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Diskrete Mathematik und Algorithmen

Diskrete Mathematik und Algorithmen. Dipl.-Ing. (FH) Christian V. Madritsch University of Applied Science Electronics and Equipment Engineering. Übersicht. CPU Architekturen Pentium Architektur Programmierbeispiel Integer Lösung mit Assemblercode Floating Point Lösung mit Assemblercode

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Diskrete Mathematik und Algorithmen

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  1. Diskrete Mathematik und Algorithmen Dipl.-Ing. (FH) Christian V. Madritsch University of Applied Science Electronics and Equipment Engineering (c) 2006 Christian V. Madritsch, FH Kärnten

  2. Übersicht • CPU Architekturen • Pentium Architektur • Programmierbeispiel • Integer Lösung mit Assemblercode • Floating Point Lösung mit Assemblercode • C167 Architektur • Programmierbeispiel • Integer Lösung mit Assemblercode • Floating Point Lösung mit Assemblercode • Diskussion (c) 2006 Christian V. Madritsch, FH Kärnten

  3. intel Pentium Architektur (c) 2006 Christian V. Madritsch, FH Kärnten

  4. Integer Calculation (i) void main (void){ int f1, f2, erg; f1 = 3.1415; f2 = 2.7; erg = f1 + f2; while(1){ erg = f1 + f2; if(erg > 2) f1 = 0; else f2 = 0; } } (c) 2006 Christian V. Madritsch, FH Kärnten

  5. Integer Calculation (ii) 1: void main (void){ 2: int f1, f2, erg; 3: f1 = 3.1415; 00401028 mov dword ptr [ebp-4],3 4: f2 = 2.7; 0040102F mov dword ptr [ebp-8],2 5: erg = f1 + f2; 00401036 mov eax,dword ptr [ebp-4] 00401039 add eax,dword ptr [ebp-8] 0040103C mov dword ptr [ebp-0Ch],eax 6: while(1){ 0040103F mov ecx,1 00401044 test ecx,ecx 00401046 je main+59h (00401069) 7: erg = f1 + f2; 00401048 mov edx,dword ptr [ebp-4] 0040104B add edx,dword ptr [ebp-8] 0040104E mov dword ptr [ebp-0Ch],edx 8: if(erg > 2) 00401051 cmp dword ptr [ebp-0Ch],2 00401055 jle main+50h (00401060) 9: f1 = 0; 00401057 mov dword ptr [ebp-4],0 10: else 0040105E jmp main+57h (00401067) 11: f2 = 0; 00401060 mov dword ptr [ebp-8],0 12: } 00401067 jmp main+2Fh (0040103f) (c) 2006 Christian V. Madritsch, FH Kärnten

  6. Floating Point Calculation (i) void main (void){ double f1, f2, erg; f1 = 3.1415; f2 = 2.7; erg = f1 + f2; while(1){ erg = f1 + f2; if(erg > 2) f1 = 0; else f2 = 0; } } (c) 2006 Christian V. Madritsch, FH Kärnten

  7. Floating Point Calculation (ii) 1: void main (void){ 2: double f1, f2, erg; 3: f1 = 3.1415; 00401028 mov dword ptr [ebp-8],0C083126Fh 0040102F mov dword ptr [ebp-4],400921CAh 4: f2 = 2.7; 00401036 mov dword ptr [ebp-10h],9999999Ah 0040103D mov dword ptr [ebp-0Ch],40059999h 5: erg = f1 + f2; 00401044 fld qword ptr [ebp-8] 00401047 fadd qword ptr [ebp-10h] 0040104A fstp qword ptr [ebp-18h] 6: while(1){ 0040104D mov eax,1 00401052 test eax,eax 00401054 je main+7Fh (0040108f) 7: erg = f1 + f2; 00401056 fld qword ptr [ebp-8] 00401059 fadd qword ptr [ebp-10h] 0040105C fstp qword ptr [ebp-18h] 8: if(erg > 2) 0040105F fld qword ptr [ebp-18h] 00401062 fcomp qword ptr [__real@8@40008000000000000000 (00423020)] 00401068 fnstsw ax 0040106A test ah,41h 0040106D jne main+6Fh (0040107f) 9: f1 = 0; 0040106F mov dword ptr [ebp-8],0 00401076 mov dword ptr [ebp-4],0 10: else 0040107D jmp main+7Dh (0040108d) 11: f2 = 0; 0040107F mov dword ptr [ebp-10h],0 00401086 mov dword ptr [ebp-0Ch],0 (c) 2006 Christian V. Madritsch, FH Kärnten

