
+ \item
+ Computer rechnen im Binärsystem.
+ \item
+ Für viele Anwendungen (z.\,B.\ I/O-Ports, Grafik, \dots) ist es notwendig,\\
+ Bits in Zahlen einzeln ansprechen zu können.
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ \begin{tabular}{rlrlrc}
+ \qquad 000 & \bf 0 \hspace*{1.5cm} & 0000 & \bf 0 & \quad 1000 & \bf 8\\
+ 001 & \bf 1 & 0001 & \bf 1 & 1001 & \bf 9\\
+ 010 & \bf 2 & 0010 & \bf 2 & 1010 & \bf A\\
+ 011 & \bf 3 & 0011 & \bf 3 & 1011 & \bf B\\[\smallskipamount]
+ 100 & \bf 4 & 0100 & \bf 4 & 1100 & \bf C\\
+ 101 & \bf 5 & 0101 & \bf 5 & 1101 & \bf D\\
+ 110 & \bf 6 & 0110 & \bf 6 & 1110 & \bf E\\
+ 111 & \bf 7 & 0111 & \bf 7 & 1111 & \bf F\\
+ \end{tabular}
+
+ \medskip
+
+ \begin{itemize}
+ \item
+ Oktal- und Hexadezimalzahlen lassen sich ziffernweise\\
+ in Binär-Zahlen umrechnen.
+ \item
+ Hexadezimalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+ gruppiert zu jeweils 4 Bits.
+ \item
+ Oktalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+ gruppiert zu jeweils 3 Bits.
+ \item
+ Trotz Taschenrechner u.\,ä.\ lohnt es sich,\\
+ die o.\,a.\ Umrechnungstabelle \textbf{auswendig} zu kennen.
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Bit-Operationen in C}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ \begin{tabular}{lll}
+ C-Operator & Verknüpfung & Anwendung \\[\smallskipamount]
+ \lstinline,&, & Und & Bits gezielt löschen \\
+ \lstinline,|, & Oder & Bits gezielt setzen \\
+ \lstinline,^, & Exklusiv-Oder & Bits gezielt invertieren \\
+ \lstinline,~, & Nicht & Alle Bits invertieren \\[\smallskipamount]
+ \lstinline,<<, & Verschiebung nach links & Maske generieren \\
+ \lstinline,>>, & Verschiebung nach rechts & Bits isolieren
+ \end{tabular}
+
+ \bigskip
+
+ Numerierung der Bits: von rechts ab 0
+
+ \medskip
+
+ \begin{tabular}{ll}
+ Bit Nr.\ 3 auf 1 setzen: &
+ \lstinline,a |= 1 << 3;, \\
+ Bit Nr.\ 4 auf 0 setzen: &
+ \lstinline,a &= ~(1 << 4);, \\
+ Bit Nr.\ 0 invertieren: &
+ \lstinline,a ^= 1 << 0;,
+ \end{tabular}
+
+ \smallskip
+
+ ~~Abfrage, ob Bit Nr.\ 1 gesetzt ist:\quad
+ \lstinline{if (a & (1 << 1))}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ C-Datentypen für Bit-Operationen:
+ \smallskip\par
+ \lstinline{#include <stdint.h>}
+ \medskip\par
+ \begin{tabular}{lllll}
+ & 8 Bit & 16 Bit & 32 Bit & 64 Bit \\
+ mit Vorzeichen & \lstinline,int8_t,
+ & \lstinline,int16_t,
+ & \lstinline,int32_t,
+ & \lstinline,int64_t, \\
+ ohne Vorzeichen & \lstinline,uint8_t,
+ & \lstinline,uint16_t,
+ & \lstinline,uint32_t,
+ & \lstinline,uint64_t,
+ \end{tabular}
+
+ \bigskip
+ \bigskip
+
+ Ausgabe:
+ \smallskip\par
+ \begin{lstlisting}
+ #include <stdio.h>
+ #include <stdint.h>
+ #include <inttypes.h>
+ ...
+ uint64_t x = 42;
+ printf ("Die Antwort lautet: %" PRIu64 "\n", x);
+ \end{lstlisting}
+
+\iffalse
+
+ \bigskip
+
+ Aufgabe: Schreiben Sie C-Funktionen, die ein "`Array von Bits"' realisieren, z.\,B.
+
+ \smallskip
+
+ \begin{tabular}[t]{ll}
+ \lstinline|void set_bit (int i);| & Bei Index $i$ auf 1 setzen \\
+ \lstinline|void clear_bit (int i);| & Bei Index $i$ auf 0 setzen \\
+ \lstinline|int get_bit (int i);| & Bei Index $i$ lesen
+ \end{tabular}
+
+ \medskip
+
+ Hinweise:
+ \begin{itemize}
+ \item
+ Die Größe des Bit-"`Arrays"' (z.\,B.\ 1000) dürfen Sie als \emph{vorher bekannt\/} voraussetzen.
+ \item
+ Sie benötigen ein Array, z.\,B.\ von \lstinline|char|- oder \lstinline|int|-Variablen.
+ \item
+ Sie benötigen eine Division (\lstinline|/|) sowie den Divisionsrest (Modulo: \lstinline|%|).
+ \end{itemize}
+
+\fi
+
+\end{frame}
+
+\subsection{I/O-Ports}
+
+\begin{frame}[fragile]
+
+% \showsection
+ \showsubsection
+ \vspace*{-1.5\medskipamount}
+ {\large\textbf{\color{structure}4.3\quad Interrupts}}
+
+ \bigskip
+
+ Kommunikation mit externen Geräten
+
+ \bigskip
+
+ \begin{center}
+ \includegraphics{io-ports-and-interrupts.pdf}
+ \end{center}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ In Output-Port schreiben = Aktoren ansteuern
+
+ Beispiel: LED
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/io.h>
+ ...
+ DDRC = 0x70;
+ PORTC = 0x40;
+ \end{lstlisting}
+ \begin{picture}(0,0)
+ \put(3,0.67){\begin{minipage}{3cm}
+ \color{red}%
+ binär: 0111\,0000\\
+ binär: 0100\,0000
+ \end{minipage}}
+ \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+ \end{picture}
+
+ \bigskip
+
+ \lstinline{DDR} = Data Direction Register\\
+ Bit = 1 für Output-Port\\
+ Bit = 0 für Input-Port
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Aus Input-Port lesen = Sensoren abfragen
+
+ Beispiel: Taster
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/io.h>
+ ...
+ DDRC = 0xfd;
+ while ((PINC & 0x02) == 0)
+ ; /* just wait */
+ \end{lstlisting}
+ \begin{picture}(0,0)(-1.5,-0.42)
+ \put(3,0.67){\begin{minipage}{3cm}
+ \color{red}%
+ binär: 1111\,1101\\
+ binär: 0000\,0010
+ \end{minipage}}
+ \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+ \end{picture}
+
+ \bigskip
+
+ \lstinline{DDR} = Data Direction Register\\
+ Bit = 1 für Output-Port\\
+ Bit = 0 für Input-Port
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+ \bigskip
+
+ Praktikumsaufgabe: Druckknopfampel
+
+\end{frame}
+
+\subsection{Interrupts}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Externes Gerät ruft (per Stromsignal) Unterprogramm auf
+
+ Zeiger hinterlegen: "`Interrupt-Vektor"'
+
+ Beispiel: eingebaute Uhr\hfill
+ \makebox(0,0)[tr]{%
+ \only<1->{\begin{minipage}[t]{4.7cm}
+ \vspace*{-0.3cm}%
+ statt Zählschleife (\lstinline{_delay_ms}):\\
+ Hauptprogramm kann\\
+ andere Dinge tun
+ \end{minipage}}%
+ }
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/interrupt.h>
+
+ ...
+
+
+ ISR (TIMER0B_COMP_vect)
+ {
+ PORTD ^= 0x40;
+ }
+ \end{lstlisting}
+ \begin{picture}(0,0)
+ \color{red}
+ \put(1.9,3.1){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-1.4,-1.0);}}}
+ \put(2.0,3.2){\makebox(0,0)[l]{"`Dies ist ein Interrupt-Handler."'}}
+ \put(2.3,2.6){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-0.6,-0.55);}}}
+ \put(2.4,2.6){\makebox(0,0)[l]{Interrupt-Vektor darauf zeigen lassen}}
+ \end{picture}
+
+ Initialisierung über spezielle Ports:
+ \lstinline{TCCR0B}, \lstinline{TIMSK0}
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+ \vspace*{-2.5cm}\hfill
+ {\color{red}Herstellerspezifisch!}%
+ \hspace*{1cm}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Externes Gerät ruft (per Stromsignal) Unterprogramm auf
+
+ Zeiger hinterlegen: "`Interrupt-Vektor"'
+
+ Beispiel: Taster\hfill
+ \makebox(0,0)[tr]{%
+ \begin{minipage}[t]{4.7cm}
+ \vspace*{-0.3cm}%
+ statt \newterm{Busy Waiting\/}:\\
+ Hauptprogramm kann\\
+ andere Dinge tun
+ \end{minipage}}
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/interrupt.h>
+ ...
+
+ ISR (INT0_vect)
+ {
+ PORTD ^= 0x40;
+ }
+ \end{lstlisting}
+
+ \medskip
+
+ Initialisierung über spezielle Ports:
+ \lstinline{EICRA}, \lstinline{EIMSK}
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+ \vspace*{-2.5cm}\hfill
+ {\color{red}Herstellerspezifisch!}%
+ \hspace*{1cm}
+
+\end{frame}
+
+\subsection{volatile-Variable}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Externes Gerät ruft (per Stromsignal) Unterprogramm auf
+
+ Zeiger hinterlegen: "`Interrupt-Vektor"'
+
+ Beispiel: Taster
+
+ \vspace*{-2.5pt}
+
+ \begin{minipage}[t]{5cm}
+ \begin{onlyenv}<1>
+ \begin{lstlisting}[gobble=8]
+ ¡#include <avr/interrupt.h>
+ ...
+
+ uint8_t key_pressed = 0;
+
+ ISR (INT0_vect)
+ {
+ key_pressed = 1;
+ }¿
+ \end{lstlisting}
+ \end{onlyenv}
+ \begin{onlyenv}<2>
+ \begin{lstlisting}[gobble=8]
+ ¡#include <avr/interrupt.h>
+ ...
+
+ volatile uint8_t key_pressed = 0;
+
+ ISR (INT0_vect)
+ {
+ key_pressed = 1;
+ }¿
+ \end{lstlisting}
+ \end{onlyenv}
+ \end{minipage}\hfill
+ \begin{minipage}[t]{6cm}
+ \begin{lstlisting}[gobble=6]
+ ¡int main (void)
+ {
+ ...
+
+ while (1)
+ {
+ while (!key_pressed)
+ ; /* just wait */
+ PORTD ^= 0x40;
+ key_pressed = 0;
+ }
+ return 0;
+ }¿
+ \end{lstlisting}
+ \end{minipage}
+
+ \pause
+ \begin{picture}(0,0)
+ \color{red}
+ \put(10.3,4.0){\makebox(0,0)[b]{\begin{minipage}{6cm}
+ \begin{center}
+ \textbf{volatile}:\\
+ Speicherzugriff\\
+ nicht wegoptimieren
+ \end{center}
+ \end{minipage}}}
+ \put(10.3,3.95){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-0.5,-0.9);}}}
+ \end{picture}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Was ist eigentlich \lstinline{PORTD}?
+
+ \bigskip
+ \pause
+
+ \lstinline[style=cmd]{avr-gcc -Wall -Os -mmcu=atmega328p blink-3.c -E}
+
+ \bigskip
+ \pause
+ \lstinline{PORTD = 0x01;}\\
+ \textarrow\quad
+ \lstinline[style=terminal]{(*(volatile uint8_t *)((0x0B) + 0x20)) = 0x01;}\\
+ \pause
+ \begin{picture}(0,2)(0,-1.7)
+ \color{red}
+ \put(5.75,0.3){$\underbrace{\rule{2.95cm}{0pt}}_{\mbox{Zahl: \lstinline|0x2B|}}$}
+ \pause
+ \put(1.55,0.3){$\underbrace{\rule{4.0cm}{0pt}}_{\mbox{\shortstack[t]{Umwandlung in Zeiger\\
+ auf \lstinline|volatile uint8_t|}}}$}
+ \pause
+ \put(1.32,-1){\makebox(0,0)[b]{\tikz{\draw[-latex](0,0)--(0,1.3)}}}
+ \put(1.12,-1.1){\makebox(0,0)[tl]{Dereferenzierung des Zeigers}}
+ \end{picture}
+
+ \pause
+ \textarrow\quad
+ \lstinline|volatile uint8_t|-Variable an Speicheradresse \lstinline|0x2B|
+
+ \pause
+ \bigskip
+ \bigskip
+
+ \textarrow\quad
+ \lstinline|PORTA = PORTB = PORTC = PORTD = 0| ist eine schlechte Idee.
