From 17af35f7138b0a4c9b2f10819f0435a98cbb668c Mon Sep 17 00:00:00 2001 From: Josh Micich Date: Wed, 29 Jul 2009 03:36:25 +0000 Subject: Bugzilla 47598 - Improved formula evaluator number comparison git-svn-id: https://svn.apache.org/repos/asf/poi/trunk@798771 13f79535-47bb-0310-9956-ffa450edef68 --- .../formula/eval/RelationalOperationEval.java | 7 +- .../org/apache/poi/ss/util/ExpandedDouble.java | 98 +++++++ src/java/org/apache/poi/ss/util/IEEEDouble.java | 44 ++++ .../org/apache/poi/ss/util/MutableFPNumber.java | 209 +++++++++++++++ .../org/apache/poi/ss/util/NormalisedDecimal.java | 271 +++++++++++++++++++ .../org/apache/poi/ss/util/NumberComparer.java | 173 ++++++++++++ .../apache/poi/ss/util/NumberToTextConverter.java | 290 +++++---------------- 7 files changed, 871 insertions(+), 221 deletions(-) create mode 100644 src/java/org/apache/poi/ss/util/ExpandedDouble.java create mode 100644 src/java/org/apache/poi/ss/util/IEEEDouble.java create mode 100644 src/java/org/apache/poi/ss/util/MutableFPNumber.java create mode 100644 src/java/org/apache/poi/ss/util/NormalisedDecimal.java create mode 100644 src/java/org/apache/poi/ss/util/NumberComparer.java (limited to 'src/java/org') diff --git a/src/java/org/apache/poi/hssf/record/formula/eval/RelationalOperationEval.java b/src/java/org/apache/poi/hssf/record/formula/eval/RelationalOperationEval.java index c678507aab..f54b7cd2bc 100644 --- a/src/java/org/apache/poi/hssf/record/formula/eval/RelationalOperationEval.java +++ b/src/java/org/apache/poi/hssf/record/formula/eval/RelationalOperationEval.java @@ -17,6 +17,8 @@ package org.apache.poi.hssf.record.formula.eval; +import org.apache.poi.ss.util.NumberComparer; + /** * Base class for all comparison operator evaluators * @@ -108,8 +110,7 @@ public abstract class RelationalOperationEval implements OperationEval { if (vb instanceof NumberEval) { NumberEval nA = (NumberEval) va; NumberEval nB = (NumberEval) vb; - // Excel considers -0.0 < 0.0 which is the same as Double.compare() - return Double.compare(nA.getNumberValue(), nB.getNumberValue()); + return NumberComparer.compare(nA.getNumberValue(), nB.getNumberValue()); } } throw new IllegalArgumentException("Bad operand types (" + va.getClass().getName() + "), (" @@ -126,7 +127,7 @@ public abstract class RelationalOperationEval implements OperationEval { } if (v instanceof NumberEval) { NumberEval ne = (NumberEval) v; - return Double.compare(0, ne.getNumberValue()); + return NumberComparer.compare(0.0, ne.getNumberValue()); } if (v instanceof StringEval) { StringEval se = (StringEval) v; diff --git a/src/java/org/apache/poi/ss/util/ExpandedDouble.java b/src/java/org/apache/poi/ss/util/ExpandedDouble.java new file mode 100644 index 0000000000..41827df044 --- /dev/null +++ b/src/java/org/apache/poi/ss/util/ExpandedDouble.java @@ -0,0 +1,98 @@ +/* ==================================================================== + 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.util; + +import java.math.BigInteger; +import static org.apache.poi.ss.util.IEEEDouble.*; + +/** + * Represents a 64 bit IEEE double quantity expressed with both decimal and binary exponents + * Does not handle negative numbers or zero + *

+ * The value of a {@link ExpandedDouble} is given by
+ * a × 2b + *
+ * where:
+ * + * a = significand
+ * b = binaryExponent - bitLength(significand) + 1
+ * + * @author Josh Micich + */ +final class ExpandedDouble { + private static final BigInteger BI_FRAC_MASK = BigInteger.valueOf(FRAC_MASK); + private static final BigInteger BI_IMPLIED_FRAC_MSB = BigInteger.valueOf(FRAC_ASSUMED_HIGH_BIT); + + private static BigInteger getFrac(long rawBits) { + return BigInteger.valueOf(rawBits).and(BI_FRAC_MASK).or(BI_IMPLIED_FRAC_MSB).shiftLeft(11); + } + + + public static ExpandedDouble fromRawBitsAndExponent(long rawBits, int exp) { + return new ExpandedDouble(getFrac(rawBits), exp); + } + + /** + * Always 64 bits long (MSB, bit-63 is '1') + */ + private final BigInteger _significand; + private final int _binaryExponent; + + public ExpandedDouble(long rawBits) { + int biasedExp = (int) (rawBits >> 52); + if (biasedExp == 0) { + // sub-normal numbers + BigInteger frac = BigInteger.valueOf(rawBits).and(BI_FRAC_MASK); + int expAdj = 64 - frac.bitLength(); + _significand = frac.shiftLeft(expAdj); + _binaryExponent = (biasedExp & 0x07FF) - 1023 - expAdj; + } else { + BigInteger frac = getFrac(rawBits); + _significand = frac; + _binaryExponent = (biasedExp & 0x07FF) - 1023; + } + } + + ExpandedDouble(BigInteger frac, int binaryExp) { + if (frac.bitLength() != 64) { + throw new IllegalArgumentException("bad bit length"); + } + _significand = frac; + _binaryExponent = binaryExp; + } + + + /** + * Convert to an equivalent {@link NormalisedDecimal} representation having 15 decimal digits of precision in the + * non-fractional bits of the significand. + */ + public NormalisedDecimal normaliseBaseTen() { + return NormalisedDecimal.create(_significand, _binaryExponent); + } + + /** + * @return the number of non-fractional bits after the MSB of the significand + */ + public int getBinaryExponent() { + return _binaryExponent; + } + + public BigInteger getSignificand() { + return _significand; + } +} diff --git a/src/java/org/apache/poi/ss/util/IEEEDouble.java b/src/java/org/apache/poi/ss/util/IEEEDouble.java new file mode 100644 index 0000000000..f5a42edca6 --- /dev/null +++ b/src/java/org/apache/poi/ss/util/IEEEDouble.java @@ -0,0 +1,44 @@ +/* ==================================================================== + 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.util; + + +/** + * For working with the internals of IEEE 754-2008 'binary64' (double precision) floating point numbers + * + * @author Josh Micich + */ +final class IEEEDouble { + private static final long EXPONENT_MASK = 0x7FF0000000000000L; + private static final int EXPONENT_SHIFT = 52; + public static final long FRAC_MASK = 0x000FFFFFFFFFFFFFL; + public static final int EXPONENT_BIAS = 1023; + public static final long FRAC_ASSUMED_HIGH_BIT = ( 1L<NaN and Infinity values + */ + public static final int BIASED_EXPONENT_SPECIAL_VALUE = 0x07FF; + + /** + * @param rawBits the 64 bit binary representation of the double value + * @return the top 12 bits (sign and biased exponent value) + */ + public static int getBiasedExponent(long rawBits) { + return (int) ((rawBits & EXPONENT_MASK) >> EXPONENT_SHIFT); + } +} diff --git a/src/java/org/apache/poi/ss/util/MutableFPNumber.java b/src/java/org/apache/poi/ss/util/MutableFPNumber.java new file mode 100644 index 0000000000..2ae93e675c --- /dev/null +++ b/src/java/org/apache/poi/ss/util/MutableFPNumber.java @@ -0,0 +1,209 @@ +/* ==================================================================== + 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.util; + +import java.math.BigInteger; + +final class MutableFPNumber { + + + // TODO - what about values between (1014-0.5) and (1014-0.05) ? + /** + * The minimum value in 'Base-10 normalised form'.
+ * When {@link #_binaryExponent} == 46 this is the the minimum {@link #_frac} value + * (1014-0.05) * 2^17 + *
+ * Values between (1014-0.05) and 1014 will be represented as '1' + * followed by 14 zeros. + * Values less than (1014-0.05) will get shifted by one more power of 10 + * + * This frac value rounds to '1' followed by fourteen zeros with an incremented decimal exponent + */ + private static final BigInteger BI_MIN_BASE = new BigInteger("0B5E620F47FFFE666", 16); + /** + * For 'Base-10 normalised form'
+ * The maximum {@link #_frac} value when {@link #_binaryExponent} == 49 + * (10^15-0.5) * 2^14 + */ + private static final BigInteger BI_MAX_BASE = new BigInteger("0E35FA9319FFFE000", 16); + + /** + * Width of a long + */ + private static final int C_64 = 64; + + /** + * Minimum precision after discarding whole 32-bit words from the significand + */ + private static final int MIN_PRECISION = 72; + private BigInteger _significand; + private int _binaryExponent; + public MutableFPNumber(BigInteger frac, int binaryExponent) { + _significand = frac; + _binaryExponent = binaryExponent; + } + + + public MutableFPNumber copy() { + return new MutableFPNumber(_significand, _binaryExponent); + } + public void normalise64bit() { + int oldBitLen = _significand.bitLength(); + int sc = oldBitLen - C_64; + if (sc == 0) { + return; + } + if (sc < 0) { + throw new IllegalStateException("Not enough precision"); + } + _binaryExponent += sc; + if (sc > 32) { + int highShift = (sc-1) & 0xFFFFE0; + _significand = _significand.shiftRight(highShift); + sc -= highShift; + oldBitLen -= highShift; + } + if (sc < 1) { + throw new IllegalStateException(); + } + _significand = Rounder.round(_significand, sc); + if (_significand.bitLength() > oldBitLen) { + sc++; + _binaryExponent++; + } + _significand = _significand.shiftRight(sc); + } + public