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Patch and unit test from Tim Allen from bug #54686 - Improve how DataFormatter handles fractions 

git-svn-id: https://svn.apache.org/repos/asf/poi/trunk@1494986 13f79535-47bb-0310-9956-ffa450edef68
tags/3.10-beta1
Nick Burch 11 years ago
parent
5f7a1597e4
commit
f9c9def944
6 changed files with 777 additions and 125 deletions
Split View Show Diff Stats
  1. 35
    123
      src/java/org/apache/poi/ss/usermodel/DataFormatter.java
  2. 271
    0
      src/java/org/apache/poi/ss/usermodel/FractionFormat.java
  3. 14
    2
      src/testcases/org/apache/poi/ss/usermodel/TestDataFormatter.java
  4. 83
    0
      src/testcases/org/apache/poi/ss/usermodel/TestFractionFormat.java
  5. 374
    0
      test-data/spreadsheet/54686_fraction_formats.txt
  6. BIN
      test-data/spreadsheet/54686_fraction_formats.xls

+ 35
- 123
src/java/org/apache/poi/ss/usermodel/DataFormatter.java View File

@@ -28,7 +28,6 @@ import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.text.FieldPosition;
import java.text.Format;
import java.text.NumberFormat;
import java.text.ParsePosition;
import java.text.SimpleDateFormat;
import java.util.ArrayList;
@@ -41,7 +40,6 @@ import java.util.Map;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

import org.apache.poi.ss.formula.eval.NotImplementedException;

/**
* DataFormatter contains methods for formatting the value stored in an
@@ -100,12 +98,10 @@ import org.apache.poi.ss.formula.eval.NotImplementedException;
* <li>simulate Excel's handling of a format string of all # when the value is 0.
* Excel will output "", <code>DataFormatter</code> will output "0".
* </ul>
* @author James May (james dot may at fmr dot com)
* @author Robert Kish
*
*/
public class DataFormatter {

private static final String defaultFractionWholePartFormat = "#";
private static final String defaultFractionFractionPartFormat = "#/##";
/** Pattern to find a number format: "0" or "#" */
private static final Pattern numPattern = Pattern.compile("[0#]+");

@@ -131,6 +127,17 @@ public class DataFormatter {
"(\\[MAGENTA\\])|(\\[RED\\])|(\\[WHITE\\])|(\\[YELLOW\\])|" +
"(\\[COLOR\\s*\\d\\])|(\\[COLOR\\s*[0-5]\\d\\])", Pattern.CASE_INSENSITIVE);

/**
* A regex to identify a fraction pattern.
* This requires that replaceAll("\\?", "#") has already been called
*/
private static final Pattern fractionPattern = Pattern.compile("(?:([#\\d]+)\\s+)?(#+)\\s*\\/\\s*([#\\d]+)");

/**
* A regex to strip junk out of fraction formats
*/
private static final Pattern fractionStripper = Pattern.compile("(\"[^\"]*\")|([^ \\?#\\d\\/]+)");

/**
* Cells formatted with a date or time format and which contain invalid date or time values
* show 255 pound signs ("#").
@@ -372,23 +379,26 @@ public class DataFormatter {
DateUtil.isValidExcelDate(cellValue)) {
return createDateFormat(formatStr, cellValue);
}
// Excel supports fractions in format strings, which Java doesn't
if (formatStr.indexOf("#/#") >= 0 || formatStr.indexOf("?/?") >= 0) {
// Strip custom text in quotes and escaped characters for now as it can cause performance problems in fractions.
String strippedFormatStr = formatStr.replaceAll("\\\\ ", " ").replaceAll("\\\\.", "").replaceAll("\"[^\"]*\"", " ");

boolean ok = true;
for (String part: strippedFormatStr.split(";")) {
int indexOfFraction = indexOfFraction(part);
if (indexOfFraction == -1 || indexOfFraction != lastIndexOfFraction(part)) {
ok = false;
break;
}
}
if (ok) {
return new FractionFormat(strippedFormatStr);
if (formatStr.indexOf("#/") >= 0 || formatStr.indexOf("?/") >= 0) {
String[] chunks = formatStr.split(";");
for (int i = 0; i < chunks.length; i++){
String chunk = chunks[i].replaceAll("\\?", "#");
Matcher matcher = fractionStripper.matcher(chunk);
chunk = matcher.replaceAll(" ");
chunk = chunk.replaceAll(" +", " ");
Matcher fractionMatcher = fractionPattern.matcher(chunk);
//take the first match
if (fractionMatcher.find()){
String wholePart = (fractionMatcher.group(1) == null) ? "" : defaultFractionWholePartFormat;
return new FractionFormat(wholePart, fractionMatcher.group(3));
}
}
// Strip custom text in quotes and escaped characters for now as it can cause performance problems in fractions.
//String strippedFormatStr = formatStr.replaceAll("\\\\ ", " ").replaceAll("\\\\.", "").replaceAll("\"[^\"]*\"", " ").replaceAll("\\?", "#");
//System.out.println("formatStr: "+strippedFormatStr);
return new FractionFormat(defaultFractionWholePartFormat, defaultFractionFractionPartFormat);
}
if (numPattern.matcher(formatStr).find()) {
@@ -402,17 +412,7 @@ public class DataFormatter {
return null;
}
private int indexOfFraction(String format) {
int i = format.indexOf("#/#");
int j = format.indexOf("?/?");
return i == -1 ? j : j == -1 ? i : Math.min(i, j);
}

private int lastIndexOfFraction(String format) {
int i = format.lastIndexOf("#/#");
int j = format.lastIndexOf("?/?");
return i == -1 ? j : j == -1 ? i : Math.max(i, j);
}

private Format createDateFormat(String pFormatStr, double cellValue) {
String formatStr = pFormatStr;
@@ -786,7 +786,7 @@ public class DataFormatter {
* @return a string value of the cell
*/
public String formatCellValue(Cell cell, FormulaEvaluator evaluator) {
if (cell == null) {
return "";
}
@@ -1018,97 +1018,9 @@ public class DataFormatter {
}
}
/**
* Format class that handles Excel style fractions, such as "# #/#" and "#/###"
*/
@SuppressWarnings("serial")
private static final class FractionFormat extends Format {
private final String str;
public FractionFormat(String s) {
str = s;
}
public String format(Number num) {
double doubleValue = num.doubleValue();
// Format may be p or p;n or p;n;z (okay we never get a z).
// Fall back to p when n or z is not specified.
String[] formatBits = str.split(";");
int f = doubleValue > 0.0 ? 0 : doubleValue < 0.0 ? 1 : 2;
String str = (f < formatBits.length) ? formatBits[f] : formatBits[0];
double wholePart = Math.floor(Math.abs(doubleValue));
double decPart = Math.abs(doubleValue) - wholePart;
if (wholePart + decPart == 0) {
return "0";
}
if (doubleValue < 0.0) {
wholePart *= -1.0;
}

// Split the format string into decimal and fraction parts
String[] parts = str.replaceAll(" *", " ").split(" ");
String[] fractParts;
if (parts.length == 2) {
fractParts = parts[1].split("/");
} else {
fractParts = str.split("/");
}
// Excel supports both #/# and ?/?, but Java only the former
for (int i=0; i<fractParts.length; i++) {
fractParts[i] = fractParts[i].replace('?', '#');
}

if (fractParts.length == 2) {
int fractPart1Length = Math.min(countHashes(fractParts[1]), 4); // Any more than 3 and we go around the loops for ever
double minVal = 1.0;
double currDenom = Math.pow(10 , fractPart1Length) - 1d;
double currNeum = 0;
for (int i = (int)(Math.pow(10, fractPart1Length)- 1d); i > 0; i--) {
for(int i2 = (int)(Math.pow(10, fractPart1Length)- 1d); i2 > 0; i2--){
if (minVal >= Math.abs((double)i2/(double)i - decPart)) {
currDenom = i;
currNeum = i2;
minVal = Math.abs((double)i2/(double)i - decPart);
}
}
}
NumberFormat neumFormatter = new DecimalFormat(fractParts[0]);
NumberFormat denomFormatter = new DecimalFormat(fractParts[1]);
if (parts.length == 2) {
NumberFormat wholeFormatter = new DecimalFormat(parts[0]);
String result = wholeFormatter.format(wholePart) + " " + neumFormatter.format(currNeum) + "/" + denomFormatter.format(currDenom);
return result;
} else {
String result = neumFormatter.format(currNeum + (currDenom * wholePart)) + "/" + denomFormatter.format(currDenom);
return result;
}
} else {
throw new IllegalArgumentException("Fraction must have 2 parts, found " + fractParts.length + " for fraction format " + this.str);
}
}
private int countHashes(String format) {
int count = 0;
for (int i=format.length()-1; i >= 0; i--) {
if (format.charAt(i) == '#') {
count++;
}
}
return count;
}

public StringBuffer format(Object obj, StringBuffer toAppendTo, FieldPosition pos) {
return toAppendTo.append(format((Number)obj));
}

public Object parseObject(String source, ParsePosition pos) {
throw new NotImplementedException("Reverse parsing not supported");
}
}

