version bump 0.3.0: cleanup

- eliminated array reduce (performance improvement) - explicit treatment of divergent values - better handling of non-integral order (fixes #3, h/t @vron) - reorganized source, removed voc dependency (fixes #2, h/t @hmalphettes) - new browser demo - more detailed test suite and coverage tests - updated travis versions for test - miscellaneous adjustments to tooling
2016-09-24 02:15:52 -04:00 · 2016-09-24 02:15:52 -04:00 · 73ee33e402
commit 73ee33e402
parent 31237637de
31 changed files with 1177 additions and 118 deletions
--- a/.flowconfig
+++ b/.flowconfig
@ -0,0 +1,19 @@
+[ignore]
+.*/node_modules/.*
+.*/dist/.*
+.*/test.js
+
+.*/bits/.*
+.*/ctest/.*
+.*/misc/.*
+.*/perf/.*
+
+.*/bessel.js
+
+[include]
+bessel.flow.js
+
+[libs]
+bits/10_types.js
+
+[options]
--- a/.gitignore
+++ b/.gitignore
@ -1 +1,2 @@
 node_modules
+misc/coverage.html
--- a/.jscs.json
+++ b/.jscs.json
@ -0,0 +1,6 @@
+{
+  "requireCommaBeforeLineBreak": true,
+  "disallowTrailingWhitespace": true,
+  "disallowTrailingComma": true
+}
+
--- a/.jshintrc
+++ b/.jshintrc
@ -0,0 +1,4 @@
+{
+	"bitwise": false,
+	"curly": false
+}
--- a/.travis.yml
+++ b/.travis.yml
@ -1,7 +1,15 @@
 language: node_js
 node_js:
-  - "0.11"
+  - "6"
+  - "5"
+  - "4.2"
+  - "0.12"
  - "0.10"
  - "0.8"
 before_install:
-  - "npm install -g mocha"
+  - "npm install -g npm@next"
+  - "npm install -g mocha voc"
+  - "npm install blanket"
+  - "npm install coveralls mocha-lcov-reporter"
+after_success:
+  - "make coveralls-spin"
--- a/69
+++ b/69
@ -1,7 +1,66 @@
-LIBRARY=bessel
+LIB=bessel
+REQS=
+ADDONS=
+AUXTARGETS=
+HTMLLINT=index.html

-$(LIBRARY).js: bessel.md
-	node_modules/.bin/voc $^ > $@
+ULIB=$(shell echo $(LIB) | tr a-z A-Z)
+DEPS=$(sort $(wildcard bits/*.js))
+TARGET=$(LIB).js
+FLOWTARGET=$(LIB).flow.js

-test mocha:
-	mocha -R spec
+## Main Targets
+
+.PHONY: all
+all: $(TARGET) $(AUXTARGETS) ## Build library and auxiliary scripts
+
+$(TARGET) $(AUXTARGETS): %.js : %.flow.js
+	node -e 'process.stdout.write(require("fs").readFileSync("$<","utf8").replace(/^[ \t]*\/\*[:#][^*]*\*\/\s*(\n)?/gm,"").replace(/\/\*[:#][^*]*\*\//gm,""))' > $@
+
+$(FLOWTARGET): $(DEPS)
+	cat $^ | tr -d '\15\32' > $@
+
+bits/01_version.js: package.json
+	echo "BESSEL.version = '"`grep version package.json | awk '{gsub(/[^0-9a-z\.-]/,"",$$2); print $$2}'`"';" > $@
+
+.PHONY: clean
+clean: ## Remove targets and build artifacts
+	rm -f $(TARGET) $(FLOWTARGET)
+
+## Testing
+
+.PHONY: test mocha
+test mocha: test.js $(TARGET) ## Run test suite
+	mocha -R spec -t 20000
+
+## Code Checking
+
+.PHONY: lint
+lint: $(TARGET) $(AUXTARGETS) ## Run jshint and jscs checks
+	@jshint --show-non-errors $(TARGET) $(AUXTARGETS)
+	@jshint --show-non-errors package.json
+	@jshint --show-non-errors --extract=always $(HTMLLINT)
+	@jscs $(TARGET) $(AUXTARGETS)
+
+.PHONY: flow
+flow: lint ## Run flow checker
+	@flow check --all --show-all-errors
+
+.PHONY: cov
+cov: misc/coverage.html ## Run coverage test
+
+misc/coverage.html: $(TARGET) test.js
+	mocha --require blanket -R html-cov -t 20000 > $@
+
+.PHONY: coveralls
+coveralls: ## Coverage Test + Send to coveralls.io
+	mocha --require blanket --reporter mocha-lcov-reporter -t 20000 | node ./node_modules/coveralls/bin/coveralls.js
+
+
+.PHONY: help
+help:
+	@grep -hE '(^[a-zA-Z_-][ a-zA-Z_-]*:.*?|^#[#*])' $(MAKEFILE_LIST) | bash misc/help.sh
+
+#* To show a spinner, append "-spin" to any target e.g. cov-spin
+%-spin:
+	@make $* & bash misc/spin.sh $$!
--- a/README.md
+++ b/README.md
@ -1,36 +1,92 @@
-# Bessel.JS
+# bessel

-Pure-JS implementation of the Bessel functions (J,Y,I,K), for node and browser
+Pure-JS implementation of Bessel functions J,Y,I,K (for the browser and nodejs).
+Emphasis on correctness and performance for integer order.

 The standard notation is used here:

- - J is the Bessel function of the first kind
- - Y is the Bessel function of the second kind
- - I is the modified Bessel function of the first kind
- - K is the modified Bessel function of the first kind
+ - `J` is the Bessel function of the first kind
+ - `Y` is the Bessel function of the second kind
+ - `I` is the modified Bessel function of the first kind
+ - `K` is the modified Bessel function of the second kind

-# Usage
+## Installation

-The functions `besselj`, `bessely`, `besseli`, `besselk` are exposed when you include
-the script `bessel.js`:
+With [npm](https://www.npmjs.org/package/bessel):

-```html>
+```bash
+$ npm install bessel
+```
+
+In the browser:
+
+```html
 <script src="bessel.js"></script>
-<script>console.log(besselj(1,2));</script>
 ```

-See `test.html` for an example
+The browser exposes a variable `BESSEL`

-In node, those four functions are exported:
+The script will manipulate `module.exports` if available (e.g. in a CommonJS
+`require` context).  This is not always desirable.  To prevent the behavior,
+define `DO_NOT_EXPORT_BESSEL`

-```js>
-var besselj01 = require('bessel').besselj(0,1);
+## Usage
+
+In all cases, the relevant function takes two arguments (`value`, `order`).
+
+The return value is a JS number.  `NaN` signals an error in calculation.
+
+- `BESSEL.besselj(x, n)` computes `J_{n}(x)`
+
+- `BESSEL.bessely(x, n)` computes `Y_{n}(x)`
+
+- `BESSEL.besseli(x, n)` computes `I_{n}(x)`
+
+- `BESSEL.besselk(x, n)` computes `K_{n}(x)`
+
+For example:
+
+```js
+> // var BESSEL = require('bessel'); // uncomment this line if in node
+> BESSEL.besselj(1.5,0)              // 0.5118276712499389
+> BESSEL.bessely(1.5,0)              // 0.38244892476502895
+> BESSEL.besseli(1.5,0)              // 1.6467232021476754
+> BESSEL.besselk(1.5,0)              // 0.2138055693236539
+
+> var Y = BESSEL.bessely
+> Y(Math.PI, 5) + Y(Math.PI, 3) - (2 * 4 / Math.PI) * Y(Math.PI, 4) // 0
 ```

-Each function follows Excel semantics `(value, function-order)`.  For example,
+## Testing

-```js>
-bessel.besselj(1.5, 1)
+`make test` will run the nodejs-based test.
+
+To generate the `excel.tsv` test cases, make a 6-column Excel Sheet:
+
+| x | n |    `BESSELI`   |    `BESSELJ`   |    `BESSELK`   |    `BESSELY`   |
+|---|---|:--------------:|:--------------:|:--------------:|:--------------:|
+| x | n |`BESSELI(A1,B1)`|`BESSELJ(A1,B1)`|`BESSELK(A1,B1)`|`BESSELY(A1,B1)`|
+
+To generate the `mma.tsv` test cases, use the Mathematica Bessel Functions:
+
+```mathematica
+(* Bessel_[value, order] *)
+F[x_,n_]:={x/2,n,BesselI[n,x/2], BesselJ[n,x/2], BesselK[n,x/2], BesselY[n,x/2]}
+Do[Print[ExportString[N[F[x,n],10],"csv"]], {n,1,3}, {x,1,20} ]
 ```

-is the value of the bessel function J1 at the point x=1.5
+Note: Each function follows Excel semantics `(value, order)`.  Other platforms
+like Mathematica reverse the argument order.
