| /* |
| * Copyright (c) 1996, 2017, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* |
| * Portions Copyright IBM Corporation, 2001. All Rights Reserved. |
| */ |
| |
| package java.math; |
| |
| import static java.math.BigInteger.LONG_MASK; |
| import java.util.Arrays; |
| |
| /** |
| * Immutable, arbitrary-precision signed decimal numbers. A |
| * {@code BigDecimal} consists of an arbitrary precision integer |
| * <i>unscaled value</i> and a 32-bit integer <i>scale</i>. If zero |
| * or positive, the scale is the number of digits to the right of the |
| * decimal point. If negative, the unscaled value of the number is |
| * multiplied by ten to the power of the negation of the scale. The |
| * value of the number represented by the {@code BigDecimal} is |
| * therefore <code>(unscaledValue × 10<sup>-scale</sup>)</code>. |
| * |
| * <p>The {@code BigDecimal} class provides operations for |
| * arithmetic, scale manipulation, rounding, comparison, hashing, and |
| * format conversion. The {@link #toString} method provides a |
| * canonical representation of a {@code BigDecimal}. |
| * |
| * <p>The {@code BigDecimal} class gives its user complete control |
| * over rounding behavior. If no rounding mode is specified and the |
| * exact result cannot be represented, an exception is thrown; |
| * otherwise, calculations can be carried out to a chosen precision |
| * and rounding mode by supplying an appropriate {@link MathContext} |
| * object to the operation. In either case, eight <em>rounding |
| * modes</em> are provided for the control of rounding. Using the |
| * integer fields in this class (such as {@link #ROUND_HALF_UP}) to |
| * represent rounding mode is deprecated; the enumeration values |
| * of the {@code RoundingMode} {@code enum}, (such as {@link |
| * RoundingMode#HALF_UP}) should be used instead. |
| * |
| * <p>When a {@code MathContext} object is supplied with a precision |
| * setting of 0 (for example, {@link MathContext#UNLIMITED}), |
| * arithmetic operations are exact, as are the arithmetic methods |
| * which take no {@code MathContext} object. (This is the only |
| * behavior that was supported in releases prior to 5.) As a |
| * corollary of computing the exact result, the rounding mode setting |
| * of a {@code MathContext} object with a precision setting of 0 is |
| * not used and thus irrelevant. In the case of divide, the exact |
| * quotient could have an infinitely long decimal expansion; for |
| * example, 1 divided by 3. If the quotient has a nonterminating |
| * decimal expansion and the operation is specified to return an exact |
| * result, an {@code ArithmeticException} is thrown. Otherwise, the |
| * exact result of the division is returned, as done for other |
| * operations. |
| * |
| * <p>When the precision setting is not 0, the rules of |
| * {@code BigDecimal} arithmetic are broadly compatible with selected |
| * modes of operation of the arithmetic defined in ANSI X3.274-1996 |
| * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those |
| * standards, {@code BigDecimal} includes many rounding modes, which |
| * were mandatory for division in {@code BigDecimal} releases prior |
| * to 5. Any conflicts between these ANSI standards and the |
| * {@code BigDecimal} specification are resolved in favor of |
| * {@code BigDecimal}. |
| * |
| * <p>Since the same numerical value can have different |
| * representations (with different scales), the rules of arithmetic |
| * and rounding must specify both the numerical result and the scale |
| * used in the result's representation. |
| * |
| * |
| * <p>In general the rounding modes and precision setting determine |
| * how operations return results with a limited number of digits when |
| * the exact result has more digits (perhaps infinitely many in the |
| * case of division and square root) than the number of digits returned. |
| * |
| * First, the |
| * total number of digits to return is specified by the |
| * {@code MathContext}'s {@code precision} setting; this determines |
| * the result's <i>precision</i>. The digit count starts from the |
| * leftmost nonzero digit of the exact result. The rounding mode |
| * determines how any discarded trailing digits affect the returned |
| * result. |
| * |
| * <p>For all arithmetic operators , the operation is carried out as |
| * though an exact intermediate result were first calculated and then |
| * rounded to the number of digits specified by the precision setting |
| * (if necessary), using the selected rounding mode. If the exact |
| * result is not returned, some digit positions of the exact result |
| * are discarded. When rounding increases the magnitude of the |
| * returned result, it is possible for a new digit position to be |
| * created by a carry propagating to a leading {@literal "9"} digit. |
| * For example, rounding the value 999.9 to three digits rounding up |
| * would be numerically equal to one thousand, represented as |
| * 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is |
| * the leading digit position of the returned result. |
| * |
| * <p>Besides a logical exact result, each arithmetic operation has a |
| * preferred scale for representing a result. The preferred |
| * scale for each operation is listed in the table below. |
| * |
| * <table class="striped" style="text-align:left"> |
| * <caption>Preferred Scales for Results of Arithmetic Operations |
| * </caption> |
| * <thead> |
| * <tr><th scope="col">Operation</th><th scope="col">Preferred Scale of Result</th></tr> |
| * </thead> |
| * <tbody> |
| * <tr><th scope="row">Add</th><td>max(addend.scale(), augend.scale())</td> |
| * <tr><th scope="row">Subtract</th><td>max(minuend.scale(), subtrahend.scale())</td> |
| * <tr><th scope="row">Multiply</th><td>multiplier.scale() + multiplicand.scale()</td> |
| * <tr><th scope="row">Divide</th><td>dividend.scale() - divisor.scale()</td> |
| * <tr><th scope="row">Square root</th><td>radicand.scale()/2</td> |
| * </tbody> |
| * </table> |
| * |
| * These scales are the ones used by the methods which return exact |
| * arithmetic results; except that an exact divide may have to use a |
| * larger scale since the exact result may have more digits. For |
| * example, {@code 1/32} is {@code 0.03125}. |
| * |
| * <p>Before rounding, the scale of the logical exact intermediate |
| * result is the preferred scale for that operation. If the exact |
| * numerical result cannot be represented in {@code precision} |
| * digits, rounding selects the set of digits to return and the scale |
| * of the result is reduced from the scale of the intermediate result |
| * to the least scale which can represent the {@code precision} |
| * digits actually returned. If the exact result can be represented |
| * with at most {@code precision} digits, the representation |
| * of the result with the scale closest to the preferred scale is |
| * returned. In particular, an exactly representable quotient may be |
| * represented in fewer than {@code precision} digits by removing |
| * trailing zeros and decreasing the scale. For example, rounding to |
| * three digits using the {@linkplain RoundingMode#FLOOR floor} |
| * rounding mode, <br> |
| * |
| * {@code 19/100 = 0.19 // integer=19, scale=2} <br> |
| * |
| * but<br> |
| * |
| * {@code 21/110 = 0.190 // integer=190, scale=3} <br> |
| * |
| * <p>Note that for add, subtract, and multiply, the reduction in |
| * scale will equal the number of digit positions of the exact result |
| * which are discarded. If the rounding causes a carry propagation to |
| * create a new high-order digit position, an additional digit of the |
| * result is discarded than when no new digit position is created. |
| * |
| * <p>Other methods may have slightly different rounding semantics. |
| * For example, the result of the {@code pow} method using the |
| * {@linkplain #pow(int, MathContext) specified algorithm} can |
| * occasionally differ from the rounded mathematical result by more |
| * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>. |
| * |
| * <p>Two types of operations are provided for manipulating the scale |
| * of a {@code BigDecimal}: scaling/rounding operations and decimal |
| * point motion operations. Scaling/rounding operations ({@link |
| * #setScale setScale} and {@link #round round}) return a |
| * {@code BigDecimal} whose value is approximately (or exactly) equal |
| * to that of the operand, but whose scale or precision is the |
| * specified value; that is, they increase or decrease the precision |
| * of the stored number with minimal effect on its value. Decimal |
| * point motion operations ({@link #movePointLeft movePointLeft} and |
| * {@link #movePointRight movePointRight}) return a |
| * {@code BigDecimal} created from the operand by moving the decimal |
| * point a specified distance in the specified direction. |
| * |
| * <p>For the sake of brevity and clarity, pseudo-code is used |
| * throughout the descriptions of {@code BigDecimal} methods. The |
| * pseudo-code expression {@code (i + j)} is shorthand for "a |
| * {@code BigDecimal} whose value is that of the {@code BigDecimal} |
| * {@code i} added to that of the {@code BigDecimal} |
| * {@code j}." The pseudo-code expression {@code (i == j)} is |
| * shorthand for "{@code true} if and only if the |
| * {@code BigDecimal} {@code i} represents the same value as the |
| * {@code BigDecimal} {@code j}." Other pseudo-code expressions |
| * are interpreted similarly. Square brackets are used to represent |
| * the particular {@code BigInteger} and scale pair defining a |
| * {@code BigDecimal} value; for example [19, 2] is the |
| * {@code BigDecimal} numerically equal to 0.19 having a scale of 2. |
| * |
| * |
| * <p>All methods and constructors for this class throw |
| * {@code NullPointerException} when passed a {@code null} object |
| * reference for any input parameter. |
| * |
| * @apiNote Care should be exercised if {@code BigDecimal} objects |
| * are used as keys in a {@link java.util.SortedMap SortedMap} or |
| * elements in a {@link java.util.SortedSet SortedSet} since |
| * {@code BigDecimal}'s <i>natural ordering</i> is <em>inconsistent |
| * with equals</em>. See {@link Comparable}, {@link |
| * java.util.SortedMap} or {@link java.util.SortedSet} for more |
| * information. |
| * |
| * @see BigInteger |
| * @see MathContext |
| * @see RoundingMode |
| * @see java.util.SortedMap |
| * @see java.util.SortedSet |
| * @author Josh Bloch |
| * @author Mike Cowlishaw |
| * @author Joseph D. Darcy |
| * @author Sergey V. Kuksenko |
| * @since 1.1 |
| */ |
| public class BigDecimal extends Number implements Comparable<BigDecimal> { |
| /** |
| * The unscaled value of this BigDecimal, as returned by {@link |
| * #unscaledValue}. |
| * |
| * @serial |
| * @see #unscaledValue |
| */ |
| private final BigInteger intVal; |
| |
| /** |
| * The scale of this BigDecimal, as returned by {@link #scale}. |
| * |
| * @serial |
| * @see #scale |
| */ |
| private final int scale; // Note: this may have any value, so |
| // calculations must be done in longs |
| |
| /** |
| * The number of decimal digits in this BigDecimal, or 0 if the |
| * number of digits are not known (lookaside information). If |
| * nonzero, the value is guaranteed correct. Use the precision() |
| * method to obtain and set the value if it might be 0. This |
| * field is mutable until set nonzero. |
| * |
| * @since 1.5 |
| */ |
| private transient int precision; |
| |
| /** |
| * Used to store the canonical string representation, if computed. |
| */ |
| private transient String stringCache; |
| |
| /** |
| * Sentinel value for {@link #intCompact} indicating the |
| * significand information is only available from {@code intVal}. |
| */ |
| static final long INFLATED = Long.MIN_VALUE; |
| |
| private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED); |
| |
| /** |
| * If the absolute value of the significand of this BigDecimal is |
| * less than or equal to {@code Long.MAX_VALUE}, the value can be |
| * compactly stored in this field and used in computations. |
| */ |
| private final transient long intCompact; |
| |
| // All 18-digit base ten strings fit into a long; not all 19-digit |
| // strings will |
| private static final int MAX_COMPACT_DIGITS = 18; |
| |
| /* Appease the serialization gods */ |
| private static final long serialVersionUID = 6108874887143696463L; |
| |
| private static final ThreadLocal<StringBuilderHelper> |
| threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() { |
| @Override |
| protected StringBuilderHelper initialValue() { |
| return new StringBuilderHelper(); |
| } |
| }; |
| |
| // Cache of common small BigDecimal values. |
| private static final BigDecimal ZERO_THROUGH_TEN[] = { |
| new BigDecimal(BigInteger.ZERO, 0, 0, 1), |
| new BigDecimal(BigInteger.ONE, 1, 0, 1), |
| new BigDecimal(BigInteger.TWO, 2, 0, 1), |
| new BigDecimal(BigInteger.valueOf(3), 3, 0, 1), |
| new BigDecimal(BigInteger.valueOf(4), 4, 0, 1), |
| new BigDecimal(BigInteger.valueOf(5), 5, 0, 1), |
| new BigDecimal(BigInteger.valueOf(6), 6, 0, 1), |
| new BigDecimal(BigInteger.valueOf(7), 7, 0, 1), |
| new BigDecimal(BigInteger.valueOf(8), 8, 0, 1), |
| new BigDecimal(BigInteger.valueOf(9), 9, 0, 1), |
| new BigDecimal(BigInteger.TEN, 10, 0, 2), |
| }; |
| |
| // Cache of zero scaled by 0 - 15 |
| private static final BigDecimal[] ZERO_SCALED_BY = { |
| ZERO_THROUGH_TEN[0], |
| new BigDecimal(BigInteger.ZERO, 0, 1, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 2, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 3, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 4, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 5, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 6, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 7, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 8, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 9, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 10, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 11, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 12, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 13, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 14, 1), |
| new BigDecimal(BigInteger.ZERO, 0, 15, 1), |
| }; |
| |
| // Half of Long.MIN_VALUE & Long.MAX_VALUE. |
| private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2; |
| private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2; |
| |
| // Constants |
| /** |
| * The value 0, with a scale of 0. |
| * |
| * @since 1.5 |
| */ |
| public static final BigDecimal ZERO = |
| ZERO_THROUGH_TEN[0]; |
| |
| /** |
| * The value 1, with a scale of 0. |
| * |
| * @since 1.5 |
| */ |
| public static final BigDecimal ONE = |
| ZERO_THROUGH_TEN[1]; |
| |
| /** |
| * The value 10, with a scale of 0. |
| * |
| * @since 1.5 |
| */ |
| public static final BigDecimal TEN = |
| ZERO_THROUGH_TEN[10]; |
| |
| /** |
| * The value 0.1, with a scale of 1. |
| */ |
| private static final BigDecimal ONE_TENTH = valueOf(1L, 1); |
| |
| /** |
| * The value 0.5, with a scale of 1. |
| */ |
| private static final BigDecimal ONE_HALF = valueOf(5L, 1); |
| |
| // Constructors |
| |
| /** |
| * Trusted package private constructor. |
| * Trusted simply means if val is INFLATED, intVal could not be null and |
| * if intVal is null, val could not be INFLATED. |
| */ |
| BigDecimal(BigInteger intVal, long val, int scale, int prec) { |
| this.scale = scale; |
| this.precision = prec; |
| this.intCompact = val; |
| this.intVal = intVal; |
| } |
| |
| /** |
| * Translates a character array representation of a |
| * {@code BigDecimal} into a {@code BigDecimal}, accepting the |
| * same sequence of characters as the {@link #BigDecimal(String)} |
| * constructor, while allowing a sub-array to be specified. |
| * |
| * @implNote If the sequence of characters is already available |
| * within a character array, using this constructor is faster than |
| * converting the {@code char} array to string and using the |
| * {@code BigDecimal(String)} constructor. |
| * |
| * @param in {@code char} array that is the source of characters. |
| * @param offset first character in the array to inspect. |
| * @param len number of characters to consider. |
| * @throws NumberFormatException if {@code in} is not a valid |
| * representation of a {@code BigDecimal} or the defined subarray |
| * is not wholly within {@code in}. |
| * @since 1.5 |
| */ |
| public BigDecimal(char[] in, int offset, int len) { |
| this(in,offset,len,MathContext.UNLIMITED); |
| } |
| |
| /** |
| * Translates a character array representation of a |
| * {@code BigDecimal} into a {@code BigDecimal}, accepting the |
| * same sequence of characters as the {@link #BigDecimal(String)} |
| * constructor, while allowing a sub-array to be specified and |
| * with rounding according to the context settings. |
| * |
| * @implNote If the sequence of characters is already available |
| * within a character array, using this constructor is faster than |
| * converting the {@code char} array to string and using the |
| * {@code BigDecimal(String)} constructor. |
| * |
| * @param in {@code char} array that is the source of characters. |
| * @param offset first character in the array to inspect. |
| * @param len number of characters to consider. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @throws NumberFormatException if {@code in} is not a valid |
| * representation of a {@code BigDecimal} or the defined subarray |
| * is not wholly within {@code in}. |
| * @since 1.5 |
| */ |
| public BigDecimal(char[] in, int offset, int len, MathContext mc) { |
| // protect against huge length. |
| if (offset + len > in.length || offset < 0) |
| throw new NumberFormatException("Bad offset or len arguments for char[] input."); |
| // This is the primary string to BigDecimal constructor; all |
| // incoming strings end up here; it uses explicit (inline) |
| // parsing for speed and generates at most one intermediate |
| // (temporary) object (a char[] array) for non-compact case. |
| |
| // Use locals for all fields values until completion |
| int prec = 0; // record precision value |
| int scl = 0; // record scale value |
| long rs = 0; // the compact value in long |
| BigInteger rb = null; // the inflated value in BigInteger |
| // use array bounds checking to handle too-long, len == 0, |
| // bad offset, etc. |
| try { |
| // handle the sign |
| boolean isneg = false; // assume positive |
| if (in[offset] == '-') { |
| isneg = true; // leading minus means negative |
| offset++; |
| len--; |
| } else if (in[offset] == '+') { // leading + allowed |
| offset++; |
| len--; |
| } |
| |
| // should now be at numeric part of the significand |
| boolean dot = false; // true when there is a '.' |
| long exp = 0; // exponent |
| char c; // current character |
| boolean isCompact = (len <= MAX_COMPACT_DIGITS); |
| // integer significand array & idx is the index to it. The array |
| // is ONLY used when we can't use a compact representation. |
| int idx = 0; |
| if (isCompact) { |
| // First compact case, we need not to preserve the character |
| // and we can just compute the value in place. |
| for (; len > 0; offset++, len--) { |
| c = in[offset]; |
| if ((c == '0')) { // have zero |
| if (prec == 0) |
| prec = 1; |
| else if (rs != 0) { |
| rs *= 10; |
| ++prec; |
| } // else digit is a redundant leading zero |
| if (dot) |
| ++scl; |
| } else if ((c >= '1' && c <= '9')) { // have digit |
| int digit = c - '0'; |
| if (prec != 1 || rs != 0) |
| ++prec; // prec unchanged if preceded by 0s |
| rs = rs * 10 + digit; |
| if (dot) |
| ++scl; |
| } else if (c == '.') { // have dot |
| // have dot |
| if (dot) // two dots |
| throw new NumberFormatException("Character array" |
| + " contains more than one decimal point."); |
| dot = true; |
| } else if (Character.isDigit(c)) { // slow path |
| int digit = Character.digit(c, 10); |
| if (digit == 0) { |
| if (prec == 0) |
| prec = 1; |
| else if (rs != 0) { |
| rs *= 10; |
| ++prec; |