int get64BitNormalisedExponent() { + return _binaryExponent + _significand.bitLength() - C_64; + + } + + @Override + public boolean equals(Object obj) { + MutableFPNumber other = (MutableFPNumber) obj; + if (_binaryExponent != other._binaryExponent) { + return false; + } + return _significand.equals(other._significand); + } + public boolean isBelowMaxRep() { + int sc = _significand.bitLength() - C_64; + return _significand.compareTo(BI_MAX_BASE.shiftLeft(sc)) < 0; + } + public boolean isAboveMinRep() { + int sc = _significand.bitLength() - C_64; + return _significand.compareTo(BI_MIN_BASE.shiftLeft(sc)) > 0; + } + public NormalisedDecimal createNormalisedDecimal(int pow10) { + // missingUnderBits is (0..3) + int missingUnderBits = _binaryExponent-39; + int fracPart = (_significand.intValue() << missingUnderBits) & 0xFFFF80; + long wholePart = _significand.shiftRight(C_64-_binaryExponent-1).longValue(); + return new NormalisedDecimal(wholePart, fracPart, pow10); + } + public void multiplyByPowerOfTen(int pow10) { + TenPower tp = TenPower.getInstance(Math.abs(pow10)); + if (pow10 < 0) { + mulShift(tp._divisor, tp._divisorShift); + } else { + mulShift(tp._multiplicand, tp._multiplierShift); + } + } + private void mulShift(BigInteger multiplicand, int multiplierShift) { + _significand = _significand.multiply(multiplicand); + _binaryExponent += multiplierShift; + // check for too much precision + int sc = (_significand.bitLength() - MIN_PRECISION) & 0xFFFFFFE0; + // mask makes multiples of 32 which optimises BigInteger.shiftRight + if (sc > 0) { + // no need to round because we have at least 8 bits of extra precision + _significand = _significand.shiftRight(sc); + _binaryExponent += sc; + } + } + + private static final class Rounder { + private static final BigInteger[] HALF_BITS; + + static { + BigInteger[] bis = new BigInteger[33]; + long acc=1; + for (int i = 1; i < bis.length; i++) { + bis[i] = BigInteger.valueOf(acc); + acc <<=1; + } + HALF_BITS = bis; + } + /** + * @param nBits number of bits to shift right + */ + public static BigInteger round(BigInteger bi, int nBits) { + if (nBits < 1) { + return bi; + } + return bi.add(HALF_BITS[nBits]); + } + } + + /** + * Holds values for quick multiplication and division by 10 + */ + private static final class TenPower { + private static final BigInteger FIVE = new BigInteger("5"); + private static final TenPower[] _cache = new TenPower[350]; + + public final BigInteger _multiplicand; + public final BigInteger _divisor; + public final int _divisorShift; + public final int _multiplierShift; + + private TenPower(int index) { + BigInteger fivePowIndex = FIVE.pow(index); + + int bitsDueToFiveFactors = fivePowIndex.bitLength(); + int px = 80 + bitsDueToFiveFactors; + BigInteger fx = BigInteger.ONE.shiftLeft(px).divide(fivePowIndex); + int adj = fx.bitLength() - 80; + _divisor = fx.shiftRight(adj); + bitsDueToFiveFactors -= adj; + + _divisorShift = -(bitsDueToFiveFactors+index+80); + int sc = fivePowIndex.bitLength() - 68; + if (sc > 0) { + _multiplierShift = index + sc; + _multiplicand = fivePowIndex.shiftRight(sc); + } else { + _multiplierShift = index; + _multiplicand = fivePowIndex; + } + } + + static TenPower getInstance(int index) { + TenPower result = _cache[index]; + if (result == null) { + result = new TenPower(index); + _cache[index] = result; + } + return result; + } + } + + public ExpandedDouble createExpandedDouble() { + return new ExpandedDouble(_significand, _binaryExponent); + } +} diff --git a/src/java/org/apache/poi/ss/util/NormalisedDecimal.java b/src/java/org/apache/poi/ss/util/NormalisedDecimal.java new file mode 100644 index 0000000000..84f4d72851 --- /dev/null +++ b/src/java/org/apache/poi/ss/util/NormalisedDecimal.java @@ -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.util; + +import java.math.BigDecimal; +import java.math.BigInteger; + +/** + * Represents a transformation of a 64 bit IEEE double quantity having a decimal exponent and a + * fixed point (15 decimal digit) significand. Some quirks of Excel's calculation behaviour are + * simpler to reproduce with numeric quantities in this format. This class is currently used to + * help: + *

    + *
  1. Comparison operations
    2. + *
  2. Conversions to text
    3. + *
+ * + *

+ * This class does not handle negative numbers or zero. + *

+ * The value of a {@link NormalisedDecimal} is given by
+ * significand × 10decimalExponent + *
