Friday, July 24, 2020
A Whole or Fractional
power( )Blog Entry #411
We return now to our run through the Super Calculator's exponentiation landscape. With all that
prompt( )ing in the power( ), squared( ), and cubed( ) functions, it occurred to me that we should talk about the a and b data types a bit before we go any further...xy input audit
For our 97 exponentiation in the previous post, the a = 9 and b = 7 inputs actually have a string data type: at
Math.pow(a, b) time, the 9 and 7 operands are converted to numbers."" and null
If we leave a
prompt( ) inputDefault field blank
and click the button, then the
prompt( ) output is the empty string; if we click the button, then the output is null (the primitive value vs. as a string). When plugged into a Math.pow( ) command, "" and null both convert to 0. FYI: Math.pow(0, 0) returns 1 even though 00 has no agreed-upon value.
Non-empty, non-numeric
Suppose we type hello in the total field (the total field is not readonly, we can do that) and try to raise it to the world power: as you would expect, helloworld returns NaN. Such inputs can be intercepted via an iterative
isNaN( ) test (admittedly at the risk of annoying the user), e.g.:b = window.prompt("Enter an exponent:", "");
while (isNaN(b)) { b = window.prompt("Your exponent must be a number:", ""); }π
In the C/d section of Blog Entry #409 we learned that the SC's key outputs a Math.PI.toFixed(15) value surrounded by parentheses. The ( and ) characters prevent the conversion of the (3.141592653589793) string to a number for an exponentiation (or trigonometric) operation; as a result,
Math.pow("(3.141592653589793)", b) returns NaN for all b except b = 0, for which the return is 1. We can easily lose the ( ) by pressing the key, i.e., eval("(3.141592653589793)") returns 3.141592653589793 (as a number, which is stringified when written to the total field), after which we can raise the pi value to whatever power we want.Root extraction
Root extraction can be expressed exponentially: finding the yth root of some number x is equivalent to raising x to the 1/y power.
We can use the original
power( ) function to calculate a x1/y root as long as the 1/y exponent is in decimal form: b = 0.5 for a square root, b = 0.25 for a 4th root, etc. As you would intuit from the preceding (π) discussion, a 1/y string's / character prevents its Math.pow( ) numberification.If we don't know 1/y's decimal equivalent, then we can divide 1 by y in advance, copy the quotient to the clipboard, and paste the quotient into the
Enter an exponent: inputDefault field when the time comes. As it happens, however, any numerator/denominator-type fraction can be eval( )ed to its decimal equivalent - cf. the SC's calc( ) function - so if we insert anif (/^1\/\d+$/.test(b)) b = eval(b); statement* after eachb = window.prompt("Enter an exponent:", ""); statement,then we can input 1/y itself into the inputDefault field.
*The /^1\/\d+$/ regexp pattern matches a 1/y string whose y character is an unsigned integer; we'd need a more complex pattern to additionally accommodate other ys.
So now, if we want to find the 7th root of 9 (maybe you would know that 1/7 = 0.14285714285714285, but I wouldn't), we're all set.
My Casio fx-85v calculator has an x1/y function, which is accessed via SHIFT-ing the key. We have the option of putting a
image on a push button:<button type="button" onclick=""><img width="" height="" style="" src="pathname/yth_root_of_x2.gif" alt="" /></button>In creating the yth_root_of_x2.gif image, I gave the x and y a 16px/13px default/
<sup> font-size ratio.You're so square root, baby
The SC's Misc section has a dedicated button
<input type="button" value="Sqrt" onclick="getinput(squareroot);">for getting the square root of a number. The button is bound to a
squareroot( ) function that is called from the getinput( ) function à la the power( ), squared( ), and cubed( ) functions.if (func == squareroot) { return squareroot(mode, a); }The
squareroot( ) function is detailed below; Mozilla's current Math.sqrt( ) page is here.function squareroot(mode, obj) {
if (mode == 1) { window.alert("This function gives you the square root of any given number"); }
if (obj.value != "" && obj.value != "0") {
aa = window.prompt("Do you want to find the square root of the current number in the total text box?", "y or n");
if (aa == "y") { doit(Math.sqrt(obj.value), obj); }
else {
a = window.prompt("Enter a number to find the square root of:", "");
more("(" + Math.sqrt(a) + ")", obj); } }
else {
a = window.prompt("Enter a number to find the square root of:", "");
doit(Math.sqrt(a), obj); } }I gave you a detailed
power( ) deconstruction earlier, do we need to do the same thing here? Nah, let's go with a quick post-mode rundown:(1) If the total.value isn't empty or 0 - if we've entered something into the total field, not necessarily a number - then we are
prompt( )ed to confirm (y or n) that we want to square-root the entered value.(a) If y, then the total.value is square-rooted and the resulting square root is written to the total field via the
doit( ) function.(b) If not y, then we are
prompt( )ed for a new value to square-root; the a prompt( ) output is square-rooted and (a1/2) is appended to the total.value via the more( ) function.(2) If the total.value is empty or 0, then we are
prompt( )ed for a value to square-root; the a prompt( ) output is square-rooted and a1/2 is written to the total field via the doit( ) function.If the SC's mode help flag is turned on (1), then we'll get a
This function gives you the square root of any given number
alert( ) messagebefore the if tests and
prompt( )ing get under way. The message could be a bit more specific: we all know that we can't take the square root of a negative number...or can we? Actually, we addressed the calculation of imaginary square roots in the It's complex section of Blog Entry #344 during our analysis of the CCC Quadratic Equation script; for the SC the corresponding code could go something like:var radicand = Number(x); // x = obj.value or a
if (radicand < 0) {
var real_root = Math.sqrt(-radicand);
var imag_root = "i \u00d7 " + real_root;
obj.value = imag_root;
return; }Otherwise,
Math.sqrt(x) returns NaN if x cannot be converted to a nonnegative number;per the Non-empty, non-numeric subsection above,
a
while (isNaN(x) || x < 0) { x = window.prompt("Your radicand must be a nonnegative number.", ""); }-type statementcan be used to intercept problematic
Math.sqrt(x) inputs.Apropos asides:
Jamie Beyore's Another Great Science Calculator has a key that executes
an external
function calc_sqrt(form) { form.expr.value = (Math.sqrt(form.expr.value)) } function whereasSaries's Rainbow Calculator has an (unsuperscripted) key that executes
an inline
document.calculator.text.value = Math.sqrt(document.calculator.text.value) statement.A standard calculator won't calculate imaginary square roots (at least my Casio won't), but if you go to Google and enter
What is the square root of -9?
in the search field and then click your keyboard's Enter/Return key, you'll get a new page with a
square root(-9) = 3i
div near the top of it.
We'll cover the SC's and functionality in the following entry.
- posted by A. Peak @ 5:34 PM
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