diff --git a/src/ol/colorlike.js b/src/ol/colorlike.js
index 834a2f83d7..bd0b0e71bd 100644
--- a/src/ol/colorlike.js
+++ b/src/ol/colorlike.js
@@ -2,7 +2,6 @@
  * @module ol/colorlike
  */
 import _ol_color_ from './color.js';
-var _ol_colorlike_ = {};
 
 
 /**
@@ -10,24 +9,23 @@ var _ol_colorlike_ = {};
  * @return {ol.ColorLike} The color as an ol.ColorLike
  * @api
  */
-_ol_colorlike_.asColorLike = function(color) {
-  if (_ol_colorlike_.isColorLike(color)) {
+export function asColorLike(color) {
+  if (isColorLike(color)) {
     return /** @type {string|CanvasPattern|CanvasGradient} */ (color);
   } else {
     return _ol_color_.asString(/** @type {ol.Color} */ (color));
   }
-};
+}
 
 
 /**
  * @param {?} color The value that is potentially an ol.ColorLike
  * @return {boolean} Whether the color is an ol.ColorLike
  */
-_ol_colorlike_.isColorLike = function(color) {
+export function isColorLike(color) {
   return (
     typeof color === 'string' ||
     color instanceof CanvasPattern ||
     color instanceof CanvasGradient
   );
-};
-export default _ol_colorlike_;
+}
diff --git a/src/ol/render/canvas/Immediate.js b/src/ol/render/canvas/Immediate.js
index 725fd05adb..cc0948ead8 100644
--- a/src/ol/render/canvas/Immediate.js
+++ b/src/ol/render/canvas/Immediate.js
@@ -7,7 +7,7 @@
 
 import {inherits} from '../../index.js';
 import _ol_array_ from '../../array.js';
-import _ol_colorlike_ from '../../colorlike.js';
+import {asColorLike} from '../../colorlike.js';
 import {intersects} from '../../extent.js';
 import GeometryType from '../../geom/GeometryType.js';
 import SimpleGeometry from '../../geom/SimpleGeometry.js';
@@ -829,7 +829,7 @@ _ol_render_canvas_Immediate_.prototype.setFillStrokeStyle = function(fillStyle,
   } else {
     var fillStyleColor = fillStyle.getColor();
     this.fillState_ = {
-      fillStyle: _ol_colorlike_.asColorLike(fillStyleColor ?
+      fillStyle: asColorLike(fillStyleColor ?
         fillStyleColor : _ol_render_canvas_.defaultFillStyle)
     };
   }
@@ -856,7 +856,7 @@ _ol_render_canvas_Immediate_.prototype.setFillStrokeStyle = function(fillStyle,
         strokeStyleWidth : _ol_render_canvas_.defaultLineWidth),
       miterLimit: strokeStyleMiterLimit !== undefined ?
         strokeStyleMiterLimit : _ol_render_canvas_.defaultMiterLimit,
-      strokeStyle: _ol_colorlike_.asColorLike(strokeStyleColor ?
+      strokeStyle: asColorLike(strokeStyleColor ?
         strokeStyleColor : _ol_render_canvas_.defaultStrokeStyle)
     };
   }
@@ -912,7 +912,7 @@ _ol_render_canvas_Immediate_.prototype.setTextStyle = function(textStyle) {
     } else {
       var textFillStyleColor = textFillStyle.getColor();
       this.textFillState_ = {
-        fillStyle: _ol_colorlike_.asColorLike(textFillStyleColor ?
+        fillStyle: asColorLike(textFillStyleColor ?
           textFillStyleColor : _ol_render_canvas_.defaultFillStyle)
       };
     }
@@ -940,7 +940,7 @@ _ol_render_canvas_Immediate_.prototype.setTextStyle = function(textStyle) {
           textStrokeStyleWidth : _ol_render_canvas_.defaultLineWidth,
         miterLimit: textStrokeStyleMiterLimit !== undefined ?
           textStrokeStyleMiterLimit : _ol_render_canvas_.defaultMiterLimit,
-        strokeStyle: _ol_colorlike_.asColorLike(textStrokeStyleColor ?
+        strokeStyle: asColorLike(textStrokeStyleColor ?
           textStrokeStyleColor : _ol_render_canvas_.defaultStrokeStyle)
       };
     }
diff --git a/src/ol/render/canvas/Replay.js b/src/ol/render/canvas/Replay.js
index a576ff7237..1a53f863ed 100644
--- a/src/ol/render/canvas/Replay.js
+++ b/src/ol/render/canvas/Replay.js
@@ -3,7 +3,7 @@
  */
 import {getUid, inherits, nullFunction} from '../../index.js';
 import _ol_array_ from '../../array.js';
-import _ol_colorlike_ from '../../colorlike.js';
+import {asColorLike} from '../../colorlike.js';
 import {buffer, clone, coordinateRelationship, createEmpty, createOrUpdate,
   createOrUpdateEmpty, extend, extendCoordinate, intersects} from '../../extent.js';
 import Relationship from '../../extent/Relationship.js';
@@ -912,14 +912,14 @@ _ol_render_canvas_Replay_.prototype.setFillStrokeStyle = function(fillStyle, str
   var state = this.state;
   if (fillStyle) {
     var fillStyleColor = fillStyle.getColor();
-    state.fillStyle = _ol_colorlike_.asColorLike(fillStyleColor ?
+    state.fillStyle = asColorLike(fillStyleColor ?
       fillStyleColor : _ol_render_canvas_.defaultFillStyle);
   } else {
     state.fillStyle = undefined;
   }
   if (strokeStyle) {
     var strokeStyleColor = strokeStyle.getColor();
-    state.strokeStyle = _ol_colorlike_.asColorLike(strokeStyleColor ?
+    state.strokeStyle = asColorLike(strokeStyleColor ?
       strokeStyleColor : _ol_render_canvas_.defaultStrokeStyle);
     var strokeStyleLineCap = strokeStyle.getLineCap();
     state.lineCap = strokeStyleLineCap !== undefined ?
diff --git a/src/ol/render/canvas/TextReplay.js b/src/ol/render/canvas/TextReplay.js
index d44c196dcd..cda2361ef5 100644
--- a/src/ol/render/canvas/TextReplay.js
+++ b/src/ol/render/canvas/TextReplay.js
@@ -2,7 +2,7 @@
  * @module ol/render/canvas/TextReplay
  */
 import {getUid, inherits} from '../../index.js';
-import _ol_colorlike_ from '../../colorlike.js';
+import {asColorLike} from '../../colorlike.js';
 import {createCanvasContext2D} from '../../dom.js';
 import {intersects} from '../../extent.js';
 import _ol_geom_flat_straightchunk_ from '../../geom/flat/straightchunk.js';
@@ -478,7 +478,7 @@ _ol_render_canvas_TextReplay_.prototype.setTextStyle = function(textStyle, declu
       if (!fillState) {
         fillState = this.textFillState_ = /** @type {ol.CanvasFillState} */ ({});
       }
-      fillState.fillStyle = _ol_colorlike_.asColorLike(
+      fillState.fillStyle = asColorLike(
           textFillStyle.getColor() || _ol_render_canvas_.defaultFillStyle);
     }
 
