# Is it me or Math::sqrt? **URL:** \ **Category:** Ruby\ **Created:** [March 31, 2008, 11:40am UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408 "2008-03-31T11:40:45Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 11:40am UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/1 "2008-03-31T11:40:45Z")
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Hello list. I’m a bit stupefied by the different results of this algorithm I implemented (Euclidean distance for 3 dimensions): # Calculates the relative distance\_to an arbitrary # Note: The algorithm is not yet optimized for speed. # Hopefully, it is accurate, though. def distance\_to(actor) ~ # Stub, will use vector math or so to approximate the true distance ~ distance = (self.x - actor.x)^2 + (self.y - actor.y)^2 + (self.z - actor.z)^2 ~ Math::sqrt(distance.abs) end actor1 = Gondor::AI::Actor.new(:x =\> 0,:y =\> 0,:z =\> 0) actor2 = Gondor::AI::Actor.new(:x =\> 16, :y =\> 16, :z =\> 16) actor1.distance(actor2) produces: 3.74165738677394 actor1 = Gondor::AI::Actor.new(:x =\> 1,:y =\> 1,:z =\> 1) actor2 = Gondor::AI::Actor.new(:x =\> 15, :y =\> 15, :z =\> 15) produces: 4.0 Why is that? From my understanding, these results should be identical (The algebraic sign is eliminated by exponent 2, everything else is addition). Another thing that has me stumped is, that Math::sqrt requires the absolute, but the result should be positive (addition of positive algebraic signs). Do I need to brush up my math more than I thought? - – Phillip G. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.8 (MingW32) Comment: Using GnuPG with Mozilla - [http://enigmail.mozdev.org](http://enigmail.mozdev.org) iEYEARECAAYFAkfwsX8ACgkQbtAgaoJTgL+4nwCeJ4ICdvn0ruCpxc9U5OTIjV8y OnsAn1nOr6/Fjk0epFFpb3sYgqHoDVhj =gHrp -----END PGP SIGNATURE----- ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 11:48am UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/2 "2008-03-31T11:48:28Z")
2008/3/31, Phillip G. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid): > # Hopefully, it is accurate, though. > > produces: 3.74165738677394 > absolute, but the result should be positive (addition of positive > OnsAn1nOr6/Fjk0epFFpb3sYgqHoDVhj > =gHrp > -----END PGP SIGNATURE----- - without words - irb(main):002:0\> (0-16)^2 =\> -14 irb(main):003:0\> (0-16) \*\* 2 =\> 256 🙂 Kind regards robert ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 11:51am UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/3 "2008-03-31T11:51:24Z")
Phillip G. wrote: > (The algebraic sign is eliminated by exponent 2, everything else is > addition). If my reading is correct the distances should be different. I am not saying that the reported distances are correct only that they should be different. Take the x axis for example: (0 - 16) \* (0 - 16) = 256 (1 - 15) \* (1 - 15) = 196 What you probably meant was: actor1 = Gondor::AI::Actor.new(:x =\> 0,:y =\> 0,:z =\> 0) actor2 = Gondor::AI::Actor.new(:x =\> 15, :y =\> 15, :z =\> 15) should be the same distance as: actor1 = Gondor::AI::Actor.new(:x =\> 1,:y =\> 1,:z =\> 1) actor2 = Gondor::AI::Actor.new(:x =\> 16, :y =\> 16, :z =\> 16) ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 12:03pm UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/4 "2008-03-31T12:03:48Z")
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Peter H. wrote: | | If my reading is correct the distances should be different. I am not | saying that the reported distances are correct only that they should be | different. Take the x axis for example: | | (0 - 16) \* (0 - 16) = 256 | (1 - 15) \* (1 - 15) = 196 | | What you probably meant was: | | actor1 = Gondor::AI::Actor.new(:x =\> 0,:y =\> 0,:z =\> 0) | actor2 = Gondor::AI::Actor.new(:x =\> 15, :y =\> 15, :z =\> 15) | | should be the same distance as: | | actor1 = Gondor::AI::Actor.new(:x =\> 1,:y =\> 1,:z =\> 1) | actor2 = Gondor::AI::Actor.new(:x =\> 16, :y =\> 16, :z =\> 16) D’oh. Forrest, meet trees. Yes, that is what I should check on, and nothing else. Thank you for that reality check. - –Phillip G. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.8 (MingW32) Comment: Using GnuPG with Mozilla - [http://enigmail.mozdev.org](http://enigmail.mozdev.org) iEYEARECAAYFAkfwtuMACgkQbtAgaoJTgL+UygCfQ1G2niZu4G60imSxX5jfPIIP TbYAn01cHltyBoe/Y3djzHiHCmDwSYGs =8QBe -----END PGP SIGNATURE----- ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 11:59am UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/5 "2008-03-31T11:59:40Z")
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Robert K. wrote: | 2008/3/31, Phillip G. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid): |\> # Calculates the relative distance\_to an arbitrary |\> # Note: The algorithm is not yet optimized for speed. |\> # Hopefully, it is accurate, though. |\> def distance\_to(actor) |\> # Stub, will use vector math or so to approximate the true distance |\> distance = (self.x - actor.x)^2 + (self.y - actor.y)^2 + (self.z - |\> actor.z)^2 |\> Math::sqrt(distance.abs) |\> end |\> |\> actor1 = Gondor::AI::Actor.new(:x =\> 0,:y =\> 0,:z =\> 0) |\> actor2 = Gondor::AI::Actor.new(:x =\> 16, :y =\> 16, :z =\> 16) |\> actor1.distance(actor2) |\> produces: 3.74165738677394 |\> |\> actor1 = Gondor::AI::Actor.new(:x =\> 1,:y =\> 1,:z =\> 1) |\> actor2 = Gondor::AI::Actor.new(:x =\> 15, :y =\> 15, :z =\> 15) |\> produces: 4.0 |\> |\> Why is that? From my understanding, these results should be identical |\> (The algebraic sign is eliminated by exponent 