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First (very rough) draft.
This commit is contained in:
John Winans
parent
a1a0aac853
commit
2323d755b5
19
book/.gitignore
vendored
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19
book/.gitignore
vendored
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@ -0,0 +1,19 @@
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book.aux
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book.brf
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book.idx
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book.ilg
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book.ind
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book.lof
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book.log
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book.pdf
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book.toc
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book.bbl
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book.blg
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book.out
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*.aux
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book.glg
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book.glo
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book.gls
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book.glsdefs
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book.ist
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*.bak
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17
book/Makefile
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17
book/Makefile
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@ -0,0 +1,17 @@
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TOP=..
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include $(TOP)/Make.rules
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TEXPATH=./numbers:./intro:./rv32:./copyright:./license
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SUBDIRS=
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all:: book.pdf
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clean::
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rm -f book.pdf */*.aux $(LATEX_CLEANFILES)
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book.pdf:: *.tex bibliography.bib
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spell:
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#find . -name "*.tex" -exec aspell --lang=en --mode=tex check "{}" \;
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find . -name "*.tex" -exec aspell --mode=tex check "{}" \;
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147
book/bibliography.bib
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147
book/bibliography.bib
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@ -0,0 +1,147 @@
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@string{IETF="Internet Engineering Task Force"}
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@manual{rvismv1v22:2017,
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title = "\href{https://github.com/riscv/riscv-isa-manual}{The RISC-V Instruction Set Manual, Volume I: User-Level ISA, Document Version 2.2}",
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organization = "\href{https://riscv.org/}{RISC-V Foundation}",
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year = 2017,
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month = 5,
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note = {Editors Andrew Waterman and Krste Asanovi\'c}
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}
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The RISC-V Instruction Set Manual
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Volume II: Privileged Architecture
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@manual{rvismv2:2017,
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title = "\href{https://github.com/riscv/riscv-isa-manual}{The RISC-V Instruction Set Manual, Volume II: Privileged Architecture, Document Version 1.10}",
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organization = "\href{https://riscv.org/}{RISC-V Foundation}",
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year = 2017,
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month = 5,
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note = {Editors Andrew Waterman and Krste Asanovi\'c}
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}
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@book{riscvreader:2017,
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title = {The RISC-V Reader: An Open Architecture Atlas},
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author = {David Patterson and Andrew Waterman},
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publisher = {Strawberry Canyon},
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month = 11,
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year = 2017,
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note = {ISBN: 978-0999249116}
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}
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@book{codriscv:2017,
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title = {Computer Organization and Design RISC-V Edition: The Hardware Software Interface},
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author = {David Patterson and John Hennessy},
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publisher = {Morgan Kaufmann},
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month = 4,
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year = 2017,
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note = {ISBN: 978-0128122754}
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@book{gcc:2017,
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title = "\href{https://gcc.gnu.org/onlinedocs/}{Using the GNU Compiler Collection (For GCC version 7.3.0)}",
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author = {Richard M. Stallman and the GCC Developer Community},
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publisher = {GNU Press},
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address = {Free Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA},
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year = 2017
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}
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@article{Decker:1985:MAT:989369.989375,
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author = {Decker, William F.},
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title = {A Modern Approach to Teaching Computer Organization and Assembly Language Programming},
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journal = {SIGCSE Bull.},
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issue_date = {December 1985},
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volume = {17},
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number = {4},
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month = 12,
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year = {1985},
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issn = {0097-8418},
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pages = {38--44},
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numpages = {7},
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url = {http://doi.acm.org/10.1145/989369.989375},
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doi = {10.1145/989369.989375},
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acmid = {989375},
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publisher = {ACM},
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address = {New York, NY, USA}
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}
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@manual{mcs85:1978,
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title = {MCS-85 User's Manual},
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organization = {Intel},
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month = 9,
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year = 1978
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}
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@manual{edtasm:1978,
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title = {TRS-80 Editor/Assembler Operation and Reference Manual},
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organization = {Radio Shack},
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year = 1978
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}
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|
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@manual{mc68000:1980,
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title = {MC68000 16--bit Microprocessor User's Manual},
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edition = {2nd},
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organization = {Motorola},
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month = 1,
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year = 1980,
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||||
note = {MC68000UM(AD2)}
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}
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@manual{ns32k:1986,
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title = {Series 32000 Databook},
|
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organization = {National Semiconductor Coprporation},
|
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year = 1986
|
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}
|
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|
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@book{assist:1983,
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title = {Assembler Language With ASSIST},
|
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author = {Ross A. Overbeek and W. E. Singletary},
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edition = {2nd},
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publisher = {Science Research Associates, Inc.},
|
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year = 1983
|
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}
|
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|
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@manual{poo:1980,
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title = {IBM System/370 Principals of Operation},
|
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edition = {7th},
|
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organization = {IBM},
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month = 3,
|
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year = 1980
|
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}
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|
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@manual{assembler370:1979,
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title = {OS/VS-DOS/VSE-VM/370 Assembler Language},
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edition = {6th},
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organization = {IBM},
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month = 3,
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year = 1979
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}
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|
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@manual{ttl74154:1979,
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title = "\href{http://www.ti.com/general/docs/lit/getliterature.tsp?baseLiteratureNumber=sdls056&fileType=pdf}{SN54154, SN74154 4--line to 16--line Decoders/Demultiplexers}",
|
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organization = {Texas Instruments},
|
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month = 12,
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year = 1972
|
||||
}
|
||||
|
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@manual{ttl74191:1979,
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title = "\href{http://www.ti.com/lit/ds/symlink/sn74ls191.pdf}{SN54190, SN54191, SN54LS190, SN54LS191, SN74190, SN74191, SN74LS190, SN74LS191 Synchronous Up/Down Counters With Down/Up Mode Control}",
|
||||
organization = {Texas Instruments},
|
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month = 3,
|
||||
year = 1988
|
||||
}
|
||||
|
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|
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|
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@Misc{IEN137,
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author = "Danny Cohen",
|
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title = "\href{http://www.ietf.org/rfc/ien/ien137.txt}{IEN 137, On Holy Wars and a Plea for Peace}",
|
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month = apr,
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year = "1980",
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note = "This note discusses the Big-Endian/Little-Endian
|
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byte/bit-order controversy, but did not settle it. A
|
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decade later, David V. James in ``Multiplexed Buses:
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The Endian Wars Continue'', {\em IEEE Micro}, {\bf
|
||||
10}(3), 9--21 (1990) continued the discussion.",
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%%% URL = "http://www.ietf.org/rfc/ien/ien137.txt",
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}
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95
book/book.tex
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95
book/book.tex
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@ -0,0 +1,95 @@
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%\documentclass[oneside,draft,letterpaper]{book}
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%\documentclass[letterpaper]{book}
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\documentclass[oneside,letterpaper]{book}
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\input{preamble}
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\input{colors}
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\input{insnformats}
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\usepackage{ENote}
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%\usepackage{showframe}
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\hypersetup{
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pdfauthor={John Winans},
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pdftitle={RISC-V Assembly Language Programming (Draft \GitRevision{})},
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pdfkeywords={RISC-V} {Assembler}
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}
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\makeindex
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%\makeglossaries
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\makenoidxglossaries
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\include{glossary}
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\begin{document}
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\include{indexrefs} % The see-references for the index
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% Why does this (apparently) have to go here????
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\newlength{\fullwidth}
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\setlength{\fullwidth}{\the\textwidth}
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\addtolength{\fullwidth}{\the\marginparsep}
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\addtolength{\fullwidth}{\the\marginparwidth}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\frontmatter
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\title{RISC-V\\Assembly Language Programming\\{\normalsize (Draft \GitRevision{})}}
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\author{John Winans\\ \href{mailto:jwinans@niu.edu}{\sf jwinans@niu.edu}}
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%\date{May }
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\maketitle
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\include{copyright/chapter}
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\tableofcontents
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%\listoffigures
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\setlength{\parskip}{10pt}
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\include{preface/chapter}
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\mainmatter
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%\include{preface/chapter}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% there should be one include here for each chapter
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%\part{Introduction}
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%\include{intro/chapter}
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\include{numbers/chapter}
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\include{toolchain/chapter}
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\include{rv32/chapter}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% These 'chapters' are lettered rather than numbered
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\appendix
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\include{license/chapter}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\backmatter
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% putting a chapter here causes it to be unnumbered
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\clearpage
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\bibliography{bibliography}
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\addcontentsline{toc}{chapter}{Bibliography}
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%\nocite{*} % force all bib items to file appear even if not cited
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%\bibliographystyle{alpha}
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\bibliographystyle{ieeetr}
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\clearpage
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\phantomsection
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\addcontentsline{toc}{chapter}{\indexname}
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\printindex
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%\clearpage
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%\phantomsection
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\glsaddall
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\printnoidxglossaries
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||||
%\printglossary
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||||
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||||
\end{document}
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5
book/colors.tex
Normal file
5
book/colors.tex
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@ -0,0 +1,5 @@
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% These are color styles used in the figures in this book.
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||||
\definecolor{c_lightblue}{HTML}{B0E0FF}
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||||
\definecolor{c_lightred}{HTML}{FFE0E0}
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||||
\definecolor{c_lightyellow}{HTML}{FFE060}
|
||||
\definecolor{c_lightgreen}{HTML}{C0FFC0}
|
||||
13
book/copyright/chapter.tex
Normal file
13
book/copyright/chapter.tex
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\thispagestyle{plain}
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||||
|
||||
Copyright \copyright\ 2018 John Winans
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|
||||
This document is made available under a Creative Commons Attribution 4.0
|
||||
International License. See \autoref{license} for more information.
|
||||
|
||||
Download your own copy of this book from github here:
|
||||
\url{https://github.com/johnwinans/rvalp}.
|
||||
|
||||
This document may contain inaccuracies or errors. The author provides no
|
||||
guarantee regarding the accuracy of this document's contents. If you
|
||||
discover that this document contains errors, please notify the author.
|
||||
93
book/glossary.tex
Normal file
93
book/glossary.tex
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\newglossaryentry{latex}
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||||
{
|
||||
name=LaTeX,
|
||||
description={Is a mark up language specially suited
|
||||
for scientific documents}
|
||||
}
|
||||
|
||||
\newglossaryentry{bit}
|
||||
{
|
||||
name=bit,
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||||
description={One binary digit}
|
||||
}
|
||||
\newglossaryentry{hit}
|
||||
{
|
||||
name={hit},
|
||||
description={One hex digit}
|
||||
}
|
||||
\newglossaryentry{byte}
|
||||
{
|
||||
name=byte,
|
||||
description={A binary value represented by 8 bits}
|
||||
}
|
||||
\newglossaryentry{HalfWord}
|
||||
{
|
||||
name={Halfword},
|
||||
description={A binary value represented by 16 bits}
|
||||
}
|
||||
\newglossaryentry{FullWord}
|
||||
{
|
||||
name={Fullword},
|
||||
description={A binary value represented by 32 bits}
|
||||
}
|
||||
\newglossaryentry{DoubleWord}
|
||||
{
|
||||
name={Doubleword},
|
||||
description={A binary value represented by 64 bits}
|
||||
}
|
||||
\newglossaryentry{QuadWord}
|
||||
{
|
||||
name={Quadword},
|
||||
description={A binary value represented by 128 bits}
|
||||
}
|
||||
\newglossaryentry{HighOrderBits}
|
||||
{
|
||||
name={High order bits},
|
||||
description={Some number of MSBs}
|
||||
}
|
||||
\newglossaryentry{LowOrderBits}
|
||||
{
|
||||
name={Low order bits},
|
||||
description={Some number of LSBs}
|
||||
}
|
||||
|
||||
\newglossaryentry{xlen}
|
||||
{
|
||||
name=XLEN,
|
||||
description={The number of bits a RISC-V x integer register
|
||||
(such as x0). For RV32 XLEN=32, RV64 XLEN=64 etc}
|
||||
}
|
||||
\newglossaryentry{rv32}
|
||||
{
|
||||
name=RV32,
|
||||
description={Short for RISC-V 32. The number 32 refers to the XLEN}
|
||||
}
|
||||
\newglossaryentry{rv64}
|
||||
{
|
||||
name=RV64,
|
||||
description={Short for RISC-V 64. The number 64 refers to the XLEN}
|
||||
}
|
||||
\newglossaryentry{overflow}
|
||||
{
|
||||
name=overflow,
|
||||
description={The situation where the result of an addition or
|
||||
subtraction operation is approaching positive or negative
|
||||
infinity and exceeds the number of bits alloted to contain
|
||||
the result. This is typically caused by high--order truncation}
|
||||
}
|
||||
\newglossaryentry{underflow}
|
||||
{
|
||||
name=underflow,
|
||||
description={The situation where the result of an addition or
|
||||
subtraction operation is approaching zero and exceeds the number
|
||||
of bits alloted to contain the result. This is typically
|
||||
caused by low--order truncation}
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\newacronym{msb}{MSB}{Most Significant Bit}
|
||||
\newacronym{lsb}{LSB}{Least Significant Bit}
|
||||
\newacronym{isa}{ISA}{Instruction Set Architecture}
|
||||
442
book/insnformats.tex
Normal file
442
book/insnformats.tex
Normal file
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|
||||
|
||||
\def\SignBoxCornerRadius{.75mm}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\BeginTikzPicture{
|
||||
\begin{tikzpicture}[x=.4cm,y=.3cm]
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\EndTikzPicture{
|
||||
\end{tikzpicture}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Print the characters within a string evenly spaced at integral node positions
|
||||
%
|
||||
% #1 The number of characters in the string
|
||||
\newcommand\DrawBitstring[2]{
|
||||
\foreach \x in {1,...,#1}%
|
||||
\draw(\x,0) node{\substring{#2}{\x}{\x}};%
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 The total size
|
||||
% #2 The string to print
|
||||
% #3 The value to use when extending to left
|
||||
\newcommand\DrawLeftExtendedBitstring[3]{
|
||||
\StrLen{#2}[\numchars]
|
||||
|
||||
\pgfmathsetmacro\leftpadd{int(#1-\numchars)}
|
||||
\foreach \x in {1,...,\leftpadd}
|
||||
\draw(\x,0) node{#3};
|
||||
|
||||
\pgfmathsetmacro\leftpadd{int(\leftpadd+1)}
|
||||
\foreach \x in {\leftpadd,...,#1}
|
||||
\pgfmathsetmacro\ix{int(\x-\leftpadd+1)}
|
||||
\draw(\x,0) node{\substring{#2}{\ix}{\ix}};
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% If the string is shorter than expected, extend with #5 to the right.
