version bump 0.3.0: tolerance adjustment
Note: The Aberth algorithm is sensitive to input errors New tests trigger an infinite loop under old tolerance, work fine with new.
This commit is contained in:
parent
804bc32c2c
commit
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2
LICENSE
2
LICENSE
@ -1,4 +1,4 @@
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Copyright (C) 2013 SheetJS
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Copyright (C) 2013-2014 SheetJS
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The MIT License (MIT)
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2
Makefile
2
Makefile
@ -2,5 +2,5 @@ frac.js: frac.md
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voc frac.md
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.PHONY: test
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test:
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test:
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mocha -R spec
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12
README.md
12
README.md
@ -37,3 +37,15 @@ For example:
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`frac.cont` implements the Aberth algorithm (input and output specifications
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match the original `frac` function)
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## Tests
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Tests generated from Excel have 4 columns. To produce a similar test:
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- Column A contains the raw values
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- Column B format "Up to one digit (1/4)"
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- Column C format "Up to two digits (21/25)"
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- Column D format "Up to three digits (312/943)"
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[](http://githalytics.com/SheetJS/frac)
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72
frac.js
72
frac.js
@ -1,42 +1,42 @@
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/* frac.js (C) 2013 SheetJS -- http://sheetjs.com */
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/* frac.js (C) 2013-2014 SheetJS -- http://sheetjs.com */
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var frac = function(x, D, mixed) {
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var n1 = Math.floor(x), d1 = 1;
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var n2 = n1+1, d2 = 1;
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if(x !== n1) while(d1 <= D && d2 <= D) {
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var m = (n1 + n2) / (d1 + d2);
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if(x === m) {
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if(d1 + d2 <= D) { d1+=d2; n1+=n2; d2=D+1; }
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else if(d1 > d2) d2=D+1;
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else d1=D+1;
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break;
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}
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else if(x < m) { n2 = n1+n2; d2 = d1+d2; }
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else { n1 = n1+n2; d1 = d1+d2; }
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var n1 = Math.floor(x), d1 = 1;
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var n2 = n1+1, d2 = 1;
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if(x !== n1) while(d1 <= D && d2 <= D) {
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var m = (n1 + n2) / (d1 + d2);
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if(x === m) {
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if(d1 + d2 <= D) { d1+=d2; n1+=n2; d2=D+1; }
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else if(d1 > d2) d2=D+1;
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else d1=D+1;
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break;
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}
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if(d1 > D) { d1 = d2; n1 = n2; }
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if(!mixed) return [0, n1, d1];
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var q = Math.floor(n1/d1);
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return [q, n1 - q*d1, d1];
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else if(x < m) { n2 = n1+n2; d2 = d1+d2; }
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else { n1 = n1+n2; d1 = d1+d2; }
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}
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if(d1 > D) { d1 = d2; n1 = n2; }
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if(!mixed) return [0, n1, d1];
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var q = Math.floor(n1/d1);
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return [q, n1 - q*d1, d1];
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};
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frac.cont = function cont(x, D, mixed) {
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var sgn = x < 0 ? -1 : 1;
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var B = x * sgn;
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var P_2 = 0, P_1 = 1, P = 0;
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var Q_2 = 1, Q_1 = 0, Q = 0;
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var A = B|0;
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while(Q_1 < D) {
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A = B|0;
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P = A * P_1 + P_2;
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Q = A * Q_1 + Q_2;
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if((B - A) < 0.0000000001) break;
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B = 1 / (B - A);
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P_2 = P_1; P_1 = P;
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Q_2 = Q_1; Q_1 = Q;
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}
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if(Q > D) { Q = Q_1; P = P_1; }
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if(Q > D) { Q = Q_2; P = P_2; }
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if(!mixed) return [0, sgn * P, Q];
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var q = Math.floor(sgn * P/Q);
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return [q, sgn*P - q*Q, Q];
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var sgn = x < 0 ? -1 : 1;
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var B = x * sgn;
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var P_2 = 0, P_1 = 1, P = 0;
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var Q_2 = 1, Q_1 = 0, Q = 0;
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var A = B|0;
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while(Q_1 < D) {
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A = B|0;
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P = A * P_1 + P_2;
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Q = A * Q_1 + Q_2;
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if((B - A) < 0.0000000005) break;
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B = 1 / (B - A);
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P_2 = P_1; P_1 = P;
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Q_2 = Q_1; Q_1 = Q;
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}
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if(Q > D) { Q = Q_1; P = P_1; }
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if(Q > D) { Q = Q_2; P = P_2; }
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if(!mixed) return [0, sgn * P, Q];
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var q = Math.floor(sgn * P/Q);
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return [q, sgn*P - q*Q, Q];
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};
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if(typeof module !== 'undefined') module.exports = frac;
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190
frac.md
190
frac.md
@ -10,74 +10,74 @@ The JS implementation walks through the algorithm.
