floor&mod.ipynb

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   "source": [
    "## floor operator & modulo operator(mod)\n",
    "\n",
    "155 / 4 = 38 with remainder 3\n",
    "\n",
    "155 = 4 * (155 // 4) + (155 % 4)\n",
    "\n",
    "### floor: the floor of a real number a is the largest integer <= a\n",
    "\n",
    "a // b is not the integer portion of a / b, it is the floor of a / b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
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     "text": [
      "floor(3.14)= 3\n",
      "floor(-3.14)= -4\n",
      "floor(-3.00000000000001)= -4\n",
      "floor(-3.0000000000000001)= -3\n"
     ]
    }
   ],
   "source": [
    "print('floor(3.14)=', floor(3.14))\n",
    "print('floor(-3.14)=', floor(-3.14))\n",
    "print('floor(-3.00000000000001)=', floor(-3.00000000000001))\n",
    "# float has limited precision in python\n",
    "print('floor(-3.0000000000000001)=', floor(-3.0000000000000001)) "
   ]
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   "source": [
    "def divider(a, b):\n",
    "    division = a / b\n",
    "    flr = a // b\n",
    "    mod = a % b\n",
    "    print('a/b=', division)\n",
    "    print('a//b=', flr)\n",
    "    print('a%b=', mod)\n",
    "    print('floor(a/b)=', math.floor(division))\n",
    "    print('trunc(a/b)=', math.trunc(division))    \n",
    "    print('equation:{0} = {1} * {2} + {3}'.format(a, b, flr, mod))"
   ]
  },
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     "text": [
      "a/b= 33.75\n",
      "a//b= 33\n",
      "a%b= 3\n",
      "floor(a/b)= 33\n",
      "trunc(a/b)= 33\n",
      "equation:135 = 4 * 33 + 3\n"
     ]
    }
   ],
   "source": [
    "# positive number\n",
    "divider(135, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a/b= -33.75\n",
      "a//b= -34\n",
      "a%b= 1\n",
      "floor(a/b)= -34\n",
      "trunc(a/b)= -33\n",
      "equation:-135 = 4 * -34 + 1\n"
     ]
    }
   ],
   "source": [
    "# nagtive number\n",
    "divider(-135, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reminder: Always satisfied the equation: a = b * (a // b) + (a % b)"
   ]
  }
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