|
||||
%
|
||||
% #1 The total size
|
||||
% #2 Num chars to extend on the right
|
||||
% #3 The string to print
|
||||
% #4 The value to use when extending to left
|
||||
% #5 The value to use when extending to right
|
||||
\newcommand\DrawDoubleExtendedBitstring[5]{
|
||||
\StrLen{#3}[\numchars]
|
||||
|
||||
\pgfmathsetmacro\leftpadd{int(#1-#2-\numchars)}
|
||||
\ifthenelse{1 > \leftpadd}
|
||||
{}
|
||||
{
|
||||
\foreach \x in {1,...,\leftpadd}
|
||||
\draw(\x,0) node{#4};
|
||||
}
|
||||
|
||||
\pgfmathsetmacro\leftpadd{int(\leftpadd+1)}
|
||||
\pgfmathsetmacro\rightpadd{int(\leftpadd+\numchars)}
|
||||
\foreach \x in {\leftpadd,...,\rightpadd}
|
||||
\pgfmathsetmacro\ix{int(\x-\leftpadd+1)}
|
||||
\draw(\x,0) node{\substring{#3}{\ix}{\ix}};
|
||||
|
||||
|
||||
%\pgfmathsetmacro\rightpadd{int(\rightpadd+1)}
|
||||
\ifthenelse{\rightpadd > #1}
|
||||
{}
|
||||
{
|
||||
\foreach \x in {\rightpadd,...,#1}
|
||||
\draw(\x,0) node{#5};
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Draw a box suitable to show the given number of bits in a
|
||||
% labeled box suitable for showing expanded binary numbers.
|
||||
%
|
||||
% #1 The number of characters to display
|
||||
\newcommand\DrawBitBox[1]{
|
||||
\draw (.5,-.75) -- (#1+.5,-.75); % box bottom
|
||||
\draw (.5,.75) -- (#1+.5,.75); % box top
|
||||
\draw (.5,-.75) -- (.5, 1.5); % left end
|
||||
\draw (#1+.5,-.75) -- (#1+.5, 1.5); % right end
|
||||
\pgfmathsetmacro\result{int(#1-1)} % calc high bit
|
||||
\node at (1,1.2) {\tiny\result}; % high bit label
|
||||
\draw(#1,1.2) node{\tiny0}; % low bit label
|
||||
|
||||
\pgfmathsetmacro\result{#1/2}
|
||||
\node at (\result,-1.2) {\tiny#1}; % size below the box
|
||||
|
||||
\pgfmathsetmacro\result{#1/2}
|
||||
\draw[->] (\result+.6,-1.2) -- (#1+.5,-1.2);
|
||||
\draw[->] (\result-.6,-1.2) -- (.5,-1.2);
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\DrawBitBoxUnsigned[1]{
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawBitBox{\numchars}
|
||||
\DrawBitstring{\numchars}{#1} % show the bits
|
||||
}
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\DrawBitBoxUnsignedPicture[1]{
|
||||
\BeginTikzPicture
|
||||
\DrawBitBoxUnsigned{#1}
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\DrawBitBoxSignedPicture[1]{
|
||||
\BeginTikzPicture
|
||||
\DrawBitBoxUnsigned{#1}
|
||||
% draw a box around the sign bit
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle};
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 The total (extended) size
|
||||
% #2 The value to use for left-side padding
|
||||
% #3 The string to extend
|
||||
\newcommand\DrawBitBoxLeftExtended[3]{
|
||||
\StrLen{#3}[\numchars]
|
||||
\pgfmathsetmacro\fill{int(#1-\numchars)}
|
||||
\begin{scope}[shift={(\fill,3.5)}]
|
||||
\DrawBitBoxUnsigned{#3}
|
||||
|
||||
% XXX IFF not zero-extending then draw a box around the sign bit
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle};
|
||||
\end{scope}
|
||||
|
||||
\DrawBitBox{#1}
|
||||
\DrawDoubleExtendedBitstring{#1}{0}{#3}{#2}{x}
|
||||
|
||||
% XXX IFF not zero-extending then draw a box around the sign bit
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (\fill+1.35, -.6) -- (\fill+1.35, .6) -- (\fill+.65, .6) -- (\fill+.65, -.6) -- cycle};
|
||||
% draw a box around the extended sign bits
|
||||
\draw (.65, -.6) -- (.65, .6) -- (\fill+.35, .6) -- (\fill+.35, -.6) -- cycle;
|
||||
|
||||
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\DrawBitBoxSignExtendedPicture[2]{
|
||||
\BeginTikzPicture
|
||||
\DrawBitBoxLeftExtended{#1}{\substring{#2}{1}{1}}{#2}
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\DrawBitBoxZeroExtendedPicture[2]{
|
||||
\BeginTikzPicture
|
||||
\DrawBitBoxLeftExtended{#1}{0}{#2}
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 Total bit length
|
||||
% #2 The string to print
|
||||
% #3 Right-side padding length
|
||||
\newcommand\DrawBitBoxSignLeftZeroRightExtendedPicture[3]{
|
||||
\BeginTikzPicture
|
||||
|
||||
\StrLen{#2}[\numchars]
|
||||
\pgfmathsetmacro\fill{int(#1-\numchars-#3)}
|
||||
\begin{scope}[shift={(\fill,3.5)}]
|
||||
\DrawBitBoxUnsigned{#2}
|
||||
% draw a box around the sign bit
|
||||
%\draw (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle;
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle};
|
||||
\end{scope}
|
||||
|
||||
\DrawBitBox{#1}
|
||||
\DrawDoubleExtendedBitstring{#1}{#3}{#2}{\substring{#2}{1}{1}}{0}
|
||||
|
||||
% Box the sign bit
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (\fill+1.35, -.6) -- (\fill+1.35, .6) -- (\fill+.65, .6) -- (\fill+.65, -.6) -- cycle};
|
||||
|
||||
\ifthenelse{\fill > 0}
|
||||
{
|
||||
% Box the left-extended sign bits
|
||||
\draw (.65, -.6) -- (.65, .6) -- (\fill+.35, .6) -- (\fill+.35, -.6) -- cycle;
|
||||
% \fill[blue!40!white] (.65, -.6) rectangle (\fill-.25, 1.2);
|
||||
}
|
||||
{}
|
||||
\ifthenelse{#3 > 0}
|
||||
{
|
||||
% Box the right-extended sign bits
|
||||
\pgfmathsetmacro\posn{int(\numchars+\fill)}
|
||||
\draw (\posn+.65, -.6) -- (\posn+.65, .6) -- (\posn+#3+.35, .6) -- (\posn+#3+.35, -.6) -- cycle;
|
||||
}
|
||||
{}
|
||||
|
||||
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Print the characters within a string evenly spaced at integral node positions
|
||||
%
|
||||
% #1 The number of characters in the string
|
||||
% #2 The string of characters to plot
|
||||
\newcommand\DrawInsnBitstring[3]{
|
||||
\pgfmathsetmacro\num{int(#1-1)}
|
||||
\foreach \x in {1,2,...,#1}
|
||||
\draw(\x,0) node{\substring{#2}{\x}{\x}};
|
||||
|
||||
\draw(#1+1,0) node[right]{#3};
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Draw a bit-separator line with labels at the given bit-offset (from the right)
|
||||
%
|
||||
% #1 Total box width
|
||||
% #2 The position that the sepatator will be drawn to the left.
|
||||
\newcommand\DrawInsnBoxSep[2]{
|
||||
\draw (#1-#2-.5,-.75) -- (#1-#2-.5, 1.5);
|
||||
\node at (#1-#2,1.2) {\tiny#2};
|
||||
\pgfmathsetmacro\result{int(#2+1)}
|
||||
\node at (#1-#2-1,1.2) {\tiny\result};
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 total characters/width
|
||||
% #2 MSB position
|
||||
% #3 LSB position
|
||||
% #4 the segment label
|
||||
\newcommand\DrawInsnBoxSeg[4]{
|
||||
\pgfmathsetmacro\leftpos{int(#1-#2)}
|
||||
\pgfmathsetmacro\rightpos{int(#1-#3)}
|
||||
|
||||
\draw (\leftpos-.5,-.75) -- (\rightpos+.5,-.75); % box bottom
|
||||
\draw (\leftpos-.5,1.75) -- (\rightpos+.5,1.75); % box top
|
||||
\draw (\leftpos-.5,-.75) -- (\leftpos-.5, 2.5); % left end
|
||||
\draw (\rightpos+.5,-.75) -- (\rightpos+.5, 2.5); % right end
|
||||
\node at (\leftpos,2.2) {\tiny#2};
|
||||
\draw(\rightpos,2.2) node{\tiny#3};
|
||||
|
||||
\pgfmathsetmacro\posn{#1-#2+(#2-#3)/2}
|
||||
\pgfmathsetmacro\range{int(#2-#3+1)}
|
||||
\node at (\posn,-1.4) {\small\range}; % the field width
|
||||
\node at (\posn,1.2) {\small#4}; % the field label
|
||||
|
||||
% % arrows showing the span of the bits... meh
|
||||
% \draw[->] (\posn+.5,-1.4) -- (\rightpos+.2,-1.4);
|
||||
% \draw[->] (\posn-.5,-1.4) -- (\leftpos-.2,-1.4);
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand\InsnStatement[1]{
|
||||
% \textbf{\large #1}\\
|
||||
% \textbf{#1}\\
|
||||
{\large #1}\\
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeBTikz[1]{
|
||||
\BeginTikzPicture
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawInsnBitstring{\numchars}{#1}{\hyperref[insnformat:btype]{B-type}}
|
||||
\DrawInsnBoxSeg{\numchars}{31}{25}{imm[12\textbar10:5]}
|
||||
\DrawInsnBoxSeg{\numchars}{24}{20}{rs2}
|
||||
\DrawInsnBoxSeg{\numchars}{19}{15}{rs1}
|
||||
\DrawInsnBoxSeg{\numchars}{14}{12}{funct3}
|
||||
\DrawInsnBoxSeg{\numchars}{11}{7}{imm[4:1\textbar11]}
|
||||
\DrawInsnBoxSeg{\numchars}{6}{0}{opcode}
|
||||
|
||||
% add some hint bits in for imm fields
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle}; % sign bit
|
||||
\draw (32-7-.5, -.75) -- (32-7-.5, .1); % imm[11]
|
||||
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
\newcommand\DrawInsnTypeBPicture[2]{
|
||||
\InsnStatement{#1}\\
|
||||
\DrawInsnTypeBTikz{#2}
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeUTikz[1]{
|
||||
\BeginTikzPicture
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawInsnBitstring{\numchars}{#1}{\hyperref[insnformat:utype]{U-type}}
|
||||
\DrawInsnBoxSeg{\numchars}{31}{12}{imm[31:12]}
|
||||
\DrawInsnBoxSeg{\numchars}{11}{7}{rd}
|
||||
\DrawInsnBoxSeg{\numchars}{6}{0}{opcode}
|
||||
|
||||
% add some hint bits in for imm fields
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle}; % sign bit
|
||||
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
\newcommand\DrawInsnTypeUPicture[2]{
|
||||
\InsnStatement{#1}\\
|
||||
\DrawInsnTypeUTikz{#2}
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeJTikz[1]{
|
||||
\BeginTikzPicture
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawInsnBitstring{\numchars}{#1}{\hyperref[insnformat:jtype]{J-type}}
|
||||
\DrawInsnBoxSeg{\numchars}{31}{12}{imm[20\textbar10:1\textbar11\textbar19:12]}
|
||||
\DrawInsnBoxSeg{\numchars}{11}{7}{rd}
|
||||
\DrawInsnBoxSeg{\numchars}{6}{0}{opcode}
|
||||
|
||||
% add some hint bits in for imm fields
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle}; % sign bit
|
||||
\draw (32-19-.5, -.75) -- (32-19.5, .1); % imm[19:12]
|
||||
\draw (32-20-.5, -.75) -- (32-20.5, .1); % imm[11]
|
||||
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
\newcommand\DrawInsnTypeJPicture[2]{
|
||||
\InsnStatement{#1}\\
|
||||
\DrawInsnTypeJTikz{#2}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeI[1]{
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawInsnBitstring{\numchars}{#1}{\hyperref[insnformat:itype]{I-type}}
|
||||
\DrawInsnBoxSeg{\numchars}{31}{20}{imm[11:0]}
|
||||
\DrawInsnBoxSeg{\numchars}{19}{15}{rs1}
|
||||
\DrawInsnBoxSeg{\numchars}{14}{12}{funct3}
|
||||
\DrawInsnBoxSeg{\numchars}{11}{7}{rd}
|
||||
\DrawInsnBoxSeg{\numchars}{6}{0}{opcode}
|
||||
|
||||
% add some hint bits in for imm fields
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle}; % sign bit
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeITikz[1]{
|
||||
\BeginTikzPicture
|
||||
\DrawInsnTypeI{#1}
|
||||
\EndTikzPicture
|
||||
}
|
||||
\newcommand\DrawInsnTypeIPicture[2]{
|
||||
\InsnStatement{#1}\\
|
||||
\DrawInsnTypeITikz{#2}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeSTikz[1]{
|
||||
\BeginTikzPicture
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawInsnBitstring{\numchars}{#1}{\hyperref[insnformat:stype]{S-type}}
|
||||
\DrawInsnBoxSeg{\numchars}{31}{25}{imm[11:5]}
|
||||
\DrawInsnBoxSeg{\numchars}{24}{20}{rs2}
|
||||
\DrawInsnBoxSeg{\numchars}{19}{15}{rs1}
|
||||
\DrawInsnBoxSeg{\numchars}{14}{12}{funct3}
|
||||
\DrawInsnBoxSeg{\numchars}{11}{7}{imm[4:0]}
|
||||
\DrawInsnBoxSeg{\numchars}{6}{0}{opcode}
|
||||
|
||||
% add some hint bits in for imm fields
|
||||
\draw {[rounded corners=\SignBoxCornerRadius] (1.35, -.6) -- (1.35, .6) -- (.65, .6) -- (.65, -.6) -- cycle}; % sign bit
|
||||
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
\newcommand\DrawInsnTypeSPicture[2]{
|
||||
\InsnStatement{#1}\\
|
||||
\DrawInsnTypeSTikz{#2}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeRShiftTikz[1]{
|
||||
\BeginTikzPicture
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawInsnBitstring{\numchars}{#1}{\hyperref[insnformat:rtype]{R-type}}
|
||||
\DrawInsnBoxSeg{\numchars}{31}{25}{funct7}
|
||||
\DrawInsnBoxSeg{\numchars}{24}{20}{shamt}
|
||||
\DrawInsnBoxSeg{\numchars}{19}{15}{rs1}
|
||||
\DrawInsnBoxSeg{\numchars}{14}{12}{funct3}
|
||||
\DrawInsnBoxSeg{\numchars}{11}{7}{rd}
|
||||
\DrawInsnBoxSeg{\numchars}{6}{0}{opcode}
|
||||
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
\newcommand\DrawInsnTypeRShiftPicture[2]{
|
||||
\InsnStatement{#1}\\
|
||||
\DrawInsnTypeRShiftTikz{#2}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% #1 the binary encoding
|
||||
\newcommand\DrawInsnTypeRTikz[1]{
|
||||
\BeginTikzPicture
|
||||
\StrLen{#1}[\numchars]
|
||||
\DrawInsnBitstring{\numchars}{#1}{\hyperref[insnformat:rtype]{R-type}}
|
||||
\DrawInsnBoxSeg{\numchars}{31}{25}{funct7}
|
||||
\DrawInsnBoxSeg{\numchars}{24}{20}{rs2}
|
||||
\DrawInsnBoxSeg{\numchars}{19}{15}{rs1}
|
||||
\DrawInsnBoxSeg{\numchars}{14}{12}{funct3}
|
||||
\DrawInsnBoxSeg{\numchars}{11}{7}{rd}
|
||||
\DrawInsnBoxSeg{\numchars}{6}{0}{opcode}
|
||||
|
||||
\EndTikzPicture
|
||||
}
|
||||
|
||||
\newcommand\DrawInsnTypeRPicture[2]{
|
||||
\InsnStatement{#1}\\
|
||||
\DrawInsnTypeRTikz{#2}
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
|
||||
% print a register name in typewriter font
|
||||
\newcommand\reg[1]{{\tt #1}}
|
||||
|
||||
|
||||
10
book/intro/chapter.tex
Normal file
10
book/intro/chapter.tex
Normal file
@ -0,0 +1,10 @@
|
||||
\chapter{Introduction}
|
||||
\label{chapter:Introduction}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Instruction Set Architecture}
|
||||
|
||||
Discuss the IMAFD, G and other ISA extensions mean.