+
+## License
+
+Please consult the attached LICENSE file for details.  All rights not explicitly
+granted by the MIT License are reserved by the Original Author.
+
+## Badges
+
+[![Build Status](https://travis-ci.org/SheetJS/bessel.svg?branch=master)](https://travis-ci.org/SheetJS/bessel)
+
+[![Coverage Status](http://img.shields.io/coveralls/SheetJS/bessel/master.svg)](https://coveralls.io/r/SheetJS/bessel?branch=master)
+
+[![Analytics](https://ga-beacon.appspot.com/UA-36810333-1/SheetJS/bessel?pixel)](https://github.com/SheetJS/bessel)
--- a/bessel.flow.js
+++ b/bessel.flow.js
@ -0,0 +1,252 @@
+/* bessel.js (C) 2013-present SheetJS -- http://sheetjs.com */
+/* vim: set ts=2: */
+/*exported BESSEL */
+var BESSEL;
+/*:: declare var DO_NOT_EXPORT_BESSEL: any; */
+/*:: declare var define: any; */
+(function (factory) {
+  /*jshint ignore:start */
+  if(typeof DO_NOT_EXPORT_BESSEL === 'undefined') {
+    if('object' === typeof exports) {
+      factory(exports);
+    } else if ('function' === typeof define && define.amd) {
+      define(function () {
+        var module = {};
+        factory(module);
+        return module;
+      });
+    } else {
+      factory(BESSEL = {});
+    }
+  } else {
+    factory(BESSEL = {});
+  }
+  /*jshint ignore:end */
+}(function(BESSEL) {
+BESSEL.version = '0.3.0';
+var M = Math;
+
+/*::
+type BesselN = (x:number) => number;
+type BesselF = (x:number, n:number) => number;
+*/
+function _horner(arr/*:Array<number>*/, v/*:number*/)/*:number*/ { for(var i = 0, z = 0; i < arr.length; ++i) z = v * z + arr[i]; return z; }
+function _bessel_iter(x/*:number*/, n/*:number*/, f0/*:number*/, f1/*:number*/, sign/*:number*/)/*:number*/ {
+  if(n === 0) return f0;
+  if(n === 1) return f1;
+  var tdx = 2 / x, f2 = f1;
+  for(var o = 1; o < n; ++o) {
+    f2 = f1 * o * tdx + sign * f0;
+    f0 = f1; f1 = f2;
+  }
+  return f2;
+}
+function _bessel_wrap(bessel0/*:BesselN*/, bessel1/*:BesselN*/, name/*:string*/, nonzero/*:number*/, sign/*:number*/)/*:BesselF*/ {
+  return function bessel(x/*:number*/,n/*:number*/) {
+    if(nonzero) {
+      if(x === 0) return (nonzero == 1 ? -Infinity : Infinity);
+      else if(x < 0) return NaN;
+    }
+    if(n === 0) return bessel0(x);
+    if(n === 1) return bessel1(x);
+    if(n < 0) return NaN;
+    n|=0;
+    var b0/*:number*/ = bessel0(x), b1/*:number*/ = bessel1(x);
+    return _bessel_iter(x, n, b0, b1, sign);
+  };
+}
+var besselj/*:BesselF*/ = (function() {
+  var W = 0.636619772; // 2 / Math.PI
+
+  var b0_a1a = [57568490574.0, -13362590354.0, 651619640.7, -11214424.18, 77392.33017, -184.9052456].reverse();
+  var b0_a2a = [57568490411.0, 1029532985.0, 9494680.718, 59272.64853, 267.8532712, 1.0].reverse();
+  var b0_a1b = [1.0, -0.1098628627e-2, 0.2734510407e-4, -0.2073370639e-5, 0.2093887211e-6].reverse();
+  var b0_a2b = [-0.1562499995e-1, 0.1430488765e-3, -0.6911147651e-5, 0.7621095161e-6, -0.934935152e-7].reverse();
+
+  function bessel0(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x * x;
+    if(x < 8) {
+      a1 = _horner(b0_a1a, y);
+      a2 = _horner(b0_a2a, y);
+      a = a1 / a2;
+    } else {
+      var xx = x - 0.785398164;
+      y = 64 / y;
+      a1 = _horner(b0_a1b, y);
+      a2 = _horner(b0_a2b, y);
+      a = M.sqrt(W/x)*(M.cos(xx)*a1-M.sin(xx)*a2*8/x);
+    }
+    return a;
+  }
+
+  var b1_a1a = [72362614232.0, -7895059235.0, 242396853.1, -2972611.439, 15704.48260, -30.16036606].reverse();
+  var b1_a2a = [144725228442.0, 2300535178.0, 18583304.74, 99447.43394, 376.9991397, 1.0].reverse();
+  var b1_a1b = [1.0, 0.183105e-2, -0.3516396496e-4, 0.2457520174e-5, -0.240337019e-6].reverse();
+  var b1_a2b = [0.04687499995, -0.2002690873e-3, 0.8449199096e-5, -0.88228987e-6, 0.105787412e-6].reverse();
+
+  function bessel1(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x*x, xx = M.abs(x) - 2.356194491;
+    if(Math.abs(x)< 8) {
+      a1 = x*_horner(b1_a1a, y);
+      a2 = _horner(b1_a2a, y);
+      a = a1 / a2;
+    } else {
+      y = 64 / 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;
+    }
+    return a;
+  }
+
+  return function besselj(x/*:number*/, n/*:number*/)/*:number*/ {
+    n = Math.round(n);
+    if(!isFinite(x)) return isNaN(x) ? x : 0;
+    if(n < 0) return ((n%2)?-1:1)*besselj(x, -n);
+    if(x < 0) return ((n%2)?-1:1)*besselj(-x, n);
+    if(n === 0) return bessel0(x);
+    if(n === 1) return bessel1(x);
+    if(x === 0) return 0;
+
+    var ret=0.0;
+    if(x > n) {
+      ret = _bessel_iter(x, n, bessel0(x), bessel1(x),-1);
+    } else {
+      var m=2*M.floor((n+M.floor(M.sqrt(40*n)))/2);
+      var jsum=false;
+      var bjp=0.0, sum=0.0;
+      var bj=1.0, bjm = 0.0;
+      var tox = 2 / x;
+      for (var j=m;j>0;j--) {
+        bjm=j*tox*bj-bjp;
+        bjp=bj;
+        bj=bjm;
+        if (M.abs(bj) > 1E10) {
+          bj *= 1E-10;
+          bjp *= 1E-10;
+          ret *= 1E-10;
+          sum *= 1E-10;
+        }
+        if (jsum) sum += bj;
+        jsum=!jsum;
+        if (j == n) ret=bjp;
+      }
+      sum=2.0*sum-bj;
+      ret /= sum;
+    }
+    return ret;
+  };
+})();
+var bessely/*:BesselF*/ = (function() {
+  var W = 0.636619772;
+
+  var b0_a1a = [-2957821389.0, 7062834065.0, -512359803.6, 10879881.29, -86327.92757, 228.4622733].reverse();
+  var b0_a2a = [40076544269.0, 745249964.8, 7189466.438, 47447.26470, 226.1030244, 1.0].reverse();
+  var b0_a1b = [1.0, -0.1098628627e-2, 0.2734510407e-4, -0.2073370639e-5, 0.2093887211e-6].reverse();
+  var b0_a2b = [-0.1562499995e-1, 0.1430488765e-3, -0.6911147651e-5, 0.7621095161e-6, -0.934945152e-7].reverse();
+
+  function bessel0(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x * x, xx = x - 0.785398164;
+    if(x < 8) {
+      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 = _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;
+  }
+
+  var b1_a1a = [-0.4900604943e13, 0.1275274390e13, -0.5153438139e11, 0.7349264551e9, -0.4237922726e7, 0.8511937935e4].reverse();
+  var b1_a2a = [0.2499580570e14, 0.4244419664e12, 0.3733650367e10, 0.2245904002e8, 0.1020426050e6, 0.3549632885e3, 1].reverse();
+  var b1_a1b = [1.0, 0.183105e-2, -0.3516396496e-4, 0.2457520174e-5, -0.240337019e-6].reverse();
+  var b1_a2b = [0.04687499995, -0.2002690873e-3, 0.8449199096e-5, -0.88228987e-6, 0.105787412e-6].reverse();
+
+  function bessel1(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x*x, xx = x - 2.356194491;
+    if(x < 8) {
+      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=_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;