/**
* Format class that does nothing and always returns a constant string.
*

+ 271
- 0
src/java/org/apache/poi/ss/usermodel/FractionFormat.java View File

@@ -0,0 +1,271 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.poi.ss.usermodel;
import java.text.FieldPosition;
import java.text.Format;
import java.text.ParsePosition;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
import org.apache.poi.ss.formula.eval.NotImplementedException;
/**
* <p>Format class that handles Excel style fractions, such as "# #/#" and "#/###"</p>
*
* <p>As of this writing, this is still not 100% accurate, but it does a reasonable job
* of trying to mimic Excel's fraction calculations. It does not currently
* maintain Excel's spacing.</p>
*
* <p>This class relies on a method lifted nearly verbatim from org.apache.math.fraction.
* If further uses for Commons Math are found, we will consider adding it as a dependency.
* For now, we have in-lined the one method to keep things simple.</p>
*/
/* One question remains...is the value of epsilon in calcFractionMaxDenom reasonable? */
@SuppressWarnings("serial")
public class FractionFormat extends Format {
private final static Pattern DENOM_FORMAT_PATTERN = Pattern.compile("(?:(#+)|(\\d+))");
//this was chosen to match the earlier limitation of max denom power
//it can be expanded to get closer to Excel's calculations
//with custom formats # #/#########
//but as of this writing, the numerators and denominators
//with formats of that nature on very small values were quite
//far from Excel's calculations
private final static int MAX_DENOM_POW = 4;
//there are two options:
//a) an exact denominator is specified in the formatString
//b) the maximum denominator can be calculated from the formatString
private final int exactDenom;
private final int maxDenom;
private final String wholePartFormatString;
/**
* Single parameter ctor
* @param denomFormatString The format string for the denominator
*/
public FractionFormat(String wholePartFormatString, String denomFormatString) {
this.wholePartFormatString = wholePartFormatString;
//init exactDenom and maxDenom
Matcher m = DENOM_FORMAT_PATTERN.matcher(denomFormatString);
int tmpExact = -1;
int tmpMax = -1;
if (m.find()){
if (m.group(2) != null){
try{
tmpExact = Integer.parseInt(m.group(2));
//if the denom is 0, fall back to the default: tmpExact=100
if (tmpExact == 0){
tmpExact = -1;
}
} catch (NumberFormatException e){
//should never happen
}
} else if (m.group(1) != null) {
int len = m.group(1).length();
len = len > MAX_DENOM_POW ? MAX_DENOM_POW : len;
tmpMax = (int)Math.pow(10, len);
} else {
tmpExact = 100;
}
}
if (tmpExact <= 0 && tmpMax <= 0){
//use 100 as the default denom if something went horribly wrong
tmpExact = 100;
}
exactDenom = tmpExact;
maxDenom = tmpMax;
}
public String format(Number num) {
double doubleValue = num.doubleValue();
boolean isNeg = (doubleValue < 0.0f) ? true : false;
double absDoubleValue = Math.abs(doubleValue);
double wholePart = Math.floor(absDoubleValue);
double decPart = absDoubleValue - wholePart;
if (wholePart + decPart == 0) {
return "0";
}
//if the absolute value is smaller than 1 over the exact or maxDenom
//you can stop here and return "0"
if (absDoubleValue < (1/Math.max(exactDenom, maxDenom))){
return "0";
}
//this is necessary to prevent overflow in the maxDenom calculation
//stink1
if (wholePart+(int)decPart == wholePart+decPart){
StringBuilder sb = new StringBuilder();
if (isNeg){
sb.append("-");
}
sb.append(Integer.toString((int)wholePart));
return sb.toString();
}
SimpleFraction fract = null;
try{
//this should be the case because of the constructor
if (exactDenom > 0){
fract = calcFractionExactDenom(decPart, exactDenom);
} else {
fract = calcFractionMaxDenom(decPart, maxDenom);
}
} catch (SimpleFractionException e){
e.printStackTrace();
return Double.toString(doubleValue);
}
StringBuilder sb = new StringBuilder();
//now format the results
if (isNeg){
sb.append("-");
}
//if whole part has to go into the numerator
if ("".equals(wholePartFormatString)){
int trueNum = (fract.getDenominator()*(int)wholePart)+fract.getNumerator();
sb.append(trueNum).append("/").append(fract.getDenominator());
return sb.toString();
}
//short circuit if fraction is 0 or 1
if (fract.getNumerator() == 0){
sb.append(Integer.toString((int)wholePart));
return sb.toString();
} else if (fract.getNumerator() == fract.getDenominator()){
sb.append(Integer.toString((int)wholePart+1));
return sb.toString();
}
//as mentioned above, this ignores the exact space formatting in Excel
if (wholePart > 0){
sb.append(Integer.toString((int)wholePart)).append(" ");
}
sb.append(fract.getNumerator()).append("/").append(fract.getDenominator());
return sb.toString();
}
public StringBuffer format(Object obj, StringBuffer toAppendTo, FieldPosition pos) {
return toAppendTo.append(format((Number)obj));
}
public Object parseObject(String source, ParsePosition pos) {
throw new NotImplementedException("Reverse parsing not supported");
}
private SimpleFraction calcFractionMaxDenom(double value, int maxDenominator)
throws SimpleFractionException{
/*
* Lifted wholesale from org.apache.math.fraction.Fraction 2.2
*/
double epsilon = 0.000000000001f;
int maxIterations = 100;
long overflow = Integer.MAX_VALUE;
double r0 = value;
long a0 = (long)Math.floor(r0);
if (Math.abs(a0) > overflow) {
throw new SimpleFractionException(
String.format("value > Integer.MAX_VALUE: %d.", a0));
}
// check for (almost) integer arguments, which should not go
// to iterations.
if (Math.abs(a0 - value) < epsilon) {
return new SimpleFraction((int) a0, 1);
}
long p0 = 1;
long q0 = 0;
long p1 = a0;
long q1 = 1;
long p2 = 0;
long q2 = 1;
int n = 0;
boolean stop = false;
do {
++n;
double r1 = 1.0 / (r0 - a0);
long a1 = (long)Math.floor(r1);
p2 = (a1 * p1) + p0;
q2 = (a1 * q1) + q0;
if ((Math.abs(p2) > overflow) || (Math.abs(q2) > overflow)) {
throw new SimpleFractionException(
String.format("Greater than overflow in loop %f, %d, %d", value, p2, q2));
}
double convergent = (double)p2 / (double)q2;
if (n < maxIterations && Math.abs(convergent - value) > epsilon && q2 < maxDenominator) {
p0 = p1;
p1 = p2;
q0 = q1;
q1 = q2;
a0 = a1;
r0 = r1;
} else {
stop = true;
}
} while (!stop);
if (n >= maxIterations) {
throw new SimpleFractionException("n greater than max iterations " + value + " : " + maxIterations);
}
if (q2 < maxDenominator) {
return new SimpleFraction((int) p2, (int) q2);
} else {
return new SimpleFraction((int) p1, (int) q1);
}
}
private SimpleFraction calcFractionExactDenom(double val, int exactDenom){
int num = (int)Math.round(val*(double)exactDenom);
return new SimpleFraction(num,exactDenom);
}
private class SimpleFraction {
private final int num;
private final int denom;
public SimpleFraction(int num, int denom) {
this.num = num;
this.denom = denom;
}
public int getNumerator() {
return num;
}
public int getDenominator() {
return denom;
}
}
private class SimpleFractionException extends Throwable{
private SimpleFractionException(String message){
super(message);
}
}
}

+ 14
- 2
src/testcases/org/apache/poi/ss/usermodel/TestDataFormatter.java View File

@@ -229,13 +229,25 @@ public class TestDataFormatter extends TestCase {
assertEquals("321 321/1000", dfUS.formatRawCellContents(321.321, -1, "# #/##########"));
// Not a valid fraction formats (too many #/# or ?/?) - hence the strange expected results
assertEquals("321 / ?/?", dfUS.formatRawCellContents(321.321, -1, "# #/# ?/?"));
/* assertEquals("321 / ?/?", dfUS.formatRawCellContents(321.321, -1, "# #/# ?/?"));
assertEquals("321 / /", dfUS.formatRawCellContents(321.321, -1, "# #/# #/#"));
assertEquals("321 ?/? ?/?", dfUS.formatRawCellContents(321.321, -1, "# ?/? ?/?"));
assertEquals("321 ?/? / /", dfUS.formatRawCellContents(321.321, -1, "# ?/? #/# #/#"));
*/

