feat(course): bo prototype
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circuit/25-1/dz/24.11.pdf
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circuit/25-1/dz/24.11.pdf
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BIN
circuit/25-2/course_project/img/bo-cs1.png
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|
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circuit/25-2/course_project/img/bo-cs2.png
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circuit/25-2/course_project/img/bo-cs2.png
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|
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circuit/25-2/course_project/img/bo-cs3.png
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circuit/25-2/course_project/img/bo-cs3.png
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|
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circuit/25-2/course_project/img/bo-ra.png
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circuit/25-2/course_project/img/bo-ra.png
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|
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circuit/25-2/course_project/img/bo-rb.png
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circuit/25-2/course_project/img/bo-rb.png
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|
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circuit/25-2/course_project/img/bo-rpr.png
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|
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circuit/25-2/course_project/img/bo-rr.png
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circuit/25-2/course_project/img/bo-rr.png
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|
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circuit/25-2/course_project/img/bo-scheme.png
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circuit/25-2/course_project/img/bo-sm.png
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|
After Width: | Height: | Size: 12 KiB |
@ -148,7 +148,7 @@ $$[A]_{\text{п}} = a_3, a_2 a_1 a_0$$
|
||||
$b_0 = 1$ & & 0 & 1 & 1 & 1 & & & & \makecell[l]{RA} \\ \hline
|
||||
& 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & \makecell[l]{RR} \\
|
||||
& 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & \makecell[l]{RR >> 1} \\
|
||||
$b_1 = 0$ & \multicolumn{8}{c}{\text{пропуск такта суммирования}} & \\ \hline
|
||||
$b_1 = 0$ & \multicolumn{9}{l}{\text{пропуск такта суммирования}} \\ \hline
|
||||
& 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & \makecell[l]{RR} \\
|
||||
& 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & \makecell[l]{RR >> 1} \\
|
||||
$b_2 = 1$ & & 0 & 1 & 1 & 1 & & & & \makecell[l]{RA} \\ \hline
|
||||
@ -222,8 +222,12 @@ $$[A]_{\text{п}} = a_3, a_2 a_1 a_0$$
|
||||
Обознач & Назначение УМНОЖЕНИЕ & ПРОВЕРКА БИТА \\ \hline
|
||||
RA & Регистр 1-го операнда, 4 разряда, множимое, параллельная загрузка, хранение & позиция бита, параллельная загрузка \\ \hline
|
||||
RB & Регистр 2-го операнда, 4 разряда, множитель, параллельная загрузка, хранение & регистр данных, параллельная загрузка \\ \hline
|
||||
RR & Регистр результата, 8 разрядов, параллельная загрузка, хранение, сдвиг вправо на 1 разряд & новое значение регистра RB, 4 разряда, параллельная загрузка, хранение \\ \hline
|
||||
RR & Регистр результата, 8 разрядов, параллельная загрузка, хранение, сдвиг вправо на 1 разряд & новое значение регистра RB, 4 старших разряда, параллельная загрузка, хранение \\ \hline
|
||||
RPR & & Регистр флага CF, 1 разряд, параллельная загрузка, хранение \\ \hline
|
||||
КС1 & Выбор множимого: RB или RR[6:3]. Формирование сигнала F0 для МУУ & \\ \hline
