Use backtick code blocks for syntax highlighting
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James Gregory
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203 changed files with 26546 additions and 25801 deletions
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63-03.md
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63-03.md
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@ -12,37 +12,41 @@ pages: 1170-1173
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**Listing 63.2 1 L63-2.ASM**
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; unoptimized dot product; 17 cycles
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fld [vec0+0] ;starts & ends on cycle 0
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fmul [vec1+0] ;starts on cycle 1
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fld [vec0+4] ;starts & ends on cycle 2
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fmul [vec1+4] ;starts on cycle 3
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fld [vec0+8] ;starts & ends on cycle 4
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fmul [vec1+8] ;starts on cycle 5
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;stalls for cycles 6-7
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faddp st(1),st(0) ;starts on cycle 8
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;stalls for cycles 9-10
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faddp st(1),st(0) ;starts on cycle 11
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;stalls for cycles 12-14
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fstp [dot] ;starts on cycle 15,
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; ends on cycle 16
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```nasm
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; unoptimized dot product; 17 cycles
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fld [vec0+0] ;starts & ends on cycle 0
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fmul [vec1+0] ;starts on cycle 1
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fld [vec0+4] ;starts & ends on cycle 2
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fmul [vec1+4] ;starts on cycle 3
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fld [vec0+8] ;starts & ends on cycle 4
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fmul [vec1+8] ;starts on cycle 5
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;stalls for cycles 6-7
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faddp st(1),st(0) ;starts on cycle 8
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;stalls for cycles 9-10
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faddp st(1),st(0) ;starts on cycle 11
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;stalls for cycles 12-14
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fstp [dot] ;starts on cycle 15,
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; ends on cycle 16
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```
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**Listing 63.3 L63-3.ASM**
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;optimized dot product; 15 cycles
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fld [vec0+0] ;starts & ends on cycle 0
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fmul [vec1+0] ;starts on cycle 1
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fld [vec0+4] ;starts & ends on cycle 2
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fmul [vec1+4] ;starts on cycle 3
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fld [vec0+8] ;starts & ends on cycle 4
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fmul [vec1+8] ;starts on cycle 5
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fxch st(1) ;no cost
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faddp st(2),st(0) ;starts on cycle 6
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;stalls for cycles 7-8
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faddp st(1),st(0) ;starts on cycle 9
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;stalls for cycles 10-12
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fstp [dot] ;starts on cycle 13,
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; ends on cycle 14
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```nasm
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;optimized dot product; 15 cycles
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fld [vec0+0] ;starts & ends on cycle 0
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fmul [vec1+0] ;starts on cycle 1
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fld [vec0+4] ;starts & ends on cycle 2
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fmul [vec1+4] ;starts on cycle 3
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fld [vec0+8] ;starts & ends on cycle 4
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fmul [vec1+8] ;starts on cycle 5
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fxch st(1) ;no cost
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faddp st(2),st(0) ;starts on cycle 6
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;stalls for cycles 7-8
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faddp st(1),st(0) ;starts on cycle 9
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;stalls for cycles 10-12
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fstp [dot] ;starts on cycle 13,
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; ends on cycle 14
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```
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### The Cross Product {#Heading8}
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@ -56,35 +60,37 @@ losing 15 cycles to stalls.
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**Listing 63.4 L63-4.ASM**
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;unoptimized cross product; 36 cycles
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fld [vec0+4] ;starts & ends on cycle 0
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fmul [vec1+8] ;starts on cycle 1
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fld [vec0+8] ;starts & ends on cycle 2
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fmul [vec1+4] ;starts on cycle 3
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;stalls for cycles 4-5
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fsubrp st(1),st(0) ;starts on cycle 6
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;stalls for cycles 7-9
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fstp [vec2+0] ;starts on cycle 10,
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; ends on cycle 11
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fld [vec0+8] ;starts & ends on cycle 12
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fmul [vec1+0] ;starts on cycle 13
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fld [vec0+0] ;starts & ends on cycle 14
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fmul [vec1+8] ;starts on cycle 15
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;stalls for cycles 16-17
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fsubrp st(1),st(0) ;starts on cycle 18
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;stalls for cycles 19-21
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fstp [vec2+4] ;starts on cycle 22,
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; ends on cycle 23
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```nasm
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;unoptimized cross product; 36 cycles
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fld [vec0+4] ;starts & ends on cycle 0
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fmul [vec1+8] ;starts on cycle 1
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fld [vec0+8] ;starts & ends on cycle 2
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fmul [vec1+4] ;starts on cycle 3
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;stalls for cycles 4-5
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fsubrp st(1),st(0) ;starts on cycle 6
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;stalls for cycles 7-9
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fstp [vec2+0] ;starts on cycle 10,