//Bug54686 patch sets default behavior of # #/## if there is a failure to parse
assertEquals("321 1/3", dfUS.formatRawCellContents(321.321, -1, "# #/# ?/?"));
assertEquals("321 1/3", dfUS.formatRawCellContents(321.321, -1, "# #/# #/#"));
assertEquals("321 1/3", dfUS.formatRawCellContents(321.321, -1, "# ?/? ?/?"));
assertEquals("321 1/3", dfUS.formatRawCellContents(321.321, -1, "# ?/? #/# #/#"));

// Where both p and n don't include a fraction, so cannot always be formatted
assertEquals("123", dfUS.formatRawCellContents(-123.321, -1, "0 ?/?;0"));
// assertEquals("123", dfUS.formatRawCellContents(-123.321, -1, "0 ?/?;0"));

//Bug54868 patch has a hit on the first string before the ";"
assertEquals("-123 1/3", dfUS.formatRawCellContents(-123.321, -1, "0 ?/?;0"));

}
/**

+ 83
- 0
src/testcases/org/apache/poi/ss/usermodel/TestFractionFormat.java View File

@@ -0,0 +1,83 @@
/* ====================================================================
Licensed to the Apache Software Foundation (ASF) under one or more
contributor license agreements. See the NOTICE file distributed with
this work for additional information regarding copyright ownership.
The ASF licenses this file to You under the Apache License, Version 2.0
(the "License"); you may not use this file except in compliance with
the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
==================================================================== */

package org.apache.poi.ss.usermodel;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.InputStreamReader;

import junit.framework.TestCase;

import org.apache.poi.hssf.HSSFTestDataSamples;
import org.apache.poi.ss.usermodel.Cell;
import org.apache.poi.ss.usermodel.DataFormatter;
import org.apache.poi.ss.usermodel.FormulaEvaluator;
import org.apache.poi.ss.usermodel.FractionFormat;
import org.apache.poi.ss.usermodel.Row;

/**
* Tests for the Fraction Formatting part of DataFormatter.
* Largely taken from bug #54686
*/
public final class TestFractionFormat extends TestCase {
public void testSingle() throws Exception {
FractionFormat f = new FractionFormat("", "##");
double val = 321.321;
String ret = f.format(val);
assertEquals("26027/81", ret);
}
public void testTruthFile() throws Exception {
File truthFile = HSSFTestDataSamples.getSampleFile("54686_fraction_formats.txt");
BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream(truthFile)));
Workbook wb = HSSFTestDataSamples.openSampleWorkbook("54686_fraction_formats.xls");
Sheet sheet = wb.getSheetAt(0);
DataFormatter formatter = new DataFormatter();
FormulaEvaluator evaluator = wb.getCreationHelper().createFormulaEvaluator();

// Skip over the header row
String truthLine = reader.readLine();
String[] headers = truthLine.split("\t");
truthLine = reader.readLine();

for (int i = 1; i < sheet.getLastRowNum() && truthLine != null; i++){
Row r = sheet.getRow(i);
String[] truths = truthLine.split("\t");
// Intentionally ignore the last column (tika-1132), for now
for (short j = 3; j < 12; j++){
Cell cell = r.getCell(j, Row.CREATE_NULL_AS_BLANK);
String formatted = clean(formatter.formatCellValue(cell, evaluator));
if (truths.length <= j){
continue;
}

String truth = clean(truths[j]);
String testKey = truths[0]+":"+truths[1]+":"+headers[j];
assertEquals(testKey, truth, formatted);
}
truthLine = reader.readLine();
}
reader.close();
}

private String clean(String s){
s = s.trim().replaceAll(" +", " ").replaceAll("- +", "-");
return s;
}
}

