// Copyright 2006 The Closure Library Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS-IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
/**
* @fileoverview Additional mathematical functions.
*/
goog.provide('goog.math');
goog.require('goog.array');
goog.require('goog.asserts');
/**
* Returns a random integer greater than or equal to 0 and less than {@code a}.
* @param {number} a The upper bound for the random integer (exclusive).
* @return {number} A random integer N such that 0 <= N < a.
*/
goog.math.randomInt = function(a) {
return Math.floor(Math.random() * a);
};
/**
* Returns a random number greater than or equal to {@code a} and less than
* {@code b}.
* @param {number} a The lower bound for the random number (inclusive).
* @param {number} b The upper bound for the random number (exclusive).
* @return {number} A random number N such that a <= N < b.
*/
goog.math.uniformRandom = function(a, b) {
return a + Math.random() * (b - a);
};
/**
* Takes a number and clamps it to within the provided bounds.
* @param {number} value The input number.
* @param {number} min The minimum value to return.
* @param {number} max The maximum value to return.
* @return {number} The input number if it is within bounds, or the nearest
* number within the bounds.
*/
goog.math.clamp = function(value, min, max) {
return Math.min(Math.max(value, min), max);
};
/**
* The % operator in JavaScript returns the remainder of a / b, but differs from
* some other languages in that the result will have the same sign as the
* dividend. For example, -1 % 8 == -1, whereas in some other languages
* (such as Python) the result would be 7. This function emulates the more
* correct modulo behavior, which is useful for certain applications such as
* calculating an offset index in a circular list.
*
* @param {number} a The dividend.
* @param {number} b The divisor.
* @return {number} a % b where the result is between 0 and b (either 0 <= x < b
* or b < x <= 0, depending on the sign of b).
*/
goog.math.modulo = function(a, b) {
var r = a % b;
// If r and b differ in sign, add b to wrap the result to the correct sign.
return (r * b < 0) ? r + b : r;
};
/**
* Performs linear interpolation between values a and b. Returns the value
* between a and b proportional to x (when x is between 0 and 1. When x is
* outside this range, the return value is a linear extrapolation).
* @param {number} a A number.
* @param {number} b A number.
* @param {number} x The proportion between a and b.
* @return {number} The interpolated value between a and b.
*/
goog.math.lerp = function(a, b, x) {
return a + x * (b - a);
};
/**
* Tests whether the two values are equal to each other, within a certain
* tolerance to adjust for floating point errors.
* @param {number} a A number.
* @param {number} b A number.
* @param {number=} opt_tolerance Optional tolerance range. Defaults
* to 0.000001. If specified, should be greater than 0.
* @return {boolean} Whether {@code a} and {@code b} are nearly equal.
*/
goog.math.nearlyEquals = function(a, b, opt_tolerance) {
return Math.abs(a - b) <= (opt_tolerance || 0.000001);
};
// TODO(user): Rename to normalizeAngle, retaining old name as deprecated
// alias.
/**
* Normalizes an angle to be in range [0-360). Angles outside this range will
* be normalized to be the equivalent angle with that range.
* @param {number} angle Angle in degrees.
* @return {number} Standardized angle.
*/
goog.math.standardAngle = function(angle) {
return goog.math.modulo(angle, 360);
};
/**
* Normalizes an angle to be in range [0-2*PI). Angles outside this range will
* be normalized to be the equivalent angle with that range.
* @param {number} angle Angle in radians.
* @return {number} Standardized angle.
*/
goog.math.standardAngleInRadians = function(angle) {
return goog.math.modulo(angle, 2 * Math.PI);
};
/**
* Converts degrees to radians.
* @param {number} angleDegrees Angle in degrees.
* @return {number} Angle in radians.
*/
goog.math.toRadians = function(angleDegrees) {
return angleDegrees * Math.PI / 180;
};
/**
* Converts radians to degrees.
* @param {number} angleRadians Angle in radians.
* @return {number} Angle in degrees.
*/
goog.math.toDegrees = function(angleRadians) {
return angleRadians * 180 / Math.PI;
};
/**
* For a given angle and radius, finds the X portion of the offset.
* @param {number} degrees Angle in degrees (zero points in +X direction).
* @param {number} radius Radius.
* @return {number} The x-distance for the angle and radius.
*/
goog.math.angleDx = function(degrees, radius) {
return radius * Math.cos(goog.math.toRadians(degrees));
};
/**
* For a given angle and radius, finds the Y portion of the offset.
