From dbe133992e504c3036a0b16e5e696417ebcbb085 Mon Sep 17 00:00:00 2001
From: pattaraporn <pattaraporn.in.59@ubu.ac.th>
Date: Thu, 8 Feb 2018 12:31:37 +0700
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---
week01/hello.py | 1 +
week02/hellomodule.py | 2 +
...merics and Error Analysis-checkpoint.ipynb | 482 ++++++++++++++++++
...apter 03 Numerics and Error Analysis.ipynb | 480 +++++++++++++++++
week03/assignment.py | 12 +
week04/__pycache__/assignment.cpython-36.pyc | Bin 0 -> 801 bytes
week04/assignment.py | 8 +
7 files changed, 985 insertions(+)
create mode 100644 week01/hello.py
create mode 100644 week02/hellomodule.py
create mode 100644 week03/.ipynb_checkpoints/Chapter 03 Numerics and Error Analysis-checkpoint.ipynb
create mode 100644 week03/Chapter 03 Numerics and Error Analysis.ipynb
create mode 100644 week03/assignment.py
create mode 100644 week04/__pycache__/assignment.cpython-36.pyc
create mode 100644 week04/assignment.py
diff --git a/week01/hello.py b/week01/hello.py
new file mode 100644
index 0000000..75d9766
--- /dev/null
+++ b/week01/hello.py
@@ -0,0 +1 @@
+print('hello world')
diff --git a/week02/hellomodule.py b/week02/hellomodule.py
new file mode 100644
index 0000000..f7c21b6
--- /dev/null
+++ b/week02/hellomodule.py
@@ -0,0 +1,2 @@
+# cookiecutter .....
+print("we' ve done it.")
diff --git a/week03/.ipynb_checkpoints/Chapter 03 Numerics and Error Analysis-checkpoint.ipynb b/week03/.ipynb_checkpoints/Chapter 03 Numerics and Error Analysis-checkpoint.ipynb
new file mode 100644
index 0000000..121028a
--- /dev/null
+++ b/week03/.ipynb_checkpoints/Chapter 03 Numerics and Error Analysis-checkpoint.ipynb
@@ -0,0 +1,482 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธเธ—เธ—เธตเน 1 เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธฒเธฃเธงเธดเน€เธเธฃเธฒเธฐเธซเนเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธ\n",
+ "\n",
+ "> Mathematically correct programming bug is **hard** to spot.\n",
+ "\n",
+ "> เธชเธกเธเธฒเธฃเธ–เธนเธเนเธ•เน...เนเธเธฃเนเธเธฃเธกเธเธดเธ”\n",
+ "\n",
+ ">> Paulgramming - 2017\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธเนเธเนเธเธฃเนเธเธฃเธก\n",
+ "## C++\n",
+ "\n",
+ "```c++\n",
+ "#include <iostream>\n",
+ "using namespace std;\n",
+ "main() {\n",
+ " float x = 1.0; \n",
+ " float y = x / 3.0;\n",
+ " cout << ((x == y * 3.0)?\"\": \"Not\") << \" Equal\" << endl;\n",
+ "}\n",
+ "```\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "# เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธเนเธเนเธเธฃเนเธเธฃเธก\n",
+ "## Java\n",
+ "\n",
+ "```java\n",
+ "public class Test {\n",
+ " public static void main(String[] a) {\n",
+ " float x = 1.0;\n",
+ " float y = x / 3.0;\n",
+ " System.out.println( ((x == y * 3.0)?\"\": \"Not\") + \" Equal\" );\n",
+ " }\n",
+ "}\n",
+ "```\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "# เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธเนเธเนเธเธฃเนเธเธฃเธก\n",
+ "## Python\n",
+ "\n",
+ "```python\n",
+ "x = 1.0\n",
+ "y = x / 3.0\n",
+ "print(\"Equal\" if x == y*3.0 else \"Not Equal\")\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# เธกเธตเธซเธฅเธฒเธขเธ•เธฑเธงเน€เธฅเธเธ—เธตเนเนเธกเน\n",