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; ends on cycle 11
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fld [vec0+8] ;starts & ends on cycle 12
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fmul [vec1+0] ;starts on cycle 13
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fld [vec0+0] ;starts & ends on cycle 14
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fmul [vec1+8] ;starts on cycle 15
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;stalls for cycles 16-17
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fsubrp st(1),st(0) ;starts on cycle 18
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;stalls for cycles 19-21
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fstp [vec2+4] ;starts on cycle 22,
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; ends on cycle 23
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fld [vec0+0] ;starts & ends on cycle 24
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fmul [vec1+4] ;starts on cycle 25
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fld [vec0+4] ;starts & ends on cycle 26
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fmul [vec1+0] ;starts on cycle 27
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;stalls for cycles 28-29
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fsubrp st(1),st(0) ;starts on cycle 30
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;stalls for cycles 31-33
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fstp [vec2+8] ;starts on cycle 34,
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; ends on cycle 35
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fld [vec0+0] ;starts & ends on cycle 24
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fmul [vec1+4] ;starts on cycle 25
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fld [vec0+4] ;starts & ends on cycle 26
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fmul [vec1+0] ;starts on cycle 27
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;stalls for cycles 28-29
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fsubrp st(1),st(0) ;starts on cycle 30
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;stalls for cycles 31-33
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fstp [vec2+8] ;starts on cycle 34,
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; ends on cycle 35
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```
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We couldn't get rid of many of the stalls in the dot product code
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because with six inputs and one output, it was impossible to interleave
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@ -101,31 +107,33 @@ of properly managing the Pentium's FP pipeline.
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**Listing 63.5 L63-5.ASM**
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;optimized cross product; 22 cycles
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fld [vec0+4] ;starts & ends on cycle 0
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fmul [vec1+8] ;starts on cycle 1
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fld [vec0+8] ;starts & ends on cycle 2
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fmul [vec1+0] ;starts on cycle 3
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fld [vec0+0] ;starts & ends on cycle 4
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fmul [vec1+4] ;starts on cycle 5
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fld [vec0+8] ;starts & ends on cycle 6
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fmul [vec1+4] ;starts on cycle 7
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fld [vec0+0] ;starts & ends on cycle 8
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fmul [vec1+8] ;starts on cycle 9
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fld [vec0+4] ;starts & ends on cycle 10
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fmul [vec1+0] ;starts on cycle 11
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fxch st(2) ;no cost
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fsubrp st(5),st(0) ;starts on cycle 12
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fsubrp st(3),st(0) ;starts on cycle 13
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fsubrp st(1),st(0) ;starts on cycle 14
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fxch st(2) ;no cost
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;stalls for cycle 15
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fstp [vec2+0] ;starts on cycle 16,
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; ends on cycle 17
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fstp [vec2+4] ;starts on cycle 18,
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; ends on cycle 19
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fstp [vec2+8] ;starts on cycle 20,
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; ends on cycle 21
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```nasm
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;optimized cross product; 22 cycles
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fld [vec0+4] ;starts & ends on cycle 0
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fmul [vec1+8] ;starts on cycle 1
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fld [vec0+8] ;starts & ends on cycle 2
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fmul [vec1+0] ;starts on cycle 3
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fld [vec0+0] ;starts & ends on cycle 4
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fmul [vec1+4] ;starts on cycle 5
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fld [vec0+8] ;starts & ends on cycle 6
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fmul [vec1+4] ;starts on cycle 7
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fld [vec0+0] ;starts & ends on cycle 8
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fmul [vec1+8] ;starts on cycle 9
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fld [vec0+4] ;starts & ends on cycle 10
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fmul [vec1+0] ;starts on cycle 11
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fxch st(2) ;no cost
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fsubrp st(5),st(0) ;starts on cycle 12
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fsubrp st(3),st(0) ;starts on cycle 13
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fsubrp st(1),st(0) ;starts on cycle 14
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fxch st(2) ;no cost
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;stalls for cycle 15
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fstp [vec2+0] ;starts on cycle 16,
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; ends on cycle 17
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fstp [vec2+4] ;starts on cycle 18,
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; ends on cycle 19
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fstp [vec2+8] ;starts on cycle 20,
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; ends on cycle 21
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```
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### Transformation {#Heading9}
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@ -140,12 +148,10 @@ transformation.)
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Transformation is calculated as:
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- - - - - -
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v1 m11 m12 m13 m14 u1
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v2 = m21 m22 m23 m24 u2
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v3 m31 m32 m33 m34 u3
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1 0 0 0 1 1
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- - - - - -
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v1 m11 m12 m13 m14 u1
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v2 = m21 m22 m23 m24 u2
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v3 m31 m32 m33 m34 u3
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1 0 0 0 1 1
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or
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