Paired single
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 rB+(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 rB+(rA) is placed back into rA.
Single Parameter Operations
These functions operate on one FPR.
ps_abs
Single floating-point absolute value on both ps0 and ps1.
ps_abs frD, frB
frD(ps0) = abs(frB(ps0)) frD(ps1) = abs(frB(ps1))
ps_mr
Move both ps0 and ps1 from one fpr to another.
ps_mr frD, frB
frD(ps0) = frB(ps0) frD(ps1) = frB(ps1)
ps_nabs
Single floating-point negative abs value on both ps0 and ps1.
ps_nabs frD, frB
frD(ps0) = -abs(frB(ps0)) frD(ps1) = -abs(frB(ps1))
ps_neg
Single floating-point negate on both ps0 and ps1.
ps_neg frD, frB
frD(ps0) = -frB(ps0) frD(ps1) = -frB(ps1)
ps_res
Reciprocal of ps0 and ps1.
ps_res frD, frB
frD(ps0) = -1/frB(ps0) frD(ps1) = -1/frB(ps1)
Accurate to a precision of 1/4096.
ps_rsqrte
Single floating-point reciprocal sqrt estimate.
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
Single floating-point add on both ps0 and ps1.
ps_add frD, frA, frB
frD(ps0) = frA(ps0) + frB(ps0) frD(ps1) = frA(ps1) + frB(ps1)
ps_sub
Single floating-point subtract on both ps0 and ps1.
ps_sub frD, frA, frB
frD(ps0) = frA(ps0) - frB(ps0) frD(ps1) = frA(ps1) - frB(ps1)
ps_mul
Single floating-point multiply on both ps0 and ps1.
ps_mul frD, frA, frC
frD(ps0) = frA(ps0) * frC(ps0) frD(ps1) = frA(ps1) * frC(ps1)
ps_div
Single floating-point divide on both ps0 and ps1.
ps_div frD, frA, frB
frD(ps0) = frA(ps0) / frB(ps0) frD(ps1) = frA(ps1) / frB(ps1)
Comparison
ps_cmpo0
Ordered compare of ps0 values.
ps_cmpo0 crfD, frA, frB ps_cmpu0 crfD, frA, frB
cfrD = frA(ps0) compare frB(ps0)
ps_cmpo1
Ordered compare of ps1 values.
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
Single floating-point madd on both ps0 and ps1.
ps_madd frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0) frD(ps1) = frA(ps1) * frC(ps1) + frB(ps1)
ps_madds0
Scalar-vector multiply-add using ps0 for scalar.
ps_madds0 frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps0) + frB(ps0) frD(ps1) = frA(ps1) * frC(ps0) + frB(ps1)
ps_madds1
Scalar-vector multiply-add using ps1 for scalar.
ps_madds1 frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps1) + frB(ps0) frD(ps1) = frA(ps1) * frC(ps1) + frB(ps1)
ps_msub
Single floating-point msub on both ps0 and ps1.
ps_msub frD, frA, frC, frB
frD(ps0) = frA(ps0) * frC(ps0) - frB(ps0) frD(ps1) = frA(ps1) * frC(ps1) - frB(ps1)
ps_muls0
Scalar-vector multiply using ps0 for scalar.
ps_muls0 frD, frA, frC
frD(ps0) = frA(ps0) * frC(ps0) frD(ps1) = frA(ps1) * frC(ps0)
ps_muls1
Scalar-vector multiply using ps1 for scalar.
ps_muls1 frD, frA, frC
frD(ps0) = frA(ps0) * frC(ps1) frD(ps1) = frA(ps1) * frC(ps1)
ps_nmadd
Single floating-point nmadd on both ps0 and ps1.
ps_nmadd frD, frA, frC, frB
frD(ps0) = -(frA(ps0) * frC(ps0) + frB(ps0)) frD(ps1) = -(frA(ps1) * frC(ps1) + frB(ps1))
ps_nmsub
Single floating-point nmsub on both ps0 and ps1.
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
Register move allowing swap/merge of ps0 values.
ps_merge00 frD, frA, frB
frD(ps0) = frA(ps0) frD(ps1) = frB(ps0)
ps_merge01
Register move allowing swap/merge of ps0 and ps1 values.
ps_merge01 frD, frA, frB
frD(ps0) = frA(ps0) frD(ps1) = frB(ps1)
ps_merge10
Register move allowing swap/merge of ps1 and ps0 values.
ps_merge10 frD, frA, frB
frD(ps0) = frA(ps1) frD(ps1) = frB(ps0)
ps_merge11
Register move allowing swap/merge of ps0 values.
ps_merge11 frD, frA, frB
frD(ps0) = frA(ps1) frD(ps1) = frB(ps1)
ps_sel
Single floating-point select on both ps0 and ps1.
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
Add a ps0 value to a ps1 value, result in ps0.
ps_sum0 frD, frA, frC, frB
frD(ps0) = frA(ps0) + frB(ps1) frD(ps1) = frC(ps1)
ps_sum1
Add a ps0 value to a ps1 value, result in ps1.
ps_sum1 frD, frA, frC, frB
frD(ps0) = frC(ps0) frD(ps1) = frA(ps0) + frB(ps1)