+ 374
- 0
test-data/spreadsheet/54686_fraction_formats.txt View File

@@ -0,0 +1,374 @@
Numerator Denominator Double 1Digit 2Digit 3Digit Half Quarter Eight Sixteenth Tenth 100th Tika-1132
4051 8750153 0.000462963 0 0 0 0 0 0 0 0 0 4051/8750153
-105 100 -1.05 -1 -1 1/20 -1 1/20 -1 -1 -1 -1 1/16 -1 1/10 -1 5/100 -1 1/20
-104 100 -1.04 -1 -1 1/25 -1 1/25 -1 -1 -1 -1 1/16 -1 -1 4/100 -1 1/25
-103 100 -1.03 -1 -1 1/33 -1 3/100 -1 -1 -1 -1 -1 -1 3/100 -1 3/100
-102 100 -1.02 -1 -1 1/50 -1 1/50 -1 -1 -1 -1 -1 -1 2/100 -1 1/50
-101 100 -1.01 -1 -1 1/99 -1 1/100 -1 -1 -1 -1 -1 -1 1/100 -1 1/100
-100 100 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-99 100 -0.99 -1 - 98/99 - 99/100 -1 -1 -1 -1 -1 - 99/100 - 99/100
-98 100 -0.98 -1 - 49/50 - 49/50 -1 -1 -1 -1 -1 - 98/100 - 49/50
-97 100 -0.97 -1 - 32/33 - 97/100 -1 -1 -1 -1 -1 - 97/100 - 97/100
-96 100 -0.96 -1 - 24/25 - 24/25 -1 -1 -1 - 15/16 -1 - 96/100 - 24/25
-95 100 -0.95 -1 - 19/20 - 19/20 -1 -1 -1 - 15/16 -1 - 95/100 - 19/20
-94 100 -0.94 -1 - 47/50 - 47/50 -1 -1 -1 - 15/16 - 9/10 - 94/100 - 47/50
-93 100 -0.93 -1 - 40/43 - 93/100 -1 -1 - 7/8 - 15/16 - 9/10 - 93/100 - 93/100
-92 100 -0.92 -1 - 23/25 - 23/25 -1 -1 - 7/8 - 15/16 - 9/10 - 92/100 - 23/25
-91 100 -0.91 -1 - 81/89 - 91/100 -1 -1 - 7/8 - 15/16 - 9/10 - 91/100 - 91/100
-90 100 -0.9 - 8/9 - 9/10 - 9/10 -1 -1 - 7/8 - 14/16 - 9/10 - 90/100 - 9/10
-89 100 -0.89 - 8/9 - 8/9 - 89/100 -1 -1 - 7/8 - 14/16 - 9/10 - 89/100 - 89/100
-88 100 -0.88 - 7/8 - 22/25 - 22/25 -1 -1 - 7/8 - 14/16 - 9/10 - 88/100 - 22/25
-87 100 -0.87 - 7/8 - 67/77 - 87/100 -1 - 3/4 - 7/8 - 14/16 - 9/10 - 87/100 - 87/100
-86 100 -0.86 - 6/7 - 43/50 - 43/50 -1 - 3/4 - 7/8 - 14/16 - 9/10 - 86/100 - 43/50
-85 100 -0.85 - 6/7 - 17/20 - 17/20 -1 - 3/4 - 7/8 - 14/16 - 9/10 - 85/100 - 17/20
-84 100 -0.84 - 5/6 - 21/25 - 21/25 -1 - 3/4 - 7/8 - 13/16 - 8/10 - 84/100 - 21/25
-83 100 -0.83 - 5/6 - 39/47 - 83/100 -1 - 3/4 - 7/8 - 13/16 - 8/10 - 83/100 - 83/100
-82 100 -0.82 - 5/6 - 41/50 - 41/50 -1 - 3/4 - 7/8 - 13/16 - 8/10 - 82/100 - 41/50
-81 100 -0.81 - 4/5 - 64/79 - 81/100 -1 - 3/4 - 6/8 - 13/16 - 8/10 - 81/100 - 81/100
-80 100 -0.8 - 4/5 - 4/5 - 4/5 -1 - 3/4 - 6/8 - 13/16 - 8/10 - 80/100 - 4/5
-79 100 -0.79 - 4/5 - 64/81 - 79/100 -1 - 3/4 - 6/8 - 13/16 - 8/10 - 79/100 - 79/100
-78 100 -0.78 - 7/9 - 39/50 - 39/50 -1 - 3/4 - 6/8 - 12/16 - 8/10 - 78/100 - 39/50
-77 100 -0.77 - 7/9 - 67/87 - 77/100 -1 - 3/4 - 6/8 - 12/16 - 8/10 - 77/100 - 77/100
-76 100 -0.76 - 3/4 - 19/25 - 19/25 -1 - 3/4 - 6/8 - 12/16 - 8/10 - 76/100 - 19/25
-75 100 -0.75 - 3/4 - 3/4 - 3/4 -1 - 3/4 - 6/8 - 12/16 - 8/10 - 75/100 - 3/4
-74 100 -0.74 - 3/4 - 37/50 - 37/50 - 1/2 - 3/4 - 6/8 - 12/16 - 7/10 - 74/100 - 37/50
-73 100 -0.73 - 3/4 - 46/63 - 73/100 - 1/2 - 3/4 - 6/8 - 12/16 - 7/10 - 73/100 - 73/100
-72 100 -0.72 - 5/7 - 18/25 - 18/25 - 1/2 - 3/4 - 6/8 - 12/16 - 7/10 - 72/100 - 18/25
-71 100 -0.71 - 5/7 - 22/31 - 71/100 - 1/2 - 3/4 - 6/8 - 11/16 - 7/10 - 71/100 - 71/100
-70 100 -0.7 - 2/3 - 7/10 - 7/10 - 1/2 - 3/4 - 6/8 - 11/16 - 7/10 - 70/100 - 7/10
-69 100 -0.69 - 2/3 - 20/29 - 69/100 - 1/2 - 3/4 - 6/8 - 11/16 - 7/10 - 69/100 - 69/100
-68 100 -0.68 - 2/3 - 17/25 - 17/25 - 1/2 - 3/4 - 5/8 - 11/16 - 7/10 - 68/100 - 17/25
-67 100 -0.67 - 2/3 - 65/97 - 67/100 - 1/2 - 3/4 - 5/8 - 11/16 - 7/10 - 67/100 - 67/100
-66 100 -0.66 - 2/3 - 33/50 - 33/50 - 1/2 - 3/4 - 5/8 - 11/16 - 7/10 - 66/100 - 33/50
-65 100 -0.65 - 2/3 - 13/20 - 13/20 - 1/2 - 3/4 - 5/8 - 10/16 - 7/10 - 65/100 - 13/20
-64 100 -0.64 - 2/3 - 16/25 - 16/25 - 1/2 - 3/4 - 5/8 - 10/16 - 6/10 - 64/100 - 16/25
-63 100 -0.63 - 5/8 - 46/73 - 63/100 - 1/2 - 3/4 - 5/8 - 10/16 - 6/10 - 63/100 - 63/100
-62 100 -0.62 - 5/8 - 31/50 - 31/50 - 1/2 - 2/4 - 5/8 - 10/16 - 6/10 - 62/100 - 31/50
-61 100 -0.61 - 3/5 - 36/59 - 61/100 - 1/2 - 2/4 - 5/8 - 10/16 - 6/10 - 61/100 - 61/100
-60 100 -0.6 - 3/5 - 3/5 - 3/5 - 1/2 - 2/4 - 5/8 - 10/16 - 6/10 - 60/100 - 3/5
-59 100 -0.59 - 3/5 - 23/39 - 59/100 - 1/2 - 2/4 - 5/8 - 9/16 - 6/10 - 59/100 - 59/100
-58 100 -0.58 - 4/7 - 29/50 - 29/50 - 1/2 - 2/4 - 5/8 - 9/16 - 6/10 - 58/100 - 29/50
-57 100 -0.57 - 4/7 - 53/93 - 57/100 - 1/2 - 2/4 - 5/8 - 9/16 - 6/10 - 57/100 - 57/100
-56 100 -0.56 - 5/9 - 14/25 - 14/25 - 1/2 - 2/4 - 4/8 - 9/16 - 6/10 - 56/100 - 14/25
-55 100 -0.55 - 5/9 - 11/20 - 11/20 - 1/2 - 2/4 - 4/8 - 9/16 - 6/10 - 55/100 - 11/20
-54 100 -0.54 - 1/2 - 27/50 - 27/50 - 1/2 - 2/4 - 4/8 - 9/16 - 5/10 - 54/100 - 27/50
-53 100 -0.53 - 1/2 - 44/83 - 53/100 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 53/100 - 53/100
-52 100 -0.52 - 1/2 - 13/25 - 13/25 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 52/100 - 13/25
-51 100 -0.51 - 1/2 - 25/49 - 51/100 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 51/100 - 51/100
-50 100 -0.5 - 1/2 - 1/2 - 1/2 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 50/100 - 1/2
-49 100 -0.49 - 1/2 - 24/49 - 49/100 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 49/100 - 49/100
-48 100 -0.48 - 1/2 - 12/25 - 12/25 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 48/100 - 12/25
-47 100 -0.47 - 1/2 - 8/17 - 47/100 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 47/100 - 47/100
-46 100 -0.46 - 1/2 - 23/50 - 23/50 - 1/2 - 2/4 - 4/8 - 7/16 - 5/10 - 46/100 - 23/50