+
+\end{frame}
+
+\subsection{Byte-Reihenfolge -- Endianness}
+\subsubsection{Konzept}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ Eine Zahl geht über mehrere Speicherzellen.\\
+ Beispiel: 16-Bit-Zahl in 2 8-Bit-Speicherzellen
+
+ \smallskip
+
+ Welche Bits liegen wo?
+
+% \pause
+ \bigskip
+
+ $1027 = 1024 + 2 + 1 = 0000\,0100\,0000\,0011_2 = 0403_{16}$
+
+% \pause
+ \bigskip
+ Speicherzellen:
+
+ \medskip
+ \begin{tabular}{|c|c|l}\cline{1-2}
+ \raisebox{-0.25ex}{04} & \raisebox{-0.25ex}{03} & \strut Big-Endian "`großes Ende zuerst"' \\\cline{1-2}
+ \multicolumn{2}{c}{} & % \pause
+ für Menschen leichter lesbar % \pause
+ \\
+ \multicolumn{3}{c}{} \\[-5pt]\cline{1-2}
+ \raisebox{-0.25ex}{03} & \raisebox{-0.25ex}{04} & \strut Little-Endian "`kleines Ende zuerst"' \\\cline{1-2}
+ \multicolumn{2}{c}{} & % \pause
+ bei Additionen effizienter
+ \end{tabular}
+
+% \pause
+ \medskip
+ \textarrow\ Geschmackssache
+% \pause\\
+ \quad\textbf{\dots\ außer bei Datenaustausch!}
+
+% \pause
+% \bigskip
+%
+% Aber: nicht verwechseln! \qquad $0304_{16} = 772$
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Eine Zahl geht über mehrere Speicherzellen.\\
+ Beispiel: 16-Bit-Zahl in 2 8-Bit-Speicherzellen
+
+ \smallskip
+
+ Welche Bits liegen wo?
+
+ \medskip
+
+ \textarrow\ Geschmackssache\\
+ \textbf{\dots\ außer bei Datenaustausch!}
+
+ \begin{itemize}
+ \item
+ Dateiformate
+ \item
+ Datenübertragung
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Dateiformate}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Audio-Formate: Reihenfolge der Bytes in 16- und 32-Bit-Zahlen
+ \begin{itemize}
+ \item
+ RIFF-WAVE-Dateien (\file{.wav}): Little-Endian
+ \item
+ Au-Dateien (\file{.au}): Big-Endian
+% \pause
+ \item
+ ältere AIFF-Dateien (\file{.aiff}): Big-Endian
+ \item
+ neuere AIFF-Dateien (\file{.aiff}): Little-Endian
+ \end{itemize}
+
+% \pause
+ \bigskip
+
+ Grafik-Formate: Reihenfolge der Bits in den Bytes
+ \begin{itemize}
+ \item
+ PBM-Dateien: Big-Endian\only<1->{, MSB first}
+ \item
+ XBM-Dateien: Little-Endian\only<1->{, LSB first}
+ \end{itemize}
+ \only<1->{MSB/LSB = most/least significant bit}
+
+\end{frame}
+
+\subsubsection{Datenübertragung}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ RS-232 (serielle Schnittstelle): LSB first
+ \item
+ I$^2$C: MSB first
+ \item
+ USB: beides
+ \pause
+ \medskip
+ \item
+ Ethernet: LSB first
+ \item
+ TCP/IP (Internet): Big-Endian
+ \end{itemize}
+
+\end{frame}
+
+\iffalse
+
+\subsection{Binärdarstellung negativer Zahlen}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Speicher ist begrenzt!\\
+ \textarrow\ feste Anzahl von Bits
+
+ \medskip
+
+ 8-Bit-Zahlen ohne Vorzeichen: \lstinline{uint8_t}\\
+ \textarrow\ Zahlenwerte von \lstinline{0x00} bis \lstinline{0xff} = 0 bis 255\\
+ \pause
+ \textarrow\ 255 + 1 = 0
+
+ \pause
+ \medskip
+
+ 8-Bit-Zahlen mit Vorzeichen: \lstinline{int8_t}\\
+ \lstinline{0xff} = 255 ist die "`natürliche"' Schreibweise für $-1$.\\
+ \pause
+ \textarrow\ Zweierkomplement
+
+ \pause
+ \medskip
+
+ Oberstes Bit = 1: negativ\\
+ Oberstes Bit = 0: positiv\\
+ \textarrow\ 127 + 1 = $-128$
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Speicher ist begrenzt!\\
+ \textarrow\ feste Anzahl von Bits
+
+ \medskip
+
+ 16-Bit-Zahlen ohne Vorzeichen:
+ \lstinline{uint16_t}\hfill\lstinline{uint8_t}\\
+ \textarrow\ Zahlenwerte von \lstinline{0x0000} bis \lstinline{0xffff}
+ = 0 bis 65535\hfill 0 bis 255\\
+ \textarrow\ 65535 + 1 = 0\hfill 255 + 1 = 0
+
+ \medskip
+
+ 16-Bit-Zahlen mit Vorzeichen:
+ \lstinline{int16_t}\hfill\lstinline{int8_t}\\
+ \lstinline{0xffff} = 66535 ist die "`natürliche"' Schreibweise für $-1$.\hfill
+ \lstinline{0xff} = 255 = $-1$\\
+ \textarrow\ Zweierkomplement
+
+ \medskip
+
+ Oberstes Bit = 1: negativ\\
+ Oberstes Bit = 0: positiv\\
+ \textarrow\ 32767 + 1 = $-32768$
+
+ \bigskip
+ Literatur: \url{http://xkcd.com/571/}
+
+\end{frame}
+
+\fi
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Frage: \emph{Für welche Zahl steht der Speicherinhalt\,
+ \raisebox{2pt}{%
+ \tabcolsep0.25em
+ \begin{tabular}{|c|c|}\hline
+ \rule{0pt}{11pt}a3 & 90 \\\hline
+ \end{tabular}}
+ (hexadezimal)?}
+
+ \pause
+ \smallskip
+ Antwort: \emph{Das kommt darauf an.} ;--)
+
+ \pause
+ \medskip
+ Little-Endian:
+
+ \smallskip
+
+ \begin{tabular}{lrl}
+ als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\
+ als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\
+ als \lstinline,int16_t,: & $-28509$\\
+ als \lstinline,uint16_t,: & $37027$\\
+ \lstinline,int32_t, oder größer: & $37027$
+ & (zusätzliche Bytes mit Nullen aufgefüllt)
+ \end{tabular}
+
+ \pause
+ \medskip
+ Big-Endian:
+
+ \smallskip
+
+ \begin{tabular}{lrl}
+ als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\
+ als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\
+ als \lstinline,int16_t,: & $-23664$\\
+ als \lstinline,uint16_t,: & $41872$\\ als \lstinline,int32_t,: & $-1550843904$ & (zusätzliche Bytes\\
+ als \lstinline,uint32_t,: & $2744123392$ & mit Nullen aufgefüllt)\\
+ als \lstinline,int64_t,: & $-6660823848880963584$\\
+ als \lstinline,uint64_t,: & $11785920224828588032$\\
+ \end{tabular}
+
+ \vspace*{-1cm}
+
+\end{frame}
+
+\subsection{Speicherausrichtung -- Alignment}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ \begin{lstlisting}
+ #include <stdint.h>
+
+ uint8_t a;
+ uint16_t b;
+ uint8_t c;
+ \end{lstlisting}
+
+ \pause
+ \bigskip
+
+ Speicheradresse durch 2 teilbar -- "`16-Bit-Alignment"'
+ \begin{itemize}
+ \item
+ 2-Byte-Operation: effizienter
+ \pause
+ \item
+ \dots\ oder sogar nur dann erlaubt
+ \pause
+ \arrowitem
+ Compiler optimiert Speicherausrichtung
+ \end{itemize}
+
+ \medskip
+
+ \pause
+ \begin{minipage}{3cm}
+ \begin{lstlisting}[gobble=6]
+ ¡uint8_t a;
+ uint8_t dummy;
+ uint16_t b;
+ uint8_t c;¿
+ \end{lstlisting}
+ \end{minipage}
+ \pause
+ \begin{minipage}{3cm}
+ \begin{lstlisting}[gobble=6]
+ ¡uint8_t a;
+ uint8_t c;
+ uint16_t b;¿
+ \end{lstlisting}
+ \end{minipage}
+
+ \pause
+ \vspace{-1.75cm}
+ \strut\hfill
+ \begin{minipage}{6.5cm}
+ Fazit:
+ \begin{itemize}
+ \item
+ \textbf{Adressen von Variablen\\
+ sind systemabhängig}
+ \item
+ Bei Definition von Datenformaten\\
+ Alignment beachten \textarrow\ effizienter
+ \end{itemize}
+ \end{minipage}
+
+\end{frame}
+
+\end{document}
diff --git a/20230523/rtech-20230523.txt b/20230523/rtech-20230523.txt
new file mode 100644
index 0000000..5dfc1ac
--- /dev/null
+++ b/20230523/rtech-20230523.txt
@@ -0,0 +1,15 @@
+Stack-Alignment beim Aufruf von printf(), 23.05.2023, 12:48:23
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+https://stackoverflow.com/questions/38335212/calling-printf-in-x86-64-using-gnu-assembler
+
+Vor dem Aufruf von printf() muß der Stack auf 16 oder 32 Bytes
+ausgerichtet sein (16- bzw. 32-Byte-Alignment).
+
+32 Bytes sind notwendig, wenn das Vektor-Register __m256
+auf den Stack gelegt wird.
+
+Innerhalb von main(): Stack nur auf 8 Bytes ausgerichtet.
+Wir subtrahieren 24 von %rsp, bevor wir printf() aufrufen.
+8 von diesen 24 Bytes verwenden wir für Variable.
+
+Bei ARMv7-A (32 Bit) scheint ein 8- oder 16-Byte-Alignment zu genügen.
diff --git a/20230523/test-arm-01.c b/20230523/test-arm-01.c
new file mode 100644
index 0000000..85b2c1b
--- /dev/null
+++ b/20230523/test-arm-01.c
@@ -0,0 +1,9 @@
+#include <stdio.h>
+
+int main (void)
+{
+ volatile int a = 7;
+ volatile int b = 6;
+ printf ("a + b = %d\n", a + b);
+ return 0;
+}
diff --git a/20230523/test-arm-01.s-arm b/20230523/test-arm-01.s-arm
new file mode 100644
index 0000000..1e0aaf0
--- /dev/null
+++ b/20230523/test-arm-01.s-arm
@@ -0,0 +1,52 @@
+ .arch armv7-a
+ .eabi_attribute 28, 1
+ .eabi_attribute 20, 1
+ .eabi_attribute 21, 1
+ .eabi_attribute 23, 3
+ .eabi_attribute 24, 1
+ .eabi_attribute 25, 1
+ .eabi_attribute 26, 2
+ .eabi_attribute 30, 1
+ .eabi_attribute 34, 1
+ .eabi_attribute 18, 4
+ .file "test-arm-01.c"
+ .text
+ .align 1
+ .global main
+ .arch armv7-a
+ .syntax unified
+ .thumb
+ .thumb_func
+ .fpu vfpv3-d16
+ .type main, %function
+main:
+ @ args = 0, pretend = 0, frame = 8
+ @ frame_needed = 0, uses_anonymous_args = 0
+ push {lr}
+ sub sp, sp, #12
+ movs r3, #7
+ str r3, [sp, #4]
+ movs r3, #6
+ str r3, [sp]
+ ldr r1, [sp, #4]
+ ldr r3, [sp]
+ add r1, r1, r3
+ ldr r0, .L3
+.LPIC0:
+ add r0, pc
+ bl printf(PLT)
+ movs r0, #0
+ add sp, sp, #12
+ @ sp needed
+ ldr pc, [sp], #4
+.L4:
+ .align 2
+.L3:
+ .word .LC0-(.LPIC0+4)
+ .size main, .-main
+ .section .rodata.str1.4,"aMS",%progbits,1
+ .align 2
+.LC0:
+ .ascii "a + b = %d\012\000"
+ .ident "GCC: (Debian 8.3.0-2) 8.3.0"
+ .section .note.GNU-stack,"",%progbits
diff --git a/20230523/test-arm-01.s-x86 b/20230523/test-arm-01.s-x86
new file mode 100644
index 0000000..bad49f5
--- /dev/null
+++ b/20230523/test-arm-01.s-x86
@@ -0,0 +1,30 @@
+ .file "test-arm-01.c"
+ .text
+ .section .rodata.str1.1,"aMS",@progbits,1
+.LC0:
+ .string "a + b = %d\n"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB11:
+ .cfi_startproc
+ subq $24, %rsp
+ .cfi_def_cfa_offset 32
+ movl $7, 12(%rsp)
+ movl $6, 8(%rsp)
+ movl 12(%rsp), %esi
+ movl 8(%rsp), %eax
+ addl %eax, %esi
+ leaq .LC0(%rip), %rdi
+ movl $0, %eax
+ call printf@PLT
+ movl $0, %eax
+ addq $24, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE11:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/test-arm-01.s-x86-Os b/20230523/test-arm-01.s-x86-Os
new file mode 100644
index 0000000..c51719a
--- /dev/null
+++ b/20230523/test-arm-01.s-x86-Os
@@ -0,0 +1,30 @@
+ .file "test-arm-01.c"
+ .text
+ .section .rodata.str1.1,"aMS",@progbits,1
+.LC0:
+ .string "a + b = %d\n"
+ .section .text.startup,"ax",@progbits
+ .globl main
+ .type main, @function
+main:
+.LFB0:
+ .cfi_startproc
+ subq $24, %rsp
+ .cfi_def_cfa_offset 32
+ leaq .LC0(%rip), %rdi
+ movl $7, 8(%rsp)
+ movl $6, 12(%rsp)
+ movl 8(%rsp), %esi
+ movl 12(%rsp), %eax
+ addl %eax, %esi
+ xorl %eax, %eax
+ call printf@PLT
+ xorl %eax, %eax
+ addq $24, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE0:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/test-arm-02.c b/20230523/test-arm-02.c
new file mode 100644
index 0000000..92b34cb
--- /dev/null
+++ b/20230523/test-arm-02.c
@@ -0,0 +1,8 @@
+#include <stdio.h>
+
+int main (void)
+{
+ volatile int a = 7;
+ volatile int b = 6;
+ return 0;
+}
diff --git a/20230523/test-arm-02.s-arm b/20230523/test-arm-02.s-arm
new file mode 100644
index 0000000..637f89b
--- /dev/null
+++ b/20230523/test-arm-02.s-arm
@@ -0,0 +1,37 @@
+ .arch armv7-a
+ .eabi_attribute 28, 1
+ .eabi_attribute 20, 1
+ .eabi_attribute 21, 1
+ .eabi_attribute 23, 3
+ .eabi_attribute 24, 1
+ .eabi_attribute 25, 1
+ .eabi_attribute 26, 2
+ .eabi_attribute 30, 1
+ .eabi_attribute 34, 1
+ .eabi_attribute 18, 4
+ .file "test-arm-02.c"
+ .text
+ .align 1
+ .global main
+ .arch armv7-a
+ .syntax unified
+ .thumb
+ .thumb_func
+ .fpu vfpv3-d16
+ .type main, %function
+main:
+ @ args = 0, pretend = 0, frame = 8
+ @ frame_needed = 0, uses_anonymous_args = 0
+ @ link register save eliminated.