* @param {number} degrees Angle in degrees (zero points in +X direction).
* @param {number} radius Radius.
* @return {number} The y-distance for the angle and radius.
*/
goog.math.angleDy = function(degrees, radius) {
return radius * Math.sin(goog.math.toRadians(degrees));
};
/**
* Computes the angle between two points (x1,y1) and (x2,y2).
* Angle zero points in the +X direction, 90 degrees points in the +Y
* direction (down) and from there we grow clockwise towards 360 degrees.
* @param {number} x1 x of first point.
* @param {number} y1 y of first point.
* @param {number} x2 x of second point.
* @param {number} y2 y of second point.
* @return {number} Standardized angle in degrees of the vector from
* x1,y1 to x2,y2.
*/
goog.math.angle = function(x1, y1, x2, y2) {
return goog.math.standardAngle(goog.math.toDegrees(Math.atan2(y2 - y1,
x2 - x1)));
};
/**
* Computes the difference between startAngle and endAngle (angles in degrees).
* @param {number} startAngle Start angle in degrees.
* @param {number} endAngle End angle in degrees.
* @return {number} The number of degrees that when added to
* startAngle will result in endAngle. Positive numbers mean that the
* direction is clockwise. Negative numbers indicate a counter-clockwise
* direction.
* The shortest route (clockwise vs counter-clockwise) between the angles
* is used.
* When the difference is 180 degrees, the function returns 180 (not -180)
* angleDifference(30, 40) is 10, and angleDifference(40, 30) is -10.
* angleDifference(350, 10) is 20, and angleDifference(10, 350) is -20.
*/
goog.math.angleDifference = function(startAngle, endAngle) {
var d = goog.math.standardAngle(endAngle) -
goog.math.standardAngle(startAngle);
if (d > 180) {
d = d - 360;
} else if (d <= -180) {
d = 360 + d;
}
return d;
};
/**
* Returns the sign of a number as per the "sign" or "signum" function.
* @param {number} x The number to take the sign of.
* @return {number} -1 when negative, 1 when positive, 0 when 0. Preserves
* signed zeros and NaN.
*/
goog.math.sign = Math.sign || function(x) {
if (x > 0) {
return 1;
}
if (x < 0) {
return -1;
}
return x; // Preserves signed zeros and NaN.
};
/**
* JavaScript implementation of Longest Common Subsequence problem.
* http://en.wikipedia.org/wiki/Longest_common_subsequence
*
* Returns the longest possible array that is subarray of both of given arrays.
*
* @param {Array<Object>} array1 First array of objects.
* @param {Array<Object>} array2 Second array of objects.
* @param {Function=} opt_compareFn Function that acts as a custom comparator
* for the array ojects. Function should return true if objects are equal,
* otherwise false.
* @param {Function=} opt_collectorFn Function used to decide what to return
* as a result subsequence. It accepts 2 arguments: index of common element
* in the first array and index in the second. The default function returns
* element from the first array.
* @return {!Array<Object>} A list of objects that are common to both arrays
* such that there is no common subsequence with size greater than the
* length of the list.
*/
goog.math.longestCommonSubsequence = function(
array1, array2, opt_compareFn, opt_collectorFn) {
var compare = opt_compareFn || function(a, b) {
return a == b;
};
var collect = opt_collectorFn || function(i1, i2) {
return array1[i1];
};
var length1 = array1.length;
var length2 = array2.length;
var arr = [];
for (var i = 0; i < length1 + 1; i++) {
arr[i] = [];
arr[i][0] = 0;
}
for (var j = 0; j < length2 + 1; j++) {
arr[0][j] = 0;
}
for (i = 1; i <= length1; i++) {
for (j = 1; j <= length2; j++) {
if (compare(array1[i - 1], array2[j - 1])) {
arr[i][j] = arr[i - 1][j - 1] + 1;
} else {
arr[i][j] = Math.max(arr[i - 1][j], arr[i][j - 1]);
}
}
}
// Backtracking
var result = [];
var i = length1, j = length2;
while (i > 0 && j > 0) {
if (compare(array1[i - 1], array2[j - 1])) {
result.unshift(collect(i - 1, j - 1));
i--;
j--;
} else {
if (arr[i - 1][j] > arr[i][j - 1]) {
i--;
} else {
j--;
}
}
}
return result;
};
/**
* Returns the sum of the arguments.
* @param {...number} var_args Numbers to add.
* @return {number} The sum of the arguments (0 if no arguments were provided,
* {@code NaN} if any of the arguments is not a valid number).