-45 100 -0.45 - 4/9 - 9/20 - 9/20 - 1/2 - 2/4 - 4/8 - 7/16 - 5/10 - 45/100 - 9/20
-44 100 -0.44 - 4/9 - 11/25 - 11/25 - 1/2 - 2/4 - 4/8 - 7/16 - 4/10 - 44/100 - 11/25
-43 100 -0.43 - 3/7 - 3/7 - 43/100 - 1/2 - 2/4 - 3/8 - 7/16 - 4/10 - 43/100 - 43/100
-42 100 -0.42 - 3/7 - 21/50 - 21/50 - 1/2 - 2/4 - 3/8 - 7/16 - 4/10 - 42/100 - 21/50
-41 100 -0.41 - 2/5 - 16/39 - 41/100 - 1/2 - 2/4 - 3/8 - 7/16 - 4/10 - 41/100 - 41/100
-40 100 -0.4 - 2/5 - 2/5 - 2/5 - 1/2 - 2/4 - 3/8 - 6/16 - 4/10 - 40/100 - 2/5
-39 100 -0.39 - 2/5 - 16/41 - 39/100 - 1/2 - 2/4 - 3/8 - 6/16 - 4/10 - 39/100 - 39/100
-38 100 -0.38 - 3/8 - 19/50 - 19/50 - 1/2 - 2/4 - 3/8 - 6/16 - 4/10 - 38/100 - 19/50
-37 100 -0.37 - 3/8 - 10/27 - 37/100 - 1/2 - 1/4 - 3/8 - 6/16 - 4/10 - 37/100 - 37/100
-36 100 -0.36 - 1/3 - 9/25 - 9/25 - 1/2 - 1/4 - 3/8 - 6/16 - 4/10 - 36/100 - 9/25
-35 100 -0.35 - 1/3 - 7/20 - 7/20 - 1/2 - 1/4 - 3/8 - 6/16 - 4/10 - 35/100 - 7/20
-34 100 -0.34 - 1/3 - 17/50 - 17/50 - 1/2 - 1/4 - 3/8 - 5/16 - 3/10 - 34/100 - 17/50
-33 100 -0.33 - 1/3 - 1/3 - 33/100 - 1/2 - 1/4 - 3/8 - 5/16 - 3/10 - 33/100 - 33/100
-32 100 -0.32 - 1/3 - 8/25 - 8/25 - 1/2 - 1/4 - 3/8 - 5/16 - 3/10 - 32/100 - 8/25
-31 100 -0.31 - 1/3 - 22/71 - 31/100 - 1/2 - 1/4 - 2/8 - 5/16 - 3/10 - 31/100 - 31/100
-30 100 -0.3 - 2/7 - 3/10 - 3/10 - 1/2 - 1/4 - 2/8 - 5/16 - 3/10 - 30/100 - 3/10
-29 100 -0.29 - 2/7 - 20/69 - 29/100 - 1/2 - 1/4 - 2/8 - 5/16 - 3/10 - 29/100 - 29/100
-28 100 -0.28 - 2/7 - 7/25 - 7/25 - 1/2 - 1/4 - 2/8 - 4/16 - 3/10 - 28/100 - 7/25
-27 100 -0.27 - 1/4 - 10/37 - 27/100 - 1/2 - 1/4 - 2/8 - 4/16 - 3/10 - 27/100 - 27/100
-26 100 -0.26 - 1/4 - 13/50 - 13/50 - 1/2 - 1/4 - 2/8 - 4/16 - 3/10 - 26/100 - 13/50
-25 100 -0.25 - 1/4 - 1/4 - 1/4 - 1/2 - 1/4 - 2/8 - 4/16 - 3/10 - 25/100 - 1/4
-24 100 -0.24 - 1/4 - 6/25 - 6/25 -0 - 1/4 - 2/8 - 4/16 - 2/10 - 24/100 - 6/25
-23 100 -0.23 - 2/9 - 3/13 - 23/100 -0 - 1/4 - 2/8 - 4/16 - 2/10 - 23/100 - 23/100
-22 100 -0.22 - 2/9 - 11/50 - 11/50 -0 - 1/4 - 2/8 - 4/16 - 2/10 - 22/100 - 11/50
-21 100 -0.21 - 1/5 - 17/81 - 21/100 -0 - 1/4 - 2/8 - 3/16 - 2/10 - 21/100 - 21/100
-20 100 -0.2 - 1/5 - 1/5 - 1/5 -0 - 1/4 - 2/8 - 3/16 - 2/10 - 20/100 - 1/5
-19 100 -0.19 - 1/5 - 15/79 - 19/100 -0 - 1/4 - 2/8 - 3/16 - 2/10 - 19/100 - 19/100
-18 100 -0.18 - 1/6 - 9/50 - 9/50 -0 - 1/4 - 1/8 - 3/16 - 2/10 - 18/100 - 9/50
-17 100 -0.17 - 1/6 - 8/47 - 17/100 -0 - 1/4 - 1/8 - 3/16 - 2/10 - 17/100 - 17/100
-16 100 -0.16 - 1/6 - 4/25 - 4/25 -0 - 1/4 - 1/8 - 3/16 - 2/10 - 16/100 - 4/25
-15 100 -0.15 - 1/7 - 3/20 - 3/20 -0 - 1/4 - 1/8 - 2/16 - 2/10 - 15/100 - 3/20
-14 100 -0.14 - 1/7 - 7/50 - 7/50 -0 - 1/4 - 1/8 - 2/16 - 1/10 - 14/100 - 7/50
-13 100 -0.13 - 1/8 - 3/23 - 13/100 -0 - 1/4 - 1/8 - 2/16 - 1/10 - 13/100 - 13/100
-12 100 -0.12 - 1/8 - 3/25 - 3/25 -0 -0 - 1/8 - 2/16 - 1/10 - 12/100 - 3/25
-11 100 -0.11 - 1/9 - 10/91 - 11/100 -0 -0 - 1/8 - 2/16 - 1/10 - 11/100 - 11/100
-10 100 -0.1 -0 - 1/10 - 1/10 -0 -0 - 1/8 - 2/16 - 1/10 - 10/100 - 1/10
-9 100 -0.09 -0 - 1/11 - 9/100 -0 -0 - 1/8 - 1/16 - 1/10 - 9/100 - 9/100
-8 100 -0.08 -0 - 2/25 - 2/25 -0 -0 - 1/8 - 1/16 - 1/10 - 8/100 - 2/25
-7 100 -0.07 -0 - 4/57 - 7/100 -0 -0 - 1/8 - 1/16 - 1/10 - 7/100 - 7/100
-6 100 -0.06 -0 - 3/50 - 3/50 -0 -0 -0 - 1/16 - 1/10 - 6/100 - 3/50
-5 100 -0.05 -0 - 1/20 - 1/20 -0 -0 -0 - 1/16 - 1/10 - 5/100 - 1/20
-4 100 -0.04 -0 - 1/25 - 1/25 -0 -0 -0 - 1/16 -0 - 4/100 - 1/25
-3 100 -0.03 -0 - 2/67 - 3/100 -0 -0 -0 -0 -0 - 3/100 - 3/100
-2 100 -0.02 -0 - 1/50 - 1/50 -0 -0 -0 -0 -0 - 2/100 - 1/50
-1 100 -0.01 -0 -0 - 1/100 -0 -0 -0 -0 -0 - 1/100 - 1/100
0 100 0 0 0 0 0 0 0 0 0 0 0
1 100 0.01 0 0 1/100 0 0 0 0 0 1/100 1/100
2 100 0.02 0 1/50 1/50 0 0 0 0 0 2/100 1/50
3 100 0.03 0 2/67 3/100 0 0 0 0 0 3/100 3/100
4 100 0.04 0 1/25 1/25 0 0 0 1/16 0 4/100 1/25
5 100 0.05 0 1/20 1/20 0 0 0 1/16 1/10 5/100 1/20
6 100 0.06 0 3/50 3/50 0 0 0 1/16 1/10 6/100 3/50
7 100 0.07 0 4/57 7/100 0 0 1/8 1/16 1/10 7/100 7/100
8 100 0.08 0 2/25 2/25 0 0 1/8 1/16 1/10 8/100 2/25
9 100 0.09 0 1/11 9/100 0 0 1/8 1/16 1/10 9/100 9/100
10 100 0.1 0 1/10 1/10 0 0 1/8 2/16 1/10 10/100 1/10
11 100 0.11 1/9 10/91 11/100 0 0 1/8 2/16 1/10 11/100 11/100
12 100 0.12 1/8 3/25 3/25 0 0 1/8 2/16 1/10 12/100 3/25
13 100 0.13 1/8 3/23 13/100 0 1/4 1/8 2/16 1/10 13/100 13/100
14 100 0.14 1/7 7/50 7/50 0 1/4 1/8 2/16 1/10 14/100 7/50
15 100 0.15 1/7 3/20 3/20 0 1/4 1/8 2/16 2/10 15/100 3/20
16 100 0.16 1/6 4/25 4/25 0 1/4 1/8 3/16 2/10 16/100 4/25
17 100 0.17 1/6 8/47 17/100 0 1/4 1/8 3/16 2/10 17/100 17/100
18 100 0.18 1/6 9/50 9/50 0 1/4 1/8 3/16 2/10 18/100 9/50
19 100 0.19 1/5 15/79 19/100 0 1/4 2/8 3/16 2/10 19/100 19/100
20 100 0.2 1/5 1/5 1/5 0 1/4 2/8 3/16 2/10 20/100 1/5
21 100 0.21 1/5 17/81 21/100 0 1/4 2/8 3/16 2/10 21/100 21/100
22 100 0.22 2/9 11/50 11/50 0 1/4 2/8 4/16 2/10 22/100 11/50
23 100 0.23 2/9 3/13 23/100 0 1/4 2/8 4/16 2/10 23/100 23/100
24 100 0.24 1/4 6/25 6/25 0 1/4 2/8 4/16 2/10 24/100 6/25
25 100 0.25 1/4 1/4 1/4 1/2 1/4 2/8 4/16 3/10 25/100 1/4
26 100 0.26 1/4 13/50 13/50 1/2 1/4 2/8 4/16 3/10 26/100 13/50
27 100 0.27 1/4 10/37 27/100 1/2 1/4 2/8 4/16 3/10 27/100 27/100
28 100 0.28 2/7 7/25 7/25 1/2 1/4 2/8 4/16 3/10 28/100 7/25
29 100 0.29 2/7 20/69 29/100 1/2 1/4 2/8 5/16 3/10 29/100 29/100
