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.)

  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 frD, d(rA), W, I

This instruction dequantizes values from the memory address in d+rA 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 point to a two-element array of u16s)