Difference between revisions of "Paired single"

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(Added complex multiplication)
(Added misc. that should finish it.)
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Paired singles are a unique part of the Gekko/[[Hardware/Broadway|Broadway]] processors used in the Gamecube and Wii. They provide fast vector math by keeping two single-precision floating point numbers in a single floating point register, and doing math across registers. This page will demonstrate how these instructions are to be used.
+
Paired singles are a unique part of the Gekko/[[Hardware/Broadway|Broadway]] processors used in the Gamecube and Wii. They provide fast vector math by keeping two single-precision floating point numbers in a single floating point register, and doing math across registers. This page will demonstrate how these instructions work.
  
 
== Quantization and Dequantization ==
 
== Quantization and Dequantization ==
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To load and store Paired-singles, one must use the psq_l and psq_st instructions respectively, or one of their variants.
 
To load and store Paired-singles, one must use the psq_l and psq_st instructions respectively, or one of their variants.
 
=== psq_l ===
 
=== psq_l ===
  psq_l     frD, d(rA), W, I
+
  psq_l     frD, d(rA), W, I
 
This instruction dequantizes values from the memory address in '''d'''+('''rA'''|0) and puts them into PS0 and PS1 in '''frD'''. If '''W''' is 1, however, it only dequantizes one number, and places that into PS0. PS1 is loaded with 1.0 always when '''W''' is 1. '''I''' specifies the GQR to use for dequantization parameters. The two numbers read from the memory are directly after each other, regardless of size (for example, if the GQR specified to load as a u16, you would have '''d'''+('''rA'''|0) point to a two-element array of u16s)
 
This instruction dequantizes values from the memory address in '''d'''+('''rA'''|0) and puts them into PS0 and PS1 in '''frD'''. If '''W''' is 1, however, it only dequantizes one number, and places that into PS0. PS1 is loaded with 1.0 always when '''W''' is 1. '''I''' specifies the GQR to use for dequantization parameters. The two numbers read from the memory are directly after each other, regardless of size (for example, if the GQR specified to load as a u16, you would have '''d'''+('''rA'''|0) point to a two-element array of u16s)
 
===== psq_lx =====
 
===== psq_lx =====
  psq_lx   frD, rA, rB, W, I
+
  psq_lx     frD, rA, rB, W, I
 
This instruction acts exactly like psq_l, except instead of ('''rA''') being offset by '''d''', it is offset by ('''rB''').
 
This instruction acts exactly like psq_l, except instead of ('''rA''') being offset by '''d''', it is offset by ('''rB''').
 
===== psq_lu =====
 
===== psq_lu =====
  psq_lu   frD, d(rA), W, I
+
  psq_lu     frD, d(rA), W, I
 
This instruction acts exactly like psq_l, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
 
This instruction acts exactly like psq_l, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
 
===== psq_lux =====
 
===== psq_lux =====
  psq_lux   frD, rA, rB, W, I
+
  psq_lux   frD, rA, rB, W, I
 
This instruction acts exactly like psq_lx, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
 
This instruction acts exactly like psq_lx, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
  
 
=== psq_st ===
 
=== psq_st ===
  psq_st   frD, d(rA), W, I
+
  psq_st     frD, d(rA), W, I
 
This instruction quantizes values from the Paired Singles in '''frD''' and places them in the memory address in '''d'''+('''rA'''|0). If '''W''' is 1, however, it only quantizes PS0. '''I''' specifies the GQR to use for dequantization parameters. The two numbers written to memory are directly after each other, regardless of size (for example, if the GQR specified to store as a u16, '''d'''+('''rA'''|0) would be treated as a two-element array of u16s)
 
This instruction quantizes values from the Paired Singles in '''frD''' and places them in the memory address in '''d'''+('''rA'''|0). If '''W''' is 1, however, it only quantizes PS0. '''I''' specifies the GQR to use for dequantization parameters. The two numbers written to memory are directly after each other, regardless of size (for example, if the GQR specified to store as a u16, '''d'''+('''rA'''|0) would be treated as a two-element array of u16s)
 
===== psq_stx =====
 
===== psq_stx =====
  psq_stx   frD, rA, rB, W, I
+
  psq_stx   frD, rA, rB, W, I
 
This instruction acts exactly like psq_st, except instead of ('''rA''') being offset by '''d''', it is offset by ('''rB''').
 
