mirror of
https://github.com/dart-lang/sdk
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eaa854b258
BUG= R=floitsch@google.com Review URL: https://codereview.chromium.org//25808002 git-svn-id: https://dart.googlecode.com/svn/branches/bleeding_edge/dart@28272 260f80e4-7a28-3924-810f-c04153c831b5
254 lines
7.4 KiB
Dart
254 lines
7.4 KiB
Dart
// Copyright (c) 2012, the Dart project authors. Please see the AUTHORS file
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// for details. All rights reserved. Use of this source code is governed by a
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// BSD-style license that can be found in the LICENSE file.
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/**
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* Mathematical constants and functions, plus a random number generator.
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*/
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library dart.math;
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part "jenkins_smi_hash.dart";
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part "point.dart";
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part "random.dart";
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part "rectangle.dart";
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/**
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* Base of the natural logarithms.
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*
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* Typically written as "e".
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*/
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const double E = 2.718281828459045;
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/**
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* Natural logarithm of 10.
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*/
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const double LN10 = 2.302585092994046;
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/**
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* Natural logarithm of 2.
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*/
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const double LN2 = 0.6931471805599453;
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/**
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* Base-2 logarithm of [E].
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*/
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const double LOG2E = 1.4426950408889634;
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/**
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* Base-10 logarithm of [E].
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*/
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const double LOG10E = 0.4342944819032518;
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/**
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* The PI constant.
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*/
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const double PI = 3.1415926535897932;
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/**
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* Square root of 1/2.
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*/
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const double SQRT1_2 = 0.7071067811865476;
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/**
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* Square root of 2.
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*/
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const double SQRT2 = 1.4142135623730951;
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/**
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* Returns the lesser of two numbers.
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*
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* Returns NaN if either argument is NaN.
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* The lesser of [:-0.0:] and [:0.0:] is [:-0.0:].
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* If the arguments are otherwise equal (including int and doubles with the
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* same mathematical value) then it is unspecified which of the two arguments
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* is returned.
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*/
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num min(num a, num b) {
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// These partially redundant type checks improve code quality for dart2js.
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// Most of the improvement is at call sites from the inferred non-null num
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// return type.
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if (a is! num) throw new ArgumentError(a);
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if (b is! num) throw new ArgumentError(b);
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if (a > b) return b;
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if (a < b) return a;
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if (b is double) {
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// Special case for NaN and -0.0. If one argument is NaN return NaN.
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// [min] must also distinguish between -0.0 and 0.0.
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if (a is double) {
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if (a == 0.0) {
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// a is either 0.0 or -0.0. b is either 0.0, -0.0 or NaN.
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// The following returns -0.0 if either a or b is -0.0, and it
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// returns NaN if b is NaN.
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return (a + b) * a * b;
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}
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}
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// Check for NaN and b == -0.0.
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if (a == 0 && b.isNegative || b.isNaN) return b;
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return a;
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}
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return a;
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}
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/**
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* Returns the larger of two numbers.
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*
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* Returns NaN if either argument is NaN.
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* The larger of [:-0.0:] and [:0.0:] is [:0.0:]. If the arguments are
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* otherwise equal (including int and doubles with the same mathematical value)
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* then it is unspecified which of the two arguments is returned.
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*/
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num max(num a, num b) {
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// These partially redundant type checks improve code quality for dart2js.
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// Most of the improvement is at call sites from the inferred non-null num
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// return type.
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if (a is! num) throw new ArgumentError(a);
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if (b is! num) throw new ArgumentError(b);
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if (a > b) return a;
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if (a < b) return b;
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if (b is double) {
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// Special case for NaN and -0.0. If one argument is NaN return NaN.
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// [max] must also distinguish between -0.0 and 0.0.
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if (a is double) {
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if (a == 0.0) {
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// a is either 0.0 or -0.0. b is either 0.0, -0.0, or NaN.
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// The following returns 0.0 if either a or b is 0.0, and it
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// returns NaN if b is NaN.
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return a + b;
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}
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}
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// Check for NaN.
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if (b.isNaN) return b;
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return a;
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}
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// max(-0.0, 0) must return 0.
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if (b == 0 && a.isNegative) return b;
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return a;
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}
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/**
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* A variant of [atan].
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*
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* Converts both arguments to doubles.
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*
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* Returns the angle between the positive x-axis and the vector ([b],[a]).