| } // else digit is a redundant leading zero |
| } else { |
| if (prec != 1 || rs != 0) |
| ++prec; // prec unchanged if preceded by 0s |
| rs = rs * 10 + digit; |
| } |
| if (dot) |
| ++scl; |
| } else if ((c == 'e') || (c == 'E')) { |
| exp = parseExp(in, offset, len); |
| // Next test is required for backwards compatibility |
| if ((int) exp != exp) // overflow |
| throw new NumberFormatException("Exponent overflow."); |
| break; // [saves a test] |
| } else { |
| throw new NumberFormatException("Character " + c |
| + " is neither a decimal digit number, decimal point, nor" |
| + " \"e\" notation exponential mark."); |
| } |
| } |
| if (prec == 0) // no digits found |
| throw new NumberFormatException("No digits found."); |
| // Adjust scale if exp is not zero. |
| if (exp != 0) { // had significant exponent |
| scl = adjustScale(scl, exp); |
| } |
| rs = isneg ? -rs : rs; |
| int mcp = mc.precision; |
| int drop = prec - mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT]; |
| // therefore, this subtract cannot overflow |
| if (mcp > 0 && drop > 0) { // do rounding |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| prec = longDigitLength(rs); |
| drop = prec - mcp; |
| } |
| } |
| } else { |
| char coeff[] = new char[len]; |
| for (; len > 0; offset++, len--) { |
| c = in[offset]; |
| // have digit |
| if ((c >= '0' && c <= '9') || Character.isDigit(c)) { |
| // First compact case, we need not to preserve the character |
| // and we can just compute the value in place. |
| if (c == '0' || Character.digit(c, 10) == 0) { |
| if (prec == 0) { |
| coeff[idx] = c; |
| prec = 1; |
| } else if (idx != 0) { |
| coeff[idx++] = c; |
| ++prec; |
| } // else c must be a redundant leading zero |
| } else { |
| if (prec != 1 || idx != 0) |
| ++prec; // prec unchanged if preceded by 0s |
| coeff[idx++] = c; |
| } |
| if (dot) |
| ++scl; |
| continue; |
| } |
| // have dot |
| if (c == '.') { |
| // have dot |
| if (dot) // two dots |
| throw new NumberFormatException("Character array" |
| + " contains more than one decimal point."); |
| dot = true; |
| continue; |
| } |
| // exponent expected |
| if ((c != 'e') && (c != 'E')) |
| throw new NumberFormatException("Character array" |
| + " is missing \"e\" notation exponential mark."); |
| exp = parseExp(in, offset, len); |
| // Next test is required for backwards compatibility |
| if ((int) exp != exp) // overflow |
| throw new NumberFormatException("Exponent overflow."); |
| break; // [saves a test] |
| } |
| // here when no characters left |
| if (prec == 0) // no digits found |
| throw new NumberFormatException("No digits found."); |
| // Adjust scale if exp is not zero. |
| if (exp != 0) { // had significant exponent |
| scl = adjustScale(scl, exp); |
| } |
| // Remove leading zeros from precision (digits count) |
| rb = new BigInteger(coeff, isneg ? -1 : 1, prec); |
| rs = compactValFor(rb); |
| int mcp = mc.precision; |
| if (mcp > 0 && (prec > mcp)) { |
| if (rs == INFLATED) { |
| int drop = prec - mcp; |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode); |
| rs = compactValFor(rb); |
| if (rs != INFLATED) { |
| prec = longDigitLength(rs); |
| break; |
| } |
| prec = bigDigitLength(rb); |
| drop = prec - mcp; |
| } |
| } |
| if (rs != INFLATED) { |
| int drop = prec - mcp; |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| prec = longDigitLength(rs); |
| drop = prec - mcp; |
| } |
| rb = null; |
| } |
| } |
| } |
| } catch (ArrayIndexOutOfBoundsException | NegativeArraySizeException e) { |
| NumberFormatException nfe = new NumberFormatException(); |
| nfe.initCause(e); |
| throw nfe; |
| } |
| this.scale = scl; |
| this.precision = prec; |
| this.intCompact = rs; |
| this.intVal = rb; |
| } |
| |
| private int adjustScale(int scl, long exp) { |
| long adjustedScale = scl - exp; |
| if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE) |
| throw new NumberFormatException("Scale out of range."); |
| scl = (int) adjustedScale; |
| return scl; |
| } |
| |
| /* |
| * parse exponent |
| */ |
| private static long parseExp(char[] in, int offset, int len){ |
| long exp = 0; |
| offset++; |
| char c = in[offset]; |
| len--; |
| boolean negexp = (c == '-'); |
| // optional sign |
| if (negexp || c == '+') { |
| offset++; |
| c = in[offset]; |
| len--; |
| } |
| if (len <= 0) // no exponent digits |
| throw new NumberFormatException("No exponent digits."); |
| // skip leading zeros in the exponent |
| while (len > 10 && (c=='0' || (Character.digit(c, 10) == 0))) { |
| offset++; |
| c = in[offset]; |
| len--; |
| } |
| if (len > 10) // too many nonzero exponent digits |
| throw new NumberFormatException("Too many nonzero exponent digits."); |
| // c now holds first digit of exponent |
| for (;; len--) { |
| int v; |
| if (c >= '0' && c <= '9') { |
| v = c - '0'; |
| } else { |
| v = Character.digit(c, 10); |
| if (v < 0) // not a digit |
| throw new NumberFormatException("Not a digit."); |
| } |
| exp = exp * 10 + v; |
| if (len == 1) |
| break; // that was final character |
| offset++; |
| c = in[offset]; |
| } |
| if (negexp) // apply sign |
| exp = -exp; |
| return exp; |
| } |
| |
| /** |
| * Translates a character array representation of a |
| * {@code BigDecimal} into a {@code BigDecimal}, accepting the |
| * same sequence of characters as the {@link #BigDecimal(String)} |
| * constructor. |
| * |
| * @implNote If the sequence of characters is already available |
| * as a character array, using this constructor is faster than |
| * converting the {@code char} array to string and using the |
| * {@code BigDecimal(String)} constructor. |
| * |
| * @param in {@code char} array that is the source of characters. |
| * @throws NumberFormatException if {@code in} is not a valid |
| * representation of a {@code BigDecimal}. |
| * @since 1.5 |
| */ |
| public BigDecimal(char[] in) { |
| this(in, 0, in.length); |
| } |
| |
| /** |
| * Translates a character array representation of a |
| * {@code BigDecimal} into a {@code BigDecimal}, accepting the |
| * same sequence of characters as the {@link #BigDecimal(String)} |
| * constructor and with rounding according to the context |
| * settings. |
| * |
| * @implNote If the sequence of characters is already available |
| * as a character array, using this constructor is faster than |
| * converting the {@code char} array to string and using the |
| * {@code BigDecimal(String)} constructor. |
| * |
| * @param in {@code char} array that is the source of characters. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @throws NumberFormatException if {@code in} is not a valid |
| * representation of a {@code BigDecimal}. |
| * @since 1.5 |
| */ |
| public BigDecimal(char[] in, MathContext mc) { |
| this(in, 0, in.length, mc); |
| } |
| |
| /** |
| * Translates the string representation of a {@code BigDecimal} |
| * into a {@code BigDecimal}. The string representation consists |
| * of an optional sign, {@code '+'} (<code> '\u002B'</code>) or |
| * {@code '-'} (<code>'\u002D'</code>), followed by a sequence of |
| * zero or more decimal digits ("the integer"), optionally |
| * followed by a fraction, optionally followed by an exponent. |
| * |
| * <p>The fraction consists of a decimal point followed by zero |
| * or more decimal digits. The string must contain at least one |
| * digit in either the integer or the fraction. The number formed |
| * by the sign, the integer and the fraction is referred to as the |
| * <i>significand</i>. |
| * |
| * <p>The exponent consists of the character {@code 'e'} |
| * (<code>'\u0065'</code>) or {@code 'E'} (<code>'\u0045'</code>) |
| * followed by one or more decimal digits. The value of the |
| * exponent must lie between -{@link Integer#MAX_VALUE} ({@link |
| * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive. |
| * |
| * <p>More formally, the strings this constructor accepts are |
| * described by the following grammar: |
| * <blockquote> |
| * <dl> |
| * <dt><i>BigDecimalString:</i> |
| * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i> |
| * <dt><i>Sign:</i> |
| * <dd>{@code +} |
| * <dd>{@code -} |
| * <dt><i>Significand:</i> |
| * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i> |
| * <dd>{@code .} <i>FractionPart</i> |
| * <dd><i>IntegerPart</i> |
| * <dt><i>IntegerPart:</i> |
| * <dd><i>Digits</i> |
| * <dt><i>FractionPart:</i> |
| * <dd><i>Digits</i> |
| * <dt><i>Exponent:</i> |
| * <dd><i>ExponentIndicator SignedInteger</i> |
| * <dt><i>ExponentIndicator:</i> |
| * <dd>{@code e} |
| * <dd>{@code E} |
| * <dt><i>SignedInteger:</i> |
| * <dd><i>Sign<sub>opt</sub> Digits</i> |
| * <dt><i>Digits:</i> |
| * <dd><i>Digit</i> |
| * <dd><i>Digits Digit</i> |
| * <dt><i>Digit:</i> |
| * <dd>any character for which {@link Character#isDigit} |
| * returns {@code true}, including 0, 1, 2 ... |
| * </dl> |
| * </blockquote> |
| * |
| * <p>The scale of the returned {@code BigDecimal} will be the |
| * number of digits in the fraction, or zero if the string |
| * contains no decimal point, subject to adjustment for any |
| * exponent; if the string contains an exponent, the exponent is |
| * subtracted from the scale. The value of the resulting scale |
| * must lie between {@code Integer.MIN_VALUE} and |
| * {@code Integer.MAX_VALUE}, inclusive. |
| * |
| * <p>The character-to-digit mapping is provided by {@link |
| * java.lang.Character#digit} set to convert to radix 10. The |
| * String may not contain any extraneous characters (whitespace, |
| * for example). |
| * |
| * <p><b>Examples:</b><br> |
| * The value of the returned {@code BigDecimal} is equal to |
| * <i>significand</i> × 10<sup> <i>exponent</i></sup>. |
| * For each string on the left, the resulting representation |
| * [{@code BigInteger}, {@code scale}] is shown on the right. |
| * <pre> |
| * "0" [0,0] |
| * "0.00" [0,2] |
| * "123" [123,0] |
| * "-123" [-123,0] |
| * "1.23E3" [123,-1] |
| * "1.23E+3" [123,-1] |
| * "12.3E+7" [123,-6] |
| * "12.0" [120,1] |
| * "12.3" [123,1] |
| * "0.00123" [123,5] |
| * "-1.23E-12" [-123,14] |
| * "1234.5E-4" [12345,5] |
| * "0E+7" [0,-7] |
| * "-0" [0,0] |
| * </pre> |
| * |
| * @apiNote For values other than {@code float} and |
| * {@code double} NaN and ±Infinity, this constructor is |
| * compatible with the values returned by {@link Float#toString} |
| * and {@link Double#toString}. This is generally the preferred |
| * way to convert a {@code float} or {@code double} into a |
| * BigDecimal, as it doesn't suffer from the unpredictability of |
| * the {@link #BigDecimal(double)} constructor. |
| * |
| * @param val String representation of {@code BigDecimal}. |
| * |
| * @throws NumberFormatException if {@code val} is not a valid |
| * representation of a {@code BigDecimal}. |
| */ |
| public BigDecimal(String val) { |
| this(val.toCharArray(), 0, val.length()); |
| } |
| |
| /** |
| * Translates the string representation of a {@code BigDecimal} |
| * into a {@code BigDecimal}, accepting the same strings as the |
| * {@link #BigDecimal(String)} constructor, with rounding |
| * according to the context settings. |
| * |
| * @param val string representation of a {@code BigDecimal}. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @throws NumberFormatException if {@code val} is not a valid |
| * representation of a BigDecimal. |
| * @since 1.5 |
| */ |
| public BigDecimal(String val, MathContext mc) { |
| this(val.toCharArray(), 0, val.length(), mc); |
| } |
| |
| /** |
| * Translates a {@code double} into a {@code BigDecimal} which |
| * is the exact decimal representation of the {@code double}'s |
| * binary floating-point value. The scale of the returned |
| * {@code BigDecimal} is the smallest value such that |
| * <code>(10<sup>scale</sup> × val)</code> is an integer. |
| * <p> |
| * <b>Notes:</b> |
| * <ol> |
| * <li> |
| * The results of this constructor can be somewhat unpredictable. |
| * One might assume that writing {@code new BigDecimal(0.1)} in |
| * Java creates a {@code BigDecimal} which is exactly equal to |
| * 0.1 (an unscaled value of 1, with a scale of 1), but it is |
| * actually equal to |
| * 0.1000000000000000055511151231257827021181583404541015625. |
| * This is because 0.1 cannot be represented exactly as a |
| * {@code double} (or, for that matter, as a binary fraction of |
| * any finite length). Thus, the value that is being passed |
| * <em>in</em> to the constructor is not exactly equal to 0.1, |
| * appearances notwithstanding. |
| * |
| * <li> |
| * The {@code String} constructor, on the other hand, is |
| * perfectly predictable: writing {@code new BigDecimal("0.1")} |
| * creates a {@code BigDecimal} which is <em>exactly</em> equal to |
| * 0.1, as one would expect. Therefore, it is generally |
| * recommended that the {@linkplain #BigDecimal(String) |
| * String constructor} be used in preference to this one. |
| * |
| * <li> |
| * When a {@code double} must be used as a source for a |
| * {@code BigDecimal}, note that this constructor provides an |
| * exact conversion; it does not give the same result as |
| * converting the {@code double} to a {@code String} using the |
| * {@link Double#toString(double)} method and then using the |
| * {@link #BigDecimal(String)} constructor. To get that result, |
| * use the {@code static} {@link #valueOf(double)} method. |
| * </ol> |
| * |
| * @param val {@code double} value to be converted to |
| * {@code BigDecimal}. |
| * @throws NumberFormatException if {@code val} is infinite or NaN. |
| */ |
| public BigDecimal(double val) { |
| this(val,MathContext.UNLIMITED); |
| } |
| |
| /** |
| * Translates a {@code double} into a {@code BigDecimal}, with |
| * rounding according to the context settings. The scale of the |
| * {@code BigDecimal} is the smallest value such that |
| * <code>(10<sup>scale</sup> × val)</code> is an integer. |
| * |
| * <p>The results of this constructor can be somewhat unpredictable |
| * and its use is generally not recommended; see the notes under |
| * the {@link #BigDecimal(double)} constructor. |
| * |
| * @param val {@code double} value to be converted to |
| * {@code BigDecimal}. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * RoundingMode is UNNECESSARY. |
| * @throws NumberFormatException if {@code val} is infinite or NaN. |
| * @since 1.5 |
| */ |
| public BigDecimal(double val, MathContext mc) { |
| if (Double.isInfinite(val) || Double.isNaN(val)) |
| throw new NumberFormatException("Infinite or NaN"); |
| // Translate the double into sign, exponent and significand, according |
| // to the formulae in JLS, Section 20.10.22. |
| long valBits = Double.doubleToLongBits(val); |
| int sign = ((valBits >> 63) == 0 ? 1 : -1); |
| int exponent = (int) ((valBits >> 52) & 0x7ffL); |
| long significand = (exponent == 0 |
| ? (valBits & ((1L << 52) - 1)) << 1 |
| : (valBits & ((1L << 52) - 1)) | (1L << 52)); |
| exponent -= 1075; |
| // At this point, val == sign * significand * 2**exponent. |
| |
| /* |
| * Special case zero to supress nonterminating normalization and bogus |
| * scale calculation. |
| */ |
| if (significand == 0) { |
| this.intVal = BigInteger.ZERO; |
| this.scale = 0; |
| this.intCompact = 0; |
| this.precision = 1; |
| return; |
| } |
| // Normalize |
| while ((significand & 1) == 0) { // i.e., significand is even |
| significand >>= 1; |
| exponent++; |
| } |
| int scl = 0; |
| // Calculate intVal and scale |
| BigInteger rb; |
| long compactVal = sign * significand; |
| if (exponent == 0) { |
| rb = (compactVal == INFLATED) ? INFLATED_BIGINT : null; |
| } else { |
| if (exponent < 0) { |
| rb = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal); |
| scl = -exponent; |
| } else { // (exponent > 0) |
| rb = BigInteger.TWO.pow(exponent).multiply(compactVal); |
| } |
| compactVal = compactValFor(rb); |
| } |
| int prec = 0; |
| int mcp = mc.precision; |
| if (mcp > 0) { // do rounding |
| int mode = mc.roundingMode.oldMode; |
| int drop; |
| if (compactVal == INFLATED) { |
| prec = bigDigitLength(rb); |
| drop = prec - mcp; |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| rb = divideAndRoundByTenPow(rb, drop, mode); |
| compactVal = compactValFor(rb); |
| if (compactVal != INFLATED) { |
| break; |
| } |
| prec = bigDigitLength(rb); |
| drop = prec - mcp; |
| } |
| } |
| if (compactVal != INFLATED) { |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; |
| } |
| rb = null; |
| } |
| } |
| this.intVal = rb; |
| this.intCompact = compactVal; |
| this.scale = scl; |
| this.precision = prec; |
| } |
| |
| /** |
| * Translates a {@code BigInteger} into a {@code BigDecimal}. |
| * The scale of the {@code BigDecimal} is zero. |
| * |
| * @param val {@code BigInteger} value to be converted to |
| * {@code BigDecimal}. |
| */ |
| public BigDecimal(BigInteger val) { |
| scale = 0; |
| intVal = val; |
| intCompact = compactValFor(val); |
| } |
| |
| /** |
| * Translates a {@code BigInteger} into a {@code BigDecimal} |
| * rounding according to the context settings. The scale of the |
| * {@code BigDecimal} is zero. |
| * |
| * @param val {@code BigInteger} value to be converted to |
| * {@code BigDecimal}. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal(BigInteger val, MathContext mc) { |
| this(val,0,mc); |
| } |
| |
| /** |
| * Translates a {@code BigInteger} unscaled value and an |
| * {@code int} scale into a {@code BigDecimal}. The value of |
| * the {@code BigDecimal} is |
| * <code>(unscaledVal × 10<sup>-scale</sup>)</code>. |
| * |
| * @param unscaledVal unscaled value of the {@code BigDecimal}. |
| * @param scale scale of the {@code BigDecimal}. |
| */ |
| public BigDecimal(BigInteger unscaledVal, int scale) { |
| // Negative scales are now allowed |
| this.intVal = unscaledVal; |
| this.intCompact = compactValFor(unscaledVal); |
| this.scale = scale; |
| } |
| |
| /** |
| * Translates a {@code BigInteger} unscaled value and an |
| * {@code int} scale into a {@code BigDecimal}, with rounding |
| * according to the context settings. The value of the |
| * {@code BigDecimal} is <code>(unscaledVal × |
| * 10<sup>-scale</sup>)</code>, rounded according to the |
| * {@code precision} and rounding mode settings. |
| * |
| * @param unscaledVal unscaled value of the {@code BigDecimal}. |
| * @param scale scale of the {@code BigDecimal}. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) { |
| long compactVal = compactValFor(unscaledVal); |
| int mcp = mc.precision; |
| int prec = 0; |
| if (mcp > 0) { // do rounding |
| int mode = mc.roundingMode.oldMode; |
| if (compactVal == INFLATED) { |
| prec = bigDigitLength(unscaledVal); |
| int drop = prec - mcp; |
| while (drop > 0) { |
| scale = checkScaleNonZero((long) scale - drop); |
| unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode); |
| compactVal = compactValFor(unscaledVal); |
| if (compactVal != INFLATED) { |
| break; |
| } |
| prec = bigDigitLength(unscaledVal); |
| drop = prec - mcp; |
| } |
| } |
| if (compactVal != INFLATED) { |
| prec = longDigitLength(compactVal); |
| int drop = prec - mcp; // drop can't be more than 18 |
| while (drop > 0) { |
| scale = checkScaleNonZero((long) scale - drop); |
| compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode); |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; |
| } |
| unscaledVal = null; |
| } |
| } |
| this.intVal = unscaledVal; |
| this.intCompact = compactVal; |
| this.scale = scale; |
| this.precision = prec; |
| } |
| |
| /** |
| * Translates an {@code int} into a {@code BigDecimal}. The |
| * scale of the {@code BigDecimal} is zero. |
| * |
| * @param val {@code int} value to be converted to |
| * {@code BigDecimal}. |
| * @since 1.5 |
| */ |
| public BigDecimal(int val) { |
| this.intCompact = val; |
| this.scale = 0; |
| this.intVal = null; |
| } |
| |
| /** |
| * Translates an {@code int} into a {@code BigDecimal}, with |
| * rounding according to the context settings. The scale of the |
| * {@code BigDecimal}, before any rounding, is zero. |
| * |
| * @param val {@code int} value to be converted to {@code BigDecimal}. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal(int val, MathContext mc) { |