  8. Infineon C167-CS Block Diagram (c) 2006 Christian V. Madritsch, FH Kärnten

  9. 16-Bit CPU Van Neumann 4-Stage Pipeline 80ns Instruction Cycle @ 25MHz 400ns Multiplication (16x16bit), 800ns Division (32/16bit) No native Floating Point support C166 Core Block Diagram (c) 2006 Christian V. Madritsch, FH Kärnten

  10. Keil C166 Development System (c) 2006 Christian V. Madritsch, FH Kärnten

  11. Integer Calculation (i) void main (void){ int f1, f2, erg; f1 = 3.1415; f2 = 2.7; erg = f1 + f2; while(1){ erg = f1 + f2; if(erg > 2) f1 = 0; else f2 = 0; } } (c) 2006 Christian V. Madritsch, FH Kärnten

  12. Integer Calculation (ii) 1: void main (void) { 2: int f1, f2, erg; 3: f1 = 3.1415; 00010002 E035 MOV R5,#0x03 4: f2 = 2.7; 00010004 E027 MOV R7,#0x02 5: erg = f1 + f2; 00010006 E056 MOV R6,#0x05 6: while(1){ 7: erg = f1 + f2; 00010008 F065 MOV R6,R5 0001000A 0067 ADD R6,R7 8: if(erg > 2) 0001000C 4862 CMP R6,#2 0001000E BD02 JMPR CC_SLE,0x010014 9: f1 = 0; 10: else 00010010 E005 MOV R5,#0x00 00010012 0DFA JMPR CC_UC,0x010008 11: f2 = 0; 00010014 E007 MOV R7,#0x00 12: } 00010016 0DF8 JMPR CC_UC,0x010008 (c) 2006 Christian V. Madritsch, FH Kärnten

  13. Floating Point Calculation (i) void main (void){ double f1, f2, erg; f1 = 3.1415; f2 = 2.7; erg = f1 + f2; while(1){ erg = f1 + f2; if(erg > 2) f1 = 0; else f2 = 0; } } (c) 2006 Christian V. Madritsch, FH Kärnten

  14. 1: void main (void) { 2: double f1, f2, erg; 000101CC 2804 SUB R0,#4 3: f1 = 3.1415; 000101CE E6F4560E MOV R4,#0x0E56 000101D2 E6F54940 MOV R5,#0x4049 000101D6 B840 MOV [R0],R4 000101D8 C4500200 MOV [R0+#0x0002],R5 4: f2 = 2.7; 000101DC E6FECDCC MOV R14,#0xCCCD 000101E0 E6FF2C40 MOV R15,#0x402C 5: erg = f1 + f2; 000101E4 E6FC92ED MOV R12,#0xED92 000101E8 E6FDBA40 MOV R13,#0x40BA 6: while(1){ 7: erg = f1 + f2; 000101EC A840 MOV R4,[R0] 000101EE D4500200 MOV R5,[R0+#0x0002] 000101F2 F06E MOV R6,R14 000101F4 F07F MOV R7,R15 000101F6 CA000600 CALLA CC_UC,?C_FPADD(0x10006) 000101FA F0C4 MOV R12,R4 000101FC F0D5 MOV R13,R5 8: if(erg > 2) 000101FE E006 MOV R6,#0x00 00010200 E6F70040 MOV R7,#0x4000 00010204 CA00EA00 CALLA CC_UC,?C_FPCMP(0x100EA) 00010208 BD05 JMPR CC_SLE,0x010214 9: f1 = 0; 10: else 0001020A E004 MOV R4,#0x00 0001020C B840 MOV [R0],R4 0001020E C4400200 MOV [R0+#0x0002],R4 00010212 0DEC JMPR CC_UC,0x0101EC 11: f2 = 0; 00010214 E00E MOV R14,#0x00 00010216 E00F MOV R15,#0x00 12: } 00010218 0DE9 JMPR CC_UC,0x0101EC Floating Point Calculation (ii) (c) 2006 Christian V. Madritsch, FH Kärnten

