# Instancing¶

The attribute descriptor lets the attribute unit compute the address of an attribute given the vertex and instance ID. Unfortunately, the way this works is rather complicated when instancing is enabled.

To explain this, first we need to explain how compute and vertex threads are dispatched. When a quad is dispatched, it receives a single, linear index. However, we need to translate that index into a (vertex id, instance id) pair. One option would be to do:

but this involves a costly division and modulus by an arbitrary number. Instead, we could pad num_vertices. We dispatch padded_num_vertices * num_instances threads instead of num_vertices * num_instances, which results in some “extra” threads with vertex_id >= num_vertices, which we have to discard. The more we pad num_vertices, the more “wasted” threads we dispatch, but the division is potentially easier.

One straightforward choice is to pad num_vertices to the next power of two, which means that the division and modulus are just simple bit shifts and masking. But the actual algorithm is a bit more complicated. The thread dispatcher has special support for dividing by 3, 5, 7, and 9, in addition to dividing by a power of two. As a result, padded_num_vertices can be 1, 3, 5, 7, or 9 times a power of two. This results in less wasted threads, since we need less padding.

padded_num_vertices is picked by the hardware. The driver just specifies the actual number of vertices. Note that padded_num_vertices is a multiple of four (presumably because threads are dispatched in groups of 4). Also, padded_num_vertices is always at least one more than num_vertices, which seems like a quirk of the hardware. For larger num_vertices, the hardware uses the following algorithm: using the binary representation of num_vertices, we look at the most significant set bit as well as the following 3 bits. Let n be the number of bits after those 4 bits. Then we set padded_num_vertices according to the following table:

high bits |
padded_num_vertices |
---|---|

1000 |
\(9 \cdot 2^n\) |

1001 |
\(5 \cdot 2^{n+1}\) |

101x |
\(3 \cdot 2^{n+2}\) |

110x |
\(7 \cdot 2^{n+1}\) |

111x |
\(2^{n+4}\) |

For example, if num_vertices = 70 is passed to glDraw(), its binary representation is 1000110, so n = 3 and the high bits are 1000, and therefore padded_num_vertices = \(9 \cdot 2^3\) = 72.

The attribute unit works in terms of the original linear_id. if num_instances = 1, then they are the same, and everything is simple. However, with instancing things get more complicated. There are four possible modes, two of them we can group together:

Use the linear_id directly. Only used when there is no instancing.

2. Use the linear_id modulo a constant. This is used for per-vertex attributes with instancing enabled by making the constant equal padded_num_vertices. Because the modulus is always padded_num_vertices, this mode only supports a modulus that is a power of 2 times 1, 3, 5, 7, or 9. The shift field specifies the power of two, while the extra_flags field specifies the odd number. If shift = n and extra_flags = m, then the modulus is \((2m + 1) \cdot 2^n\). As an example, if num_vertices = 70, then as computed above, padded_num_vertices = \(9 \cdot 2^3\), so we should set extra_flags = 4 and shift = 3. Note that we must exactly follow the hardware algorithm used to get padded_num_vertices in order to correctly implement per-vertex attributes.

3. Divide the linear_id by a constant. In order to correctly implement instance divisors, we have to divide linear_id by padded_num_vertices times to user-specified divisor. So first we compute padded_num_vertices, again following the exact same algorithm that the hardware uses, then multiply it by the GL-level divisor to get the hardware-level divisor. This case is further divided into two more cases. If the hardware-level divisor is a power of two, then we just need to shift. The shift amount is specified by the shift field, so that the hardware-level divisor is just \(2^\text{shift}\).

If it isn’t a power of two, then we have to divide by an arbitrary integer. For that, we use the well-known technique of multiplying by an approximation of the inverse. The driver must compute the magic multiplier and shift amount, and then the hardware does the multiplication and shift. The hardware and driver also use the “round-down” optimization as described in https://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf. The hardware further assumes the multiplier is between \(2^{31}\) and \(2^{32}\), so the high bit is implicitly set to 1 even though it is set to 0 by the driver – presumably this simplifies the hardware multiplier a little. The hardware first multiplies linear_id by the multiplier and takes the high 32 bits, then applies the round-down correction if extra_flags = 1, then finally shifts right by the shift field.

There are some differences between ridiculousfish’s algorithm and the Mali hardware algorithm, which means that the reference code from ridiculousfish doesn’t always produce the right constants. Mali does not use the pre-shift optimization, since that would make a hardware implementation slower (it would have to always do the pre-shift, multiply, and post-shift operations). It also forces the multiplier to be at least \(2^{31}\), which means that the exponent is entirely fixed, so there is no trial-and-error. Altogether, given the divisor d, the algorithm the driver must follow is:

Set shift = \(\lfloor \log_2(d) \rfloor\).

Compute \(m = \lceil 2^{shift + 32} / d \rceil\) and \(e = 2^{shift + 32} % d\).

If \(e <= 2^{shift}\), then we need to use the round-down algorithm. Set magic_divisor = m - 1 and extra_flags = 1. 4. Otherwise, set magic_divisor = m and extra_flags = 0.