| int mcp = mc.precision; |
| long compactVal = val; |
| int scl = 0; |
| int prec = 0; |
| if (mcp > 0) { // do rounding |
| prec = longDigitLength(compactVal); |
| int drop = prec - mcp; // drop can't be more than 18 |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; |
| } |
| } |
| this.intVal = null; |
| this.intCompact = compactVal; |
| this.scale = scl; |
| this.precision = prec; |
| } |
| |
| /** |
| * Translates a {@code long} into a {@code BigDecimal}. The |
| * scale of the {@code BigDecimal} is zero. |
| * |
| * @param val {@code long} value to be converted to {@code BigDecimal}. |
| * @since 1.5 |
| */ |
| public BigDecimal(long val) { |
| this.intCompact = val; |
| this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null; |
| this.scale = 0; |
| } |
| |
| /** |
| * Translates a {@code long} into a {@code BigDecimal}, with |
| * rounding according to the context settings. The scale of the |
| * {@code BigDecimal}, before any rounding, is zero. |
| * |
| * @param val {@code long} value to be converted to {@code BigDecimal}. |
| * @param mc the context to use. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal(long val, MathContext mc) { |
| int mcp = mc.precision; |
| int mode = mc.roundingMode.oldMode; |
| int prec = 0; |
| int scl = 0; |
| BigInteger rb = (val == INFLATED) ? INFLATED_BIGINT : null; |
| if (mcp > 0) { // do rounding |
| if (val == INFLATED) { |
| prec = 19; |
| int drop = prec - mcp; |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| rb = divideAndRoundByTenPow(rb, drop, mode); |
| val = compactValFor(rb); |
| if (val != INFLATED) { |
| break; |
| } |
| prec = bigDigitLength(rb); |
| drop = prec - mcp; |
| } |
| } |
| if (val != INFLATED) { |
| prec = longDigitLength(val); |
| int drop = prec - mcp; |
| while (drop > 0) { |
| scl = checkScaleNonZero((long) scl - drop); |
| val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| prec = longDigitLength(val); |
| drop = prec - mcp; |
| } |
| rb = null; |
| } |
| } |
| this.intVal = rb; |
| this.intCompact = val; |
| this.scale = scl; |
| this.precision = prec; |
| } |
| |
| // Static Factory Methods |
| |
| /** |
| * Translates a {@code long} unscaled value and an |
| * {@code int} scale into a {@code BigDecimal}. |
| * |
| * @apiNote This static factory method is provided in preference |
| * to a ({@code long}, {@code int}) constructor because it allows |
| * for reuse of frequently used {@code BigDecimal} values. |
| * |
| * @param unscaledVal unscaled value of the {@code BigDecimal}. |
| * @param scale scale of the {@code BigDecimal}. |
| * @return a {@code BigDecimal} whose value is |
| * <code>(unscaledVal × 10<sup>-scale</sup>)</code>. |
| */ |
| public static BigDecimal valueOf(long unscaledVal, int scale) { |
| if (scale == 0) |
| return valueOf(unscaledVal); |
| else if (unscaledVal == 0) { |
| return zeroValueOf(scale); |
| } |
| return new BigDecimal(unscaledVal == INFLATED ? |
| INFLATED_BIGINT : null, |
| unscaledVal, scale, 0); |
| } |
| |
| /** |
| * Translates a {@code long} value into a {@code BigDecimal} |
| * with a scale of zero. |
| * |
| * @apiNote This static factory method is provided in preference |
| * to a ({@code long}) constructor because it allows for reuse of |
| * frequently used {@code BigDecimal} values. |
| * |
| * @param val value of the {@code BigDecimal}. |
| * @return a {@code BigDecimal} whose value is {@code val}. |
| */ |
| public static BigDecimal valueOf(long val) { |
| if (val >= 0 && val < ZERO_THROUGH_TEN.length) |
| return ZERO_THROUGH_TEN[(int)val]; |
| else if (val != INFLATED) |
| return new BigDecimal(null, val, 0, 0); |
| return new BigDecimal(INFLATED_BIGINT, val, 0, 0); |
| } |
| |
| static BigDecimal valueOf(long unscaledVal, int scale, int prec) { |
| if (scale == 0 && unscaledVal >= 0 && unscaledVal < ZERO_THROUGH_TEN.length) { |
| return ZERO_THROUGH_TEN[(int) unscaledVal]; |
| } else if (unscaledVal == 0) { |
| return zeroValueOf(scale); |
| } |
| return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null, |
| unscaledVal, scale, prec); |
| } |
| |
| static BigDecimal valueOf(BigInteger intVal, int scale, int prec) { |
| long val = compactValFor(intVal); |
| if (val == 0) { |
| return zeroValueOf(scale); |
| } else if (scale == 0 && val >= 0 && val < ZERO_THROUGH_TEN.length) { |
| return ZERO_THROUGH_TEN[(int) val]; |
| } |
| return new BigDecimal(intVal, val, scale, prec); |
| } |
| |
| static BigDecimal zeroValueOf(int scale) { |
| if (scale >= 0 && scale < ZERO_SCALED_BY.length) |
| return ZERO_SCALED_BY[scale]; |
| else |
| return new BigDecimal(BigInteger.ZERO, 0, scale, 1); |
| } |
| |
| /** |
| * Translates a {@code double} into a {@code BigDecimal}, using |
| * the {@code double}'s canonical string representation provided |
| * by the {@link Double#toString(double)} method. |
| * |
| * @apiNote This is generally the preferred way to convert a |
| * {@code double} (or {@code float}) into a {@code BigDecimal}, as |
| * the value returned is equal to that resulting from constructing |
| * a {@code BigDecimal} from the result of using {@link |
| * Double#toString(double)}. |
| * |
| * @param val {@code double} to convert to a {@code BigDecimal}. |
| * @return a {@code BigDecimal} whose value is equal to or approximately |
| * equal to the value of {@code val}. |
| * @throws NumberFormatException if {@code val} is infinite or NaN. |
| * @since 1.5 |
| */ |
| public static BigDecimal valueOf(double val) { |
| // Reminder: a zero double returns '0.0', so we cannot fastpath |
| // to use the constant ZERO. This might be important enough to |
| // justify a factory approach, a cache, or a few private |
| // constants, later. |
| return new BigDecimal(Double.toString(val)); |
| } |
| |
| // Arithmetic Operations |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this + |
| * augend)}, and whose scale is {@code max(this.scale(), |
| * augend.scale())}. |
| * |
| * @param augend value to be added to this {@code BigDecimal}. |
| * @return {@code this + augend} |
| */ |
| public BigDecimal add(BigDecimal augend) { |
| if (this.intCompact != INFLATED) { |
| if ((augend.intCompact != INFLATED)) { |
| return add(this.intCompact, this.scale, augend.intCompact, augend.scale); |
| } else { |
| return add(this.intCompact, this.scale, augend.intVal, augend.scale); |
| } |
| } else { |
| if ((augend.intCompact != INFLATED)) { |
| return add(augend.intCompact, augend.scale, this.intVal, this.scale); |
| } else { |
| return add(this.intVal, this.scale, augend.intVal, augend.scale); |
| } |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this + augend)}, |
| * with rounding according to the context settings. |
| * |
| * If either number is zero and the precision setting is nonzero then |
| * the other number, rounded if necessary, is used as the result. |
| * |
| * @param augend value to be added to this {@code BigDecimal}. |
| * @param mc the context to use. |
| * @return {@code this + augend}, rounded as necessary. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal add(BigDecimal augend, MathContext mc) { |
| if (mc.precision == 0) |
| return add(augend); |
| BigDecimal lhs = this; |
| |
| // If either number is zero then the other number, rounded and |
| // scaled if necessary, is used as the result. |
| { |
| boolean lhsIsZero = lhs.signum() == 0; |
| boolean augendIsZero = augend.signum() == 0; |
| |
| if (lhsIsZero || augendIsZero) { |
| int preferredScale = Math.max(lhs.scale(), augend.scale()); |
| BigDecimal result; |
| |
| if (lhsIsZero && augendIsZero) |
| return zeroValueOf(preferredScale); |
| result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc); |
| |
| if (result.scale() == preferredScale) |
| return result; |
| else if (result.scale() > preferredScale) { |
| return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, preferredScale); |
| } else { // result.scale < preferredScale |
| int precisionDiff = mc.precision - result.precision(); |
| int scaleDiff = preferredScale - result.scale(); |
| |
| if (precisionDiff >= scaleDiff) |
| return result.setScale(preferredScale); // can achieve target scale |
| else |
| return result.setScale(result.scale() + precisionDiff); |
| } |
| } |
| } |
| |
| long padding = (long) lhs.scale - augend.scale; |
| if (padding != 0) { // scales differ; alignment needed |
| BigDecimal arg[] = preAlign(lhs, augend, padding, mc); |
| matchScale(arg); |
| lhs = arg[0]; |
| augend = arg[1]; |
| } |
| return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc); |
| } |
| |
| /** |
| * Returns an array of length two, the sum of whose entries is |
| * equal to the rounded sum of the {@code BigDecimal} arguments. |
| * |
| * <p>If the digit positions of the arguments have a sufficient |
| * gap between them, the value smaller in magnitude can be |
| * condensed into a {@literal "sticky bit"} and the end result will |
| * round the same way <em>if</em> the precision of the final |
| * result does not include the high order digit of the small |
| * magnitude operand. |
| * |
| * <p>Note that while strictly speaking this is an optimization, |
| * it makes a much wider range of additions practical. |
| * |
| * <p>This corresponds to a pre-shift operation in a fixed |
| * precision floating-point adder; this method is complicated by |
| * variable precision of the result as determined by the |
| * MathContext. A more nuanced operation could implement a |
| * {@literal "right shift"} on the smaller magnitude operand so |
| * that the number of digits of the smaller operand could be |
| * reduced even though the significands partially overlapped. |
| */ |
| private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) { |
| assert padding != 0; |
| BigDecimal big; |
| BigDecimal small; |
| |
| if (padding < 0) { // lhs is big; augend is small |
| big = lhs; |
| small = augend; |
| } else { // lhs is small; augend is big |
| big = augend; |
| small = lhs; |
| } |
| |
| /* |
| * This is the estimated scale of an ulp of the result; it assumes that |
| * the result doesn't have a carry-out on a true add (e.g. 999 + 1 => |
| * 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 => |
| * 98.8) |
| */ |
| long estResultUlpScale = (long) big.scale - big.precision() + mc.precision; |
| |
| /* |
| * The low-order digit position of big is big.scale(). This |
| * is true regardless of whether big has a positive or |
| * negative scale. The high-order digit position of small is |
| * small.scale - (small.precision() - 1). To do the full |
| * condensation, the digit positions of big and small must be |
| * disjoint *and* the digit positions of small should not be |
| * directly visible in the result. |
| */ |
| long smallHighDigitPos = (long) small.scale - small.precision() + 1; |
| if (smallHighDigitPos > big.scale + 2 && // big and small disjoint |
| smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible |
| small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3)); |
| } |
| |
| // Since addition is symmetric, preserving input order in |
| // returned operands doesn't matter |
| BigDecimal[] result = {big, small}; |
| return result; |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this - |
| * subtrahend)}, and whose scale is {@code max(this.scale(), |
| * subtrahend.scale())}. |
| * |
| * @param subtrahend value to be subtracted from this {@code BigDecimal}. |
| * @return {@code this - subtrahend} |
| */ |
| public BigDecimal subtract(BigDecimal subtrahend) { |
| if (this.intCompact != INFLATED) { |
| if ((subtrahend.intCompact != INFLATED)) { |
| return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale); |
| } else { |
| return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale); |
| } |
| } else { |
| if ((subtrahend.intCompact != INFLATED)) { |
| // Pair of subtrahend values given before pair of |
| // values from this BigDecimal to avoid need for |
| // method overloading on the specialized add method |
| return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale); |
| } else { |
| return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale); |
| } |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)}, |
| * with rounding according to the context settings. |
| * |
| * If {@code subtrahend} is zero then this, rounded if necessary, is used as the |
| * result. If this is zero then the result is {@code subtrahend.negate(mc)}. |
| * |
| * @param subtrahend value to be subtracted from this {@code BigDecimal}. |
| * @param mc the context to use. |
| * @return {@code this - subtrahend}, rounded as necessary. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) { |
| if (mc.precision == 0) |
| return subtract(subtrahend); |
| // share the special rounding code in add() |
| return add(subtrahend.negate(), mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is <code>(this × |
| * multiplicand)</code>, and whose scale is {@code (this.scale() + |
| * multiplicand.scale())}. |
| * |
| * @param multiplicand value to be multiplied by this {@code BigDecimal}. |
| * @return {@code this * multiplicand} |
| */ |
| public BigDecimal multiply(BigDecimal multiplicand) { |
| int productScale = checkScale((long) scale + multiplicand.scale); |
| if (this.intCompact != INFLATED) { |
| if ((multiplicand.intCompact != INFLATED)) { |
| return multiply(this.intCompact, multiplicand.intCompact, productScale); |
| } else { |
| return multiply(this.intCompact, multiplicand.intVal, productScale); |
| } |
| } else { |
| if ((multiplicand.intCompact != INFLATED)) { |
| return multiply(multiplicand.intCompact, this.intVal, productScale); |
| } else { |
| return multiply(this.intVal, multiplicand.intVal, productScale); |
| } |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is <code>(this × |
| * multiplicand)</code>, with rounding according to the context settings. |
| * |
| * @param multiplicand value to be multiplied by this {@code BigDecimal}. |
| * @param mc the context to use. |
| * @return {@code this * multiplicand}, rounded as necessary. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) { |
| if (mc.precision == 0) |
| return multiply(multiplicand); |
| int productScale = checkScale((long) scale + multiplicand.scale); |
| if (this.intCompact != INFLATED) { |
| if ((multiplicand.intCompact != INFLATED)) { |
| return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc); |
| } else { |
| return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc); |
| } |
| } else { |
| if ((multiplicand.intCompact != INFLATED)) { |
| return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc); |
| } else { |
| return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc); |
| } |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this / |
| * divisor)}, and whose scale is as specified. If rounding must |
| * be performed to generate a result with the specified scale, the |
| * specified rounding mode is applied. |
| * |
| * @deprecated The method {@link #divide(BigDecimal, int, RoundingMode)} |
| * should be used in preference to this legacy method. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @param scale scale of the {@code BigDecimal} quotient to be returned. |
| * @param roundingMode rounding mode to apply. |
| * @return {@code this / divisor} |
| * @throws ArithmeticException if {@code divisor} is zero, |
| * {@code roundingMode==ROUND_UNNECESSARY} and |
| * the specified scale is insufficient to represent the result |
| * of the division exactly. |
| * @throws IllegalArgumentException if {@code roundingMode} does not |
| * represent a valid rounding mode. |
| * @see #ROUND_UP |
| * @see #ROUND_DOWN |
| * @see #ROUND_CEILING |
| * @see #ROUND_FLOOR |
| * @see #ROUND_HALF_UP |
| * @see #ROUND_HALF_DOWN |
| * @see #ROUND_HALF_EVEN |
| * @see #ROUND_UNNECESSARY |
| */ |
| @Deprecated(since="9") |
| public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) { |
| if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY) |
| throw new IllegalArgumentException("Invalid rounding mode"); |
| if (this.intCompact != INFLATED) { |
| if ((divisor.intCompact != INFLATED)) { |
| return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode); |
| } else { |
| return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode); |
| } |
| } else { |
| if ((divisor.intCompact != INFLATED)) { |
| return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode); |
| } else { |
| return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode); |
| } |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this / |
| * divisor)}, and whose scale is as specified. If rounding must |
| * be performed to generate a result with the specified scale, the |
| * specified rounding mode is applied. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @param scale scale of the {@code BigDecimal} quotient to be returned. |
| * @param roundingMode rounding mode to apply. |
| * @return {@code this / divisor} |
| * @throws ArithmeticException if {@code divisor} is zero, |
| * {@code roundingMode==RoundingMode.UNNECESSARY} and |
| * the specified scale is insufficient to represent the result |
| * of the division exactly. |
| * @since 1.5 |
| */ |
| public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) { |
| return divide(divisor, scale, roundingMode.oldMode); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this / |
| * divisor)}, and whose scale is {@code this.scale()}. If |
| * rounding must be performed to generate a result with the given |
| * scale, the specified rounding mode is applied. |
| * |
| * @deprecated The method {@link #divide(BigDecimal, RoundingMode)} |
| * should be used in preference to this legacy method. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @param roundingMode rounding mode to apply. |
| * @return {@code this / divisor} |
| * @throws ArithmeticException if {@code divisor==0}, or |
| * {@code roundingMode==ROUND_UNNECESSARY} and |
| * {@code this.scale()} is insufficient to represent the result |
| * of the division exactly. |
| * @throws IllegalArgumentException if {@code roundingMode} does not |
| * represent a valid rounding mode. |
| * @see #ROUND_UP |
| * @see #ROUND_DOWN |
| * @see #ROUND_CEILING |
| * @see #ROUND_FLOOR |
| * @see #ROUND_HALF_UP |
| * @see #ROUND_HALF_DOWN |
| * @see #ROUND_HALF_EVEN |
| * @see #ROUND_UNNECESSARY |
| */ |
| @Deprecated(since="9") |
| public BigDecimal divide(BigDecimal divisor, int roundingMode) { |
| return this.divide(divisor, scale, roundingMode); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this / |
| * divisor)}, and whose scale is {@code this.scale()}. If |
| * rounding must be performed to generate a result with the given |
| * scale, the specified rounding mode is applied. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @param roundingMode rounding mode to apply. |
| * @return {@code this / divisor} |
| * @throws ArithmeticException if {@code divisor==0}, or |
| * {@code roundingMode==RoundingMode.UNNECESSARY} and |
| * {@code this.scale()} is insufficient to represent the result |
| * of the division exactly. |
| * @since 1.5 |
| */ |
| public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) { |
| return this.divide(divisor, scale, roundingMode.oldMode); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this / |
| * divisor)}, and whose preferred scale is {@code (this.scale() - |
| * divisor.scale())}; if the exact quotient cannot be |
| * represented (because it has a non-terminating decimal |
| * expansion) an {@code ArithmeticException} is thrown. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @throws ArithmeticException if the exact quotient does not have a |
| * terminating decimal expansion |
| * @return {@code this / divisor} |
| * @since 1.5 |
| * @author Joseph D. Darcy |
| */ |
| public BigDecimal divide(BigDecimal divisor) { |
| /* |
| * Handle zero cases first. |
| */ |
| if (divisor.signum() == 0) { // x/0 |
| if (this.signum() == 0) // 0/0 |
| throw new ArithmeticException("Division undefined"); // NaN |
| throw new ArithmeticException("Division by zero"); |
| } |
| |
| // Calculate preferred scale |
