Re^2: Seeing if two numbers have the same sign ($x / abs $x)

[WoodyWeaver]

<obsMathRef>
lodin's observation and syphilis' cantrip come from the same underlying mathematical principles.

Triangle equality:
for vectors a, b,

||a+b|| <= ||a|| + ||b||, with equality iff a is a positive scalar multiple of b

(Note here || is "norm", not or.)

Angle between two vectors:
The angle theta between two vectors a, b satisfies

cos theta = (a dot b) / (||a|| ||b||)

(That the second theorem implies the first is left as an exercise for the reader. :-)

For one dimensional vectors ("numbers") the norm is the absolute value, and there are only two "directions" -- out along the positive axis and out along the negative axis. So syphilis is applying the triangle equality, while lodin is computing the cosine directly (note cos 0 = 1 -> "same sign" while cos 180 degrees = -1 -> "opposite sign").
</obsMathRef>

We now return to our regular interpretation of line noise as script.

--woody

[lodin]

lodin is computing the cosine directly (note cos 0 = 1 -> "same sign" while cos 180 degrees = -1 -> "opposite sign").

Maybe this is what you mean, but I don't actually calculate the angle (or cosine) between $_[0] and $_[1]. I calculate the respective angles of $_[0] and $_[1] against the positive axis, and compare them.

Equivalently, you could also view it as I'm taking the norm of the two 1D vectors $_[0] and $_[1], which gives me two unit vectors pointing in the direction of $_[0] and $_[1], which I then test for equality. If they're equal, they point in the same direction, and in 1D that means they have the same sign.

lodin

[WoodyWeaver]

arg, eyes are getting old. You are absolutely right. I was thinking of the "trick" people had described about taking the product and checking if positive; you are indeed normalizing the vectors and checking for equality.