  15. C167FPS.LIB (i) • FP_ADD • calls: FP_GETOPN • calls: FG_XSUB • calls: FP_OPRSL • calls: FP_RSLNR • calls: FP_NOERR (c) 2006 Christian V. Madritsch, FH Kärnten

  16. C167FPS.LIB (ii) ?C_FPADD: 00010006 CA006801 CALLA CC_UC,?C_FPGETOPN(0x10168) 0001000A 46FAFF00 CMP R10,#0x00FF 0001000E 3D10 JMPR CC_NZ,0x010030 00010010 46F78000 CMP R7,#0x0080 00010014 3D13 JMPR CC_NZ,0x01003C 00010016 46F9FF00 CMP R9,#0x00FF 0001001A 3D07 JMPR CC_NZ,0x01002A 0001001C 46F58000 CMP R5,#0x0080 00010020 3D0D JMPR CC_NZ,0x01003C 00010022 2AF2F280 BCMP R2.0,R2.8 00010026 6D0A JMPR CC_N,0x01003C 00010028 0D0B JMPR CC_UC,0x010040 0001002A 4AF2F280 BMOV R2.0,R2.8 0001002E 0D08 JMPR CC_UC,0x010040 00010030 46F9FF00 CMP R9,#0x00FF 00010034 3D07 JMPR CC_NZ,?C_FPXSUB(0x10044) 00010036 46F58000 CMP R5,#0x0080 0001003A 2D02 JMPR CC_Z,0x010040 0001003C EA008E01 JMPA CC_UC,?C_FPNANRSL(0x1018E) 00010040 EA009601 JMPA CC_UC,?C_FPINFRSL(0x10196) 20 LOCs (c) 2006 Christian V. Madritsch, FH Kärnten

  17. C167FPS.LIB (iii) ?C_FPGETOPN: 00010168 F095 MOV R9,R5 0001016A 5C19 SHL R9,#0x01 0001016C 4A88F210 BMOV R2.0,C 00010170 7C89 SHR R9,#0x08 00010172 3A88F537 BMOVN R5.7,Z 00010176 E003 MOV R3,#0x00 00010178 E10B MOVB RH5,#0x00 0001017A F0A7 MOV R10,R7 0001017C 5C1A SHL R10,#0x01 0001017E 4A88F218 BMOV R2.8,C 00010182 7C8A SHR R10,#0x08 00010184 3A88F737 BMOVN R7.7,Z 00010188 E008 MOV R8,#0x00 0001018A E10F MOVB RH7,#0x00 0001018C CB00 RET 15 LOCs (c) 2006 Christian V. Madritsch, FH Kärnten

