conferences/fosdem2024/fosdem2024_bigint/fosdem2024_bigint.tex

   1 % Copyright 2024 Jacob Lifshay
   2
   3 \documentclass{beamer}
   4 \usepackage{beamerthemesplit}
   5 \usetheme{default}
   6 \usepackage[english]{babel}
   7 \usepackage{tikz}
   8 \usepackage{minted}
   9 \usemintedstyle{monokai}
  10 \definecolor{codebg}{rgb}{0.1,0.09,0.08}
  11 \newminted[codeenv]{python3}{escapeinside=@@,fontsize=\small,bgcolor=codebg}
  12 \newmintinline[codeinline]{python3}{escapeinside=@@,fontsize=\small,bgcolor=codebg}
  13
  14 \title[Fast Big-Integer Arithmetic on SVP64 ...]{
  15     Fast Big-Integer Arithmetic on SVP64 at up to 256-bits/cycle and beyond
  16 }
  17
  18 \author{Jacob R. Lifshay}
  19
  20 \date{FOSDEM 2024}
  21
  22 \logo{\includegraphics[height=0.5cm]{../../../images/lsoclogo.png}}
  23
  24 \begin{document}
  25
  26 \begin{frame}
  27     \titlepage
  28 \end{frame}
  29
  30 \begin{frame}[fragile]
  31     \frametitle{What is SVP64?}
  32     \begin{itemize}
  33         \item Vectorization Extension for PowerISA developed by \href{https://libre-soc.org}{Libre-SOC}
  34         \pause
  35         \item Basically, a way to modify nearly any PowerISA instruction to run it in a HW loop.
  36         \pause \\
  37         \medskip
  38         Simple Example:
  39         \begin{codeenv}
  40 setvl 0, 0, 3, 0, 1, 1 # makes stuff run 3 times
  41 sv.add *r3, *r15, r12  # adds 3 times
  42 @\pause@
  43 # expands to:
  44 add r3, r15, r12  # no * means r12 doesn't increment
  45 add r4, r16, r12  # * means r3 and r15 increment
  46 add r5, r17, r12
  47         \end{codeenv}
  48     \end{itemize}
  49 \end{frame}
  50
  51 \begin{frame}[fragile]
  52     \frametitle{Big-Integer Addition on SVP64}
  53     How can we use SVP64 to add 256-bit integers?
  54     \pause
  55     \begin{codeenv}
  56 setvl 0, 0, 4, 0, 1, 1 # makes stuff run 4 times
  57 addic r0, r0, 0  # clear CA (carry flag)
  58 sv.adde *r4, *r4, *r8  # carry-propagating add
  59 @\pause@
  60 # expands to:
  61 addic r0, r0, 0  # clear CA (carry flag)
  62 adde r4, r4, r8
  63 adde r5, r5, r9
  64 adde r6, r6, r10
  65 adde r7, r7, r11
  66     \end{codeenv}
  67 \end{frame}
  68
  69 \begin{frame}[fragile]
  70     \frametitle{Big-Integer Addition on SVP64}
  71     How can we use SVP64 to add 256-bit integers?
  72     \medbreak
  73     \input{sv.adde.dia-tex}
  74 \end{frame}
  75
  76 \begin{frame}
  77     \frametitle{Big-Integer Addition on an example CPU}
  78     Disclaimer:
  79     SVP64 is designed for everything from tiny to big and fast CPUs, this example only shows a hypothetical big and fast CPU design
  80 \end{frame}
  81
  82 \begin{frame}
  83     \frametitle{Big-Integer Addition on an example CPU}
  84     \input{bigint-add-pipe.dia-tex}
  85 \end{frame}
  86
  87 \begin{frame}[fragile]
  88     \frametitle{Big-Integer Multiply on SVP64}
  89     How can we use SVP64 to Multiply a 64-bit by a 256-bit integer?
  90     \pause
  91     \begin{itemize}
  92         \item new instruction: \codeinline{maddedu RT, RA, RB, RC}
  93         \pause
  94         \item $64 \times 64 + 64 \rightarrow 128$-bit Multiply-Add
  95         \pause
  96         \item Semantics as used in this presentation (somewhat simplified):
  97         \begin{codeenv}
  98 result = (RA * RB) + RC
  99 RT = LSB_HALF(result)
 100 RC = MSB_HALF(result)
 101         \end{codeenv}
 102     \end{itemize}
 103 \end{frame}
 104
 105 \begin{frame}[fragile]
 106     \frametitle{Big-Integer Multiply on SVP64}
 107     How can we use SVP64 to Multiply a 64-bit by a 256-bit integer?
 108     \pause
 109     \begin{codeenv}
 110 # 64-bit input in r3
 111 # 256-bit input in r20-23
 112 # 320-bit output in r4-8
 113 setvl 0, 0, 4, 0, 1, 1 # makes stuff run 4 times
 114 li r8, 0  # clear carry register
 115 sv.maddedu *r4, r3, *r20, r8  # carrying multiply
 116 @\pause@
 117 # expands to:
 118 li r8, 0
 119 maddedu r4, r3, r20, r8
 120 maddedu r5, r3, r21, r8
 121 maddedu r6, r3, r22, r8
 122 maddedu r7, r3, r23, r8
 123     \end{codeenv}
 124 \end{frame}
 125
 126 \begin{frame}
 127 \end{frame}
 128
 129 \end{document}