+  }
+
+  return _bessel_wrap(bessel0, bessel1, 'BESSELY', 1, -1);
+})();
+var besseli/*:BesselF*/ = (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/*:number*/)/*:number*/ {
+    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/*:number*/)/*:number*/ {
+    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/*:number*/, n/*:number*/)/*:number*/ {
+    n = Math.round(n);
+    if(n === 0) return bessel0(x);
+    if(n === 1) return bessel1(x);
+    if(n < 0) return NaN;
+    if(M.abs(x) === 0) return 0;
+    if(x == Infinity) return Infinity;
+
+    var ret = 0.0, j, tox = 2 / M.abs(x), bip = 0.0, bi=1.0, bim=0.0;
+    var m=2*M.round((n+M.round(M.sqrt(40*n)))/2);
+    for (j=m;j>0;j--) {
+      bim=j*tox*bi + bip;
+      bip=bi; bi=bim;
+      if (M.abs(bi) > 1E10) {
+        bi *= 1E-10;
+        bip *= 1E-10;
+        ret *= 1E-10;
+      }
+      if(j == n) ret = bip;
+    }
+    ret *= besseli(x, 0) / bi;
+    return x < 0 && (n%2) ? -ret : ret;
+  };
+
+})();
+
+var besselk/*:BesselF*/ = (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/*:number*/)/*:number*/ {
+    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/*:number*/)/*:number*/ {
+    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);
+})();
+BESSEL.besselj = besselj;
+BESSEL.bessely = bessely;
+BESSEL.besseli = besseli;
+BESSEL.besselk = besselk;
+}));
--- a/bessel.js
+++ b/bessel.js
@ -1,55 +1,85 @@
+/* bessel.js (C) 2013-present SheetJS -- http://sheetjs.com */
+/* vim: set ts=2: */
+/*exported BESSEL */
+var BESSEL;
+(function (factory) {
+  /*jshint ignore:start */
+  if(typeof DO_NOT_EXPORT_BESSEL === 'undefined') {
+    if('object' === typeof exports) {
+      factory(exports);
+    } else if ('function' === typeof define && define.amd) {
+      define(function () {
+        var module = {};
+        factory(module);
+        return module;
+      });
+    } else {
+      factory(BESSEL = {});
+    }
+  } else {
+    factory(BESSEL = {});
+  }
+  /*jshint ignore:end */
+}(function(BESSEL) {
+BESSEL.version = '0.3.0';
 var M = Math;
-function _horner(arr, v) { return arr.reduce(function(z,w){return v * z + w;},0); };
+
+function _horner(arr, v) { for(var i = 0, z = 0; i < arr.length; ++i) z = v * z + arr[i]; return z; }
 function _bessel_iter(x, n, f0, f1, sign) {
-  if(!sign) sign = -1;
-  var tdx = 2 / x, f2;
  if(n === 0) return f0;
  if(n === 1) return f1;
-  for(var o = 1; o != n; ++o) {
+  var tdx = 2 / x, f2 = f1;
+  for(var o = 1; o < n; ++o) {
    f2 = f1 * o * tdx + sign * f0;
    f0 = f1; f1 = f2;
  }
-  return f1;
+  return f2;
 }
 function _bessel_wrap(bessel0, bessel1, name, nonzero, sign) {
  return function bessel(x,n) {
+    if(nonzero) {
+      if(x === 0) return (nonzero == 1 ? -Infinity : Infinity);
+      else if(x < 0) return NaN;
+    }
    if(n === 0) return bessel0(x);
    if(n === 1) return bessel1(x);
-    if(n < 0) throw name + ': Order (' + n + ') must be nonnegative';
-    if(nonzero == 1 && x === 0) throw name + ': Undefined when x == 0';
-    if(nonzero == 2 && x <= 0) throw name + ': Undefined when x <= 0';
+    if(n < 0) return NaN;
+    n|=0;
    var b0 = bessel0(x), b1 = bessel1(x);
    return _bessel_iter(x, n, b0, b1, sign);
  };
 }
 var besselj = (function() {
-  var b0_a1a = [57568490574.0,-13362590354.0,651619640.7,-11214424.18,77392.33017,-184.9052456].reverse();
-  var b0_a2a = [57568490411.0,1029532985.0,9494680.718,59272.64853,267.8532712,1.0].reverse();
-  var b0_a1b = [1.0, -0.1098628627e-2, 0.2734510407e-4, -0.2073370639e-5, 0.2093887211e-6].reverse();
-  var b0_a2b = [-0.1562499995e-1, 0.1430488765e-3, -0.6911147651e-5, 0.7621095161e-6, -0.934935152e-7].reverse();
  var W = 0.636619772; // 2 / Math.PI

+  var b0_a1a = [57568490574.0, -13362590354.0, 651619640.7, -11214424.18, 77392.33017, -184.9052456].reverse();
+  var b0_a2a = [57568490411.0, 1029532985.0, 9494680.718, 59272.64853, 267.8532712, 1.0].reverse();
+  var b0_a1b = [1.0, -0.1098628627e-2, 0.2734510407e-4, -0.2073370639e-5, 0.2093887211e-6].reverse();
+  var b0_a2b = [-0.1562499995e-1, 0.1430488765e-3, -0.6911147651e-5, 0.7621095161e-6, -0.934935152e-7].reverse();
+
  function bessel0(x) {
-    var a, a1, a2, y = x * x, xx = M.abs(x) - 0.785398164;
-    if(M.abs(x) < 8) {
+    var a=0, a1=0, a2=0, y = x * x;
+    if(x < 8) {
      a1 = _horner(b0_a1a, y);
      a2 = _horner(b0_a2a, y);
-      a = a1/a2;
-    }
-    else {
+      a = a1 / a2;
+    } else {
+      var xx = x - 0.785398164;
      y = 64 / 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));
+      a = M.sqrt(W/x)*(M.cos(xx)*a1-M.sin(xx)*a2*8/x);
    }
    return a;
  }
-  var b1_a1a = [72362614232.0,-7895059235.0,242396853.1,-2972611.439, 15704.48260, -30.16036606].reverse();
+
+  var b1_a1a = [72362614232.0, -7895059235.0, 242396853.1, -2972611.439, 15704.48260, -30.16036606].reverse();
  var b1_a2a = [144725228442.0, 2300535178.0, 18583304.74, 99447.43394, 376.9991397, 1.0].reverse();
  var b1_a1b = [1.0, 0.183105e-2, -0.3516396496e-4, 0.2457520174e-5, -0.240337019e-6].reverse();
  var b1_a2b = [0.04687499995, -0.2002690873e-3, 0.8449199096e-5, -0.88228987e-6, 0.105787412e-6].reverse();
+
  function bessel1(x) {
-    var a, a1, a2, y = x*x, xx = M.abs(x) - 2.356194491;
+    var a=0, a1=0, a2=0, y = x*x, xx = M.abs(x) - 2.356194491;
    if(Math.abs(x)< 8) {
      a1 = x*_horner(b1_a1a, y);
      a2 = _horner(b1_a2a, y);
@ -63,22 +93,26 @@ var besselj = (function() {
    }
    return a;
  }
+
  return function besselj(x, n) {
    n = Math.round(n);
-    if(n === 0) return bessel0(M.abs(x));
-    if(n === 1) return bessel1(M.abs(x));
-    if(n < 0) throw 'BESSELJ: Order (' + n + ') must be nonnegative';
-    if(M.abs(x) === 0) return 0;
+    if(!isFinite(x)) return isNaN(x) ? x : 0;
+    if(n < 0) return ((n%2)?-1:1)*besselj(x, -n);
+    if(x < 0) return ((n%2)?-1:1)*besselj(-x, n);
+    if(n === 0) return bessel0(x);
+    if(n === 1) return bessel1(x);
+    if(x === 0) return 0;

-    var ret, j, tox = 2 / M.abs(x), m, jsum, sum, bjp, bj, bjm;
-    if(M.abs(x) > n) {
-      ret = _bessel_iter(x, n, bessel0(M.abs(x)), bessel1(M.abs(x)),-1);
+    var ret=0.0;
+    if(x > n) {
+      ret = _bessel_iter(x, n, bessel0(x), bessel1(x),-1);
    } else {
-      m=2*M.floor((n+M.floor(M.sqrt(40*n)))/2);
-      jsum=0;
-      bjp=ret=sum=0.0;
-      bj=1.0;
-      for (j=m;j>0;j--) {
+      var m=2*M.floor((n+M.floor(M.sqrt(40*n)))/2);
+      var jsum=false;
+      var bjp=0.0, sum=0.0;
