Use Math.hypot, instead of Math.sqrt with manual squaring (#12973)

When the PDF.js project started `Math.hypot` didn't exist yet, and until recently we still supported browsers (IE 11) without a native `Math.hypot` implementation; please see this compatibility information: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/hypot#browser_compatibility

Furthermore, somewhat recently there were performance improvements of `Math.hypot` in Firefox; see https://bugzilla.mozilla.org/show_bug.cgi?id=1648820

Finally, this patch also replaces a couple of multiplications with the exponentiation operator.

src/core/colorspace.js

@@ -1364,7 +1364,7 @@ const LabCS = (function LabCSClosure() {
   function fn_g(x) {
     let result;
     if (x >= 6 / 29) {
-      result = x * x * x;
+      result = x ** 3;
     } else {
       result = (108 / 841) * (x - 4 / 29);
     }

src/core/evaluator.js

@@ -2077,20 +2077,19 @@ class PartialEvaluator {
       textContentItem.transform = trm;
       if (!font.vertical) {
         textContentItem.width = 0;
-        textContentItem.height = Math.sqrt(trm[2] * trm[2] + trm[3] * trm[3]);
+        textContentItem.height = Math.hypot(trm[2], trm[3]);
         textContentItem.vertical = false;
       } else {
-        textContentItem.width = Math.sqrt(trm[0] * trm[0] + trm[1] * trm[1]);
+        textContentItem.width = Math.hypot(trm[0], trm[1]);
         textContentItem.height = 0;
         textContentItem.vertical = true;
       }
 
-      var a = textState.textLineMatrix[0];
-      var b = textState.textLineMatrix[1];
-      var scaleLineX = Math.sqrt(a * a + b * b);
-      a = textState.ctm[0];
-      b = textState.ctm[1];
-      var scaleCtmX = Math.sqrt(a * a + b * b);
+      const scaleLineX = Math.hypot(
+        textState.textLineMatrix[0],
+        textState.textLineMatrix[1]
+      );
+      const scaleCtmX = Math.hypot(textState.ctm[0], textState.ctm[1]);
       textContentItem.textAdvanceScale = scaleCtmX * scaleLineX;
       textContentItem.lastAdvanceWidth = 0;
       textContentItem.lastAdvanceHeight = 0;

src/core/pattern.js

@@ -164,13 +164,8 @@ Shadings.RadialAxial = (function RadialAxialClosure() {
     ) {
       // Radial gradient only currently works if either circle is fully within
       // the other circle.
-      var x1 = this.coordsArr[0];
-      var y1 = this.coordsArr[1];
-      var r1 = this.coordsArr[2];
-      var x2 = this.coordsArr[3];
-      var y2 = this.coordsArr[4];
-      var r2 = this.coordsArr[5];
-      var distance = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
+      const [x1, y1, r1, x2, y2, r2] = this.coordsArr;
+      const distance = Math.hypot(x1 - x2, y1 - y2);
       if (r1 <= r2 + distance && r2 <= r1 + distance) {
         warn("Unsupported radial gradient.");
       }

src/display/canvas.js

@@ -1576,7 +1576,7 @@ const CanvasGraphics = (function CanvasGraphicsClosure() {
     },
     setTextMatrix: function CanvasGraphics_setTextMatrix(a, b, c, d, e, f) {
       this.current.textMatrix = [a, b, c, d, e, f];
-      this.current.textMatrixScale = Math.sqrt(a * a + b * b);
+      this.current.textMatrixScale = Math.hypot(a, b);
 
       this.current.x = this.current.lineX = 0;
       this.current.y = this.current.lineY = 0;
@@ -2455,12 +2455,14 @@ const CanvasGraphics = (function CanvasGraphicsClosure() {
       ctx.scale(1 / width, -1 / height);
 
       const currentTransform = ctx.mozCurrentTransformInverse;
-      const a = currentTransform[0],
-        b = currentTransform[1];
-      let widthScale = Math.max(Math.sqrt(a * a + b * b), 1);
-      const c = currentTransform[2],
-        d = currentTransform[3];
-      let heightScale = Math.max(Math.sqrt(c * c + d * d), 1);
+      let widthScale = Math.max(
+        Math.hypot(currentTransform[0], currentTransform[1]),
+        1
+      );
+      let heightScale = Math.max(
+        Math.hypot(currentTransform[2], currentTransform[3]),
+        1
+      );
 
       let imgToPaint, tmpCanvas, tmpCtx;
       // typeof check is needed due to node.js support, see issue #8489

src/display/svg.js

@@ -735,7 +735,7 @@ if (typeof PDFJSDev === "undefined" || PDFJSDev.test("GENERIC")) {
     setTextMatrix(a, b, c, d, e, f) {
       const current = this.current;
       current.textMatrix = current.lineMatrix = [a, b, c, d, e, f];
-      current.textMatrixScale = Math.sqrt(a * a + b * b);
+      current.textMatrixScale = Math.hypot(a, b);
 
       current.x = current.lineX = 0;
       current.y = current.lineY = 0;

src/display/text_layer.js

@@ -89,7 +89,7 @@ const renderTextLayer = (function renderTextLayerClosure() {
     if (style.vertical) {
       angle += Math.PI / 2;
     }
-    const fontHeight = Math.sqrt(tx[2] * tx[2] + tx[3] * tx[3]);
+    const fontHeight = Math.hypot(tx[2], tx[3]);
     let fontAscent = fontHeight;
     if (style.ascent) {
       fontAscent = style.ascent * fontAscent;

src/shared/util.js

@@ -720,7 +720,7 @@ class Util {
 
     // Solve the second degree polynomial to get roots.
     const first = (a + d) / 2;
-    const second = Math.sqrt((a + d) * (a + d) - 4 * (a * d - c * b)) / 2;
+    const second = Math.sqrt((a + d) ** 2 - 4 * (a * d - c * b)) / 2;
     const sx = first + second || 1;
     const sy = first - second || 1;
 

web/ui_utils.js

@@ -655,7 +655,7 @@ function getPDFFileNameFromURL(url, defaultFilename = "document.pdf") {
 }
 
 function normalizeWheelEventDirection(evt) {
-  let delta = Math.sqrt(evt.deltaX * evt.deltaX + evt.deltaY * evt.deltaY);
+  let delta = Math.hypot(evt.deltaX, evt.deltaY);
   const angle = Math.atan2(evt.deltaY, evt.deltaX);
   if (-0.25 * Math.PI < angle && angle < 0.75 * Math.PI) {
     // All that is left-up oriented has to change the sign.