30 100 0.3 2/7 3/10 3/10 1/2 1/4 2/8 5/16 3/10 30/100 3/10
31 100 0.31 1/3 22/71 31/100 1/2 1/4 2/8 5/16 3/10 31/100 31/100
32 100 0.32 1/3 8/25 8/25 1/2 1/4 3/8 5/16 3/10 32/100 8/25
33 100 0.33 1/3 1/3 33/100 1/2 1/4 3/8 5/16 3/10 33/100 33/100
34 100 0.34 1/3 17/50 17/50 1/2 1/4 3/8 5/16 3/10 34/100 17/50
35 100 0.35 1/3 7/20 7/20 1/2 1/4 3/8 6/16 4/10 35/100 7/20
36 100 0.36 1/3 9/25 9/25 1/2 1/4 3/8 6/16 4/10 36/100 9/25
37 100 0.37 3/8 10/27 37/100 1/2 1/4 3/8 6/16 4/10 37/100 37/100
38 100 0.38 3/8 19/50 19/50 1/2 2/4 3/8 6/16 4/10 38/100 19/50
39 100 0.39 2/5 16/41 39/100 1/2 2/4 3/8 6/16 4/10 39/100 39/100
40 100 0.4 2/5 2/5 2/5 1/2 2/4 3/8 6/16 4/10 40/100 2/5
41 100 0.41 2/5 16/39 41/100 1/2 2/4 3/8 7/16 4/10 41/100 41/100
42 100 0.42 3/7 21/50 21/50 1/2 2/4 3/8 7/16 4/10 42/100 21/50
43 100 0.43 3/7 3/7 43/100 1/2 2/4 3/8 7/16 4/10 43/100 43/100
44 100 0.44 4/9 11/25 11/25 1/2 2/4 4/8 7/16 4/10 44/100 11/25
45 100 0.45 4/9 9/20 9/20 1/2 2/4 4/8 7/16 5/10 45/100 9/20
46 100 0.46 1/2 23/50 23/50 1/2 2/4 4/8 7/16 5/10 46/100 23/50
47 100 0.47 1/2 8/17 47/100 1/2 2/4 4/8 8/16 5/10 47/100 47/100
48 100 0.48 1/2 12/25 12/25 1/2 2/4 4/8 8/16 5/10 48/100 12/25
49 100 0.49 1/2 24/49 49/100 1/2 2/4 4/8 8/16 5/10 49/100 49/100
50 100 0.5 1/2 1/2 1/2 1/2 2/4 4/8 8/16 5/10 50/100 1/2
51 100 0.51 1/2 25/49 51/100 1/2 2/4 4/8 8/16 5/10 51/100 51/100
52 100 0.52 1/2 13/25 13/25 1/2 2/4 4/8 8/16 5/10 52/100 13/25
53 100 0.53 1/2 44/83 53/100 1/2 2/4 4/8 8/16 5/10 53/100 53/100
54 100 0.54 1/2 27/50 27/50 1/2 2/4 4/8 9/16 5/10 54/100 27/50
55 100 0.55 5/9 11/20 11/20 1/2 2/4 4/8 9/16 6/10 55/100 11/20
56 100 0.56 5/9 14/25 14/25 1/2 2/4 4/8 9/16 6/10 56/100 14/25
57 100 0.57 4/7 53/93 57/100 1/2 2/4 5/8 9/16 6/10 57/100 57/100
58 100 0.58 4/7 29/50 29/50 1/2 2/4 5/8 9/16 6/10 58/100 29/50
59 100 0.59 3/5 23/39 59/100 1/2 2/4 5/8 9/16 6/10 59/100 59/100
60 100 0.6 3/5 3/5 3/5 1/2 2/4 5/8 10/16 6/10 60/100 3/5
61 100 0.61 3/5 36/59 61/100 1/2 2/4 5/8 10/16 6/10 61/100 61/100
62 100 0.62 5/8 31/50 31/50 1/2 2/4 5/8 10/16 6/10 62/100 31/50
63 100 0.63 5/8 46/73 63/100 1/2 3/4 5/8 10/16 6/10 63/100 63/100
64 100 0.64 2/3 16/25 16/25 1/2 3/4 5/8 10/16 6/10 64/100 16/25
65 100 0.65 2/3 13/20 13/20 1/2 3/4 5/8 10/16 7/10 65/100 13/20
66 100 0.66 2/3 33/50 33/50 1/2 3/4 5/8 11/16 7/10 66/100 33/50
67 100 0.67 2/3 65/97 67/100 1/2 3/4 5/8 11/16 7/10 67/100 67/100
68 100 0.68 2/3 17/25 17/25 1/2 3/4 5/8 11/16 7/10 68/100 17/25
69 100 0.69 2/3 20/29 69/100 1/2 3/4 6/8 11/16 7/10 69/100 69/100
70 100 0.7 2/3 7/10 7/10 1/2 3/4 6/8 11/16 7/10 70/100 7/10
71 100 0.71 5/7 22/31 71/100 1/2 3/4 6/8 11/16 7/10 71/100 71/100
72 100 0.72 5/7 18/25 18/25 1/2 3/4 6/8 12/16 7/10 72/100 18/25
73 100 0.73 3/4 46/63 73/100 1/2 3/4 6/8 12/16 7/10 73/100 73/100
74 100 0.74 3/4 37/50 37/50 1/2 3/4 6/8 12/16 7/10 74/100 37/50
75 100 0.75 3/4 3/4 3/4 1 3/4 6/8 12/16 8/10 75/100 3/4
76 100 0.76 3/4 19/25 19/25 1 3/4 6/8 12/16 8/10 76/100 19/25
77 100 0.77 7/9 67/87 77/100 1 3/4 6/8 12/16 8/10 77/100 77/100
78 100 0.78 7/9 39/50 39/50 1 3/4 6/8 12/16 8/10 78/100 39/50
79 100 0.79 4/5 64/81 79/100 1 3/4 6/8 13/16 8/10 79/100 79/100
80 100 0.8 4/5 4/5 4/5 1 3/4 6/8 13/16 8/10 80/100 4/5
81 100 0.81 4/5 64/79 81/100 1 3/4 6/8 13/16 8/10 81/100 81/100
82 100 0.82 5/6 41/50 41/50 1 3/4 7/8 13/16 8/10 82/100 41/50
83 100 0.83 5/6 39/47 83/100 1 3/4 7/8 13/16 8/10 83/100 83/100
84 100 0.84 5/6 21/25 21/25 1 3/4 7/8 13/16 8/10 84/100 21/25
85 100 0.85 6/7 17/20 17/20 1 3/4 7/8 14/16 9/10 85/100 17/20
86 100 0.86 6/7 43/50 43/50 1 3/4 7/8 14/16 9/10 86/100 43/50
87 100 0.87 7/8 67/77 87/100 1 3/4 7/8 14/16 9/10 87/100 87/100
88 100 0.88 7/8 22/25 22/25 1 1 7/8 14/16 9/10 88/100 22/25
89 100 0.89 8/9 8/9 89/100 1 1 7/8 14/16 9/10 89/100 89/100
90 100 0.9 8/9 9/10 9/10 1 1 7/8 14/16 9/10 90/100 9/10
91 100 0.91 1 81/89 91/100 1 1 7/8 15/16 9/10 91/100 91/100
92 100 0.92 1 23/25 23/25 1 1 7/8 15/16 9/10 92/100 23/25
93 100 0.93 1 40/43 93/100 1 1 7/8 15/16 9/10 93/100 93/100
94 100 0.94 1 47/50 47/50 1 1 1 15/16 9/10 94/100 47/50
95 100 0.95 1 19/20 19/20 1 1 1 15/16 1 95/100 19/20
96 100 0.96 1 24/25 24/25 1 1 1 15/16 1 96/100 24/25
97 100 0.97 1 32/33 97/100 1 1 1 1 1 97/100 97/100
98 100 0.98 1 49/50 49/50 1 1 1 1 1 98/100 49/50
99 100 0.99 1 98/99 99/100 1 1 1 1 1 99/100 99/100
100 100 1 1 1 1 1 1 1 1 1 1 1
101 100 1.01 1 1 1/99 1 1/100 1 1 1 1 1 1 1/100 1 1/100
102 100 1.02 1 1 1/50 1 1/50 1 1 1 1 1 1 2/100 1 1/50
103 100 1.03 1 1 1/33 1 3/100 1 1 1 1 1 1 3/100 1 3/100
104 100 1.04 1 1 1/25 1 1/25 1 1 1 1 1/16 1 1 4/100 1 1/25
105 100 1.05 1 1 1/20 1 1/20 1 1 1 1 1/16 1 1/10 1 5/100 1 1/20
106 100 1.06 1 1 3/50 1 3/50 1 1 1 1 1/16 1 1/10 1 6/100 1 3/50
107 100 1.07 1 1 4/57 1 7/100 1 1 1 1/8 1 1/16 1 1/10 1 7/100 1 7/100
108 100 1.08 1 1 2/25 1 2/25 1 1 1 1/8 1 1/16 1 1/10 1 8/100 1 2/25
109 100 1.09 1 1 1/11 1 9/100 1 1 1 1/8 1 1/16 1 1/10 1 9/100 1 9/100
110 100 1.1 1 1/9 1 1/10 1 1/10 1 1 1 1/8 1 2/16 1 1/10 1 10/100 1 1/10
111 100 1.11 1 1/9 1 1/9 1 11/100 1 1 1 1/8 1 2/16 1 1/10 1 11/100 1 11/100
112 100 1.12 1 1/8 1 3/25 1 3/25 1 1 1 1/8 1 2/16 1 1/10 1 12/100 1 3/25
113 100 1.13 1 1/8 1 10/77 1 13/100 1 1 1/4 1 1/8 1 2/16 1 1/10 1 13/100 1 13/100
114 100 1.14 1 1/7 1 7/50 1 7/50 1 1 1/4 1 1/8 1 2/16 1 1/10 1 14/100 1 7/50