|
||||
|
||||
|
||||
427
book/license/chapter.tex
Normal file
427
book/license/chapter.tex
Normal file
@ -0,0 +1,427 @@
|
||||
\chapter{Attribution 4.0 International}
|
||||
\label{license}
|
||||
|
||||
\begin{scriptsize}
|
||||
|
||||
Creative Commons Corporation ("Creative Commons") is not a law firm and
|
||||
does not provide legal services or legal advice. Distribution of
|
||||
Creative Commons public licenses does not create a lawyer-client or
|
||||
other relationship. Creative Commons makes its licenses and related
|
||||
information available on an "as-is" basis. Creative Commons gives no
|
||||
warranties regarding its licenses, any material licensed under their
|
||||
terms and conditions, or any related information. Creative Commons
|
||||
disclaims all liability for damages resulting from their use to the
|
||||
fullest extent possible.
|
||||
|
||||
\subsection*{Using Creative Commons Public Licenses}
|
||||
|
||||
Creative Commons public licenses provide a standard set of terms and
|
||||
conditions that creators and other rights holders may use to share
|
||||
original works of authorship and other material subject to copyright
|
||||
and certain other rights specified in the public license below. The
|
||||
following considerations are for informational purposes only, are not
|
||||
exhaustive, and do not form part of our licenses.
|
||||
|
||||
Considerations for licensors: Our public licenses are
|
||||
intended for use by those authorized to give the public
|
||||
permission to use material in ways otherwise restricted by
|
||||
copyright and certain other rights. Our licenses are
|
||||
irrevocable. Licensors should read and understand the terms
|
||||
and conditions of the license they choose before applying it.
|
||||
Licensors should also secure all rights necessary before
|
||||
applying our licenses so that the public can reuse the
|
||||
material as expected. Licensors should clearly mark any
|
||||
material not subject to the license. This includes other
|
||||
CC--licensed material, or material used under an exception or
|
||||
limitation to copyright. More considerations for licensors:
|
||||
\url{http://wiki.creativecommons.org/Considerations_for_licensors}
|
||||
|
||||
Considerations for the public: By using one of our public
|
||||
licenses, a licensor grants the public permission to use the
|
||||
licensed material under specified terms and conditions. If
|
||||
the licensor's permission is not necessary for any reason--for
|
||||
example, because of any applicable exception or limitation to
|
||||
copyright--then that use is not regulated by the license. Our
|
||||
licenses grant only permissions under copyright and certain
|
||||
other rights that a licensor has authority to grant. Use of
|
||||
the licensed material may still be restricted for other
|
||||
reasons, including because others have copyright or other
|
||||
rights in the material. A licensor may make special requests,
|
||||
such as asking that all changes be marked or described.
|
||||
Although not required by our licenses, you are encouraged to
|
||||
respect those requests where reasonable. More considerations
|
||||
for the public:
|
||||
\url{http://wiki.creativecommons.org/Considerations_for_licensees}\\
|
||||
|
||||
\hrule
|
||||
|
||||
\subsection*{Creative Commons Attribution 4.0 International Public License}
|
||||
|
||||
By exercising the Licensed Rights (defined below), You accept and agree
|
||||
to be bound by the terms and conditions of this Creative Commons
|
||||
Attribution 4.0 International Public License ("Public License"). To the
|
||||
extent this Public License may be interpreted as a contract, You are
|
||||
granted the Licensed Rights in consideration of Your acceptance of
|
||||
these terms and conditions, and the Licensor grants You such rights in
|
||||
consideration of benefits the Licensor receives from making the
|
||||
Licensed Material available under these terms and conditions.
|
||||
|
||||
|
||||
\subsection*{Section 1. Definitions}
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] Adapted Material means material subject to Copyright and Similar
|
||||
Rights that is derived from or based upon the Licensed Material
|
||||
and in which the Licensed Material is translated, altered,
|
||||
arranged, transformed, or otherwise modified in a manner requiring
|
||||
permission under the Copyright and Similar Rights held by the
|
||||
Licensor. For purposes of this Public License, where the Licensed
|
||||
Material is a musical work, performance, or sound recording,
|
||||
Adapted Material is always produced where the Licensed Material is
|
||||
synched in timed relation with a moving image.
|
||||
|
||||
\item[b.] Adapter's License means the license You apply to Your Copyright
|
||||
and Similar Rights in Your contributions to Adapted Material in
|
||||
accordance with the terms and conditions of this Public License.
|
||||
|
||||
\item[c.] Copyright and Similar Rights means copyright and/or similar rights
|
||||
closely related to copyright including, without limitation,
|
||||
performance, broadcast, sound recording, and Sui Generis Database
|
||||
Rights, without regard to how the rights are labeled or
|
||||
categorized. For purposes of this Public License, the rights
|
||||
specified in Section 2(b)(1)-(2) are not Copyright and Similar
|
||||
Rights.
|
||||
|
||||
\item[d.] Effective Technological Measures means those measures that, in the
|
||||
absence of proper authority, may not be circumvented under laws
|
||||
fulfilling obligations under Article 11 of the WIPO Copyright
|
||||
Treaty adopted on December 20, 1996, and/or similar international
|
||||
agreements.
|
||||
|
||||
\item[e.] Exceptions and Limitations means fair use, fair dealing, and/or
|
||||
any other exception or limitation to Copyright and Similar Rights
|
||||
that applies to Your use of the Licensed Material.
|
||||
|
||||
\item[f.] Licensed Material means the artistic or literary work, database,
|
||||
or other material to which the Licensor applied this Public
|
||||
License.
|
||||
|
||||
\item[g.] Licensed Rights means the rights granted to You subject to the
|
||||
terms and conditions of this Public License, which are limited to
|
||||
all Copyright and Similar Rights that apply to Your use of the
|
||||
Licensed Material and that the Licensor has authority to license.
|
||||
|
||||
\item[h.] Licensor means the individual(s) or entity(ies) granting rights
|
||||
under this Public License.
|
||||
|
||||
\item[i.] Share means to provide material to the public by any means or
|
||||
process that requires permission under the Licensed Rights, such
|
||||
as reproduction, public display, public performance, distribution,
|
||||
dissemination, communication, or importation, and to make material
|
||||
available to the public including in ways that members of the
|
||||
public may access the material from a place and at a time
|
||||
individually chosen by them.
|
||||
|
||||
\item[j.] Sui Generis Database Rights means rights other than copyright
|
||||
resulting from Directive 96/9/EC of the European Parliament and of
|
||||
the Council of 11 March 1996 on the legal protection of databases,
|
||||
as amended and/or succeeded, as well as other essentially
|
||||
equivalent rights anywhere in the world.
|
||||
|
||||
\item[k.] You means the individual or entity exercising the Licensed Rights
|
||||
under this Public License. Your has a corresponding meaning.
|
||||
\end{itemize}
|
||||
|
||||
\subsection*{Section 2. Scope}
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] License grant.
|
||||
|
||||
\begin{itemize}
|
||||
\item[1.] Subject to the terms and conditions of this Public License,
|
||||
the Licensor hereby grants You a worldwide, royalty-free,
|
||||
non-sublicensable, non-exclusive, irrevocable license to
|
||||
exercise the Licensed Rights in the Licensed Material to:
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] reproduce and Share the Licensed Material, in whole or
|
||||
in part; and
|
||||
|
||||
\item[b.] produce, reproduce, and Share Adapted Material.
|
||||
\end{itemize}
|
||||
|
||||
\item[2.] Exceptions and Limitations. For the avoidance of doubt, where
|
||||
Exceptions and Limitations apply to Your use, this Public
|
||||
License does not apply, and You do not need to comply with
|
||||
its terms and conditions.
|
||||
|
||||
\item[3.] Term. The term of this Public License is specified in Section
|
||||
6(a).
|
||||
|
||||
\item[4.] Media and formats; technical modifications allowed. The
|
||||
Licensor authorizes You to exercise the Licensed Rights in
|
||||
all media and formats whether now known or hereafter created,
|
||||
and to make technical modifications necessary to do so. The
|
||||
Licensor waives and/or agrees not to assert any right or
|
||||
authority to forbid You from making technical modifications
|
||||
necessary to exercise the Licensed Rights, including
|
||||
technical modifications necessary to circumvent Effective
|
||||
Technological Measures. For purposes of this Public License,
|
||||
simply making modifications authorized by this Section 2(a)
|
||||
(4) never produces Adapted Material.
|
||||
|
||||
\item[5.] Downstream recipients.
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] Offer from the Licensor -- Licensed Material. Every
|
||||
recipient of the Licensed Material automatically
|
||||
receives an offer from the Licensor to exercise the
|
||||
Licensed Rights under the terms and conditions of this
|
||||
Public License.
|
||||
|
||||
\item[b.] No downstream restrictions. You may not offer or impose
|
||||
any additional or different terms or conditions on, or
|
||||
apply any Effective Technological Measures to, the
|
||||
Licensed Material if doing so restricts exercise of the
|
||||
Licensed Rights by any recipient of the Licensed
|
||||
Material.
|
||||
\end{itemize}
|
||||
|
||||
\item[6.] No endorsement. Nothing in this Public License constitutes or
|
||||
may be construed as permission to assert or imply that You
|
||||
are, or that Your use of the Licensed Material is, connected
|
||||
with, or sponsored, endorsed, or granted official status by,
|
||||
the Licensor or others designated to receive attribution as
|
||||
provided in Section 3(a)(1)(A)(i).
|
||||
\end{itemize}
|
||||
|
||||
\item[b.] Other rights.
|
||||
|
||||
\begin{itemize}
|
||||
\item[1.] Moral rights, such as the right of integrity, are not
|
||||
licensed under this Public License, nor are publicity,
|
||||
privacy, and/or other similar personality rights; however, to
|
||||
the extent possible, the Licensor waives and/or agrees not to
|
||||
assert any such rights held by the Licensor to the limited
|
||||
extent necessary to allow You to exercise the Licensed
|
||||
Rights, but not otherwise.
|
||||
|
||||
\item[2.] Patent and trademark rights are not licensed under this
|
||||
Public License.
|
||||
|
||||
\item[3.] To the extent possible, the Licensor waives any right to
|
||||
collect royalties from You for the exercise of the Licensed
|
||||
Rights, whether directly or through a collecting society
|
||||
under any voluntary or waivable statutory or compulsory
|
||||
licensing scheme. In all other cases the Licensor expressly
|
||||
reserves any right to collect such royalties.
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\subsection*{Section 3. License Conditions}
|
||||
|
||||
Your exercise of the Licensed Rights is expressly made subject to the
|
||||
following conditions.