+ "x = 1.0\n",
+ "y = x / 3.0\n",
+ "#print(\"Equal\" if x == y*3.0 else \"Not Equal\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธกเธตเธซเธฅเธฒเธขเธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธเธญเธกเน€เธเนเธเธเนเธฒเนเนเธกเนเนเธ”เน\n",
+ "\n",
+ "* เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธเธญเธกเธเธดเธงเน€เธ•เธญเธฃเนเธ•เนเธญเธเธเธฃเธฐเธกเธฒเธ“เธเธฒเธฃ (Inexact numbers)\n",
+ " * เธเนเธฒเธญเธ•เธฃเธฃเธเธขเธฐ (irrational numbers) $\\pi, \\e, ...$\n",
+ " * เธเนเธฒเธ•เธฃเธฃเธเธขเธฐ (rational numbers) เธ—เธตเนเนเธกเนเธชเธฒเธกเธฒเธฃเธ–เนเธเธฅเธเน€เธเนเธเน€เธฅเธเธเธฒเธเธชเธญเธเนเธ”เน\n",
+ "```python\n",
+ "0.1 + 0.2 == 0.3\n",
+ "```\n",
+ "\n",
+ "* เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธเธญเธกเธเธดเธงเน€เธ•เธญเธฃเนเธชเธฒเธกเธฒเธฃเธ–เน€เธเนเธเธเนเธฒเนเธ”เนเธ•เธฃเธ (Exact numbers)\n",
+ "> เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธชเธฒเธกเธฒเธฃเธ–เนเธเธฅเธเนเธซเนเน€เธเนเธเน€เธฅเธเธเธฒเธเธชเธญเธเนเธ”เน"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Floating-Point Binary\n",
+ "\n",
+ "> เธ•เธฑเธงเน€เธฅเธ(number) เน€เธเธตเธขเธเนเธ—เธเธ”เนเธงเธขเธชเธฒเธขเธเธญเธเน€เธฅเธเน€เธ”เธตเนเธขเธง(digit) เนเธ”เธขเธเธณเธเธงเธเธเธญเธเน€เธฅเธเน€เธ”เธตเนเธขเธง เธเธถเนเธเธญเธขเธนเนเธเธฑเธ เน€เธฅเธเธเธฒเธ(base)\n",
+ "\n",
+ "เนเธเธฃเธฐเธเธเธเธณเธเธงเธเธเธฑเธเธเธญเธเธเธเน€เธฃเธฒเธเธฐเน€เธเนเธเน€เธฅเธเธเธฒเธ 10 เนเธ”เธขเธกเธต digit เธ—เธตเนเนเธเนเนเธ”เนเนเธ”เนเนเธเน 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\n",
+ "เธขเธเธ•เธฑเธงเธญเธขเนเธฒเธเธ•เธฑเธงเน€เธฅเธเนเธเน€เธฅเธเธเธฒเธ 10 เน€เธเนเธ 128 77 12100 เน€เธเนเธเธ•เนเธ\n",
+ "\n",
+ "เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเนเธเนเนเธเธเธญเธกเธเธดเธงเน€เธ•เธญเธฃเนเธเธฐเน€เธเนเธเน€เธฅเธเธเธฒเธ 2 เนเธ”เธขเธกเธต digit เธ—เธตเนเนเธเนเนเธ”เน เนเธ”เนเนเธเน 0 เนเธฅเธฐ 1 \n",
+ "เธขเธเธ•เธฑเธงเธญเธขเนเธฒเธเธ•เธฑเธงเน€เธฅเธเนเธเน€เธฅเธเธเธฒเธ 2 เน€เธเนเธ 1, 101, 1101 เน€เธเนเธเธ•เนเธ"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Terminology\n",
+ "** Bit **\n",
+ ": 0 or 1\n",
+ "\n",
+ "** Byte ** \n",
+ ": 8 bits\n",
+ "\n",
+ "** Real **\n",
+ ": 4 bytes **single precision**\n",
+ ": 8 bytes **double precision**\n",
+ "\n",
+ "** Integer **\n",
+ ": 1, 2, 4, or 8 byte signed\n",
+ ": 1, 2, 4, or 8 byte unsigned\n",
+ "\n",
+ "> เธเธถเนเธเธญเธขเธนเนเธเธฑเธเธ เธฒเธฉเธฒเนเธเธฃเนเธเธฃเธกเธงเนเธฒเธเธฐเนเธเนเธชเธฒเธขเธ—เธตเนเธกเธตเธเธงเธฒเธกเธขเธฒเธงเน€เธ—เนเธฒเนเธซเธฃเน 8, 16, 32 เธซเธฃเธทเธญ 64 เน€เธเนเธเธ•เนเธ\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธเนเธญเธ•เธเธฅเธ\n",
+ "\n",
+ "* เน€เธเธทเนเธญเธเนเธฒเธขเธ•เนเธญเธเธฒเธฃเธเธณเธเธงเธ“เน€เธฃเธฒเธเธฐเนเธเนเธชเธฒเธขเธ—เธตเนเธกเธตเธเธงเธฒเธกเธขเธฒเธง 8 เนเธฅเธฐเน€เธเธตเธขเธเนเธขเธเน€เธเนเธเธเธฅเธธเนเธกเธฅเธฐ 4 เน€เธเธทเนเธญเธเนเธฒเธขเธ•เนเธญเธเธฒเธฃเธเธณเธเธงเธ \n",
+ "\n",
+ "> เน€เธเนเธ 1 = 0000 0001\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Binary $\\rightarrow$ Integer\n",
+ "\n",
+ "| | | | | | | | |\n",
+ "|------|------|------|------|------|------|------|------|\n",
+ "| 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |\n",