+ sub sp, sp, #8
+ movs r3, #7
+ str r3, [sp, #4]
+ movs r3, #6
+ str r3, [sp]
+ movs r0, #0
+ add sp, sp, #8
+ @ sp needed
+ bx lr
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-2) 8.3.0"
+ .section .note.GNU-stack,"",%progbits
diff --git a/20230523/test-arm-02.s-avr b/20230523/test-arm-02.s-avr
new file mode 100644
index 0000000..c615369
--- /dev/null
+++ b/20230523/test-arm-02.s-avr
@@ -0,0 +1,40 @@
+ .file "test-arm-02.c"
+__SP_H__ = 0x3e
+__SP_L__ = 0x3d
+__SREG__ = 0x3f
+__tmp_reg__ = 0
+__zero_reg__ = 1
+ .text
+.global main
+ .type main, @function
+main:
+ push r28
+ push r29
+ rcall .
+ rcall .
+ in r28,__SP_L__
+ in r29,__SP_H__
+/* prologue: function */
+/* frame size = 4 */
+/* stack size = 6 */
+.L__stack_usage = 6
+ ldi r24,lo8(7)
+ ldi r25,0
+ std Y+2,r25
+ std Y+1,r24
+ ldi r24,lo8(6)
+ ldi r25,0
+ std Y+4,r25
+ std Y+3,r24
+ ldi r24,0
+ ldi r25,0
+/* epilogue start */
+ pop __tmp_reg__
+ pop __tmp_reg__
+ pop __tmp_reg__
+ pop __tmp_reg__
+ pop r29
+ pop r28
+ ret
+ .size main, .-main
+ .ident "GCC: (GNU) 5.4.0"
diff --git a/20230523/test-arm-02.s-x86 b/20230523/test-arm-02.s-x86
new file mode 100644
index 0000000..b7f6937
--- /dev/null
+++ b/20230523/test-arm-02.s-x86
@@ -0,0 +1,16 @@
+ .file "test-arm-02.c"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB11:
+ .cfi_startproc
+ movl $7, -4(%rsp)
+ movl $6, -8(%rsp)
+ movl $0, %eax
+ ret
+ .cfi_endproc
+.LFE11:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/test-arm-03.c b/20230523/test-arm-03.c
new file mode 100644
index 0000000..1dc41ef
--- /dev/null
+++ b/20230523/test-arm-03.c
@@ -0,0 +1,10 @@
+#include <stdio.h>
+
+int main (void)
+{
+ volatile int a = 7;
+ volatile int b = 6;
+ volatile int c = 9;
+ volatile int d = 11;
+ return 0;
+}
diff --git a/20230523/test-arm-03.s-x86 b/20230523/test-arm-03.s-x86
new file mode 100644
index 0000000..d04b263
--- /dev/null
+++ b/20230523/test-arm-03.s-x86
@@ -0,0 +1,18 @@
+ .file "test-arm-03.c"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB11:
+ .cfi_startproc
+ movl $7, -4(%rsp)
+ movl $6, -8(%rsp)
+ movl $9, -12(%rsp)
+ movl $11, -16(%rsp)
+ movl $0, %eax
+ ret
+ .cfi_endproc
+.LFE11:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/test-arm-04.c b/20230523/test-arm-04.c
new file mode 100644
index 0000000..acbd05c
--- /dev/null
+++ b/20230523/test-arm-04.c
@@ -0,0 +1,11 @@
+#include <stdio.h>
+
+int main (void)
+{
+ volatile int a = 7;
+ volatile int b = 6;
+ volatile int c = 9;
+ volatile int d = 11;
+ volatile int e = 13;
+ return 0;
+}
diff --git a/20230523/test-arm-04.s-x86 b/20230523/test-arm-04.s-x86
new file mode 100644
index 0000000..379ed72
--- /dev/null
+++ b/20230523/test-arm-04.s-x86
@@ -0,0 +1,19 @@
+ .file "test-arm-04.c"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB11:
+ .cfi_startproc
+ movl $7, -4(%rsp)
+ movl $6, -8(%rsp)
+ movl $9, -12(%rsp)
+ movl $11, -16(%rsp)
+ movl $13, -20(%rsp)
+ movl $0, %eax
+ ret
+ .cfi_endproc
+.LFE11:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230523/test-arm-05.c b/20230523/test-arm-05.c
new file mode 100644
index 0000000..21e888b
--- /dev/null
+++ b/20230523/test-arm-05.c
@@ -0,0 +1,12 @@
+#include <stdio.h>
+
+int main (void)
+{
+ volatile int a = 7;
+ volatile int b = 6;
+ volatile int c = 9;
+ volatile int d = 11;
+ volatile int e = 13;
+ volatile int f = 17;
+ return 0;
+}
diff --git a/20230523/test-arm-05.s-x86 b/20230523/test-arm-05.s-x86
new file mode 100644
index 0000000..cc84fec
--- /dev/null
+++ b/20230523/test-arm-05.s-x86
@@ -0,0 +1,20 @@
+ .file "test-arm-05.c"
+ .text
+ .globl main
+ .type main, @function
+main:
+.LFB11:
+ .cfi_startproc
+ movl $7, -4(%rsp)
+ movl $6, -8(%rsp)
+ movl $9, -12(%rsp)
+ movl $11, -16(%rsp)
+ movl $13, -20(%rsp)
+ movl $17, -24(%rsp)
+ movl $0, %eax
+ ret
+ .cfi_endproc
+.LFE11:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230524/buffer-overflow-01.c b/20230524/buffer-overflow-01.c
new file mode 100644
index 0000000..8dfffe0
--- /dev/null
+++ b/20230524/buffer-overflow-01.c
@@ -0,0 +1,10 @@
+#include <stdio.h>
+
+int main (void)
+{
+ char name[10];
+ printf ("Ihr Name: ");
+ scanf ("%s", name);
+ printf ("Hallo, %s! :-)\n", name);
+ return 0;
+}
diff --git a/20230524/buffer-overflow-02.c b/20230524/buffer-overflow-02.c
new file mode 100644
index 0000000..dd84b2a
--- /dev/null
+++ b/20230524/buffer-overflow-02.c
@@ -0,0 +1,10 @@
+#include <stdio.h>
+
+int main (void)
+{
+ char name[10];
+ printf ("Ihr Name: ");
+ gets (name);
+ printf ("Hallo, %s! :-)\n", name);
+ return 0;
+}
diff --git a/20230524/io-ports-and-interrupts.pdf b/20230524/io-ports-and-interrupts.pdf
new file mode 120000
index 0000000..bcd46f7
--- /dev/null
+++ b/20230524/io-ports-and-interrupts.pdf
@@ -0,0 +1 @@
+../common/io-ports-and-interrupts.pdf
\ No newline at end of file
diff --git a/20230524/logo-hochschule-bochum-cvh-text-v2.pdf b/20230524/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000..4aa99b8
--- /dev/null
+++ b/20230524/logo-hochschule-bochum-cvh-text-v2.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum-cvh-text-v2.pdf
\ No newline at end of file
diff --git a/20230524/logo-hochschule-bochum.pdf b/20230524/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20230524/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20230524/parameters-01-O0-stack-4.s b/20230524/parameters-01-O0-stack-4.s
new file mode 100644
index 0000000..7bc1707
--- /dev/null
+++ b/20230524/parameters-01-O0-stack-4.s
@@ -0,0 +1,56 @@
+ .file "parameters-01.c"
+ .text
+ .globl sum
+ .type sum, @function
+sum:
+.LFB0:
+ .cfi_startproc
+ pushq %rbp
+ .cfi_def_cfa_offset 16
+ .cfi_offset 6, -16
+ movq %rsp, %rbp
+ .cfi_def_cfa_register 6
+ movl %edi, -4(%rbp)
+ movl %esi, -8(%rbp)
+ movl -4(%rbp), %edx
+ movl -8(%rbp), %eax
+ addl %edx, %eax
+ popq %rbp
+ .cfi_def_cfa 7, 8
+ ret
+ .cfi_endproc
+.LFE0:
+ .size sum, .-sum
+ .section .rodata
+.LC0:
+ .string "c = %d\n"
+ .text
+ .globl main
+ .type main, @function
+main: # #include <stdio.h>
+.LFB1: #
+ .cfi_startproc # int sum (int a, int b)
+ pushq %rbp # {
+ .cfi_def_cfa_offset 16 # return a + b;
+ .cfi_offset 6, -16 # }
+ movq %rsp, %rbp #
+ .cfi_def_cfa_register 6 # int main (void)
+ subq $5, %rsp # vorher: 16 # {
+ movl $6, %esi # int c = sum (7, 6);
+ movl $7, %edi # printf ("c = %d\n", c);
+ call sum # return 0;
+ movl %eax, -4(%rbp) # }
+ movl -4(%rbp), %eax
+ movl %eax, %esi
+ leaq .LC0(%rip), %rdi
+ movl $0, %eax
+ call printf@PLT
+ movl $0, %eax
+ leave # leave = movq %rbp, %rsp
+ .cfi_def_cfa 7, 8 # popq %rbp
+ ret
+ .cfi_endproc
+.LFE1:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230524/parameters-01-O0.s b/20230524/parameters-01-O0.s
new file mode 100644
index 0000000..7b4fc50
--- /dev/null
+++ b/20230524/parameters-01-O0.s
@@ -0,0 +1,56 @@
+ .file "parameters-01.c"
+ .text
+ .globl sum
+ .type sum, @function
+sum:
+.LFB0:
+ .cfi_startproc
+ pushq %rbp
+ .cfi_def_cfa_offset 16
+ .cfi_offset 6, -16
+ movq %rsp, %rbp
+ .cfi_def_cfa_register 6
+ movl %edi, -4(%rbp)
+ movl %esi, -8(%rbp)
+ movl -4(%rbp), %edx
+ movl -8(%rbp), %eax
+ addl %edx, %eax
+ popq %rbp
+ .cfi_def_cfa 7, 8
+ ret
+ .cfi_endproc
+.LFE0:
+ .size sum, .-sum
+ .section .rodata
+.LC0:
+ .string "c = %d\n"
+ .text
+ .globl main
+ .type main, @function
+main: ; #include <stdio.h>
+.LFB1: ;
+ .cfi_startproc ; int sum (int a, int b)
+ pushq %rbp ; {
+ .cfi_def_cfa_offset 16 ; return a + b;
+ .cfi_offset 6, -16 ; }
+ movq %rsp, %rbp ;
+ .cfi_def_cfa_register 6 ; int main (void)
+ subq $16, %rsp ; {
+ movl $6, %esi ; int c = sum (7, 6);
+ movl $7, %edi ; printf ("c = %d\n", c);
+ call sum ; return 0;
+ movl %eax, -4(%rbp) ; }
+ movl -4(%rbp), %eax
+ movl %eax, %esi
+ leaq .LC0(%rip), %rdi
+ movl $0, %eax
+ call printf@PLT
+ movl $0, %eax
+ leave ; leave = movq %rbp, %rsp
+ .cfi_def_cfa 7, 8 ; popq %rbp
+ ret
+ .cfi_endproc
+.LFE1:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230524/parameters-01.c b/20230524/parameters-01.c
new file mode 100644
index 0000000..7b973a0
--- /dev/null
+++ b/20230524/parameters-01.c
@@ -0,0 +1,13 @@
+#include <stdio.h>
+
+int sum (int a, int b)
+{
+ return a + b;
+}
+
+int main (void)
+{
+ int c = sum (7, 6);
+ printf ("c = %d\n", c);
+ return 0;
+}
diff --git a/20230524/parameters-01.s b/20230524/parameters-01.s
new file mode 100644
index 0000000..cdaaee4
--- /dev/null
+++ b/20230524/parameters-01.s
@@ -0,0 +1,36 @@
+ .file "parameters-01.c"
+ .text
+ .globl sum
+ .type sum, @function
+sum:
+.LFB11:
+ .cfi_startproc
+ leal (%rdi,%rsi), %eax
+ ret
+ .cfi_endproc
+.LFE11:
+ .size sum, .-sum
