# Difference between revisions of "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 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.

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

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

```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  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))
```