+      var bj=1.0, bjm = 0.0;
+      var tox = 2 / x;
+      for (var j=m;j>0;j--) {
        bjm=j*tox*bj-bjp;
        bjp=bj;
        bj=bjm;
@ -95,18 +129,19 @@ var besselj = (function() {
      sum=2.0*sum-bj;
      ret /= sum;
    }
-    return x < 0 && (n%2) ? -ret : ret;
+    return ret;
  };
 })();
 var bessely = (function() {
+  var W = 0.636619772;
+
  var b0_a1a = [-2957821389.0, 7062834065.0, -512359803.6, 10879881.29, -86327.92757, 228.4622733].reverse();
  var b0_a2a = [40076544269.0, 745249964.8, 7189466.438, 47447.26470, 226.1030244, 1.0].reverse();
  var b0_a1b = [1.0, -0.1098628627e-2, 0.2734510407e-4, -0.2073370639e-5, 0.2093887211e-6].reverse();
  var b0_a2b = [-0.1562499995e-1, 0.1430488765e-3, -0.6911147651e-5, 0.7621095161e-6, -0.934945152e-7].reverse();

-  var W = 0.636619772;
  function bessel0(x) {
-    var a, a1, a2, y = x * x, xx = x - 0.785398164;
+    var a=0, a1=0, a2=0, y = x * x, xx = x - 0.785398164;
    if(x < 8) {
      a1 = _horner(b0_a1a, y);
      a2 = _horner(b0_a2a, y);
@ -124,8 +159,9 @@ var bessely = (function() {
  var b1_a2a = [0.2499580570e14, 0.4244419664e12, 0.3733650367e10, 0.2245904002e8, 0.1020426050e6, 0.3549632885e3, 1].reverse();
  var b1_a1b = [1.0, 0.183105e-2, -0.3516396496e-4, 0.2457520174e-5, -0.240337019e-6].reverse();
  var b1_a2b = [0.04687499995, -0.2002690873e-3, 0.8449199096e-5, -0.88228987e-6, 0.105787412e-6].reverse();
+
  function bessel1(x) {
-    var a, a1, a2, y = x*x, xx = x - 2.356194491;
+    var a=0, a1=0, a2=0, y = x*x, xx = x - 2.356194491;
    if(x < 8) {
      a1 = x*_horner(b1_a1a, y);
      a2 = _horner(b1_a2a, y);
@ -144,6 +180,7 @@ var bessely = (function() {
 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 _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));
@ -151,6 +188,7 @@ var besseli = (function() {

  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 * _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));
@ -159,14 +197,13 @@ var besseli = (function() {
  return function besseli(x, n) {
    n = Math.round(n);
    if(n === 0) return bessel0(x);
-    if(n == 1) return bessel1(x);
-    if(n < 0) throw 'BESSELI Order (' + n + ') must be nonnegative';
+    if(n === 1) return bessel1(x);
+    if(n < 0) return NaN;
    if(M.abs(x) === 0) return 0;
+    if(x == Infinity) return Infinity;

-    var ret, j, tox = 2 / M.abs(x), m, bip, bi, bim;
-    m=2*M.round((n+M.round(M.sqrt(40*n)))/2);
-    bip=ret=0.0;
-    bi=1.0;
+    var ret = 0.0, j, tox = 2 / M.abs(x), bip = 0.0, bi=1.0, bim=0.0;
+    var m=2*M.round((n+M.round(M.sqrt(40*n)))/2);
    for (j=m;j>0;j--) {
      bim=j*tox*bi + bip;
      bip=bi; bi=bim;
@ -186,24 +223,24 @@ var besseli = (function() {
 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) + _horner(b0_a, x*x/4);
-    return M.exp(-x)/M.sqrt(x)*_horner(b0_b, 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)*_horner(b1_a, x*x/4);
+    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);
 })();
-if(typeof exports !== "undefined") {
-  exports.besselj = besselj;
-  exports.bessely = bessely;
-  exports.besseli = besseli;
-  exports.besselk = besselk;
-}
-
+BESSEL.besselj = besselj;
+BESSEL.bessely = bessely;
+BESSEL.besseli = besseli;
+BESSEL.besselk = besselk;
+}));
--- a/bessel.md
+++ b/bessel.md
@ -14,7 +14,7 @@ var M = Math;
 The methods use an approximating polynomial and evaluate using Horner's method:

 ```
-function _horner(arr, v) { return arr.reduce(function(z,w){return v * z + w;},0); };
+function _horner(arr/*:Array<number>*/, v/*:number*/) { return arr.reduce(function(z,w){return v * z + w;},0); }
 ```

 ## Recurrence
@ -29,7 +29,7 @@ So rather than go back and try to find solution for each order, we will build
 solutions for `n=0` and `n=1` and then apply the recurrence.  The helper:

 ```js
-function _bessel_iter(x, n, f0, f1, sign) {
+function _bessel_iter(x/*:number*/, n/*:number*/, f0/*:number*/, f1/*:number*/, sign/*:?number*/) {
  if(!sign) sign = -1;
  var tdx = 2 / x, f2;
  if(n === 0) return f0;
@ -48,7 +48,7 @@ checks since `Y_n` is undefined at 0 and `K_n` is real only when `x>0`

 ```
 function _bessel_wrap(bessel0, bessel1, name, nonzero, sign) {
-  return function bessel(x,n) {
+  return function bessel(x/*:number*/,n/*:number*/) {
    if(n === 0) return bessel0(x);
    if(n === 1) return bessel1(x);
    if(n < 0) throw name + ': Order (' + n + ') must be nonnegative';
@ -143,7 +143,7 @@ For large values of x, the aforementioned iteration is fine, but for small
 values the expressions quickly blow up.  Hence a more careful iteration is used:

 ```
-  return function besselj(x, n) {
+  return function besselj(x/*:number*/, n/*:number*/) {
    n = Math.round(n);
    if(n === 0) return bessel0(M.abs(x));
    if(n === 1) return bessel1(M.abs(x));
@ -246,7 +246,7 @@ var besseli = (function() {
    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) {
+  return function besseli(x/*:number*/, n/*:number*/) {
    n = Math.round(n);
    if(n === 0) return bessel0(x);
    if(n == 1) return bessel1(x);
--- a/bits/00_header.js
+++ b/bits/00_header.js
@ -0,0 +1,25 @@
+/* bessel.js (C) 2013-present SheetJS -- http://sheetjs.com */
+/* vim: set ts=2: */
+/*exported BESSEL */
+var BESSEL;
+/*:: declare var DO_NOT_EXPORT_BESSEL: any; */
+/*:: declare var define: any; */
+(function (factory) {
+  /*jshint ignore:start */
+  if(typeof DO_NOT_EXPORT_BESSEL === 'undefined') {
+    if('object' === typeof exports) {
+      factory(exports);
+    } else if ('function' === typeof define && define.amd) {
+      define(function () {
+        var module = {};
+        factory(module);
+        return module;
+      });
+    } else {
+      factory(BESSEL = {});
+    }
+  } else {
+    factory(BESSEL = {});
+  }
+  /*jshint ignore:end */
+}(function(BESSEL) {
--- a/bits/01_version.js
+++ b/bits/01_version.js
@ -0,0 +1 @@
+BESSEL.version = '0.3.0';
--- a/bits/02_helpers.js
+++ b/bits/02_helpers.js
@ -0,0 +1,2 @@
+var M = Math;
+
--- a/bits/10_types.js
+++ b/bits/10_types.js
@ -0,0 +1,4 @@
+/*::
+type BesselN = (x:number) => number;
+type BesselF = (x:number, n:number) => number;
+*/
--- a/bits/20_helpers.js
+++ b/bits/20_helpers.js
@ -0,0 +1 @@
+function _horner(arr/*:Array<number>*/, v/*:number*/)/*:number*/ { for(var i = 0, z = 0; i < arr.length; ++i) z = v * z + arr[i]; return z; }
--- a/bits/30_iter.js
+++ b/bits/30_iter.js
@ -0,0 +1,10 @@
+function _bessel_iter(x/*:number*/, n/*:number*/, f0/*:number*/, f1/*:number*/, sign/*:number*/)/*:number*/ {
