Paired single
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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 pointer register, and multiplying across between registers. This page will demonstrate how these instructions are to be used.
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
This instruction gets the absolute values of both paired-singles in frB, and stores them in the paired-singles in frD.
ps_mr
ps_mr frD, frB
This instruction moves both paired-singles in frB into the paired-singles in frD.
ps_nabs
ps_nabs frD, frB
This instruction gets the negative absolute values of both paired-singles in frB, and stores them in the paired-singles in frD.
ps_neg
ps_neg frD, frB
This instruction negates the values of both paired-singles in frB, and stores them in the paired-singles in frD.
ps_res
ps_res frD, frB
This instruction gets an estimate of the reciprocals of both paired-singles in frB accurate to a precision of 1/4096, and stores them in the paired-singles in frD.
ps_rsqrte
ps_rsqrte frD, frB
This instruction gets an estimate of the reciprocals of the square roots of both paired-singles in frB accurate to a precision of 1/4096, and stores them in the paired-singles in frD.