Misc/abrash-black-book
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James Gregory 2013-12-30 18:34:31 +11:00
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@ -38,8 +38,8 @@
### The Cross Product {#Heading8}
When last we looked at the cross product, we found that it’s handy for
generating a vector that’s normal to two other vectors. The cross
When last we looked at the cross product, we found that it's handy for
generating a vector that's normal to two other vectors. The cross
product is calculated as [u~2~v~3~-u~3~v~2~ u~3~v~1~-u~1~v~3~
u~1~v~2~-u~2~v~1~]. The theoretical minimum cycle count for the cross
product is 21 cycles. Listing 63.4 shows a straightforward
@ -78,7 +78,7 @@ losing 15 cycles to stalls.
fstp [vec2+8] ;starts on cycle 34,
; ends on cycle 35
We couldn’t get rid of many of the stalls in the dot product code
We couldn't get rid of many of the stalls in the dot product code
because with six inputs and one output, it was impossible to interleave
all the operations. However, the cross product, with three outputs, is
much more amenable to optimization. In fact, three is the magic number;
@ -89,7 +89,7 @@ only one cycle to a stall, the cycle before the first FST; the relevant
FSUB has just finished on the preceding cycle, so we run into the extra
cycle of latency associated with FST. Listing 63.5 is more than 60
percent faster than Listing 63.4, a striking illustration of the power
of properly managing the Pentium’s FP pipeline.
of properly managing the Pentium's FP pipeline.
**Listing 63.5 L63-5.ASM**
@ -124,7 +124,7 @@ of properly managing the Pentium’s FP pipeline.
Transforming a point, for example from worldspace to viewspace, is one
of the most heavily used FP operations in realtime 3-D. Conceptually,
transformation is nothing more than three dot products and three
additions, as I will discuss in Chapter 61. (Note that I’m talking about
additions, as I will discuss in Chapter 61. (Note that I'm talking about
a subset of a general 4x4 transformation matrix, where the fourth row is
always implicitly [0 0 0 1]. This limited form suffices for common
transformations, and does 25 percent less work than a full 4x4