115 100 1.15 1 1/7 1 3/20 1 3/20 1 1 1/4 1 1/8 1 2/16 1 1/10 1 15/100 1 3/20
116 100 1.16 1 1/6 1 4/25 1 4/25 1 1 1/4 1 1/8 1 3/16 1 2/10 1 16/100 1 4/25
117 100 1.17 1 1/6 1 9/53 1 17/100 1 1 1/4 1 1/8 1 3/16 1 2/10 1 17/100 1 17/100
118 100 1.18 1 1/6 1 9/50 1 9/50 1 1 1/4 1 1/8 1 3/16 1 2/10 1 18/100 1 9/50
119 100 1.19 1 1/5 1 15/79 1 19/100 1 1 1/4 1 2/8 1 3/16 1 2/10 1 19/100 1 19/100
120 100 1.2 1 1/5 1 1/5 1 1/5 1 1 1/4 1 2/8 1 3/16 1 2/10 1 20/100 1 1/5
121 100 1.21 1 1/5 1 17/81 1 21/100 1 1 1/4 1 2/8 1 3/16 1 2/10 1 21/100 1 21/100
122 100 1.22 1 2/9 1 11/50 1 11/50 1 1 1/4 1 2/8 1 4/16 1 2/10 1 22/100 1 11/50
123 100 1.23 1 2/9 1 20/87 1 23/100 1 1 1/4 1 2/8 1 4/16 1 2/10 1 23/100 1 23/100
124 100 1.24 1 1/4 1 6/25 1 6/25 1 1 1/4 1 2/8 1 4/16 1 2/10 1 24/100 1 6/25
125 100 1.25 1 1/4 1 1/4 1 1/4 1 1/2 1 1/4 1 2/8 1 4/16 1 3/10 1 25/100 1 1/4
126 100 1.26 1 1/4 1 13/50 1 13/50 1 1/2 1 1/4 1 2/8 1 4/16 1 3/10 1 26/100 1 13/50
127 100 1.27 1 1/4 1 10/37 1 27/100 1 1/2 1 1/4 1 2/8 1 4/16 1 3/10 1 27/100 1 27/100
-103 201 -0.512437811 - 1/2 - 41/80 - 103/201 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 51/100 - 103/201
-100 201 -0.497512438 - 1/2 - 1/2 - 100/201 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 50/100 - 100/201
-97 201 -0.482587065 - 1/2 - 14/29 - 97/201 - 1/2 - 2/4 - 4/8 - 8/16 - 5/10 - 48/100 - 97/201
-94 201 -0.467661692 - 1/2 - 29/62 - 94/201 - 1/2 - 2/4 - 4/8 - 7/16 - 5/10 - 47/100 - 94/201
-91 201 -0.452736318 - 4/9 - 24/53 - 91/201 - 1/2 - 2/4 - 4/8 - 7/16 - 5/10 - 45/100 - 91/201
-88 201 -0.437810945 - 4/9 - 7/16 - 88/201 - 1/2 - 2/4 - 4/8 - 7/16 - 4/10 - 44/100 - 88/201
-85 201 -0.422885572 - 3/7 - 11/26 - 85/201 - 1/2 - 2/4 - 3/8 - 7/16 - 4/10 - 42/100 - 85/201
-82 201 -0.407960199 - 2/5 - 31/76 - 82/201 - 1/2 - 2/4 - 3/8 - 7/16 - 4/10 - 41/100 - 82/201
-79 201 -0.393034826 - 2/5 - 11/28 - 79/201 - 1/2 - 2/4 - 3/8 - 6/16 - 4/10 - 39/100 - 79/201
-76 201 -0.378109453 - 3/8 - 31/82 - 76/201 - 1/2 - 2/4 - 3/8 - 6/16 - 4/10 - 38/100 - 76/201
-73 201 -0.36318408 - 1/3 - 4/11 - 73/201 - 1/2 - 1/4 - 3/8 - 6/16 - 4/10 - 36/100 - 73/201
-70 201 -0.348258706 - 1/3 - 31/89 - 70/201 - 1/2 - 1/4 - 3/8 - 6/16 - 3/10 - 35/100 - 70/201
-67 201 -0.333333333 - 1/3 - 1/3 - 1/3 - 1/2 - 1/4 - 3/8 - 5/16 - 3/10 - 33/100 - 1/3
-64 201 -0.31840796 - 1/3 - 7/22 - 64/201 - 1/2 - 1/4 - 3/8 - 5/16 - 3/10 - 32/100 - 64/201
-61 201 -0.303482587 - 1/3 - 17/56 - 61/201 - 1/2 - 1/4 - 2/8 - 5/16 - 3/10 - 30/100 - 61/201
-58 201 -0.288557214 - 2/7 - 15/52 - 58/201 - 1/2 - 1/4 - 2/8 - 5/16 - 3/10 - 29/100 - 58/201
-55 201 -0.273631841 - 2/7 - 26/95 - 55/201 - 1/2 - 1/4 - 2/8 - 4/16 - 3/10 - 27/100 - 55/201
-52 201 -0.258706468 - 1/4 - 15/58 - 52/201 - 1/2 - 1/4 - 2/8 - 4/16 - 3/10 - 26/100 - 52/201
-49 201 -0.243781095 - 1/4 - 10/41 - 49/201 -0 - 1/4 - 2/8 - 4/16 - 2/10 - 24/100 - 49/201
-46 201 -0.228855721 - 2/9 - 19/83 - 46/201 -0 - 1/4 - 2/8 - 4/16 - 2/10 - 23/100 - 46/201
-43 201 -0.213930348 - 1/5 - 3/14 - 43/201 -0 - 1/4 - 2/8 - 3/16 - 2/10 - 21/100 - 43/201
-40 201 -0.199004975 - 1/5 - 1/5 - 40/201 -0 - 1/4 - 2/8 - 3/16 - 2/10 - 20/100 - 40/201
-37 201 -0.184079602 - 1/5 - 7/38 - 37/201 -0 - 1/4 - 1/8 - 3/16 - 2/10 - 18/100 - 37/201
-34 201 -0.169154229 - 1/6 - 11/65 - 34/201 -0 - 1/4 - 1/8 - 3/16 - 2/10 - 17/100 - 34/201
-31 201 -0.154228856 - 1/6 - 2/13 - 31/201 -0 - 1/4 - 1/8 - 2/16 - 2/10 - 15/100 - 31/201
-28 201 -0.139303483 - 1/7 - 11/79 - 28/201 -0 - 1/4 - 1/8 - 2/16 - 1/10 - 14/100 - 28/201
-25 201 -0.124378109 - 1/8 - 1/8 - 25/201 -0 -0 - 1/8 - 2/16 - 1/10 - 12/100 - 25/201
-22 201 -0.109452736 - 1/9 - 7/64 - 22/201 -0 -0 - 1/8 - 2/16 - 1/10 - 11/100 - 22/201
-19 201 -0.094527363 -0 - 7/74 - 19/201 -0 -0 - 1/8 - 2/16 - 1/10 - 9/100 - 19/201
-16 201 -0.07960199 -0 - 7/88 - 16/201 -0 -0 - 1/8 - 1/16 - 1/10 - 8/100 - 16/201
-13 201 -0.064676617 -0 - 2/31 - 13/201 -0 -0 - 1/8 - 1/16 - 1/10 - 6/100 - 13/201
-10 201 -0.049751244 -0 - 1/20 - 10/201 -0 -0 -0 - 1/16 -0 - 5/100 - 10/201
-7 201 -0.034825871 -0 - 3/86 - 7/201 -0 -0 -0 - 1/16 -0 - 3/100 - 7/201
-4 201 -0.019900498 -0 - 1/50 - 4/201 -0 -0 -0 -0 -0 - 2/100 - 4/201
-1 201 -0.004975124 -0 -0 - 1/201 -0 -0 -0 -0 -0 -0 - 1/201
2 201 0.009950249 0 0 2/201 0 0 0 0 0 1/100 2/201
5 201 0.024875622 0 1/40 5/201 0 0 0 0 0 2/100 5/201
8 201 0.039800995 0 1/25 8/201 0 0 0 1/16 0 4/100 8/201
11 201 0.054726368 0 4/73 11/201 0 0 0 1/16 1/10 5/100 11/201
14 201 0.069651741 0 3/43 14/201 0 0 1/8 1/16 1/10 7/100 14/201
17 201 0.084577114 0 6/71 17/201 0 0 1/8 1/16 1/10 8/100 17/201
20 201 0.099502488 0 1/10 20/201 0 0 1/8 2/16 1/10 10/100 20/201
23 201 0.114427861 1/9 4/35 23/201 0 0 1/8 2/16 1/10 11/100 23/201
26 201 0.129353234 1/8 11/85 26/201 0 1/4 1/8 2/16 1/10 13/100 26/201
29 201 0.144278607 1/7 14/97 29/201 0 1/4 1/8 2/16 1/10 14/100 29/201
32 201 0.15920398 1/6 7/44 32/201 0 1/4 1/8 3/16 2/10 16/100 32/201
35 201 0.174129353 1/6 4/23 35/201 0 1/4 1/8 3/16 2/10 17/100 35/201
38 201 0.189054726 1/5 7/37 38/201 0 1/4 2/8 3/16 2/10 19/100 38/201
41 201 0.2039801 1/5 10/49 41/201 0 1/4 2/8 3/16 2/10 20/100 41/201
44 201 0.218905473 2/9 7/32 44/201 0 1/4 2/8 4/16 2/10 22/100 44/201
47 201 0.233830846 1/4 18/77 47/201 0 1/4 2/8 4/16 2/10 23/100 47/201