This instruction acts exactly like psq_st, except instead of ('''rA''') being offset by '''d''', it is offset by ('''rB''').
 
===== psq_stu =====
 
===== psq_stu =====
  psq_stu   frD, d(rA), W, I
+
  psq_stu   frD, d(rA), W, I
 
This instruction acts exactly like psq_st, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
 
This instruction acts exactly like psq_st, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
 
===== psq_stux =====
 
===== psq_stux =====
  psq_stux frD, rA, rB, W, I
+
  psq_stux   frD, rA, rB, W, I
 
This instruction acts exactly like psq_stx, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
 
This instruction acts exactly like psq_stx, except '''rA''' cannot be 0, and '''d'''+('''rA''') is placed back into '''rA'''.
  
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These functions operate on one FPR.
 
These functions operate on one FPR.
 
=== ps_abs ===
 
=== ps_abs ===
  ps_abs   frD, frB
+
  ps_abs     frD, frB
  
 
  frD(ps0) = abs(frB(ps0))
 
  frD(ps0) = abs(frB(ps0))
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=== ps_mr ===
 
=== ps_mr ===
  ps_mr     frD, frB
+
  ps_mr     frD, frB
  
 
  frD(ps0) = frB(ps0)
 
  frD(ps0) = frB(ps0)
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=== ps_nabs ===
 
=== ps_nabs ===
  ps_nabs   frD, frB
+
  ps_nabs   frD, frB
  
 
  frD(ps0) = -abs(frB(ps0))
 
  frD(ps0) = -abs(frB(ps0))
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=== ps_neg ===
 
=== ps_neg ===
  ps_neg   frD, frB
+
  ps_neg     frD, frB
  
 
  frD(ps0) = -frB(ps0)
 
  frD(ps0) = -frB(ps0)
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=== ps_res ===
 
=== ps_res ===
  ps_res   frD, frB
+
  ps_res     frD, frB
  
 
  frD(ps0) = -1/frB(ps0)
 
  frD(ps0) = -1/frB(ps0)
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=== ps_rsqrte ===
 
=== ps_rsqrte ===
  ps_rsqrte frD, frB
+
  ps_rsqrte frD, frB
  
 
  frD(ps0) = -1/sqrt(frB(ps0))
 
  frD(ps0) = -1/sqrt(frB(ps0))
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Simple everyday math.
 
Simple everyday math.
 
=== ps_add ===
 
=== ps_add ===
  ps_add   frD, frA, frB
+
  ps_add     frD, frA, frB
  
 
  frD(ps0) = frA(ps0) + frB(ps0)
 
  frD(ps0) = frA(ps0) + frB(ps0)
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=== ps_div ===
 
=== ps_div ===
  ps_div   frD, frA, frB
+
  ps_div     frD, frA, frB
  
 
  frD(ps0) = frA(ps0) / frB(ps0)
 
  frD(ps0) = frA(ps0) / frB(ps0)
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=== ps_mul ===
 
=== ps_mul ===
  ps_mul   frD, frA, frC
+
  ps_mul     frD, frA, frC
  
 
  frD(ps0) = frA(ps0) * frC(ps0)
 
  frD(ps0) = frA(ps0) * frC(ps0)
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=== ps_sub ===
 
=== ps_sub ===
  ps_sub   frD, frA, frB
+
  ps_sub     frD, frA, frB
  
 
  frD(ps0) = frA(ps0) - frB(ps0)
 
  frD(ps0) = frA(ps0) - frB(ps0)
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== Comparison ==
 
== Comparison ==
 
=== ps_cmpo0 ===
 
=== ps_cmpo0 ===
  ps_cmpo0 crfD, frA, frB
+
  ps_cmpo0   crfD, frA, frB
  ps_cmpu0 crfD, frA, frB
+
  ps_cmpu0   crfD, frA, frB
  
 
  cfrD = frA(ps0) compare frB(ps0)
 
  cfrD = frA(ps0) compare frB(ps0)
  