+ "|$2^7$ |$2^6$ |$2^5$ |$2^4$ |$2^3$ |$2^2$ |$2^1$ |$2^0$ |\n",
+ "\n",
+ "$1\\times2^7 + 1\\times2^6 + 1\\times2^5 + 0\\times2^4 + 0\\times2^3 + 1\\times2^2 + 1\\times2^1 + 1\\times2^0$\n",
+ "\n",
+ "$1\\times 128+ 1\\times 64 + 1\\times 32 + 0\\times 16 + 0\\times 8 + 1\\times 4 + 1\\times 2 + 1 \\times 1$\n",
+ "\n",
+ "\n",
+ "$128 + 64 + 32 + 0 + 0 + 4 + 2 + 1$\n",
+ "\n",
+ "**Answer**\n",
+ "> $231$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เน€เธเธตเธขเธเนเธเธฃเนเธเธฃเธกเธ—เธ”เธชเธญเธ\n",
+ "\n",
+ "* เธเธณเธเธงเธ“เธซเธฒเธเธฅเธฅเธฑเธเธเน\n",
+ "```python\n",
+ "1*2**7 + 1*2**6 + 1*2**5 + 0*2**4 + 0*2**3 + 1*2**2 + 1*2**1 + 1*2**0\n",
+ "```\n",
+ "\n",
+ "* เธเธณเธชเธฑเนเธเนเธเธฅเธเน€เธฅเธเธเธฒเธเธ•เนเธฒเธเน\n",
+ "```python\n",
+ "int('11100111', 2) # เนเธเธฅเธ str '11100111' เธเธฒเธ 2 เน€เธเนเธ int\n",
+ "oct(35) # เนเธเธฅเธ 35 เธเธฒเธเธชเธดเธ เนเธซเนเน€เธเนเธเธเธฒเธ 8\n",
+ "hex(35) # เนเธเธฅเธ 35 เธเธฒเธเธชเธดเธ เนเธซเนเน€เธเนเธเธเธฒเธ 16\n",
+ "bin(35) # เนเธเธฅเธ 35 เธเธฒเธเธชเธดเธ เนเธซเนเน€เธเนเธเธเธฒเธ 2\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#int('11100111', 2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "#### Exercise\n",
+ "เธเธเนเธชเธ”เธเธเธฒเธฃเนเธเธฅเธเธ•เธฑเธงเน€เธฅเธเธเธฒเธเธชเธญเธเธ•เนเธญเนเธเธเธตเนเน€เธเนเธเธเธณเธเธงเธเน€เธ•เนเธก\n",
+ "* 10011001\n",
+ "* 00010011\n",
+ "* 00011111"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Binary $\\rightarrow$ Float\n",
+ "เธเธณเธซเธเธ”เธ•เธณเนเธซเธเนเธเธ—เธตเนเน€เธฅเธเธชเธญเธเธเธณเธฅเธฑเธเน€เธเนเธเธจเธนเธเธขเน (fix-point representation)\n",
+ "\n",
+ "| | | | | | | | |\n",
+ "|------|------|------|------|------|------|------|------|\n",
+ "| 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |\n",
+ "|$2^5$ |$2^4$ |$2^3$ |$2^2$ |$2^1$ |$2^0$ |$2^-1$ |$2^-2$ |\n",
+ "\n",
+ "$1\\times 2^5+1\\times 2^4+1\\times 2^3+0\\times 2^2+9\\times 2^1+1\\times 2^0+1\\times 2^{-1}+1\\times 2^{-2}$\n",
+ "\n",
+ "$1\\times2^5 + 1\\times2^4 + 1\\times2^3 +0\\times 2^2+0\\times2^1+1\\times 1+\\frac{1}{2}+\\frac{1}{4}$\n",
+ "\n",
+ "$32 + 16 + 8 + 0 + 0 + 1 + 0.5 + 0.25$\n",
+ "\n",
+ "**Answer**\n",
+ "> 57.75"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#1*2**5 + 1*2**4 + 1*2**3 + 0*2**2 + 0*2**1 + 1*2**0 + 1*2**(-1) + 1*2**(-2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "#### Binary Fixed-Point Arithmetic\n",
+ "| | | | | | | | | |\n",
+ "|------|------|------|------|------|------|------|------|------|\n",
+ "| 1 | 1 | 1 | ... | 0 | 0 | ... | 1 | 1 |\n",
+ "| sign ||$2^{m-1}$ |$2^{m-2}$ | ... |$2^0$ |$2^{-1}$ | ... |$2^{-n+1}$ |$2^{-n}$ |\n",
+ "\n",
+ "* Parameters: $m, n \\in Z$\n",
+ "* $m$ เธเธงเธฒเธกเธขเธฒเธงเธเธญเธเธชเธฒเธข(เธเธณเธเธงเธ bit) เธ—เธตเนเนเธเนเน€เธเนเธเธเธณเธเธงเธเน€เธ•เนเธก(integer portion)\n",
+ "* $n$ เธเธงเธฒเธกเธขเธฒเธงเธเธญเธเธชเธฒเธข(เธเธณเธเธงเธ bit) เธ—เธตเนเนเธเนเน€เธเนเธเธ•เธฑเธงเธซเธฒเธฃ(fractional portion)\n",
+ "* เธเธงเธฒเธกเธขเธฒเธงเธ—เธฑเนเธเธซเธกเธ”เธเธญเธเธชเธฒเธขเน€เธเนเธ $m+n+1$ เธฃเธงเธกเธเธฑเธ bit เธ—เธตเนเนเธเนเธเธญเธเน€เธเธฃเธทเนเธญเธเธซเธกเธฒเธข (+/-)\n",