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] Attribution.
|
||||
|
||||
\begin{itemize}
|
||||
\item[1.] If You Share the Licensed Material (including in modified
|
||||
form), You must:
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] retain the following if it is supplied by the Licensor
|
||||
with the Licensed Material:
|
||||
|
||||
\begin{itemize}
|
||||
\item[i.] identification of the creator(s) of the Licensed
|
||||
Material and any others designated to receive
|
||||
attribution, in any reasonable manner requested by
|
||||
the Licensor (including by pseudonym if
|
||||
designated);
|
||||
|
||||
\item[ii.] a copyright notice;
|
||||
|
||||
\item[iii.] a notice that refers to this Public License;
|
||||
|
||||
\item[iv.] a notice that refers to the disclaimer of
|
||||
warranties;
|
||||
|
||||
\item[v.] a URI or hyperlink to the Licensed Material to the
|
||||
extent reasonably practicable;
|
||||
\end{itemize}
|
||||
|
||||
\item[b.] indicate if You modified the Licensed Material and
|
||||
retain an indication of any previous modifications; and
|
||||
|
||||
\item[c.] indicate the Licensed Material is licensed under this
|
||||
Public License, and include the text of, or the URI or
|
||||
hyperlink to, this Public License.
|
||||
\end{itemize}
|
||||
|
||||
\item[2.] You may satisfy the conditions in Section 3(a)(1) in any
|
||||
reasonable manner based on the medium, means, and context in
|
||||
which You Share the Licensed Material. For example, it may be
|
||||
reasonable to satisfy the conditions by providing a URI or
|
||||
hyperlink to a resource that includes the required
|
||||
information.
|
||||
|
||||
\item[3.] If requested by the Licensor, You must remove any of the
|
||||
information required by Section 3(a)(1)(A) to the extent
|
||||
reasonably practicable.
|
||||
|
||||
\item[4.] If You Share Adapted Material You produce, the Adapter's
|
||||
License You apply must not prevent recipients of the Adapted
|
||||
Material from complying with this Public License.
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\subsection*{Section 4. Sui Generis Database Rights}
|
||||
|
||||
Where the Licensed Rights include Sui Generis Database Rights that
|
||||
apply to Your use of the Licensed Material:
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] for the avoidance of doubt, Section 2(a)(1) grants You the right
|
||||
to extract, reuse, reproduce, and Share all or a substantial
|
||||
portion of the contents of the database;
|
||||
|
||||
\item[b.] if You include all or a substantial portion of the database
|
||||
contents in a database in which You have Sui Generis Database
|
||||
Rights, then the database in which You have Sui Generis Database
|
||||
Rights (but not its individual contents) is Adapted Material; and
|
||||
|
||||
\item[c.] You must comply with the conditions in Section 3(a) if You Share
|
||||
all or a substantial portion of the contents of the database.
|
||||
\end{itemize}
|
||||
|
||||
For the avoidance of doubt, this Section 4 supplements and does not
|
||||
replace Your obligations under this Public License where the Licensed
|
||||
Rights include other Copyright and Similar Rights.
|
||||
|
||||
|
||||
\subsection*{Section 5. Disclaimer of Warranties and Limitation of Liability}
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] UNLESS OTHERWISE SEPARATELY UNDERTAKEN BY THE LICENSOR, TO THE
|
||||
EXTENT POSSIBLE, THE LICENSOR OFFERS THE LICENSED MATERIAL AS-IS
|
||||
AND AS-AVAILABLE, AND MAKES NO REPRESENTATIONS OR WARRANTIES OF
|
||||
ANY KIND CONCERNING THE LICENSED MATERIAL, WHETHER EXPRESS,
|
||||
IMPLIED, STATUTORY, OR OTHER. THIS INCLUDES, WITHOUT LIMITATION,
|
||||
WARRANTIES OF TITLE, MERCHANTABILITY, FITNESS FOR A PARTICULAR
|
||||
PURPOSE, NON-INFRINGEMENT, ABSENCE OF LATENT OR OTHER DEFECTS,
|
||||
ACCURACY, OR THE PRESENCE OR ABSENCE OF ERRORS, WHETHER OR NOT
|
||||
KNOWN OR DISCOVERABLE. WHERE DISCLAIMERS OF WARRANTIES ARE NOT
|
||||
ALLOWED IN FULL OR IN PART, THIS DISCLAIMER MAY NOT APPLY TO YOU.
|
||||
|
||||
\item[b.] TO THE EXTENT POSSIBLE, IN NO EVENT WILL THE LICENSOR BE LIABLE
|
||||
TO YOU ON ANY LEGAL THEORY (INCLUDING, WITHOUT LIMITATION,
|
||||
NEGLIGENCE) OR OTHERWISE FOR ANY DIRECT, SPECIAL, INDIRECT,
|
||||
INCIDENTAL, CONSEQUENTIAL, PUNITIVE, EXEMPLARY, OR OTHER LOSSES,
|
||||
COSTS, EXPENSES, OR DAMAGES ARISING OUT OF THIS PUBLIC LICENSE OR
|
||||
USE OF THE LICENSED MATERIAL, EVEN IF THE LICENSOR HAS BEEN
|
||||
ADVISED OF THE POSSIBILITY OF SUCH LOSSES, COSTS, EXPENSES, OR
|
||||
DAMAGES. WHERE A LIMITATION OF LIABILITY IS NOT ALLOWED IN FULL OR
|
||||
IN PART, THIS LIMITATION MAY NOT APPLY TO YOU.
|
||||
|
||||
\item[c.] The disclaimer of warranties and limitation of liability provided
|
||||
above shall be interpreted in a manner that, to the extent
|
||||
possible, most closely approximates an absolute disclaimer and
|
||||
waiver of all liability.
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\subsection*{Section 6. Term and Termination}
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] This Public License applies for the term of the Copyright and
|
||||
Similar Rights licensed here. However, if You fail to comply with
|
||||
this Public License, then Your rights under this Public License
|
||||
terminate automatically.
|
||||
|
||||
\item[b.] Where Your right to use the Licensed Material has terminated under
|
||||
Section 6(a), it reinstates:
|
||||
|
||||
\begin{itemize}
|
||||
\item[1.] automatically as of the date the violation is cured, provided
|
||||
it is cured within 30 days of Your discovery of the
|
||||
violation; or
|
||||
|
||||
\item[2.] upon express reinstatement by the Licensor.
|
||||
\end{itemize}
|
||||
|
||||
For the avoidance of doubt, this Section 6(b) does not affect any
|
||||
right the Licensor may have to seek remedies for Your violations
|
||||
of this Public License.
|
||||
|
||||
\item[c.] For the avoidance of doubt, the Licensor may also offer the
|
||||
Licensed Material under separate terms or conditions or stop
|
||||
distributing the Licensed Material at any time; however, doing so
|
||||
will not terminate this Public License.
|
||||
|
||||
\item[d.] Sections 1, 5, 6, 7, and 8 survive termination of this Public
|
||||
License.
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\subsection*{Section 7. Other Terms and Conditions}
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] The Licensor shall not be bound by any additional or different
|
||||
terms or conditions communicated by You unless expressly agreed.
|
||||
|
||||
\item[b.] Any arrangements, understandings, or agreements regarding the
|
||||
Licensed Material not stated herein are separate from and
|
||||
independent of the terms and conditions of this Public License.
|
||||
\end{itemize}
|
||||
|
||||
\subsection*{Section 8. Interpretation}
|
||||
|
||||
\begin{itemize}
|
||||
\item[a.] For the avoidance of doubt, this Public License does not, and
|
||||
shall not be interpreted to, reduce, limit, restrict, or impose
|
||||
conditions on any use of the Licensed Material that could lawfully
|
||||
be made without permission under this Public License.
|
||||
|
||||
\item[b.] To the extent possible, if any provision of this Public License is
|
||||
deemed unenforceable, it shall be automatically reformed to the
|
||||
minimum extent necessary to make it enforceable. If the provision
|
||||
cannot be reformed, it shall be severed from this Public License
|
||||
without affecting the enforceability of the remaining terms and
|
||||
conditions.
|
||||
|
||||
\item[c.] No term or condition of this Public License will be waived and no
|
||||
failure to comply consented to unless expressly agreed to by the
|
||||
Licensor.
|
||||
|
||||
\item[d.] Nothing in this Public License constitutes or may be interpreted
|
||||
as a limitation upon, or waiver of, any privileges and immunities
|
||||
that apply to the Licensor or You, including from the legal
|
||||
processes of any jurisdiction or authority.\\
|
||||
\end{itemize}
|
||||
|
||||
\hrule
|
||||
|
||||
Creative Commons is not a party to its public
|
||||
licenses. Notwithstanding, Creative Commons may elect to apply one of
|
||||
its public licenses to material it publishes and in those instances
|
||||
will be considered the Licensor. The text of the Creative Commons
|
||||
public licenses is dedicated to the public domain under the CC0 Public
|
||||
Domain Dedication. Except for the limited purpose of indicating that
|
||||
material is shared under a Creative Commons public license or as
|
||||
otherwise permitted by the Creative Commons policies published at
|
||||
\url{http://creativecommons.org/policies}, Creative Commons does not authorize the
|
||||
use of the trademark ``Creative Commons'' or any other trademark or logo
|
||||
of Creative Commons without its prior written consent including,
|
||||
without limitation, in connection with any unauthorized modifications
|
||||
to any of its public licenses or any other arrangements,
|
||||
understandings, or agreements concerning use of licensed material. For
|
||||
the avoidance of doubt, this paragraph does not form part of the
|
||||
public licenses.
|
||||
|
||||
Creative Commons may be contacted at \url{http://creativecommons.org}.
|
||||
|
||||
\end{scriptsize}
|
||||
750
book/numbers/chapter.tex
Normal file
750
book/numbers/chapter.tex
Normal file
@ -0,0 +1,750 @@
|
||||
\chapter{Number Systems}
|
||||
\label{chapter:NumberSystems}
|
||||
|
||||
RISC-V systems represent information using binary values stored in
|
||||
little-endian order.\footnote{See\cite{IEN137} for some history of
|
||||
the big/little-endian ``controversy.''}
|
||||
|
||||
\section{Integers}
|
||||
|
||||
A binary integer is constructed with only 1s and 0s in the same
|
||||
manner as decimal numbers are constructed with values from 0 to 9.
|
||||
|
||||
Counting in binary is the same as in decimal. For example, when
|
||||
adding 1 to 9, the carry is added to the next place value. When
|
||||
subtracting 1 from 0, a borrow is required and so on.
|
||||
|
||||
Figure~\autoref{Figure:integers} shows an abridged table of the
|
||||
decimal, binary and hexadecimal values from 0 to 129.
|
||||
|
||||
\begin{figure}[ht]
|
||||
\begin{center}
|
||||
\begin{tabular}{|c|c|c||c|c|c|c|c|c|c|c||c|c|}
|
||||
\hline
|
||||
\multicolumn{3}{|c||}{Decimal} & \multicolumn{8}{|c||}{Binary} & \multicolumn{2}{|c|}{Hex}\\
|
||||
\hline
|
||||
$10^2$ & $10^1$ & $10^0$ & $2^7$ & $2^6$ & $2^5$ & $2^4$ & $2^3$ & $2^2$ & $2^1$ & $2^0$ & $16^1$ & $16^0$ \\
|
||||
\hline
|
||||
100 & 10 & 1 & 128 & 64 & 32 & 16 & 8 & 4 & 2 & 1 & 16 & 1 \\
|
||||
\hline \hline
|
||||
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
|
||||
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\
|
||||
0 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\
|
||||
0 & 0 & 3 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 3 \\
|
||||
0 & 0 & 4 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 4 \\
|
||||
0 & 0 & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 5 \\
|
||||
0 & 0 & 6 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 6 \\
|
||||
0 & 0 & 7 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 7 \\
|
||||
0 & 0 & 8 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 8 \\
|
||||
0 & 0 & 9 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 9 \\
|
||||
0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & a \\
|
||||
0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & b \\
|
||||
0 & 1 & 2 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & c \\
|
||||
0 & 1 & 3 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & d \\
|
||||
0 & 1 & 4 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & e \\
|
||||
0 & 1 & 5 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & f \\
|
||||
0 & 1 & 6 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\
|
||||
0 & 1 & 7 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 \\
|
||||
\hline
|
||||
\multicolumn{3}{|c||}{\ldots} & \multicolumn{8}{|c||}{\ldots} & \multicolumn{2}{|c|}{\ldots}\\
|
||||
\hline
|
||||
1 & 2 & 5 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 7 & d \\
|
||||
1 & 2 & 6 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 7 & e \\
|
||||
1 & 2 & 7 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 7 & f \\
|
||||
1 & 2 & 8 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 8 & 0 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
\captionof{figure}{Counting in decimal, binary and hexadecimal.}
|
||||
\label{Figure:integers}
|
||||
\end{figure}
|
||||
|
||||
|
||||
One way to look at this table is on a per--row basis where each place
|
||||
value is represented by the base raised to the power of the place value
|
||||
position (shown in the column headings.) This is useful when
|
||||
converting arbitrary values between bases. For example to interpret
|
||||
the decimal value on the fourth row:
|
||||
\[ 0 \times 10^2 + 0 \times 10^1 + 3 \times 10^0 = 3_{10} \]
|
||||
And to interpret binary value on the same row by converting it to decimal:
|
||||
\[ 0 \times 2^7 + 0 \times 2^6 +0 \times 2^5 +0 \times 2^4 +0 \times 2^3 +0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 3_{10} \]
|
||||
And the same for the hexadecimal value:
|
||||
\[ 0 \times 16^1 + 3 \times 16^0 = 3_{10} \]
|
||||
|
||||
|
||||
Another way to look at this table is on a per--column basis. When
|
||||
tasked with drawing such a table by hand, it might be useful
|
||||
to observe that, just as in decimal, the right--most column will
|
||||
cycle through all of the values represented in the chosen base
|
||||
then cycle back to zero and repeat. (For example, in binary this
|
||||
pattern is 0-1-0-1-0-1-0-\ldots) The next column in each base
|
||||
will cycle in the same manner except each of the values is repeated
|
||||
as many times as is represented by the place value (in the case of
|
||||
decimal, $10^1$ times, binary $2^1$ times, hex $16^1$ times. Again,
|
||||
the for binary numbers this pattern is 0-0-1-1-0-0-1-1-\ldots)
|
||||
This continues for as many columns as are needed to represent the
|
||||
magnitude of the desired number.