+ .section .rodata.str1.1,"aMS",@progbits,1
+.LC0:
+ .string "c = %d\n"
+ .text
+ .globl main
+ .type main, @function
+main: ; #include <stdio.h>
+.LFB12: ;
+ .cfi_startproc ; int sum (int a, int b)
+ subq $8, %rsp ; {
+ .cfi_def_cfa_offset 16 ; return a + b;
+ movl $13, %esi ; }
+ leaq .LC0(%rip), %rdi ;
+ movl $0, %eax ; int main (void)
+ call printf@PLT ; {
+ movl $0, %eax ; int c = sum (7, 6);
+ addq $8, %rsp ; printf ("c = %d\n", c);
+ .cfi_def_cfa_offset 8 ; return 0;
+ ret ; }
+ .cfi_endproc
+.LFE12:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230524/parameters-02.c b/20230524/parameters-02.c
new file mode 100644
index 0000000..95f916d
--- /dev/null
+++ b/20230524/parameters-02.c
@@ -0,0 +1,16 @@
+#include <stdio.h>
+
+void print (int h, int e, int l1, int l2, int o1,
+ int comma, int space,
+ int w, int o2, int r, int l3, int d,
+ int bang, int newline)
+{
+ printf ("%c%c%c%c%c%c%c%c%c%c%c%c%c%c",
+ h, e, l1, l2, o1, comma, space, w, o2, r, l3, d, bang, newline);
+}
+
+int main (void)
+{
+ print ('H', 'e', 'l', 'l', 'o', ',', ' ', 'w', 'o', 'r', 'l', 'd', '!', '\n');
+ return 0;
+}
diff --git a/20230524/parameters-02.s b/20230524/parameters-02.s
new file mode 100644
index 0000000..c6d3a6b
--- /dev/null
+++ b/20230524/parameters-02.s
@@ -0,0 +1,92 @@
+ .file "parameters-02.c"
+ .text
+ .section .rodata.str1.1,"aMS",@progbits,1
+.LC0:
+ .string "%c%c%c%c%c%c%c%c%c%c%c%c%c%c"
+ .text
+ .globl print
+ .type print, @function
+print:
+.LFB11:
+ .cfi_startproc
+ subq $16, %rsp
+ .cfi_def_cfa_offset 24
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 32
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 40
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 48
+ movl 80(%rsp), %eax
+ pushq %rax
+ .cfi_def_cfa_offset 56
+ movl 80(%rsp), %eax # #include <stdio.h>
+ pushq %rax #
+ .cfi_def_cfa_offset 64 # void print (int h, int e, int l1, int l2, int o1,
+ movl 80(%rsp), %eax # int comma, int space,
+ pushq %rax # int w, int o2, int r, int l3, int d,
+ .cfi_def_cfa_offset 72 # int bang, int newline)
+ movl 80(%rsp), %eax # {
+ pushq %rax # printf ("%c%c%c%c%c%c%c%c%c%c%c%c%c%c",
+ .cfi_def_cfa_offset 80 # h, e, l1, l2, o1, comma, space, w, o2, r, l3, d, bang, newline);
+ movl 80(%rsp), %eax # }
+ pushq %rax #
+ .cfi_def_cfa_offset 88 # int main (void)
+ pushq %r9 # {
+ .cfi_def_cfa_offset 96 # print ('H', 'e', 'l', 'l', 'o', ',', ' ', 'w', 'o', 'r', 'l', 'd', '!', '\n');
+ movl %r8d, %r9d # return 0;
+ movl %ecx, %r8d
+ movl %edx, %ecx
+ movl %esi, %edx
+ movl %edi, %esi
+ leaq .LC0(%rip), %rdi
+ movl $0, %eax
+ call printf@PLT
+ addq $88, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE11:
+ .size print, .-print
+ .globl main
+ .type main, @function
+main:
+.LFB12:
+ .cfi_startproc
+ subq $8, %rsp
+ .cfi_def_cfa_offset 16
+ pushq $10
+ .cfi_def_cfa_offset 24
+ pushq $33
+ .cfi_def_cfa_offset 32
+ pushq $100
+ .cfi_def_cfa_offset 40
+ pushq $108
+ .cfi_def_cfa_offset 48
+ pushq $114
+ .cfi_def_cfa_offset 56
+ pushq $111
+ .cfi_def_cfa_offset 64
+ pushq $119
+ .cfi_def_cfa_offset 72
+ pushq $32
+ .cfi_def_cfa_offset 80
+ movl $44, %r9d
+ movl $111, %r8d
+ movl $108, %ecx
+ movl $108, %edx
+ movl $101, %esi
+ movl $72, %edi
+ call print
+ movl $0, %eax
+ addq $72, %rsp
+ .cfi_def_cfa_offset 8
+ ret
+ .cfi_endproc
+.LFE12:
+ .size main, .-main
+ .ident "GCC: (Debian 8.3.0-6) 8.3.0"
+ .section .note.GNU-stack,"",@progbits
diff --git a/20230524/pgslides.sty b/20230524/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20230524/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/20230524/rtech-20230524.pdf b/20230524/rtech-20230524.pdf
new file mode 100644
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diff --git a/20230524/rtech-20230524.tex b/20230524/rtech-20230524.tex
new file mode 100644
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--- /dev/null
+++ b/20230524/rtech-20230524.tex
@@ -0,0 +1,1761 @@
+% rtech-20230524.pdf - Lecture Slides on Computer Technology
+% Copyright (C) 2012, 2013, 2014, 2021, 2022, 2023 Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document. If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document. If not, see <http://creativecommons.org/licenses/>.
+
+% README: Der CPU-Stack, hardwarenahe Programmierung
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{pdftricks}
+%\usepackage[obeyfamily=false,mathrm=mathsf,textrm=sffamily]{siunitx}
+%\usepackage{eurosym}
+\usepackage{tikz}
+
+\newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+\newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+
+\lstdefinestyle{asm}{basicstyle=\color{structure},
+ language={},
+ gobble=4}
+
+\begin{psinputs}
+ \usepackage[utf8]{inputenc}
+ \usepackage[german]{babel}
+ \usepackage[T1]{fontenc}
+ \usepackage{helvet}
+ \renewcommand*\familydefault{\sfdefault}
+ \usepackage{pstricks,pst-grad,pst-circ-pg}
+ \newcommand{\invisible}{\tiny\color{white}}
+ \psset{unit=1cm}
+ \psset{logicLabelstyle=\invisible}
+ \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+ \psset{logicSymbolstyle=\logicSymbol}
+ \newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+ \newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+\end{psinputs}
+
+\title{Rechnertechnik}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{24.\ Mai 2022}
+
+\begin{document}
+
+\maketitleframe
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+ \shownosectionnonumber
+
+ \begin{itemize}
+ \item[\textbf{1}] \textbf{Einführung}
+ \item[\textbf{2}] \textbf{Vom Schaltkreis zum Computer}
+ \item[\textbf{3}] \textbf{Assember-Programmierung}
+ \begin{itemize}
+ \item[3.1] Struktur von Assembler-Programmen
+ \item[3.2] Beispiel: Redcode
+ \color{medgreen}
+ \item[3.3] Architekturmerkmale von Prozessore
+ \color{orange}
+ \item[3.4] Der CPU-Stack
+ \color{red}
+ \item[3.5] Computer-Sprachen
+ \end{itemize}
+% \color{gray}
+ \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+% \item[\textbf{6}] \textbf{Anwender-Software}
+% \item[\textbf{7}] \textbf{Bus-Systeme}
+% \item[\textbf{8}] \textbf{Pipelining}
+% \item[\textbf{9}] \textbf{Ausblick}
+ \item[\textbf{\dots\hspace{-0.75em}}]
+ \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{2}
+\section{Assembler-Programmierung}
+\setcounter{subsection}{2}
+\subsection{Architekturmerkmale von Prozessoren}
+\subsubsection{Speicherarchitekturen}
+
+\begin{frame}
+
+ \showsubsection
+
+ Oder: Jede Assembler-Sprache ist anders.
+
+ \bigskip
+
+ \showsubsubsection
+
+ Bezeichnungen
+ \begin{itemize}
+ \item
+ \newterm{Bit\/} = 0 oder 1 -- kleinste Einheit an Information
+ \item
+ \newterm{Byte\/} = Zusammenfassung mehrerer \newterm{Bits}\\
+ zu einer Binärzahl, die ein Zeichen (\newterm{Character\/}) darstellen kann,\\
+ häufig 8 Bits (\newterm{Oktett\/})
+ \item
+ \newterm{Speicherwort\/} = Zusammenfassung mehrerer Bits\\
+ zu der kleinsten adressierbaren Einheit, häufig 1 Byte
+ \item
+ \newterm{RAM\/} = \newterm{Random Access Memory\/} = Hauptspeicher
+ \item
+ \newterm{ROM\/} = \newterm{Read Only Memory\/} = nur lesbarer Speicher
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsection
+
+ Verschiedene Arten von Speicher
+ \begin{itemize}
+ \item
+ \newterm{Prozessor-Register}\\
+ können direkt mit ALU verbunden werden,\\
+ besonders schnell (Flipflops),\\
+ überschaubare Anzahl von Registern
+ \item
+ \newterm{Hauptspeicher}\\
+ kann direkt adressiert und mit Prozessor-Registern abgeglichen werden,\\
+ heute i.\,d.\,R.\ dynamischer Speicher (Kondensatoren)
+ \item
+ \newterm{I/O-Ports}\\
+ sind spezielle Speicheradressen, über die\\
+ mit externen Geräten kommuniziert wird
+ \item
+ \newterm{Massenspeicher}\\
+ liegt auf externem Gerät, wird über I/O-Ports angesprochen,\\
+ Festplatte, Flash-Speicher, \dots
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ \newterm{Von-Neumann-Architektur}\\
+ Es gibt nur 1 Hauptspeicher, in dem sich sowohl die Befehle\\
+ als auch die Daten befinden.
+
+ \begin{onlyenv}<1>
+ \smallskip
+
+ Vorteil: Flexibilität in der Speichernutzung
+
+ Nachteil: Befehle können überschrieben werden.\\
+ $\longrightarrow$ Abstürze und Malware möglich
+ \end{onlyenv}
+
+ \pause
+ \item
+ \newterm{Harvard-Architektur}\\
+ Es gibt 2 Hauptspeicher. In einem befinden sich die Befehle,\\
+ im anderen die Daten.
+
+ \begin{onlyenv}<2>
+ \smallskip
+
+ Vorteil: Befehle können nicht überschrieben werden\\
+ $\longrightarrow$ sicherer als Von-Neumann-Architektur
+
+ Nachteile: Leitungen zum Speicher (Bus) müssen doppelt vorhanden sein,\\
+ freier Befehlsspeicher kann nicht für Daten genutzt werden.