+ "* เธเธงเธฒเธกเธฃเธนเนเน€เธเธดเนเธกเน€เธ•เธดเธก: [Fixed-Point Numbers](https://en.wikibooks.org/wiki/Floating_Point/Fixed-Point_Numbers)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Error in Binary Fixed-Point Arithmetic\n",
+ "\n",
+ "** เธชเธกเธกเธ•เธดเธงเนเธฒเธกเธตเนเธเน 2 bit เนเธซเนเนเธเน ** \n",
+ "\n",
+ "> $m = 1, n=1$ เนเธ”เธขเธ—เธตเนเนเธกเนเธเธดเธ” sign bit\n",
+ "\n",
+ "$0.1 \\times 0.1 = 0.01 \\approx 0.0$ \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Binary Floating-Point Arithmetic\n",
+ "1. IEEE single precision format\n",
+ "\n",
+ "| 0 | 1-8 | 9-31 |\n",
+ "|:----:|:-------------:|:-----------------:|\n",
+ "| $s$ | $e$ | $f$ |\n",
+ "| $0$ | $00001001$ | $0011011...01$ |\n",
+ "\n",
+ "$ = (-1)^s \\times 2^{e-127} \\times 1.f $\n",
+ "\n",
+ "เนเธ”เธขเธ—เธตเน\n",
+ " * **sign** $s \\in {0, 1}$\n",
+ " * **biased exponent** $0 \\le e \\le 255$\n",
+ " * **exponent** $p=e-127$ so $-126 \\le p \\le 127$\n",
+ " * **significand** $1.f$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Binary Floating-Point Arithmetic \n",
+ "2. IEEE double precision format\n",
+ "\n",
+ "| 0 | 1-11 | 12-63 |\n",
+ "|:----:|:-------------:|:-----------------:|\n",
+ "| $s$ | $e$ | $f$ |\n",
+ "| $0$ | $00001000111$ | $0011011...01$ |\n",
+ "\n",
+ "$ = (-1)^s \\times 2^{e-1023} \\times 1.f $\n",
+ "\n",
+ "เนเธ”เธขเธ—เธตเน\n",
+ " * **sign** $s \\in {0, 1}$\n",
+ " * **biased exponent** $0 \\le e \\le 2047$\n",
+ " * **exponent** $p=e-1023$ so $-1022 \\le p \\le 1024$\n",
+ " * **significand** $x = 1.f$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Example \n",
+ "\n",
+ "เธเธเน€เธเธตเธขเธเธเธณเธชเธฑเนเธเน€เธเธทเนเธญเธซเธฒเธเนเธฒเธเธญเธเธ•เธฑเธงเน€เธฅเธเธ•เธฒเธกเธเนเธญเธ•เนเธญเธเธณเธซเธเธ”เธ•เนเธญเนเธเธเธตเน เนเธ”เธขเนเธเน IEEE single precision format\n",
+ "> 0 1111 0000 0000 1010 0000 0000 0000 000\n",
+ " \n",
+ "**Answer** \n",
+ "เธซเธฒเธเนเธฒ $s, e, f$ เธเธฒเธเนเธเธ—เธขเน\n",
+ "> $s = 0$\n",
+ "\n",
+ "> $e$ = 11110000\n",
+ "\n",
+ "> $f$ = 0000101 \n",
+ "\n",
+ "```python\n",
+ "s = 0\n",
+ "e = int('11110000', 2)\n",
+ "x = 1 + 0*2**(-1) + 0*2**(-2) + 0*2**(-3) + 0*2**(-4) + 1*2**(-5) + 0*2**(-6) + 1*2**(-7)\n",
+ "print( (-1)**s * 2**(e-127) * x )\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Exercise \n",
+ "1. เธเธเน€เธเธตเธขเธเธเธณเธชเธฑเนเธเน€เธเธทเนเธญเธซเธฒเธเนเธฒเธเธญเธเธ•เธฑเธงเน€เธฅเธเธ•เธฒเธกเธเนเธญเธ•เนเธญเธเธณเธซเธเธ”เธ•เนเธญเนเธเธเธตเน เนเธ”เธขเนเธเน IEEE single precision format\n",
+ " * $s = 0$\n",
+ " * $e$ = 1111 0000 0000\n",
+ " * $f$ = 0000 1010 \n",
+ " \n",
+ "2. เธเธเน€เธเธตเธขเธเธเธณเธชเธฑเนเธเน€เธเธทเนเธญเธซเธฒเธเนเธฒเธเธญเธเธ•เธฑเธงเน€เธฅเธเธ•เธฒเธกเธเนเธญเธ•เนเธญเธเธณเธซเธเธ”เธ•เนเธญเนเธเธเธตเน เนเธ”เธขเนเธเน IEEE double precision format\n",
+ " * $s = 1$\n",
+ " * $e$ = 0000 0011 0000\n",
+ " * $f$ = 0110 1010 \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Error Calculation\n",
+ "\n",
+ "* **Absolute Error** \n",
+ " $\\rightarrow E_{abs} = \\| x_0 - x \\|$\n",
+ "* **Relative Error**\n",
+ " $\\rightarrow E_{rel} = \\frac { E_{abs} }{x} $\n",
+ "* **Percentage Error**\n",
+ " $\\rightarrow E_{per} = E_{rel} \\times 100$"