| int preferredScale = saturateLong((long) this.scale - divisor.scale); |
| |
| if (this.signum() == 0) // 0/y |
| return zeroValueOf(preferredScale); |
| else { |
| /* |
| * If the quotient this/divisor has a terminating decimal |
| * expansion, the expansion can have no more than |
| * (a.precision() + ceil(10*b.precision)/3) digits. |
| * Therefore, create a MathContext object with this |
| * precision and do a divide with the UNNECESSARY rounding |
| * mode. |
| */ |
| MathContext mc = new MathContext( (int)Math.min(this.precision() + |
| (long)Math.ceil(10.0*divisor.precision()/3.0), |
| Integer.MAX_VALUE), |
| RoundingMode.UNNECESSARY); |
| BigDecimal quotient; |
| try { |
| quotient = this.divide(divisor, mc); |
| } catch (ArithmeticException e) { |
| throw new ArithmeticException("Non-terminating decimal expansion; " + |
| "no exact representable decimal result."); |
| } |
| |
| int quotientScale = quotient.scale(); |
| |
| // divide(BigDecimal, mc) tries to adjust the quotient to |
| // the desired one by removing trailing zeros; since the |
| // exact divide method does not have an explicit digit |
| // limit, we can add zeros too. |
| if (preferredScale > quotientScale) |
| return quotient.setScale(preferredScale, ROUND_UNNECESSARY); |
| |
| return quotient; |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this / |
| * divisor)}, with rounding according to the context settings. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @param mc the context to use. |
| * @return {@code this / divisor}, rounded as necessary. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY} or |
| * {@code mc.precision == 0} and the quotient has a |
| * non-terminating decimal expansion. |
| * @since 1.5 |
| */ |
| public BigDecimal divide(BigDecimal divisor, MathContext mc) { |
| int mcp = mc.precision; |
| if (mcp == 0) |
| return divide(divisor); |
| |
| BigDecimal dividend = this; |
| long preferredScale = (long)dividend.scale - divisor.scale; |
| // Now calculate the answer. We use the existing |
| // divide-and-round method, but as this rounds to scale we have |
| // to normalize the values here to achieve the desired result. |
| // For x/y we first handle y=0 and x=0, and then normalize x and |
| // y to give x' and y' with the following constraints: |
| // (a) 0.1 <= x' < 1 |
| // (b) x' <= y' < 10*x' |
| // Dividing x'/y' with the required scale set to mc.precision then |
| // will give a result in the range 0.1 to 1 rounded to exactly |
| // the right number of digits (except in the case of a result of |
| // 1.000... which can arise when x=y, or when rounding overflows |
| // The 1.000... case will reduce properly to 1. |
| if (divisor.signum() == 0) { // x/0 |
| if (dividend.signum() == 0) // 0/0 |
| throw new ArithmeticException("Division undefined"); // NaN |
| throw new ArithmeticException("Division by zero"); |
| } |
| if (dividend.signum() == 0) // 0/y |
| return zeroValueOf(saturateLong(preferredScale)); |
| int xscale = dividend.precision(); |
| int yscale = divisor.precision(); |
| if(dividend.intCompact!=INFLATED) { |
| if(divisor.intCompact!=INFLATED) { |
| return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc); |
| } else { |
| return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc); |
| } |
| } else { |
| if(divisor.intCompact!=INFLATED) { |
| return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc); |
| } else { |
| return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc); |
| } |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is the integer part |
| * of the quotient {@code (this / divisor)} rounded down. The |
| * preferred scale of the result is {@code (this.scale() - |
| * divisor.scale())}. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @return The integer part of {@code this / divisor}. |
| * @throws ArithmeticException if {@code divisor==0} |
| * @since 1.5 |
| */ |
| public BigDecimal divideToIntegralValue(BigDecimal divisor) { |
| // Calculate preferred scale |
| int preferredScale = saturateLong((long) this.scale - divisor.scale); |
| if (this.compareMagnitude(divisor) < 0) { |
| // much faster when this << divisor |
| return zeroValueOf(preferredScale); |
| } |
| |
| if (this.signum() == 0 && divisor.signum() != 0) |
| return this.setScale(preferredScale, ROUND_UNNECESSARY); |
| |
| // Perform a divide with enough digits to round to a correct |
| // integer value; then remove any fractional digits |
| |
| int maxDigits = (int)Math.min(this.precision() + |
| (long)Math.ceil(10.0*divisor.precision()/3.0) + |
| Math.abs((long)this.scale() - divisor.scale()) + 2, |
| Integer.MAX_VALUE); |
| BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits, |
| RoundingMode.DOWN)); |
| if (quotient.scale > 0) { |
| quotient = quotient.setScale(0, RoundingMode.DOWN); |
| quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale); |
| } |
| |
| if (quotient.scale < preferredScale) { |
| // pad with zeros if necessary |
| quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY); |
| } |
| |
| return quotient; |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is the integer part |
| * of {@code (this / divisor)}. Since the integer part of the |
| * exact quotient does not depend on the rounding mode, the |
| * rounding mode does not affect the values returned by this |
| * method. The preferred scale of the result is |
| * {@code (this.scale() - divisor.scale())}. An |
| * {@code ArithmeticException} is thrown if the integer part of |
| * the exact quotient needs more than {@code mc.precision} |
| * digits. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @param mc the context to use. |
| * @return The integer part of {@code this / divisor}. |
| * @throws ArithmeticException if {@code divisor==0} |
| * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result |
| * requires a precision of more than {@code mc.precision} digits. |
| * @since 1.5 |
| * @author Joseph D. Darcy |
| */ |
| public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) { |
| if (mc.precision == 0 || // exact result |
| (this.compareMagnitude(divisor) < 0)) // zero result |
| return divideToIntegralValue(divisor); |
| |
| // Calculate preferred scale |
| int preferredScale = saturateLong((long)this.scale - divisor.scale); |
| |
| /* |
| * Perform a normal divide to mc.precision digits. If the |
| * remainder has absolute value less than the divisor, the |
| * integer portion of the quotient fits into mc.precision |
| * digits. Next, remove any fractional digits from the |
| * quotient and adjust the scale to the preferred value. |
| */ |
| BigDecimal result = this.divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN)); |
| |
| if (result.scale() < 0) { |
| /* |
| * Result is an integer. See if quotient represents the |
| * full integer portion of the exact quotient; if it does, |
| * the computed remainder will be less than the divisor. |
| */ |
| BigDecimal product = result.multiply(divisor); |
| // If the quotient is the full integer value, |
| // |dividend-product| < |divisor|. |
| if (this.subtract(product).compareMagnitude(divisor) >= 0) { |
| throw new ArithmeticException("Division impossible"); |
| } |
| } else if (result.scale() > 0) { |
| /* |
| * Integer portion of quotient will fit into precision |
| * digits; recompute quotient to scale 0 to avoid double |
| * rounding and then try to adjust, if necessary. |
| */ |
| result = result.setScale(0, RoundingMode.DOWN); |
| } |
| // else result.scale() == 0; |
| |
| int precisionDiff; |
| if ((preferredScale > result.scale()) && |
| (precisionDiff = mc.precision - result.precision()) > 0) { |
| return result.setScale(result.scale() + |
| Math.min(precisionDiff, preferredScale - result.scale) ); |
| } else { |
| return stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale); |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}. |
| * |
| * <p>The remainder is given by |
| * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}. |
| * Note that this is <em>not</em> the modulo operation (the result can be |
| * negative). |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @return {@code this % divisor}. |
| * @throws ArithmeticException if {@code divisor==0} |
| * @since 1.5 |
| */ |
| public BigDecimal remainder(BigDecimal divisor) { |
| BigDecimal divrem[] = this.divideAndRemainder(divisor); |
| return divrem[1]; |
| } |
| |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (this % |
| * divisor)}, with rounding according to the context settings. |
| * The {@code MathContext} settings affect the implicit divide |
| * used to compute the remainder. The remainder computation |
| * itself is by definition exact. Therefore, the remainder may |
| * contain more than {@code mc.getPrecision()} digits. |
| * |
| * <p>The remainder is given by |
| * {@code this.subtract(this.divideToIntegralValue(divisor, |
| * mc).multiply(divisor))}. Note that this is not the modulo |
| * operation (the result can be negative). |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided. |
| * @param mc the context to use. |
| * @return {@code this % divisor}, rounded as necessary. |
| * @throws ArithmeticException if {@code divisor==0} |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}, or {@code mc.precision} |
| * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would |
| * require a precision of more than {@code mc.precision} digits. |
| * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext) |
| * @since 1.5 |
| */ |
| public BigDecimal remainder(BigDecimal divisor, MathContext mc) { |
| BigDecimal divrem[] = this.divideAndRemainder(divisor, mc); |
| return divrem[1]; |
| } |
| |
| /** |
| * Returns a two-element {@code BigDecimal} array containing the |
| * result of {@code divideToIntegralValue} followed by the result of |
| * {@code remainder} on the two operands. |
| * |
| * <p>Note that if both the integer quotient and remainder are |
| * needed, this method is faster than using the |
| * {@code divideToIntegralValue} and {@code remainder} methods |
| * separately because the division need only be carried out once. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided, |
| * and the remainder computed. |
| * @return a two element {@code BigDecimal} array: the quotient |
| * (the result of {@code divideToIntegralValue}) is the initial element |
| * and the remainder is the final element. |
| * @throws ArithmeticException if {@code divisor==0} |
| * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext) |
| * @see #remainder(java.math.BigDecimal, java.math.MathContext) |
| * @since 1.5 |
| */ |
| public BigDecimal[] divideAndRemainder(BigDecimal divisor) { |
| // we use the identity x = i * y + r to determine r |
| BigDecimal[] result = new BigDecimal[2]; |
| |
| result[0] = this.divideToIntegralValue(divisor); |
| result[1] = this.subtract(result[0].multiply(divisor)); |
| return result; |
| } |
| |
| /** |
| * Returns a two-element {@code BigDecimal} array containing the |
| * result of {@code divideToIntegralValue} followed by the result of |
| * {@code remainder} on the two operands calculated with rounding |
| * according to the context settings. |
| * |
| * <p>Note that if both the integer quotient and remainder are |
| * needed, this method is faster than using the |
| * {@code divideToIntegralValue} and {@code remainder} methods |
| * separately because the division need only be carried out once. |
| * |
| * @param divisor value by which this {@code BigDecimal} is to be divided, |
| * and the remainder computed. |
| * @param mc the context to use. |
| * @return a two element {@code BigDecimal} array: the quotient |
| * (the result of {@code divideToIntegralValue}) is the |
| * initial element and the remainder is the final element. |
| * @throws ArithmeticException if {@code divisor==0} |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}, or {@code mc.precision} |
| * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would |
| * require a precision of more than {@code mc.precision} digits. |
| * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext) |
| * @see #remainder(java.math.BigDecimal, java.math.MathContext) |
| * @since 1.5 |
| */ |
| public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) { |
| if (mc.precision == 0) |
| return divideAndRemainder(divisor); |
| |
| BigDecimal[] result = new BigDecimal[2]; |
| BigDecimal lhs = this; |
| |
| result[0] = lhs.divideToIntegralValue(divisor, mc); |
| result[1] = lhs.subtract(result[0].multiply(divisor)); |
| return result; |
| } |
| |
| /** |
| * Returns an approximation to the square root of {@code this} |
| * with rounding according to the context settings. |
| * |
| * <p>The preferred scale of the returned result is equal to |
| * {@code this.scale()/2}. The value of the returned result is |
| * always within one ulp of the exact decimal value for the |
| * precision in question. If the rounding mode is {@link |
| * RoundingMode#HALF_UP HALF_UP}, {@link RoundingMode#HALF_DOWN |
| * HALF_DOWN}, or {@link RoundingMode#HALF_EVEN HALF_EVEN}, the |
| * result is within one half an ulp of the exact decimal value. |
| * |
| * <p>Special case: |
| * <ul> |
| * <li> The square root of a number numerically equal to {@code |
| * ZERO} is numerically equal to {@code ZERO} with a preferred |
| * scale according to the general rule above. In particular, for |
| * {@code ZERO}, {@code ZERO.sqrt(mc).equals(ZERO)} is true with |
| * any {@code MathContext} as an argument. |
| * </ul> |
| * |
| * @param mc the context to use. |
| * @return the square root of {@code this}. |
| * @throws ArithmeticException if {@code this} is less than zero. |
| * @throws ArithmeticException if an exact result is requested |
| * ({@code mc.getPrecision()==0}) and there is no finite decimal |
| * expansion of the exact result |
| * @throws ArithmeticException if |
| * {@code (mc.getRoundingMode()==RoundingMode.UNNECESSARY}) and |
| * the exact result cannot fit in {@code mc.getPrecision()} |
| * digits. |
| * @see BigInteger#sqrt() |
| * @since 9 |
| */ |
| public BigDecimal sqrt(MathContext mc) { |
| int signum = signum(); |
| if (signum == 1) { |
| /* |
| * The following code draws on the algorithm presented in |
| * "Properly Rounded Variable Precision Square Root," Hull and |
| * Abrham, ACM Transactions on Mathematical Software, Vol 11, |
| * No. 3, September 1985, Pages 229-237. |
| * |
| * The BigDecimal computational model differs from the one |
| * presented in the paper in several ways: first BigDecimal |
| * numbers aren't necessarily normalized, second many more |
| * rounding modes are supported, including UNNECESSARY, and |
| * exact results can be requested. |
| * |
| * The main steps of the algorithm below are as follows, |
| * first argument reduce the value to the numerical range |
| * [1, 10) using the following relations: |
| * |
| * x = y * 10 ^ exp |
| * sqrt(x) = sqrt(y) * 10^(exp / 2) if exp is even |
| * sqrt(x) = sqrt(y/10) * 10 ^((exp+1)/2) is exp is odd |
| * |
| * Then use Newton's iteration on the reduced value to compute |
| * the numerical digits of the desired result. |
| * |
| * Finally, scale back to the desired exponent range and |
| * perform any adjustment to get the preferred scale in the |
| * representation. |
| */ |
| |
| // The code below favors relative simplicity over checking |
| // for special cases that could run faster. |
| |
| int preferredScale = this.scale()/2; |
| BigDecimal zeroWithFinalPreferredScale = valueOf(0L, preferredScale); |
| |
| // First phase of numerical normalization, strip trailing |
| // zeros and check for even powers of 10. |
| BigDecimal stripped = this.stripTrailingZeros(); |
| int strippedScale = stripped.scale(); |
| |
| // Numerically sqrt(10^2N) = 10^N |
| if (stripped.isPowerOfTen() && |
| strippedScale % 2 == 0) { |
| BigDecimal result = valueOf(1L, strippedScale/2); |
| if (result.scale() != preferredScale) { |
| // Adjust to requested precision and preferred |
| // scale as appropriate. |
| result = result.add(zeroWithFinalPreferredScale, mc); |
| } |
| return result; |
| } |
| |
| // After stripTrailingZeros, the representation is normalized as |
| // |
| // unscaledValue * 10^(-scale) |
| // |
| // where unscaledValue is an integer with the mimimum |
| // precision for the cohort of the numerical value. To |
| // allow binary floating-point hardware to be used to get |
| // approximately a 15 digit approximation to the square |
| // root, it is helpful to instead normalize this so that |
| // the significand portion is to right of the decimal |
| // point by roughly (scale() - precision() +1). |
| |
| // Now the precision / scale adjustment |
| int scaleAdjust = 0; |
| int scale = stripped.scale() - stripped.precision() + 1; |
| if (scale % 2 == 0) { |
| scaleAdjust = scale; |
| } else { |
| scaleAdjust = scale - 1; |
| } |
| |
| BigDecimal working = stripped.scaleByPowerOfTen(scaleAdjust); |
| |
| assert // Verify 0.1 <= working < 10 |
| ONE_TENTH.compareTo(working) <= 0 && working.compareTo(TEN) < 0; |
| |
| // Use good ole' Math.sqrt to get the initial guess for |
| // the Newton iteration, good to at least 15 decimal |
| // digits. This approach does incur the cost of a |
| // |
| // BigDecimal -> double -> BigDecimal |
| // |
| // conversion cycle, but it avoids the need for several |
| // Newton iterations in BigDecimal arithmetic to get the |
| // working answer to 15 digits of precision. If many fewer |
| // than 15 digits were needed, it might be faster to do |
| // the loop entirely in BigDecimal arithmetic. |
| // |
| // (A double value might have as much many as 17 decimal |
| // digits of precision; it depends on the relative density |
| // of binary and decimal numbers at different regions of |
| // the number line.) |
| // |
| // (It would be possible to check for certain special |
| // cases to avoid doing any Newton iterations. For |
| // example, if the BigDecimal -> double conversion was |
| // known to be exact and the rounding mode had a |
| // low-enough precision, the post-Newton rounding logic |
| // could be applied directly.) |
| |
| BigDecimal guess = new BigDecimal(Math.sqrt(working.doubleValue())); |
| int guessPrecision = 15; |
| int originalPrecision = mc.getPrecision(); |
| int targetPrecision; |
| |
| // If an exact value is requested, it must only need about |
| // half of the input digits to represent since multiplying |
| // an N digit number by itself yield a 2N-1 digit or 2N |
| // digit result. |
| if (originalPrecision == 0) { |
| targetPrecision = stripped.precision()/2 + 1; |
| } else { |
| targetPrecision = originalPrecision; |
| } |
| |
| // When setting the precision to use inside the Newton |
| // iteration loop, take care to avoid the case where the |
| // precision of the input exceeds the requested precision |
| // and rounding the input value too soon. |
| BigDecimal approx = guess; |
| int workingPrecision = working.precision(); |
| do { |
| int tmpPrecision = Math.max(Math.max(guessPrecision, targetPrecision + 2), |
| workingPrecision); |
| MathContext mcTmp = new MathContext(tmpPrecision, RoundingMode.HALF_EVEN); |
| // approx = 0.5 * (approx + fraction / approx) |
| approx = ONE_HALF.multiply(approx.add(working.divide(approx, mcTmp), mcTmp)); |
| guessPrecision *= 2; |
| } while (guessPrecision < targetPrecision + 2); |
| |
| BigDecimal result; |
| RoundingMode targetRm = mc.getRoundingMode(); |
| if (targetRm == RoundingMode.UNNECESSARY || originalPrecision == 0) { |
| RoundingMode tmpRm = |
| (targetRm == RoundingMode.UNNECESSARY) ? RoundingMode.DOWN : targetRm; |
| MathContext mcTmp = new MathContext(targetPrecision, tmpRm); |
| result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mcTmp); |
| |
| // If result*result != this numerically, the square |
| // root isn't exact |
| if (this.subtract(result.multiply(result)).compareTo(ZERO) != 0) { |
| throw new ArithmeticException("Computed square root not exact."); |
| } |
| } else { |
| result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mc); |
| } |