  18. ?C_FPXSUB: 00010044 48A0 CMP R10,#0 00010046 2D06 JMPR CC_Z,0x010054 00010048 4890 CMP R9,#0 0001004A 3D06 JMPR CC_NZ,0x010058 0001004C F057 MOV R5,R7 0001004E F046 MOV R4,R6 00010050 F09A MOV R9,R10 00010052 F145 MOVB RL2,RH2 00010054 EA00B801 JMPA CC_UC,?C_FPNOERR(0x101B8) 00010058 409A CMP R9,R10 0001005A 9D0C JMPR CC_NC,0x010074 0001005C F015 MOV R1,R5 0001005E F057 MOV R5,R7 00010060 F071 MOV R7,R1 00010062 F014 MOV R1,R4 00010064 F046 MOV R4,R6 00010066 F061 MOV R6,R1 00010068 F019 MOV R1,R9 0001006A F09A MOV R9,R10 0001006C F0A1 MOV R10,R1 0001006E F124 MOVB RL1,RL2 00010070 F145 MOVB RL2,RH2 00010072 F152 MOVB RH2,RL1 00010074 F019 MOV R1,R9 00010076 201A SUB R1,R10 00010078 2D0B JMPR CC_Z,0x010090 0001007A 46F11900 CMP R1,#0x0019 0001007E 9DEA JMPR CC_NC,0x010054 00010080 5AF6F80F BOR R8.15,R6.0 00010084 7C16 SHR R6,#0x01 70 LOCs 00010086 4AF7F60F BMOV R6.15,R7.0 0001008A 7C17 SHR R7,#0x01 0001008C 2811 SUB R1,#1 0001008E 3DF8 JMPR CC_NZ,0x010080 00010090 2AF2F280 BCMP R2.0,R2.8 00010094 6D0E JMPR CC_N,0x0100B2 00010096 0038 ADD R3,R8 00010098 1046 ADDC R4,R6 0001009A 1057 ADDC R5,R7 0001009C 9AF50780 JNB R5.8,0x0100AE 000100A0 0891 ADD R9,#1 000100A2 5AF4F30F BOR R3.15,R4.0 000100A6 7C14 SHR R4,#0x01 000100A8 4AF5F40F BMOV R4.15,R5.0 000100AC 7C15 SHR R5,#0x01 000100AE EA00A201 JMPA CC_UC,?C_FPOPRSL(0x101A2) // jump 000100B2 2038 SUB R3,R8 000100B4 3046 SUBC R4,R6 000100B6 3057 SUBC R5,R7 000100B8 EA20C601 JMPA CC_Z,?C_FPZERRSL(0x101C6) 000100BC 9D07 JMPR CC_NC,0x0100CC 000100BE B140 CPLB RL2 000100C0 9130 CPL R3 000100C2 9140 CPL R4 000100C4 9150 CPL R5 000100C6 0831 ADD R3,#1 000100C8 1840 ADDC R4,#0 000100CA 1850 ADDC R5,#0 000100CC 8AF5EF70 JB R5.7,0x0100AE 000100D0 0033 ADD R3,R3 000100D2 1044 ADDC R4,R4 000100D4 1055 ADDC R5,R5 000100D6 2891 SUB R9,#1 000100D8 8AF50570 JB R5.7,0x0100E6 000100DC 0044 ADD R4,R4 000100DE 1055 ADDC R5,R5 000100E0 2891 SUB R9,#1 000100E2 9AF5FB70 JNB R5.7,0x0100DC 000100E6 EA00AE01 JMPA CC_UC,?C_FPRSLNR(0x101AE) C167FPS.LIB (iv) (c) 2006 Christian V. Madritsch, FH Kärnten

  19. C167FPS.LIB (v) ?C_FPOPRSL: 000101A2 9AF304F0 JNB R3.15,?C_FPRSLNR(0x101AE) 000101A6 0841 ADD R4,#1 000101A8 19A0 ADDCB RL5,#0 000101AA 9D01 JMPR CC_NC,?C_FPRSLNR(0x101AE) 000101AC 0891 ADD R9,#1 ?C_FPRSLNR: 000101AE 4890 CMP R9,#0 000101B0 BD0A JMPR CC_SLE,?C_FPZERRSL(0x101C6) 000101B2 46F9FF00 CMP R9,#0x00FF 000101B6 DDEF JMPR CC_SGE,?C_FPINFRSL(0x10196) ?C_FPNOERR: 000101B8 66F57F00 AND R5,#0x007F 000101BC 5C79 SHL R9,#0x07 000101BE 4AF2F90F BMOV R9.15,R2.0 000101C2 7059 OR R5,R9 000101C4 CB00 RET 14 LOCs (c) 2006 Christian V. Madritsch, FH Kärnten

  20. Diskussion • Der C166 Core unterstützt nur Integer (16-Bit) Operationen. • Floating Point (float, double) Operationen werden in Software nachgebildet. • Daraus folgt: • Floating Point Operationen sind (durchschnittlich) um den Faktor 100 langsamer als Integer Operationen • Der Speicherplatzbedarf für Daten und Programm ist um den den Faktor 150 - 200 größer als bei Integer Operationen • Dies relativiert sich, da die Bibliothek C167FPS.lib nur einmal eingebunden wird (c) 2006 Christian V. Madritsch, FH Kärnten

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