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# JS Implementation
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In this version, the return value is `[quotient, numerator, denominator]`,
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where `quotient == 0` for improper fractions. The interpretation is
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In this version, the return value is `[quotient, numerator, denominator]`,
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where `quotient == 0` for improper fractions. The interpretation is
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`x ~ quotient + numerator / denominator` where `0 <= numerator < denominator`
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and `quotient <= x` for negative `x`.
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```js>frac.js
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/* frac.js (C) 2013 SheetJS -- http://sheetjs.com */
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/* frac.js (C) 2013-2014 SheetJS -- http://sheetjs.com */
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var frac = function(x, D, mixed) {
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```
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The goal is to maintain a feasible fraction (with bounded denominator) below
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the target and another fraction above the target. The lower bound is
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the target and another fraction above the target. The lower bound is
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`floor(x) / 1` and the upper bound is `(floor(x) + 1) / 1`. We keep track of
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the numerators and denominators separately:
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```
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var n1 = Math.floor(x), d1 = 1;
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var n2 = n1+1, d2 = 1;
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var n1 = Math.floor(x), d1 = 1;
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var n2 = n1+1, d2 = 1;
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```
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If `x` is not integral, we bisect using mediants until a denominator exceeds
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our target:
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```
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if(x !== n1) while(d1 <= D && d2 <= D) {
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if(x !== n1) while(d1 <= D && d2 <= D) {
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```
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The mediant is the sum of the numerators divided by the sum of demoninators:
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```
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var m = (n1 + n2) / (d1 + d2);
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var m = (n1 + n2) / (d1 + d2);
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```
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If we happened to stumble upon the exact value, then we choose the closer one
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(the mediant if the denominator is within bounds, or the bound with the larger
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denominator)
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denominator)
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```
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if(x === m) {
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if(d1 + d2 <= D) { d1+=d2; n1+=n2; d2=D+1; }
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else if(d1 > d2) d2=D+1;
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else d1=D+1;
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break;
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}
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if(x === m) {
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if(d1 + d2 <= D) { d1+=d2; n1+=n2; d2=D+1; }
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else if(d1 > d2) d2=D+1;
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else d1=D+1;
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break;
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}
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```
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Otherwise shrink the range:
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```
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else if(x < m) { n2 = n1+n2; d2 = d1+d2; }
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else { n1 = n1+n2; d1 = d1+d2; }
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}
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else if(x < m) { n2 = n1+n2; d2 = d1+d2; }
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else { n1 = n1+n2; d1 = d1+d2; }
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}
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```
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At this point, `d1 > D` or `d2 > D` (but not both -- keep track of how `d1` and
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`d2` change). So we merely return the desired values:
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```
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if(d1 > D) { d1 = d2; n1 = n2; }
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if(!mixed) return [0, n1, d1];
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var q = Math.floor(n1/d1);
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return [q, n1 - q*d1, d1];
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if(d1 > D) { d1 = d2; n1 = n2; }
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if(!mixed) return [0, n1, d1];
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var q = Math.floor(n1/d1);
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return [q, n1 - q*d1, d1];
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};
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```
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## Continued Fraction Method
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The continued fraction technique is employed by various spreadsheet programs.
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The continued fraction technique is employed by various spreadsheet programs.