|
||||
КС2 & Формирование знака для КС3 & Новое значение RB с установленным битом для КС3. Формирование RPR \\ \hline
|
||||
КС3 & Загрузка результата суммирования в RR[6:3] или знака в RR[7] & Загрузка нового значения RB с установленным битом в RR[6:3] \\ \hline
|
||||
SM & 4-разрядный сумматор. Пропуск такта & \\ \hline
|
||||
& &
|
||||
\end{tabular}
|
||||
\caption{Элементы функциональной схемы}
|
||||
@ -231,4 +235,186 @@ $$[A]_{\text{п}} = a_3, a_2 a_1 a_0$$
|
||||
\end{minipage}
|
||||
\end{figure}
|
||||
|
||||
\newpage
|
||||
\subsection{Проектирование логических элементов блока операций}
|
||||
\subsubsection{Регистр первого операнда RA}
|
||||
|
||||
Данный регистр является четырёхразрядным регистром хранения. Наиболее подходящим для реализации функций регистра RA является регистр FD4CE
|
||||
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
Таблица управляющих сигналов RA
|
||||
\begin{tabular}{|c|c|}
|
||||
\hline
|
||||
Y0 & Назначение \\ \hline
|
||||
0 & Хранение \\ \hline
|
||||
1 & Загрузка \\ \hline
|
||||
\end{tabular}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.69\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.3\textwidth]{bo-ra}
|
||||
\caption{Логическая схема RA}
|
||||
\label{bo-ra}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\subsubsection{Регистр второго операнда RB}
|
||||
|
||||
Данный регистр является четырёхразрядным регистром хранения. Наиболее подходящим для реализации функций регистра RB является регистр FD4CE
|
||||
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
Таблица управляющих сигналов RB
|
||||
\begin{tabular}{|c|c|}
|
||||
\hline
|
||||
Y0 & Назначение \\ \hline
|
||||
0 & Хранение \\ \hline
|
||||
1 & Загрузка \\ \hline
|
||||
\end{tabular}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.69\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.3\textwidth]{bo-rb}
|
||||
\caption{Логическая схема RB}
|
||||
\label{bo-rb}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\subsubsection{Регистр результата RR}
|
||||
|
||||
Данный регистр является 8-разрядным регистром с логическим сдвигом вправо на 1 разряд, хранением, параллельной загрузкой. Наиболее подходящим для реализации функции регистра RR является регистр SR8CLE
|
||||
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
Таблица управляющих сигналов RR
|
||||
\begin{tabular}{|c|c|c|}
|
||||
\hline
|
||||
Y5 & Y4 & Назначение \\ \hline
|
||||
0 & 0 & Хранение \\ \hline
|
||||
0 & 1 & Загрузка \\ \hline
|
||||
1 & 0 & SHR \\ \hline
|
||||
\end{tabular}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.69\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.8\textwidth]{bo-rr}
|
||||
\caption{Логическая схема RR}
|
||||
\label{bo-rr}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\subsubsection{Регистр признака RPR}
|
||||
|
||||
Данный регистр является 1-разрядным с хранением и загрузкой. Наиболее подходящим для реализации функции регистра RPR является
|
||||
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
Таблица управляющих сигналов RPR
|
||||
\begin{tabular}{|c|c|}
|
||||
\hline
|
||||
Y7 & Назначение \\ \hline
|
||||
0 & Хранение \\ \hline
|
||||
1 & Загрузка \\ \hline
|
||||
\end{tabular}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.69\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.3\textwidth]{bo-rpr}
|
||||
\caption{Логическая схема RPR}
|
||||
\label{bo-rpr}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\subsubsection{Комбинационная схема КC1}
|
||||
|
||||
С помощью комбинационной схемы КС1 осуществляется выбор множимого из RB или RR[6:3], а также формируется сигнал F0 для МУУ
|
||||
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