|
||||
|
||||
Another item worth noting is that any even binary number will always
|
||||
have a 0 LSB and odd numbers will always have a 1 LSB.
|
||||
|
||||
As is customary in decimal, leading zeroes are sometimes not shown
|
||||
for readability.
|
||||
|
||||
The relationship between binary and hex values is also worth taking
|
||||
note. Because $2^4 = 16$, there is a clean and simple grouping
|
||||
of 4 \gls{bit}s to 1 \gls{hit}. There is no such relationship
|
||||
between binary and decimal.
|
||||
|
||||
Writing and reading numbers in binary that are longer than 8 bits
|
||||
is cumbersome and prone to error. The simple conversion between
|
||||
binary and hex makes hex a convenient shorthand for expressing
|
||||
binary values in many situations.
|
||||
|
||||
For example, consider the following value expressed in binary,
|
||||
hexadecimal and decimal (spaced to show the relationship
|
||||
between binary and hex):
|
||||
|
||||
\begin{verbatim}
|
||||
Binary value: 0010 0111 1011 1010 1100 1100 1111 0101
|
||||
Hex Value: 2 7 B A C C F 5
|
||||
Decimal Value: 666553589
|
||||
\end{verbatim}
|
||||
|
||||
Empirically we can see that grouping the bits into sets of four
|
||||
allows an easy conversion to hex and expressing it as such is
|
||||
$\frac{1}{4}$ as long as in binary while at the same time
|
||||
allowing for easy conversion back to binary.
|
||||
|
||||
The decimal value in this example does not easily convey a sense
|
||||
of the binary value.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Converting Between Bases}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{From Binary to Decimal}
|
||||
\label{section:bindec}
|
||||
|
||||
Alas, it is occasionally necessary to convert between decimal,
|
||||
binary and/or hex.
|
||||
|
||||
To convert from binary to decimal, put the decimal value of the place values
|
||||
{\ldots8 4 2 1} over the binary digits like this:
|
||||
|
||||
\begin{verbatim}
|
||||
128 64 32 16 8 4 2 1
|
||||
0 0 0 1 1 0 1 1
|
||||
\end{verbatim}
|
||||
|
||||
Now sum the place--values that are expressed in decimal for each
|
||||
bit with the value of 1: $16+8+2+1$. The integer binary value
|
||||
$00011011_2$ represents the decimal value $27_{10}$.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{From Binary to Hexadecimal}
|
||||
\label{section:binhex}
|
||||
|
||||
Conversion from binary to hex involves grouping the bits into
|
||||
sets of four and then performing the same summing process as
|
||||
shown above. If there is not a multiple of four bits then
|
||||
extend the binary to the left with zeroes to make it so.
|
||||
|
||||
Grouping the bits into sets of four and summing:
|
||||
|
||||
\begin{verbatim}
|
||||
Place: 8 4 2 1 8 4 2 1 8 4 2 1 8 4 2 1
|
||||
Binary: 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0
|
||||
Decimal: 4+2 =6 8+4+ 1=13 8+ 2 =10 8+4+2 =14
|
||||
\end{verbatim}
|
||||
|
||||
After the summing, convert each decimal value to hex. The decimal
|
||||
values from 0--9 are the same values in hex. Because we don't have any
|
||||
more numerals to represent the values from 10-15, we use the first 6
|
||||
letters (See the right--most column of \autoref{Figure:integers}.)
|
||||
Fortunately there are only six hex mappings involving letters. Thus
|
||||
it is reasonable to memorize them.
|
||||
|
||||
Continuing this example:
|
||||
|
||||
\begin{verbatim}
|
||||
Decimal: 6 13 10 14
|
||||
Hex: 6 D A E
|
||||
\end{verbatim}
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{From Hexadecimal to Binary}
|
||||
|
||||
Again, the four--bit mapping between binary and hex makes this
|
||||
task as straight forward as using a look-up table.
|
||||
|
||||
For each \gls{hit} (Hex digIT), translate it to its unique four--bit pattern.
|
||||
Perform this task either by memorizing each of the 16 patterns
|
||||
or by converting each hit to decimal first and then converting
|
||||
each four--bit binary value to decimal using the place--value summing
|
||||
method discussed in \autoref{section:bindec}.
|
||||
|
||||
For example:
|
||||
|
||||
\begin{verbatim}
|
||||
Hex: 4 C
|
||||
Binary: 0 1 0 0 1 1 0 0
|
||||
Decimal: 128 64 32 16 8 4 2 1
|
||||
Sum: 64+ 8+4 = 76
|
||||
\end{verbatim}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{From Decimal to Binary}
|
||||
|
||||
To convert arbitrary decimal numbers to binary, extend the list
|
||||
of binary place values until it exceeds the value of the decimal
|
||||
number being converted. Then make successive subtractions of each
|
||||
of the place values that would yield a non-negative result.
|
||||
|
||||
For example, to convert $1234_{10}$ to binary:
|
||||
|
||||
\begin{verbatim}
|
||||
Place values: 2048-1024-512-256-128-64-32-16-8-4-2-1
|
||||
|
||||
0 2048 (too big)
|
||||
1 1234 - 1024 = 210
|
||||
0 512 (too big)
|
||||
0 256 (too big)
|
||||
1 210 - 128 = 82
|
||||
1 82 - 64 = 18
|
||||
0 32 (too big)
|
||||
1 18 - 16 = 2
|
||||
0 8 (too big)
|
||||
0 4 (too big)
|
||||
1 2 - 2 = 0
|
||||
0 1 (too big)
|
||||
\end{verbatim}
|
||||
|
||||
The answer using this notation is listed vertically
|
||||
in the left column with the \acrshort{msb} on the top and
|
||||
the \acrshort{lsb} on the bottom line: $010011010010_2$.
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{From Decimal to Hex}
|
||||
|
||||
Conversion from decimal to hex can be done by using the place
|
||||
values for base--16 and the same math as from decimal to binary
|
||||
or by first converting the decimal value to binary and then
|
||||
from binary to hex by using the methods discussed above.
|
||||
|
||||
Because binary and hex are so closely related, performing
|
||||
a conversion by way of binary is quite straight forward.
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Addition of Binary Numbers}
|
||||
|
||||
The addition of binary numbers can be performed long--hand the
|
||||
same way decimal addition is taught in grade school. In fact binary
|
||||
addition is easier since it only involves adding 0 or 1.
|
||||
|
||||
The first thing to note that in any number base $0+0=0$, $0+1=1$, and
|
||||
$1+0=1$. Since there is no ``two'' in binary (just like there is
|
||||
no ``ten'' decimal) adding $1+1$ results in a zero with a carry as
|
||||
in: $1+1=10_2$ and in: $1+1+1=11_2$. Using these five sums, any two
|
||||
binary integers can be added.
|
||||
|
||||
For example:
|
||||
|
||||
\begin{verbatim}
|
||||
111111 1111 <== carries
|
||||
0110101111001111 <== addend
|
||||
+ 0000011101100011 <== addend
|
||||
------------------
|
||||
0111001100110010 <== sum
|
||||
\end{verbatim}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Signed Numbers}
|
||||
|
||||
There are multiple methods used to represent signed binary integers.
|
||||
The method used by most modern computers is called ``two's complement.''
|
||||
|
||||
A two's complement number is encoded in such a manner as to simplify
|
||||
the hardware used to add, subtract and compare integers.
|
||||
|
||||
A simple method of thinking about two's complement numbers is to
|
||||
negate the place value of the \acrshort{msb}. For example, the
|
||||
number one is represented the same as discussed before:
|
||||
|
||||
\begin{verbatim}
|
||||
-128 64 32 16 8 4 2 1
|
||||
0 0 0 0 0 0 0 1
|
||||
\end{verbatim}
|
||||
|
||||
The \acrshort{msb} of any negative number in this format will always
|
||||
be 1. For example the value $-1_{10}$ is:
|
||||
|
||||
\begin{verbatim}
|
||||
-128 64 32 16 8 4 2 1
|
||||
1 1 1 1 1 1 1 1
|
||||
\end{verbatim}
|
||||
|
||||
\ldots because: $-128+64+32+16+8+4+2+1=-1$.
|
||||
|
||||
This format has the virtue of allowing the same addition logic
|
||||
discussed above to be used to calculate $-1+1=0$.
|
||||
|
||||
\begin{verbatim}
|
||||
-128 64 32 16 8 4 2 1 <== place value
|
||||
1 1 1 1 1 1 1 1 0 <== carries
|
||||
1 1 1 1 1 1 1 1 <== addend (-1)
|
||||
+ 0 0 0 0 0 0 0 1 <== addend (1)
|
||||
----------------------
|
||||
1 0 0 0 0 0 0 0 0 <== sum (0 with an overflow)
|
||||
\end{verbatim}
|
||||
|
||||
In order for this to work, the \gls{overflow} carry out of the
|
||||
sum of the MSBs is ignored.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{Converting between Positive and Negative}
|
||||
|
||||
Changing the sign on two's complement numbers can be described as
|
||||
inverting all of the bits (which is also known as the one's complement)
|
||||
and then add one.
|
||||
|
||||
For example, inverting the number {\em four}:
|
||||
|
||||
\begin{verbatim}
|
||||
-128 64 32 16 8 4 2 1
|
||||
0 0 0 0 0 1 0 0 <== 4
|
||||
|
||||
1 1 <== carries
|
||||
1 1 1 1 1 0 1 1 <== one's complement of 4
|
||||
+ 0 0 0 0 0 0 0 1 <== plus 1
|
||||
----------------------
|
||||
1 1 1 1 1 1 0 0 <== -4
|
||||
\end{verbatim}
|
||||
|
||||
This can be verified by adding 5 to the result and observe that
|
||||
the sum is 1:
|
||||
|
||||
\begin{verbatim}
|
||||
-128 64 32 16 8 4 2 1
|
||||
1 1 1 1 1 <== carries
|
||||
1 1 1 1 1 1 0 0 <== -4
|
||||
+ 0 0 0 0 0 1 0 1 <== 5
|
||||
----------------------
|
||||
1 0 0 0 0 0 0 0 1
|
||||
\end{verbatim}
|
||||
|
||||
Note that the changing of the sign using this method is symmetric
|
||||
in that it is identical when converting from negative to positive
|
||||
and when converting from positive to negative: flip the bits and
|
||||
add 1.
|
||||
|
||||
For example, changing the value -4 to 4 to illustrate the
|
||||
reverse of the conversion above:
|
||||
|
||||
\begin{verbatim}
|
||||
-128 64 32 16 8 4 2 1
|
||||
1 1 1 1 1 1 0 0 <== -4
|
||||
|
||||
1 1 <== carries
|
||||
0 0 0 0 0 0 1 1 <== one's complement of -4
|
||||
+ 0 0 0 0 0 0 0 1 <== plus 1
|
||||
----------------------
|
||||
0 0 0 0 0 1 0 0 <== 4
|
||||
\end{verbatim}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Subtraction of Binary Numbers}
|
||||
|
||||
|
||||
Subtraction of binary numbers is performed by first negating
|
||||
the subtrahend and then adding the two numbers. Due to the
|
||||
nature of two's complement numbers this will work for both
|
||||
signed and unsigned numbers.
|
||||
\enote{This section needs more examples of subtracting
|
||||
signed an unsigned numbers and a discussion on how
|
||||
signedness is not relevant until the results are interpreted.
|
||||
For example adding $-4+ -8=-12$ using two 8--bit numbers
|
||||
is the same as adding $252+248=500$ and truncating the result
|
||||
to 244.}
|
||||
|
||||
To calculate $-4-8 = -12$
|
||||
|
||||
\begin{verbatim}
|
||||
-128 64 32 16 8 4 2 1
|
||||
1 1 1 1 1 1 0 0 <== -4
|
||||
- 0 0 0 0 1 0 0 0 <== 8
|
||||
|
||||
|
||||
1 1 1 <== carries
|
||||
1 1 1 1 0 1 1 1 <== one's complement of -8
|
||||
+ 0 0 0 0 0 0 0 1 <== plus 1
|
||||
----------------------
|
||||
1 1 1 1 1 0 0 0 <== -8
|
||||
|
||||
|
||||
1 1 1 1 <== carries
|
||||
1 1 1 1 1 1 0 0 <== -4
|
||||
+ 1 1 1 1 1 0 0 0 <== -8
|
||||
----------------------
|
||||
1 1 1 1 1 0 1 0 0 < == -12
|
||||
\end{verbatim}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Truncation and Overflow}
|
||||
|
||||
Disscuss the details of truncation and overflow here.
|
||||
\enote{This chapter should be made consistent in its use of
|
||||
{\em truncation} and {\em overflow} as occur with signed and unsigned
|
||||
addition and subtraction.}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Logical/Boolean Functions}
|
||||
|
||||
Unlike addition and subtraction, boolean functions apply
|
||||
on a per--bit basis.
|
||||
%in that they do not impact neighboring bits.
|
||||
%by generating things like a carry or a borrow.
|
||||
When applied to multi--bit values, each bit position is operated upon
|
||||
independantly of the other bits.
|
||||
\enote{This is unclear. Need to define bit positions and probably
|
||||
should add basic truth table diagrams.}
|
||||
\enote{Need to define 1 as true and 0 as false somewhere.}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{NOT}
|
||||
|
||||
The {\em NOT} operator applies to a single operand and represents the
|
||||
opposite of the input.