+ ]
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "celltoolbar": "Slideshow",
+ "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": "3.6.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/week03/Chapter 03 Numerics and Error Analysis.ipynb b/week03/Chapter 03 Numerics and Error Analysis.ipynb
new file mode 100644
index 0000000..df4f30a
--- /dev/null
+++ b/week03/Chapter 03 Numerics and Error Analysis.ipynb
@@ -0,0 +1,480 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธเธ—เธ—เธตเน 1 เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธฒเธฃเธงเธดเน€เธเธฃเธฒเธฐเธซเนเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธ\n",
+ "\n",
+ "> Mathematically correct programming bug is **hard** to spot.\n",
+ "\n",
+ "> เธชเธกเธเธฒเธฃเธ–เธนเธเนเธ•เน...เนเธเธฃเนเธเธฃเธกเธเธดเธ”\n",
+ "\n",
+ ">> Paulgramming - 2017\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธเนเธเนเธเธฃเนเธเธฃเธก\n",
+ "## C++\n",
+ "\n",
+ "```c++\n",
+ "#include <iostream>\n",
+ "using namespace std;\n",
+ "main() {\n",
+ " float x = 1.0; \n",
+ " float y = x / 3.0;\n",
+ " cout << ((x == y * 3.0)?\"\": \"Not\") << \" Equal\" << endl;\n",
+ "}\n",
+ "```\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "# เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธเนเธเนเธเธฃเนเธเธฃเธก\n",
+ "## Java\n",
+ "\n",
+ "```java\n",
+ "public class Test {\n",
+ " public static void main(String[] a) {\n",
+ " float x = 1.0;\n",
+ " float y = x / 3.0;\n",
+ " System.out.println( ((x == y * 3.0)?\"\": \"Not\") + \" Equal\" );\n",
+ " }\n",
+ "}\n",
+ "```\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "# เธ•เธฑเธงเน€เธฅเธเนเธฅเธฐเธเธงเธฒเธกเธเธฅเธฒเธ”เน€เธเธฅเธทเนเธญเธเนเธเนเธเธฃเนเธเธฃเธก\n",
+ "## Python\n",
+ "\n",
+ "```python\n",
+ "x = 1.0\n",
+ "y = x / 3.0\n",
+ "print(\"Equal\" if x == y*3.0 else \"Not Equal\")\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# เธกเธตเธซเธฅเธฒเธขเธ•เธฑเธงเน€เธฅเธเธ—เธตเนเนเธกเน\n",
+ "x = 1.0\n",
+ "y = x / 3.0\n",
+ "#print(\"Equal\" if x == y*3.0 else \"Not Equal\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธกเธตเธซเธฅเธฒเธขเธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธเธญเธกเน€เธเนเธเธเนเธฒเนเนเธกเนเนเธ”เน\n",
+ "\n",
+ "* เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธเธญเธกเธเธดเธงเน€เธ•เธญเธฃเนเธ•เนเธญเธเธเธฃเธฐเธกเธฒเธ“เธเธฒเธฃ (Inexact numbers)\n",
+ " * เธเนเธฒเธญเธ•เธฃเธฃเธเธขเธฐ (irrational numbers) $\\pi, \\e, ...$\n",
+ " * เธเนเธฒเธ•เธฃเธฃเธเธขเธฐ (rational numbers) เธ—เธตเนเนเธกเนเธชเธฒเธกเธฒเธฃเธ–เนเธเธฅเธเน€เธเนเธเน€เธฅเธเธเธฒเธเธชเธญเธเนเธ”เน\n",
+ "```python\n",
+ "0.1 + 0.2 == 0.3\n",
+ "```\n",
+ "\n",
+ "* เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธเธญเธกเธเธดเธงเน€เธ•เธญเธฃเนเธชเธฒเธกเธฒเธฃเธ–เน€เธเนเธเธเนเธฒเนเธ”เนเธ•เธฃเธ (Exact numbers)\n",
+ "> เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเธชเธฒเธกเธฒเธฃเธ–เนเธเธฅเธเนเธซเนเน€เธเนเธเน€เธฅเธเธเธฒเธเธชเธญเธเนเธ”เน"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Floating-Point Binary\n",
+ "\n",