@@ -503,7 +503,7 @@ _ol_render_canvas_TextReplay_.prototype.setTextStyle = function(textStyle, declu
           lineWidth === undefined ? _ol_render_canvas_.defaultLineWidth : lineWidth;
       strokeState.miterLimit =
           miterLimit === undefined ? _ol_render_canvas_.defaultMiterLimit : miterLimit;
-      strokeState.strokeStyle = _ol_colorlike_.asColorLike(
+      strokeState.strokeStyle = asColorLike(
           textStrokeStyle.getColor() || _ol_render_canvas_.defaultStrokeStyle);
     }
 
diff --git a/src/ol/render/webgl/Replay.js b/src/ol/render/webgl/Replay.js
index 4cd71cfce5..33fdbd83e3 100644
--- a/src/ol/render/webgl/Replay.js
+++ b/src/ol/render/webgl/Replay.js
@@ -5,7 +5,7 @@ import {inherits} from '../../index.js';
 import {getCenter} from '../../extent.js';
 import _ol_render_VectorContext_ from '../VectorContext.js';
 import _ol_transform_ from '../../transform.js';
-import _ol_vec_Mat4_ from '../../vec/Mat4.js';
+import {create, fromTransform} from '../../vec/mat4.js';
 import _ol_webgl_ from '../../webgl.js';
 
 /**
@@ -64,7 +64,7 @@ var _ol_render_webgl_Replay_ = function(tolerance, maxExtent) {
    * @private
    * @type {Array.<number>}
    */
-  this.tmpMat4_ = _ol_vec_Mat4_.create();
+  this.tmpMat4_ = create();
 
