[encoding] BumpEstimator utility

Several vello stages dynamically bump allocate intermediate data
structures. Due to graphics API limitations the backing memory
for these data structures must have been allocated at the time of
command submission even though the precise memory requirements
are unknown.

Vello currently works around this issue in two ways (see #366):
1. Vello currently prescribes a mechanism in which allocation failures
   get detected by fencing back to the CPU. The client responds to
   this event by creating larger GPU buffers using the bump
   allocator state obtained via read-back. The client has the
   choice of dropping skipping a frame or submitting the fine
   stage only after any allocations failures get resolved.

2. The encoding crate hard-codes the buffers to be large enough to be
   able to render paris-30k, making it unlikely for simple scenes to
   under-allocate. This comes at the cost of a fixed memory watermark
   of >50MB.

There may be situations when neither of these solutions are desirable
while the cost of additional CPU-side pre-processing is not considered
prohibitive for performance. It may also be acceptable to pay the cost
of generally allocating more than what's required in order to make the
this problem go away entirely (except perhaps for OOM situations).

In that spirit, this change introduces the beginnings of a
heuristic-based conservative memory estimation utility. It currently
estimates only the LineSoup buffer (which contains the curve flattening
output) within a factor of 1.1x-3.3x on the Vello test scenes (paris-30k
is estimated at 1.5x the actual requirement).

- Curves are estimated using Wang's formula which is fast to evaluate
  but produces a less optimal result than Vello's analytic approach.
  The overestimation is more pronounced with increased curvature
  variation.

- Explicit lines (such as line-tos) get estimated precisely

- Only the LineSoup buffer is supported.

- A BumpEstimator is integrated with the Scene API (gated by a feature
  flag) but the results are currently unused. Glyph runs are not
  supported as the estimator is not yet aware of the path data stored
  in glyph cache.

Cargo.toml

@@ -38,6 +38,10 @@ repository.workspace = true
 
 [features]
 default = ["wgpu"]
+# Enables GPU memory usage estimation. This performs additional computations
+# in order to estimate the minimum required allocations for buffers backing
+# bump-allocated GPU memory.
+bump_estimate = ["vello_encoding/bump_estimate"]
 hot_reload = []
 buffer_labels = []
 

crates/encoding/Cargo.toml

@@ -7,10 +7,16 @@ repository.workspace = true
 
 [features]
 default = ["full"]
+
 # Enables support for the full pipeline including late-bound
 # resources (gradients, images and glyph runs)
 full = ["skrifa", "guillotiere"]
 
+# Enables an optional GPU memory usage estimation utility. This can be used to
+# perform additional computations in order to estimate the minimum required allocations
+# for buffers backing bump-allocated GPU memory.
+bump_estimate = []
+
 [dependencies]
 bytemuck = { workspace = true }
 skrifa = { workspace = true, optional = true }