|
||||
\enote{Need to define unary, binary and ternary operators without
|
||||
confusing binary operators with binary numbers.}
|
||||
|
||||
If the input is 1 then the output is 0. If the input is 0 then the
|
||||
output is 1. In other words, the output value is {\em not} that of the
|
||||
input value.
|
||||
|
||||
This text will use the operator used in the C language when discussing
|
||||
the {\em NOT} operator in symbolic form. Specifically the tilde: `\verb@~@'.
|
||||
|
||||
\begin{verbatim}
|
||||
~ 1 1 1 1 0 1 0 1 <== A
|
||||
-----------------
|
||||
0 0 0 0 1 0 1 0 <== output
|
||||
\end{verbatim}
|
||||
|
||||
In a line of code the above might read like this: \verb@output = ~A@
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{AND}
|
||||
|
||||
The boolean {\em and} function has two or more inputs and the output is a
|
||||
single bit. The output is 1 if and only if all of the input values are 1.
|
||||
Otherwise it is 0.
|
||||
|
||||
This text will use the operator used in the C language when discussing
|
||||
the {\em AND} operator in symbolic form. Specifically the ampersand: `\verb@&@'.
|
||||
|
||||
This function works like it does in spoken language. For example
|
||||
if A is 1 {\em AND} B is 1 then the output is 1 (true).
|
||||
Otherwise the output is 0 (false). For example:
|
||||
|
||||
\begin{verbatim}
|
||||
1 1 1 1 0 1 0 1 <== A
|
||||
& 1 0 0 1 0 0 1 1 <== B
|
||||
-----------------
|
||||
1 0 0 1 0 0 0 1 <== output
|
||||
\end{verbatim}
|
||||
|
||||
In a line of code the above might read like this: \verb@output = A & B@
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{OR}
|
||||
|
||||
The boolean {\em or} function has two or more inputs and the output is a
|
||||
single bit. The output is 1 if at least one of the input values are 1.
|
||||
|
||||
This text will use the operator used in the C language when discussing
|
||||
the {\em OR} operator in symbolic form. Specifically the pipe: `\verb@|@'.
|
||||
|
||||
This function works like it does in spoken language. For example
|
||||
if A is 1 {\em OR} B is 1 then the output is 1 (true).
|
||||
Otherwise the output is 0 (false). For example:
|
||||
|
||||
\begin{verbatim}
|
||||
1 1 1 1 0 1 0 1 <== A
|
||||
| 1 0 0 1 0 0 1 1 <== B
|
||||
-----------------
|
||||
1 1 1 1 0 1 1 1 <== output
|
||||
\end{verbatim}
|
||||
|
||||
In a line of code the above might read like this: \verb@output = A | B@
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{XOR}
|
||||
|
||||
The boolean {\em exclusive or} function has two or more inputs and the
|
||||
output is a single bit. The output is 1 if only an odd number of inputs
|
||||
are 1. Otherwise the output will be 0.
|
||||
|
||||
This text will use the operator used in the C language when discussing
|
||||
the {\em XOR} operator in symbolic form. Specifically the carrot: `\verb@^@'.
|
||||
|
||||
Note that when {\em XOR} is used with two inputs, the output
|
||||
is set to 1 (true) when the inputs have different values and 0
|
||||
(false) when the inputs both have the same value.
|
||||
|
||||
For example:
|
||||
|
||||
\begin{verbatim}
|
||||
1 1 1 1 0 1 0 1 <== A
|
||||
^ 1 0 0 1 0 0 1 1 <== B
|
||||
-----------------
|
||||
0 1 1 0 0 1 1 0 <== output
|
||||
\end{verbatim}
|
||||
|
||||
In a line of code the above might read like this: \verb@output = A ^ B@
|
||||
|
||||
|
||||
|
||||
%\section{Context}
|
||||
%
|
||||
%Numbers can be interpreted differently depending on the context in
|
||||
%which they are used. For example a number may represent the quantity
|
||||
%of millimeters between two points. It may enumerate a
|
||||
%a letter of the alphabet -- ie. $01000001=A$, $01000010=B$,
|
||||
%$01000011=C$\ldots\ In fact, any finite set of items can be identified
|
||||
%(enumerated) by a assigning a code number to each element in this fashon.
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{IEEE-754 Floating Point Number Representation}
|
||||
\label{chapter::floatingpoint}
|
||||
|
||||
This section provides an overview of the IEEE-754 32-bit binary floating
|
||||
point format.
|
||||
|
||||
\begin{itemize}
|
||||
\item Recall that the place values for integer binary numbers are:
|
||||
\begin{verbatim}
|
||||
... 128 64 32 16 8 4 2 1
|
||||
\end{verbatim}
|
||||
\item We can extend this to the right in binary similar to the way we do for
|
||||
decimal numbers:
|
||||
\begin{verbatim}
|
||||
... 128 64 32 16 8 4 2 1 . 1/2 1/4 1/8 1/16 1/32 1/64 1/128 ...
|
||||
\end{verbatim}
|
||||
The `.' in a binary number is a binary point, not a decimal point.
|
||||
|
||||
\item We use scientific notation as in $2.7 \times 10^{-47}$ to express either
|
||||
small fractions or large numbers when we are not concerned every last digit
|
||||
needed to represent the entire, exact, value of a number.
|
||||
|
||||
\item The format of a number in scientific notation is $mantissa \times base^{exponent}$
|
||||
|
||||
\item In binary we have $mantissa \times 2^{exponent}$
|
||||
|
||||
\item IEEE--754 format requires binary numbers to be {\em normalized} to
|
||||
$1.significand \times 2^{exponent}$ where the {\em significand}
|
||||
is the portion of the {\em mantissa} that is to the right of the binary--point.
|
||||
|
||||
\begin{itemize}
|
||||
\item The unnormalized binary value of $-2.625$ is $10.101$
|
||||
\item The normalized value of $-2.625$ is $1.0101 \times 2^1$
|
||||
\end{itemize}
|
||||
|
||||
\item We need not store the `1.' because {\em all} normalized floating
|
||||
point numbers will start that way. Thus we can save memory when storing
|
||||
normalized values by adding 1 to the significand.
|
||||
|
||||
{
|
||||
\small
|
||||
\setlength{\unitlength}{.15in}
|
||||
\begin{picture}(32,4)(0,0)
|
||||
\put(0,1){\line(1,0){32}} % bottom line
|
||||
\put(0,2){\line(1,0){32}} % top line
|
||||
|
||||
\put(0,1){\line(0,1){2}} % left vertical
|
||||
\put(0,2){\makebox(1,1){\tiny 31}} % left end bit number marker
|
||||
|
||||
\put(32,1){\line(0,1){2}} % vertical right end
|
||||
\put(31,2){\makebox(1,1){\tiny 0}} % right end bit number marker
|
||||
|
||||
\put(0,0){\makebox(1,1){\small sign}}
|
||||
\put(1,0){\makebox(8,1){\small exponent}}
|
||||
\put(9,0){\makebox(23,1){\small significand}}
|
||||
|
||||
\put(0,1){\makebox(1,1){1}} % sign
|
||||
|
||||
\put(1,1){\line(0,1){2}} % seperator
|
||||
\put(1,2){\makebox(1,1){\tiny 30}} % bit marker
|
||||
|
||||
\put(1,1){\makebox(1,1){1}} % exponent
|
||||
\put(2,1){\makebox(1,1){0}}
|
||||
\put(3,1){\makebox(1,1){0}}
|
||||
\put(4,1){\makebox(1,1){0}}
|
||||
\put(5,1){\makebox(1,1){0}}
|
||||
\put(6,1){\makebox(1,1){0}}
|
||||
\put(7,1){\makebox(1,1){0}}
|
||||
\put(8,1){\makebox(1,1){0}}
|
||||
|
||||
\put(8,2){\makebox(1,1){\tiny 23}} % bit marker
|
||||
\put(9,1){\line(0,1){2}} % seperator
|
||||
\put(9,2){\makebox(1,1){\tiny 22}} % bit marker
|
||||
|
||||
\put(9,1){\makebox(1,1){0}}
|
||||
\put(10,1){\makebox(1,1){1}}
|
||||
\put(11,1){\makebox(1,1){0}}
|
||||
\put(12,1){\makebox(1,1){1}}
|
||||
\put(13,1){\makebox(1,1){0}}
|
||||
\put(14,1){\makebox(1,1){0}}
|
||||
\put(15,1){\makebox(1,1){0}}
|
||||
\put(16,1){\makebox(1,1){0}}
|
||||
\put(17,1){\makebox(1,1){0}}
|
||||
\put(18,1){\makebox(1,1){0}}
|
||||
\put(19,1){\makebox(1,1){0}}
|
||||
\put(20,1){\makebox(1,1){0}}
|
||||
\put(21,1){\makebox(1,1){0}}
|
||||
\put(22,1){\makebox(1,1){0}}
|
||||
\put(23,1){\makebox(1,1){0}}
|
||||
\put(24,1){\makebox(1,1){0}}
|
||||
\put(25,1){\makebox(1,1){0}}
|
||||
\put(26,1){\makebox(1,1){0}}
|
||||
\put(27,1){\makebox(1,1){0}}
|
||||
\put(28,1){\makebox(1,1){0}}
|
||||
\put(29,1){\makebox(1,1){0}}
|
||||
\put(30,1){\makebox(1,1){0}}
|
||||
\put(31,1){\makebox(1,1){0}}
|
||||
\end{picture}
|
||||
}
|
||||
|
||||
%\item $-((1 + \frac{1}{4} + \frac{1}{16}) \times 2^{128-127}) = -(1 \frac{5}{16} \times 2^{1}) = -(1.3125 \times 2^{1}) = -2.625$
|
||||
\item $-((1 + \frac{1}{4} + \frac{1}{16}) \times 2^{128-127}) = -((1 + \frac{1}{4} + \frac{1}{16}) \times 2^1) = -(2 + \frac{1}{2} + \frac{1}{8}) = -(2 + .5 + .125) = -2.625$
|
||||
|
||||
\item IEEE754 formats:
|
||||
|
||||
\begin{tabular}{|l|l|l|}
|
||||
\hline
|
||||
& IEEE754 32--bit & IEEE754 64--bit \\
|
||||
\hline
|
||||
sign & 1 bit & 1 bit \\
|
||||
exponent & 8 bits (excess--127) & 11 bits (excess-1023) \\
|
||||
mantissa & 23 bits & 52 bits \\
|
||||
max exponent & 127 & 1023 \\
|
||||
min exponent & -126 & -1022 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
\item When the exponent is all ones, the mantissa is all zeros, and
|
||||
the sign is zero, the number represents positive infinity.
|
||||
|
||||
\item When the exponent is all ones, the mantissa is all zeros, and
|
||||
the sign is one, the number represents negative infinity.
|
||||
|
||||
\item Note that the binary representation of an IEEE754 number in memory
|
||||
can be compared for magnitude with another one using the same logic as for
|
||||
comparing two's complement signed integers because the magnitude of an
|
||||
IEEE number grows upward and downward in the same fashion as signed integers.
|
||||
This is why we use excess notation and locate the significand's sign bit on
|
||||
the left of the exponent.
|
||||
|
||||
\item Note that zero is a special case number. Recall that a normalized
|
||||
number has an implied 1--bit to the left of the significand\ldots\ which
|
||||
means that there is no way to represent zero!
|
||||
Zero is represented by an exponent of all--zeros and a significand of
|
||||
all--zeros. This definition allows for a positive and a negative zero
|
||||
if we observe that the sign can be either 1 or 0.
|
||||
|
||||
\item On the number-line, numbers between zero and the smallest fraction in
|
||||
either direction are in the {\em \gls{underflow}} areas.
|
||||
\enote{Need to add the standard lecture numberline diagram showing
|
||||
where the over/under--flow areas are and why.}
|
||||
|
||||
\item On the number line, numbers greater than the mantissa of all--ones and the
|
||||
largest exponent allowed are in the {\em \gls{overflow}} areas.
|
||||
|
||||
\item Note that numbers have a higher resolution on the number--line when the
|
||||
exponent is smaller.
|
||||
\end{itemize}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Floating Point Number Accuracy}
|
||||
Due to the finite number of bits used to store the value of a floating point
|
||||
number, it is not possible to represent every one of the infinite values
|
||||
on the real number line. The following C programs illustrate this point.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{Powers Of Two}
|
||||
Just like the integer numbers, the powers of two that have bits to represent
|
||||
them can be represented perfectly\ldots\ as can their sums (provided that the
|
||||
significand requires no more than 23 bits.)
|
||||
|
||||
\listing{powersoftwo.c}{Precise Powers of Two}
|
||||
\listing{powersoftwo.out}{Output from {\tt powersoftwo.c}}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{Clean Decimal Numbers}
|
||||
When dealing with decimal values, you will find that they don't map simply
|
||||
into binary floating point values.
|
||||
% (the same holds true for binary integer numbers).
|
||||
|
||||
Note how the decimal numbers are not accurately represented as they get larger.
|
||||
The decimal number on line 10 of \listingRef{cleandecimal.out}
|
||||
can be perfectly represented in IEEE format. However, a problem arises in
|
||||
the 11Th loop iteration. It is due to the fact that the
|
||||
binary number can not be represented accurately in IEEE format. Its least
|
||||
significant bits were truncated in a best-effort attempt at rounding the value
|
||||
off in order to fit the value into the bits provided. This is an example of
|
||||
{\em low order truncation}. Once this happens, the value of \verb@x.f@ is
|
||||
no longer as precise as it could be given more bits in which to save its value.