Таблица управляющих сигналов КС1
|
||||
\begin{tabular}{|c|c|}
|
||||
\hline
|
||||
Y6 & Назначение \\ \hline
|
||||
0 & Выбор RB \\ \hline
|
||||
1 & Выбор RR[6:3] \\ \hline
|
||||
\end{tabular}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.69\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.8\textwidth]{bo-cs1}
|
||||
\caption{Логическая схема КС1}
|
||||
\label{bo-cs1}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\newpage
|
||||
\subsubsection{Комбинационная схема КC2}
|
||||
|
||||
С помощью комбинационной схемы КС2 осуществляется формирование знака для операции умножени, формирование нового значения RB с установленным битом и формирование флага CF для операции установки бита
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.6\textwidth]{bo-cs2}
|
||||
\caption{Логическая схема КС2}
|
||||
\label{bo-cs2}
|
||||
\end{figure}
|
||||
|
||||
\newpage
|
||||
\subsubsection{Комбинационная схема КC3}
|
||||
|
||||
С помощью комбинационной схемы КС3 осуществляется загрузка промежуточной суммы в RR[6:3] и знака в RR[7] в операции умножения, нового значения RB с установленными битами в RR[6:3] в операции установки бита
|
||||
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
Таблица управляющих сигналов КС3
|
||||
\begin{tabular}{|c|c|c|}
|
||||
\hline
|
||||
Y3 & Y2 & Назначение \\ \hline
|
||||
0 & 0 & сумма в RR[6:3] \\ \hline
|
||||
0 & 1 & знак RR[7] \\ \hline
|
||||
1 & 0 & значение RB в RR[6:3] \\ \hline
|
||||
\end{tabular}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.69\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.8\textwidth]{bo-cs3}
|
||||
\caption{Логическая схема КС3}
|
||||
\label{bo-cs3}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\newpage
|
||||
\subsubsection{Сумматор SM}
|
||||
|
||||
4-разрядный, старшие разряды множимого и множителя, carry input установлены в 0
|
||||
|
||||
\begin{minipage}{\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=0.6\textwidth]{bo-sm}
|
||||
\caption{Логическая схема SM}
|
||||
\label{bo-sm}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\newpage
|
||||
\subsection{Логическая схема блока операций}
|
||||
|
||||
\begin{minipage}{\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{bo-scheme}
|
||||
\caption{Логическая схема БО}
|
||||
\label{bo-scheme}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
@ -1,386 +0,0 @@
|
||||
{
|
||||
"cells": [
|
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{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from numba import cuda\n",
|
||||
"from numba import vectorize\n",
|
||||
"import numpy as np"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"U8_MAX = 0xFFFFFFFFFFFFFFFF\n",
|
||||
"U32_MAX = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF\n",
|
||||
"\n",
|
||||
"def bignum_to_u32(num):\n",
|
||||
" res = np.empty(4, np.uint64)\n",
|
||||
" res[0] = num & U8_MAX\n",
|
||||
" res[1] = (num >> 64) & U8_MAX\n",
|
||||
" res[2] = (num >> 128) & U8_MAX\n",
|
||||
" res[3] = (num >> 192) & U8_MAX\n",
|
||||
" return res\n",
|
||||
"\n",
|
||||
"def u32_to_bignum(arr):\n",
|
||||
" return int(arr[3]) << 192 | \\\n",
|
||||
" int(arr[2]) << 128 | \\\n",
|
||||
" int(arr[1]) << 64 | \\\n",
|
||||
" int(arr[0]) \n",
|
||||
"\n",
|
||||
"Gx = bignum_to_u32(55066263022277343669578718895168534326250603453777594175500187360389116729240)\n",
|
||||
"Gy = bignum_to_u32(32670510020758816978083085130507043184471273380659243275938904335757337482424)\n",
|
||||
"p = bignum_to_u32(2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 67,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"@cuda.jit('void(u8[:], u8[:], u8[:])', device=True)\n",