 
=== ps_cmpo1 ===
 
=== ps_cmpo1 ===
  ps_cmpo1 crfD, frA, frB
+
  ps_cmpo1   crfD, frA, frB
  ps_cmpu1 crfD, frA, frB
+
  ps_cmpu1   crfD, frA, frB
  
 
  cfrD = frA(ps1) compare frB(ps1)
 
  cfrD = frA(ps1) compare frB(ps1)
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These instructions multiply in complex ways
 
These instructions multiply in complex ways
 
=== ps_madd ===
 
=== ps_madd ===
  ps_madd   frD, frA, frC, frB
+
  ps_madd   frD, frA, frC, frB
  
 
  frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0)
 
  frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0)
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=== ps_madds0 ===
 
=== ps_madds0 ===
  ps_madds0 frD, frA, frC, frB
+
  ps_madds0 frD, frA, frC, frB
  
 
  frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0)
 
  frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0)
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=== ps_madds1 ===
 
=== ps_madds1 ===
  ps_madds1 frD, frA, frC, frB
+
  ps_madds1 frD, frA, frC, frB
  
 
  frD(ps0) = frA(ps0) * frC(ps1) + frB(ps0)
 
  frD(ps0) = frA(ps0) * frC(ps1) + frB(ps0)
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=== ps_msub ===
 
=== ps_msub ===
  ps_msub   frD, frA, frC, frB
+
  ps_msub   frD, frA, frC, frB
  
 
  frD(ps0) = frA(ps0) * frC(ps0) - frB(ps0)
 
  frD(ps0) = frA(ps0) * frC(ps0) - frB(ps0)
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=== ps_muls0 ===
 
=== ps_muls0 ===
  ps_muls0 frD, frA, frC
+
  ps_muls0   frD, frA, frC
  
 
  frD(ps0) = frA(ps0) * frC(ps0)
 
  frD(ps0) = frA(ps0) * frC(ps0)
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=== ps_muls1 ===
 
=== ps_muls1 ===
  ps_muls1 frD, frA, frC
+
  ps_muls1   frD, frA, frC
  
 
  frD(ps0) = frA(ps0) * frC(ps1)
 
  frD(ps0) = frA(ps0) * frC(ps1)
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=== ps_nmadd ===
 
=== ps_nmadd ===
  ps_nmadd frD, frA, frC, frB
+
  ps_nmadd   frD, frA, frC, frB
  
 
  frD(ps0) = -(frA(ps0) * frC(ps0) + frB(ps0))
 
  frD(ps0) = -(frA(ps0) * frC(ps0) + frB(ps0))
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=== ps_nmsub ===
 
=== ps_nmsub ===
  ps_nmsub frD, frA, frC, frB
+
  ps_nmsub   frD, frA, frC, frB
  
 
  frD(ps0) = -(frA(ps0) * frC(ps0) - frB(ps0))
 
  frD(ps0) = -(frA(ps0) * frC(ps0) - frB(ps0))
 
  frD(ps1) = -(frA(ps1) * frC(ps1) - frB(ps1))
 
  frD(ps1) = -(frA(ps1) * frC(ps1) - frB(ps1))
 +
 +
== Miscellaneous ==
 +
Whatever doesn't fit into the other categories
 +
=== ps_merge00 ===
 +
ps_merge00 frD, frA, frB
 +
 +
frD(ps0) = frA(ps0)
 +
frD(ps1) = frB(ps0)
 +
 +
=== ps_merge01 ===
 +
ps_merge01 frD, frA, frB
 +
 +
frD(ps0) = frA(ps0)
 +
frD(ps1) = frB(ps1)
 +
 +
=== ps_merge10 ===
 +
ps_merge10 frD, frA, frB
 +
 +
frD(ps0) = frA(ps1)
 +
frD(ps1) = frB(ps0)
 +
 +
=== ps_merge11 ===
 +
ps_merge11 frD, frA, frB
 +
 +
frD(ps0) = frA(ps1)
 +
frD(ps1) = frB(ps1)
 +
 +
=== ps_sel ===
 +
ps_sel    frD, frA, frC, frB
 +
 +
if(frA(ps0) >= 0)
 +
        frD(ps0) = frC(ps0)
 +
else
 +
        frD(ps0) = frB(ps0)
 +
if(frA(ps1) >= 0)
 +
        frD(ps1) = frC(ps1)
 +
else
 +
        frD(ps1) = frB(ps1)
 +
 +
=== ps_sum0 ===
 +
ps_sum0    frD, frA, frC, frB
 +
 +
frD(ps0) = frA(ps0) + frB(ps1)
 +
frD(ps1) = frC(ps1)
 +
 +
=== ps_sum1 ===
 +
ps_sum1    frD, frA, frC, frB
 +
 +
frD(ps0) = frC(ps0)
 +
frD(ps1) = frA(ps0) + frB(ps1)