+  if(n === 0) return f0;
+  if(n === 1) return f1;
+  var tdx = 2 / x, f2 = f1;
+  for(var o = 1; o < n; ++o) {
+    f2 = f1 * o * tdx + sign * f0;
+    f0 = f1; f1 = f2;
+  }
+  return f2;
+}
--- a/bits/40_wrapper.js
+++ b/bits/40_wrapper.js
@ -0,0 +1,14 @@
+function _bessel_wrap(bessel0/*:BesselN*/, bessel1/*:BesselN*/, name/*:string*/, nonzero/*:number*/, sign/*:number*/)/*:BesselF*/ {
+  return function bessel(x/*:number*/,n/*:number*/) {
+    if(nonzero) {
+      if(x === 0) return (nonzero == 1 ? -Infinity : Infinity);
+      else if(x < 0) return NaN;
+    }
+    if(n === 0) return bessel0(x);
+    if(n === 1) return bessel1(x);
+    if(n < 0) return NaN;
+    n|=0;
+    var b0/*:number*/ = bessel0(x), b1/*:number*/ = bessel1(x);
+    return _bessel_iter(x, n, b0, b1, sign);
+  };
+}
--- a/bits/50_besselj.js
+++ b/bits/50_besselj.js
@ -0,0 +1,83 @@
+var besselj/*:BesselF*/ = (function() {
+  var W = 0.636619772; // 2 / Math.PI
+
+  var b0_a1a = [57568490574.0, -13362590354.0, 651619640.7, -11214424.18, 77392.33017, -184.9052456].reverse();
+  var b0_a2a = [57568490411.0, 1029532985.0, 9494680.718, 59272.64853, 267.8532712, 1.0].reverse();
+  var b0_a1b = [1.0, -0.1098628627e-2, 0.2734510407e-4, -0.2073370639e-5, 0.2093887211e-6].reverse();
+  var b0_a2b = [-0.1562499995e-1, 0.1430488765e-3, -0.6911147651e-5, 0.7621095161e-6, -0.934935152e-7].reverse();
+
+  function bessel0(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x * x;
+    if(x < 8) {
+      a1 = _horner(b0_a1a, y);
+      a2 = _horner(b0_a2a, y);
+      a = a1 / a2;
+    } else {
+      var xx = x - 0.785398164;
+      y = 64 / y;
+      a1 = _horner(b0_a1b, y);
+      a2 = _horner(b0_a2b, y);
+      a = M.sqrt(W/x)*(M.cos(xx)*a1-M.sin(xx)*a2*8/x);
+    }
+    return a;
+  }
+
+  var b1_a1a = [72362614232.0, -7895059235.0, 242396853.1, -2972611.439, 15704.48260, -30.16036606].reverse();
+  var b1_a2a = [144725228442.0, 2300535178.0, 18583304.74, 99447.43394, 376.9991397, 1.0].reverse();
+  var b1_a1b = [1.0, 0.183105e-2, -0.3516396496e-4, 0.2457520174e-5, -0.240337019e-6].reverse();
+  var b1_a2b = [0.04687499995, -0.2002690873e-3, 0.8449199096e-5, -0.88228987e-6, 0.105787412e-6].reverse();
+
+  function bessel1(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x*x, xx = M.abs(x) - 2.356194491;
+    if(Math.abs(x)< 8) {
+      a1 = x*_horner(b1_a1a, y);
+      a2 = _horner(b1_a2a, y);
+      a = a1 / a2;
+    } else {
+      y = 64 / 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;
+    }
+    return a;
+  }
+
+  return function besselj(x/*:number*/, n/*:number*/)/*:number*/ {
+    n = Math.round(n);
+    if(!isFinite(x)) return isNaN(x) ? x : 0;
+    if(n < 0) return ((n%2)?-1:1)*besselj(x, -n);
+    if(x < 0) return ((n%2)?-1:1)*besselj(-x, n);
+    if(n === 0) return bessel0(x);
+    if(n === 1) return bessel1(x);
+    if(x === 0) return 0;
+
+    var ret=0.0;
+    if(x > n) {
+      ret = _bessel_iter(x, n, bessel0(x), bessel1(x),-1);
+    } else {
+      var m=2*M.floor((n+M.floor(M.sqrt(40*n)))/2);
+      var jsum=false;
+      var bjp=0.0, sum=0.0;
+      var bj=1.0, bjm = 0.0;
+      var tox = 2 / x;
+      for (var j=m;j>0;j--) {
+        bjm=j*tox*bj-bjp;
+        bjp=bj;
+        bj=bjm;
+        if (M.abs(bj) > 1E10) {
+          bj *= 1E-10;
+          bjp *= 1E-10;
+          ret *= 1E-10;
+          sum *= 1E-10;
+        }
+        if (jsum) sum += bj;
+        jsum=!jsum;
+        if (j == n) ret=bjp;
+      }
+      sum=2.0*sum-bj;
+      ret /= sum;
+    }
+    return ret;
+  };
+})();
--- a/bits/60_bessely.js
+++ b/bits/60_bessely.js
@ -0,0 +1,45 @@
+var bessely/*:BesselF*/ = (function() {
+  var W = 0.636619772;
+
+  var b0_a1a = [-2957821389.0, 7062834065.0, -512359803.6, 10879881.29, -86327.92757, 228.4622733].reverse();
+  var b0_a2a = [40076544269.0, 745249964.8, 7189466.438, 47447.26470, 226.1030244, 1.0].reverse();
+  var b0_a1b = [1.0, -0.1098628627e-2, 0.2734510407e-4, -0.2073370639e-5, 0.2093887211e-6].reverse();
+  var b0_a2b = [-0.1562499995e-1, 0.1430488765e-3, -0.6911147651e-5, 0.7621095161e-6, -0.934945152e-7].reverse();
+
+  function bessel0(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x * x, xx = x - 0.785398164;
+    if(x < 8) {
+      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 = _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;
+  }
+
+  var b1_a1a = [-0.4900604943e13, 0.1275274390e13, -0.5153438139e11, 0.7349264551e9, -0.4237922726e7, 0.8511937935e4].reverse();
+  var b1_a2a = [0.2499580570e14, 0.4244419664e12, 0.3733650367e10, 0.2245904002e8, 0.1020426050e6, 0.3549632885e3, 1].reverse();
+  var b1_a1b = [1.0, 0.183105e-2, -0.3516396496e-4, 0.2457520174e-5, -0.240337019e-6].reverse();
+  var b1_a2b = [0.04687499995, -0.2002690873e-3, 0.8449199096e-5, -0.88228987e-6, 0.105787412e-6].reverse();
+
+  function bessel1(x/*:number*/)/*:number*/ {
+    var a=0, a1=0, a2=0, y = x*x, xx = x - 2.356194491;
+    if(x < 8) {
+      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=_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;
+  }
+
+  return _bessel_wrap(bessel0, bessel1, 'BESSELY', 1, -1);
+})();
--- a/bits/70_besseli.js
+++ b/bits/70_besseli.js
@ -0,0 +1,43 @@
+var besseli/*:BesselF*/ = (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/*:number*/)/*:number*/ {
+    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/*:number*/)/*:number*/ {
+    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/*:number*/, n/*:number*/)/*:number*/ {
+    n = Math.round(n);
+    if(n === 0) return bessel0(x);
+    if(n === 1) return bessel1(x);
+    if(n < 0) return NaN;
+    if(M.abs(x) === 0) return 0;
+    if(x == Infinity) return Infinity;
+
+    var ret = 0.0, j, tox = 2 / M.abs(x), bip = 0.0, bi=1.0, bim=0.0;
+    var m=2*M.round((n+M.round(M.sqrt(40*n)))/2);
+    for (j=m;j>0;j--) {
+      bim=j*tox*bi + bip;
+      bip=bi; bi=bim;
+      if (M.abs(bi) > 1E10) {
+        bi *= 1E-10;
+        bip *= 1E-10;
+        ret *= 1E-10;
+      }
+      if(j == n) ret = bip;
+    }
+    ret *= besseli(x, 0) / bi;
+    return x < 0 && (n%2) ? -ret : ret;
+  };
+
+})();
+
--- a/bits/80_besselk.js
+++ b/bits/80_besselk.js
@ -0,0 +1,19 @@
+var besselk/*:BesselF*/ = (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/*:number*/)/*:number*/ {
+    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/*:number*/)/*:number*/ {
+    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);
+})();
--- a/bits/90_exports.js
+++ b/bits/90_exports.js