+ "> เธ•เธฑเธงเน€เธฅเธ(number) เน€เธเธตเธขเธเนเธ—เธเธ”เนเธงเธขเธชเธฒเธขเธเธญเธเน€เธฅเธเน€เธ”เธตเนเธขเธง(digit) เนเธ”เธขเธเธณเธเธงเธเธเธญเธเน€เธฅเธเน€เธ”เธตเนเธขเธง เธเธถเนเธเธญเธขเธนเนเธเธฑเธ เน€เธฅเธเธเธฒเธ(base)\n",
+ "\n",
+ "เนเธเธฃเธฐเธเธเธเธณเธเธงเธเธเธฑเธเธเธญเธเธเธเน€เธฃเธฒเธเธฐเน€เธเนเธเน€เธฅเธเธเธฒเธ 10 เนเธ”เธขเธกเธต digit เธ—เธตเนเนเธเนเนเธ”เนเนเธ”เนเนเธเน 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\n",
+ "เธขเธเธ•เธฑเธงเธญเธขเนเธฒเธเธ•เธฑเธงเน€เธฅเธเนเธเน€เธฅเธเธเธฒเธ 10 เน€เธเนเธ 128 77 12100 เน€เธเนเธเธ•เนเธ\n",
+ "\n",
+ "เธ•เธฑเธงเน€เธฅเธเธ—เธตเนเนเธเนเนเธเธเธญเธกเธเธดเธงเน€เธ•เธญเธฃเนเธเธฐเน€เธเนเธเน€เธฅเธเธเธฒเธ 2 เนเธ”เธขเธกเธต digit เธ—เธตเนเนเธเนเนเธ”เน เนเธ”เนเนเธเน 0 เนเธฅเธฐ 1 \n",
+ "เธขเธเธ•เธฑเธงเธญเธขเนเธฒเธเธ•เธฑเธงเน€เธฅเธเนเธเน€เธฅเธเธเธฒเธ 2 เน€เธเนเธ 1, 101, 1101 เน€เธเนเธเธ•เนเธ"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Terminology\n",
+ "** Bit **\n",
+ ": 0 or 1\n",
+ "\n",
+ "** Byte ** \n",
+ ": 8 bits\n",
+ "\n",
+ "** Real **\n",
+ ": 4 bytes **single precision**\n",
+ ": 8 bytes **double precision**\n",
+ "\n",
+ "** Integer **\n",
+ ": 1, 2, 4, or 8 byte signed\n",
+ ": 1, 2, 4, or 8 byte unsigned\n",
+ "\n",
+ "> เธเธถเนเธเธญเธขเธนเนเธเธฑเธเธ เธฒเธฉเธฒเนเธเธฃเนเธเธฃเธกเธงเนเธฒเธเธฐเนเธเนเธชเธฒเธขเธ—เธตเนเธกเธตเธเธงเธฒเธกเธขเธฒเธงเน€เธ—เนเธฒเนเธซเธฃเน 8, 16, 32 เธซเธฃเธทเธญ 64 เน€เธเนเธเธ•เนเธ\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เธเนเธญเธ•เธเธฅเธ\n",
+ "\n",
+ "* เน€เธเธทเนเธญเธเนเธฒเธขเธ•เนเธญเธเธฒเธฃเธเธณเธเธงเธ“เน€เธฃเธฒเธเธฐเนเธเนเธชเธฒเธขเธ—เธตเนเธกเธตเธเธงเธฒเธกเธขเธฒเธง 8 เนเธฅเธฐเน€เธเธตเธขเธเนเธขเธเน€เธเนเธเธเธฅเธธเนเธกเธฅเธฐ 4 เน€เธเธทเนเธญเธเนเธฒเธขเธ•เนเธญเธเธฒเธฃเธเธณเธเธงเธ \n",
+ "\n",
+ "> เน€เธเนเธ 1 = 0000 0001\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Binary $\\rightarrow$ Integer\n",
+ "\n",
+ "| | | | | | | | |\n",
+ "|------|------|------|------|------|------|------|------|\n",
+ "| 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |\n",
+ "|$2^7$ |$2^6$ |$2^5$ |$2^4$ |$2^3$ |$2^2$ |$2^1$ |$2^0$ |\n",
+ "\n",
+ "$1\\times2^7 + 1\\times2^6 + 1\\times2^5 + 0\\times2^4 + 0\\times2^3 + 1\\times2^2 + 1\\times2^1 + 1\\times2^0$\n",
+ "\n",
+ "$1\\times 128+ 1\\times 64 + 1\\times 32 + 0\\times 16 + 0\\times 8 + 1\\times 4 + 1\\times 2 + 1 \\times 1$\n",
+ "\n",
+ "\n",
+ "$128 + 64 + 32 + 0 + 0 + 4 + 2 + 1$\n",
+ "\n",
+ "**Answer**\n",
+ "> $231$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# เน€เธเธตเธขเธเนเธเธฃเนเธเธฃเธกเธ—เธ”เธชเธญเธ\n",
+ "\n",
+ "* เธเธณเธเธงเธ“เธซเธฒเธเธฅเธฅเธฑเธเธเน\n",
+ "```python\n",
+ "1*2**7 + 1*2**6 + 1*2**5 + 0*2**4 + 0*2**3 + 1*2**2 + 1*2**1 + 1*2**0\n",
+ "```\n",
+ "\n",
+ "* เธเธณเธชเธฑเนเธเนเธเธฅเธเน€เธฅเธเธเธฒเธเธ•เนเธฒเธเน\n",
+ "```python\n",
+ "int('11100111', 2) # เนเธเธฅเธ str '11100111' เธเธฒเธ 2 เน€เธเนเธ int\n",
+ "oct(35) # เนเธเธฅเธ 35 เธเธฒเธเธชเธดเธ เนเธซเนเน€เธเนเธเธเธฒเธ 8\n",
+ "hex(35) # เนเธเธฅเธ 35 เธเธฒเธเธชเธดเธ เนเธซเนเน€เธเนเธเธเธฒเธ 16\n",
+ "bin(35) # เนเธเธฅเธ 35 เธเธฒเธเธชเธดเธ เนเธซเนเน€เธเนเธเธเธฒเธ 2\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#int('11100111', 2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "#### Exercise\n",