Revision as of 22:52, 10 July 2010

Paired singles are a unique part of the Gekko/Broadway processors used in the Gamecube and Wii. They provide fast vector math by keeping two single-precision floating point numbers in a single floating point register, and doing math across registers. This page will demonstrate how these instructions work.

Quantization and Dequantization

All numbers must be quantized before being put into Paired Singles. For conversion from non-floats, in order to allow for greater flexibility, there is a form of scaling implemented. All quantization is controlled by the GQRs (Graphics Quantization Registers). The GQRs are 32bit registers containing the conversion types and scaling factors for storing and loading. (During loading, it dequantizes. During storing, it quantizes.)

GQR
  31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
Access U R/W U R/W
Field L_Scale L_Type
  15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Access U R/W U R/W
Field S_Scale S_Type
Field Description
L_* Values for dequantization.
S_* Values for quantization.
Scale Signed. During dequantization divide the number by (2^scale). During quantization, multiply the number by (2^scale).
Type 0: Float (this does no scaling during de/quantization), 4: Unsigned 8bit, 5: Unsigned 16bit, 6: Signed 8bit, 7: Signed 16bit.


Loading and Storing

To load and store Paired-singles, one must use the psq_l and psq_st instructions respectively, or one of their variants.

psq_l

psq_l      frD, d(rA), W, I

This instruction dequantizes values from the memory address in d+(rA|0) and puts them into PS0 and PS1 in frD. If W is 1, however, it only dequantizes one number, and places that into PS0. PS1 is loaded with 1.0 always when W is 1. I specifies the GQR to use for dequantization parameters. The two numbers read from the memory are directly after each other, regardless of size (for example, if the GQR specified to load as a u16, you would have d+(rA|0) point to a two-element array of u16s)

psq_lx
psq_lx     frD, rA, rB, W, I

This instruction acts exactly like psq_l, except instead of (rA) being offset by d, it is offset by (rB).

psq_lu
psq_lu     frD, d(rA), W, I

This instruction acts exactly like psq_l, except rA cannot be 0, and d+(rA) is placed back into rA.

psq_lux
psq_lux    frD, rA, rB, W, I

This instruction acts exactly like psq_lx, except rA cannot be 0, and d+(rA) is placed back into rA.

psq_st

psq_st     frD, d(rA), W, I

This instruction quantizes values from the Paired Singles in frD and places them in the memory address in d+(rA|0). If W is 1, however, it only quantizes PS0. I specifies the GQR to use for dequantization parameters. The two numbers written to memory are directly after each other, regardless of size (for example, if the GQR specified to store as a u16, d+(rA|0) would be treated as a two-element array of u16s)

psq_stx
psq_stx    frD, rA, rB, W, I

This instruction acts exactly like psq_st, except instead of (rA) being offset by d, it is offset by (rB).

psq_stu
psq_stu    frD, d(rA), W, I

This instruction acts exactly like psq_st, except rA cannot be 0, and d+(rA) is placed back into rA.

psq_stux
psq_stux   frD, rA, rB, W, I

This instruction acts exactly like psq_stx, except rA cannot be 0, and d+(rA) is placed back into rA.

Single Parameter Operations

These functions operate on one FPR.

ps_abs

ps_abs     frD, frB
frD(ps0) = abs(frB(ps0))
frD(ps1) = abs(frB(ps1))

ps_mr

ps_mr      frD, frB
frD(ps0) = frB(ps0)
frD(ps1) = frB(ps1)

ps_nabs

ps_nabs    frD, frB
frD(ps0) = -abs(frB(ps0))
frD(ps1) = -abs(frB(ps1))

ps_neg

ps_neg     frD, frB
frD(ps0) = -frB(ps0)
frD(ps1) = -frB(ps1)

ps_res

ps_res     frD, frB
frD(ps0) = -1/frB(ps0)
frD(ps1) = -1/frB(ps1)

Accurate to a precision of 1/4096.

ps_rsqrte

ps_rsqrte  frD, frB
frD(ps0) = -1/sqrt(frB(ps0))
frD(ps1) = -1/sqrt(frB(ps1))

Accurate to a precision of 1/4096.

