Comparing version 1.0.1 to 1.0.2
@@ -36,4 +36,3 @@ /* frac.js (C) 2012-2015 SheetJS -- http://sheetjs.com */ | ||
} | ||
if(Q > D) { Q = Q_1; P = P_1; } | ||
if(Q > D) { Q = Q_2; P = P_2; } | ||
if(Q > D) { if(Q_1 > D) { Q = Q_2; P = P_2; } else { Q = Q_1; P = P_1; } } | ||
if(!mixed) return [0, sgn * P, Q]; | ||
@@ -40,0 +39,0 @@ var q = Math.floor(sgn * P/Q); |
/* frac.js (C) 2012-2015 SheetJS -- http://sheetjs.com */ | ||
var frac=function(x,D,mixed){var n1=Math.floor(x),d1=1;var n2=n1+1,d2=1;if(x!==n1)while(d1<=D&&d2<=D){var m=(n1+n2)/(d1+d2);if(x===m){if(d1+d2<=D){d1+=d2;n1+=n2;d2=D+1}else if(d1>d2)d2=D+1;else d1=D+1;break}else if(x<m){n2=n1+n2;d2=d1+d2}else{n1=n1+n2;d1=d1+d2}}if(d1>D){d1=d2;n1=n2}if(!mixed)return[0,n1,d1];var q=Math.floor(n1/d1);return[q,n1-q*d1,d1]};frac.cont=function cont(x,D,mixed){var sgn=x<0?-1:1;var B=x*sgn;var P_2=0,P_1=1,P=0;var Q_2=1,Q_1=0,Q=0;var A=Math.floor(B);while(Q_1<D){A=Math.floor(B);P=A*P_1+P_2;Q=A*Q_1+Q_2;if(B-A<5e-10)break;B=1/(B-A);P_2=P_1;P_1=P;Q_2=Q_1;Q_1=Q}if(Q>D){Q=Q_1;P=P_1}if(Q>D){Q=Q_2;P=P_2}if(!mixed)return[0,sgn*P,Q];var q=Math.floor(sgn*P/Q);return[q,sgn*P-q*Q,Q]};if(typeof module!=="undefined"&&typeof DO_NOT_EXPORT_FRAC==="undefined")module.exports=frac; | ||
var frac=function(x,D,mixed){var n1=Math.floor(x),d1=1;var n2=n1+1,d2=1;if(x!==n1)while(d1<=D&&d2<=D){var m=(n1+n2)/(d1+d2);if(x===m){if(d1+d2<=D){d1+=d2;n1+=n2;d2=D+1}else if(d1>d2)d2=D+1;else d1=D+1;break}else if(x<m){n2=n1+n2;d2=d1+d2}else{n1=n1+n2;d1=d1+d2}}if(d1>D){d1=d2;n1=n2}if(!mixed)return[0,n1,d1];var q=Math.floor(n1/d1);return[q,n1-q*d1,d1]};frac.cont=function cont(x,D,mixed){var sgn=x<0?-1:1;var B=x*sgn;var P_2=0,P_1=1,P=0;var Q_2=1,Q_1=0,Q=0;var A=Math.floor(B);while(Q_1<D){A=Math.floor(B);P=A*P_1+P_2;Q=A*Q_1+Q_2;if(B-A<5e-10)break;B=1/(B-A);P_2=P_1;P_1=P;Q_2=Q_1;Q_1=Q}if(Q>D){if(Q_1>D){Q=Q_2;P=P_2}else{Q=Q_1;P=P_1}}if(!mixed)return[0,sgn*P,Q];var q=Math.floor(sgn*P/Q);return[q,sgn*P-q*Q,Q]};if(typeof module!=="undefined"&&typeof DO_NOT_EXPORT_FRAC==="undefined")module.exports=frac; |
@@ -36,4 +36,3 @@ /* frac.js (C) 2012-2015 SheetJS -- http://sheetjs.com */ | ||
} | ||
if(Q > D) { Q = Q_1; P = P_1; } | ||
if(Q > D) { Q = Q_2; P = P_2; } | ||
if(Q > D) { if(Q_1 > D) { Q = Q_2; P = P_2; } else { Q = Q_1; P = P_1; } } | ||
if(!mixed) return [0, sgn * P, Q]; | ||
@@ -40,0 +39,0 @@ var q = Math.floor(sgn * P/Q); |
@@ -36,4 +36,3 @@ /* frac.js (C) 2012-2015 SheetJS -- http://sheetjs.com */ | ||
} | ||
if(Q > D) { Q = Q_1; P = P_1; } | ||
if(Q > D) { Q = Q_2; P = P_2; } | ||
if(Q > D) { if(Q_1 > D) { Q = Q_2; P = P_2; } else { Q = Q_1; P = P_1; } } | ||
if(!mixed) return [0, sgn * P, Q]; | ||
@@ -40,0 +39,0 @@ var q = Math.floor(sgn * P/Q); |
10
frac.md
@@ -150,7 +150,6 @@ # Target | ||
In case we end up overstepping, walk back an iteration or two: | ||
In case we end up overstepping, walk back to the last valid iteration: | ||
``` | ||
if(Q > D) { Q = Q_1; P = P_1; } | ||
if(Q > D) { Q = Q_2; P = P_2; } | ||
if(Q > D) { if(Q_1 > D) { Q = Q_2; P = P_2; } else { Q = Q_1; P = P_1; } } | ||
``` | ||
@@ -189,3 +188,3 @@ | ||
function xlline(o,j,m,w) { | ||
it(j, function(done) { | ||
it(j, function() { | ||
var d, q, qq; | ||
@@ -207,3 +206,2 @@ for(var i = j*w; i < m-3 && i < (j+1)*w; ++i) { | ||
