What does matter in processor for speed?

Few days back, i got to know that this is not necessary that i7 should be better than i5. I was totally shocked. My question is why is i7 is not faster than i5 as my name it means that i7 is faster than i5. As my knowledge i7 processor is having 7 processors and i5 is having 5 processors. In processor, which thing matters the most in the processor.

How to speed up the calculation of a multi-dimension matrix involving symbolic integral?

The following program succeeds in getting matrix CC, but it takes time badly, especially in the case varNumber becomes larger just as the following varNumber = 35. Who can speed up the process of calculation? Thanks!

ClearAll["Global`*"]; varNumber = 35; end = Infinity; s1 = 112*^9; s2 = 25*^9; s3 = 15.1; s4 = 5.5*10^-9;  a[m_] := Exp[-x/2]*LaguerreL[m, x]; b[m_, i_, j_, l_] := Integrate[a[m]*x^i*D[a[l], {x, j}], {x, 0, end}];  d[m_, i_, j_, l_] :=   Integrate[   a[m]*x^i*D[     a[l], {x, j}]*(DiracDelta[x] -       DiracDelta[x - end]), {x, -Infinity, Infinity}];  c[1, 1][m_, l_] := s2*d[m, 0, 1, l] + s2*b[m, 0, 2, l]; c[1, 2][m_, l_] := 0; c[1, 3][m_, l_] := 0; c[2, 1][m_, l_] := 0; c[2, 2][m_, l_] := s1*d[m, 0, 1, l] + s1*b[m, 0, 2, l]; c[2, 3][m_, l_] := s3*d[m, 0, 1, l] + s3*b[m, 0, 2, l]; c[3, 1][m_, l_] := 0; c[3, 2][m_, l_] := s3*d[m, 0, 1, l] + s3*b[m, 0, 2, l]; c[3, 3][m_, l_] := -s4*d[m, 0, 1, l] - s4*b[m, 0, 2, l];  CC = ArrayFlatten@     Table[c[m, n][i, j], {m, 3}, {n, 3}, {i, 0, varNumber - 1}, {j, 0,        varNumber - 1}]; // AbsoluteTiming {2283.69, Null} 

What is a Centaur Thief’s Climb Speed?

A Thief archetype Rogue’s Second-Story Work ability states:

…you gain the ability to climb faster than normal; climbing no longer costs you extra movement. (PHB 97)

However, the Centaurs Equine Build racial ability says:

In addition, any climb that requires hands and feet is especially difficult for you because of your equine legs. When you make such a climb, each foot of movement costs you 4 extra feet, instead of the normal 1 extra foot. (GGR 16)

Both of these in my opinion are specific, in the “specific beats general” type of rulings, but does one supersede the other? Would a Centaur Thief climb 40 feet or 8 feet (1+4 extra feet) per round?

When you run out of climbing speed, can you still climb with your normal speed at a penalty?

Let’s say you’re a 40 speed, 15 climbing speed creature. There’s an initial ledge at 20 feet, but you’re trying to reach the top at 25 feet.

From the Player’s Handbook, page 182:

While climbing or swimming, each foot of movement costs 1 extra foot (2 extra feet in difficult terrain), unless a creature has a climbing or swimming speed. At the GM’s option, climbing a slippery vertical surface or one with few handholds requires a successful Strength (Athletics) check. Similarly, gaining any distance in rough water might require a successful Strength (Athletics) check.


However, on page 190:

If you have more than one speed, such as your walking speed and a flying speed, you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you’ve already moved from the new speed. The result determines how much farther you can move. If the result is 0 or less, you can’t use the new speed during the current move.


Combined with this information, there may be an odd scenario where a character has moved their maximum climbing speed.

Can they:

  1. Move the 15 feet up the cliff, and cannot reach neither the ledge or the top?
  2. Move their normal speed at twice the cost, allowing them to climb up to 20 feet in this turn and reach the ledge? (40/2= 20 feet)
  3. Move the 15 feet of climbing speed up the cliff, and are able to spend the rest of their speed (40-15 = 25 left) at the extra foot cost, since they “no longer have a climbing speed”, putting them at the very top of the cliff (25/2=10 [rounded down]), 15+10 =25 feet)?

Do class features that give a flying speed count as magical in relation to falling rules?

There are some classes, like the vengeance paladin’s capstone or the Tempest Cleric’s 17th level Stormborn feature, that grant a flying speed to a creature.

Is this considered ‘magical’ flight or is it mundane flight?

I’m thinking of this with regard to the rules on falling when a creature has their speed reduced to 0 or if knocked prone:

If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic

Is there a functional difference between having a listed climb speed and being able to climb at full walking speed?

The normal rules for climbing state that:

Each foot of movement costs 1 extra foot (2 extra feet in difficult terrain) when you’re climbing, swimming, or crawling. You ignore this extra cost if you have a climbing speed and use it to climb, or a swimming speed and use it to swim. At the DM’s option, climbing a slippery vertical surface or one with few handholds requires a successful Strength (Athletics) check. Similarly, gaining any distance in rough water might require a successful Strength (Athletics) check.

(noting that the basic rules version of the same neglects to clarify that you actually have to be using your climbing speed to benefit, and accidentally suggests that your listed climbing speed is irrelevant if your walking speed is faster)

The Thief rogue archetype has the ability Second-Story Work which provides the following benefit:

When you choose this archetype at 3rd level, you gain the ability to climb faster than normal; climbing no longer costs you extra movement.

The Athlete feat, as one of its benefits, offers the same effect:

Climbing doesn’t cost you extra movement.

As far as I can tell, a 3rd level Thief or an Athlete functionally has a climbing speed equal to their normal walking speed, but they definitely don’t actually have a climbing speed. Unlike in previous editions, having a climbing speed doesn’t seem to offer any side benefits, such as a bonus to skill/ability checks made to climb in difficult circumstances.

Is there any mechanical difference between having an actual climbing speed equal to walking speed or having the ability to climb with your walking speed without penalty? Are there any other abilities or effects a character might be subject to where the distinction is meaningful?