   /**
    * @protected
@@ -308,11 +308,11 @@ _ol_render_webgl_Replay_.prototype.replay = function(context,
   }
 
   gl.uniformMatrix4fv(locations.u_projectionMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, projectionMatrix));
+      fromTransform(this.tmpMat4_, projectionMatrix));
   gl.uniformMatrix4fv(locations.u_offsetScaleMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, offsetScaleMatrix));
+      fromTransform(this.tmpMat4_, offsetScaleMatrix));
   gl.uniformMatrix4fv(locations.u_offsetRotateMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, offsetRotateMatrix));
+      fromTransform(this.tmpMat4_, offsetRotateMatrix));
   gl.uniform1f(locations.u_opacity, opacity);
 
   // draw!
diff --git a/src/ol/render/webgl/TextReplay.js b/src/ol/render/webgl/TextReplay.js
index fb71dd66a1..f83e51b2db 100644
--- a/src/ol/render/webgl/TextReplay.js
+++ b/src/ol/render/webgl/TextReplay.js
@@ -2,7 +2,7 @@
  * @module ol/render/webgl/TextReplay
  */
 import {getUid, inherits} from '../../index.js';
-import _ol_colorlike_ from '../../colorlike.js';
+import {asColorLike} from '../../colorlike.js';
 import {createCanvasContext2D} from '../../dom.js';
 import GeometryType from '../../geom/GeometryType.js';
 import _ol_has_ from '../../has.js';
@@ -359,7 +359,7 @@ _ol_render_webgl_TextReplay_.prototype.setTextStyle = function(textStyle) {
       state.fillColor = null;
     } else {
       var textFillStyleColor = textFillStyle.getColor();
-      state.fillColor = _ol_colorlike_.asColorLike(textFillStyleColor ?
+      state.fillColor = asColorLike(textFillStyleColor ?
         textFillStyleColor : _ol_render_webgl_.defaultFillStyle);
     }
     if (!textStrokeStyle) {
@@ -367,7 +367,7 @@ _ol_render_webgl_TextReplay_.prototype.setTextStyle = function(textStyle) {
       state.lineWidth = 0;
     } else {
       var textStrokeStyleColor = textStrokeStyle.getColor();
-      state.strokeColor = _ol_colorlike_.asColorLike(textStrokeStyleColor ?
+      state.strokeColor = asColorLike(textStrokeStyleColor ?
         textStrokeStyleColor : _ol_render_webgl_.defaultStrokeStyle);
       state.lineWidth = textStrokeStyle.getWidth() || _ol_render_webgl_.defaultLineWidth;
       state.lineCap = textStrokeStyle.getLineCap() || _ol_render_webgl_.defaultLineCap;
diff --git a/src/ol/renderer/webgl/Layer.js b/src/ol/renderer/webgl/Layer.js
index e92d04c9a4..6d0801b40c 100644
--- a/src/ol/renderer/webgl/Layer.js
+++ b/src/ol/renderer/webgl/Layer.js
@@ -9,7 +9,7 @@ import _ol_renderer_Layer_ from '../Layer.js';
 import _ol_renderer_webgl_defaultmapshader_ from '../webgl/defaultmapshader.js';
 import _ol_renderer_webgl_defaultmapshader_Locations_ from '../webgl/defaultmapshader/Locations.js';
 import _ol_transform_ from '../../transform.js';
-import _ol_vec_Mat4_ from '../../vec/Mat4.js';
+import {create, fromTransform} from '../../vec/mat4.js';
 import _ol_webgl_ from '../../webgl.js';
 import _ol_webgl_Buffer_ from '../../webgl/Buffer.js';
 import _ol_webgl_Context_ from '../../webgl/Context.js';
@@ -76,7 +76,7 @@ var _ol_renderer_webgl_Layer_ = function(mapRenderer, layer) {
    * @type {Array.<number>}
    * @private
    */
-  this.tmpMat4_ = _ol_vec_Mat4_.create();
+  this.tmpMat4_ = create();
 
   /**
    * @private
@@ -173,9 +173,9 @@ _ol_renderer_webgl_Layer_.prototype.composeFrame = function(frameState, layerSta
   }
 