+ \end{onlyenv}
+
+ \pause
+ \item
+ Weitere Kombinationen\\
+ Hauptspeicher und I/O-Ports gemeinsam oder getrennt,\\
+ Hauptspeicher und Prozessorregister gemeinsam oder getrennt
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ Beispiele:
+ \begin{itemize}
+ \item
+ Intel IA-32, AMD64:\\
+ Von-Neumann-Architektur (plus Speicherschutzmechanismen),\\
+ Prozessorregister und I/O-Ports vom Hauptspeicher getrennt
+ \item
+ Atmel AVR (z.\,B.\ ATmega):\\
+ Harvard-Architektur\\
+ (Befehlsspeicher als Flash-Speicher grundsätzlich auch schreibbar),\\
+ Prozessorregister und I/O-Ports in gemeinsamem Adressbereich mit Hauptspeicher
+ \item
+ 6502, Renesas 740-CPU, Renesas-38000-Mikrocontroller:\\
+ Von-Neumann-Architektur,\\
+ I/O-Ports in gemeinsamem Adressbereich mit Hauptspeicher,\\
+ Prozessorregister und Hauptspeicher getrennt
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Registerarchitekturen}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ \vspace*{-\medskipamount}
+
+ \begin{itemize}
+ \item
+ Mehrere Register, einzeln ansprechbar
+ \item
+ \newterm{Akkumulator\/}: Nur 1 Register kann rechnen.
+ \item
+ \newterm{Stack-Architektur\/}: Stapel, "`umgekehrte Polnische Notation"'
+ \end{itemize}
+
+% \pause
+
+ Operationen: typischerweise nur
+ \lstinline{=}, \lstinline{+=}, \lstinline{-=}, \lstinline{*=}, \lstinline{/=}, \dots
+
+% \pause
+ \medskip
+
+ Beispiel: \lstinline{c = a + 2 * b;}
+
+% \pause
+ \medskip
+
+ \begin{minipage}[t]{2cm}
+ C, Java:\smallskip\par
+ \begin{lstlisting}[gobble=6]
+ R = b;
+ R *= 2;
+ R += a;
+ c = R;
+ \end{lstlisting}
+ \end{minipage}%\pause
+ \begin{minipage}[t]{4cm}
+ Mehrere Register:\smallskip\par
+ \begin{lstlisting}[style=asm,gobble=6]
+ movl (b), %eax
+ imull $2, %eax, %eax
+ addl (a), %eax
+ movl %eax, (c)
+ \end{lstlisting}
+ \smallskip\par
+ (IA-32-Assembler)
+ \end{minipage}%\pause
+ \begin{minipage}[t]{3cm}
+ Akkumulator:\smallskip\par
+ \begin{lstlisting}[style=asm,gobble=6]
+ load (b)
+ mul $2
+ add (a)
+ store (c)
+ \end{lstlisting}
+ \smallskip\par
+ (Pseudo-Assembler)
+ \end{minipage}%\pause
+ \begin{minipage}[t]{3cm}
+ Register-Stack:\smallskip\par
+ \begin{lstlisting}[style=asm,gobble=6]
+ push (a)
+ push (b)
+ push $2
+ mul
+ add
+ pop (c)
+ \end{lstlisting}
+ \end{minipage}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ Beispiele:
+ \begin{itemize}
+ \item
+ Intel IA-32, AMD64:\\
+ Mehrere Register, für verschiedene Zwecke spezialisiert (unübersichtlich),\\[\smallskipamount]
+ Fließkommaregister: Stack-Architektur
+ \item
+ Atmel AVR (z.\,B.\ ATmega):\\
+ 32 Register
+ \item
+ 6502, Renesas 740-CPU, Renesas-38000-Mikrocontroller:\\
+ 3 Register: A, X, Y. Nur A kann rechnen $\longrightarrow$ Akkumulator
+ \item
+ Java Virtual Machine (JVM):\\
+ Stack-Architektur
+ \item
+ Redcode:\\
+ Jede Speicherzelle fungiert als Register
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Befehlssätze}
+
+\begin{frame}
+
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ \newterm{Reduced Instruction Set Computer (RISC)}
+
+ \smallskip
+
+ wenige, wenig mächtige Befehle
+
+ \begin{onlyenv}<1>
+ \textarrow\ Programmierung in Assembler für Menschen unkomfortabel\\
+ \textarrow\ schnelle Abarbeitung der Befehle
+
+ \medskip
+
+ Beispiel: Atmel AVR
+ \begin{itemize}
+ \item
+ Der ``load immediate''-Befehl funktioniert nur
+ für die Register 16 bis 31,\\
+ nicht für die Register 0 bis 15.
+ \item
+ Die meisten Befehle werden in nur 1 Taktzyklus abgearbeitet.
+ \end{itemize}
+
+ \medskip
+
+ Beispiel: Redcode ICWS-86
+ \begin{itemize}
+ \item
+ Es gibt indirekte Adressierung mit Prä-Dekrement,\\
+ aber nicht mit Prä-Inkrement.
+ \item
+ Alle Befehle werden in nur 1 Taktzyklus abgearbeitet.
+ \end{itemize}
+ \end{onlyenv}
+
+ \pause
+ \medskip
+ \item
+ \newterm{Complex Instruction Set Computer (CISC)}
+
+ \smallskip
+
+ Umfangreiche Befehlssätze, mächtige Befehle
+
+ \begin{onlyenv}<2>
+ \textarrow\ komfortable manuelle Programmierung in Assembler\\
+ \textarrow\ längere Abarbeitungszeit der einzelnen Befehle
+
+ \smallskip
+
+ Realisierung: "`Prozessor im Prozessor"' -- \newterm{Mikroprogramme}
+
+ \medskip
+
+ Beispiel: Intel IA-32, AMD64
+ \begin{itemize}
+ \item
+ Es gibt spezielle Befehle für BCD- und String-Operationen.
+ \item
+ Befehle benötigen meistens 2 oder mehr,\\
+ gelegentlich (z.\,B.\ Fließkomma-Operationen) auch über 100 Taktzyklen.
+ \end{itemize}
+ \end{onlyenv}
+
+ \medskip
+ \pause
+ \item
+ \newterm{Very Long Instruction Word (VLIW)\/} und\\
+ \newterm{Explicitly Parallel Instruction Computing (EPIC)}
+
+ \smallskip
+
+ mehrere Befehle gleichzeitig ausführbar
+
+ \begin{onlyenv}<3>
+ \textarrow\ mehr Rechenleistung möglich\\
+ \textarrow\ Programmierung sehr aufwendig
+
+ \medskip
+
+ Beispiel: Intel IA-64
+ \end{onlyenv}
+
+ \pause
+ \medskip
+ \item
+ \newterm{Orthogonaler Befehlssatz}
+
+ \smallskip
+
+ Jeder Befehl ist mit jeder Adressierungsart kombinierbar.
+
+ \medskip
+
+ Beispiel: Redcode
+ \end{itemize}
+ \vspace*{-4cm}
+
+\end{frame}
+
+\subsection{Der CPU-Stack\label{CPU-Stack}}
+\addtocounter{subsubsection}{-1}
+\subsubsection{Was ist ein Stack?}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ \bigskip
+
+\iffalse
+
+ \begin{minipage}[b]{6cm}
+ \begin{center}
+ "`First In -- First Out"'
+
+ \bigskip
+
+ \begin{picture}(6,4)
+ \thicklines
+ \color{structure}
+ \put(0.5,0){\line(1,0){5}}
+
+ \put(3.5,0){\only<1-5>{\line(0,1){1}}}
+ \put(4.5,0){\only<1-4>{\line(0,1){1}}}
+ \put(3.5,1){\only<1-4>{\line(1,0){1}}}
+ \put(4.0,0.5){\only<1-4>{\makebox(0,0){\lstinline{3}}}}
+ \put(3.0,1.5){\only<1>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(3.0,1.5){\only<1>{\makebox(0,0)[b]{\lstinline{push (3)}}}}
+
+ \put(2.5,0){\only<2-6>{\line(0,1){1}}}
+ \put(2.5,1){\only<2-5>{\line(1,0){1}}}
+ \put(3.0,0.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
+ \put(2.0,1.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(2.0,1.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
+
+ \put(1.5,0){\only<3-6>{\line(0,1){1}}}
+ \put(1.5,1){\only<3-6>{\line(1,0){1}}}
+ \put(2.0,0.5){\only<3-6>{\makebox(0,0){\lstinline{137}}}}
+ \put(1.0,1.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(1.0,1.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
+
+ \put(4.55,1.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(5.00,1.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
+
+ \put(3.55,1.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,1.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
+
+ \put(2.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(3.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
+ \end{picture}
+
+ \bigskip
+
+ FIFO = Queue = Reihe
+ \end{center}
+ \end{minipage}\hfill
+
+\fi
+
+ \begin{minipage}[b]{6cm}
+ \begin{center}
+ "`Last In -- First Out"'
+
+ \bigskip
+
+ \begin{picture}(6,4)
+ \thicklines
+ \color{structure}
+ \put(1.5,0){\line(1,0){3}}
+
+ \put(2.5,0){\line(0,1){1}}
+ \put(3.5,0){\line(0,1){1}}
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+
+ \put(2.5,1){\only<2-5>{\line(0,1){1}}}
+ \put(3.5,1){\only<2-5>{\line(0,1){1}}}
+ \put(2.5,2){\only<2-5>{\line(1,0){1}}}
+ \put(3.0,1.5){\only<2-5>{\makebox(0,0){\lstinline{7}}}}
+ \put(2.0,2.5){\only<2>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(2.0,2.5){\only<2>{\makebox(0,0)[b]{\lstinline{push (7)}}}}
+
+ \put(2.5,2){\only<3-4>{\line(0,1){1}}}
+ \put(3.5,2){\only<3-4>{\line(0,1){1}}}
+ \put(2.5,3){\only<3-4>{\line(1,0){1}}}
+ \put(3.0,2.5){\only<3-4>{\makebox(0,0){\lstinline{137}}}}
+ \put(2.0,3.5){\only<3>{\makebox(0,0)[tl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,-0.45);}}}}
+ \put(2.0,3.5){\only<3>{\makebox(0,0)[b]{\lstinline{push (137)}}}}
+
+ \put(3.55,3.05){\only<4>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,3.60){\only<4>{\makebox(0,0)[b]{\lstinline{pop ()}: 137}}}
+
+ \put(3.55,2.05){\only<5>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,2.60){\only<5>{\makebox(0,0)[b]{\lstinline{pop ()}: 7}}}
+
+ \put(3.55,1.05){\only<6>{\makebox(0,0)[bl]{\tikz{\draw[-latex, line width=1pt](0,0)--(0.45,0.45);}}}}
+ \put(4.00,1.60){\only<6>{\makebox(0,0)[b]{\lstinline{pop ()}: 3}}}
+ \end{picture}
+
+ \bigskip
+
+ LIFO = Stack = Stapel
+ \end{center}
+ \end{minipage}
+
+%
+% \dots
+
+\end{frame}
+\subsubsection{Implementierung}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Speicher, in dem Werte "`gestapelt"' werden: \newterm{Stack}
+
+ \begin{itemize}
+ \item
+ Speicherbereich (ein array) reservieren
+ \item
+ Variable (typischerweise: Prozessorregister) als
+ \newterm{Stack Pointer\/} reservieren \textarrow\ \lstinline{SP}
+ \item
+ Assembler-Befehl \lstinline[style=asm]{push foo}: \quad
+ \lstinline{*SP++ = foo;}
+ \begin{itemize}
+ \item
+ In der Speicherzelle,
+ auf die der Stack Pointer \lstinline{SP} gerade zeigt,\\
+ den Wert \lstinline{foo} speichern.
+ \item
+ Danach den Stack Pointer inkrementieren (um 1 erhöhen).
+ \end{itemize}
+ \item
+ Assembler-Befehl \lstinline[style=asm]{pop bar}: \quad
+ \lstinline{bar = *--SP;}
+ \begin{itemize}
+ \item
+ Zuerst den Stack Pointer dekrementieren (um 1 erniedrigen).
+ \item
+ Danach aus der Speicherzelle,\\
+ auf die der Stack Pointer \lstinline{SP} gerade zeigt,\\
+ einen Wert lesen und in der Variablen \lstinline{bar} speichern.
+ \end{itemize}
+ \end{itemize}
+
+% \pause
+ \medskip
+ Speziell: Unterprogramme
+
+\end{frame}
+
+\subsubsection{Unterprogramme}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ Funktion mit 2 ganzzahligen Parametern \lstinline{a} und \lstinline{b}\\
+ und einem ganzzahligem Rückgabewert:
+ \vspace{\medskipamount}
+ \begin{lstlisting}[xleftmargin=1em]
+ int sum (int a, int b)
+ {
+ return a + b;
+ }
+ \end{lstlisting}
+
+ \bigskip
+
+ Aufruf der Funktion:
+ \vspace{\medskipamount}
+ \begin{lstlisting}[xleftmargin=1em]
+ int c = sum (7, 6);
+ \end{lstlisting}
+
+ \bigskip
+
+ (Methoden = spezielle Funktionen)
+
+ \vfill
+
+ \textarrow\ Wie funktioniert das?
