Simplify singularValueDecompose2dScale in order to make it using less memory

In using the Firefox profiler (with JS allocations tracking) and wuppertal.pdf, I noticed
we were using a bit too much memory for a function which is supposed to just compute 2 numbers.
The memory used by itself isn't so important but having a too much objects lead to waste some time
to gc them.

So this patch aims to simplify it a bit.

src/display/canvas.js

@@ -63,6 +63,9 @@ const FULL_CHUNK_HEIGHT = 16;
 // creating a new DOMMatrix object each time we need it.
 const SCALE_MATRIX = new DOMMatrix();
 
+// Used to get some coordinates.
+const XY = new Float32Array(2);
+
 /**
  * Overrides certain methods on a 2d ctx so that when they are called they
  * will also call the same method on the destCtx. The methods that are
@@ -527,9 +530,9 @@ class CanvasExtraState {
       }
       // Stroked paths can be outside of the path bounding box by 1/2 the line
       // width.
-      const scale = Util.singularValueDecompose2dScale(transform);
-      const xStrokePad = (scale[0] * this.lineWidth) / 2;
-      const yStrokePad = (scale[1] * this.lineWidth) / 2;
+      Util.singularValueDecompose2dScale(transform, XY);
+      const xStrokePad = (XY[0] * this.lineWidth) / 2;
+      const yStrokePad = (XY[1] * this.lineWidth) / 2;
       box[0] -= xStrokePad;
       box[1] -= yStrokePad;
       box[2] += xStrokePad;
@@ -782,15 +785,14 @@ function getImageSmoothingEnabled(transform, interpolate) {
     return true;
   }
 
-  const scale = Util.singularValueDecompose2dScale(transform);
+  Util.singularValueDecompose2dScale(transform, XY);
   // Round to a 32bit float so that `<=` check below will pass for numbers that
   // are very close, but not exactly the same 64bit floats.
-  scale[0] = Math.fround(scale[0]);
-  scale[1] = Math.fround(scale[1]);
   const actualScale = Math.fround(
     OutputScale.pixelRatio * PixelsPerInch.PDF_TO_CSS_UNITS
   );
-  return scale[0] <= actualScale && scale[1] <= actualScale;
+  // `XY` is a Float32Array.
+  return XY[0] <= actualScale && XY[1] <= actualScale;
 }
 
 const LINE_CAP_STYLES = ["butt", "round", "square"];
@@ -1963,12 +1965,12 @@ class CanvasGraphics {
             [a, b, c, d, 0, 0],
             invPatternTransform
           );
-          const [sx, sy] = Util.singularValueDecompose2dScale(transf);
+          Util.singularValueDecompose2dScale(transf, XY);
 
           // Cancel the pattern scaling of the line width.
           // If sx and sy are different, unfortunately we can't do anything and
           // we'll have a rendering bug.
-          ctx.lineWidth *= Math.max(sx, sy) / fontSize;
+          ctx.lineWidth *= Math.max(XY[0], XY[1]) / fontSize;
           ctx.stroke(
             this.#getScaledPath(path, currentTransform, patternStrokeTransform)
           );
@@ -2648,9 +2650,7 @@ class CanvasGraphics {
         rect[2] = width;
         rect[3] = height;
 
-        const [scaleX, scaleY] = Util.singularValueDecompose2dScale(
-          getCurrentTransform(this.ctx)
-        );
+        Util.singularValueDecompose2dScale(getCurrentTransform(this.ctx), XY);
         const { viewportScale } = this;
         const canvasWidth = Math.ceil(
           width * this.outputScaleX * viewportScale
@@ -2668,7 +2668,7 @@ class CanvasGraphics {
         this.annotationCanvas.savedCtx = this.ctx;
         this.ctx = context;
         this.ctx.save();
-        this.ctx.setTransform(scaleX, 0, 0, -scaleY, 0, height * scaleY);
+        this.ctx.setTransform(XY[0], 0, 0, -XY[1], 0, height * XY[1]);
 