crates/encoding/src/config.rs

@@ -37,6 +37,73 @@ pub struct BumpAllocators {
     pub lines: u32,
 }
 
+#[derive(Default)]
+pub struct BumpAllocatorMemory {
+    pub total: u32,
+    pub binning: BufferSize<u32>,
+    pub ptcl: BufferSize<u32>,
+    pub tile: BufferSize<Tile>,
+    pub seg_counts: BufferSize<SegmentCount>,
+    pub segments: BufferSize<PathSegment>,
+    pub lines: BufferSize<LineSoup>,
+}
+
+impl BumpAllocators {
+    pub fn memory(&self) -> BumpAllocatorMemory {
+        let binning = BufferSize::new(self.binning);
+        let ptcl = BufferSize::new(self.ptcl);
+        let tile = BufferSize::new(self.tile);
+        let seg_counts = BufferSize::new(self.seg_counts);
+        let segments = BufferSize::new(self.segments);
+        let lines = BufferSize::new(self.lines);
+        BumpAllocatorMemory {
+            total: binning.size_in_bytes()
+                + ptcl.size_in_bytes()
+                + tile.size_in_bytes()
+                + seg_counts.size_in_bytes()
+                + segments.size_in_bytes()
+                + lines.size_in_bytes(),
+            binning,
+            ptcl,
+            tile,
+            seg_counts,
+            segments,
+            lines,
+        }
+    }
+}
+
+impl std::fmt::Display for BumpAllocatorMemory {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(
+            f,
+            "\n \
+                 \tTotal:\t\t\t{} bytes ({:.2} KB | {:.2} MB)\n\
+                 \tBinning\t\t\t{} elements ({} bytes)\n\
+                 \tPTCL\t\t\t{} elements ({} bytes)\n\
+                 \tTile:\t\t\t{} elements ({} bytes)\n\
+                 \tSegment Counts:\t\t{} elements ({} bytes)\n\
+                 \tSegments:\t\t{} elements ({} bytes)\n\
+                 \tLines:\t\t\t{} elements ({} bytes)",
+            self.total,
+            self.total as f32 / (1 << 10) as f32,
+            self.total as f32 / (1 << 20) as f32,
+            self.binning.len(),
+            self.binning.size_in_bytes(),
+            self.ptcl.len(),
+            self.ptcl.size_in_bytes(),
+            self.tile.len(),
+            self.tile.size_in_bytes(),
+            self.seg_counts.len(),
+            self.seg_counts.size_in_bytes(),
+            self.segments.len(),
+            self.segments.size_in_bytes(),
+            self.lines.len(),
+            self.lines.size_in_bytes()
+        )
+    }
+}
+
 /// Storage of indirect dispatch size values.
 ///
 /// The original plan was to reuse [`BumpAllocators`], but the WebGPU compatible