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{minipage}[t]{5.5cm}
+ Parameter:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \item
+ CPU-Stack
+ \end{itemize}
+
+ \smallskip
+
+ Rückgabewert:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \end{itemize}
+ \end{minipage}%
+ \begin{minipage}[t]{5cm}
+ Aufruf:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{push IP}\\
+ \lstinline[style=asm]{jmp foo}
+ {\color{red}\boldmath $\longleftarrow$ mov \#foo IP}\\
+ \textarrow\ \lstinline[style=asm]{call foo}
+ \end{itemize}
+ Rücksprung:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{pop IP}\\
+ \textarrow\ \lstinline[style=asm]{ret}
+ \end{itemize}
+ \end{minipage}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{minipage}[t]{5.5cm}
+ Parameter:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \item
+ CPU-Stack
+ \end{itemize}
+
+ \smallskip
+
+ Rückgabewert:
+ \begin{itemize}
+ \item
+ Prozessorregister
+ \end{itemize}
+ \end{minipage}%
+ \begin{minipage}[t]{5cm}
+ Aufruf:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{push IP}\\
+ \lstinline[style=asm]{jmp foo}
+ {\color{red}\boldmath $\longleftarrow$ mov \#foo IP}\\
+ \textarrow\ \lstinline[style=asm]{call foo}
+ \end{itemize}
+ Rücksprung:
+ \begin{itemize}
+ \item
+ \lstinline[style=asm]{pop IP}\\
+ \textarrow\ \lstinline[style=asm]{ret}
+ \end{itemize}
+ \end{minipage}
+
+ \bigskip
+
+ \subsubsection{Lokale Variable}
+ \showsubsubsection
+
+ \dots\ speichert man oft ebenfalls auf dem Stack.
+
+ \smallskip
+
+ Speicherplatz reservieren: Stack-Pointer modifizieren
+
+ \medskip
+
+ \newterm{Buffer Overflow\/}:\\[0.5\smallskipamount]
+ Über die Grenzen einer lokalen Variablen hinausschreiben,\\
+ dabei Rücksprungadresse überschreiben \textarrow\ Absturz
+
+\end{frame}
+
+\subsubsection{Register sichern}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Ein Unterprogramm verändert Registerinhalte.
+ \begin{itemize}
+ \item
+ im Hauptprogramm nötigenfalls vor Aufruf sichern
+ \item
+ im Unterprogramm vor Benutzung sichern
+ \item
+ Kombinationen (manche Register so, manche so)
+ \end{itemize}
+
+\end{frame}
+
+\subsection{Computer-Sprachen}
+\subsubsection{Maschinensprache}
+
+\iffalse
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ \strut\hfill
+ \begin{minipage}{6.5cm}
+ \vspace*{-1.7cm}
+ \small
+ Computer
+ \begin{itemize}\itemsep0pt
+ \item Rechenwerk (ALU)
+ \item Speicher: Register,\\
+ adressierbarer Hauptspeicher
+ \item Takt: Befehle abarbeiten
+ \item Peripherie: Kommunikation\\
+ mit der Außenwelt
+ \arrowitem in Maschinensprache programmierbar
+ \end{itemize}
+ \end{minipage}\hspace*{-0.5cm}
+
+ In jedem Takt:
+ \begin{itemize}
+ \item
+ dort aus dem Hauptspeicher lesen, wohin das Register \lstinline{IP} zeigt\\
+ \textarrow\ \newterm{Befehl\/} (\newterm{Instruction\/} -- \lstinline{IP} = \newterm{Instruction Pointer\/})
+ \item
+ den \newterm{Befehl\/} an den \newterm{Funktion\/}-Eingang der \newterm{ALU\/} legen
+ \item
+ auf ähnliche Weise weitere Daten an den \newterm{Akkumulator\/}-\\
+ und den \newterm{Daten\/}-Eingang der \newterm{ALU\/} legen
+ \item
+ auf ähnliche Weise den \newterm{Ergebnis\/}-Ausgang der \newterm{ALU}\\
+ in den Hauptspeicher schreiben
+ \textarrow\ Befehl ausgeführt
+ \item
+ Register \lstinline{IP} hochzählen
+ \textarrow\ nächster Befehl
+ \arrowitem
+ Maschinensprache
+ \end{itemize}
+
+\end{frame}
+
+\fi
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\\
+ arithmetische Befehle\\
+ unbedingte und bedingte Sprungbefehle
+ \arrowitem
+ Der Computer kann "`alles"' -- \newterm{Turing-Vollständigkeit}
+ \bigskip
+ \item
+ Maschinensprache = Zahlen \textarrow\ für Menschen schwer handhabbar
+ \arrowitem
+ Namen für die Befehle: \newterm{Mnemonics}
+ \arrowitem
+ \newterm{Assembler\/}-Sprache
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{\strut{\protect\color{gray}Maschinensprache \protect\textarrow\ }Assembler}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ Beispiel: Intel-x86-16-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{mov}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{inc}, \lstinline{dec},
+ \lstinline{xor}, \lstinline{cmp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{jmp}, \lstinline{jz}, \lstinline{jae}, \dots
+ \item
+ Register\hfill
+ \lstinline{ax}, \lstinline{bx}, \dots
+ \end{itemize}
+
+% \begin{onlyenv}<1>
+% \begin{center}
+%% \includegraphics[width=10cm]{programm-screenshot.png}
+% \vspace*{-0.5cm}
+% \end{center}
+% \end{onlyenv}
+% \begin{onlyenv}<2->
+
+ \bigskip
+
+ Beispiel: Atmel-AVR-8-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{ldi}, \lstinline{lds}, \lstinline{sti}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{subi},
+ \lstinline{eor}, \lstinline{cp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{rjmp}, \lstinline{brsh}, \lstinline{brlo}, \dots
+ \item
+ Register\hfill
+ \lstinline{r0}, \lstinline{r1}, \dots
+ \end{itemize}
+
+ \bigskip
+
+ \textarrow\ für jeden Prozessor anders
+
+% \end{onlyenv}
+
+\end{frame}
+
+\subsubsection{\strut{\protect\color{gray}Maschinensprache \protect\textarrow\ Assembler \protect\textarrow\ }Hochsprachen}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ Beispiel: Intel-x86-16-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{mov}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{inc}, \lstinline{dec},
+ \lstinline{xor}, \lstinline{cmp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{jmp}, \lstinline{jz}, \lstinline{jae}, \dots
+ \item
+ Register\hfill
+ \lstinline{ax}, \lstinline{bx}, \dots
+ \end{itemize}
+
+ \bigskip
+
+ Beispiel: Atmel-AVR-8-Bit-Assembler
+
+ \begin{itemize}
+ \item
+ Lade- und Speicher-Befehle\hfill
+ \lstinline{ldi}, \lstinline{lds}, \lstinline{sti}, \dots\\
+ arithmetische Befehle\hfill
+ \lstinline{add}, \lstinline{sub}, \lstinline{subi},
+ \lstinline{eor}, \lstinline{cp}, \dots\\
+ unbedingte und bedingte Sprungbefehle\hfill
+ \lstinline{rjmp}, \lstinline{brsh}, \lstinline{brlo}, \dots
+ \item
+ Register\hfill
+ \lstinline{r0}, \lstinline{r1}, \dots
+ \end{itemize}
+
+ \bigskip
+
+ \textarrow\ für jeden Prozessor anders
+
+ \bigskip
+
+ Hochsprache \textarrow\ für jeden Prozessor gleich
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ Compiler-Sprachen
+ \begin{itemize}
+ \item
+ \newterm{Compiler\/} übersetzt Hochsprachen-\newterm{Quelltext\/} in die Assembler-Sprache
+ \item
+ \newterm{Assembler\/} übersetzt Assembler-Quelltext in die Maschinensprache
+ \item
+ Compiler und Assembler sind Programme,\\
+ geschrieben in Maschinensprache, Assembler oder einer Hochsprache
+ \item
+ Beispiele: Fortran, Algol, Pascal, Ada, C, C++, \dots
+ \end{itemize}
+
+ \pause
+ \medskip
+ Interpreter- oder Skript-Sprachen
+ \begin{itemize}
+ \item
+ \newterm{Interpreter\/} liest Hochsprachen-\newterm{Quelltext\/} und führt ihn sofort aus
+ \item
+ Der Interpreter ist ein Programm,\\
+ geschrieben in Maschinensprache, Assembler oder einer Hochsprache
+ \item
+ Beispiele: Unix-Shell, BASIC, Perl, Python, \dots
+ \end{itemize}
+
+ \pause
+ \medskip
+ Kombinationen
+ \begin{itemize}
+ \item
+ \newterm{Compiler\/} erzeugt \newterm{Zwischencode\/} für eine \newterm{virtuelle Maschine}
+ \item
+ \newterm{Interpreter\/} liest Hochsprachen-\newterm{Zwischencode\/} und führt ihn sofort aus
+ \item
+ Die virtuelle Maschine ist ein Programm,
+ geschrieben in Maschinensprache, Assembler, einer Hoch- oder Skript-Sprache
+ \item
+ Beispiele: UCSD-Pascal, Java, \dots
+ \end{itemize}
+ \medskip
+
+\end{frame}
+
+\section{Hardwarenahe Programmierung}
+\subsection{Bit-Operationen}
+\subsubsection{Zahlensysteme}
+
+\begin{frame}[fragile]
+
+ \showsection
+ \vspace*{-\smallskipamount}
+ \showsubsection
+ \vspace*{-\medskipamount}
+ \showsubsubsection
+
+ \begin{tabular}{rlrl}
+ Basis & Name & Beispiel & Anwendung \\[\smallskipamount]
+ 2 & Binärsystem & 1\,0000\,0011 & Bit-Operationen \\
+ 8 & Oktalsystem & \lstinline,0403, & Dateizugriffsrechte (Unix) \\
+ 10 & Dezimalsystem & \lstinline,259, & Alltag \\
+ 16 & Hexadezimalsystem & \lstinline,0x103, & Bit-Operationen \\
+ 256 & (keiner gebräuchlich) & 0.0.1.3 & IP-Adressen (IPv4)
+ \end{tabular}
+
+ \bigskip
+
+ \begin{itemize}
+ \item
+ Computer rechnen im Binärsystem.
+ \item
+ Für viele Anwendungen (z.\,B.\ I/O-Ports, Grafik, \dots) ist es notwendig,\\
+ Bits in Zahlen einzeln ansprechen zu können.
+ \end{itemize}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ \begin{tabular}{rlrlrc}
+ \qquad 000 & \bf 0 \hspace*{1.5cm} & 0000 & \bf 0 & \quad 1000 & \bf 8\\
+ 001 & \bf 1 & 0001 & \bf 1 & 1001 & \bf 9\\
+ 010 & \bf 2 & 0010 & \bf 2 & 1010 & \bf A\\
+ 011 & \bf 3 & 0011 & \bf 3 & 1011 & \bf B\\[\smallskipamount]
+ 100 & \bf 4 & 0100 & \bf 4 & 1100 & \bf C\\
+ 101 & \bf 5 & 0101 & \bf 5 & 1101 & \bf D\\
+ 110 & \bf 6 & 0110 & \bf 6 & 1110 & \bf E\\
+ 111 & \bf 7 & 0111 & \bf 7 & 1111 & \bf F\\
+ \end{tabular}
+
+ \medskip
+
+ \begin{itemize}
+ \item
+ Oktal- und Hexadezimalzahlen lassen sich ziffernweise\\
+ in Binär-Zahlen umrechnen.
+ \item
+ Hexadezimalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+ gruppiert zu jeweils 4 Bits.
+ \item
+ Oktalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+ gruppiert zu jeweils 3 Bits.
+ \item
+ Trotz Taschenrechner u.\,ä.\ lohnt es sich,\\
+ die o.\,a.\ Umrechnungstabelle \textbf{auswendig} zu kennen.
