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JavaScript: The First Parts
Part TwoDouglas Crockford
Yahoo! Inc.
Learn to Program• Values• Variables• Expressions• Branching• Loops
• Functions• Recursion• Arrays• Objects• Trees
Values• Booleans• Numbers• Strings• null• undefined
Boolean• true• false
• Named for George Boole
• && and• || or• ! not
Numbers• Modern computers like to represent
numbers in binary (base 2).
27 26 25 24 23 22 21 20
128
64 32 16 8 4 2 1
Numbers• Binary numbers usually come in fixed
sizes, such as 8, 16, 32, 64.• The number of bits determines the
range of the values.
Number of bits
8 16 32 64
Maximum value
255 65535
4294967295
18446744073709551615
Numbers• JavaScript provides only one number
type.• It is a 64-bit binary floating-point number.
• Floating point numbers can cover an enormous range.
• 5E-324 to 1.7976931348623157E308
... 211
210
29 28 27 26 25 24 23 22 21 20 2-1 2-2
2-3
2-4 2-5
2-6 2-7
2-8
2-9 2-10 2-11 ...
mantissa or significand
But it comes at a cost.• Most decimal fractions cannot be
represented accurately.
• A decimal fraction requires an infinite number of bits, but mantissas are finite.
... 211
210
29 28 27 26 25 24 23 22 21 20 2-1 2-2
2-3
2-4 2-5
2-6 2-7
2-8
2-9 2-10 2-11 ...
mantissa or significand
But it comes at a cost.• Most decimal fractions cannot be
represented accurately.
• The associative and distributive laws do not hold.
(a + b) + c ≠ a + (b + c)
... 211
210
29 28 27 26 25 24 23 22 21 20 2-1 2-2
2-3
2-4 2-5
2-6 2-7
2-8
2-9 2-10 2-11 ...
abc
Integers that fit entirely within the mantissa are safe.
Write a program to compute safe_max
• There are integers such that adding 1 will not result in a larger integer. Such integers are unsafe integers.
Write a program to compute safe_max
• There are integers such that adding 1 will not result in a larger integer. Such integers are unsafe integers.
• We want to find the largest positive safe integer. Adding 1 to it produces an unsafe integer.
Write a program to compute safe_max
• There are integers such that adding 1 will not result in a larger integer. Such integers are unsafe integers.
• We want to find the largest positive safe integer. Adding 1 to it produces an unsafe integer.
• This will require a loop and a variable, in which we produce and test candidate integers.
First Attemptvar safe_max = function () {
var integer = 1;
while (integer + 1 !== integer) {
integer = integer + 1;
}
return integer; };
• Go to the JSMVHS group• Go to files• Get template1.txt• Start a text editor, such as Crimson
Editor.• Edit the template, save it as
safe_max.html
<html><head><title>template1.html</title><style>div[id] { border: 1px solid black; margin: 1em; padding: 1em;}</style></head><body><script src="http://www.ADsafe.org/adsafe.js"></script>
<div id="MAX_"><p>Compute the largest safe integer.</p><p id="MAX_RESULT"></p><script>"use strict";ADSAFE.go("MAX_", function (dom, lib) {
// The safe_max function, as written, is too slow.// It will not be allowed to finished.// It needs to be corrected.
var safe_max = function () { var integer = 1; while (integer + 1 !== integer) { integer = integer + 1; } return integer; };
dom.q('#MAX_RESULT').value(safe_max());});</script></div>
</body></html>
First Attemptvar safe_max = function () {
var integer = 1;
while (integer + 1 !== integer) {
integer = integer + 1;
}
return integer; };
Second Attemptvar safe_max = function () {
var integer = 1;
while (integer + 1 !== integer) {
integer = integer * 2;
}
return integer; };
9007199254740992 • nine quadrillion seven trillion one
hundred ninety nine billion two hundred fifty four million seven hundred forty thousand nine hundred ninety two
• Integer operations are exact if the safe_max limit is never exceeded.
• If safe_max is exceeded, this might be false:
(a + 1) - 1 === a
eps• eps is that smallest number which,
when added to 1 produces a number that is larger than 1.
• eps is short for epsilon.
... 211
210
29 28 27 26 25 24 23 22 21 20 2-1 2-2
2-3
2-4 2-5
2-6 2-7
2-8
2-9 2-10 2-11 ...
mantissa or significand
First attemptvar compute_eps = function () {
var eps = 1;
while (1 + eps !== 1) {
eps = eps / 2;
}
return eps;
};
var eps = compute_eps();
Test the resultvar test_eps = function (e) {
if (1 + e <= 1) {
alert("Test failed.");
}
};
test_eps(eps);
Why did it fail?
Second attemptvar compute_eps = function () { var eps, next = 1; while (1 + next !== 1) { eps = next; next = next / 2; } return eps;};var eps = compute_eps();
Learn to Program• Values• Variables• Expressions• Branching• Loops
• Functions• Recursion• Arrays• Objects• Trees
Array• An array is a collection of values.• Each value is given a number.• The first value is 0, not 1.• Create an array with the [ ]
operator.• Access an element of an array with
the [ ] operator.
http://jsmvhs.crockford.com/yellowbox.html
• data = [17, 19, 23, 29];• data.length• data[0]• data[1]• data[2] = 0• data[data[2]]• data[3]• data[4]• data[4] = 31• data.length
Looping• The for statement can be used to
visit every element of an array.var alert_array = function (array) {
var i;
for (i = 0; i < array.length; i = i + 1) {
alert(array[i]);
}
};
alert_array([36, 42, 10]);
Assignment 2• Write an average_array function
that takes an array of numbers and returns the average of its elements.
• Use template1 to package it in an HTML page.
• Add it to your assignments folder.