| |
| if (result.scale() != preferredScale) { |
| // The preferred scale of an add is |
| // max(addend.scale(), augend.scale()). Therefore, if |
| // the scale of the result is first minimized using |
| // stripTrailingZeros(), adding a zero of the |
| // preferred scale rounding the correct precision will |
| // perform the proper scale vs precision tradeoffs. |
| result = result.stripTrailingZeros(). |
| add(zeroWithFinalPreferredScale, |
| new MathContext(originalPrecision, RoundingMode.UNNECESSARY)); |
| } |
| assert squareRootResultAssertions(result, mc); |
| return result; |
| } else { |
| switch (signum) { |
| case -1: |
| throw new ArithmeticException("Attempted square root " + |
| "of negative BigDecimal"); |
| case 0: |
| return valueOf(0L, scale()/2); |
| |
| default: |
| throw new AssertionError("Bad value from signum"); |
| } |
| } |
| } |
| |
| private boolean isPowerOfTen() { |
| return BigInteger.ONE.equals(this.unscaledValue()); |
| } |
| |
| /** |
| * For nonzero values, check numerical correctness properties of |
| * the computed result for the chosen rounding mode. |
| * |
| * For the directed roundings, for DOWN and FLOOR, result^2 must |
| * be {@code <=} the input and (result+ulp)^2 must be {@code >} the |
| * input. Conversely, for UP and CEIL, result^2 must be {@code >=} the |
| * input and (result-ulp)^2 must be {@code <} the input. |
| */ |
| private boolean squareRootResultAssertions(BigDecimal result, MathContext mc) { |
| if (result.signum() == 0) { |
| return squareRootZeroResultAssertions(result, mc); |
| } else { |
| RoundingMode rm = mc.getRoundingMode(); |
| BigDecimal ulp = result.ulp(); |
| BigDecimal neighborUp = result.add(ulp); |
| // Make neighbor down accurate even for powers of ten |
| if (this.isPowerOfTen()) { |
| ulp = ulp.divide(TEN); |
| } |
| BigDecimal neighborDown = result.subtract(ulp); |
| |
| // Both the starting value and result should be nonzero and positive. |
| if (result.signum() != 1 || |
| this.signum() != 1) { |
| return false; |
| } |
| |
| switch (rm) { |
| case DOWN: |
| case FLOOR: |
| return |
| result.multiply(result).compareTo(this) <= 0 && |
| neighborUp.multiply(neighborUp).compareTo(this) > 0; |
| |
| case UP: |
| case CEILING: |
| return |
| result.multiply(result).compareTo(this) >= 0 && |
| neighborDown.multiply(neighborDown).compareTo(this) < 0; |
| |
| case HALF_DOWN: |
| case HALF_EVEN: |
| case HALF_UP: |
| BigDecimal err = result.multiply(result).subtract(this).abs(); |
| BigDecimal errUp = neighborUp.multiply(neighborUp).subtract(this); |
| BigDecimal errDown = this.subtract(neighborDown.multiply(neighborDown)); |
| // All error values should be positive so don't need to |
| // compare absolute values. |
| |
| int err_comp_errUp = err.compareTo(errUp); |
| int err_comp_errDown = err.compareTo(errDown); |
| |
| return |
| errUp.signum() == 1 && |
| errDown.signum() == 1 && |
| |
| err_comp_errUp <= 0 && |
| err_comp_errDown <= 0 && |
| |
| ((err_comp_errUp == 0 ) ? err_comp_errDown < 0 : true) && |
| ((err_comp_errDown == 0 ) ? err_comp_errUp < 0 : true); |
| // && could check for digit conditions for ties too |
| |
| default: // Definition of UNNECESSARY already verified. |
| return true; |
| } |
| } |
| } |
| |
| private boolean squareRootZeroResultAssertions(BigDecimal result, MathContext mc) { |
| return this.compareTo(ZERO) == 0; |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is |
| * <code>(this<sup>n</sup>)</code>, The power is computed exactly, to |
| * unlimited precision. |
| * |
| * <p>The parameter {@code n} must be in the range 0 through |
| * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link |
| * #ONE}. |
| * |
| * Note that future releases may expand the allowable exponent |
| * range of this method. |
| * |
| * @param n power to raise this {@code BigDecimal} to. |
| * @return <code>this<sup>n</sup></code> |
| * @throws ArithmeticException if {@code n} is out of range. |
| * @since 1.5 |
| */ |
| public BigDecimal pow(int n) { |
| if (n < 0 || n > 999999999) |
| throw new ArithmeticException("Invalid operation"); |
| // No need to calculate pow(n) if result will over/underflow. |
| // Don't attempt to support "supernormal" numbers. |
| int newScale = checkScale((long)scale * n); |
| return new BigDecimal(this.inflated().pow(n), newScale); |
| } |
| |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is |
| * <code>(this<sup>n</sup>)</code>. The current implementation uses |
| * the core algorithm defined in ANSI standard X3.274-1996 with |
| * rounding according to the context settings. In general, the |
| * returned numerical value is within two ulps of the exact |
| * numerical value for the chosen precision. Note that future |
| * releases may use a different algorithm with a decreased |
| * allowable error bound and increased allowable exponent range. |
| * |
| * <p>The X3.274-1996 algorithm is: |
| * |
| * <ul> |
| * <li> An {@code ArithmeticException} exception is thrown if |
| * <ul> |
| * <li>{@code abs(n) > 999999999} |
| * <li>{@code mc.precision == 0} and {@code n < 0} |
| * <li>{@code mc.precision > 0} and {@code n} has more than |
| * {@code mc.precision} decimal digits |
| * </ul> |
| * |
| * <li> if {@code n} is zero, {@link #ONE} is returned even if |
| * {@code this} is zero, otherwise |
| * <ul> |
| * <li> if {@code n} is positive, the result is calculated via |
| * the repeated squaring technique into a single accumulator. |
| * The individual multiplications with the accumulator use the |
| * same math context settings as in {@code mc} except for a |
| * precision increased to {@code mc.precision + elength + 1} |
| * where {@code elength} is the number of decimal digits in |
| * {@code n}. |
| * |
| * <li> if {@code n} is negative, the result is calculated as if |
| * {@code n} were positive; this value is then divided into one |
| * using the working precision specified above. |
| * |
| * <li> The final value from either the positive or negative case |
| * is then rounded to the destination precision. |
| * </ul> |
| * </ul> |
| * |
| * @param n power to raise this {@code BigDecimal} to. |
| * @param mc the context to use. |
| * @return <code>this<sup>n</sup></code> using the ANSI standard X3.274-1996 |
| * algorithm |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}, or {@code n} is out |
| * of range. |
| * @since 1.5 |
| */ |
| public BigDecimal pow(int n, MathContext mc) { |
| if (mc.precision == 0) |
| return pow(n); |
| if (n < -999999999 || n > 999999999) |
| throw new ArithmeticException("Invalid operation"); |
| if (n == 0) |
| return ONE; // x**0 == 1 in X3.274 |
| BigDecimal lhs = this; |
| MathContext workmc = mc; // working settings |
| int mag = Math.abs(n); // magnitude of n |
| if (mc.precision > 0) { |
| int elength = longDigitLength(mag); // length of n in digits |
| if (elength > mc.precision) // X3.274 rule |
| throw new ArithmeticException("Invalid operation"); |
| workmc = new MathContext(mc.precision + elength + 1, |
| mc.roundingMode); |
| } |
| // ready to carry out power calculation... |
| BigDecimal acc = ONE; // accumulator |
| boolean seenbit = false; // set once we've seen a 1-bit |
| for (int i=1;;i++) { // for each bit [top bit ignored] |
| mag += mag; // shift left 1 bit |
| if (mag < 0) { // top bit is set |
| seenbit = true; // OK, we're off |
| acc = acc.multiply(lhs, workmc); // acc=acc*x |
| } |
| if (i == 31) |
| break; // that was the last bit |
| if (seenbit) |
| acc=acc.multiply(acc, workmc); // acc=acc*acc [square] |
| // else (!seenbit) no point in squaring ONE |
| } |
| // if negative n, calculate the reciprocal using working precision |
| if (n < 0) // [hence mc.precision>0] |
| acc=ONE.divide(acc, workmc); |
| // round to final precision and strip zeros |
| return doRound(acc, mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is the absolute value |
| * of this {@code BigDecimal}, and whose scale is |
| * {@code this.scale()}. |
| * |
| * @return {@code abs(this)} |
| */ |
| public BigDecimal abs() { |
| return (signum() < 0 ? negate() : this); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is the absolute value |
| * of this {@code BigDecimal}, with rounding according to the |
| * context settings. |
| * |
| * @param mc the context to use. |
| * @return {@code abs(this)}, rounded as necessary. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal abs(MathContext mc) { |
| return (signum() < 0 ? negate(mc) : plus(mc)); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (-this)}, |
| * and whose scale is {@code this.scale()}. |
| * |
| * @return {@code -this}. |
| */ |
| public BigDecimal negate() { |
| if (intCompact == INFLATED) { |
| return new BigDecimal(intVal.negate(), INFLATED, scale, precision); |
| } else { |
| return valueOf(-intCompact, scale, precision); |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (-this)}, |
| * with rounding according to the context settings. |
| * |
| * @param mc the context to use. |
| * @return {@code -this}, rounded as necessary. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @since 1.5 |
| */ |
| public BigDecimal negate(MathContext mc) { |
| return negate().plus(mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose |
| * scale is {@code this.scale()}. |
| * |
| * <p>This method, which simply returns this {@code BigDecimal} |
| * is included for symmetry with the unary minus method {@link |
| * #negate()}. |
| * |
| * @return {@code this}. |
| * @see #negate() |
| * @since 1.5 |
| */ |
| public BigDecimal plus() { |
| return this; |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (+this)}, |
| * with rounding according to the context settings. |
| * |
| * <p>The effect of this method is identical to that of the {@link |
| * #round(MathContext)} method. |
| * |
| * @param mc the context to use. |
| * @return {@code this}, rounded as necessary. A zero result will |
| * have a scale of 0. |
| * @throws ArithmeticException if the result is inexact but the |
| * rounding mode is {@code UNNECESSARY}. |
| * @see #round(MathContext) |
| * @since 1.5 |
| */ |
| public BigDecimal plus(MathContext mc) { |
| if (mc.precision == 0) // no rounding please |
| return this; |
| return doRound(this, mc); |
| } |
| |
| /** |
| * Returns the signum function of this {@code BigDecimal}. |
| * |
| * @return -1, 0, or 1 as the value of this {@code BigDecimal} |
| * is negative, zero, or positive. |
| */ |
| public int signum() { |
| return (intCompact != INFLATED)? |
| Long.signum(intCompact): |
| intVal.signum(); |
| } |
| |
| /** |
| * Returns the <i>scale</i> of this {@code BigDecimal}. If zero |
| * or positive, the scale is the number of digits to the right of |
| * the decimal point. If negative, the unscaled value of the |
| * number is multiplied by ten to the power of the negation of the |
| * scale. For example, a scale of {@code -3} means the unscaled |
| * value is multiplied by 1000. |
| * |
| * @return the scale of this {@code BigDecimal}. |
| */ |
| public int scale() { |
| return scale; |
| } |
| |
| /** |
| * Returns the <i>precision</i> of this {@code BigDecimal}. (The |
| * precision is the number of digits in the unscaled value.) |
| * |
| * <p>The precision of a zero value is 1. |
| * |
| * @return the precision of this {@code BigDecimal}. |
| * @since 1.5 |
| */ |
| public int precision() { |
| int result = precision; |
| if (result == 0) { |
| long s = intCompact; |
| if (s != INFLATED) |
| result = longDigitLength(s); |
| else |
| result = bigDigitLength(intVal); |
| precision = result; |
| } |
| return result; |
| } |
| |
| |
| /** |
| * Returns a {@code BigInteger} whose value is the <i>unscaled |
| * value</i> of this {@code BigDecimal}. (Computes <code>(this * |
| * 10<sup>this.scale()</sup>)</code>.) |
| * |
| * @return the unscaled value of this {@code BigDecimal}. |
| * @since 1.2 |
| */ |
| public BigInteger unscaledValue() { |
| return this.inflated(); |
| } |
| |
| // Rounding Modes |
| |
| /** |
| * Rounding mode to round away from zero. Always increments the |
| * digit prior to a nonzero discarded fraction. Note that this rounding |
| * mode never decreases the magnitude of the calculated value. |
| * |
| * @deprecated Use {@link RoundingMode#UP} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_UP = 0; |
| |
| /** |
| * Rounding mode to round towards zero. Never increments the digit |
| * prior to a discarded fraction (i.e., truncates). Note that this |
| * rounding mode never increases the magnitude of the calculated value. |
| * |
| * @deprecated Use {@link RoundingMode#DOWN} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_DOWN = 1; |
| |
| /** |
| * Rounding mode to round towards positive infinity. If the |
| * {@code BigDecimal} is positive, behaves as for |
| * {@code ROUND_UP}; if negative, behaves as for |
| * {@code ROUND_DOWN}. Note that this rounding mode never |
| * decreases the calculated value. |
| * |
| * @deprecated Use {@link RoundingMode#CEILING} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_CEILING = 2; |
| |
| /** |
| * Rounding mode to round towards negative infinity. If the |
| * {@code BigDecimal} is positive, behave as for |
| * {@code ROUND_DOWN}; if negative, behave as for |
| * {@code ROUND_UP}. Note that this rounding mode never |
| * increases the calculated value. |
| * |
| * @deprecated Use {@link RoundingMode#FLOOR} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_FLOOR = 3; |
| |
| /** |
| * Rounding mode to round towards {@literal "nearest neighbor"} |
| * unless both neighbors are equidistant, in which case round up. |
| * Behaves as for {@code ROUND_UP} if the discarded fraction is |
| * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note |
| * that this is the rounding mode that most of us were taught in |
| * grade school. |
| * |
| * @deprecated Use {@link RoundingMode#HALF_UP} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_HALF_UP = 4; |
| |
| /** |
| * Rounding mode to round towards {@literal "nearest neighbor"} |
| * unless both neighbors are equidistant, in which case round |
| * down. Behaves as for {@code ROUND_UP} if the discarded |
| * fraction is {@literal >} 0.5; otherwise, behaves as for |
| * {@code ROUND_DOWN}. |
| * |
| * @deprecated Use {@link RoundingMode#HALF_DOWN} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_HALF_DOWN = 5; |
| |
| /** |
| * Rounding mode to round towards the {@literal "nearest neighbor"} |
| * unless both neighbors are equidistant, in which case, round |
| * towards the even neighbor. Behaves as for |
| * {@code ROUND_HALF_UP} if the digit to the left of the |
| * discarded fraction is odd; behaves as for |
| * {@code ROUND_HALF_DOWN} if it's even. Note that this is the |
| * rounding mode that minimizes cumulative error when applied |
| * repeatedly over a sequence of calculations. |
| * |
| * @deprecated Use {@link RoundingMode#HALF_EVEN} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_HALF_EVEN = 6; |
| |
| /** |
| * Rounding mode to assert that the requested operation has an exact |
| * result, hence no rounding is necessary. If this rounding mode is |
| * specified on an operation that yields an inexact result, an |
| * {@code ArithmeticException} is thrown. |
| * |
| * @deprecated Use {@link RoundingMode#UNNECESSARY} instead. |
| */ |
| @Deprecated(since="9") |
| public static final int ROUND_UNNECESSARY = 7; |
| |
| |
| // Scaling/Rounding Operations |
| |
| /** |
| * Returns a {@code BigDecimal} rounded according to the |
| * {@code MathContext} settings. If the precision setting is 0 then |
| * no rounding takes place. |
| * |
| * <p>The effect of this method is identical to that of the |
| * {@link #plus(MathContext)} method. |
| * |
| * @param mc the context to use. |
| * @return a {@code BigDecimal} rounded according to the |
| * {@code MathContext} settings. |
| * @throws ArithmeticException if the rounding mode is |
| * {@code UNNECESSARY} and the |
| * {@code BigDecimal} operation would require rounding. |
| * @see #plus(MathContext) |
| * @since 1.5 |
| */ |
| public BigDecimal round(MathContext mc) { |
| return plus(mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose scale is the specified |
| * value, and whose unscaled value is determined by multiplying or |
| * dividing this {@code BigDecimal}'s unscaled value by the |
| * appropriate power of ten to maintain its overall value. If the |
| * scale is reduced by the operation, the unscaled value must be |
| * divided (rather than multiplied), and the value may be changed; |
| * in this case, the specified rounding mode is applied to the |
| * division. |
| * |
| * @apiNote Since BigDecimal objects are immutable, calls of |
| * this method do <em>not</em> result in the original object being |
| * modified, contrary to the usual convention of having methods |
| * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>. |
| * Instead, {@code setScale} returns an object with the proper |
| * scale; the returned object may or may not be newly allocated. |
| * |
| * @param newScale scale of the {@code BigDecimal} value to be returned. |
| * @param roundingMode The rounding mode to apply. |
| * @return a {@code BigDecimal} whose scale is the specified value, |
| * and whose unscaled value is determined by multiplying or |
| * dividing this {@code BigDecimal}'s unscaled value by the |
| * appropriate power of ten to maintain its overall value. |
| * @throws ArithmeticException if {@code roundingMode==UNNECESSARY} |
| * and the specified scaling operation would require |
| * rounding. |
| * @see RoundingMode |
| * @since 1.5 |
| */ |
| public BigDecimal setScale(int newScale, RoundingMode roundingMode) { |
| return setScale(newScale, roundingMode.oldMode); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose scale is the specified |
| * value, and whose unscaled value is determined by multiplying or |
| * dividing this {@code BigDecimal}'s unscaled value by the |
| * appropriate power of ten to maintain its overall value. If the |
| * scale is reduced by the operation, the unscaled value must be |
| * divided (rather than multiplied), and the value may be changed; |
| * in this case, the specified rounding mode is applied to the |
| * division. |
| * |
| * @apiNote Since BigDecimal objects are immutable, calls of |
| * this method do <em>not</em> result in the original object being |
| * modified, contrary to the usual convention of having methods |
| * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>. |
| * Instead, {@code setScale} returns an object with the proper |
| * scale; the returned object may or may not be newly allocated. |
| * |
| * @deprecated The method {@link #setScale(int, RoundingMode)} should |
| * be used in preference to this legacy method. |
| * |
| * @param newScale scale of the {@code BigDecimal} value to be returned. |
| * @param roundingMode The rounding mode to apply. |
| * @return a {@code BigDecimal} whose scale is the specified value, |
| * and whose unscaled value is determined by multiplying or |
| * dividing this {@code BigDecimal}'s unscaled value by the |
| * appropriate power of ten to maintain its overall value. |
| * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY} |
| * and the specified scaling operation would require |
| * rounding. |
| * @throws IllegalArgumentException if {@code roundingMode} does not |
| * represent a valid rounding mode. |
| * @see #ROUND_UP |
| * @see #ROUND_DOWN |
| * @see #ROUND_CEILING |
| * @see #ROUND_FLOOR |
| * @see #ROUND_HALF_UP |
| * @see #ROUND_HALF_DOWN |
| * @see #ROUND_HALF_EVEN |
| * @see #ROUND_UNNECESSARY |
| */ |
| @Deprecated(since="9") |
| public BigDecimal setScale(int newScale, int roundingMode) { |
| if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY) |
| throw new IllegalArgumentException("Invalid rounding mode"); |
| |
| int oldScale = this.scale; |
| if (newScale == oldScale) // easy case |
| return this; |
| if (this.signum() == 0) // zero can have any scale |
| return zeroValueOf(newScale); |
| if(this.intCompact!=INFLATED) { |
| long rs = this.intCompact; |