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Note that this technique is inferior to the mediant method (at least, according
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to the desired goal of most accurately approximating the floating point number)
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@ -90,64 +90,64 @@ frac.cont = function cont(x, D, mixed) {
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Note that the variables are implicitly indexed at `k` (so `B` refers to `b_k`):
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```
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var sgn = x < 0 ? -1 : 1;
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var B = x * sgn;
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var P_2 = 0, P_1 = 1, P = 0;
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var Q_2 = 1, Q_1 = 0, Q = 0;
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var A = B|0;
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var sgn = x < 0 ? -1 : 1;
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var B = x * sgn;
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var P_2 = 0, P_1 = 1, P = 0;
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var Q_2 = 1, Q_1 = 0, Q = 0;
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var A = B|0;
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```
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> Iterate
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> ... for k = 0,1,...,K, where K is the first instance of k where
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> ... for k = 0,1,...,K, where K is the first instance of k where
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> either q_{k+1} > Q or b_{k+1} is undefined (b_k = a_k).
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```
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while(Q_1 < D) {
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while(Q_1 < D) {
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```
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> a_k = [b_k], i.e., the greatest integer <= b_k
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```
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A = B|0;
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A = B|0;
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```
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> p_k = a_k p_{k-1} + p_{k-2}
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> q_k = a_k q_{k-1} + q_{k-2}
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```
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P = A * P_1 + P_2;
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Q = A * Q_1 + Q_2;
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P = A * P_1 + P_2;
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Q = A * Q_1 + Q_2;
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```
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> b_{k+1} = (b_{k} - a_{k})^{-1}
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> b_{k+1} = (b_{k} - a_{k})^{-1}
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```
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if((B - A) < 0.0000000001) break;
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if((B - A) < 0.0000000005) break;
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```
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At the end of each iteration, advance `k` by one step:
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```
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B = 1 / (B - A);
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P_2 = P_1; P_1 = P;
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Q_2 = Q_1; Q_1 = Q;
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}
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```
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B = 1 / (B - A);
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P_2 = P_1; P_1 = P;
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Q_2 = Q_1; Q_1 = Q;
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}
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```
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In case we end up overstepping, walk back an iteration or two:
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In case we end up overstepping, walk back an iteration or two:
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```
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if(Q > D) { Q = Q_1; P = P_1; }
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if(Q > D) { Q = Q_2; P = P_2; }
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if(Q > D) { Q = Q_1; P = P_1; }
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if(Q > D) { Q = Q_2; P = P_2; }
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```
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The final result is `r = (sgn x)p_k / q_k`:
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```
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if(!mixed) return [0, sgn * P, Q];
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var q = Math.floor(sgn * P/Q);
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return [q, sgn*P - q*Q, Q];
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if(!mixed) return [0, sgn * P, Q];
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var q = Math.floor(sgn * P/Q);
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return [q, sgn*P - q*Q, Q];
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};
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```
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@ -163,34 +163,44 @@ if(typeof module !== 'undefined') module.exports = frac;
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var fs = require('fs'), assert = require('assert');
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var frac;
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describe('source', function() { it('should load', function() { frac = require('./'); }); });
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var xltestfiles=[
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['xl.00001.tsv', 10000],
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['xl.0001.tsv', 10000],
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['xl.001.tsv', 10000],