@ -0,0 +1,4 @@
+BESSEL.besselj = besselj;
+BESSEL.bessely = bessely;
+BESSEL.besseli = besseli;
+BESSEL.besselk = besselk;
--- a/bits/99_footer.js
+++ b/bits/99_footer.js
@ -0,0 +1 @@
+}));
--- a/index.html
+++ b/index.html
@ -0,0 +1,84 @@
+<!DOCTYPE html>
+<!-- bessel.js (C) 2013-present SheetJS http://sheetjs.com -->
+<!-- vim: set ts=2: -->
+<html>
+  <head>
+    <title>Bessel Live Demo</title>
+    <script src="bessel.js"></script>
+    <script src="https://cdn.rawgit.com/SheetJS/printj/master/printj.js"></script>
+  </head>
+  <body>
+    <b>Bessel Live Demo</b><br />
+    <a href="https://github.com/SheetJS/bessel">Source Code</a><br />
+    <a href="https://github.com/SheetJS/bessel/issues">Issues?  Something look weird?  Click here and report an issue</a><br />
+    <br />
+    <table>
+      <tr><td><b>Number:</b></td><td><input type="text" id="val" value="1.5"></td></tr>
+      <tr><td><b>Order:</b></td><td><input type="text" id="ord" value="1"></td></tr>
+      <tr><td colspan="2">&nbsp;</td></tr>
+      <tr><td colspan="2"><b><pre id="jt">J</pre></b></td></tr>
+      <tr><td colspan="2"><b><pre id="yt">Y</pre></b></td></tr>
+      <tr><td colspan="2"><b><pre id="it">I</pre></b></td></tr>
+      <tr><td colspan="2"><b><pre id="kt">K</pre></b></td></tr>
+    </table>
+  </body>
+  <script>
+    /*jshint browser:true */
+    var V = document.getElementById('val');
+    var O = document.getElementById('ord');
+    var J = document.getElementById('jt');
+    var Y = document.getElementById('yt');
+    var I = document.getElementById('it');
+    var K = document.getElementById('kt');
+
+    function update() {
+      var v = Number(V.value);
+      var o = Number(O.value);
+      if(v !== v) { J.innerHTML=Y.innerHTML=I.innerHTML=K.innerHTML = "Value |" + V.value + "| not valid"; return; }
+      if(o !== o) { J.innerHTML=Y.innerHTML=I.innerHTML=K.innerHTML = "Order |" + O.value + "| not valid"; return; }
+      o |= 0;
+      try { J.innerHTML = PRINTJ.sprintf("J(%.11g, %d) = %+.11g", v, o, BESSEL.besselj(v, o)); } catch(e) { J.innerHTML = String(e); }
+      try { Y.innerHTML = PRINTJ.sprintf("Y(%.11g, %d) = %+.11g", v, o, BESSEL.bessely(v, o)); } catch(e) { Y.innerHTML = String(e); }
+      try { I.innerHTML = PRINTJ.sprintf("I(%.11g, %d) = %+.11g", v, o, BESSEL.besseli(v, o)); } catch(e) { I.innerHTML = String(e); }
+      try { K.innerHTML = PRINTJ.sprintf("K(%.11g, %d) = %+.11g", v, o, BESSEL.besselk(v, o)); } catch(e) { K.innerHTML = String(e); }
+    }
+
+    /* Bind to relevant events */
+    if(O.addEventListener) {
+      O.addEventListener('keyup', update);
+      V.addEventListener('keyup', update);
+      J.addEventListener('change', update);
+      Y.addEventListener('change', update);
+      I.addEventListener('change', update);
+      K.addEventListener('change', update);
+    } else if(O.attachEvent) {
+      O.attachEvent('onkeyup', update);
+      V.attachEvent('onkeyup', update);
+      J.attachEvent('onchange', update);
+      Y.attachEvent('onchange', update);
+      I.attachEvent('onchange', update);
+      K.attachEvent('onchange', update);
+    } else {
+      O.oninput = update;
+      V.oninput = update;
+      J.onchange = update;
+      Y.onchange = update;
+      I.onchange = update;
+      K.onchange = update;
+    }
+
+    window.onload = function() { update(); };
+  </script>
+  <script type="text/javascript">
+    var _gaq = _gaq || [];
+    _gaq.push(['_setAccount', 'UA-36810333-1']);
+    _gaq.push(['_trackPageview']);
+
+    (function() {
+      var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
+      ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
+      var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
+    })();
+  </script>
+</html>
+
--- a/misc/help.sh
+++ b/misc/help.sh
@ -0,0 +1,42 @@
+#!/bin/bash
+# make_help.sh -- process listing of targets and special items in Makefile
+# Copyright (C) 2016-present  SheetJS
+#
+# usage in makefile: pipe the output of the following command:
+#     @grep -hE '(^[a-zA-Z_-][ a-zA-Z_-]*:.*?|^#[#*])' $(MAKEFILE_LIST)
+#
+# lines starting with "## " are treated as subtitles
+# lines starting with "#* " are treated as plaintext comments
+# multiple targets with "## " after the ":" are rendered as separate targets
+# if the presumed default target is labeled, it will be assigned a unique color
+
+awk '
+BEGIN{recipes=0;}
+	!/#[#*] .*$/ {next;}
+	{multi=0; isrecipe=0;}
+	/^[^#]*:/ {isrecipe=1; ++recipes;}
+	/^[^ :]* .*:/ {multi=1}
+	multi==0 && isrecipe>0 { if(recipes > 1) print; else print $0, "[default]"; next}
+	isrecipe == 0 {print; next}
+	multi>0 {
+		k=split($0, msg, "##"); m=split($0, a, ":"); n=split(a[1], b, " ");
+		for(i=1; i<=n; ++i) print b[i] ":", "##" msg[2], (recipes==1 && i==1 ? "[default]" : "")
+	}
+END {}
+' | if [[ -t 1 ]]; then
+awk '
+BEGIN {FS = ":.*?## "}
+	{color=36}
+	/\[default\]/ {color=35}
+	NF==1 && /^##/ {color=34}
+	NF==1 && /^#\*/ {color=20; $1 = substr($1, 4)}
+	{printf "\033[" color "m%-20s\033[0m %s\n", $1, $2;}
+END{}' -
+else
+awk '
+BEGIN {FS = ":.*?## "}
+	/^#\* / {$1 = substr($1, 4)}
+	{printf "%-20s %s\n", $1, $2;}
+END{}' -
+fi
+
--- a/misc/spin.sh
+++ b/misc/spin.sh
@ -0,0 +1,14 @@
+#!/bin/bash
+# spin.sh -- show a spinner (for coverage test)
+# Copyright (C) 2014-present  SheetJS
+
+wpid=$1
+delay=1
+str="|/-\\"
+while [ $(ps -a|awk '$1=='$wpid' {print $1}') ]; do
+  t=${str#?}
+  printf " [%c]" "$str"
+  str=$t${str%"$t"}
+  sleep $delay
+  printf "\b\b\b\b"
+done
--- a/package.json
+++ b/package.json
@ -1,19 +1,26 @@
 {
 	"name": "bessel",
-	"version": "0.2.0",
+	"version": "0.3.0",
 	"author": "SheetJS",
-	"description": "Bessel Functions in pure JS",
-	"keywords": ["bessel", "math", "specfun"],
-	"main": "bessel.js",
-	"repository": { "type": "git", "url": "https://github.com/SheetJS/bessel" },
-	"license": "MIT",
+	"description": "Pure-JS Bessel Functions",
+	"keywords": [ "bessel", "math", "specfun" ],
+	"main": "./bessel",
+	"dependencies": {
+	},
+	"devDependencies": {
+		"mocha":"",
+		"voc":""
+	},
+	"repository": { "type":"git", "url":"git://github.com/SheetJS/bessel.git" },
 	"scripts": {
 		"test": "make test"
 	},
-	"dependencies": {
-		"voc":""
+	"config": {
+		"blanket": {
+			"pattern": "bessel.js"
+		}
 	},
-	"devDependencies": {
-		"mocha":""
-	}
+	"bugs": { "url": "https://github.com/SheetJS/bessel/issues" },
+	"license": "MIT",
+	"engines": { "node": ">=0.8" }
 }
--- a/test.html
+++ b/test.html
@ -1,4 +0,0 @@