| if (newScale > oldScale) { |
| int raise = checkScale((long) newScale - oldScale); |
| if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) { |
| return valueOf(rs,newScale); |
| } |
| BigInteger rb = bigMultiplyPowerTen(raise); |
| return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0); |
| } else { |
| // newScale < oldScale -- drop some digits |
| // Can't predict the precision due to the effect of rounding. |
| int drop = checkScale((long) oldScale - newScale); |
| if (drop < LONG_TEN_POWERS_TABLE.length) { |
| return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale); |
| } else { |
| return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale); |
| } |
| } |
| } else { |
| if (newScale > oldScale) { |
| int raise = checkScale((long) newScale - oldScale); |
| BigInteger rb = bigMultiplyPowerTen(this.intVal,raise); |
| return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0); |
| } else { |
| // newScale < oldScale -- drop some digits |
| // Can't predict the precision due to the effect of rounding. |
| int drop = checkScale((long) oldScale - newScale); |
| if (drop < LONG_TEN_POWERS_TABLE.length) |
| return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, |
| newScale); |
| else |
| return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale); |
| } |
| } |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose scale is the specified |
| * value, and whose value is numerically equal to this |
| * {@code BigDecimal}'s. Throws an {@code ArithmeticException} |
| * if this is not possible. |
| * |
| * <p>This call is typically used to increase the scale, in which |
| * case it is guaranteed that there exists a {@code BigDecimal} |
| * of the specified scale and the correct value. The call can |
| * also be used to reduce the scale if the caller knows that the |
| * {@code BigDecimal} has sufficiently many zeros at the end of |
| * its fractional part (i.e., factors of ten in its integer value) |
| * to allow for the rescaling without changing its value. |
| * |
| * <p>This method returns the same result as the two-argument |
| * versions of {@code setScale}, but saves the caller the trouble |
| * of specifying a rounding mode in cases where it is irrelevant. |
| * |
| * @apiNote Since {@code BigDecimal} objects are immutable, |
| * calls of this method do <em>not</em> result in the original |
| * object being modified, contrary to the usual convention of |
| * having methods named <code>set<i>X</i></code> mutate field |
| * <i>{@code X}</i>. Instead, {@code setScale} returns an |
| * object with the proper scale; the returned object may or may |
| * not be newly allocated. |
| * |
| * @param newScale scale of the {@code BigDecimal} value to be returned. |
| * @return a {@code BigDecimal} whose scale is the specified value, and |
| * whose unscaled value is determined by multiplying or dividing |
| * this {@code BigDecimal}'s unscaled value by the appropriate |
| * power of ten to maintain its overall value. |
| * @throws ArithmeticException if the specified scaling operation would |
| * require rounding. |
| * @see #setScale(int, int) |
| * @see #setScale(int, RoundingMode) |
| */ |
| public BigDecimal setScale(int newScale) { |
| return setScale(newScale, ROUND_UNNECESSARY); |
| } |
| |
| // Decimal Point Motion Operations |
| |
| /** |
| * Returns a {@code BigDecimal} which is equivalent to this one |
| * with the decimal point moved {@code n} places to the left. If |
| * {@code n} is non-negative, the call merely adds {@code n} to |
| * the scale. If {@code n} is negative, the call is equivalent |
| * to {@code movePointRight(-n)}. The {@code BigDecimal} |
| * returned by this call has value <code>(this × |
| * 10<sup>-n</sup>)</code> and scale {@code max(this.scale()+n, |
| * 0)}. |
| * |
| * @param n number of places to move the decimal point to the left. |
| * @return a {@code BigDecimal} which is equivalent to this one with the |
| * decimal point moved {@code n} places to the left. |
| * @throws ArithmeticException if scale overflows. |
| */ |
| public BigDecimal movePointLeft(int n) { |
| // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE |
| int newScale = checkScale((long)scale + n); |
| BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0); |
| return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num; |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} which is equivalent to this one |
| * with the decimal point moved {@code n} places to the right. |
| * If {@code n} is non-negative, the call merely subtracts |
| * {@code n} from the scale. If {@code n} is negative, the call |
| * is equivalent to {@code movePointLeft(-n)}. The |
| * {@code BigDecimal} returned by this call has value <code>(this |
| * × 10<sup>n</sup>)</code> and scale {@code max(this.scale()-n, |
| * 0)}. |
| * |
| * @param n number of places to move the decimal point to the right. |
| * @return a {@code BigDecimal} which is equivalent to this one |
| * with the decimal point moved {@code n} places to the right. |
| * @throws ArithmeticException if scale overflows. |
| */ |
| public BigDecimal movePointRight(int n) { |
| // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE |
| int newScale = checkScale((long)scale - n); |
| BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0); |
| return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num; |
| } |
| |
| /** |
| * Returns a BigDecimal whose numerical value is equal to |
| * ({@code this} * 10<sup>n</sup>). The scale of |
| * the result is {@code (this.scale() - n)}. |
| * |
| * @param n the exponent power of ten to scale by |
| * @return a BigDecimal whose numerical value is equal to |
| * ({@code this} * 10<sup>n</sup>) |
| * @throws ArithmeticException if the scale would be |
| * outside the range of a 32-bit integer. |
| * |
| * @since 1.5 |
| */ |
| public BigDecimal scaleByPowerOfTen(int n) { |
| return new BigDecimal(intVal, intCompact, |
| checkScale((long)scale - n), precision); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} which is numerically equal to |
| * this one but with any trailing zeros removed from the |
| * representation. For example, stripping the trailing zeros from |
| * the {@code BigDecimal} value {@code 600.0}, which has |
| * [{@code BigInteger}, {@code scale}] components equals to |
| * [6000, 1], yields {@code 6E2} with [{@code BigInteger}, |
| * {@code scale}] components equals to [6, -2]. If |
| * this BigDecimal is numerically equal to zero, then |
| * {@code BigDecimal.ZERO} is returned. |
| * |
| * @return a numerically equal {@code BigDecimal} with any |
| * trailing zeros removed. |
| * @since 1.5 |
| */ |
| public BigDecimal stripTrailingZeros() { |
| if (intCompact == 0 || (intVal != null && intVal.signum() == 0)) { |
| return BigDecimal.ZERO; |
| } else if (intCompact != INFLATED) { |
| return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE); |
| } else { |
| return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE); |
| } |
| } |
| |
| // Comparison Operations |
| |
| /** |
| * Compares this {@code BigDecimal} with the specified |
| * {@code BigDecimal}. Two {@code BigDecimal} objects that are |
| * equal in value but have a different scale (like 2.0 and 2.00) |
| * are considered equal by this method. This method is provided |
| * in preference to individual methods for each of the six boolean |
| * comparison operators ({@literal <}, ==, |
| * {@literal >}, {@literal >=}, !=, {@literal <=}). The |
| * suggested idiom for performing these comparisons is: |
| * {@code (x.compareTo(y)} <<i>op</i>> {@code 0)}, where |
| * <<i>op</i>> is one of the six comparison operators. |
| * |
| * @param val {@code BigDecimal} to which this {@code BigDecimal} is |
| * to be compared. |
| * @return -1, 0, or 1 as this {@code BigDecimal} is numerically |
| * less than, equal to, or greater than {@code val}. |
| */ |
| @Override |
| public int compareTo(BigDecimal val) { |
| // Quick path for equal scale and non-inflated case. |
| if (scale == val.scale) { |
| long xs = intCompact; |
| long ys = val.intCompact; |
| if (xs != INFLATED && ys != INFLATED) |
| return xs != ys ? ((xs > ys) ? 1 : -1) : 0; |
| } |
| int xsign = this.signum(); |
| int ysign = val.signum(); |
| if (xsign != ysign) |
| return (xsign > ysign) ? 1 : -1; |
| if (xsign == 0) |
| return 0; |
| int cmp = compareMagnitude(val); |
| return (xsign > 0) ? cmp : -cmp; |
| } |
| |
| /** |
| * Version of compareTo that ignores sign. |
| */ |
| private int compareMagnitude(BigDecimal val) { |
| // Match scales, avoid unnecessary inflation |
| long ys = val.intCompact; |
| long xs = this.intCompact; |
| if (xs == 0) |
| return (ys == 0) ? 0 : -1; |
| if (ys == 0) |
| return 1; |
| |
| long sdiff = (long)this.scale - val.scale; |
| if (sdiff != 0) { |
| // Avoid matching scales if the (adjusted) exponents differ |
| long xae = (long)this.precision() - this.scale; // [-1] |
| long yae = (long)val.precision() - val.scale; // [-1] |
| if (xae < yae) |
| return -1; |
| if (xae > yae) |
| return 1; |
| if (sdiff < 0) { |
| // The cases sdiff <= Integer.MIN_VALUE intentionally fall through. |
| if ( sdiff > Integer.MIN_VALUE && |
| (xs == INFLATED || |
| (xs = longMultiplyPowerTen(xs, (int)-sdiff)) == INFLATED) && |
| ys == INFLATED) { |
| BigInteger rb = bigMultiplyPowerTen((int)-sdiff); |
| return rb.compareMagnitude(val.intVal); |
| } |
| } else { // sdiff > 0 |
| // The cases sdiff > Integer.MAX_VALUE intentionally fall through. |
| if ( sdiff <= Integer.MAX_VALUE && |
| (ys == INFLATED || |
| (ys = longMultiplyPowerTen(ys, (int)sdiff)) == INFLATED) && |
| xs == INFLATED) { |
| BigInteger rb = val.bigMultiplyPowerTen((int)sdiff); |
| return this.intVal.compareMagnitude(rb); |
| } |
| } |
| } |
| if (xs != INFLATED) |
| return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1; |
| else if (ys != INFLATED) |
| return 1; |
| else |
| return this.intVal.compareMagnitude(val.intVal); |
| } |
| |
| /** |
| * Compares this {@code BigDecimal} with the specified |
| * {@code Object} for equality. Unlike {@link |
| * #compareTo(BigDecimal) compareTo}, this method considers two |
| * {@code BigDecimal} objects equal only if they are equal in |
| * value and scale (thus 2.0 is not equal to 2.00 when compared by |
| * this method). |
| * |
| * @param x {@code Object} to which this {@code BigDecimal} is |
| * to be compared. |
| * @return {@code true} if and only if the specified {@code Object} is a |
| * {@code BigDecimal} whose value and scale are equal to this |
| * {@code BigDecimal}'s. |
| * @see #compareTo(java.math.BigDecimal) |
| * @see #hashCode |
| */ |
| @Override |
| public boolean equals(Object x) { |
| if (!(x instanceof BigDecimal)) |
| return false; |
| BigDecimal xDec = (BigDecimal) x; |
| if (x == this) |
| return true; |
| if (scale != xDec.scale) |
| return false; |
| long s = this.intCompact; |
| long xs = xDec.intCompact; |
| if (s != INFLATED) { |
| if (xs == INFLATED) |
| xs = compactValFor(xDec.intVal); |
| return xs == s; |
| } else if (xs != INFLATED) |
| return xs == compactValFor(this.intVal); |
| |
| return this.inflated().equals(xDec.inflated()); |
| } |
| |
| /** |
| * Returns the minimum of this {@code BigDecimal} and |
| * {@code val}. |
| * |
| * @param val value with which the minimum is to be computed. |
| * @return the {@code BigDecimal} whose value is the lesser of this |
| * {@code BigDecimal} and {@code val}. If they are equal, |
| * as defined by the {@link #compareTo(BigDecimal) compareTo} |
| * method, {@code this} is returned. |
| * @see #compareTo(java.math.BigDecimal) |
| */ |
| public BigDecimal min(BigDecimal val) { |
| return (compareTo(val) <= 0 ? this : val); |
| } |
| |
| /** |
| * Returns the maximum of this {@code BigDecimal} and {@code val}. |
| * |
| * @param val value with which the maximum is to be computed. |
| * @return the {@code BigDecimal} whose value is the greater of this |
| * {@code BigDecimal} and {@code val}. If they are equal, |
| * as defined by the {@link #compareTo(BigDecimal) compareTo} |
| * method, {@code this} is returned. |
| * @see #compareTo(java.math.BigDecimal) |
| */ |
| public BigDecimal max(BigDecimal val) { |
| return (compareTo(val) >= 0 ? this : val); |
| } |
| |
| // Hash Function |
| |
| /** |
| * Returns the hash code for this {@code BigDecimal}. Note that |
| * two {@code BigDecimal} objects that are numerically equal but |
| * differ in scale (like 2.0 and 2.00) will generally <em>not</em> |
| * have the same hash code. |
| * |
| * @return hash code for this {@code BigDecimal}. |
| * @see #equals(Object) |
| */ |
| @Override |
| public int hashCode() { |
| if (intCompact != INFLATED) { |
| long val2 = (intCompact < 0)? -intCompact : intCompact; |
| int temp = (int)( ((int)(val2 >>> 32)) * 31 + |
| (val2 & LONG_MASK)); |
| return 31*((intCompact < 0) ?-temp:temp) + scale; |
| } else |
| return 31*intVal.hashCode() + scale; |
| } |
| |
| // Format Converters |
| |
| /** |
| * Returns the string representation of this {@code BigDecimal}, |
| * using scientific notation if an exponent is needed. |
| * |
| * <p>A standard canonical string form of the {@code BigDecimal} |
| * is created as though by the following steps: first, the |
| * absolute value of the unscaled value of the {@code BigDecimal} |
| * is converted to a string in base ten using the characters |
| * {@code '0'} through {@code '9'} with no leading zeros (except |
| * if its value is zero, in which case a single {@code '0'} |
| * character is used). |
| * |
| * <p>Next, an <i>adjusted exponent</i> is calculated; this is the |
| * negated scale, plus the number of characters in the converted |
| * unscaled value, less one. That is, |
| * {@code -scale+(ulength-1)}, where {@code ulength} is the |
| * length of the absolute value of the unscaled value in decimal |
| * digits (its <i>precision</i>). |
| * |
| * <p>If the scale is greater than or equal to zero and the |
| * adjusted exponent is greater than or equal to {@code -6}, the |
| * number will be converted to a character form without using |
| * exponential notation. In this case, if the scale is zero then |
| * no decimal point is added and if the scale is positive a |
| * decimal point will be inserted with the scale specifying the |
| * number of characters to the right of the decimal point. |
| * {@code '0'} characters are added to the left of the converted |
| * unscaled value as necessary. If no character precedes the |
| * decimal point after this insertion then a conventional |
| * {@code '0'} character is prefixed. |
| * |
| * <p>Otherwise (that is, if the scale is negative, or the |
| * adjusted exponent is less than {@code -6}), the number will be |
| * converted to a character form using exponential notation. In |
| * this case, if the converted {@code BigInteger} has more than |
| * one digit a decimal point is inserted after the first digit. |
| * An exponent in character form is then suffixed to the converted |
| * unscaled value (perhaps with inserted decimal point); this |
| * comprises the letter {@code 'E'} followed immediately by the |
| * adjusted exponent converted to a character form. The latter is |
| * in base ten, using the characters {@code '0'} through |
| * {@code '9'} with no leading zeros, and is always prefixed by a |
| * sign character {@code '-'} (<code>'\u002D'</code>) if the |
| * adjusted exponent is negative, {@code '+'} |
| * (<code>'\u002B'</code>) otherwise). |
| * |
| * <p>Finally, the entire string is prefixed by a minus sign |
| * character {@code '-'} (<code>'\u002D'</code>) if the unscaled |
| * value is less than zero. No sign character is prefixed if the |
| * unscaled value is zero or positive. |
| * |
| * <p><b>Examples:</b> |
| * <p>For each representation [<i>unscaled value</i>, <i>scale</i>] |
| * on the left, the resulting string is shown on the right. |
| * <pre> |
| * [123,0] "123" |
| * [-123,0] "-123" |
| * [123,-1] "1.23E+3" |
| * [123,-3] "1.23E+5" |
| * [123,1] "12.3" |
| * [123,5] "0.00123" |
| * [123,10] "1.23E-8" |
| * [-123,12] "-1.23E-10" |
| * </pre> |
| * |
| * <b>Notes:</b> |
| * <ol> |
| * |
| * <li>There is a one-to-one mapping between the distinguishable |
| * {@code BigDecimal} values and the result of this conversion. |
| * That is, every distinguishable {@code BigDecimal} value |
| * (unscaled value and scale) has a unique string representation |
| * as a result of using {@code toString}. If that string |
| * representation is converted back to a {@code BigDecimal} using |
| * the {@link #BigDecimal(String)} constructor, then the original |
| * value will be recovered. |
| * |
| * <li>The string produced for a given number is always the same; |
| * it is not affected by locale. This means that it can be used |
| * as a canonical string representation for exchanging decimal |
| * data, or as a key for a Hashtable, etc. Locale-sensitive |
| * number formatting and parsing is handled by the {@link |
| * java.text.NumberFormat} class and its subclasses. |
| * |
| * <li>The {@link #toEngineeringString} method may be used for |
| * presenting numbers with exponents in engineering notation, and the |
| * {@link #setScale(int,RoundingMode) setScale} method may be used for |
| * rounding a {@code BigDecimal} so it has a known number of digits after |
| * the decimal point. |
| * |
| * <li>The digit-to-character mapping provided by |
| * {@code Character.forDigit} is used. |
| * |
| * </ol> |
| * |
| * @return string representation of this {@code BigDecimal}. |
| * @see Character#forDigit |
| * @see #BigDecimal(java.lang.String) |
| */ |
| @Override |
| public String toString() { |
| String sc = stringCache; |
| if (sc == null) { |
| stringCache = sc = layoutChars(true); |
| } |
| return sc; |
| } |
| |
| /** |
| * Returns a string representation of this {@code BigDecimal}, |
| * using engineering notation if an exponent is needed. |
| * |
| * <p>Returns a string that represents the {@code BigDecimal} as |
| * described in the {@link #toString()} method, except that if |
| * exponential notation is used, the power of ten is adjusted to |
| * be a multiple of three (engineering notation) such that the |
| * integer part of nonzero values will be in the range 1 through |
| * 999. If exponential notation is used for zero values, a |
| * decimal point and one or two fractional zero digits are used so |
| * that the scale of the zero value is preserved. Note that |
| * unlike the output of {@link #toString()}, the output of this |
| * method is <em>not</em> guaranteed to recover the same [integer, |
| * scale] pair of this {@code BigDecimal} if the output string is |
| * converting back to a {@code BigDecimal} using the {@linkplain |
| * #BigDecimal(String) string constructor}. The result of this method meets |
| * the weaker constraint of always producing a numerically equal |
| * result from applying the string constructor to the method's output. |
| * |
| * @return string representation of this {@code BigDecimal}, using |
| * engineering notation if an exponent is needed. |
| * @since 1.5 |
| */ |
| public String toEngineeringString() { |
| return layoutChars(false); |
| } |
| |
| /** |
| * Returns a string representation of this {@code BigDecimal} |
| * without an exponent field. For values with a positive scale, |
| * the number of digits to the right of the decimal point is used |
| * to indicate scale. For values with a zero or negative scale, |
| * the resulting string is generated as if the value were |
| * converted to a numerically equal value with zero scale and as |
| * if all the trailing zeros of the zero scale value were present |
| * in the result. |
| * |
| * The entire string is prefixed by a minus sign character '-' |
| * (<code>'\u002D'</code>) if the unscaled value is less than |
| * zero. No sign character is prefixed if the unscaled value is |
| * zero or positive. |
| * |
| * Note that if the result of this method is passed to the |
| * {@linkplain #BigDecimal(String) string constructor}, only the |