+ "เธเธเนเธชเธ”เธเธเธฒเธฃเนเธเธฅเธเธ•เธฑเธงเน€เธฅเธเธเธฒเธเธชเธญเธเธ•เนเธญเนเธเธเธตเนเน€เธเนเธเธเธณเธเธงเธเน€เธ•เนเธก\n",
+ "* 10011001\n",
+ "* 00010011\n",
+ "* 00011111"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Binary $\\rightarrow$ Float\n",
+ "เธเธณเธซเธเธ”เธ•เธณเนเธซเธเนเธเธ—เธตเนเน€เธฅเธเธชเธญเธเธเธณเธฅเธฑเธเน€เธเนเธเธจเธนเธเธขเน (fix-point representation)\n",
+ "\n",
+ "| | | | | | | | |\n",
+ "|------|------|------|------|------|------|------|------|\n",
+ "| 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |\n",
+ "|$2^5$ |$2^4$ |$2^3$ |$2^2$ |$2^1$ |$2^0$ |$2^-1$ |$2^-2$ |\n",
+ "\n",
+ "$1\\times 2^5+1\\times 2^4+1\\times 2^3+0\\times 2^2+9\\times 2^1+1\\times 2^0+1\\times 2^{-1}+1\\times 2^{-2}$\n",
+ "\n",
+ "$1\\times2^5 + 1\\times2^4 + 1\\times2^3 +0\\times 2^2+0\\times2^1+1\\times 1+\\frac{1}{2}+\\frac{1}{4}$\n",
+ "\n",
+ "$32 + 16 + 8 + 0 + 0 + 1 + 0.5 + 0.25$\n",
+ "\n",
+ "**Answer**\n",
+ "> 57.75"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#1*2**5 + 1*2**4 + 1*2**3 + 0*2**2 + 0*2**1 + 1*2**0 + 1*2**(-1) + 1*2**(-2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "#### Binary Fixed-Point Arithmetic\n",
+ "| | | | | | | | | |\n",
+ "|------|------|------|------|------|------|------|------|------|\n",
+ "| 1 | 1 | 1 | ... | 0 | 0 | ... | 1 | 1 |\n",
+ "| sign ||$2^{m-1}$ |$2^{m-2}$ | ... |$2^0$ |$2^{-1}$ | ... |$2^{-n+1}$ |$2^{-n}$ |\n",
+ "\n",
+ "* Parameters: $m, n \\in Z$\n",
+ "* $m$ เธเธงเธฒเธกเธขเธฒเธงเธเธญเธเธชเธฒเธข(เธเธณเธเธงเธ bit) เธ—เธตเนเนเธเนเน€เธเนเธเธเธณเธเธงเธเน€เธ•เนเธก(integer portion)\n",
+ "* $n$ เธเธงเธฒเธกเธขเธฒเธงเธเธญเธเธชเธฒเธข(เธเธณเธเธงเธ bit) เธ—เธตเนเนเธเนเน€เธเนเธเธ•เธฑเธงเธซเธฒเธฃ(fractional portion)\n",
+ "* เธเธงเธฒเธกเธขเธฒเธงเธ—เธฑเนเธเธซเธกเธ”เธเธญเธเธชเธฒเธขเน€เธเนเธ $m+n+1$ เธฃเธงเธกเธเธฑเธ bit เธ—เธตเนเนเธเนเธเธญเธเน€เธเธฃเธทเนเธญเธเธซเธกเธฒเธข (+/-)\n",
+ "* เธเธงเธฒเธกเธฃเธนเนเน€เธเธดเนเธกเน€เธ•เธดเธก: [Fixed-Point Numbers](https://en.wikibooks.org/wiki/Floating_Point/Fixed-Point_Numbers)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Error in Binary Fixed-Point Arithmetic\n",
+ "\n",
+ "** เธชเธกเธกเธ•เธดเธงเนเธฒเธกเธตเนเธเน 2 bit เนเธซเนเนเธเน ** \n",
+ "\n",
+ "> $m = 1, n=1$ เนเธ”เธขเธ—เธตเนเนเธกเนเธเธดเธ” sign bit\n",
+ "\n",
+ "$0.1 \\times 0.1 = 0.01 \\approx 0.0$ \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Binary Floating-Point Arithmetic\n",
+ "1. IEEE single precision format\n",
+ "\n",
+ "| 0 | 1-8 | 9-31 |\n",
+ "|:----:|:-------------:|:-----------------:|\n",
+ "| $s$ | $e$ | $f$ |\n",
+ "| $0$ | $00001001$ | $0011011...01$ |\n",
+ "\n",
+ "$ = (-1)^s \\times 2^{e-127} \\times 1.f $\n",
+ "\n",
+ "เนเธ”เธขเธ—เธตเน\n",
+ " * **sign** $s \\in {0, 1}$\n",
+ " * **biased exponent** $0 \\le e \\le 255$\n",
+ " * **exponent** $p=e-127$ so $-126 \\le p \\le 127$\n",
+ " * **significand** $1.f$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Binary Floating-Point Arithmetic \n",
+ "2. IEEE double precision format\n",
+ "\n",
+ "| 0 | 1-11 | 12-63 |\n",
+ "|:----:|:-------------:|:-----------------:|\n",
+ "| $s$ | $e$ | $f$ |\n",
+ "| $0$ | $00001000111$ | $0011011...01$ |\n",