|
||||
|
||||
\listing{cleandecimal.c}{Print Clean Decimal Numbers}
|
||||
\listing{cleandecimal.out}{Output from {\tt cleandecimal.c}}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsubsection{Accumulation of Error}
|
||||
These rounding errors can be exaggerated when the number we multiply
|
||||
the \verb@x.f@ value by is, itself, something that can not be accurately
|
||||
represented in IEEE
|
||||
form.\footnote{Applications requiring accurate decimal values, such as
|
||||
financial accounting systems, can use a packed--decimal numeric format
|
||||
to avoid unexpected oddities caused by the use of binary numbers.}
|
||||
\enote{In a lecture one would show that one tenth is a repeating
|
||||
non--terminating binary number that gets truncated. This discussion
|
||||
should be reproduced here in text form.}
|
||||
|
||||
For example, if we multiply our \verb@x.f@ value by $\frac{1}{10}$ each time,
|
||||
we can never be accurate and we start accumulating errors immediately.
|
||||
|
||||
\listing{erroraccumulation.c}{Accumulation of Error}
|
||||
\listing{erroraccumulation.out}{Output from {\tt erroraccumulation.c}}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Reducing Error Accumulation}
|
||||
In order to use floating point numbers in a program without causing
|
||||
excessive rounding problems an algorithm can be redesigned such that the
|
||||
accumulation is eliminated.
|
||||
This example is similar to the previous one, but this time we recalculate the
|
||||
desired value from a known--accurate integer value.
|
||||
Some rounding errors remain present, but they can not accumulate.
|
||||
|
||||
\listing{errorcompensation.c}{Accumulation of Error}
|
||||
\listing{errorcompensation.out}{Output from {\tt erroraccumulation.c}}
|
||||
22
book/numbers/cleandecimal.c
Normal file
22
book/numbers/cleandecimal.c
Normal file
@ -0,0 +1,22 @@
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <unistd.h>
|
||||
|
||||
union floatbin
|
||||
{
|
||||
unsigned int i;
|
||||
float f;
|
||||
};
|
||||
int main()
|
||||
{
|
||||
union floatbin x, y;
|
||||
int i;
|
||||
|
||||
x.f = 10;
|
||||
while (x.f <= 10000000000000.0)
|
||||
{
|
||||
y.f = -x.f;
|
||||
printf("%25.10f = %08x %25.10f = %08x\n", x.f, x.i, y.f, y.i);
|
||||
x.f = x.f*10.0;
|
||||
}
|
||||
}
|
||||
13
book/numbers/cleandecimal.out
Normal file
13
book/numbers/cleandecimal.out
Normal file
@ -0,0 +1,13 @@
|
||||
10.0000000000 = 41200000 -10.0000000000 = c1200000
|
||||
100.0000000000 = 42c80000 -100.0000000000 = c2c80000
|
||||
1000.0000000000 = 447a0000 -1000.0000000000 = c47a0000
|
||||
10000.0000000000 = 461c4000 -10000.0000000000 = c61c4000
|
||||
100000.0000000000 = 47c35000 -100000.0000000000 = c7c35000
|
||||
1000000.0000000000 = 49742400 -1000000.0000000000 = c9742400
|
||||
10000000.0000000000 = 4b189680 -10000000.0000000000 = cb189680
|
||||
100000000.0000000000 = 4cbebc20 -100000000.0000000000 = ccbebc20
|
||||
1000000000.0000000000 = 4e6e6b28 -1000000000.0000000000 = ce6e6b28
|
||||
10000000000.0000000000 = 501502f9 -10000000000.0000000000 = d01502f9
|
||||
99999997952.0000000000 = 51ba43b7 -99999997952.0000000000 = d1ba43b7
|
||||
999999995904.0000000000 = 5368d4a5 -999999995904.0000000000 = d368d4a5
|
||||
9999999827968.0000000000 = 551184e7 -9999999827968.0000000000 = d51184e7
|
||||
22
book/numbers/erroraccumulation.c
Normal file
22
book/numbers/erroraccumulation.c
Normal file
@ -0,0 +1,22 @@
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <unistd.h>
|
||||
|
||||
union floatbin
|
||||
{
|
||||
unsigned int i;
|
||||
float f;
|
||||
};
|
||||
int main()
|
||||
{
|
||||
union floatbin x, y;
|
||||
int i;
|
||||
|
||||
x.f = .1;
|
||||
while (x.f <= 2.0)
|
||||
{
|
||||
y.f = -x.f;
|
||||
printf("%25.10f = %08x %25.10f = %08x\n", x.f, x.i, y.f, y.i);
|
||||
x.f += .1;
|
||||
}
|
||||
}
|
||||
19
book/numbers/erroraccumulation.out
Normal file
19
book/numbers/erroraccumulation.out
Normal file
@ -0,0 +1,19 @@
|
||||
0.1000000015 = 3dcccccd -0.1000000015 = bdcccccd
|
||||
0.2000000030 = 3e4ccccd -0.2000000030 = be4ccccd
|
||||
0.3000000119 = 3e99999a -0.3000000119 = be99999a
|
||||
0.4000000060 = 3ecccccd -0.4000000060 = becccccd
|
||||
0.5000000000 = 3f000000 -0.5000000000 = bf000000
|
||||
0.6000000238 = 3f19999a -0.6000000238 = bf19999a
|
||||
0.7000000477 = 3f333334 -0.7000000477 = bf333334
|
||||
0.8000000715 = 3f4cccce -0.8000000715 = bf4cccce
|
||||
0.9000000954 = 3f666668 -0.9000000954 = bf666668
|
||||
1.0000001192 = 3f800001 -1.0000001192 = bf800001
|
||||
1.1000001431 = 3f8cccce -1.1000001431 = bf8cccce
|
||||
1.2000001669 = 3f99999b -1.2000001669 = bf99999b
|
||||
1.3000001907 = 3fa66668 -1.3000001907 = bfa66668
|
||||
1.4000002146 = 3fb33335 -1.4000002146 = bfb33335
|
||||
1.5000002384 = 3fc00002 -1.5000002384 = bfc00002
|
||||
1.6000002623 = 3fcccccf -1.6000002623 = bfcccccf
|
||||
1.7000002861 = 3fd9999c -1.7000002861 = bfd9999c
|
||||
1.8000003099 = 3fe66669 -1.8000003099 = bfe66669
|
||||
1.9000003338 = 3ff33336 -1.9000003338 = bff33336
|
||||
24
book/numbers/errorcompensation.c
Normal file
24
book/numbers/errorcompensation.c
Normal file
@ -0,0 +1,24 @@
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <unistd.h>
|
||||
|
||||
union floatbin
|
||||
{
|
||||
unsigned int i;
|
||||
float f;
|
||||
};
|
||||
int main()
|
||||
{
|
||||
union floatbin x, y;
|
||||
int i;
|
||||
|
||||
i = 1;
|
||||
while (i <= 20)
|
||||
{
|
||||
x.f = i/10.0;
|
||||
y.f = -x.f;
|
||||
printf("%25.10f = %08x %25.10f = %08x\n", x.f, x.i, y.f, y.i);
|
||||
i++;
|
||||
}
|
||||
return(0);
|
||||
}
|
||||
20
book/numbers/errorcompensation.out
Normal file
20
book/numbers/errorcompensation.out
Normal file
@ -0,0 +1,20 @@
|
||||
0.1000000015 = 3dcccccd -0.1000000015 = bdcccccd
|
||||
0.2000000030 = 3e4ccccd -0.2000000030 = be4ccccd
|
||||
0.3000000119 = 3e99999a -0.3000000119 = be99999a
|
||||
0.4000000060 = 3ecccccd -0.4000000060 = becccccd
|
||||
0.5000000000 = 3f000000 -0.5000000000 = bf000000
|
||||
0.6000000238 = 3f19999a -0.6000000238 = bf19999a
|
||||
0.6999999881 = 3f333333 -0.6999999881 = bf333333
|
||||
0.8000000119 = 3f4ccccd -0.8000000119 = bf4ccccd
|
||||
0.8999999762 = 3f666666 -0.8999999762 = bf666666
|
||||
1.0000000000 = 3f800000 -1.0000000000 = bf800000
|
||||
1.1000000238 = 3f8ccccd -1.1000000238 = bf8ccccd
|
||||
1.2000000477 = 3f99999a -1.2000000477 = bf99999a
|
||||
1.2999999523 = 3fa66666 -1.2999999523 = bfa66666
|
||||
1.3999999762 = 3fb33333 -1.3999999762 = bfb33333
|
||||
1.5000000000 = 3fc00000 -1.5000000000 = bfc00000
|
||||
1.6000000238 = 3fcccccd -1.6000000238 = bfcccccd
|
||||
1.7000000477 = 3fd9999a -1.7000000477 = bfd9999a
|
||||
1.7999999523 = 3fe66666 -1.7999999523 = bfe66666
|
||||
1.8999999762 = 3ff33333 -1.8999999762 = bff33333
|
||||
2.0000000000 = 40000000 -2.0000000000 = c0000000
|
||||
22
book/numbers/powersoftwo.c
Normal file
22
book/numbers/powersoftwo.c
Normal file
@ -0,0 +1,22 @@
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <unistd.h>
|
||||
|
||||
union floatbin
|
||||
{
|
||||
unsigned int i;
|
||||
float f;
|
||||
};
|
||||
int main()
|
||||
{
|
||||
union floatbin x;
|
||||
union floatbin y;
|
||||
int i;
|
||||
x.f = 1.0;
|
||||
while (x.f > 1.0/1024.0)
|
||||
{
|
||||
y.f = -x.f;
|
||||
printf("%25.10f = %08x %25.10f = %08x\n", x.f, x.i, y.f, y.i);
|
||||
x.f = x.f/2.0;
|
||||
}
|
||||
}
|
||||
10
book/numbers/powersoftwo.out
Normal file
10
book/numbers/powersoftwo.out
Normal file
@ -0,0 +1,10 @@
|
||||
1.0000000000 = 3f800000 -1.0000000000 = bf800000
|
||||
0.5000000000 = 3f000000 -0.5000000000 = bf000000
|
||||
0.2500000000 = 3e800000 -0.2500000000 = be800000
|
||||
0.1250000000 = 3e000000 -0.1250000000 = be000000
|
||||
0.0625000000 = 3d800000 -0.0625000000 = bd800000
|
||||
0.0312500000 = 3d000000 -0.0312500000 = bd000000
|
||||
0.0156250000 = 3c800000 -0.0156250000 = bc800000
|
||||
0.0078125000 = 3c000000 -0.0078125000 = bc000000
|
||||
0.0039062500 = 3b800000 -0.0039062500 = bb800000
|
||||
0.0019531250 = 3b000000 -0.0019531250 = bb000000
|
||||
261
book/preamble.tex
Normal file
261
book/preamble.tex
Normal file
@ -0,0 +1,261 @@
|
||||
|
||||
\oddsidemargin=.82in
|
||||
\evensidemargin=1.82in
|
||||
|
||||
%\topmargin=-.5in
|
||||
\headheight=12pt
|
||||
\headsep=20pt
|
||||
|
||||
\hoffset=-1.2in % for 8.5x11
|
||||
%\voffset=-1.15in % for 8.5x11
|
||||
\voffset=-.8in % for 8.5x11
|
||||
%\textheight=9.75in % for 8.5x11
|
||||
\textheight=9in % for 8.5x11
|
||||
%\textheight=8.75in % for 8.5x11
|
||||
|
||||
%\textwidth=348pt % for 8.5x11
|
||||
%\textwidth=6in % for 8.5x11
|
||||
\textwidth=6.25in % for 8.5x11
|
||||
|
||||
\marginparsep=7pt
|
||||
%\marginparwidth=71pt
|
||||
%\marginparwidth=1.25in
|
||||
%\marginparwidth=1.5in
|
||||
\marginparwidth=1.25in
|
||||
\footskip=36pt
|
||||
\marginparpush=5pt
|
||||
|
||||
|
||||
\usepackage{ifthen}
|
||||
\usepackage{stringstrings} % so can count characters in a string
|
||||
\usepackage{xstring} % so can count characters in a string
|
||||
|
||||
\usepackage[pass]{geometry}
|
||||
\usepackage{color} % Necessary for colored links
|
||||
|
||||
% load makeidx BEFORE hyperref to make the index clickable
|
||||
% load makeidx AFTER hyperref if want to use showidx
|
||||
%\usepackage{makeidx}
|
||||
\usepackage[pagebackref]{hyperref}
|
||||
\hypersetup{
|
||||
colorlinks=true, %set true if you want colored links
|
||||
linkcolor=blue %choose some color if you want links to stand out
|
||||
}
|
||||
|
||||
\usepackage{makeidx,showidx} % showidx breaks hyperref when loaded before hyperref
|
||||
|
||||
|
||||
|
||||
%\usepackage{url}
|
||||
|
||||
\usepackage{lastpage}
|
||||
\usepackage{fancyhdr}
|
||||
|
||||
\usepackage{amsmath}
|
||||
\numberwithin{equation}{section}
|
||||
\usepackage{amsfonts} % I hear these are also good to load
|
||||
\usepackage{amssymb} % I hear these are also good to load
|
||||
|
||||
%\usepackage{picture}
|
||||
%\usepackage{epstopdf}
|
||||
%\usepackage{graphicx}
|
||||
\usepackage{epsfig}
|
||||
\usepackage{tikz-timing}
|
||||
\usepackage{tikz}
|
||||
%\usepackage{timing}
|
||||
\usepackage{float}
|
||||
\usepackage{fancyvrb}
|
||||
\usepackage{caption}
|
||||
\usepackage{placeins}
|
||||
|
||||
\usepackage{listings}
|
||||
|
||||
\usepackage[toc]{glossaries}
|
||||
%\renewcommand*{\glsclearpage}{}
|
||||
|
||||
\usepackage{pifont}
|
||||
\usepackage{layout}
|
||||
|
||||
\usepackage{xcolor}
|
||||
\usepackage{textcomp} % for the trademark symbol
|
||||
|
||||
%\usepackage[obeyspaces]{url}
|
||||
\usepackage{fink} % deprecated in favor of currfile
|
||||
%\usepackage{currfile} % dut... doesn't emit the local include path properly
|
||||
|
||||
\usepackage{MyFigs}
|
||||
|
||||
\def\code#1{\url{#1}}
|
||||
|
||||
% The exercise environment
|
||||
\usepackage{exercise}
|
||||
|
||||
\renewcommand{\ExerciseHeader}{%
|
||||
\textbf{\large\ExerciseHeaderDifficulty\ExerciseName\ %
|
||||
\ExerciseHeaderNB\ExerciseHeaderTitle\ExerciseHeaderOrigin}\medskip}
|
||||
|
||||
\renewcommand{\ExePartHeader}{%
|
||||
\medskip\emph{\large\ExePartHeaderDifficulty\ExePartName %
|
||||
\ExePartHeaderNB \ExePartHeaderTitle\\
|
||||
}}
|
||||
|
||||
%\renewcommand{\ExePartHeader}{%
|
||||
%\medskip\emph{\large\ExePartHeaderDifficulty Part \ExePartHeaderNB %
|
||||
%\quad \ExePartName\ExePartHeaderTitle}}
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%\DefineVerbatimEnvironment%
|
||||
%{Code}{Verbatim}
|
||||