-<script src="bessel.js"></script>
-<script>
-console.log(besselj(1,2));
-</script>
--- a/test.js
+++ b/test.js
@ -1,22 +1,124 @@
-var assert = require('assert');
-var bessel;
-describe('When using bessel functions', function() {
-  before(function() {
-    bessel = require('./bessel');
-  });
-  it('It must load besseli', function() {
-    assert.equal(typeof bessel.besseli, 'function');
-  });
-  it('It must compute the Modified Bessel function at 1.5 with an order of 1 (0.981666)', function() {
-    assert(Math.floor((bessel.besseli(1.5, 1) - 0.981666) * 10e6) < 10);
-  });
-  it('It must compute the Bessel function at 1.9 with an order of 2 (0.329926)', function() {
-    assert(Math.floor((bessel.besselj(1.9, 2) - 0.329926) * 10e6) < 10);
-  });
-  it('It must compute the Modified Bessel function at 1.5 with an order of 1 (0.277388)', function() {
-    assert(Math.floor((bessel.besselk(1.5, 1) - 0.277388) * 10e6) < 10);
-  });
-  it('It must compute Weber\'s Bessel function at 2.5 with an order of 1 (0.145918)', function() {
-    assert(Math.floor((bessel.besselk(2.5, 1) - 0.981666) * 10e6) < 10);
+/* vim: set ts=2: */
+var X;
+if(typeof require !== 'undefined') {
+  assert = require('assert');
+  describe('source',function(){
+    it('should load',function(){X=require('./');});
+    it('all bessel functions', function() {
+      assert.equal(typeof X.besseli, 'function');
+      assert.equal(typeof X.besselj, 'function');
+      assert.equal(typeof X.besselk, 'function');
+      assert.equal(typeof X.bessely, 'function');
+    });
  });
+} else { X = BESSEL; }
+
+function approx(a, b, t) { return Math.abs((a - b) / (Math.abs(a) + Math.abs(b))) <= t; }
+
+function chk(func, x, n, v, F, t) {
+  var V = func(x,n);
+  if(!approx(V, v, t) && v != V && !(isNaN(v) && isNaN(V))) throw new Error(F + "(" + x + "," + n + ") = " + V + " !~ " + v);
+}
+
+var funcs = ['besseli', 'besselj', 'besselk', 'bessely'];
+
+var tests = {
+'besseli': [
+  [1.5, 1, 0.981666],
+  [1.9, 2, 0.603272435],
+  [2.5, 1, 2.516716242]
+],
+'besselj': [
+  [1.5, 1, 0.557936508],
+  [1.9, 2, 0.329925829],
+  [2.5, 1, 0.497094103]
+],
+'besselk': [
+  [1.5, 1, 0.277388],
+  [1.9, 2, 0.296909301],
+  [2.5, 1, 0.073890816]
+],
+'bessely': [
+  [1.5, 1, -0.412308627],
+  [1.9, 2, -0.669878674],
+  [2.5, 1, 0.14591814]
+] };
+
+describe('correctness', function() {
+  funcs.forEach(function(F) { it(F, function() {
+    tests[F].forEach(function(t) { chk(X[F], t[0], t[1], t[2], F, 1e-6); });
+  });});
+
+  if(typeof require != 'undefined') {
+    var fs = require('fs');
+    it('excel', function() {
+      var xl = fs.readFileSync("test_files/excel.tsv", 'ascii').split("\n").map(function(l) { return l.split("\t");});
+      xl.forEach(function(l) { if(l.length < 6) return;
+        var x=Number(l[0]), n=Number(l[1]);
+        var i=Number(l[2]), j=Number(l[3]), k=Number(l[4]), y=Number(l[5]);
+        chk(X.besseli, x, n, i, 'besseli', 1e-4);
+        chk(X.besselj, x, n, j, 'besselj', 1e-4);
+        chk(X.besselk, x, n, k, 'besselk', 1e-4);
+        chk(X.bessely, x, n, y, 'bessely', 1e-4);
+      });
+    });
+    it('mma', function() {
+      var mma = fs.readFileSync("test_files/mma.tsv", 'ascii').split("\n").map(function(l) { return l.split("\t");});
+      mma.forEach(function(l) { if(l.length < 6) return;
+        var x=Number(l[0]), n=Number(l[1]);
+        var i=Number(l[2]), j=Number(l[3]), k=Number(l[4]), y=Number(l[5]);
+        chk(X.besseli, x, n, i, 'besseli', 1e-5);
+        chk(X.besselj, x, n, j, 'besselj', 1e-5);
+        chk(X.besselk, x, n, k, 'besselk', 1e-5);
+        chk(X.bessely, x, n, y, 'bessely', 1e-5);
+      });
+    });
+  }
+});
+
+var rand = [
+	0.3946086812775882,  3.946086812775882,  39.46086812775882,
+	0.03119419917289612, 0.3119419917289612,  3.119419917289612,
+	0.18311903629136062, 1.8311903629136062, 18.311903629136062,
+	0.5317681126599452,  5.317681126599452,  53.17681126599452,
+	0.37724541457032235, 3.7724541457032235, 37.724541457032235,
+	0.8287802926845655,  8.287802926845655,  82.87802926845655,
+	0.7197724866379658,  7.197724866379658,  71.97724866379658
+];
+
+describe('properties', function() {
+	var t = 1e-4;
+	it('limiting behavior', function() {
+		chk(X.besselj, 0, 0, 1, 'besselj', 1e-6);
+		chk(X.besseli, 0, 0, 1, 'besseli', 1e-6);
+		chk(X.besselk, 0, 0, Infinity, 'besselk', 1e-6);
+		chk(X.bessely, 0, 0, -Infinity, 'bessely', 1e-6);
+		for(var i = 1; i < 20; ++i) {
+			chk(X.besselj, 0, i, 0, 'besselj', 1e-6);
+			chk(X.besseli, 0, i, 0, 'besseli', 1e-6);
+		}
+	});
+	it('besselj', function() {
+		var F = "BESSELJ", f = X.besselj;
+		rand.forEach(function(r) {
+			for(var n = 0; n < 20; ++n) {
+				var pp = f( r,  n), pn = f( r, -n), np = f(-r,  n), nn = f(-r, -n);
+				if((n%2)) {
+					/* besselj odd if n is odd */
+					if(!approx(np, -pp, t)) throw new Error(F + " np[" + np + "] != -pp[" + (-pp) + "] (" + r + "," + n + ")");
+					if(!approx(nn, -pn, t)) throw new Error(F + " nn[" + nn + "] != -pn[" + (-pn) + "] (" + r + "," + n + ")");
+					/* asymmetric in n */
+					if(!approx(pn, -pp, t)) throw new Error(F + " pn[" + pn + "] != -pp[" + (-pp) + "] (" + r + "," + n + ")");
+					if(!approx(nn, -np, t)) throw new Error(F + " nn[" + nn + "] != -pn[" + (-pn) + "] (" + r + "," + n + ")");
+				} else {
+					/* besselj even if n is even */
+					if(!approx(np, pp, t)) throw new Error(F + " np[" + np + "] != pp[" + (pp) + "] (" + r + "," + n + ")");
+					if(!approx(nn, pn, t)) throw new Error(F + " nn[" + nn + "] != pn[" + (pn) + "] (" + r + "," + n + ")");
+					/* symmetric in n */
+					if(!approx(pn, pp, t)) throw new Error(F + " pn[" + pn + "] != pp[" + (pp) + "] (" + r + "," + n + ")");
+					if(!approx(nn, np, t)) throw new Error(F + " nn[" + nn + "] != pn[" + (pn) + "] (" + r + "," + n + ")");
+				}
+			}
+		});
+	});
 });
--- a/test_files/excel.tsv
+++ b/test_files/excel.tsv
@ -0,0 +1,60 @@
+0.5	1	0.257894303	0.242268458	1.656441128	-1.471472392
+1	1	0.565159098	0.440050586	0.601907232	-0.781212821
+1.5	1	0.981666428	0.557936508	0.277387804	-0.412308627
+2	1	1.590636857	0.576724808	0.13986588	-0.107032432
+2.5	1	2.516716242	0.497094103	0.073890816	0.145918138
+3	1	3.953370217	0.339058958	0.040156431	0.324674424
+3.5	1	6.205834932	0.137377527	0.022239393	0.410188417
+4	1	9.759465157	-0.066043328	0.012483499	0.397925709
+4.5	1	15.38922293	-0.231060432	0.007078095	0.300997321
+5	1	24.33564185	-0.327579139	0.004044613	0.14786314
+5.5	1	38.58816378	-0.341438216	0.002325569	-0.023758243