crates/encoding/src/estimate.rs

@@ -0,0 +1,288 @@
+// Copyright 2024 The Vello authors
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+//! This utility provides conservative size estimation for buffer allocations backing
+//! GPU bump memory. This estimate relies on heuristics and naturally overestimates.
+
+use super::{BufferSize, BumpAllocatorMemory, Transform};
+use peniko::kurbo::{Cap, Join, PathEl, Stroke, Vec2};
+
+const RSQRT_OF_TOL: f64 = 2.2360679775; // tol = 0.2
+
+#[derive(Clone, Default)]
+pub struct BumpEstimator {
+    // TODO: support binning
+    // TODO: support ptcl
+    // TODO: support tile
+    // TODO: support segment counts
+    // TODO: support segments
+    lines: LineSoup,
+}
+
+impl BumpEstimator {
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    pub fn reset(&mut self) {
+        *self = Self::default();
+    }
+
+    /// Combine the counts of this estimator with `other` after applying an optional `transform`.
+    pub fn append(&mut self, other: &Self, transform: Option<&Transform>) {
+        self.lines.add(&other.lines, transform_scale(transform));
+    }
+
+    pub fn count_path(
+        &mut self,
+        path: impl Iterator<Item = PathEl>,
+        t: &Transform,
+        stroke: Option<&Stroke>,
+    ) {
+        let mut caps = 1;
+        let mut joins: u32 = 0;
+        let mut lineto_lines = 0;
+        let mut fill_close_lines = 1;
+        let mut curve_lines = 0;
+        let mut curve_count = 0;
+
+        // Track the path state to correctly count empty paths and close joins.
+        let mut first_pt = None;
+        let mut last_pt = None;
+        for el in path {
+            match el {
+                PathEl::MoveTo(p0) => {
+                    first_pt = Some(p0);
+                    if last_pt.is_none() {
+                        continue;
+                    }
+                    caps += 1;
+                    joins = joins.saturating_sub(1);
+                    last_pt = None;
+                    fill_close_lines += 1;
+                }
+                PathEl::ClosePath => {
+                    if last_pt.is_some() {
+                        joins += 1;
+                        lineto_lines += 1;
+                    }
+                    last_pt = first_pt;
+                }
+                PathEl::LineTo(p0) => {
+                    last_pt = Some(p0);
+                    joins += 1;
+                    lineto_lines += 1;
+                }
+                PathEl::QuadTo(p1, p2) => {
+                    let Some(p0) = last_pt.or(first_pt) else {
+                        continue;
+                    };
+                    curve_count += 1;
+                    curve_lines +=
+                        wang::quadratic(RSQRT_OF_TOL, p0.to_vec2(), p1.to_vec2(), p2.to_vec2(), t);
+                    last_pt = Some(p2);
+                    joins += 1;
+                }
+                PathEl::CurveTo(p1, p2, p3) => {
+                    let Some(p0) = last_pt.or(first_pt) else {
+                        continue;
+                    };
+                    curve_count += 1;
+                    curve_lines += wang::cubic(
+                        RSQRT_OF_TOL,
+                        p0.to_vec2(),
+                        p1.to_vec2(),
+                        p2.to_vec2(),
+                        p3.to_vec2(),
+                        t,
+                    );
+                    last_pt = Some(p3);
+                    joins += 1;
+                }
+            }
+        }
+        let Some(style) = stroke else {
+            self.lines.linetos += lineto_lines + fill_close_lines;
+            self.lines.curves += curve_lines;
+            self.lines.curve_count += curve_count;
+            return;
+        };
+
+        // For strokes, double-count the lines to estimate offset curves.
+        self.lines.linetos += 2 * lineto_lines;
+        self.lines.curves += 2 * curve_lines;
+        self.lines.curve_count += 2 * curve_count;
+
+        let round_scale = transform_scale(Some(t));
+        let width = style.width as f32;
+        self.count_stroke_caps(style.start_cap, width, caps, round_scale);
+        self.count_stroke_caps(style.end_cap, width, caps, round_scale);
+        self.count_stroke_joins(style.join, width, joins, round_scale);
+    }
+
+    /// Produce the final total, applying an optional transform to all content.
+    pub fn tally(&self, transform: Option<&Transform>) -> BumpAllocatorMemory {
+        let scale = transform_scale(transform);
+        let binning = BufferSize::new(0);
+        let ptcl = BufferSize::new(0);
+        let tile = BufferSize::new(0);
+        let seg_counts = BufferSize::new(0);
+        let segments = BufferSize::new(0);
+        let lines = BufferSize::new(self.lines.tally(scale));
+        BumpAllocatorMemory {
+            total: binning.size_in_bytes()
+                + ptcl.size_in_bytes()
+                + tile.size_in_bytes()
+                + seg_counts.size_in_bytes()
+                + lines.size_in_bytes(),
+            binning,
+            ptcl,
+            tile,
+            seg_counts,
+            segments,
+            lines,
+        }
+    }
+
+    fn count_stroke_caps(&mut self, style: Cap, width: f32, count: u32, scale: f32) {
+        match style {
+            Cap::Butt => self.lines.linetos += count,
+            Cap::Square => self.lines.linetos += 3 * count,
