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 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.

Basic Math

Simple everyday math.

ps_add

ps_add    frD, frA, frB

This instruction adds the paired-singles in frA to the ones in frB, then stores the results in the paired-singles in frD.

ps_div

ps_div    frD, frA, frB

This instruction divides the paired-singles in frA by the ones in frB, then stores the results in the paired-singles in frD.

ps_mul

ps_mul    frD, frA, frC

This instruction multiplies the paired-singles in frA by the ones in frC, then stores the results in the paired-singles in frD.

ps_sub

ps_sub    frD, frA, frB

This instruction subtracts the paired-singles in frB from the ones in frA, then stores the results in the paired-singles in frD.