From 31237637de54abece1ebf05944b3859c677b4c3b Mon Sep 17 00:00:00 2001 From: SheetJS Date: Sun, 3 Aug 2014 23:02:30 -0400 Subject: [PATCH] version bump 0.2.0: avoid prototype abuse h/t @malphettes --- .travis.yml | 1 + bessel.md | 53 ++++++++++++++++++++++++++-------------------------- package.json | 2 +- 3 files changed, 28 insertions(+), 28 deletions(-) diff --git a/.travis.yml b/.travis.yml index a1f55b5..dba96e7 100644 --- a/.travis.yml +++ b/.travis.yml @@ -1,5 +1,6 @@ language: node_js node_js: + - "0.11" - "0.10" - "0.8" before_install: diff --git a/bessel.md b/bessel.md index ace1082..b532abc 100644 --- a/bessel.md +++ b/bessel.md @@ -11,11 +11,10 @@ var M = Math; ## Horner Method -The methods use an approximating polynomial and evaluate using Horner's method. -In true JS form, let us define an `Array` prototype method: +The methods use an approximating polynomial and evaluate using Horner's method: ``` -Array.prototype.horner = function(v) { return this.reduce(function(z,w){return v * z + w;},0); }; +function _horner(arr, v) { return arr.reduce(function(z,w){return v * z + w;},0); }; ``` ## Recurrence @@ -97,8 +96,8 @@ For small `x`, the direct Laurent approximation gives better results. ``` if(M.abs(x) < 8) { - a1 = b0_a1a.horner(y); - a2 = b0_a2a.horner(y); + a1 = _horner(b0_a1a, y); + a2 = _horner(b0_a2a, y); a = a1/a2; } ``` @@ -108,8 +107,8 @@ For larger `x`, the Chebyshev approach is taken: ``` else { y = 64 / y; - a1 = b0_a1b.horner(y); - a2 = b0_a2b.horner(y); + a1 = _horner(b0_a1b, y); + a2 = _horner(b0_a2b, y); a = M.sqrt(W/M.abs(x))*(M.cos(xx)*a1-M.sin(xx)*a2*8/M.abs(x)); } return a; @@ -126,13 +125,13 @@ A similar approach is taken for the first-order bessel function function bessel1(x) { var a, a1, a2, y = x*x, xx = M.abs(x) - 2.356194491; if(Math.abs(x)< 8) { - a1 = x*b1_a1a.horner(y); - a2 = b1_a2a.horner(y); + a1 = x*_horner(b1_a1a, y); + a2 = _horner(b1_a2a, y); a = a1 / a2; } else { y = 64 / y; - a1=b1_a1b.horner(y); - a2=b1_a2b.horner(y); + a1=_horner(b1_a1b, y); + a2=_horner(b1_a2b, y); a=M.sqrt(W/M.abs(x))*(M.cos(xx)*a1-M.sin(xx)*a2*8/M.abs(x)); if(x < 0) a = -a; } @@ -194,13 +193,13 @@ var bessely = (function() { function bessel0(x) { var a, a1, a2, y = x * x, xx = x - 0.785398164; if(x < 8) { - a1 = b0_a1a.horner(y); - a2 = b0_a2a.horner(y); + a1 = _horner(b0_a1a, y); + a2 = _horner(b0_a2a, y); a = a1/a2 + W * besselj(x,0) * M.log(x); } else { y = 64 / y; - a1 = b0_a1b.horner(y); - a2 = b0_a2b.horner(y); + a1 = _horner(b0_a1b, y); + a2 = _horner(b0_a2b, y); a = M.sqrt(W/x)*(M.sin(xx)*a1+M.cos(xx)*a2*8/x); } return a; @@ -213,13 +212,13 @@ var bessely = (function() { function bessel1(x) { var a, a1, a2, y = x*x, xx = x - 2.356194491; if(x < 8) { - a1 = x*b1_a1a.horner(y); - a2 = b1_a2a.horner(y); + a1 = x*_horner(b1_a1a, y); + a2 = _horner(b1_a2a, y); a = a1/a2 + W * (besselj(x,1) * M.log(x) - 1 / x); } else { y = 64 / y; - a1=b1_a1b.horner(y); - a2=b1_a2b.horner(y); + a1=_horner(b1_a1b, y); + a2=_horner(b1_a2b, y); a=M.sqrt(W/x)*(M.sin(xx)*a1+M.cos(xx)*a2*8/x); } return a; @@ -236,15 +235,15 @@ var besseli = (function() { var b0_a = [1.0, 3.5156229, 3.0899424, 1.2067492, 0.2659732, 0.360768e-1, 0.45813e-2].reverse(); var b0_b = [0.39894228, 0.1328592e-1, 0.225319e-2, -0.157565e-2, 0.916281e-2, -0.2057706e-1, 0.2635537e-1, -0.1647633e-1, 0.392377e-2].reverse(); function bessel0(x) { - if(x <= 3.75) return b0_a.horner(x*x/(3.75*3.75)); - return M.exp(M.abs(x))/M.sqrt(M.abs(x))*b0_b.horner(3.75/M.abs(x)); + if(x <= 3.75) return _horner(b0_a, x*x/(3.75*3.75)); + return M.exp(M.abs(x))/M.sqrt(M.abs(x))*_horner(b0_b, 3.75/M.abs(x)); } var b1_a = [0.5, 0.87890594, 0.51498869, 0.15084934, 0.2658733e-1, 0.301532e-2, 0.32411e-3].reverse(); var b1_b = [0.39894228, -0.3988024e-1, -0.362018e-2, 0.163801e-2, -0.1031555e-1, 0.2282967e-1, -0.2895312e-1, 0.1787654e-1, -0.420059e-2].reverse(); function bessel1(x) { - if(x < 3.75) return x * b1_a.horner(x*x/(3.75*3.75)); - return (x < 0 ? -1 : 1) * M.exp(M.abs(x))/M.sqrt(M.abs(x))*b1_b.horner(3.75/M.abs(x)); + if(x < 3.75) return x * _horner(b1_a, x*x/(3.75*3.75)); + return (x < 0 ? -1 : 1) * M.exp(M.abs(x))/M.sqrt(M.abs(x))*_horner(b1_b, 3.75/M.abs(x)); } return function besseli(x, n) { @@ -278,15 +277,15 @@ var besselk = (function() { var b0_a = [-0.57721566, 0.42278420, 0.23069756, 0.3488590e-1, 0.262698e-2, 0.10750e-3, 0.74e-5].reverse(); var b0_b = [1.25331414, -0.7832358e-1, 0.2189568e-1, -0.1062446e-1, 0.587872e-2, -0.251540e-2, 0.53208e-3].reverse(); function bessel0(x) { - if(x <= 2) return -M.log(x/2)*besseli(x,0) + b0_a.horner(x*x/4); - return M.exp(-x)/M.sqrt(x)*b0_b.horner(2/x); + if(x <= 2) return -M.log(x/2)*besseli(x,0) + _horner(b0_a, x*x/4); + return M.exp(-x)/M.sqrt(x)*_horner(b0_b, 2/x); } var b1_a = [1.0, 0.15443144, -0.67278579, -0.18156897, -0.1919402e-1, -0.110404e-2, -0.4686e-4].reverse(); var b1_b = [1.25331414, 0.23498619, -0.3655620e-1, 0.1504268e-1, -0.780353e-2, 0.325614e-2, -0.68245e-3].reverse(); function bessel1(x) { - if(x <= 2) return M.log(x/2)*besseli(x,1) + (1/x)*b1_a.horner(x*x/4); - return M.exp(-x)/M.sqrt(x)*b1_b.horner(2/x); + if(x <= 2) return M.log(x/2)*besseli(x,1) + (1/x)*_horner(b1_a, x*x/4); + return M.exp(-x)/M.sqrt(x)*_horner(b1_b, 2/x); } return _bessel_wrap(bessel0, bessel1, 'BESSELK', 2, 1); diff --git a/package.json b/package.json index a887a12..ec15861 100644 --- a/package.json +++ b/package.json @@ -1,6 +1,6 @@ { "name": "bessel", - "version": "0.1.1", + "version": "0.2.0", "author": "SheetJS", "description": "Bessel Functions in pure JS", "keywords": ["bessel", "math", "specfun"],