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['xl.01.tsv', 10000]
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];
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function line(o,j,m) {
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it(j, function(done) {
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var d, q, qq;
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for(var i = j*100; i < m-3 && i < (j+1)*100; ++i) {
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d = o[i].split("\t");
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function xlline(o,j,m,w) {
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it(j, function(done) {
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var d, q, qq;
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for(var i = j*w; i < m-3 && i < (j+1)*w; ++i) {
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d = o[i].split("\t");
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q = frac.cont(Number(d[0]), 9, true);
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qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? q[1] + "/" + q[2] : " ") : "0 ";
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assert.equal(qq, d[1], d[1] + " 1");
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q = frac.cont(Number(d[0]), 9, true);
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qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? q[1] + "/" + q[2] : " ") : "0 ";
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assert.equal(qq, d[1], d[1] + " 1");
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q = frac.cont(Number(d[0]), 99, true);
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qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") : " ") : "0 ";
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assert.equal(qq, d[2], d[2] + " 2");
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q = frac.cont(Number(d[0]), 99, true);
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qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") : " ") : "0 ";
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assert.equal(qq, d[2], d[2] + " 2");
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q = frac.cont(Number(d[0]), 999, true);
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qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 100 ? " " : "") + (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") + (q[2]<100?" ":""): " ") : "0 ";
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assert.equal(qq, d[3], d[3] + " 3");
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}
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done();
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});
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q = frac.cont(Number(d[0]), 999, true);
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qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 100 ? " " : "") + (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") + (q[2]<100?" ":""): " ") : "0 ";
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assert.equal(qq, d[3], d[3] + " 3");
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}
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done();
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});
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}
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function parsetest(o) {
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for(var j = 0, m = o.length-3; j < m/100; ++j) line(o,j,m);
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function parsexl(f,w) {
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if(!fs.existsSync(f)) return;
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var o = fs.readFileSync(f, 'utf-8').split("\n");
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for(var j = 0, m = o.length-3; j < m/w; ++j) xlline(o,j,m,w);
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}
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describe('xl.00001.tsv', function() {
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var o = fs.readFileSync('./test_files/xl.00001.tsv', 'utf-8').split("\n");
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parsetest(o);
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xltestfiles.forEach(function(x) {
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var f = './test_files/' + x[0];
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describe(x[0], function() {
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parsexl(f,x[1]);
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});
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});
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```
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@ -201,7 +211,7 @@ frac.js: frac.md
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voc frac.md
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.PHONY: test
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test:
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test:
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mocha -R spec
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```
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@ -209,24 +219,32 @@ test:
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```json>package.json
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{
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"name": "frac",
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"version": "0.2.1",
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"author": "SheetJS",
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"description": "Rational approximation with bounded denominator",
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"keywords": [ "math", "fraction", "rational", "approximation" ],
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"main": "./frac.js",
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"dependencies": {},
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"devDependencies": {"mocha":""},
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"repository": {
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"type":"git",
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"url": "git://github.com/SheetJS/frac.git"
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},
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"scripts": {