|
||||
"def add_u32(a, b, out):\n",
|
||||
" carry = np.uint64(0)\n",
|
||||
" for i in range(4):\n",
|
||||
" ai = a[i]\n",
|
||||
" bi = b[i]\n",
|
||||
" outi = ai + bi\n",
|
||||
" out[i] = outi + carry\n",
|
||||
" carry = outi < ai or outi == U8_MAX and carry\n",
|
||||
"\n",
|
||||
"@cuda.jit('void(u8[:], u8[:], u8[:])', device=True)\n",
|
||||
"def sub_u32(a, b, out):\n",
|
||||
" borrow = np.uint64(0)\n",
|
||||
" for i in range(4):\n",
|
||||
" ai = a[i]\n",
|
||||
" bi = b[i]\n",
|
||||
" outi = ai - bi\n",
|
||||
" out[i] = outi - borrow\n",
|
||||
" borrow = ai < bi or outi == 0 and borrow\n",
|
||||
"\n",
|
||||
"@cuda.jit('void(u8[:], u8)', device=True)\n",
|
||||
"def shr_u32(out, bits):\n",
|
||||
" bits = np.uint64(bits)\n",
|
||||
" lost = np.uint64(0)\n",
|
||||
" for i in range(4):\n",
|
||||
" outi = out[3 - i]\n",
|
||||
" out[3 - i] = (outi >> bits) | lost\n",
|
||||
" lost = outi << (np.uint64(64) - bits)\n",
|
||||
" \n",
|
||||
"@cuda.jit('void(u8[:], u8[:], u8[:])', device=True)\n",
|
||||
"def mul_u32(a, b, out):\n",
|
||||
" for i in range(4):\n",
|
||||
" out[i] = 0\n",
|
||||
" \n",
|
||||
" for i in range(255, -1, -1):\n",
|
||||
" quad_pos = np.uint64(i // 64)\n",
|
||||
" bit_pos = np.uint64(i % 64)\n",
|
||||
" bit = b[quad_pos] >> bit_pos\n",
|
||||
" if bit % 2 == 1:\n",
|
||||
" add_u32(a, out, out)\n",
|
||||
" \n",
|
||||
" shr_u32(out, 1)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 78,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"failed on shr 0b0 0b110000000110100101\n",
|
||||
"failed on shr 0b11111111111111111111111111111111111111111111111111111111111111111111111111111111111111 0b1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111011111100100000111011\n",
|
||||
"failed on shr 0b11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 0b111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111010100000101111100111110110011110100011011000010010\n",
|
||||
"failed on shr 0b111111111111111111111111111111111111111111111111111 0b111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110101100000010111101100110100111110011000000011010\n",
|
||||
"failed on shr 0b1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 0b11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111101011110\n",
|
||||
"failed on shr 0b1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 0b11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100010100000001110001001100001111\n",
|
||||
"failed on shr 0b0 0b11110100110111011010100011011110011010000010011101010\n",
|
||||
"failed on shr 0b0 0b10000010101011110110111000000100100010011110111111011101111\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"/home/appuser/Miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:7: RuntimeWarning: overflow encountered in ulong_scalars\n",
|
||||
" import sys\n",
|
||||
"/home/appuser/Miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:28: RuntimeWarning: overflow encountered in ulong_scalars\n",
|
||||
"/home/appuser/Miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:17: RuntimeWarning: overflow encountered in ulong_scalars\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"from random import randint\n",
|
||||
"\n",
|
||||
"@cuda.jit('void(u8[:], u8[:], u8[:])')\n",
|
||||
"def mul_u32_ker(a, b, out):\n",
|
||||
" mul_u32(a, b, out)\n",
|
||||
"\n",
|
||||
"for i in range(10):\n",
|
||||
" a = randint(0, U8_MAX)\n",
|
||||
" b = randint(0, U8_MAX)\n",
|
||||
" bit = randint(0, 256)\n",
|
||||
" a32 = bignum_to_u32(a)\n",
|
||||
" b32 = bignum_to_u32(b)\n",
|
||||
" out32 = np.empty(4, np.uint64)\n",
|
||||
" \n",
|
||||