+            Cap::Round => {
+                self.lines.curves += count * estimate_arc_lines(width as f32, scale);
+                self.lines.curve_count += 1;
+            }
+        }
+    }
+
+    fn count_stroke_joins(&mut self, style: Join, width: f32, count: u32, scale: f32) {
+        match style {
+            Join::Bevel => self.lines.linetos += count,
+            Join::Miter => self.lines.linetos += 2 * count,
+            Join::Round => {
+                self.lines.curves += count * estimate_arc_lines(width as f32, scale);
+                self.lines.curve_count += 1;
+            }
+        }
+    }
+}
+
+fn estimate_arc_lines(stroke_width: f32, scale: f32) -> u32 {
+    // These constants need to be kept consistent with the definitions in `flatten_arc` in
+    // flatten.wgsl.
+    const MIN_THETA: f32 = 1e-4;
+    const TOL: f32 = 0.1;
+    let radius = TOL.max(scale * stroke_width * 0.5);
+    let theta = (2. * (1. - TOL / radius).acos()).max(MIN_THETA);
+    let arc_lines = ((std::f32::consts::FRAC_PI_2 / theta).ceil() as u32).max(1);
+    arc_lines
+}
+
+#[derive(Clone, Default)]
+struct LineSoup {
+    // Explicit lines (such as linetos and non-round stroke caps/joins) and Bezier curves
+    // get tracked separately to ensure that explicit lines remain scale invariant.
+    linetos: u32,
+    curves: u32,
+
+    // Curve count is simply used to ensure a minimum number of lines get counted for each curve
+    // at very small scales to reduce the chance of under-allocating.
+    curve_count: u32,
+}
+
+impl LineSoup {
+    fn tally(&self, scale: f32) -> u32 {
+        let curves = self
+            .scaled_curve_line_count(scale)
+            .max(5 * self.curve_count);
+
+        self.linetos + curves
+    }
+
+    fn scaled_curve_line_count(&self, scale: f32) -> u32 {
+        (self.curves as f32 * scale.sqrt()).ceil() as u32
+    }
+
+    fn add(&mut self, other: &LineSoup, scale: f32) {
+        self.linetos += other.linetos;
+        self.curves += other.scaled_curve_line_count(scale);
+        self.curve_count += other.curve_count;
+    }
+}
+
+// TODO: The 32-bit Vec2 definition from cpu_shaders/util.rs could come in handy here.
+fn transform(t: &Transform, v: Vec2) -> Vec2 {
+    Vec2::new(
+        t.matrix[0] as f64 * v.x + t.matrix[2] as f64 * v.y,
+        t.matrix[1] as f64 * v.x + t.matrix[3] as f64 * v.y,
+    )
+}
+
+fn transform_scale(t: Option<&Transform>) -> f32 {
+    match t {
+        Some(t) => {
+            let m = t.matrix;
+            let v1x = m[0] + m[3];
+            let v2x = m[0] - m[3];
+            let v1y = m[1] - m[2];
+            let v2y = m[1] + m[2];
+            (v1x * v1x + v1y * v1y).sqrt() + (v2x * v2x + v2y * v2y).sqrt()
+        }
+        None => 1.,
+    }
+}
+
+/// Wang's Formula (as described in Pyramid Algorithms by Ron Goldman, 2003, Chapter 5, Section
+/// 5.6.3 on Bezier Approximation) is a fast method for computing a lower bound on the number of
+/// recursive subdivisions required to approximate a Bezier curve within a certain tolerance. The
+/// formula for a Bezier curve of degree `n`, control points p[0]...p[n], and number of levels of
+/// subdivision `l`, and flattening tolerance `tol` is defined as follows:
+///
+///     m = max([length(p[k+2] - 2 * p[k+1] + p[k]) for (0 <= k <= n-2)])
+///     l >= log_4((n * (n - 1) * m) / (8 * tol))
+///
+/// For recursive subdivisions that split a curve into 2 segments at each level, the minimum number
+/// of segments is given by 2^l. From the formula above it follows that:
+///
+///                 segments >= 2^l >= 2^log_4(x)                      (1)
+///               segments^2 >= 2^(2*log_4(x)) >= 4^log_4(x)           (2)
+///               segments^2 >= x
+///                 segments >= sqrt((n * (n - 1) * m) / (8 * tol))    (3)
+///
+/// Wang's formula computes an error bound on recursive subdivion based on the second derivative of
+/// the curve and results in a suboptimal estimate when the curvature within the curve has a lot of
+/// variation. This is expected to frequently overshoot the flattening formula used in vello (based
+/// on a numerical approximation of an integral over the continuous change in the number of flattened
+/// segments, with an error expressed in terms of curvature and infinitesimal arclength), which is
+/// closer to optimal.
+mod wang {
+    use super::*;
+
+    // The curve degree term sqrt(n * (n - 1) / 8) specialized for cubics:
+    //
+    //    sqrt(3 * (3 - 1) / 8)
+    //
+    const SQRT_OF_DEGREE_TERM_CUBIC: f64 = 0.86602540378;
+
+    // The curve degree term sqrt(n * (n - 1) / 8) specialized for quadratics:
+    //
+    //    sqrt(2 * (2 - 1) / 8)
+    //
+    const SQRT_OF_DEGREE_TERM_QUAD: f64 = 0.5;
+
+    pub fn quadratic(rsqrt_of_tol: f64, p0: Vec2, p1: Vec2, p2: Vec2, t: &Transform) -> u32 {
+        let v = -2. * p1 + p0 + p2;
+        let v = transform(t, v); // transform is distributive
+        let m = v.length();
+        (SQRT_OF_DEGREE_TERM_QUAD * m.sqrt() * rsqrt_of_tol).ceil() as u32
+    }
+
+    pub fn cubic(rsqrt_of_tol: f64, p0: Vec2, p1: Vec2, p2: Vec2, p3: Vec2, t: &Transform) -> u32 {
+        let v1 = -2. * p1 + p0 + p2;
+        let v2 = -2. * p2 + p1 + p3;
+        let v1 = transform(t, v1);
+        let v2 = transform(t, v2);
+        let m = v1.length().max(v2.length()) as f64;
+        (SQRT_OF_DEGREE_TERM_CUBIC * m.sqrt() * rsqrt_of_tol).ceil() as u32
+    }
+}