+ * where:
+ * + * significand = wholePart + fractionalPart / 224
+ * + * @author Josh Micich + */ +final class NormalisedDecimal { + /** + * Number of powers of ten contained in the significand + */ + private static final int EXPONENT_OFFSET = 14; + + private static final BigDecimal BD_2_POW_24 = new BigDecimal(BigInteger.ONE.shiftLeft(24)); + + /** + * log10(2)×220 + */ + private static final int LOG_BASE_10_OF_2_TIMES_2_POW_20 = 315653; // 315652.8287 + + /** + * 219 + */ + private static final int C_2_POW_19 = 1 << 19; + + + /** + * the value of {@link #_fractionalPart} that represents 0.5 + */ + private static final int FRAC_HALF = 0x800000; + + /** + * 1015 + */ + private static final long MAX_REP_WHOLE_PART = 0x38D7EA4C68000L; + + + + public static NormalisedDecimal create(BigInteger frac, int binaryExponent) { + // estimate pow2&pow10 first, perform optional mulShift, then normalize + int pow10; + if (binaryExponent > 49 || binaryExponent < 46) { + + // working with ints (left shifted 20) instead of doubles + // x = 14.5 - binaryExponent * log10(2); + int x = (29 << 19) - binaryExponent * LOG_BASE_10_OF_2_TIMES_2_POW_20; + x += C_2_POW_19; // round + pow10 = -(x >> 20); + } else { + pow10 = 0; + } + MutableFPNumber cc = new MutableFPNumber(frac, binaryExponent); + if (pow10 != 0) { + cc.multiplyByPowerOfTen(-pow10); + } + + switch (cc.get64BitNormalisedExponent()) { + case 46: + if (cc.isAboveMinRep()) { + break; + } + case 44: + case 45: + cc.multiplyByPowerOfTen(1); + pow10--; + break; + case 47: + case 48: + break; + case 49: + if (cc.isBelowMaxRep()) { + break; + } + case 50: + cc.multiplyByPowerOfTen(-1); + pow10++; + break; + + default: + throw new IllegalStateException("Bad binary exp " + cc.get64BitNormalisedExponent() + "."); + } + cc.normalise64bit(); + + return cc.createNormalisedDecimal(pow10); + } + + /** + * Rounds at the digit with value 10decimalExponent + */ + public NormalisedDecimal roundUnits() { + long wholePart = _wholePart; + if (_fractionalPart >= FRAC_HALF) { + wholePart++; + } + + int de = _relativeDecimalExponent; + + if (wholePart < MAX_REP_WHOLE_PART) { + return new NormalisedDecimal(wholePart, 0, de); + } + return new NormalisedDecimal(wholePart/10, 0, de+1); + } + + /** + * The decimal exponent increased by one less than the digit count of {@link #_wholePart} + */ + private final int _relativeDecimalExponent; + /** + * The whole part of the significand (typically 15 digits). + * + * 47-50 bits long (MSB may be anywhere from bit 46 to 49) + * LSB is units bit. + */ + private final long _wholePart; + /** + * The fractional part of the significand. + * 24 bits (only top 14-17 bits significant): a value between 0x000000 and 0xFFFF80 + */ + private final int _fractionalPart; + + + NormalisedDecimal(long wholePart, int fracPart, int decimalExponent) { + _wholePart = wholePart; + _fractionalPart = fracPart; + _relativeDecimalExponent = decimalExponent; + } + + + /** + * Convert to an equivalent {@link ExpandedDouble} representation (binary frac and exponent). + * The resulting transformed object is easily converted to a 64 bit IEEE double: + *

+ * The sign bit must be obtained from somewhere else. + * @return a new {@link NormalisedDecimal} normalised to base 2 representation. + */ + public ExpandedDouble normaliseBaseTwo() { + MutableFPNumber cc = new MutableFPNumber(composeFrac(), 39); + cc.multiplyByPowerOfTen(_relativeDecimalExponent); + cc.normalise64bit(); + return cc.createExpandedDouble(); + } + + /** + * @return the significand as a fixed point number (with 24 fraction bits and 47-50 whole bits) + */ + BigInteger composeFrac() { + long wp = _wholePart; + int fp = _fractionalPart; + return new BigInteger(new byte[] { + (byte) (wp >> 56), // N.B. assuming sign bit is zero + (byte) (wp >> 48), + (byte) (wp >> 40), + (byte) (wp >> 32), + (byte) (wp >> 24), + (byte) (wp >> 16), + (byte) (wp >> 8), + (byte) (wp >> 0), + (byte) (fp >> 16), + (byte) (fp >> 8), + (byte) (fp >> 0), + }); + } + + public String getSignificantDecimalDigits() { + return Long.toString(_wholePart); + } + /** + * Rounds the first whole digit position (considers only units digit, not frational part). + * Caller should check total digit count of result to see whether the rounding operation caused + * a carry out of the most significant digit + */ + public String getSignificantDecimalDigitsLastDigitRounded() { + long wp = _wholePart + 5; // rounds last digit + StringBuilder sb = new StringBuilder(24); + sb.append(wp); + sb.setCharAt(sb.length()-1, '0'); + return sb.toString(); + } + + /** + * @return the number of powers of 10 which have been extracted from the significand and binary exponent. + */ + public int getDecimalExponent() { + return _relativeDecimalExponent+EXPONENT_OFFSET; + } + + /** + * assumes both this and other are normalised + */ + public int compareNormalised(NormalisedDecimal other) { + int cmp = _relativeDecimalExponent - other._relativeDecimalExponent; + if (cmp != 0) { + return cmp; + } + if (_wholePart > other._wholePart) { + return 1; + } + if (_wholePart < other._wholePart) { + return -1; + } + return _fractionalPart - other._fractionalPart; + } + public BigDecimal getFractionalPart() { + return new BigDecimal(_fractionalPart).divide(BD_2_POW_24); + } + + private String getFractionalDigits() { + if (_fractionalPart == 0) { + return "0"; + } + return getFractionalPart().toString().substring(2); + } + + @Override + public String toString() { + + StringBuilder sb = new StringBuilder(); + sb.append(getClass().getName()); + sb.append(" ["); + String ws = String.valueOf(_wholePart); + sb.append(ws.charAt(0)); + sb.append('.'); + sb.append(ws.substring(1)); + sb.append(' '); + sb.append(getFractionalDigits()); + sb.append("E"); + sb.append(getDecimalExponent()); + sb.append("]"); + return sb.toString(); + } +} diff --git a/src/java/org/apache/poi/ss/util/NumberComparer.java b/src/java/org/apache/poi/ss/util/NumberComparer.java new file mode 100644 index 0000000000..49a27d2aab --- /dev/null +++ b/src/java/org/apache/poi/ss/util/NumberComparer.java @@ -0,0 +1,173 @@ +/* ==================================================================== + 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.util; + +import static org.apache.poi.ss.util.IEEEDouble.*; + +/** + * Excel compares numbers using different rules to those of java, so + * {@link Double#compare(double, double)} won't do. + * + * + * @author Josh Micich + */ +public final class NumberComparer { + + /** + * This class attempts to reproduce Excel's behaviour for comparing numbers. Results are + * mostly the same as those from {@link Double#compare(double, double)} but with some + * rounding. For numbers that are very close, this code converts to a format having 15 + * decimal digits of precision and a decimal exponent, before completing the comparison. + *

+ * In Excel formula evaluation, expressions like "(0.06-0.01)=0.05" evaluate to "TRUE" even + * though the equivalent java expression is false. In examples like this, + * Excel achieves the effect by having additional logic for comparison operations. + *

+ *

+ * Note - Excel also gives special treatment to expressions like "0.06-0.01-0.05" which + * evaluates to "0" (in java, rounding anomalies give a result of 6.9E-18). The special + * behaviour here is for different reasons to the example above: If the last operator in a + * cell formula is '+' or '-' and the result is less than 250 times smaller than + * first operand, the result is rounded to zero. + * Needless to say, the two rules are not consistent and it is relatively easy to find + * examples that satisfy
+ * "A=B" is "TRUE" but "A-B" is not "0"
+ * and
+ * "A=B" is "FALSE" but "A-B" is "0"
+ *
+ * This rule (for rounding the result of a final addition or subtraction), has not been + * implemented in POI (as of Jul-2009). + * + * @return negative, 0, or positive according to the standard Excel comparison + * of values a and b. + */ + public static int compare(double a, double b) { + long rawBitsA = Double.doubleToLongBits(a); + long rawBitsB = Double.doubleToLongBits(b); + + int biasedExponentA = getBiasedExponent(rawBitsA); + int biasedExponentB = getBiasedExponent(rawBitsB); + + if (biasedExponentA == BIASED_EXPONENT_SPECIAL_VALUE) { + throw new IllegalArgumentException("Special double values are not allowed: " + toHex(a)); + } + if (biasedExponentB == BIASED_EXPONENT_SPECIAL_VALUE) { + throw new IllegalArgumentException("Special double values are not allowed: " + toHex(a)); + } + + int cmp; + + // sign bit is in the same place for long and double: + boolean aIsNegative = rawBitsA < 0; + boolean bIsNegative = rawBitsB < 0; + + // compare signs + if (aIsNegative != bIsNegative) { + // Excel seems to have 'normal' comparison behaviour around zero (no rounding) + // even -0.0 < +0.0 (which is not quite the initial conclusion of bug 47198) + return aIsNegative ? -1 : +1; + } + + // then compare magnitudes (IEEE 754 has exponent bias specifically to allow this) + cmp = biasedExponentA - biasedExponentB; + int absExpDiff = Math.abs(cmp); + if (absExpDiff > 1) { + return aIsNegative ? -cmp : cmp; + } + + if (absExpDiff == 1) { + // special case exponent differs by 1. There is still a chance that with rounding the two quantities could end up the same + + } else { + // else - sign and exponents equal + if (rawBitsA == rawBitsB) { + // fully equal - exit here + return 0; + } + } + if (biasedExponentA == 0) { + if (biasedExponentB == 0) { + return compareSubnormalNumbers(rawBitsA & FRAC_MASK, rawBitsB & FRAC_MASK, aIsNegative); + } + // else biasedExponentB is 1 + return -compareAcrossSubnormalThreshold(rawBitsB, rawBitsA, aIsNegative); + } + if (biasedExponentB == 0) { + // else biasedExponentA is 1 + return +compareAcrossSubnormalThreshold(rawBitsA, rawBitsB, aIsNegative); + } + + // sign and exponents same, but fractional bits are different + + ExpandedDouble edA = ExpandedDouble.fromRawBitsAndExponent(rawBitsA, biasedExponentA - EXPONENT_BIAS); + ExpandedDouble edB = ExpandedDouble.fromRawBitsAndExponent(rawBitsB, biasedExponentB - EXPONENT_BIAS); + NormalisedDecimal ndA = edA.normaliseBaseTen().roundUnits(); + NormalisedDecimal ndB = edB.normaliseBaseTen().roundUnits(); + cmp = ndA.compareNormalised(ndB); + if (aIsNegative) { + return -cmp; + } + return cmp; + } + + /** + * If both numbers are subnormal, Excel seems to use standard comparison rules + */ + private static int compareSubnormalNumbers(long fracA, long fracB, boolean isNegative) { + int cmp = fracA > fracB ? +1 : fracA < fracB ? -1 : 0; + + return isNegative ? -cmp : cmp; + } + + + + /** + * Usually any normal number is greater (in magnitude) than any subnormal number. + * However there are some anomalous cases around the threshold where Excel produces screwy results + * @param isNegative both values are either negative or positive. This parameter affects the sign of the comparison result + * @return usually isNegative ? -1 : +1 + */ + private static int compareAcrossSubnormalThreshold(long normalRawBitsA, long subnormalRawBitsB, boolean isNegative) { + long fracB = subnormalRawBitsB & FRAC_MASK; + if (fracB == 0) { + // B is zero, so A is definitely greater than B + return isNegative ? -1 : +1; + } + long fracA = normalRawBitsA & FRAC_MASK; + if (fracA <= 0x0000000000000007L && fracB >= 0x000FFFFFFFFFFFFAL) { + // Both A and B close to threshold - weird results + if (fracA == 0x0000000000000007L && fracB == 0x000FFFFFFFFFFFFAL) { + // special case + return 0; + } + // exactly the opposite + return isNegative ? +1 : -1; + } + // else - typical case A and B is not close to threshold + return isNegative ? -1 : +1; + } + + + + /** + * for formatting double values in error messages + */ + private static String toHex(double a) { + return "0x" + Long.toHexString(Double.doubleToLongBits(a)).toUpperCase(); + } +} diff --git a/src/java/org/apache/poi/ss/util/NumberToTextConverter.java b/src/java/org/apache/poi/ss/util/NumberToTextConverter.java index efcb012fcc..c5b8d936b7 100644 --- a/src/java/org/apache/poi/ss/util/NumberToTextConverter.java +++ b/src/java/org/apache/poi/ss/util/NumberToTextConverter.java @@ -17,8 +17,6 @@ package org.apache.poi.ss.util; -import java.math.BigDecimal; -import java.math.BigInteger; /** * Excel converts numbers to text with different rules to those of java, so @@ -113,21 +111,9 @@ import java.math.BigInteger; */ public final class NumberToTextConverter { - private static final long expMask = 0x7FF0000000000000L; - private static final long FRAC_MASK= 0x000FFFFFFFFFFFFFL; - private static final int EXPONENT_SHIFT = 52; - private static final int FRAC_BITS_WIDTH = EXPONENT_SHIFT; - private static final int EXPONENT_BIAS = 1023; - private static final long FRAC_ASSUMED_HIGH_BIT = ( 1L<> EXPONENT_SHIFT); - if (biasedExponent == 0) { + if (rawBits == 0) { + return isNegative ? "-0" : "0"; + } + ExpandedDouble ed = new ExpandedDouble(rawBits); + if (ed.getBinaryExponent() < -1022) { // value is 'denormalised' which means it is less than 2^-1022 // excel displays all these numbers as zero, even though calculations work OK return isNegative ? "-0" : "0"; } - - int exponent = biasedExponent - EXPONENT_BIAS; - - long fracBits = FRAC_ASSUMED_HIGH_BIT | rawBits & FRAC_MASK; - - - // Start by converting double value to BigDecimal - BigDecimal bd; - if (biasedExponent == 0x07FF) { + if (ed.getBinaryExponent() == 1024) { // Special number NaN /Infinity + // Normally one would not create HybridDecimal objects from these values + // except in these cases Excel really tries to render them as if they were normal numbers if(rawBits == EXCEL_NAN_BITS) { return "3.484840871308E+308"; } // This is where excel really gets it wrong - // Special numbers like Infinity and Nan are interpreted according to + // Special numbers like Infinity and NaN are interpreted according to // the standard rules below. isNegative = false; // except that the sign bit is ignored } - bd = convertToBigDecimal(exponent, fracBits); - - return formatBigInteger(isNegative, bd.unscaledValue(), bd.scale()); - } - - private static BigDecimal convertToBigDecimal(int exponent, long fracBits) { - byte[] joob = { - (byte) (fracBits >> 48), - (byte) (fracBits >> 40), - (byte) (fracBits >> 32), - (byte) (fracBits >> 24), - (byte) (fracBits >> 16), - (byte) (fracBits >> 8), - (byte) (fracBits >> 0), - }; - - BigInteger bigInt = new BigInteger(joob); - int lastSigBitIndex = exponent-FRAC_BITS_WIDTH; - if(lastSigBitIndex < 0) { - BigInteger shifto = new BigInteger("1").shiftLeft(-lastSigBitIndex); - int scale = 1 -(int) (lastSigBitIndex/LOG2_10); - BigDecimal bd1 = new BigDecimal(bigInt); - BigDecimal bdShifto = new BigDecimal(shifto); - return bd1.divide(bdShifto, scale, BigDecimal.ROUND_HALF_UP); + NormalisedDecimal nd = ed.normaliseBaseTen(); + StringBuilder sb = new StringBuilder(MAX_TEXT_LEN+1); + if (isNegative) { + sb.append('-'); } - BigInteger sl = bigInt.shiftLeft(lastSigBitIndex); - return new BigDecimal(sl); + convertToText(sb, nd); + return sb.toString(); } - - private static String formatBigInteger(boolean isNegative, BigInteger unscaledValue, int scale) { - - if (scale < 0) { - throw new RuntimeException("negative scale"); - } - - StringBuffer sb = new StringBuffer(unscaledValue.toString()); - int numberOfLeadingZeros = -1; - - int unscaledLength = sb.length(); - if (scale > 0 && scale >= unscaledLength) { - // less than one - numberOfLeadingZeros = scale-unscaledLength; - formatLessThanOne(sb, numberOfLeadingZeros+1); + private static void convertToText(StringBuilder sb, NormalisedDecimal pnd) { + NormalisedDecimal rnd = pnd.roundUnits(); + int decExponent = rnd.getDecimalExponent(); + String decimalDigits; + if (Math.abs(decExponent)>98) { + decimalDigits = rnd.getSignificantDecimalDigitsLastDigitRounded(); + if (decimalDigits.length() == 16) { + // rounding caused carry + decExponent++; + } } else { - int decimalPointIndex = unscaledLength - scale; - formatGreaterThanOne(sb, decimalPointIndex); - } - if(isNegative) { - sb.insert(0, '-'); + decimalDigits = rnd.getSignificantDecimalDigits(); } - return sb.toString(); - } - - private static int getNumberOfSignificantFiguresDisplayed(int exponent) { - int nLostDigits; // number of significand digits lost due big exponents - if(exponent > 99) { - // any exponent greater than 99 has 3 digits instead of 2 - nLostDigits = 1; - } else if (exponent < -98) { - // For some weird reason on the negative side - // step is occurs from -98 to -99 (not from -99 to -100) - nLostDigits = 1; + int countSigDigits = countSignifantDigits(decimalDigits); + if (decExponent < 0) { + formatLessThanOne(sb, decimalDigits, decExponent, countSigDigits); } else { - nLostDigits = 0; + formatGreaterThanOne(sb, decimalDigits, decExponent, countSigDigits); } - return DEFAULT_COUNT_SIGNIFICANT_DIGITS - nLostDigits; - } - - private static boolean needsScientificNotation(int nDigits) { - return nDigits > MAX_TEXT_LEN; } - private static void formatGreaterThanOne(StringBuffer sb, int nIntegerDigits) { + private static void formatLessThanOne(StringBuilder sb, String decimalDigits, int decExponent, + int countSigDigits) { + int nLeadingZeros = -decExponent - 1; + int normalLength = 2 + nLeadingZeros + countSigDigits; // 2 == "0.".length() - int maxSigFigs = getNumberOfSignificantFiguresDisplayed(nIntegerDigits); - int decimalPointIndex = nIntegerDigits; - boolean roundCausedCarry = performRound(sb, 0, maxSigFigs); - - int endIx = Math.min(maxSigFigs, sb.length()-1); - - int nSigFigures; - if(roundCausedCarry) { - sb.insert(0, '1'); - decimalPointIndex++; - nSigFigures = 1; - } else { - nSigFigures = countSignifantDigits(sb, endIx); - } - - if(needsScientificNotation(decimalPointIndex)) { - sb.setLength(nSigFigures); - if (nSigFigures > 1) { - sb.insert(1, '.'); + if (needsScientificNotation(normalLength)) { + sb.append(decimalDigits.charAt(0)); + if (countSigDigits > 1) { + sb.append('.'); + sb.append(decimalDigits.subSequence(1, countSigDigits)); } - sb.append("E+"); - appendExp(sb, decimalPointIndex-1); + sb.append("E-"); + appendExp(sb, -decExponent); return; } - if(isAllZeros(sb, decimalPointIndex, maxSigFigs)) { - sb.setLength(decimalPointIndex); - return; + sb.append("0."); + for (int i=nLeadingZeros; i>0; i--) { + sb.append('0'); } - // else some sig-digits after the decimal point - sb.setLength(nSigFigures); - sb.insert(decimalPointIndex, '.'); + sb.append(decimalDigits.subSequence(0, countSigDigits)); } - /** - * @param sb initially contains just the significant digits - * @param pAbsExponent to be inserted (after "0.") at the start of the number - */ - private static void formatLessThanOne(StringBuffer sb, int pAbsExponent) { - if (sb.charAt(0) == 0) { - throw new IllegalArgumentException("First digit of significand should be non-zero"); + private static void formatGreaterThanOne(StringBuilder sb, String decimalDigits, int decExponent, int countSigDigits) { + + if (decExponent > 19) { + // scientific notation + sb.append(decimalDigits.charAt(0)); + if (countSigDigits>1) { + sb.append('.'); + sb.append(decimalDigits.subSequence(1, countSigDigits)); + } + sb.append("E+"); + appendExp(sb, decExponent); + return; } - if (pAbsExponent < 1) { - throw new IllegalArgumentException("abs(exponent) must be positive"); + int nFractionalDigits = countSigDigits - decExponent-1; + if (nFractionalDigits > 0) { + sb.append(decimalDigits.subSequence(0, decExponent+1)); + sb.append('.'); + sb.append(decimalDigits.subSequence(decExponent+1, countSigDigits)); + return; } - - int numberOfLeadingZeros = pAbsExponent-1; - int absExponent = pAbsExponent; - int maxSigFigs = getNumberOfSignificantFiguresDisplayed(-absExponent); - - boolean roundCausedCarry = performRound(sb, 0, maxSigFigs); - int nRemainingSigFigs; - if(roundCausedCarry) { - absExponent--; - numberOfLeadingZeros--; - nRemainingSigFigs = 1; - sb.setLength(0); - sb.append("1"); - } else { - nRemainingSigFigs = countSignifantDigits(sb, 0 + maxSigFigs); - sb.setLength(nRemainingSigFigs); + sb.append(decimalDigits.subSequence(0, countSigDigits)); + for (int i=-nFractionalDigits; i>0; i--) { + sb.append('0'); } + } - int normalLength = 2 + numberOfLeadingZeros + nRemainingSigFigs; // 2 == "0.".length() - - if (needsScientificNotation(normalLength)) { - if (sb.length()>1) { - sb.insert(1, '.'); - } - sb.append('E'); - sb.append('-'); - appendExp(sb, absExponent); - } else { - sb.insert(0, "0."); - for(int i=numberOfLeadingZeros; i>0; i--) { - sb.insert(2, '0'); - } - } + private static boolean needsScientificNotation(int nDigits) { + return nDigits > MAX_TEXT_LEN; } - private static int countSignifantDigits(StringBuffer sb, int startIx) { - int result=startIx; + private static int countSignifantDigits(String sb) { + int result=sb.length()-1; while(sb.charAt(result) == '0') { result--; if(result < 0) { @@ -338,68 +248,12 @@ public final class NumberToTextConverter { return result + 1; } - private static void appendExp(StringBuffer sb, int val) { + private static void appendExp(StringBuilder sb, int val) { if(val < 10) { sb.append('0'); sb.append((char)('0' + val)); return; } sb.append(val); - - } - - - private static boolean isAllZeros(StringBuffer sb, int startIx, int endIx) { - for(int i=startIx; i<=endIx && itrue if carry (out of the MS digit) occurred - */ - private static boolean performRound(StringBuffer sb, int firstSigFigIx, int nSigFigs) { - int nextDigitIx = firstSigFigIx + nSigFigs; - if(nextDigitIx == sb.length()) { - return false; // nothing to do - digit to be rounded is at the end of the buffer - } - if(nextDigitIx > sb.length()) { - throw new RuntimeException("Buffer too small to fit all significant digits"); - } - boolean hadCarryOutOfFirstDigit; - if(sb.charAt(nextDigitIx) < '5') { - // change to digit - hadCarryOutOfFirstDigit = false; - } else { - hadCarryOutOfFirstDigit = roundAndCarry(sb, nextDigitIx); - } - // clear out the rest of the digits after the rounded digit - // (at least the nearby digits) - int endIx = Math.min(nextDigitIx + MAX_EXTRA_ZEROS, sb.length()); - for(int i = nextDigitIx; i