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* The result, in radians, is in the range -PI..PI.
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*
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* If [b] is positive, this is the same as [:atan(b/a):].
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*
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* The result is negative when [a] is negative (including when [a] is the
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* double -0.0).
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*
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* If [a] is equal to zero, the vector ([b],[a]) is considered parallel to
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* the x-axis, even if [b] is also equal to zero. The sign of [b] determines
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* the direction of the vector along the x-axis.
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*
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* Returns NaN if either argument is NaN.
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*/
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external double atan2(num a, num b);
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/**
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* Returns [x] to the power of [exponent].
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*
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* If [x] is an [int] and [exponent] is a non-negative [int], the result is
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* an [int], otherwise both arguments are converted to doubles first, and the
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* result is a [double].
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*
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* For integers, the power is always equal to the mathematical result of `x` to
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* the power `exponent`, only limited by the available memory.
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*
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* For doubles, `pow(x, y)` handles edge cases as follows:
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*
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* - if `y` is zero (0.0 or -0.0), the result is always 1.0.
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* - if `x` is 1.0, the result is always 1.0.
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* - otherwise, if either `x` or `y` is NaN then the result is NaN.
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* - if `x` is negative (but not -0.0) and `y` is a finite non-integer, the
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* result is NaN.
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* - if `x` is Infinity and `y` is negative, the result is 0.0.
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* - if `x` is Infinity and `y` is positive, the result is Infinity.
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* - if `x` is 0.0 and `y` is negative, the result is Infinity.
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* - if `x` is 0.0 and `y` is positive, the result is 0.0.
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* - if `x` is -Infinity or -0.0 and `y` is an odd integer, then the result is
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* `-pow(-x ,y)`.
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* - if `x` is -Infinity or -0.0 and `y` is not an odd integer, then the result
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* is the same as `pow(-x , y)`.
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* - if `y` is Infinity and the absolute value of `x` is less than 1, the
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* result is 0.0.
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* - if `y` is Infinity and `x` is -1, the result is 1.0.
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* - if `y` is Infinity and the absolute value of `x` is greater than 1,
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* the result is Infinity.
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* - if `y` is -Infinity, the result is `1/pow(x, Infinity)`.
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*
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* This corresponds to the `pow` function defined in the IEEE Standard 754-2008.
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*
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* Notice that an [int] result cannot overflow, but a [double] result might
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* be [double.INFINITY].
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*/
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external num pow(num x, num exponent);
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/**
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* Converts [x] to a double and returns the sine of the value.
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*
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* If [x] is not a finite number, the result is NaN.
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*/
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external double sin(num x);
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/**
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* Converts [x] to a double and returns the cosine of the value.
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*
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* If [x] is not a finite number, the result is NaN.
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*/
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external double cos(num x);
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/**
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* Converts [x] to a double and returns the tangent of the value.
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*
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* The tangent function is equivalent to [:sin(x)/cos(x):] and may be
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* infinite (positive or negative) when [:cos(x):] is equal to zero.
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* If [x] is not a finite number, the result is NaN.
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*/
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external double tan(num x);
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/**
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* Converts [x] to a double and returns the arc cosine of the value.
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*
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* Returns a value in the range -PI..PI, or NaN if [x] is outside
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* the range -1..1.
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*/
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external double acos(num x);
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/**
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* Converts [x] to a double and returns the arc sine of the value.
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* Returns a value in the range -PI..PI, or NaN if [x] is outside
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* the range -1..1.
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*/
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external double asin(num x);
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/**
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* Converts [x] to a dobule and returns the arc tangent of the vlaue.
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* Returns a value in the range -PI/2..PI/2, or NaN if [x] is NaN.
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*/
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external double atan(num x);
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/**
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* Converts [x] to a double and returns the positive square root of the value.
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*
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* Returns -0.0 if [x] is -0.0, and NaN if [x] is otherwise negative or NaN.
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*/
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external double sqrt(num x);
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/**
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* Converts [x] to a double and returns the natural exponent, [E],
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* to the power [x].
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* Returns NaN if [x] is NaN.
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*/
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external double exp(num x);
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/**
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* Converts [x] to a double and returns the natural logarithm of the value.
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* Returns negative infinity if [x] is equal to zero.
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* Returns NaN if [x] is NaN or less than zero.
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*/
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external double log(num x);
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