{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Everything you wanted to know about Floating Point numbers\n",
    "\n",
    "### A practitioners guide to numerical analysis\n",
    "\n",
    "by Avik Sengupta\n",
    "\n",
    "2023-10-23"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### <a href=\"https://youtu.be/x3qBNuWluMY?t=73\">Video of the talk</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "using BenchmarkTools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Table of contents\n",
    "\n",
    "* IEEE Floating Point representation\n",
    "* Special forms\n",
    "* Rounding\n",
    "* SIMD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Institute of Electrical and Electronics Engineers (IEEE) Floating Point representation\n",
    "\n",
    "#### Decimal floating point numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|Scientific notation\t|Fixed-point value  | Sign |Significand\t|Exponent|\n",
    "| :-: | :-: | :-: | :-: | -: |\n",
    "|1.5 ⋅ 10⁴\t|15000 | + | 1.5\t|4|\n",
    "|-2.001 ⋅ 10²\t|-200.1|- | 2.001\t|2\t|\n",
    "|5 ⋅ 10⁻³\t|0.005|+| 5\t|-3\t|\n",
    "|6.667 ⋅ 10⁻¹¹\t|0.00000000006667| + | 6.667\t|-11\t|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Integer part of a decimal-based significand: $$1 \\le [\\mathrm{significand}] \\le 9, \\quad 9 = 10 - 1$$.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Binary floating point numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$(-)1.b_1 b_2 b_3 \\ldots b_d = (-1)^s \\times \\left( 1 + \\frac{b_1}{2} + \\frac{b_2}{2^2} + \\frac{b_3}{2^3} + \\ldots + \\frac{b_d}{2^d} \\right) \\times 2^E$$\n",
    "\n",
    "1. $d$ is fixed, usually by hardware; some or all $b_i$ can be zeros.\n",
    "\n",
    "1. The integer part of the significand is always 1 ($1 \\le [\\mathrm{significand}] \\le 2-1 = 1$)\n",
    "\n",
    "1. There is a finite number of binary floating point. There are exactly $2^d$ foating point numbers $x$, $1 \\le x <2$ corresponding to $E=0$ in the expression above. The same number of floating points numbers $x$ is for intervals $2 \\le x <4$, $\\;4 \\le x <8$, $\\ldots$, $2^k \\le x <2^{k+1}$, $k = 0, \\pm1, \\pm2, \\ldots$.\n",
    "\n",
    "1. The separation between 1.0 and the next binary floating point number is called machine epsilon: $$\\epsilon = 2^{-d}$$.\n",
    "\n",
    "1. If $E_{max}$ is the largest possible value of the Exponent, the largest floating point number is\n",
    "$$\\left( 1 + \\frac{1}{2} + \\frac{1}{2^2} + \\frac{1}{2^3} + \\ldots + \\frac{1}{2^d} \\right) \\times 2^{E_{max}} = \\left( 2 - \\frac{1}{2^{d+1}}  \\right) \\times 2^{E_{max}} \\approx 2^{E_{max} + 1} $$.\n",
    "\n",
    "Similarly, if $E_{min}$ is the smallest possible value of the Exponent, ($E_{min} < 0$), the smallest positive floating point number is\n",
    "$$\\left( 1 + \\frac{0}{2} + \\frac{0}{2^2} + \\frac{0}{2^3} + \\ldots + \\frac{1}{2^d} \\right) \\times 2^{E_{min}} = \\left( 1 + \\frac{1}{2^{d}}  \\right) \\times 2^{E_{min}} \\approx 2^{E_{min}} $$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "IEEE standard:"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:bc5eb99b-5fd6-45e6-96bd-312393d279a7.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Sign bit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "bitstring(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "bitstring(-1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "function floatbits(x::Float64)\n",
    "    b = bitstring(x)\n",
    "    b[1:1] * \"|\" * b[2:12] * \"|\" * b[13:end]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The exponent (powers of 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "function exponent(x::Float64)\n",
    "    parse(Int, bitstring(x)[2:12], base=2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "exponent(1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Significand\n",
    "\n",
    "The Signifcand stored as 52 bits, and is interpreted as *1.b₁b₂…b₅₂* i.e. \n",
    "$$1 + \\frac{b_1}{2} + \\frac{b_2}{4} + \\frac{b_3}{8} + \\ldots + \\frac{b_n}{2^n} + \\ldots + \\frac{b_{52}}{2^{52}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "1 * 2^(1023-1023)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "(1 + 1/2) * 2 ^ (1023-1023)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(1.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "(1 + 1/2 + 1/2^2) * 2 ^ (1023-1023)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(15.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "exponent(15.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "(1 + 1/2 + 1/4 + 1/8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "1.875 * 2^(1026-1023)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Approximate representation\n",
    "\n",
    "Not all decimal numbers are exactly representable as binary floating point number. \n",
    "And many decimal values can be approximated by the same floating number. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0.1 > 1//10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(0.10000000000000001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "bitstring(0.10000000000000001) == bitstring(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Machine epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "eps(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "nextfloat(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(nextfloat(0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "nextfloat(0.1) - 0.1 == eps(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Special Forms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Signed Zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(-0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0.0 == -0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0.0 === -0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Infinity\n",