         resetCtxToDefault(this.ctx);
       } else {

src/display/pattern_helper.js

@@ -398,16 +398,18 @@ class MeshShadingPattern extends BaseShadingPattern {
 
   getPattern(ctx, owner, inverse, pathType) {
     applyBoundingBox(ctx, this._bbox);
-    let scale;
+    const scale = new Float32Array(2);
     if (pathType === PathType.SHADING) {
-      scale = Util.singularValueDecompose2dScale(getCurrentTransform(ctx));
-    } else {
+      Util.singularValueDecompose2dScale(getCurrentTransform(ctx), scale);
+    } else if (this.matrix) {
       // Obtain scale from matrix and current transformation matrix.
-      scale = Util.singularValueDecompose2dScale(owner.baseTransform);
-      if (this.matrix) {
-        const matrixScale = Util.singularValueDecompose2dScale(this.matrix);
-        scale = [scale[0] * matrixScale[0], scale[1] * matrixScale[1]];
-      }
+      Util.singularValueDecompose2dScale(this.matrix, scale);
+      const [matrixScaleX, matrixScaleY] = scale;
+      Util.singularValueDecompose2dScale(owner.baseTransform, scale);
+      scale[0] *= matrixScaleX;
+      scale[1] *= matrixScaleY;
+    } else {
+      Util.singularValueDecompose2dScale(owner.baseTransform, scale);
     }
 
     // Rasterizing on the main thread since sending/queue large canvases
@@ -517,12 +519,12 @@ class TilingPattern {
     const height = y1 - y0;
 
     // Obtain scale from matrix and current transformation matrix.
-    const matrixScale = Util.singularValueDecompose2dScale(this.matrix);
-    const curMatrixScale = Util.singularValueDecompose2dScale(
-      this.baseTransform
-    );
-    const combinedScaleX = matrixScale[0] * curMatrixScale[0];
-    const combinedScaleY = matrixScale[1] * curMatrixScale[1];
+    const scale = new Float32Array(2);
+    Util.singularValueDecompose2dScale(this.matrix, scale);
+    const [matrixScaleX, matrixScaleY] = scale;
+    Util.singularValueDecompose2dScale(this.baseTransform, scale);
+    const combinedScaleX = matrixScaleX * scale[0];
+    const combinedScaleY = matrixScaleY * scale[1];
 
     let canvasWidth = width,
       canvasHeight = height,

src/shared/util.js

@@ -732,23 +732,17 @@ class Util {
   // This calculation uses Singular Value Decomposition.
   // The SVD can be represented with formula A = USV. We are interested in the
   // matrix S here because it represents the scale values.
-  static singularValueDecompose2dScale(m) {
-    const transpose = [m[0], m[2], m[1], m[3]];
-
+  static singularValueDecompose2dScale([m0, m1, m2, m3], output) {
     // Multiply matrix m with its transpose.
-    const a = m[0] * transpose[0] + m[1] * transpose[2];
-    const b = m[0] * transpose[1] + m[1] * transpose[3];
-    const c = m[2] * transpose[0] + m[3] * transpose[2];
-    const d = m[2] * transpose[1] + m[3] * transpose[3];
+    const a = m0 ** 2 + m1 ** 2;
+    const b = m0 * m2 + m1 * m3;
+    const c = m2 ** 2 + m3 ** 2;
 
     // Solve the second degree polynomial to get roots.
-    const first = (a + d) / 2;
-    const second = Math.sqrt((a + d) ** 2 - 4 * (a * d - c * b)) / 2;
-    const sx = first + second || 1;
-    const sy = first - second || 1;
-
-    // Scale values are the square roots of the eigenvalues.
-    return [Math.sqrt(sx), Math.sqrt(sy)];
+    const first = (a + c) / 2;
+    const second = Math.sqrt(first ** 2 - (a * c - b ** 2));
+    output[0] = Math.sqrt(first + second || 1);
+    output[1] = Math.sqrt(first - second || 1);
   }
 
   // Normalize rectangle rect=[x1, y1, x2, y2] so that (x1,y1) < (x2,y2)