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Bit-Operationen in Assembler}
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ \begin{tabular}{lll}
+ Operation & Verknüpfung & Anwendung \\[\smallskipamount]
+ \lstinline,and, & Und & Bits gezielt löschen \\
+ \lstinline,or, & Oder & Bits gezielt setzen \\
+ \lstinline,eor, & Exklusiv-Oder & Bits gezielt invertieren \\[\smallskipamount]
+ \lstinline,com, & Nicht (Einer-Komplement) & Alle Bits invertieren \\[\smallskipamount]
+ \lstinline,lsl, & Verschiebung nach links & Maske generieren \\
+% \lstinline,lsr, & Verschiebung nach rechts & Bits isolieren
+ \end{tabular}
+
+ \bigskip
+
+ Numerierung der Bits: von rechts ab 0
+
+ \medskip
+
+ \begin{tabular}{ll}
+ Bit Nr.\ 3 auf 1 setzen: &
+% \lstinline,a |= 1 << 3;, \\
+ Oder-Verknüpfung mit einer\\&um 3 nach links geschobenen 1
+ \hfill\lstinline|0000|\,\lstinline|1000|\\[\smallskipamount]
+ Bit Nr.\ 4 auf 0 setzen: &
+% \lstinline,a &= ~(1 << 4);, \\
+ Und-Verknüpfung mit dem Einer-Komplement \qquad\quad\strut\\&einer um 4 nach links geschobenen 1
+ \hfill\lstinline|1110|\,\lstinline|1111|\\[\smallskipamount]
+ Bit Nr.\ 0 invertieren: &
+% \lstinline,a ^= 1 << 0;,
+ Exklusiv-Oder-Verknüpfung mit einer\\&um 0 nach links geschobenen 1
+ \hfill\lstinline|0000|\,\lstinline|0001|\\[\smallskipamount]
+ Ist Bit Nr.\ 1 eine Null? &
+ Ergibt eine Und-Verknüpfung mit einer um 1\\&nach links geschobenen 1 den Wert 0?
+ \hfill\lstinline|0000|\,\lstinline|0010|
+ \end{tabular}
+
+% \smallskip
+%
+% ~~Abfrage, ob Bit Nr.\ 1 gesetzt ist:\quad
+% \lstinline{if (a & (1 << 1))}
+
+\end{frame}
+
+\iffalse
+
+\begin{frame}[fragile]
+
+ \showsubsubsection
+
+ C-Datentypen für Bit-Operationen:
+ \smallskip\par
+ \lstinline{#include <stdint.h>}
+ \medskip\par
+ \begin{tabular}{lllll}
+ & 8 Bit & 16 Bit & 32 Bit & 64 Bit \\
+ mit Vorzeichen & \lstinline,int8_t,
+ & \lstinline,int16_t,
+ & \lstinline,int32_t,
+ & \lstinline,int64_t, \\
+ ohne Vorzeichen & \lstinline,uint8_t,
+ & \lstinline,uint16_t,
+ & \lstinline,uint32_t,
+ & \lstinline,uint64_t,
+ \end{tabular}
+
+ \bigskip
+ \bigskip
+
+ Ausgabe:
+ \smallskip\par
+ \begin{lstlisting}
+ #include <stdio.h>
+ #include <stdint.h>
+ #include <inttypes.h>
+ ...
+ uint64_t x = 42;
+ printf ("Die Antwort lautet: %" PRIu64 "\n", x);
+ \end{lstlisting}
+
+\end{frame}
+
+\subsection{I/O-Ports}
+
+\begin{frame}[fragile]
+
+% \showsection
+ \showsubsection
+ \vspace*{-1.5\medskipamount}
+ {\large\textbf{\color{structure}4.3\quad Interrupts}}
+
+ \bigskip
+
+ Kommunikation mit externen Geräten
+
+ \bigskip
+
+ \begin{center}
+ \includegraphics{io-ports-and-interrupts.pdf}
+ \end{center}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ In Output-Port schreiben = Aktoren ansteuern
+
+ Beispiel: LED
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/io.h>
+ ...
+ DDRC = 0x70;
+ PORTC = 0x40;
+ \end{lstlisting}
+ \begin{picture}(0,0)
+ \put(3,0.67){\begin{minipage}{3cm}
+ \color{red}%
+ binär: 0111\,0000\\
+ binär: 0100\,0000
+ \end{minipage}}
+ \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+ \end{picture}
+
+ \bigskip
+
+ \lstinline{DDR} = Data Direction Register\\
+ Bit = 1 für Output-Port\\
+ Bit = 0 für Input-Port
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Aus Input-Port lesen = Sensoren abfragen
+
+ Beispiel: Taster
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/io.h>
+ ...
+ DDRC = 0xfd;
+ while ((PINC & 0x02) == 0)
+ ; /* just wait */
+ \end{lstlisting}
+ \begin{picture}(0,0)(-1.5,-0.42)
+ \put(3,0.67){\begin{minipage}{3cm}
+ \color{red}%
+ binär: 1111\,1101\\
+ binär: 0000\,0010
+ \end{minipage}}
+ \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+ \end{picture}
+
+ \bigskip
+
+ \lstinline{DDR} = Data Direction Register\\
+ Bit = 1 für Output-Port\\
+ Bit = 0 für Input-Port
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+ \bigskip
+
+ Praktikumsaufgabe: Druckknopfampel
+
+\end{frame}
+
+\subsection{Interrupts}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Externes Gerät ruft (per Stromsignal) Unterprogramm auf
+
+ Zeiger hinterlegen: "`Interrupt-Vektor"'
+
+ Beispiel: eingebaute Uhr\hfill
+ \makebox(0,0)[tr]{%
+ \only<1->{\begin{minipage}[t]{4.7cm}
+ \vspace*{-0.3cm}%
+ statt Zählschleife (\lstinline{_delay_ms}):\\
+ Hauptprogramm kann\\
+ andere Dinge tun
+ \end{minipage}}%
+ }
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/interrupt.h>
+
+ ...
+
+
+ ISR (TIMER0B_COMP_vect)
+ {
+ PORTD ^= 0x40;
+ }
+ \end{lstlisting}
+ \begin{picture}(0,0)
+ \color{red}
+ \put(1.9,3.1){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-1.4,-1.0);}}}
+ \put(2.0,3.2){\makebox(0,0)[l]{"`Dies ist ein Interrupt-Handler."'}}
+ \put(2.3,2.6){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-0.6,-0.55);}}}
+ \put(2.4,2.6){\makebox(0,0)[l]{Interrupt-Vektor darauf zeigen lassen}}
+ \end{picture}
+
+ Initialisierung über spezielle Ports:
+ \lstinline{TCCR0B}, \lstinline{TIMSK0}
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+ \vspace*{-2.5cm}\hfill
+ {\color{red}Herstellerspezifisch!}%
+ \hspace*{1cm}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Externes Gerät ruft (per Stromsignal) Unterprogramm auf
+
+ Zeiger hinterlegen: "`Interrupt-Vektor"'
+
+ Beispiel: Taster\hfill
+ \makebox(0,0)[tr]{%
+ \begin{minipage}[t]{4.7cm}
+ \vspace*{-0.3cm}%
+ statt \newterm{Busy Waiting\/}:\\
+ Hauptprogramm kann\\
+ andere Dinge tun
+ \end{minipage}}
+
+ \medskip
+
+ \begin{lstlisting}
+ #include <avr/interrupt.h>
+ ...
+
+ ISR (INT0_vect)
+ {
+ PORTD ^= 0x40;
+ }
+ \end{lstlisting}
+
+ \medskip
+
+ Initialisierung über spezielle Ports:
+ \lstinline{EICRA}, \lstinline{EIMSK}
+
+ \bigskip
+
+ \emph{Details: siehe Datenblatt und Schaltplan}
+
+ \vspace*{-2.5cm}\hfill
+ {\color{red}Herstellerspezifisch!}%
+ \hspace*{1cm}
+
+\end{frame}
+
+\subsection{volatile-Variable}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Externes Gerät ruft (per Stromsignal) Unterprogramm auf
+
+ Zeiger hinterlegen: "`Interrupt-Vektor"'
+
+ Beispiel: Taster
+
+ \vspace*{-2.5pt}
+
+ \begin{minipage}[t]{5cm}
+ \begin{onlyenv}<1>
+ \begin{lstlisting}[gobble=8]
+ ¡#include <avr/interrupt.h>
+ ...
+
+ uint8_t key_pressed = 0;
+
+ ISR (INT0_vect)
+ {
+ key_pressed = 1;
+ }¿
+ \end{lstlisting}
+ \end{onlyenv}
+ \begin{onlyenv}<2>
+ \begin{lstlisting}[gobble=8]
+ ¡#include <avr/interrupt.h>
+ ...
+
+ volatile uint8_t key_pressed = 0;
+
+ ISR (INT0_vect)
+ {
+ key_pressed = 1;
+ }¿
+ \end{lstlisting}
+ \end{onlyenv}
+ \end{minipage}\hfill
+ \begin{minipage}[t]{6cm}
+ \begin{lstlisting}[gobble=6]
+ ¡int main (void)
+ {
+ ...
+
+ while (1)
+ {
+ while (!key_pressed)
+ ; /* just wait */
+ PORTD ^= 0x40;
+ key_pressed = 0;
+ }
+ return 0;
+ }¿
+ \end{lstlisting}
+ \end{minipage}
+
+ \pause
+ \begin{picture}(0,0)
+ \color{red}
+ \put(10.3,4.0){\makebox(0,0)[b]{\begin{minipage}{6cm}
+ \begin{center}
+ \textbf{volatile}:\\
+ Speicherzugriff\\
+ nicht wegoptimieren
+ \end{center}
+ \end{minipage}}}
+ \put(10.3,3.95){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-0.5,-0.9);}}}
+ \end{picture}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Was ist eigentlich \lstinline{PORTD}?
+
+ \bigskip
+ \pause
+
+ \lstinline[style=cmd]{avr-gcc -Wall -Os -mmcu=atmega328p blink-3.c -E}
+
+ \bigskip
+ \pause
+ \lstinline{PORTD = 0x01;}\\
+ \textarrow\quad
+ \lstinline[style=terminal]{(*(volatile uint8_t *)((0x0B) + 0x20)) = 0x01;}\\
+ \pause
+ \begin{picture}(0,2)(0,-1.7)
+ \color{red}
+ \put(5.75,0.3){$\underbrace{\rule{2.95cm}{0pt}}_{\mbox{Zahl: \lstinline|0x2B|}}$}
+ \pause
+ \put(1.55,0.3){$\underbrace{\rule{4.0cm}{0pt}}_{\mbox{\shortstack[t]{Umwandlung in Zeiger\\
+ auf \lstinline|volatile uint8_t|}}}$}
+ \pause
+ \put(1.32,-1){\makebox(0,0)[b]{\tikz{\draw[-latex](0,0)--(0,1.3)}}}
+ \put(1.12,-1.1){\makebox(0,0)[tl]{Dereferenzierung des Zeigers}}
+ \end{picture}
+
+ \pause
+ \textarrow\quad
+ \lstinline|volatile uint8_t|-Variable an Speicheradresse \lstinline|0x2B|
+
+ \pause
+ \bigskip
+ \bigskip
+
+ \textarrow\quad
+ \lstinline|PORTA = PORTB = PORTC = PORTD = 0| ist eine schlechte Idee.
+
+\end{frame}
+
+\subsection{Byte-Reihenfolge -- Endianness}
+\subsubsection{Konzept}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+ \showsubsubsection
+
+ Eine Zahl geht über mehrere Speicherzellen.\\
+ Beispiel: 16-Bit-Zahl in 2 8-Bit-Speicherzellen
+
+ \smallskip
+
+ Welche Bits liegen wo?
+
+% \pause
+ \bigskip
+
+ $1027 = 1024 + 2 + 1 = 0000\,0100\,0000\,0011_2 = 0403_{16}$
+
+% \pause
+ \bigskip
+ Speicherzellen:
+
+ \medskip
+ \begin{tabular}{|c|c|l}\cline{1-2}
+ \raisebox{-0.25ex}{04} & \raisebox{-0.25ex}{03} & \strut Big-Endian "`großes Ende zuerst"' \\\cline{1-2}
+ \multicolumn{2}{c}{} & % \pause
+ für Menschen leichter lesbar % \pause
+ \\
+ \multicolumn{3}{c}{} \\[-5pt]\cline{1-2}
+ \raisebox{-0.25ex}{03} & \raisebox{-0.25ex}{04} & \strut Little-Endian "`kleines Ende zuerst"' \\\cline{1-2}
+ \multicolumn{2}{c}{} & % \pause
+ bei Additionen effizienter
+ \end{tabular}
+
+% \pause
+ \medskip
+ \textarrow\ Geschmackssache
+% \pause\\
+ \quad\textbf{\dots\ außer bei Datenaustausch!}
+
+% \pause
+% \bigskip
+%
+% Aber: nicht verwechseln! \qquad $0304_{16} = 772$
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Eine Zahl geht über mehrere Speicherzellen.\\
+ Beispiel: 16-Bit-Zahl in 2 8-Bit-Speicherzellen
+
+ \smallskip
+
+ Welche Bits liegen wo?