   gl.uniformMatrix4fv(locations.u_texCoordMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, this.getTexCoordMatrix()));
+      fromTransform(this.tmpMat4_, this.getTexCoordMatrix()));
   gl.uniformMatrix4fv(locations.u_projectionMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, this.getProjectionMatrix()));
+      fromTransform(this.tmpMat4_, this.getProjectionMatrix()));
   gl.uniform1f(locations.u_opacity, layerState.opacity);
   gl.bindTexture(_ol_webgl_.TEXTURE_2D, this.getTexture());
   gl.drawArrays(_ol_webgl_.TRIANGLE_STRIP, 0, 4);
diff --git a/src/ol/style/RegularShape.js b/src/ol/style/RegularShape.js
index 91d9f32add..f1c9525dc4 100644
--- a/src/ol/style/RegularShape.js
+++ b/src/ol/style/RegularShape.js
@@ -2,7 +2,7 @@
  * @module ol/style/RegularShape
  */
 import {inherits} from '../index.js';
-import _ol_colorlike_ from '../colorlike.js';
+import {asColorLike} from '../colorlike.js';
 import {createCanvasContext2D} from '../dom.js';
 import _ol_has_ from '../has.js';
 import _ol_ImageState_ from '../ImageState.js';
@@ -327,7 +327,7 @@ _ol_style_RegularShape_.prototype.render_ = function(atlasManager) {
     if (strokeStyle === null) {
       strokeStyle = _ol_render_canvas_.defaultStrokeStyle;
     }
-    strokeStyle = _ol_colorlike_.asColorLike(strokeStyle);
+    strokeStyle = asColorLike(strokeStyle);
     strokeWidth = this.stroke_.getWidth();
     if (strokeWidth === undefined) {
       strokeWidth = _ol_render_canvas_.defaultLineWidth;
@@ -457,7 +457,7 @@ _ol_style_RegularShape_.prototype.draw_ = function(renderOptions, context, x, y)
     if (color === null) {
       color = _ol_render_canvas_.defaultFillStyle;
     }
-    context.fillStyle = _ol_colorlike_.asColorLike(color);
+    context.fillStyle = asColorLike(color);
     context.fill();
   }
   if (this.stroke_) {
diff --git a/src/ol/vec/Mat4.js b/src/ol/vec/mat4.js
similarity index 75%
rename from src/ol/vec/Mat4.js
rename to src/ol/vec/mat4.js
index dd662b3528..1ab9600ea6 100644
--- a/src/ol/vec/Mat4.js
+++ b/src/ol/vec/mat4.js
@@ -1,15 +1,14 @@
 /**
- * @module ol/vec/Mat4
+ * @module ol/vec/mat4
  */
-var _ol_vec_Mat4_ = {};
 
 
 /**
  * @return {Array.<number>} 4x4 matrix representing a 3D identity transform.
  */
-_ol_vec_Mat4_.create = function() {
+export function create() {
   return [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1];
-};
+}
 
 
 /**
@@ -17,7 +16,7 @@ _ol_vec_Mat4_.create = function() {
  * @param {ol.Transform} transform Transformation matrix.
  * @return {Array.<number>} 2D transformation matrix as flattened 4x4 matrix.
  */
-_ol_vec_Mat4_.fromTransform = function(mat4, transform) {
+export function fromTransform(mat4, transform) {
   mat4[0] = transform[0];
   mat4[1] = transform[1];
   mat4[4] = transform[2];
@@ -25,5 +24,4 @@ _ol_vec_Mat4_.fromTransform = function(mat4, transform) {
   mat4[12] = transform[4];
   mat4[13] = transform[5];
   return mat4;
-};
-export default _ol_vec_Mat4_;
+}
diff --git a/test/spec/ol/vec/mat4.test.js b/test/spec/ol/vec/mat4.test.js
index 7109131c5b..9b76cfcaf8 100644
--- a/test/spec/ol/vec/mat4.test.js
+++ b/test/spec/ol/vec/mat4.test.js
@@ -1,20 +1,20 @@
-import _ol_vec_Mat4_ from '../../../../src/ol/vec/Mat4.js';
+import {create, fromTransform} from '../../../../src/ol/vec/mat4.js';
 
 
-describe('ol.vec.Mat4', function() {
+describe('mat4', function() {
 
-  describe('ol.vec.Mat4.create()', function() {
+  describe('mat4.create()', function() {
     it('returns the expected matrix', function() {
-      expect(_ol_vec_Mat4_.create()).to.eql(
+      expect(create()).to.eql(
           [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]);
     });
   });
 
-  describe('ol.vec.Mat4.fromTransform()', function() {
+  describe('mat4.fromTransform()', function() {
     it('sets the expected transform on the matrix', function() {
       var transform = [1, 2, 3, 4, 5, 6];
-      var result = _ol_vec_Mat4_.create();
-      expect(_ol_vec_Mat4_.fromTransform(result, transform)).to.eql(
+      var result = create();
+      expect(fromTransform(result, transform)).to.eql(
           [1, 2, 0, 0, 3, 4, 0, 0, 0, 0, 1, 0, 5, 6, 0, 1]);
       expect(result).to.eql(
           [1, 2, 0, 0, 3, 4, 0, 0, 0, 0, 1, 0, 5, 6, 0, 1]);