} | ||
done(); | ||
}); | ||
@@ -247,3 +245,3 @@ } | ||
"name": "frac", | ||
"version": "1.0.1", | ||
"version": "1.0.2", | ||
"author": "SheetJS", | ||
@@ -250,0 +248,0 @@ "description": "Rational approximation with bounded denominator", |
{ | ||
"name": "frac", | ||
"version": "1.0.1", | ||
"version": "1.0.2", | ||
"author": "SheetJS", | ||
@@ -5,0 +5,0 @@ "description": "Rational approximation with bounded denominator", |
@@ -12,2 +12,4 @@ # frac | ||
### JS | ||
With [npm](https://www.npmjs.org/package/frac): | ||
@@ -25,5 +27,11 @@ | ||
### Python | ||
From [PyPI](https://pypi.python.org/pypi/frac): | ||
$ pip install frac | ||
## Usage | ||
The exported `frac` function takes three arguments: | ||
In all cases, the relevant function takes 3 arguments: | ||
@@ -38,15 +46,45 @@ - `x` the number we wish to approximate | ||
### JS | ||
The exported `frac` function implements the Mediant method. | ||
`frac.cont` implements the Aberth algorithm | ||
For example: | ||
``` | ||
```js | ||
> // var frac = require('frac'); // uncomment this line if in node | ||
> frac(Math.PI,100); // [ 0, 22, 7 ] | ||
> frac(Math.PI,100,true); // [ 3, 1, 7 ] | ||
> frac(-Math.PI,100); // [ 0, -22, 7 ] | ||
> frac(-Math.PI,100,true); // [ -4, 6, 7 ] // the approximation is (-4) + (6/7) | ||
> frac(1.3, 9); // [ 0, 9, 7 ] // 1.3 ~ 9/7 | ||
> frac(1.3, 9, true); // [ 1, 2, 7 ] // 1.3 ~ 1 + 2/7 | ||
> frac(-1.3, 9); // [ 0, -9, 7 ] // -1.3 ~ -9/7 | ||
> frac(-1.3, 9, true); // [ -2, 5, 7 ] // -1.3 ~ -2 + 5/7 | ||
> frac.cont(1.3, 9); // [ 0, 4, 3 ] // 1.3 ~ 4/3 | ||
> frac.cont(1.3, 9, true); // [ 1, 1, 3 ] // 1.3 ~ 1 + 1/3 | ||
> frac.cont(-1.3, 9); // [ 0, -4, 3 ] // -1.3 ~ -4/3 | ||
> frac.cont(-1.3, 9, true); // [ -2, 2, 3 ] // -1.3 ~ -2 + 2/3 | ||
``` | ||
`frac.cont` implements the Aberth algorithm (input and output specifications | ||
match the original `frac` function) | ||
### Python | ||
`frac.med` implements Mediant method. | ||
`frac.cont` implements Aberth algorithm | ||
For example: | ||
```py | ||
>>> import frac | ||
>>> frac.med(1.3, 9) # [ 0, 9, 7 ] | ||
>>> frac.med(1.3, 9, True) # [ 1, 2, 7 ] | ||
>>> frac.med(-1.3, 9) # [ 0, -9, 7 ] | ||
>>> frac.med(-1.3, 9, True) # [ -2, 5, 7 ] | ||
>>> frac.cont(1.3, 9) # [ 0, 4, 3 ] | ||
>>> frac.cont(1.3, 9, True) # [ 1, 1, 3 ] | ||
>>> frac.cont(-1.3, 9) # [ 0, -4, 3 ] | ||
>>> frac.cont(-1.3, 9, True) # [ -2, 2, 3 ] | ||
``` | ||
## Testing | ||
@@ -74,2 +112,2 @@ | ||
[![githalytics.com alpha](https://cruel-carlota.pagodabox.com/731e31b3a26382ccd5d213b9e74ea552 "githalytics.com")](http://githalytics.com/SheetJS/frac) | ||
[![Analytics](https://ga-beacon.appspot.com/UA-36810333-1/SheetJS/frac?pixel)](https://github.com/SheetJS/frac) |
@@ -13,3 +13,3 @@ var fs = require('fs'), assert = require('assert'); | ||
function xlline(o,j,m,w) { | ||
it(j, function(done) { | ||
it(j, function() { | ||
var d, q, qq; | ||
@@ -31,3 +31,2 @@ for(var i = j*w; i < m-3 && i < (j+1)*w; ++i) { | ||
} | ||
done(); | ||
}); | ||
@@ -34,0 +33,0 @@ } |
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Found 1 instance in 1 package
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Found 1 instance in 1 package
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