50 201 0.248756219 1/4 1/4 50/201 0 1/4 2/8 4/16 2/10 25/100 50/201
53 201 0.263681592 1/4 24/91 53/201 1/2 1/4 2/8 4/16 3/10 26/100 53/201
56 201 0.278606965 2/7 17/61 56/201 1/2 1/4 2/8 4/16 3/10 28/100 56/201
59 201 0.293532338 2/7 27/92 59/201 1/2 1/4 2/8 5/16 3/10 29/100 59/201
62 201 0.308457711 1/3 29/94 62/201 1/2 1/4 2/8 5/16 3/10 31/100 62/201
65 201 0.323383085 1/3 11/34 65/201 1/2 1/4 3/8 5/16 3/10 32/100 65/201
68 201 0.338308458 1/3 23/68 68/201 1/2 1/4 3/8 5/16 3/10 34/100 68/201
71 201 0.353233831 1/3 6/17 71/201 1/2 1/4 3/8 6/16 4/10 35/100 71/201
74 201 0.368159204 3/8 7/19 74/201 1/2 1/4 3/8 6/16 4/10 37/100 74/201
77 201 0.383084577 3/8 18/47 77/201 1/2 2/4 3/8 6/16 4/10 38/100 77/201
80 201 0.39800995 2/5 39/98 80/201 1/2 2/4 3/8 6/16 4/10 40/100 80/201
83 201 0.412935323 2/5 19/46 83/201 1/2 2/4 3/8 7/16 4/10 41/100 83/201
86 201 0.427860697 3/7 3/7 86/201 1/2 2/4 3/8 7/16 4/10 43/100 86/201
89 201 0.44278607 4/9 31/70 89/201 1/2 2/4 4/8 7/16 4/10 44/100 89/201
92 201 0.457711443 1/2 27/59 92/201 1/2 2/4 4/8 7/16 5/10 46/100 92/201
95 201 0.472636816 1/2 26/55 95/201 1/2 2/4 4/8 8/16 5/10 47/100 95/201
98 201 0.487562189 1/2 39/80 98/201 1/2 2/4 4/8 8/16 5/10 49/100 98/201
101 201 0.502487562 1/2 1/2 101/201 1/2 2/4 4/8 8/16 5/10 50/100 101/201
104 201 0.517412935 1/2 15/29 104/201 1/2 2/4 4/8 8/16 5/10 52/100 104/201
107 201 0.532338308 1/2 33/62 107/201 1/2 2/4 4/8 9/16 5/10 53/100 107/201
110 201 0.547263682 5/9 29/53 110/201 1/2 2/4 4/8 9/16 5/10 55/100 110/201
113 201 0.562189055 5/9 9/16 113/201 1/2 2/4 4/8 9/16 6/10 56/100 113/201
116 201 0.577114428 4/7 15/26 116/201 1/2 2/4 5/8 9/16 6/10 58/100 116/201
119 201 0.592039801 3/5 45/76 119/201 1/2 2/4 5/8 9/16 6/10 59/100 119/201
122 201 0.606965174 3/5 17/28 122/201 1/2 2/4 5/8 10/16 6/10 61/100 122/201
125 201 0.621890547 5/8 51/82 125/201 1/2 2/4 5/8 10/16 6/10 62/100 125/201
128 201 0.63681592 2/3 7/11 128/201 1/2 3/4 5/8 10/16 6/10 64/100 128/201
131 201 0.651741294 2/3 58/89 131/201 1/2 3/4 5/8 10/16 7/10 65/100 131/201
134 201 0.666666667 2/3 2/3 2/3 1/2 3/4 5/8 11/16 7/10 67/100 2/3
137 201 0.68159204 2/3 15/22 137/201 1/2 3/4 5/8 11/16 7/10 68/100 137/201
140 201 0.696517413 2/3 39/56 140/201 1/2 3/4 6/8 11/16 7/10 70/100 140/201
143 201 0.711442786 5/7 37/52 143/201 1/2 3/4 6/8 11/16 7/10 71/100 143/201
146 201 0.726368159 5/7 69/95 146/201 1/2 3/4 6/8 12/16 7/10 73/100 146/201
149 201 0.741293532 3/4 43/58 149/201 1/2 3/4 6/8 12/16 7/10 74/100 149/201
152 201 0.756218905 3/4 31/41 152/201 1 3/4 6/8 12/16 8/10 76/100 152/201
155 201 0.771144279 7/9 64/83 155/201 1 3/4 6/8 12/16 8/10 77/100 155/201
158 201 0.786069652 4/5 11/14 158/201 1 3/4 6/8 13/16 8/10 79/100 158/201
161 201 0.800995025 4/5 4/5 161/201 1 3/4 6/8 13/16 8/10 80/100 161/201
164 201 0.815920398 4/5 31/38 164/201 1 3/4 7/8 13/16 8/10 82/100 164/201
167 201 0.830845771 5/6 54/65 167/201 1 3/4 7/8 13/16 8/10 83/100 167/201
170 201 0.845771144 5/6 11/13 170/201 1 3/4 7/8 14/16 8/10 85/100 170/201
173 201 0.860696517 6/7 68/79 173/201 1 3/4 7/8 14/16 9/10 86/100 173/201
176 201 0.875621891 7/8 7/8 176/201 1 1 7/8 14/16 9/10 88/100 176/201
179 201 0.890547264 8/9 57/64 179/201 1 1 7/8 14/16 9/10 89/100 179/201
182 201 0.905472637 1 67/74 182/201 1 1 7/8 14/16 9/10 91/100 182/201
185 201 0.92039801 1 81/88 185/201 1 1 7/8 15/16 9/10 92/100 185/201
188 201 0.935323383 1 29/31 188/201 1 1 7/8 15/16 9/10 94/100 188/201
191 201 0.950248756 1 19/20 191/201 1 1 1 15/16 1 95/100 191/201
194 201 0.965174129 1 83/86 194/201 1 1 1 15/16 1 97/100 194/201
197 201 0.980099502 1 49/50 197/201 1 1 1 1 1 98/100 197/201
200 201 0.995024876 1 1 200/201 1 1 1 1 1 1 200/201
203 201 1.009950249 1 1 1 2/201 1 1 1 1 1 1 1/100 1 2/201
206 201 1.024875622 1 1 1/40 1 5/201 1 1 1 1 1 1 2/100 1 5/201
209 201 1.039800995 1 1 1/25 1 8/201 1 1 1 1 1/16 1 1 4/100 1 8/201
212 201 1.054726368 1 1 4/73 1 11/201 1 1 1 1 1/16 1 1/10 1 5/100 1 11/201
215 201 1.069651741 1 1 3/43 1 14/201 1 1 1 1/8 1 1/16 1 1/10 1 7/100 1 14/201
218 201 1.084577114 1 1 6/71 1 17/201 1 1 1 1/8 1 1/16 1 1/10 1 8/100 1 17/201
221 201 1.099502488 1 1 1/10 1 20/201 1 1 1 1/8 1 2/16 1 1/10 1 10/100 1 20/201
224 201 1.114427861 1 1/9 1 4/35 1 23/201 1 1 1 1/8 1 2/16 1 1/10 1 11/100 1 23/201
227 201 1.129353234 1 1/8 1 11/85 1 26/201 1 1 1/4 1 1/8 1 2/16 1 1/10 1 13/100 1 26/201
230 201 1.144278607 1 1/7 1 14/97 1 29/201 1 1 1/4 1 1/8 1 2/16 1 1/10 1 14/100 1 29/201
233 201 1.15920398 1 1/6 1 7/44 1 32/201 1 1 1/4 1 1/8 1 3/16 1 2/10 1 16/100 1 32/201
236 201 1.174129353 1 1/6 1 4/23 1 35/201 1 1 1/4 1 1/8 1 3/16 1 2/10 1 17/100 1 35/201
239 201 1.189054726 1 1/5 1 7/37 1 38/201 1 1 1/4 1 2/8 1 3/16 1 2/10 1 19/100 1 38/201
242 201 1.2039801 1 1/5 1 10/49 1 41/201 1 1 1/4 1 2/8 1 3/16 1 2/10 1 20/100 1 41/201
245 201 1.218905473 1 2/9 1 7/32 1 44/201 1 1 1/4 1 2/8 1 4/16 1 2/10 1 22/100 1 44/201
248 201 1.233830846 1 1/4 1 18/77 1 47/201 1 1 1/4 1 2/8 1 4/16 1 2/10 1 23/100 1 47/201
251 201 1.248756219 1 1/4 1 1/4 1 50/201 1 1 1/4 1 2/8 1 4/16 1 2/10 1 25/100 1 50/201
254 201 1.263681592 1 1/4 1 24/91 1 53/201 1 1/2 1 1/4 1 2/8 1 4/16 1 3/10 1 26/100 1 53/201

BIN
test-data/spreadsheet/54686_fraction_formats.xls View File


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