+
+ \medskip
+
+ \textarrow\ Geschmackssache\\
+ \textbf{\dots\ außer bei Datenaustausch!}
+
+ \begin{itemize}
+ \item
+ Dateiformate
+ \item
+ Datenübertragung
+ \end{itemize}
+
+\end{frame}
+
+\subsubsection{Dateiformate}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ Audio-Formate: Reihenfolge der Bytes in 16- und 32-Bit-Zahlen
+ \begin{itemize}
+ \item
+ RIFF-WAVE-Dateien (\file{.wav}): Little-Endian
+ \item
+ Au-Dateien (\file{.au}): Big-Endian
+% \pause
+ \item
+ ältere AIFF-Dateien (\file{.aiff}): Big-Endian
+ \item
+ neuere AIFF-Dateien (\file{.aiff}): Little-Endian
+ \end{itemize}
+
+% \pause
+ \bigskip
+
+ Grafik-Formate: Reihenfolge der Bits in den Bytes
+ \begin{itemize}
+ \item
+ PBM-Dateien: Big-Endian\only<1->{, MSB first}
+ \item
+ XBM-Dateien: Little-Endian\only<1->{, LSB first}
+ \end{itemize}
+ \only<1->{MSB/LSB = most/least significant bit}
+
+\end{frame}
+
+\subsubsection{Datenübertragung}
+
+\begin{frame}
+
+ \showsubsection
+ \showsubsubsection
+
+ \begin{itemize}
+ \item
+ RS-232 (serielle Schnittstelle): LSB first
+ \item
+ I$^2$C: MSB first
+ \item
+ USB: beides
+ \pause
+ \medskip
+ \item
+ Ethernet: LSB first
+ \item
+ TCP/IP (Internet): Big-Endian
+ \end{itemize}
+
+\end{frame}
+
+\iffalse
+
+\subsection{Binärdarstellung negativer Zahlen}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Speicher ist begrenzt!\\
+ \textarrow\ feste Anzahl von Bits
+
+ \medskip
+
+ 8-Bit-Zahlen ohne Vorzeichen: \lstinline{uint8_t}\\
+ \textarrow\ Zahlenwerte von \lstinline{0x00} bis \lstinline{0xff} = 0 bis 255\\
+ \pause
+ \textarrow\ 255 + 1 = 0
+
+ \pause
+ \medskip
+
+ 8-Bit-Zahlen mit Vorzeichen: \lstinline{int8_t}\\
+ \lstinline{0xff} = 255 ist die "`natürliche"' Schreibweise für $-1$.\\
+ \pause
+ \textarrow\ Zweierkomplement
+
+ \pause
+ \medskip
+
+ Oberstes Bit = 1: negativ\\
+ Oberstes Bit = 0: positiv\\
+ \textarrow\ 127 + 1 = $-128$
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Speicher ist begrenzt!\\
+ \textarrow\ feste Anzahl von Bits
+
+ \medskip
+
+ 16-Bit-Zahlen ohne Vorzeichen:
+ \lstinline{uint16_t}\hfill\lstinline{uint8_t}\\
+ \textarrow\ Zahlenwerte von \lstinline{0x0000} bis \lstinline{0xffff}
+ = 0 bis 65535\hfill 0 bis 255\\
+ \textarrow\ 65535 + 1 = 0\hfill 255 + 1 = 0
+
+ \medskip
+
+ 16-Bit-Zahlen mit Vorzeichen:
+ \lstinline{int16_t}\hfill\lstinline{int8_t}\\
+ \lstinline{0xffff} = 66535 ist die "`natürliche"' Schreibweise für $-1$.\hfill
+ \lstinline{0xff} = 255 = $-1$\\
+ \textarrow\ Zweierkomplement
+
+ \medskip
+
+ Oberstes Bit = 1: negativ\\
+ Oberstes Bit = 0: positiv\\
+ \textarrow\ 32767 + 1 = $-32768$
+
+ \bigskip
+ Literatur: \url{http://xkcd.com/571/}
+
+\end{frame}
+
+\fi
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Frage: \emph{Für welche Zahl steht der Speicherinhalt\,
+ \raisebox{2pt}{%
+ \tabcolsep0.25em
+ \begin{tabular}{|c|c|}\hline
+ \rule{0pt}{11pt}a3 & 90 \\\hline
+ \end{tabular}}
+ (hexadezimal)?}
+
+ \pause
+ \smallskip
+ Antwort: \emph{Das kommt darauf an.} ;--)
+
+ \pause
+ \medskip
+ Little-Endian:
+
+ \smallskip
+
+ \begin{tabular}{lrl}
+ als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\
+ als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\
+ als \lstinline,int16_t,: & $-28509$\\
+ als \lstinline,uint16_t,: & $37027$\\
+ \lstinline,int32_t, oder größer: & $37027$
+ & (zusätzliche Bytes mit Nullen aufgefüllt)
+ \end{tabular}
+
+ \pause
+ \medskip
+ Big-Endian:
+
+ \smallskip
+
+ \begin{tabular}{lrl}
+ als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\
+ als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\
+ als \lstinline,int16_t,: & $-23664$\\
+ als \lstinline,uint16_t,: & $41872$\\ als \lstinline,int32_t,: & $-1550843904$ & (zusätzliche Bytes\\
+ als \lstinline,uint32_t,: & $2744123392$ & mit Nullen aufgefüllt)\\
+ als \lstinline,int64_t,: & $-6660823848880963584$\\
+ als \lstinline,uint64_t,: & $11785920224828588032$\\
+ \end{tabular}
+
+ \vspace*{-1cm}
+
+\end{frame}
+
+\subsection{Speicherausrichtung -- Alignment}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ \begin{lstlisting}
+ #include <stdint.h>
+
+ uint8_t a;
+ uint16_t b;
+ uint8_t c;
+ \end{lstlisting}
+
+ \pause
+ \bigskip
+
+ Speicheradresse durch 2 teilbar -- "`16-Bit-Alignment"'
+ \begin{itemize}
+ \item
+ 2-Byte-Operation: effizienter
+ \pause
+ \item
+ \dots\ oder sogar nur dann erlaubt
+ \pause
+ \arrowitem
+ Compiler optimiert Speicherausrichtung
+ \end{itemize}
+
+ \medskip
+
+ \pause
+ \begin{minipage}{3cm}
+ \begin{lstlisting}[gobble=6]
+ ¡uint8_t a;
+ uint8_t dummy;
+ uint16_t b;
+ uint8_t c;¿
+ \end{lstlisting}
+ \end{minipage}
+ \pause
+ \begin{minipage}{3cm}
+ \begin{lstlisting}[gobble=6]
+ ¡uint8_t a;
+ uint8_t c;
+ uint16_t b;¿
+ \end{lstlisting}
+ \end{minipage}
+
+ \pause
+ \vspace{-1.75cm}
+ \strut\hfill
+ \begin{minipage}{6.5cm}
+ Fazit:
+ \begin{itemize}
+ \item
+ \textbf{Adressen von Variablen\\
+ sind systemabhängig}
+ \item
+ Bei Definition von Datenformaten\\
+ Alignment beachten \textarrow\ effizienter
+ \end{itemize}
+ \end{minipage}
+
+\end{frame}
+
+\fi
+
+\end{document}
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new file mode 100644
index 0000000..bf353a0
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+ } ifelse
+ [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
+ a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
+ setdash 1 setlinecap stroke
+} def
+%
+/SymbolLine { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt
+ { %XYLength SymStep div abs cvi
+ /nSym SymStep abs cvi def }
+ { /nSym XYLength SymStep div cvi def }
+ ifelse
+ 0.5 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ /deltaX XLength nSym div def
+ /deltaY YLength nSym div def
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ nSym {
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ currentpoint translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+ /YA YB def /XA XB def
+ } repeat
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ XA YA translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ pop % delete the mark symbol
+} def
+%
+/LineFill { % hv ------------ patch 7 -------------
+ gsave
+ abs /hatchWidthInc ED
+ abs /hatchSepInc ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ 2 setlinecap
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ x2 x1 sub 1 add {
+ x1 a mul y1 moveto 0 y2 rlineto stroke
+ /x1 x1 1 add
+ hatchWidthInc 0 gt { CLW add } if
+ def
+ hatchSepInc 0 gt hatchWidthInc 0 gt or {
+ /a a hatchSepInc add def
+ CLW hatchWidthInc add SLW
+ } if
+ } repeat
+ grestore
+ pop pop } def
+%
+/DotFill {% on stack: dot radius
+ /dotRadius ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform
+ pathbbox % llx lly urx ury of smallest bounding box
+ /y2 ED /x2 ED /y1 ED /x1 ED
+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clip
+ newpath
+ /yA y1 dotRadius add CLW add def
+ /xA0 x1 dotRadius add CLW add def
+ Ny {
+ /xA xA0 def
+ Nx {
+ newpath
+ xA yA dotRadius 0 360 arc
+ SolidDot { gsave fill grestore } if
+ stroke
+ xA a add /xA ED
+ } repeat
+ yA a add /yA ED
+ } repeat
+ grestore
+} def
+%
+/PenroseFill {% on stack: scaling factor
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
+ { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
+ [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
+ i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
+ mul j l + S rmoveto}F i L j L stroke }F}F}F}F
+ grestore
+ pop pop
+} def
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /ma a neg def
+ /ha a 2 div def
+ /mha ha neg def
+ /tile {
+ rand dup 2 idiv 2 mul eq { 90 rotate } if
+ mha mha moveto ha mha lineto
+ ha ha lineto mha ha lineto
+% closepath .1 setlinewidth stroke
+ contents
+ } def
+ /contents{
+ 0 ha moveto ha 0 lineto
+ 0 mha moveto mha 0 lineto
+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+%%%%%%%%%%%%%%%%% tools %%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort {
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a
+end
+} def
+%
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 622 2012-01-01 15:36:14Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.02, 2012/01/01
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 645 2012-02-12 09:09:51Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.13, 2011/11/21.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+/tx@NodeDict 400 dict def tx@NodeDict begin
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+end
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
+GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {
+LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {
+LPutVar VPutLine } def LPutVar } def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
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+%
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+% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry,
+% W. Schmidt, P. Lehman",
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+% date = "27nov06",
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+% email = "tex-fonts@@tug.org",
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+%
+% Character code assignments were made as follows:
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+% positions, because some Windows users cannot easily reencode the
+% fonts, and it makes no difference on other systems. The only Windows
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+% irritation not having them in TeX positions.
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+% PostScript MacRoman TeXBase1
+% -------------- -------------- --------------
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diff --git a/common/io-ports-and-interrupts.pdf b/common/io-ports-and-interrupts.pdf
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diff --git a/common/io-ports-and-interrupts.tex b/common/io-ports-and-interrupts.tex
new file mode 100644
index 0000000..149f95b
--- /dev/null
+++ b/common/io-ports-and-interrupts.tex
@@ -0,0 +1,43 @@
+\documentclass{article}
+
+\usepackage[utf8]{inputenc}
+\usepackage[german]{babel}
+\usepackage[T1]{fontenc}
+\usepackage{helvet}
+\renewcommand*\familydefault{\sfdefault}
+\usepackage{pstricks,pst-node}
+
+\pagestyle{empty}
+
+\begin{document}
+ \psset{unit=1cm}%
+ \begin{pspicture}(0,0)(10,6)
+ \rput(0,0){\psframe[framearc=0.25](2,5)}
+ \rput(1,4.5){\makebox(0,0)[t]{Prozessor}}
+ \rput(2.0,3.7){\pnode{p0}}
+ \rput(2.0,3.3){\pnode{q0}}
+ \rput(2.0,1.0){\pnode{i0}}
+ \rput(2.12,1.2){\pnode{j0}}
+ \rput(2.02,1.3){\pnode{k0}}
+ \rput(2.12,1.4){\pnode{l0}}
+ \rput(3.5,1.4){\pnode{m0}}
+ \rput(8,0){\psframe[framearc=0.25](2,5)}
+ \rput(9,4.5){\makebox(0,0)[t]{\shortstack{externes\\Gerät}}}
+ \rput(8.0,3.7){\pnode{p1}}
+ \rput(7.88,3.3){\pnode{q1}}
+ \rput(7.98,3.2){\pnode{r1}}
+ \rput(7.88,3.1){\pnode{s1}}
+ \rput(6.5,3.1){\pnode{t1}}
+ \rput(8.0,1.0){\pnode{i1}}
+ \rput(8.0,1.2){\pnode{j1}}
+ \ncline{->}{p0}{p1}
+ \ncline{q0}{q1}
+ \nccurve[angleB=90]{q1}{r1}
+ \nccurve[angleA=-90]{r1}{s1}
+ \ncline{->}{s1}{t1}
+ \rput(2.2,3.8){\makebox(0,0)[lb]{Prozessor schreibt in Output-Port}}
+ \rput(2.2,3.1){\makebox(0,0)[lt]{Prozessor liest Input-Port}}
+ \ncline{->}{i1}{i0}
+ \rput(7.8,1.1){\makebox(0,0)[rb]{externes Gerät ruft Interrupt auf}}
+ \end{pspicture}
+\end{document}
--
GitLab