+6	1	61.34193694	-0.276683859	0.00134392	-0.175010349
+6.5	1	97.73501304	-0.153841304	0.000779894	-0.274091281
+7	1	156.0390965	-0.004682826	0.000454182	-0.302667244
+7.5	1	249.5843679	0.135248424	0.000265297	-0.25912852
+8	1	399.8731348	0.234628387	0.000155369	-0.158060462
+8.5	1	641.6198938	0.273115291	9.11973E-05	-0.02616868
+9	1	1030.914709	0.245307412	5.3637E-05	0.104314575
+9.5	1	1658.453068	0.161262274	3.1602E-05	0.203179899
+10	1	2670.988321	0.04347225	1.86488E-05	0.249015424
+0.5	2	0.031906148	0.030604023	7.550183547	-5.441370834
+1	2	0.135747667	0.114903485	1.624838884	-1.650682613
+1.5	2	0.337834621	0.232087679	0.583655974	-0.932193761
+2	2	0.688948449	0.352834208	0.25375976	-0.617408098
+2.5	2	1.276466159	0.446059058	0.121460207	-0.381335848
+3	2	2.245212431	0.486091263	0.061510459	-0.160400399
+3.5	2	3.832012072	0.458629185	0.032307122	0.045371436
+4	2	6.422189499	0.364128143	0.017401426	0.215903599
+4.5	2	10.64151731	0.217848984	0.009545677	0.328481596
+5	2	17.50561501	0.046565119	0.005308944	0.367662879
+5.5	2	28.66258571	-0.117315483	0.00298437	0.330841237
+6	2	46.7870949	-0.242873213	0.001691968	0.229857908
+6.5	2	76.22054669	-0.307430389	0.000965899	0.088906659
+7	2	124.01131	-0.301417224	0.000554562	-0.0605266
+7.5	2	201.6054825	-0.230273411	0.000319924	-0.186414216
+8	2	327.5958389	-0.112993711	0.000185313	-0.263036605
+8.5	2	532.1925545	0.022323169	0.000107716	-0.276362442
+9	2	864.4962206	0.144846369	6.28006E-05	-0.226755682
+9.5	2	1404.333008	0.2278787	3.67109E-05	-0.128435911
+10	2	2281.518997	0.254630214	2.15098E-05	-0.005868083
+0.5	3	0.002645112	0.00256373	62.0579095	-42.05949428
+1	3	0.022168424	0.019563354	7.101262769	-5.821517632
+1.5	3	0.080774114	0.060963951	1.833803735	-2.073541401
+2	3	0.21273996	0.12894325	0.6473854	-1.127783765
+2.5	3	0.474370413	0.216600403	0.268227146	-0.756055495
+3	3	0.959753625	0.309062865	0.122170376	-0.538541623
+3.5	3	1.826392593	0.386770113	0.059161818	-0.358335346
+4	3	3.337275843	0.430171471	0.029884924	-0.18202211
+4.5	3	5.930096274	0.424703973	0.015563141	-0.009013679
+5	3	10.3311502	0.364831234	0.008291768	0.146267163
+5.5	3	17.7426483	0.256117865	0.00449602	0.264370052
+6	3	30.15054042	0.114768384	0.002471898	0.328248955
+6.5	3	50.83005827	-0.035346628	0.001374294	0.328803071
+7	3	85.17548647	-0.167555588	0.000771075	0.268080616
+7.5	3	142.0614436	-0.25806091	0.000435923	0.159707605
+8	3	236.0752263	-0.291125242	0.000248026	0.026542159
+8.5	3	391.1763672	-0.26261027	0.000141887	-0.103884234
+9	3	646.6942118	-0.180931248	8.15484E-05	-0.205094878
+9.5	3	1067.155009	-0.065313348	4.70593E-05	-0.257258177
+10	3	1758.380739	0.058379836	2.72527E-05	-0.251362657
--- a/test_files/mma.tsv
+++ b/test_files/mma.tsv
@ -0,0 +1,60 @@
+0.5	1	0.2578943054 0.2422684577 1.65644112 -1.471472393
+1	1	0.565159104	0.4400505857	0.6019072302	-0.7812128213
+1.5	1	0.9816664286	0.5579365079	0.2773878005	-0.412308627
+2	1	1.590636855	0.5767248078	0.1398658818	-0.1070324315
+2.5	1	2.516716245	0.4970941025	0.07389081635	0.145918138
+3	1	3.953370217	0.3390589585	0.04015643113	0.3246744248
+3.5	1	6.205834922	0.1373775274	0.02223939293	0.4101884179
+4	1	9.759465154	-0.06604332802	0.01248349889	0.3979257106
+4.5	1	15.38922275	-0.2310604319	0.007078094909	0.3009973231
+5	1	24.33564214	-0.3275791376	0.004044613445	0.1478631434
+5.5	1	38.58816462	-0.3414382154	0.002325569009	-0.02375823896
+6	1	61.34193678	-0.2766838581	0.001343919718	-0.1750103443
+6.5	1	97.73501077	-0.1538413014	0.0007798943982	-0.274091274
+7	1	156.0390929	-0.004682823482	0.0004541824869	-0.302667237
+7.5	1	249.5843654	0.1352484276	0.0002652973901	-0.2591285105
+8	1	399.8731368	0.2346363469	0.0001553692118	-0.1580604617
+8.5	1	641.6199025	0.2731219637	0.00009119724775	-0.0261686794
+9	1	1030.914723	0.2453117866	0.00005363701638	0.1043145752
+9.5	1	1658.453078	0.1612644308	0.00003160203411	0.2031798994
+10	1	2670.988304	0.04347274617	0.00001864877345	0.2490154242
+0.5	2	0.03190614918	0.03060402346	7.550183551	-5.441370837
+1	2	0.1357476698	0.1149034849	1.624838899	-1.650682607
+1.5	2	0.3378346183	0.2320876721	0.5836559633	-0.9321937598
+2	2	0.6889484477	0.3528340286	0.2537597546	-0.6174081042
+2.5	2	1.276466148	0.4460590584	0.1214602063	-0.3813358492
+3	2	2.245212441	0.4860912606	0.06151045847	-0.1604003935
+3.5	2	3.832012048	0.4586291842	0.0323071217	0.04537143773
+4	2	6.422189375	0.3641281459	0.01740142553	0.2159035946
+4.5	2	10.6415173	0.2178489837	0.009545677203	0.3284815967
+5	2	17.50561497	0.04656511628	0.005308943712	0.3676628826
+5.5	2	28.66258529	-0.1173154816	0.002984370024	0.3308412333
+6	2	46.78709472	-0.24287321	0.001691967567	0.2298579025
+6.5	2	76.22054724	-0.3074303906	0.0009658992748	0.08890665832
+7	2	124.0113105	-0.3014172201	0.0005545621667	-0.06052660947
+7.5	2	201.6054807	-0.2302734105	0.0003199235871	-0.1864142223
+8	2	327.5958315	-0.1129917204	0.0001853130082	-0.2630366048
+8.5	2	532.1925382	0.02232473961	0.0001077157423	-0.2763624417
+9	2	864.496194	0.1448473415	0.00006280064993	-0.2267556816
+9.5	2	1404.332974	0.2278791542	0.00003671094477	-0.1284359105
+10	2	2281.518968	0.2546303137	0.00002150981701	-0.005868082442
+0.5	3	0.002645111969	0.002563729995	62.05790953	-42.0594943
+1	3	0.02216842492	0.01956335398	7.101262825	-5.821517606
+1.5	3	0.08077411302	0.06096395114	1.833803702	-2.073541399
+2	3	0.2127399592	0.1289432495	0.6473853909	-1.127783777
+2.5	3	0.4743704088	0.216600391	0.2682271464	-0.7560554968
+3	3	0.9597536295	0.3090627223	0.1221703758	-0.5385416161
+3.5	3	1.826392582	0.3867701117	0.05916181773	-0.3583353462
+4	3	3.337275778	0.4301714739	0.02988492442	-0.182022116
+4.5	3	5.930096266	0.424703973	0.01556314131	-0.009013681594
+5	3	10.33115017	0.3648312306	0.008291768415	0.1462671627
+5.5	3	17.74264804	0.2561178651	0.004496019935	0.264370045
+6	3	30.1505403	0.1147683848	0.002471898096	0.328248946
+6.5	3	50.83005863	-0.03534663129	0.001374293952	0.3288030637
+7	3	85.17548684	-0.167555588	0.0007710751536	0.268080603
+7.5	3	142.0614424	-0.2580609132	0.0004359233032	0.1597075919
+8	3	236.075221	-0.2911322071	0.0002480257159	0.02654215932
+8.5	3	391.1763552	-0.2626162039	0.0001418870088	-0.1038842343
+9	3	646.6941919	-0.1809351903	0.00008154841635	-0.2050948781
+9.5	3	1067.154983	-0.06531531322	0.00004705927401	-0.2572581775
+10	3	1758.380717	0.05837937931	0.00002725270026	-0.2513626572
				`@ -0,0 +1 @@`
				`function _horner(arr/:Array<number>/, v/:number/)/:number/ { for(var i = 0, z = 0; i < arr.length; ++i) z = v * z + arr[i]; return z; }`