    "\n",
    "is represented with an exponent of all ones, and signicand of all zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(Inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(-Inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Not A Number (NaN)\n",
    "\n",
    "is represented with an exponent of all ones, and a non zero significand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "floatbits(NaN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "NaN == NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "NaN === NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0/0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0/0 == 0/0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "1.5/0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Rounding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0.1 + 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "big(0.1) + big(0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0.1 + 0.2 - (big(0.1) + big(0.2))  < 2 * eps(0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "eps(0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Floating point operations are not associative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "(0.1 + 0.2) + 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "0.1 + (0.2 + 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "sum([1.0, 10e100, 1.0, -10e100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "1.0 + 10e100 + 1.0 +  -10e100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cancellation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Errors can blow up when subtracting two numbers that are close together. \n",
    "Consider the following function, which can be shown to be:   `f(x) < 0.5 ∀ x`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "f(x) = (1 - cos(x))/x^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "f(1.2e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "cos(1.2e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "1-0.9999999999999999"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "1.1102230246251565e-16 / 1.44e-16"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fixed by rewriting to equivalent form, without subtraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "f2(x) = 0.5 * (sin(x/2) / (x/2))^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "f2(1.2e-8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Special Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "sin(π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "sin(1000_000π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "sinpi(1000_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "cospi(10000000000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "cos(10000000000000pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\exp(x) = \\sum_{n=0}^\\infty \\frac{x^n}{n!} = 1 + x + \\frac12 x^2 + \\dots$$\n",
    "Therefore, for $x \\ll 1$, we have $\\exp(x) \\approx 1 + x$ \\\n",
    "Hence cancellation can occur when calculating $\\exp(x) -1$, for $x \\ll 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "exp(1e-13) - 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "expm1(1e-13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. SIMD\n",
    "\n",
    "128 (SSE), 256 (AVX) or 512 (AVX512) bit parallel operations"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:b761b744-5fb1-42ee-8036-d3164716a8cb.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets take a simple function that sums the element of a function in a loop. \n",
    "One version of the code adds an `@simd` annotation in front of the loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "function mysum_simd(a::Vector)\n",
    "    total = zero(eltype(a))\n",
    "    @simd for x in a\n",
    "        total += x\n",
    "    end\n",
    "    return total\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "@code_native debuginfo=:none dump_module=false mysum_simd(rand(Float64 , 100000)) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second version is functionally the same, but without the `@simd` annotation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "function mysum_basic(a::Vector)\n",
    "    total = zero(eltype(a))\n",
    "    for x in a\n",
    "        total += x\n",
    "    end\n",
    "    return total\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "@code_native debuginfo=:none dump_module=false mysum_basic(rand(Float64 , 100000)) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The native code generated for the SIMD  version shows many more parallel optimisations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Benchmarking SIMD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "rand_array_1D = rand(1000_000);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "@btime mysum_simd(rand_array_1D);\n",
    "@btime mysum_basic(rand_array_1D);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The SIMD version is significantly faster in this case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Further Reading\n",
    "\n",
    "  * Nicholas J Higham , *The Accuracy and Stability of Numerical Algorithms*,\n",
    "    2nd Edition, 2002"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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