| * numerical value of this {@code BigDecimal} will necessarily be |
| * recovered; the representation of the new {@code BigDecimal} |
| * may have a different scale. In particular, if this |
| * {@code BigDecimal} has a negative scale, the string resulting |
| * from this method will have a scale of zero when processed by |
| * the string constructor. |
| * |
| * (This method behaves analogously to the {@code toString} |
| * method in 1.4 and earlier releases.) |
| * |
| * @return a string representation of this {@code BigDecimal} |
| * without an exponent field. |
| * @since 1.5 |
| * @see #toString() |
| * @see #toEngineeringString() |
| */ |
| public String toPlainString() { |
| if(scale==0) { |
| if(intCompact!=INFLATED) { |
| return Long.toString(intCompact); |
| } else { |
| return intVal.toString(); |
| } |
| } |
| if(this.scale<0) { // No decimal point |
| if(signum()==0) { |
| return "0"; |
| } |
| int trailingZeros = checkScaleNonZero((-(long)scale)); |
| StringBuilder buf; |
| if(intCompact!=INFLATED) { |
| buf = new StringBuilder(20+trailingZeros); |
| buf.append(intCompact); |
| } else { |
| String str = intVal.toString(); |
| buf = new StringBuilder(str.length()+trailingZeros); |
| buf.append(str); |
| } |
| for (int i = 0; i < trailingZeros; i++) { |
| buf.append('0'); |
| } |
| return buf.toString(); |
| } |
| String str ; |
| if(intCompact!=INFLATED) { |
| str = Long.toString(Math.abs(intCompact)); |
| } else { |
| str = intVal.abs().toString(); |
| } |
| return getValueString(signum(), str, scale); |
| } |
| |
| /* Returns a digit.digit string */ |
| private String getValueString(int signum, String intString, int scale) { |
| /* Insert decimal point */ |
| StringBuilder buf; |
| int insertionPoint = intString.length() - scale; |
| if (insertionPoint == 0) { /* Point goes right before intVal */ |
| return (signum<0 ? "-0." : "0.") + intString; |
| } else if (insertionPoint > 0) { /* Point goes inside intVal */ |
| buf = new StringBuilder(intString); |
| buf.insert(insertionPoint, '.'); |
| if (signum < 0) |
| buf.insert(0, '-'); |
| } else { /* We must insert zeros between point and intVal */ |
| buf = new StringBuilder(3-insertionPoint + intString.length()); |
| buf.append(signum<0 ? "-0." : "0."); |
| for (int i=0; i<-insertionPoint; i++) { |
| buf.append('0'); |
| } |
| buf.append(intString); |
| } |
| return buf.toString(); |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code BigInteger}. |
| * This conversion is analogous to the |
| * <i>narrowing primitive conversion</i> from {@code double} to |
| * {@code long} as defined in |
| * <cite>The Java™ Language Specification</cite>: |
| * any fractional part of this |
| * {@code BigDecimal} will be discarded. Note that this |
| * conversion can lose information about the precision of the |
| * {@code BigDecimal} value. |
| * <p> |
| * To have an exception thrown if the conversion is inexact (in |
| * other words if a nonzero fractional part is discarded), use the |
| * {@link #toBigIntegerExact()} method. |
| * |
| * @return this {@code BigDecimal} converted to a {@code BigInteger}. |
| * @jls 5.1.3 Narrowing Primitive Conversion |
| */ |
| public BigInteger toBigInteger() { |
| // force to an integer, quietly |
| return this.setScale(0, ROUND_DOWN).inflated(); |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code BigInteger}, |
| * checking for lost information. An exception is thrown if this |
| * {@code BigDecimal} has a nonzero fractional part. |
| * |
| * @return this {@code BigDecimal} converted to a {@code BigInteger}. |
| * @throws ArithmeticException if {@code this} has a nonzero |
| * fractional part. |
| * @since 1.5 |
| */ |
| public BigInteger toBigIntegerExact() { |
| // round to an integer, with Exception if decimal part non-0 |
| return this.setScale(0, ROUND_UNNECESSARY).inflated(); |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code long}. |
| * This conversion is analogous to the |
| * <i>narrowing primitive conversion</i> from {@code double} to |
| * {@code short} as defined in |
| * <cite>The Java™ Language Specification</cite>: |
| * any fractional part of this |
| * {@code BigDecimal} will be discarded, and if the resulting |
| * "{@code BigInteger}" is too big to fit in a |
| * {@code long}, only the low-order 64 bits are returned. |
| * Note that this conversion can lose information about the |
| * overall magnitude and precision of this {@code BigDecimal} value as well |
| * as return a result with the opposite sign. |
| * |
| * @return this {@code BigDecimal} converted to a {@code long}. |
| * @jls 5.1.3 Narrowing Primitive Conversion |
| */ |
| @Override |
| public long longValue(){ |
| return (intCompact != INFLATED && scale == 0) ? |
| intCompact: |
| toBigInteger().longValue(); |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code long}, checking |
| * for lost information. If this {@code BigDecimal} has a |
| * nonzero fractional part or is out of the possible range for a |
| * {@code long} result then an {@code ArithmeticException} is |
| * thrown. |
| * |
| * @return this {@code BigDecimal} converted to a {@code long}. |
| * @throws ArithmeticException if {@code this} has a nonzero |
| * fractional part, or will not fit in a {@code long}. |
| * @since 1.5 |
| */ |
| public long longValueExact() { |
| if (intCompact != INFLATED && scale == 0) |
| return intCompact; |
| // If more than 19 digits in integer part it cannot possibly fit |
| if ((precision() - scale) > 19) // [OK for negative scale too] |
| throw new java.lang.ArithmeticException("Overflow"); |
| // Fastpath zero and < 1.0 numbers (the latter can be very slow |
| // to round if very small) |
| if (this.signum() == 0) |
| return 0; |
| if ((this.precision() - this.scale) <= 0) |
| throw new ArithmeticException("Rounding necessary"); |
| // round to an integer, with Exception if decimal part non-0 |
| BigDecimal num = this.setScale(0, ROUND_UNNECESSARY); |
| if (num.precision() >= 19) // need to check carefully |
| LongOverflow.check(num); |
| return num.inflated().longValue(); |
| } |
| |
| private static class LongOverflow { |
| /** BigInteger equal to Long.MIN_VALUE. */ |
| private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE); |
| |
| /** BigInteger equal to Long.MAX_VALUE. */ |
| private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE); |
| |
| public static void check(BigDecimal num) { |
| BigInteger intVal = num.inflated(); |
| if (intVal.compareTo(LONGMIN) < 0 || |
| intVal.compareTo(LONGMAX) > 0) |
| throw new java.lang.ArithmeticException("Overflow"); |
| } |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to an {@code int}. |
| * This conversion is analogous to the |
| * <i>narrowing primitive conversion</i> from {@code double} to |
| * {@code short} as defined in |
| * <cite>The Java™ Language Specification</cite>: |
| * any fractional part of this |
| * {@code BigDecimal} will be discarded, and if the resulting |
| * "{@code BigInteger}" is too big to fit in an |
| * {@code int}, only the low-order 32 bits are returned. |
| * Note that this conversion can lose information about the |
| * overall magnitude and precision of this {@code BigDecimal} |
| * value as well as return a result with the opposite sign. |
| * |
| * @return this {@code BigDecimal} converted to an {@code int}. |
| * @jls 5.1.3 Narrowing Primitive Conversion |
| */ |
| @Override |
| public int intValue() { |
| return (intCompact != INFLATED && scale == 0) ? |
| (int)intCompact : |
| toBigInteger().intValue(); |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to an {@code int}, checking |
| * for lost information. If this {@code BigDecimal} has a |
| * nonzero fractional part or is out of the possible range for an |
| * {@code int} result then an {@code ArithmeticException} is |
| * thrown. |
| * |
| * @return this {@code BigDecimal} converted to an {@code int}. |
| * @throws ArithmeticException if {@code this} has a nonzero |
| * fractional part, or will not fit in an {@code int}. |
| * @since 1.5 |
| */ |
| public int intValueExact() { |
| long num; |
| num = this.longValueExact(); // will check decimal part |
| if ((int)num != num) |
| throw new java.lang.ArithmeticException("Overflow"); |
| return (int)num; |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code short}, checking |
| * for lost information. If this {@code BigDecimal} has a |
| * nonzero fractional part or is out of the possible range for a |
| * {@code short} result then an {@code ArithmeticException} is |
| * thrown. |
| * |
| * @return this {@code BigDecimal} converted to a {@code short}. |
| * @throws ArithmeticException if {@code this} has a nonzero |
| * fractional part, or will not fit in a {@code short}. |
| * @since 1.5 |
| */ |
| public short shortValueExact() { |
| long num; |
| num = this.longValueExact(); // will check decimal part |
| if ((short)num != num) |
| throw new java.lang.ArithmeticException("Overflow"); |
| return (short)num; |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code byte}, checking |
| * for lost information. If this {@code BigDecimal} has a |
| * nonzero fractional part or is out of the possible range for a |
| * {@code byte} result then an {@code ArithmeticException} is |
| * thrown. |
| * |
| * @return this {@code BigDecimal} converted to a {@code byte}. |
| * @throws ArithmeticException if {@code this} has a nonzero |
| * fractional part, or will not fit in a {@code byte}. |
| * @since 1.5 |
| */ |
| public byte byteValueExact() { |
| long num; |
| num = this.longValueExact(); // will check decimal part |
| if ((byte)num != num) |
| throw new java.lang.ArithmeticException("Overflow"); |
| return (byte)num; |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code float}. |
| * This conversion is similar to the |
| * <i>narrowing primitive conversion</i> from {@code double} to |
| * {@code float} as defined in |
| * <cite>The Java™ Language Specification</cite>: |
| * if this {@code BigDecimal} has too great a |
| * magnitude to represent as a {@code float}, it will be |
| * converted to {@link Float#NEGATIVE_INFINITY} or {@link |
| * Float#POSITIVE_INFINITY} as appropriate. Note that even when |
| * the return value is finite, this conversion can lose |
| * information about the precision of the {@code BigDecimal} |
| * value. |
| * |
| * @return this {@code BigDecimal} converted to a {@code float}. |
| * @jls 5.1.3 Narrowing Primitive Conversion |
| */ |
| @Override |
| public float floatValue(){ |
| if(intCompact != INFLATED) { |
| if (scale == 0) { |
| return (float)intCompact; |
| } else { |
| /* |
| * If both intCompact and the scale can be exactly |
| * represented as float values, perform a single float |
| * multiply or divide to compute the (properly |
| * rounded) result. |
| */ |
| if (Math.abs(intCompact) < 1L<<22 ) { |
| // Don't have too guard against |
| // Math.abs(MIN_VALUE) because of outer check |
| // against INFLATED. |
| if (scale > 0 && scale < FLOAT_10_POW.length) { |
| return (float)intCompact / FLOAT_10_POW[scale]; |
| } else if (scale < 0 && scale > -FLOAT_10_POW.length) { |
| return (float)intCompact * FLOAT_10_POW[-scale]; |
| } |
| } |
| } |
| } |
| // Somewhat inefficient, but guaranteed to work. |
| return Float.parseFloat(this.toString()); |
| } |
| |
| /** |
| * Converts this {@code BigDecimal} to a {@code double}. |
| * This conversion is similar to the |
| * <i>narrowing primitive conversion</i> from {@code double} to |
| * {@code float} as defined in |
| * <cite>The Java™ Language Specification</cite>: |
| * if this {@code BigDecimal} has too great a |
| * magnitude represent as a {@code double}, it will be |
| * converted to {@link Double#NEGATIVE_INFINITY} or {@link |
| * Double#POSITIVE_INFINITY} as appropriate. Note that even when |
| * the return value is finite, this conversion can lose |
| * information about the precision of the {@code BigDecimal} |
| * value. |
| * |
| * @return this {@code BigDecimal} converted to a {@code double}. |
| * @jls 5.1.3 Narrowing Primitive Conversion |
| */ |
| @Override |
| public double doubleValue(){ |
| if(intCompact != INFLATED) { |
| if (scale == 0) { |
| return (double)intCompact; |
| } else { |
| /* |
| * If both intCompact and the scale can be exactly |
| * represented as double values, perform a single |
| * double multiply or divide to compute the (properly |
| * rounded) result. |
| */ |
| if (Math.abs(intCompact) < 1L<<52 ) { |
| // Don't have too guard against |
| // Math.abs(MIN_VALUE) because of outer check |
| // against INFLATED. |
| if (scale > 0 && scale < DOUBLE_10_POW.length) { |
| return (double)intCompact / DOUBLE_10_POW[scale]; |
| } else if (scale < 0 && scale > -DOUBLE_10_POW.length) { |
| return (double)intCompact * DOUBLE_10_POW[-scale]; |
| } |
| } |
| } |
| } |
| // Somewhat inefficient, but guaranteed to work. |
| return Double.parseDouble(this.toString()); |
| } |
| |
| /** |
| * Powers of 10 which can be represented exactly in {@code |
| * double}. |
| */ |
| private static final double DOUBLE_10_POW[] = { |
| 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5, |
| 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11, |
| 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17, |
| 1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22 |
| }; |
| |
| /** |
| * Powers of 10 which can be represented exactly in {@code |
| * float}. |
| */ |
| private static final float FLOAT_10_POW[] = { |
| 1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f, |
| 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f |
| }; |
| |
| /** |
| * Returns the size of an ulp, a unit in the last place, of this |
| * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal} |
| * value is the positive distance between this value and the |
| * {@code BigDecimal} value next larger in magnitude with the |
| * same number of digits. An ulp of a zero value is numerically |
| * equal to 1 with the scale of {@code this}. The result is |
| * stored with the same scale as {@code this} so the result |
| * for zero and nonzero values is equal to {@code [1, |
| * this.scale()]}. |
| * |
| * @return the size of an ulp of {@code this} |
| * @since 1.5 |
| */ |
| public BigDecimal ulp() { |
| return BigDecimal.valueOf(1, this.scale(), 1); |
| } |
| |
| // Private class to build a string representation for BigDecimal object. |
| // "StringBuilderHelper" is constructed as a thread local variable so it is |
| // thread safe. The StringBuilder field acts as a buffer to hold the temporary |
| // representation of BigDecimal. The cmpCharArray holds all the characters for |
| // the compact representation of BigDecimal (except for '-' sign' if it is |
| // negative) if its intCompact field is not INFLATED. It is shared by all |
| // calls to toString() and its variants in that particular thread. |
| static class StringBuilderHelper { |
| final StringBuilder sb; // Placeholder for BigDecimal string |
| final char[] cmpCharArray; // character array to place the intCompact |
| |
| StringBuilderHelper() { |
| sb = new StringBuilder(); |
| // All non negative longs can be made to fit into 19 character array. |
| cmpCharArray = new char[19]; |
| } |
| |
| // Accessors. |
| StringBuilder getStringBuilder() { |
| sb.setLength(0); |
| return sb; |
| } |
| |
| char[] getCompactCharArray() { |
| return cmpCharArray; |
| } |
| |
| /** |
| * Places characters representing the intCompact in {@code long} into |
| * cmpCharArray and returns the offset to the array where the |
| * representation starts. |
| * |
| * @param intCompact the number to put into the cmpCharArray. |
| * @return offset to the array where the representation starts. |
| * Note: intCompact must be greater or equal to zero. |
| */ |
| int putIntCompact(long intCompact) { |
| assert intCompact >= 0; |
| |
| long q; |
| int r; |
| // since we start from the least significant digit, charPos points to |
| // the last character in cmpCharArray. |
| int charPos = cmpCharArray.length; |
| |
| // Get 2 digits/iteration using longs until quotient fits into an int |
| while (intCompact > Integer.MAX_VALUE) { |
| q = intCompact / 100; |
| r = (int)(intCompact - q * 100); |
| intCompact = q; |
| cmpCharArray[--charPos] = DIGIT_ONES[r]; |
| cmpCharArray[--charPos] = DIGIT_TENS[r]; |
| } |
| |
| // Get 2 digits/iteration using ints when i2 >= 100 |
| int q2; |
| int i2 = (int)intCompact; |
| while (i2 >= 100) { |
| q2 = i2 / 100; |
| r = i2 - q2 * 100; |
| i2 = q2; |
| cmpCharArray[--charPos] = DIGIT_ONES[r]; |
| cmpCharArray[--charPos] = DIGIT_TENS[r]; |
| } |
| |
| cmpCharArray[--charPos] = DIGIT_ONES[i2]; |
| if (i2 >= 10) |
| cmpCharArray[--charPos] = DIGIT_TENS[i2]; |
| |
| return charPos; |
| } |
| |
| static final char[] DIGIT_TENS = { |
| '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', |
| '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', |
| '2', '2', '2', '2', '2', '2', '2', '2', '2', '2', |
| '3', '3', '3', '3', '3', '3', '3', '3', '3', '3', |
| '4', '4', '4', '4', '4', '4', '4', '4', '4', '4', |
| '5', '5', '5', '5', '5', '5', '5', '5', '5', '5', |
| '6', '6', '6', '6', '6', '6', '6', '6', '6', '6', |
| '7', '7', '7', '7', '7', '7', '7', '7', '7', '7', |
| '8', '8', '8', '8', '8', '8', '8', '8', '8', '8', |
| '9', '9', '9', '9', '9', '9', '9', '9', '9', '9', |
| }; |
| |
| static final char[] DIGIT_ONES = { |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', |
| }; |
| } |
| |
| /** |
| * Lay out this {@code BigDecimal} into a {@code char[]} array. |
| * The Java 1.2 equivalent to this was called {@code getValueString}. |
| * |
| * @param sci {@code true} for Scientific exponential notation; |
| * {@code false} for Engineering |
| * @return string with canonical string representation of this |
| * {@code BigDecimal} |
| */ |
| private String layoutChars(boolean sci) { |
| if (scale == 0) // zero scale is trivial |
| return (intCompact != INFLATED) ? |
| Long.toString(intCompact): |
| intVal.toString(); |
| if (scale == 2 && |
| intCompact >= 0 && intCompact < Integer.MAX_VALUE) { |
| // currency fast path |
| int lowInt = (int)intCompact % 100; |
| int highInt = (int)intCompact / 100; |
| return (Integer.toString(highInt) + '.' + |
| StringBuilderHelper.DIGIT_TENS[lowInt] + |
| StringBuilderHelper.DIGIT_ONES[lowInt]) ; |
| } |
| |
| StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get(); |
| char[] coeff; |
| int offset; // offset is the starting index for coeff array |
| // Get the significand as an absolute value |
| if (intCompact != INFLATED) { |
| offset = sbHelper.putIntCompact(Math.abs(intCompact)); |
| coeff = sbHelper.getCompactCharArray(); |
| } else { |
| offset = 0; |
| coeff = intVal.abs().toString().toCharArray(); |
| } |
| |
| // Construct a buffer, with sufficient capacity for all cases. |
| // If E-notation is needed, length will be: +1 if negative, +1 |
| // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent. |
| // Otherwise it could have +1 if negative, plus leading "0.00000" |
| StringBuilder buf = sbHelper.getStringBuilder(); |
| if (signum() < 0) // prefix '-' if negative |
| buf.append('-'); |
| int coeffLen = coeff.length - offset; |
| long adjusted = -(long)scale + (coeffLen -1); |
| if ((scale >= 0) && (adjusted >= -6)) { // plain number |
| int pad = scale - coeffLen; // count of padding zeros |
| if (pad >= 0) { // 0.xxx form |
| buf.append('0'); |
| buf.append('.'); |
| for (; pad>0; pad--) { |
| buf.append('0'); |
| } |
| buf.append(coeff, offset, coeffLen); |
| } else { // xx.xx form |
| buf.append(coeff, offset, -pad); |
| buf.append('.'); |
| buf.append(coeff, -pad + offset, scale); |
| } |
| } else { // E-notation is needed |
| if (sci) { // Scientific notation |
| buf.append(coeff[offset]); // first character |
| if (coeffLen > 1) { // more to come |
| buf.append('.'); |
| buf.append(coeff, offset + 1, coeffLen - 1); |
| } |
| } else { // Engineering notation |
| int sig = (int)(adjusted % 3); |
| if (sig < 0) |
| sig += 3; // [adjusted was negative] |
| adjusted -= sig; // now a multiple of 3 |
| sig++; |
| if (signum() == 0) { |