*/
goog.math.sum = function(var_args) {
return /** @type {number} */ (goog.array.reduce(arguments,
function(sum, value) {
return sum + value;
}, 0));
};
/**
* Returns the arithmetic mean of the arguments.
* @param {...number} var_args Numbers to average.
* @return {number} The average of the arguments ({@code NaN} if no arguments
* were provided or any of the arguments is not a valid number).
*/
goog.math.average = function(var_args) {
return goog.math.sum.apply(null, arguments) / arguments.length;
};
/**
* Returns the unbiased sample variance of the arguments. For a definition,
* see e.g. http://en.wikipedia.org/wiki/Variance
* @param {...number} var_args Number samples to analyze.
* @return {number} The unbiased sample variance of the arguments (0 if fewer
* than two samples were provided, or {@code NaN} if any of the samples is
* not a valid number).
*/
goog.math.sampleVariance = function(var_args) {
var sampleSize = arguments.length;
if (sampleSize < 2) {
return 0;
}
var mean = goog.math.average.apply(null, arguments);
var variance = goog.math.sum.apply(null, goog.array.map(arguments,
function(val) {
return Math.pow(val - mean, 2);
})) / (sampleSize - 1);
return variance;
};
/**
* Returns the sample standard deviation of the arguments. For a definition of
* sample standard deviation, see e.g.
* http://en.wikipedia.org/wiki/Standard_deviation
* @param {...number} var_args Number samples to analyze.
* @return {number} The sample standard deviation of the arguments (0 if fewer
* than two samples were provided, or {@code NaN} if any of the samples is
* not a valid number).
*/
goog.math.standardDeviation = function(var_args) {
return Math.sqrt(goog.math.sampleVariance.apply(null, arguments));
};
/**
* Returns whether the supplied number represents an integer, i.e. that is has
* no fractional component. No range-checking is performed on the number.
* @param {number} num The number to test.
* @return {boolean} Whether {@code num} is an integer.
*/
goog.math.isInt = function(num) {
return isFinite(num) && num % 1 == 0;
};
/**
* Returns whether the supplied number is finite and not NaN.
* @param {number} num The number to test.
* @return {boolean} Whether {@code num} is a finite number.
*/
goog.math.isFiniteNumber = function(num) {
return isFinite(num) && !isNaN(num);
};
/**
* @param {number} num The number to test.
* @return {boolean} Whether it is negative zero.
*/
goog.math.isNegativeZero = function(num) {
return num == 0 && 1 / num < 0;
};
/**
* Returns the precise value of floor(log10(num)).
* Simpler implementations didn't work because of floating point rounding
* errors. For example
* <ul>
* <li>Math.floor(Math.log(num) / Math.LN10) is off by one for num == 1e+3.
* <li>Math.floor(Math.log(num) * Math.LOG10E) is off by one for num == 1e+15.
* <li>Math.floor(Math.log10(num)) is off by one for num == 1e+15 - 1.
* </ul>
* @param {number} num A floating point number.
* @return {number} Its logarithm to base 10 rounded down to the nearest
* integer if num > 0. -Infinity if num == 0. NaN if num < 0.
*/
goog.math.log10Floor = function(num) {
if (num > 0) {
var x = Math.round(Math.log(num) * Math.LOG10E);
return x - (parseFloat('1e' + x) > num);
}
return num == 0 ? -Infinity : NaN;
};
/**
* A tweaked variant of {@code Math.floor} which tolerates if the passed number
* is infinitesimally smaller than the closest integer. It often happens with
* the results of floating point calculations because of the finite precision
* of the intermediate results. For example {@code Math.floor(Math.log(1000) /
* Math.LN10) == 2}, not 3 as one would expect.
* @param {number} num A number.
* @param {number=} opt_epsilon An infinitesimally small positive number, the
* rounding error to tolerate.
* @return {number} The largest integer less than or equal to {@code num}.
*/
goog.math.safeFloor = function(num, opt_epsilon) {
goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);
return Math.floor(num + (opt_epsilon || 2e-15));
};
/**
* A tweaked variant of {@code Math.ceil}. See {@code goog.math.safeFloor} for
* details.
* @param {number} num A number.
* @param {number=} opt_epsilon An infinitesimally small positive number, the
* rounding error to tolerate.
* @return {number} The smallest integer greater than or equal to {@code num}.
*/
goog.math.safeCeil = function(num, opt_epsilon) {
goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);
return Math.ceil(num - (opt_epsilon || 2e-15));
};
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