" add_u32.py_func(a32, b32, out32)\n",
|
||||
" out = (a + b) % (U32_MAX + 1)\n",
|
||||
" if out != u32_to_bignum(out32):\n",
|
||||
" print(\"failed on add\")\n",
|
||||
" \n",
|
||||
" sub_u32.py_func(a32, b32, out32)\n",
|
||||
" out = (a - b) % (U32_MAX + 1)\n",
|
||||
" if out != u32_to_bignum(out32):\n",
|
||||
" print(\"failed on sub\")\n",
|
||||
" \n",
|
||||
" shr_u32.py_func(out32, bit)\n",
|
||||
" out >>= bit\n",
|
||||
" if out != u32_to_bignum(out32):\n",
|
||||
" print(\"failed on shr\", bin(out), bin(u32_to_bignum(out32)))\n",
|
||||
" \n",
|
||||
" #mul_u32_ker(a32, b32, out32)\n",
|
||||
" #out = (a * b) % (U32_MAX + 1)\n",
|
||||
" #if out != u32_to_bignum(out32):\n",
|
||||
" # print(\"failed on mul\", a, b, u32_to_bignum(out32))\n",
|
||||
" "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 43,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def cmp_ge256(a, b):\n",
|
||||
" # return True if a >= b\n",
|
||||
" # compare from most significant word\n",
|
||||
" for i in range(3, -1, -1):\n",
|
||||
" ai = a[i]\n",
|
||||
" bi = b[i]\n",
|
||||
" if ai > bi:\n",
|
||||
" return True\n",
|
||||
" elif ai < bi:\n",
|
||||
" return False\n",
|
||||
" return True # equal\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def sub256(a, b, out):\n",
|
||||
" # assume a >= b, perform out = a - b\n",
|
||||
" borrow = 0\n",
|
||||
" for i in range(4):\n",
|
||||
" ai = a[i]\n",
|
||||
" bi = b[i]\n",
|
||||
" # compute ai - bi - borrow\n",
|
||||
" tmp = ai - bi\n",
|
||||
" borrow1 = 1 if tmp > ai else 0 # tmp < 0 -> wrapping -> tmp > ai\n",
|
||||
" tmp2 = tmp - borrow\n",
|
||||
" borrow2 = 1 if tmp2 > tmp else 0\n",
|
||||
" out[i] = tmp2\n",
|
||||
" borrow = 1 if (borrow1 or borrow2) else 0\n",
|
||||
" # if borrow != 0 then a < b (but we assumed a>=b)\n",
|
||||
"\n",
|
||||
"# 64x64 -> 128 using 32-bit split\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def mul64wide(x, y):\n",
|
||||
" MASK32 = (1 << 32) - 1\n",
|
||||
" x_lo = x & MASK32\n",
|
||||
" x_hi = x >> 32\n",
|
||||
" y_lo = y & MASK32\n",
|
||||
" y_hi = y >> 32\n",
|
||||
"\n",
|
||||
" p0 = x_lo * y_lo # <= 64 bits\n",
|
||||
" p1 = x_lo * y_hi # <= 64 bits\n",
|
||||
" p2 = x_hi * y_lo # <= 64 bits\n",
|
||||
" p3 = x_hi * y_hi # <= 64 bits\n",
|
||||
"\n",
|
||||
" # combine: p0 + (p1<<32) + (p2<<32) + (p3<<64)\n",
|
||||
" mid = p1 + p2\n",
|
||||
" carry_mid = 0\n",
|
||||
" # lower 64:\n",
|
||||
" low = (p0 + ((mid & MASK32) << 32)) & ((1 << 64) - 1)\n",
|
||||
" # carry from lower additions\n",
|
||||
" if (p0 + ((mid & MASK32) << 32)) >> 64:\n",
|
||||
" carry_mid = 1\n",
|
||||
" high = p3 + (mid >> 32) + carry_mid\n",
|
||||
" # low, high are 64-bit parts of 128-bit product\n",
|
||||
" return low & ((1 << 64) - 1), high & ((1 << 64) - 1)\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def mul256_full(a, b, out8):\n",
|
||||
" # out8 must be length 8 (little-endian) to hold full 512-bit product\n",
|
||||
" # Initialize\n",
|
||||
" for i in range(8):\n",
|
||||
" out8[i] = 0\n",
|
||||
"\n",
|
||||
" # schoolbook: for i in 0..3, j in 0..3\n",
|
||||
" temp = cuda.local.array(8, dtype=np.uint64) # local accumulator\n",
|
||||
" for i in range(8):\n",
|
||||
" temp[i] = 0\n",
|
||||
"\n",
|
||||
" for i in range(4):\n",
|
||||
" ai = a[i]\n",
|
||||
" for j in range(4):\n",
|
||||
" bj = b[j]\n",
|
||||
" lo, hi = mul64wide(ai, bj) # 128-bit product\n",
|
||||
" k = i + j\n",
|
||||
" # add lo to temp[k], handle carry\n",
|
||||
" s, c = add64_carry(temp[k], lo, 0)\n",
|
||||
" temp[k] = s\n",
|
||||
" # propagate carry to next word together with hi\n",
|
||||
" carry = hi + c\n",
|
||||
" t_idx = k + 1\n",