Basic Math

Simple everyday math.

ps_add

ps_add     frD, frA, frB
frD(ps0) = frA(ps0) + frB(ps0)
frD(ps1) = frA(ps1) + frB(ps1)

ps_div

ps_div     frD, frA, frB
frD(ps0) = frA(ps0) / frB(ps0)
frD(ps1) = frA(ps1) / frB(ps1)

ps_mul

ps_mul     frD, frA, frC
frD(ps0) = frA(ps0) * frC(ps0)
frD(ps1) = frA(ps1) * frC(ps1)

ps_sub

ps_sub     frD, frA, frB
frD(ps0) = frA(ps0) - frB(ps0)
frD(ps1) = frA(ps1) - frB(ps1)

Comparison

ps_cmpo0

ps_cmpo0   crfD, frA, frB
ps_cmpu0   crfD, frA, frB
cfrD = frA(ps0) compare frB(ps0)

ps_cmpo1

ps_cmpo1   crfD, frA, frB
ps_cmpu1   crfD, frA, frB
cfrD = frA(ps1) compare frB(ps1)

Complex Multiply

These instructions multiply in complex ways

ps_madd

ps_madd    frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0)
frD(ps1) = frA(ps1) * frC(ps1) + frB(ps1)

ps_madds0

ps_madds0  frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0)
frD(ps1) = frA(ps1) * frC(ps0) + frB(ps1)

ps_madds1

ps_madds1  frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps1) + frB(ps0)
frD(ps1) = frA(ps1) * frC(ps1) + frB(ps1)

ps_msub

ps_msub    frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps0) - frB(ps0)
frD(ps1) = frA(ps1) * frC(ps1) - frB(ps1)

ps_muls0

ps_muls0   frD, frA, frC
frD(ps0) = frA(ps0) * frC(ps0)
frD(ps1) = frA(ps1) * frC(ps0)

ps_muls1

ps_muls1   frD, frA, frC
frD(ps0) = frA(ps0) * frC(ps1)
frD(ps1) = frA(ps1) * frC(ps1)

ps_nmadd

ps_nmadd   frD, frA, frC, frB
frD(ps0) = -(frA(ps0) * frC(ps0) + frB(ps0))
frD(ps1) = -(frA(ps1) * frC(ps1) + frB(ps1))

ps_nmsub

ps_nmsub   frD, frA, frC, frB
frD(ps0) = -(frA(ps0) * frC(ps0) - frB(ps0))
frD(ps1) = -(frA(ps1) * frC(ps1) - frB(ps1))

Miscellaneous

Whatever doesn't fit into the other categories

ps_merge00

ps_merge00 frD, frA, frB
frD(ps0) = frA(ps0)
frD(ps1) = frB(ps0)

ps_merge01

ps_merge01 frD, frA, frB
frD(ps0) = frA(ps0)
frD(ps1) = frB(ps1)

ps_merge10

ps_merge10 frD, frA, frB
frD(ps0) = frA(ps1)
frD(ps1) = frB(ps0)

ps_merge11

ps_merge11 frD, frA, frB
frD(ps0) = frA(ps1)
frD(ps1) = frB(ps1)

ps_sel

ps_sel     frD, frA, frC, frB
if(frA(ps0) >= 0)
        frD(ps0) = frC(ps0)
else
        frD(ps0) = frB(ps0)
if(frA(ps1) >= 0)
        frD(ps1) = frC(ps1)
else
        frD(ps1) = frB(ps1)

ps_sum0

ps_sum0    frD, frA, frC, frB
frD(ps0) = frA(ps0) + frB(ps1)
frD(ps1) = frC(ps1)

ps_sum1

ps_sum1    frD, frA, frC, frB
frD(ps0) = frC(ps0)
frD(ps1) = frA(ps0) + frB(ps1)