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"test": "make test"
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},
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"bugs": { "url": "https://github.com/SheetJS/frac/issues" },
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"engines": { "node": ">=0.8" }
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"name": "frac",
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"version": "0.3.0",
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"author": "SheetJS",
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"description": "Rational approximation with bounded denominator",
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"keywords": [ "math", "fraction", "rational", "approximation" ],
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"main": "./frac.js",
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"dependencies": {},
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"devDependencies": {"mocha":"","voc":""},
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"repository": {
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"type":"git",
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"url": "git://github.com/SheetJS/frac.git"
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},
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"scripts": {
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"test": "make test"
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},
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"bugs": { "url": "https://github.com/SheetJS/frac/issues" },
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||||
"engines": { "node": ">=0.8" }
|
||||
}
|
||||
```
|
||||
|
||||
And to make sure that test files are not included in npm:
|
||||
```>.npmignore
|
||||
./test_files
|
||||
```
|
||||
|
||||
```>.gitignore
|
||||
.gitignore
|
||||
.npmignore
|
||||
```
|
||||
|
||||
34
package.json
34
package.json
@ -1,19 +1,19 @@
|
||||
{
|
||||
"name": "frac",
|
||||
"version": "0.2.1",
|
||||
"author": "SheetJS",
|
||||
"description": "Rational approximation with bounded denominator",
|
||||
"keywords": [ "math", "fraction", "rational", "approximation" ],
|
||||
"main": "./frac.js",
|
||||
"dependencies": {},
|
||||
"devDependencies": {"mocha":""},
|
||||
"repository": {
|
||||
"type":"git",
|
||||
"url": "git://github.com/SheetJS/frac.git"
|
||||
},
|
||||
"scripts": {
|
||||
"test": "make test"
|
||||
},
|
||||
"bugs": { "url": "https://github.com/SheetJS/frac/issues" },
|
||||
"engines": { "node": ">=0.8" }
|
||||
"name": "frac",
|
||||
"version": "0.3.0",
|
||||
"author": "SheetJS",
|
||||
"description": "Rational approximation with bounded denominator",
|
||||
"keywords": [ "math", "fraction", "rational", "approximation" ],
|
||||
"main": "./frac.js",
|
||||
"dependencies": {},
|
||||
"devDependencies": {"mocha":"","voc":""},
|
||||
"repository": {
|
||||
"type":"git",
|
||||
"url": "git://github.com/SheetJS/frac.git"
|
||||
},
|
||||
"scripts": {
|
||||
"test": "make test"
|
||||
},
|
||||
"bugs": { "url": "https://github.com/SheetJS/frac/issues" },
|
||||
"engines": { "node": ">=0.8" }
|
||||
}
|
||||
|
||||
54
test.js
54
test.js
@ -1,32 +1,42 @@
|
||||
var fs = require('fs'), assert = require('assert');
|
||||
var frac;
|
||||
describe('source', function() { it('should load', function() { frac = require('./'); }); });
|
||||
var xltestfiles=[
|
||||
['xl.00001.tsv', 10000],
|
||||
['xl.0001.tsv', 10000],
|
||||
['xl.001.tsv', 10000],
|
||||
['xl.01.tsv', 10000]
|
||||
];
|
||||
|
||||
function line(o,j,m) {
|
||||
it(j, function(done) {
|
||||
var d, q, qq;
|
||||
for(var i = j*100; i < m-3 && i < (j+1)*100; ++i) {
|
||||
d = o[i].split("\t");
|
||||
function xlline(o,j,m,w) {
|
||||
it(j, function(done) {
|
||||
var d, q, qq;
|
||||
for(var i = j*w; i < m-3 && i < (j+1)*w; ++i) {
|
||||
d = o[i].split("\t");
|
||||
|
||||
q = frac.cont(Number(d[0]), 9, true);
|
||||
qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? q[1] + "/" + q[2] : " ") : "0 ";
|
||||
assert.equal(qq, d[1], d[1] + " 1");
|
||||
q = frac.cont(Number(d[0]), 9, true);
|
||||
qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? q[1] + "/" + q[2] : " ") : "0 ";
|
||||
assert.equal(qq, d[1], d[1] + " 1");
|
||||
|
||||
q = frac.cont(Number(d[0]), 99, true);
|
||||
qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") : " ") : "0 ";
|
||||
assert.equal(qq, d[2], d[2] + " 2");
|
||||
q = frac.cont(Number(d[0]), 99, true);
|
||||
qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") : " ") : "0 ";
|
||||
assert.equal(qq, d[2], d[2] + " 2");
|
||||
|
||||
q = frac.cont(Number(d[0]), 999, true);
|
||||
qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 100 ? " " : "") + (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") + (q[2]<100?" ":""): " ") : "0 ";
|
||||
assert.equal(qq, d[3], d[3] + " 3");
|
||||
}
|
||||
done();
|
||||
});
|
||||
q = frac.cont(Number(d[0]), 999, true);
|
||||
qq = (q[0]||q[1]) ? (q[0] || "") + " " + (q[1] ? (q[1] < 100 ? " " : "") + (q[1] < 10 ? " " : "") + q[1] + "/" + q[2] + (q[2]<10?" ":"") + (q[2]<100?" ":""): " ") : "0 ";
|
||||
assert.equal(qq, d[3], d[3] + " 3");
|
||||
}
|
||||
done();
|
||||
});
|
||||
}
|
||||
function parsetest(o) {
|
||||
for(var j = 0, m = o.length-3; j < m/100; ++j) line(o,j,m);
|
||||
function parsexl(f,w) {
|
||||
if(!fs.existsSync(f)) return;
|
||||
var o = fs.readFileSync(f, 'utf-8').split("\n");
|
||||
for(var j = 0, m = o.length-3; j < m/w; ++j) xlline(o,j,m,w);
|
||||
}
|
||||
describe('xl.00001.tsv', function() {
|
||||
var o = fs.readFileSync('./test_files/xl.00001.tsv', 'utf-8').split("\n");
|
||||
parsetest(o);
|
||||
xltestfiles.forEach(function(x) {
|
||||
var f = './test_files/' + x[0];
|
||||
describe(x[0], function() {
|
||||
parsexl(f,x[1]);
|
||||
});
|
||||
});
|
||||
|
||||
848576
test_files/xl.00001.tsv
848576
test_files/xl.00001.tsv
File diff suppressed because it is too large
Load Diff
1048576
test_files/xl.0001.tsv
Normal file
1048576
test_files/xl.0001.tsv
Normal file
File diff suppressed because it is too large
Load Diff
1048576
test_files/xl.001.tsv
Normal file
1048576
test_files/xl.001.tsv
Normal file
File diff suppressed because it is too large
Load Diff
1048576
test_files/xl.01.tsv
Normal file
1048576
test_files/xl.01.tsv
Normal file
File diff suppressed because it is too large
Load Diff
Loading…
Reference in New Issue
Block a user