2, everything else is |\> addition). |\> |\> Another thing that has me stumped is, that Math::sqrt requires the |\> absolute, but the result should be positive (addition of positive |\> algebraic signs). |\> |\> Do I need to brush up my math more than I thought? | | - without words - | | irb(main):002:0\> (0-16)^2 | =\> -14 | irb(main):003:0\> (0-16) \*\* 2 | =\> 256 | | 🙂 | | Kind regards | | robert | I’ve replaced ^2 with \*\* 2, but that doesn’t seem to change the magnitude of the error (Though, the results “feels” more correct now, so thanks for that). The results are still different, as you can see: 24.2487113059643 for actor1’s x,y,z = 1, and actor2’s x,y,z = 15 27.712812921102 for actor1’s x,y,z = 0, and actor2’s x,y,z = 16 However, since the coordinates are subtracted on their respective axises, I guess that my assumption on the “error” is incorrect, and that I do get the correct value. However, intuitively, the distance between these two points should be the same. Hmmmm… - – Phillip G. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.8 (MingW32) Comment: Using GnuPG with Mozilla - [http://enigmail.mozdev.org](http://enigmail.mozdev.org) iEYEARECAAYFAkfwtewACgkQbtAgaoJTgL+8oACfelpzNMjMyhvl6x4tfJi6M/2f /m4AnA0T46orBD6hnv7g6YCsb60PZdzC =ANtA -----END PGP SIGNATURE----- ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 12:50pm UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/6 "2008-03-31T12:50:45Z")
2008/3/31, Phillip G. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid): > I’ve replaced ^2 with \*\* 2, but that doesn’t seem to change the > magnitude of the error (Though, the results “feels” more correct now, so > thanks for that). Is this really true after Peter’s response? Looks ok to me: irb(main):001:0\> Math.sqrt(3 \* (16-1)\*\*2) =\> 25.9807621135332 irb(main):002:0\> Math.sqrt(3 \* (15-0)\*\*2) =\> 25.9807621135332 Cheers robert ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 2:32pm UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/7 "2008-03-31T14:32:39Z")
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Robert K. wrote: | 2008/3/31, Phillip G. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid): |\> I’ve replaced ^2 with \*\* 2, but that doesn’t seem to change the |\> magnitude of the error (Though, the results “feels” more correct now, so |\> thanks for that). | | Is this really true after Peter’s response? Looks ok to me: | | irb(main):001:0\> Math.sqrt(3 \* (16-1)\*\*2) | =\> 25.9807621135332 | irb(main):002:0\> Math.sqrt(3 \* (15-0)\*\*2) | =\> 25.9807621135332 Yeah, the mistake was clearly mine. Fixing my assumption helped with fixing the bug. Though, this time the bug was a PBKAC. A hint should’ve been that I needed Fixnum#abs to properly calculate the square root required by the algorithm. Which shows that flying solo has its dangers. Thanks for correcting me. 🙂 - – Phillip G. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.8 (MingW32) Comment: Using GnuPG with Mozilla - [http://enigmail.mozdev.org](http://enigmail.mozdev.org) iEYEARECAAYFAkfw2WIACgkQbtAgaoJTgL/mEACdFRpZKC3v4DxJa2+lDodoGYuN wLcAn13rWNycC4RCnn7V2YeZeR6UQ8vI =5Iq9 -----END PGP SIGNATURE----- ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 2:51pm UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/8 "2008-03-31T14:51:45Z")
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Robert K. wrote: | 2008/3/31, Phillip G. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid): | | Often it’s helpful to try parts of an algorithm in IRB. That way you | easily find bugs as this one. 🙂 The difficulty is, that my assumptions were broken. And even with irb, the assumptions _I_ make aren’t checked. Neither would unit tests or similar things: If my assumptions are incorrect, and I don’t know it, I’ll write tests and code that validate my assumptions. The difficulty, if one is working alone, to find a way to check assumptions (and looking up the math formula for calculating the Euclidean distance between two points helped my catch another assumption I made, fortunately), which co-workers or so could provide. Ah, well, this just shows that I have to check my assumptions, too, and perform due diligence when working on something. Which is blatantly obvious, of course, but I needed that reminder, obviously. I’m just glad that I only write code in a vacuum, but don’t exist in one. 😛 - – Phillip G. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.8 (MingW32) Comment: Using GnuPG with Mozilla - [http://enigmail.mozdev.org](http://enigmail.mozdev.org) iEYEARECAAYFAkfw3kYACgkQbtAgaoJTgL+lHwCfRmMN9JLjszwU0S+s+au4cJPc l20AnRTtcp2y4kygn++M8Dbadxw2DrLE =v+RD -----END PGP SIGNATURE----- ---
**Author:** ![Phillip\_G](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/7ab992/32.png) [@Phillip\_G](https://www.ruby-forum.com/u/Phillip_G)\ **Post date:** [March 31, 2008, 2:35pm UTC](https://www.ruby-forum.com/t/is-it-me-or-math-sqrt/133408/9 "2008-03-31T14:35:39Z")
2008/3/31, Phillip G. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid): > Yeah, the mistake was clearly mine. Fixing my assumption helped with > fixing the bug. Though, this time the bug was a PBKAC. > > A hint should’ve been that I needed Fixnum#abs to properly calculate the > square root required by the algorithm. Yes, that was what got me wondering. > Which shows that flying solo has its dangers. Often it’s helpful to try parts of an algorithm in IRB. That way you easily find bugs as this one. 🙂 Kind regards robert