+ "\n",
+ "$ = (-1)^s \\times 2^{e-1023} \\times 1.f $\n",
+ "\n",
+ "เนเธ”เธขเธ—เธตเน\n",
+ " * **sign** $s \\in {0, 1}$\n",
+ " * **biased exponent** $0 \\le e \\le 2047$\n",
+ " * **exponent** $p=e-1023$ so $-1022 \\le p \\le 1024$\n",
+ " * **significand** $x = 1.f$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Example \n",
+ "\n",
+ "เธเธเน€เธเธตเธขเธเธเธณเธชเธฑเนเธเน€เธเธทเนเธญเธซเธฒเธเนเธฒเธเธญเธเธ•เธฑเธงเน€เธฅเธเธ•เธฒเธกเธเนเธญเธ•เนเธญเธเธณเธซเธเธ”เธ•เนเธญเนเธเธเธตเน เนเธ”เธขเนเธเน IEEE single precision format\n",
+ "> 0 1111 0000 0000 1010 0000 0000 0000 000\n",
+ " \n",
+ "**Answer** \n",
+ "เธซเธฒเธเนเธฒ $s, e, f$ เธเธฒเธเนเธเธ—เธขเน\n",
+ "> $s = 0$\n",
+ "\n",
+ "> $e$ = 11110000\n",
+ "\n",
+ "> $f$ = 0000101 \n",
+ "\n",
+ "```python\n",
+ "s = 0\n",
+ "e = int('11110000', 2)\n",
+ "x = 1 + 0*2**(-1) + 0*2**(-2) + 0*2**(-3) + 0*2**(-4) + 1*2**(-5) + 0*2**(-6) + 1*2**(-7)\n",
+ "print( (-1)**s * 2**(e-127) * x )\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Exercise \n",
+ "1. เธเธเน€เธเธตเธขเธเธเธณเธชเธฑเนเธเน€เธเธทเนเธญเธซเธฒเธเนเธฒเธเธญเธเธ•เธฑเธงเน€เธฅเธเธ•เธฒเธกเธเนเธญเธ•เนเธญเธเธณเธซเธเธ”เธ•เนเธญเนเธเธเธตเน เนเธ”เธขเนเธเน IEEE single precision format\n",
+ " * $s = 0$\n",
+ " * $e$ = 1111 0000 0000\n",
+ " * $f$ = 0000 1010 \n",
+ " \n",
+ "2. เธเธเน€เธเธตเธขเธเธเธณเธชเธฑเนเธเน€เธเธทเนเธญเธซเธฒเธเนเธฒเธเธญเธเธ•เธฑเธงเน€เธฅเธเธ•เธฒเธกเธเนเธญเธ•เนเธญเธเธณเธซเธเธ”เธ•เนเธญเนเธเธเธตเน เนเธ”เธขเนเธเน IEEE double precision format\n",
+ " * $s = 1$\n",
+ " * $e$ = 0000 0011 0000\n",
+ " * $f$ = 0110 1010 \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Error Calculation\n",
+ "\n",
+ "* **Absolute Error** \n",
+ " $\\rightarrow E_{abs} = \\| x_0 - x \\|$\n",
+ "* **Relative Error**\n",
+ " $\\rightarrow E_{rel} = \\frac { E_{abs} }{x} $\n",
+ "* **Percentage Error**\n",
+ " $\\rightarrow E_{per} = E_{rel} \\times 100$"
+ ]
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "celltoolbar": "Slideshow",
+ "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": "3.5.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/week03/assignment.py b/week03/assignment.py
new file mode 100644
index 0000000..3b85884
--- /dev/null
+++ b/week03/assignment.py
@@ -0,0 +1,12 @@
+def value (v,pos=4,ne=3):
+
+ sign = -1 if v[0]==1 else 1
+ return sign*sum([v[i]*2**(pos-i) for i in range(1,(pos+ne)+1)] )
+ print( value(v,4,3) )
+
+
+def values(v, pos, ne):
+ aa=list(map(int,v))
+ sign = -1 if aa[0] == 1 else 1
+ return sign * sum([aa[i] * 2 ** (pos - i) for i in range(1, (pos + ne) + 1)])
+
diff --git a/week04/__pycache__/assignment.cpython-36.pyc b/week04/__pycache__/assignment.cpython-36.pyc
new file mode 100644
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diff --git a/week04/assignment.py b/week04/assignment.py
new file mode 100644
index 0000000..93f5180
--- /dev/null
+++ b/week04/assignment.py
@@ -0,0 +1,8 @@
+def single_prec(v):
+
+ return (-1)**int(v[0])*sum([int(v[i])*2**(8-i) for i in range(1,23)])
+
+def double_prec(v):
+
+ return (-1)**int(v[0])*sum([int(v[i])*2**(11-i) for i in range(1,23)])
+
--
2.18.1