%{frame=single,numbers=left,numbersep=2mm,framesep=3mm}
|
||||
%%%,numbersep=2mm,frame=lines,framerule=0.8mm,framesep=5mm
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% [1] = filename to include
|
||||
% [2] = title of the code sample
|
||||
% A label will be generated as: Code:#1
|
||||
%\newcommand{\xxxx}[2]{%
|
||||
% \label{Code:#1} %
|
||||
% \VerbatimInput[frame=single,numbers=left,numbersep=2mm,framesep=3mm,label={#2}]{#1}}
|
||||
|
||||
\newcommand{\theListingFontFamily}{\ttfamily\small}
|
||||
%\newcommand{\theListingFontFamily}{\ttfamily\footnotesize}
|
||||
%\newcommand{\theListingFontFamily}{\ttfamily\scriptsize}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% [1] = place for additional listing parameters, default: language=C
|
||||
% [2] = filepath
|
||||
% [3] = Description of the listing
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand{\listing}[3][language=C]{%
|
||||
\lstinputlisting[ %
|
||||
numbers=left,numberstyle=\tiny,stepnumber=1,numbersep=8pt, %
|
||||
breaklines=true, %
|
||||
frame=single %
|
||||
showtabs=false, %
|
||||
basicstyle=\theListingFontFamily, %
|
||||
showstringspaces=false, %
|
||||
tabsize=4, %
|
||||
showlines=true, % show all blank lines
|
||||
#1, %
|
||||
captionpos=t,frame=tblr,label={lst:\detokenize{#2}},caption={{\tt \detokenize{#2}}\\\hspace{\textwidth}{\small #3}}]{\detokenize{#2}}}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\newcommand{\listingRef}[1]{\autoref{lst:\detokenize{#1}}}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\lstnewenvironment{tty}
|
||||
{\lstset{language=sh, %
|
||||
numbers=left,numberstyle=\tiny,stepnumber=1,numbersep=8pt, %
|
||||
breaklines=true, %
|
||||
frame=l, %
|
||||
showtabs=false, %
|
||||
basicstyle=\theListingFontFamily, %
|
||||
showstringspaces=false, %
|
||||
tabsize=4, %
|
||||
showlines=true, % show all blank lines
|
||||
basicstyle=\theListingFontFamily}}
|
||||
{}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% A footer that shall appear on every page
|
||||
|
||||
%\newcommand{\MyFoot}{{\sf\scriptsize Copyright \copyright\ 2014, 2015 John Winans. All Rights Reserved}\\
|
||||
%\vspace{.05in}
|
||||
%\scriptsize\FooterText}
|
||||
|
||||
\newcommand{\MyFoot}{\scriptsize\FooterText}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\pagestyle{fancy}
|
||||
|
||||
% supress normal headings and footers
|
||||
\fancyhf{}
|
||||
|
||||
% heading and footing rules
|
||||
\renewcommand{\headrulewidth}{1pt}
|
||||
\renewcommand{\footrulewidth}{1pt}
|
||||
|
||||
|
||||
%\def\DiscardOneCharacter#1{}
|
||||
% Sub-footer that shows the version control version string in the lfoot defined above
|
||||
\ifdefined\GitFileName
|
||||
% \newcommand{\FooterText}{\tt \GitFileName \currfilename\\
|
||||
\newcommand{\FooterText}{\tt \GitFileName \finkpath\\
|
||||
\GitDescription}
|
||||
\else
|
||||
\newcommand{\FooterText}{\emph{--UNKNOWN--}}
|
||||
\fi
|
||||
|
||||
%\lhead{\leftmark}
|
||||
%\rhead{\rightmark}
|
||||
\fancyhead[LE]{\leftmark}
|
||||
\fancyhead[RO]{\rightmark}
|
||||
|
||||
\newcommand{\PageNumber}{Page \thepage\ of \pageref*{LastPage}}
|
||||
%\rfoot{Page \thepage\ of \pageref{LastPage}}
|
||||
%\lfoot{\MyFoot}
|
||||
|
||||
\fancyfoot[LE,RO]{\PageNumber}
|
||||
\fancyfoot[RE,LO]{\MyFoot}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% override the plain page style so the first page of a
|
||||
% chapter still has a footer on it (but no header).
|
||||
|
||||
\fancypagestyle{plain}{%
|
||||
\renewcommand{\headrulewidth}{0pt} %
|
||||
\fancyhf{} % clear all header and footer fields
|
||||
\fancyfoot[LE,RO]{\PageNumber}
|
||||
\fancyfoot[RE,LO]{\MyFoot}
|
||||
%\lfoot{\MyFoot} %
|
||||
%\rfoot{Page \thepage\ of \pageref*{LastPage}}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\setlength{\parindent}{0pt}
|
||||
\setlength{\parskip}{.51em}
|
||||
|
||||
% How deep should we enumerate the section/subsection/subsubsections
|
||||
% 3=all the way
|
||||
\setcounter{secnumdepth}{3}
|
||||
|
||||
% How many section-levels to show in the TOC.
|
||||
% 4=all of them
|
||||
\setcounter{tocdepth}{4}
|
||||
%\setcounter{tocdepth}{1}
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Presentation styles for things like names links and
|
||||
% window objects in figures.
|
||||
|
||||
% how should we present a window name
|
||||
\newcommand{\windowname}[1]{{\em #1}}
|
||||
|
||||
% How should we present the name of an object in a figure
|
||||
% that can be interacted with.
|
||||
\newcommand{\linkname}[1]{{\bf #1}}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% fix some annoying things
|
||||
|
||||
\newcommand{\tm}{\textsuperscript{TM}}
|
||||
\newcommand{\rtm}{\textsuperscript{\textregistered}}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% A command to make a colored background box whilst in math mode:
|
||||
\newcommand{\MathHilight}[1]{\colorbox{yellow}{\ensuremath{#1}}}
|
||||
|
||||
\usepackage{tcolorbox}
|
||||
%\tcbset{colback=blue!20!white}
|
||||
\tcbset{colback=green!20!white}
|
||||
|
||||
49
book/preface/chapter.tex
Normal file
49
book/preface/chapter.tex
Normal file
@ -0,0 +1,49 @@
|
||||
\chapter{Preface}
|
||||
\label{chapter:Preface}
|
||||
|
||||
I set out to this book because I couldn't find it in a single volume elsewhere.
|
||||
|
||||
The closest thing to what I sought when deciding to collect my thoughts
|
||||
into this document would be select portions of
|
||||
{\em The RISC-V Instruction Set Manual, Volume I: User-Level ISA, Document Version 2.2}\cite{rvismv1v22:2017},
|
||||
{The RISC-V Reader}\cite{riscvreader:2017}, and
|
||||
{Computer Organization and Design RISC-V Edition: The Hardware Software Interface}\cite{codriscv:2017}.
|
||||
|
||||
There {\em are} some terse guides around the Internet that are suitable
|
||||
for those that already know an assembly language. With all the (deserved)
|
||||
excitement brewing over system organization (and the need to compress the
|
||||
time out of university courses targeting assembly language
|
||||
programming~\cite{Decker:1985:MAT:989369.989375}),
|
||||
it is no surprise that RISC-V texts for the beginning assembly programmer
|
||||
are not (yet) available.
|
||||
|
||||
When I got started in computing I learned how to count in binary
|
||||
in a high school electronics course using data sheets for integrated
|
||||
circuits such as the 74191\cite{ttl74191:1979} and 74154\cite{ttl74154:1979}
|
||||
prior to knowing that assembly language even existed.
|
||||
|
||||
I learned assembler from data sheets and texts (that are still sitting on
|
||||
my shelves) such as:
|
||||
\begin{itemize}
|
||||
\item The MCS-85 User's Manual\cite{mcs85:1978}
|
||||
\item The EDTASM Manual\cite{edtasm:1978}
|
||||
\item The MC68000 User's Manual\cite{mc68000:1980}
|
||||
\item Assembler Language With ASSIST\cite{assist:1983}
|
||||
\item IBM System/370 Principals of Operation\cite{poo:1980}
|
||||
\item OS/VS-DOS/VSE-VM/370 Assembler Language\cite{assembler370:1979}
|
||||
%\item The Series 32000 Databook\cite{ns32k:1986}
|
||||
\item \ldots\ and several others
|
||||
\end{itemize}
|
||||
|
||||
One way or another all of them discuss each CPU instruction in excruciating detail
|
||||
with both a logical and narrative description. For RISC--V this is
|
||||
also the case for the {\em RISC-V Reader}\cite{riscvreader:2017} and the
|
||||
{\em Computer Organization and Design RISC-V Edition}\cite{codriscv:2017} books
|
||||
and is also present in this text (I consider that to be the minimal
|
||||
level of responsibility.)
|
||||
|
||||
Where I hope this text will differentiate itself from the existing RISC-V
|
||||
titles is in its attempt to address the needs of those learning assembly
|
||||
language for the first time. To this end I have primed this project with
|
||||
some of the material from old handouts I used when teaching assembly language
|
||||
programming in the late '80s.
|
||||
1688
book/rv32/chapter.tex
Normal file
1688
book/rv32/chapter.tex
Normal file
File diff suppressed because it is too large
Load Diff
93
book/toolchain/chapter.tex
Normal file
93
book/toolchain/chapter.tex
Normal file
@ -0,0 +1,93 @@
|
||||
\chapter{The RISC-V GNU Toolchain}
|
||||
|
||||
This chapter discusses the GNU toolchain elements used to
|
||||
experiment with the material in this book.
|
||||
|
||||
The\enote{It would be good to find some Mac and Windows users to write
|
||||
and test proper variations on this section to address those systems.
|
||||
Pull requests, welcome!}
|
||||
instructions and examples here were all implemented on Ubuntu 16.04 LTS.
|
||||
|
||||
Install custom code in a location that will not cause interference with
|
||||
other applications and allow for easy cleanup. These instructions
|
||||
install the toolchain in \verb@/usr/local/riscv@. At any time
|
||||
you can remove the lot and start over by executing the following
|
||||
command:
|
||||
|
||||
\begin{verbatim}
|
||||
rm -rf /usr/local/riscv/*
|
||||
\end{verbatim}
|
||||
|
||||
|
||||
Tested on Ubuntu 16.04 LTS.
|
||||
18.04 was just released\ldots\ update accordingly.
|
||||
|
||||
These are the only commands that you should perform as root when installing
|
||||
the toolchain:
|
||||
|
||||
\begin{verbatim}
|
||||
sudo apt-get install autoconf automake autotools-dev curl libmpc-dev \
|
||||
libmpfr-dev libgmp-dev gawk build-essential bison flex texinfo gperf \
|
||||
libtool patchutils bc zlib1g-dev libexpat-dev
|
||||
sudo mkdir -p /usr/local/riscv/
|
||||
chmod 777 /usr/local/riscv/
|
||||
\end{verbatim}
|
||||
|
||||
All other commands should be executed as a regular user. This will eliminate the
|
||||
possibility of clobbering system files that should not be touched when tinkering with
|
||||
the toolchain applicaitons.
|
||||
|
||||
To download, compile and ``install'' the toolchain:
|
||||
|
||||
\begin{verbatim}
|
||||
# riscv toolchain:
|
||||
#
|
||||
# https://riscv.org/software-tools/risc-v-gnu-compiler-toolchain/
|
||||
|
||||
git clone --recursive https://github.com/riscv/riscv-gnu-toolchain
|
||||
cd riscv-gnu-toolchain
|
||||
./configure --prefix=/usr/local/riscv --with-arch=rv32im --with-abi=ilp32
|
||||
make
|
||||
make install
|
||||
\end{verbatim}
|
||||
|
||||
Need to discuss augmenting the PATH environment variable.
|
||||
|
||||
Discuss the choice of ilp32 as well as what the other variations would do.
|
||||
|
||||
Discuss rv32im and note that the details are found in \autoref{chapter:RV32}.
|
||||
|
||||
Disciuss installing and using one of the RISC-V simulators
|
||||
here.
|
||||
|
||||
Describe the pre-processor, compiler, assemler and linker.
|
||||
|
||||
Source, object, and binary files
|
||||
|
||||
Assembly syntax (label: mnemonic op1, op2, op3 \# comment).
|
||||
|
||||
text, data, bss, stack
|
||||
|
||||
Labels and scope.
|
||||
|
||||
Forward \& backward references to throw--away labels.
|
||||
|
||||
The entry address of an application.
|
||||
|
||||
.s file contain assembler code.
|
||||
.S (or .sx) files contain assembler code that must be preprocessed.~\cite[p.~29]{gcc:2017}
|
||||
|
||||
Pre-processing conditional assembly using \#if.
|
||||
|
||||
Building with \verb@-mabi=ilp32 -march=rv32i -mno-fdiv -mno-div@ to match
|
||||
the config options on the toolchain.
|
||||
|
||||
Linker scripts.
|
||||
|
||||
Makefiles
|
||||
|
||||
objdump
|
||||
|
||||
nm
|
||||
|
||||
hexdump -C
|
||||
Loading…
x
Reference in New Issue
Block a user