|
||||
" while carry != 0:\n",
|
||||
" s2, c2 = add64_carry(temp[t_idx], carry, 0)\n",
|
||||
" temp[t_idx] = s2\n",
|
||||
" # compute new carry (0/1) from addition\n",
|
||||
" carry = 1 if c2 else 0\n",
|
||||
" t_idx += 1\n",
|
||||
" # t_idx never exceeds 7 because i+j <= 6, plus propagation safe\n",
|
||||
" # copy to out8\n",
|
||||
" for i in range(8):\n",
|
||||
" out8[i] = temp[i]\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def mul256_lo(a, b, out4):\n",
|
||||
" # compute full product and keep lower 4 words\n",
|
||||
" out8 = cuda.local.array(8, dtype=np.uint64)\n",
|
||||
" mul256_full(a, b, out8)\n",
|
||||
" for i in range(4):\n",
|
||||
" out4[i] = out8[i]\n",
|
||||
"\n",
|
||||
"# --------------------\n",
|
||||
"# division: binary long division\n",
|
||||
"# --------------------\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def shl1_256_inplace(x):\n",
|
||||
" # x <<= 1 (inplace)\n",
|
||||
" carry = 0\n",
|
||||
" for i in range(4):\n",
|
||||
" new_carry = (x[i] >> 63) & 1\n",
|
||||
" x[i] = (x[i] << 1) & ((1 << 64) - 1)\n",
|
||||
" x[i] |= carry\n",
|
||||
" carry = new_carry\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def shr1_256_getbit(x):\n",
|
||||
" # shift right by 1, return LSB (bit 0) before shift\n",
|
||||
" lsb = x[0] & 1\n",
|
||||
" carry = 0\n",
|
||||
" for i in range(3, -1, -1):\n",
|
||||
" new_carry = x[i] & 1\n",
|
||||
" x[i] = (x[i] >> 1) | (carry << 63)\n",
|
||||
" carry = new_carry\n",
|
||||
" return lsb\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def get_bit256(x, idx):\n",
|
||||
" # idx: 0..255, 0 = least significant bit\n",
|
||||
" w = idx // 64\n",
|
||||
" b = idx % 64\n",
|
||||
" return (x[w] >> b) & 1\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def set_bit256(x, idx):\n",
|
||||
" w = idx // 64\n",
|
||||
" b = idx % 64\n",
|
||||
" x[w] |= (1 << b)\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def copy256(src, dst):\n",
|
||||
" for i in range(4):\n",
|
||||
" dst[i] = src[i]\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def zero256(x):\n",
|
||||
" for i in range(4):\n",
|
||||
" x[i] = 0\n",
|
||||
"\n",
|
||||
"@cuda.jit(device=True)\n",
|
||||
"def divmod256(dividend, divisor, q, r):\n",
|
||||
" # Binary long division (restoring), bit-by-bit from MSB..LSB\n",
|
||||
" # q,r are output arrays (4 words). dividend/divisor are input arrays.\n",
|
||||
" # edge cases\n",
|
||||
" zero = True\n",
|
||||
" for i in range(4):\n",
|
||||
" if divisor[i] != 0:\n",
|
||||
" zero = False\n",
|
||||
" break\n",
|
||||
" if zero:\n",
|
||||
" # division by zero — define q=0,r=dividend (user must avoid)\n",
|
||||
" for i in range(4):\n",
|
||||
" q[i] = 0\n",
|
||||
" r[i] = dividend[i]\n",
|
||||
" return\n",
|
||||
"\n",
|
||||
" zero256(q)\n",
|
||||
" zero256(r)\n",
|
||||
" # iterate bits from highest (255) down to 0\n",
|
||||
" for i in range(255, -1, -1):\n",
|
||||
" # left shift r by 1\n",
|
||||
" shl1_256_inplace(r)\n",
|
||||
" # bring in bit i of dividend\n",
|
||||
" if get_bit256(dividend, i):\n",
|
||||
" r[0] |= 1 # set lsb\n",
|
||||
" # if r >= divisor then r -= divisor and set q[i] = 1\n",
|
||||
" if cmp_ge256(r, divisor):\n",
|
||||
" # r = r - divisor\n",
|
||||
" tmp = cuda.local.array(4, dtype=np.uint64)\n",
|
||||
" sub256(r, divisor, tmp)\n",
|
||||
" for k in range(4):\n",
|
||||
" r[k] = tmp[k]\n",
|
||||
" # set q bit i\n",
|
||||
" w = i // 64\n",
|
||||
" b = i % 64\n",
|
||||
" q[w] |= (1 << b)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.6.10"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2
|
||||
}
|
||||
Reference in New Issue
Block a user