| switch (sig) { |
| case 1: |
| buf.append('0'); // exponent is a multiple of three |
| break; |
| case 2: |
| buf.append("0.00"); |
| adjusted += 3; |
| break; |
| case 3: |
| buf.append("0.0"); |
| adjusted += 3; |
| break; |
| default: |
| throw new AssertionError("Unexpected sig value " + sig); |
| } |
| } else if (sig >= coeffLen) { // significand all in integer |
| buf.append(coeff, offset, coeffLen); |
| // may need some zeros, too |
| for (int i = sig - coeffLen; i > 0; i--) { |
| buf.append('0'); |
| } |
| } else { // xx.xxE form |
| buf.append(coeff, offset, sig); |
| buf.append('.'); |
| buf.append(coeff, offset + sig, coeffLen - sig); |
| } |
| } |
| if (adjusted != 0) { // [!sci could have made 0] |
| buf.append('E'); |
| if (adjusted > 0) // force sign for positive |
| buf.append('+'); |
| buf.append(adjusted); |
| } |
| } |
| return buf.toString(); |
| } |
| |
| /** |
| * Return 10 to the power n, as a {@code BigInteger}. |
| * |
| * @param n the power of ten to be returned (>=0) |
| * @return a {@code BigInteger} with the value (10<sup>n</sup>) |
| */ |
| private static BigInteger bigTenToThe(int n) { |
| if (n < 0) |
| return BigInteger.ZERO; |
| |
| if (n < BIG_TEN_POWERS_TABLE_MAX) { |
| BigInteger[] pows = BIG_TEN_POWERS_TABLE; |
| if (n < pows.length) |
| return pows[n]; |
| else |
| return expandBigIntegerTenPowers(n); |
| } |
| |
| return BigInteger.TEN.pow(n); |
| } |
| |
| /** |
| * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n. |
| * |
| * @param n the power of ten to be returned (>=0) |
| * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and |
| * in the meantime, the BIG_TEN_POWERS_TABLE array gets |
| * expanded to the size greater than n. |
| */ |
| private static BigInteger expandBigIntegerTenPowers(int n) { |
| synchronized(BigDecimal.class) { |
| BigInteger[] pows = BIG_TEN_POWERS_TABLE; |
| int curLen = pows.length; |
| // The following comparison and the above synchronized statement is |
| // to prevent multiple threads from expanding the same array. |
| if (curLen <= n) { |
| int newLen = curLen << 1; |
| while (newLen <= n) { |
| newLen <<= 1; |
| } |
| pows = Arrays.copyOf(pows, newLen); |
| for (int i = curLen; i < newLen; i++) { |
| pows[i] = pows[i - 1].multiply(BigInteger.TEN); |
| } |
| // Based on the following facts: |
| // 1. pows is a private local varible; |
| // 2. the following store is a volatile store. |
| // the newly created array elements can be safely published. |
| BIG_TEN_POWERS_TABLE = pows; |
| } |
| return pows[n]; |
| } |
| } |
| |
| private static final long[] LONG_TEN_POWERS_TABLE = { |
| 1, // 0 / 10^0 |
| 10, // 1 / 10^1 |
| 100, // 2 / 10^2 |
| 1000, // 3 / 10^3 |
| 10000, // 4 / 10^4 |
| 100000, // 5 / 10^5 |
| 1000000, // 6 / 10^6 |
| 10000000, // 7 / 10^7 |
| 100000000, // 8 / 10^8 |
| 1000000000, // 9 / 10^9 |
| 10000000000L, // 10 / 10^10 |
| 100000000000L, // 11 / 10^11 |
| 1000000000000L, // 12 / 10^12 |
| 10000000000000L, // 13 / 10^13 |
| 100000000000000L, // 14 / 10^14 |
| 1000000000000000L, // 15 / 10^15 |
| 10000000000000000L, // 16 / 10^16 |
| 100000000000000000L, // 17 / 10^17 |
| 1000000000000000000L // 18 / 10^18 |
| }; |
| |
| private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = { |
| BigInteger.ONE, |
| BigInteger.valueOf(10), |
| BigInteger.valueOf(100), |
| BigInteger.valueOf(1000), |
| BigInteger.valueOf(10000), |
| BigInteger.valueOf(100000), |
| BigInteger.valueOf(1000000), |
| BigInteger.valueOf(10000000), |
| BigInteger.valueOf(100000000), |
| BigInteger.valueOf(1000000000), |
| BigInteger.valueOf(10000000000L), |
| BigInteger.valueOf(100000000000L), |
| BigInteger.valueOf(1000000000000L), |
| BigInteger.valueOf(10000000000000L), |
| BigInteger.valueOf(100000000000000L), |
| BigInteger.valueOf(1000000000000000L), |
| BigInteger.valueOf(10000000000000000L), |
| BigInteger.valueOf(100000000000000000L), |
| BigInteger.valueOf(1000000000000000000L) |
| }; |
| |
| private static final int BIG_TEN_POWERS_TABLE_INITLEN = |
| BIG_TEN_POWERS_TABLE.length; |
| private static final int BIG_TEN_POWERS_TABLE_MAX = |
| 16 * BIG_TEN_POWERS_TABLE_INITLEN; |
| |
| private static final long THRESHOLDS_TABLE[] = { |
| Long.MAX_VALUE, // 0 |
| Long.MAX_VALUE/10L, // 1 |
| Long.MAX_VALUE/100L, // 2 |
| Long.MAX_VALUE/1000L, // 3 |
| Long.MAX_VALUE/10000L, // 4 |
| Long.MAX_VALUE/100000L, // 5 |
| Long.MAX_VALUE/1000000L, // 6 |
| Long.MAX_VALUE/10000000L, // 7 |
| Long.MAX_VALUE/100000000L, // 8 |
| Long.MAX_VALUE/1000000000L, // 9 |
| Long.MAX_VALUE/10000000000L, // 10 |
| Long.MAX_VALUE/100000000000L, // 11 |
| Long.MAX_VALUE/1000000000000L, // 12 |
| Long.MAX_VALUE/10000000000000L, // 13 |
| Long.MAX_VALUE/100000000000000L, // 14 |
| Long.MAX_VALUE/1000000000000000L, // 15 |
| Long.MAX_VALUE/10000000000000000L, // 16 |
| Long.MAX_VALUE/100000000000000000L, // 17 |
| Long.MAX_VALUE/1000000000000000000L // 18 |
| }; |
| |
| /** |
| * Compute val * 10 ^ n; return this product if it is |
| * representable as a long, INFLATED otherwise. |
| */ |
| private static long longMultiplyPowerTen(long val, int n) { |
| if (val == 0 || n <= 0) |
| return val; |
| long[] tab = LONG_TEN_POWERS_TABLE; |
| long[] bounds = THRESHOLDS_TABLE; |
| if (n < tab.length && n < bounds.length) { |
| long tenpower = tab[n]; |
| if (val == 1) |
| return tenpower; |
| if (Math.abs(val) <= bounds[n]) |
| return val * tenpower; |
| } |
| return INFLATED; |
| } |
| |
| /** |
| * Compute this * 10 ^ n. |
| * Needed mainly to allow special casing to trap zero value |
| */ |
| private BigInteger bigMultiplyPowerTen(int n) { |
| if (n <= 0) |
| return this.inflated(); |
| |
| if (intCompact != INFLATED) |
| return bigTenToThe(n).multiply(intCompact); |
| else |
| return intVal.multiply(bigTenToThe(n)); |
| } |
| |
| /** |
| * Returns appropriate BigInteger from intVal field if intVal is |
| * null, i.e. the compact representation is in use. |
| */ |
| private BigInteger inflated() { |
| if (intVal == null) { |
| return BigInteger.valueOf(intCompact); |
| } |
| return intVal; |
| } |
| |
| /** |
| * Match the scales of two {@code BigDecimal}s to align their |
| * least significant digits. |
| * |
| * <p>If the scales of val[0] and val[1] differ, rescale |
| * (non-destructively) the lower-scaled {@code BigDecimal} so |
| * they match. That is, the lower-scaled reference will be |
| * replaced by a reference to a new object with the same scale as |
| * the other {@code BigDecimal}. |
| * |
| * @param val array of two elements referring to the two |
| * {@code BigDecimal}s to be aligned. |
| */ |
| private static void matchScale(BigDecimal[] val) { |
| if (val[0].scale < val[1].scale) { |
| val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY); |
| } else if (val[1].scale < val[0].scale) { |
| val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY); |
| } |
| } |
| |
| private static class UnsafeHolder { |
| private static final jdk.internal.misc.Unsafe unsafe |
| = jdk.internal.misc.Unsafe.getUnsafe(); |
| private static final long intCompactOffset |
| = unsafe.objectFieldOffset(BigDecimal.class, "intCompact"); |
| private static final long intValOffset |
| = unsafe.objectFieldOffset(BigDecimal.class, "intVal"); |
| |
| static void setIntCompact(BigDecimal bd, long val) { |
| unsafe.putLong(bd, intCompactOffset, val); |
| } |
| |
| static void setIntValVolatile(BigDecimal bd, BigInteger val) { |
| unsafe.putObjectVolatile(bd, intValOffset, val); |
| } |
| } |
| |
| /** |
| * Reconstitute the {@code BigDecimal} instance from a stream (that is, |
| * deserialize it). |
| * |
| * @param s the stream being read. |
| */ |
| private void readObject(java.io.ObjectInputStream s) |
| throws java.io.IOException, ClassNotFoundException { |
| // Read in all fields |
| s.defaultReadObject(); |
| // validate possibly bad fields |
| if (intVal == null) { |
| String message = "BigDecimal: null intVal in stream"; |
| throw new java.io.StreamCorruptedException(message); |
| // [all values of scale are now allowed] |
| } |
| UnsafeHolder.setIntCompact(this, compactValFor(intVal)); |
| } |
| |
| /** |
| * Serialize this {@code BigDecimal} to the stream in question |
| * |
| * @param s the stream to serialize to. |
| */ |
| private void writeObject(java.io.ObjectOutputStream s) |
| throws java.io.IOException { |
| // Must inflate to maintain compatible serial form. |
| if (this.intVal == null) |
| UnsafeHolder.setIntValVolatile(this, BigInteger.valueOf(this.intCompact)); |
| // Could reset intVal back to null if it has to be set. |
| s.defaultWriteObject(); |
| } |
| |
| /** |
| * Returns the length of the absolute value of a {@code long}, in decimal |
| * digits. |
| * |
| * @param x the {@code long} |
| * @return the length of the unscaled value, in deciaml digits. |
| */ |
| static int longDigitLength(long x) { |
| /* |
| * As described in "Bit Twiddling Hacks" by Sean Anderson, |
| * (http://graphics.stanford.edu/~seander/bithacks.html) |
| * integer log 10 of x is within 1 of (1233/4096)* (1 + |
| * integer log 2 of x). The fraction 1233/4096 approximates |
| * log10(2). So we first do a version of log2 (a variant of |
| * Long class with pre-checks and opposite directionality) and |
| * then scale and check against powers table. This is a little |
| * simpler in present context than the version in Hacker's |
| * Delight sec 11-4. Adding one to bit length allows comparing |
| * downward from the LONG_TEN_POWERS_TABLE that we need |
| * anyway. |
| */ |
| assert x != BigDecimal.INFLATED; |
| if (x < 0) |
| x = -x; |
| if (x < 10) // must screen for 0, might as well 10 |
| return 1; |
| int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12; |
| long[] tab = LONG_TEN_POWERS_TABLE; |
| // if r >= length, must have max possible digits for long |
| return (r >= tab.length || x < tab[r]) ? r : r + 1; |
| } |
| |
| /** |
| * Returns the length of the absolute value of a BigInteger, in |
| * decimal digits. |
| * |
| * @param b the BigInteger |
| * @return the length of the unscaled value, in decimal digits |
| */ |
| private static int bigDigitLength(BigInteger b) { |
| /* |
| * Same idea as the long version, but we need a better |
| * approximation of log10(2). Using 646456993/2^31 |
| * is accurate up to max possible reported bitLength. |
| */ |
| if (b.signum == 0) |
| return 1; |
| int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31); |
| return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1; |
| } |
| |
| /** |
| * Check a scale for Underflow or Overflow. If this BigDecimal is |
| * nonzero, throw an exception if the scale is outof range. If this |
| * is zero, saturate the scale to the extreme value of the right |
| * sign if the scale is out of range. |
| * |
| * @param val The new scale. |
| * @throws ArithmeticException (overflow or underflow) if the new |
| * scale is out of range. |
| * @return validated scale as an int. |
| */ |
| private int checkScale(long val) { |
| int asInt = (int)val; |
| if (asInt != val) { |
| asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE; |
| BigInteger b; |
| if (intCompact != 0 && |
| ((b = intVal) == null || b.signum() != 0)) |
| throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); |
| } |
| return asInt; |
| } |
| |
| /** |
| * Returns the compact value for given {@code BigInteger}, or |
| * INFLATED if too big. Relies on internal representation of |
| * {@code BigInteger}. |
| */ |
| private static long compactValFor(BigInteger b) { |
| int[] m = b.mag; |
| int len = m.length; |
| if (len == 0) |
| return 0; |
| int d = m[0]; |
| if (len > 2 || (len == 2 && d < 0)) |
| return INFLATED; |
| |
| long u = (len == 2)? |
| (((long) m[1] & LONG_MASK) + (((long)d) << 32)) : |
| (((long)d) & LONG_MASK); |
| return (b.signum < 0)? -u : u; |
| } |
| |
| private static int longCompareMagnitude(long x, long y) { |
| if (x < 0) |
| x = -x; |
| if (y < 0) |
| y = -y; |
| return (x < y) ? -1 : ((x == y) ? 0 : 1); |
| } |
| |
| private static int saturateLong(long s) { |
| int i = (int)s; |
| return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE); |
| } |
| |
| /* |
| * Internal printing routine |
| */ |
| private static void print(String name, BigDecimal bd) { |
| System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n", |
| name, |
| bd.intCompact, |
| bd.intVal, |
| bd.scale, |
| bd.precision); |
| } |
| |
| /** |
| * Check internal invariants of this BigDecimal. These invariants |
| * include: |
| * |
| * <ul> |
| * |
| * <li>The object must be initialized; either intCompact must not be |
| * INFLATED or intVal is non-null. Both of these conditions may |
| * be true. |
| * |
| * <li>If both intCompact and intVal and set, their values must be |
| * consistent. |
| * |
| * <li>If precision is nonzero, it must have the right value. |
| * </ul> |
| * |
| * Note: Since this is an audit method, we are not supposed to change the |
| * state of this BigDecimal object. |
| */ |
| private BigDecimal audit() { |
| if (intCompact == INFLATED) { |
| if (intVal == null) { |
| print("audit", this); |
| throw new AssertionError("null intVal"); |
| } |
| // Check precision |
| if (precision > 0 && precision != bigDigitLength(intVal)) { |
| print("audit", this); |
| throw new AssertionError("precision mismatch"); |
| } |
| } else { |
| if (intVal != null) { |
| long val = intVal.longValue(); |
| if (val != intCompact) { |
| print("audit", this); |
| throw new AssertionError("Inconsistent state, intCompact=" + |
| intCompact + "\t intVal=" + val); |
| } |
| } |
| // Check precision |
| if (precision > 0 && precision != longDigitLength(intCompact)) { |
| print("audit", this); |
| throw new AssertionError("precision mismatch"); |
| } |
| } |
| return this; |
| } |
| |
| /* the same as checkScale where value!=0 */ |
| private static int checkScaleNonZero(long val) { |
| int asInt = (int)val; |
| if (asInt != val) { |
| throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); |
| } |
| return asInt; |
| } |
| |
| private static int checkScale(long intCompact, long val) { |
| int asInt = (int)val; |
| if (asInt != val) { |
| asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE; |
| if (intCompact != 0) |
| throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); |
| } |
| return asInt; |
| } |
| |
| private static int checkScale(BigInteger intVal, long val) { |
| int asInt = (int)val; |
| if (asInt != val) { |
| asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE; |
| if (intVal.signum() != 0) |
| throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); |
| } |
| return asInt; |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} rounded according to the MathContext |
| * settings; |
| * If rounding is needed a new {@code BigDecimal} is created and returned. |
| * |
| * @param val the value to be rounded |
| * @param mc the context to use. |
| * @return a {@code BigDecimal} rounded according to the MathContext |
| * settings. May return {@code value}, if no rounding needed. |
| * @throws ArithmeticException if the rounding mode is |
| * {@code RoundingMode.UNNECESSARY} and the |
| * result is inexact. |
| */ |
| private static BigDecimal doRound(BigDecimal val, MathContext mc) { |
| int mcp = mc.precision; |
| boolean wasDivided = false; |
| if (mcp > 0) { |
| BigInteger intVal = val.intVal; |
| long compactVal = val.intCompact; |
| int scale = val.scale; |
| int prec = val.precision(); |
| int mode = mc.roundingMode.oldMode; |
| int drop; |
| if (compactVal == INFLATED) { |
| drop = prec - mcp; |
| while (drop > 0) { |
| scale = checkScaleNonZero((long) scale - drop); |
| intVal = divideAndRoundByTenPow(intVal, drop, mode); |
| wasDivided = true; |
| compactVal = compactValFor(intVal); |
| if (compactVal != INFLATED) { |
| prec = longDigitLength(compactVal); |
| break; |
| } |
| prec = bigDigitLength(intVal); |
| drop = prec - mcp; |
| } |
| } |
| if (compactVal != INFLATED) { |
| drop = prec - mcp; // drop can't be more than 18 |
| while (drop > 0) { |
| scale = checkScaleNonZero((long) scale - drop); |
| compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| wasDivided = true; |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; |
| intVal = null; |
| } |
| } |
| return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val; |
| } |
| return val; |
| } |
| |
| /* |
| * Returns a {@code BigDecimal} created from {@code long} value with |
| * given scale rounded according to the MathContext settings |
| */ |
| private static BigDecimal doRound(long compactVal, int scale, MathContext mc) { |
| int mcp = mc.precision; |
| if (mcp > 0 && mcp < 19) { |
| int prec = longDigitLength(compactVal); |
| int drop = prec - mcp; // drop can't be more than 18 |
| while (drop > 0) { |
| scale = checkScaleNonZero((long) scale - drop); |
| compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; |
| } |
| return valueOf(compactVal, scale, prec); |
| } |
| return valueOf(compactVal, scale); |
| } |
| |
| /* |
| * Returns a {@code BigDecimal} created from {@code BigInteger} value with |
| * given scale rounded according to the MathContext settings |
| */ |
| private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) { |
| int mcp = mc.precision; |
| int prec = 0; |
| if (mcp > 0) { |
| long compactVal = compactValFor(intVal); |
| int mode = mc.roundingMode.oldMode; |
| int drop; |
| if (compactVal == INFLATED) { |
| prec = bigDigitLength(intVal); |
| drop = prec - mcp; |
| while (drop > 0) { |
| scale = checkScaleNonZero((long) scale - drop); |
| intVal = divideAndRoundByTenPow(intVal, drop, mode); |
| compactVal = compactValFor(intVal); |
| if (compactVal != INFLATED) { |
| break; |
| } |
| prec = bigDigitLength(intVal); |
| drop = prec - mcp; |
| } |
| } |
| if (compactVal != INFLATED) { |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; // drop can't be more than 18 |
| while (drop > 0) { |
| scale = checkScaleNonZero((long) scale - drop); |
| compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); |
| prec = longDigitLength(compactVal); |
| drop = prec - mcp; |
| } |
| return valueOf(compactVal,scale,prec); |
| } |
| } |
| return new BigDecimal(intVal,INFLATED,scale,prec); |
| } |
| |
| /* |
| * Divides {@code BigInteger} value by ten power. |
| */ |
| private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) { |
| if (tenPow < LONG_TEN_POWERS_TABLE.length) |
| intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode); |
| else |
| intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode); |
| return intVal; |
| } |
| |
| /** |
| * Internally used for division operation for division {@code long} by |
| * {@code long}. |
| * The returned {@code BigDecimal} object is the quotient whose scale is set |
| * to the passed in scale. If the remainder is not zero, it will be rounded |
| * based on the passed in roundingMode. Also, if the remainder is zero and |
| * the last parameter, i.e. preferredScale is NOT equal to scale, the |
| * trailing zeros of the result is stripped to match the preferredScale. |
| */ |
| private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode, |
| int preferredScale) { |
| |
| int qsign; // quotient sign |
| long q = ldividend / ldivisor; // store quotient in long |
| if (roundingMode == ROUND_DOWN && scale == preferredScale) |
| return valueOf(q, scale); |
| long r = ldividend % ldivisor; // store remainder in long |
| qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1; |
| if (r != 0) { |
| boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r); |
| return valueOf((increment ? q + qsign : q), scale); |
| } else { |
| if (preferredScale != scale) |
| return createAndStripZerosToMatchScale(q, scale, preferredScale); |
| else |
| return valueOf(q, scale); |
| } |
| } |
| |
| /** |
| * Divides {@code long} by {@code long} and do rounding based on the |
| * passed in roundingMode. |
| */ |
| private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) { |
| int qsign; // quotient sign |
| long q = ldividend / ldivisor; // store quotient in long |
| if (roundingMode == ROUND_DOWN) |
| return q; |
| long r = ldividend % ldivisor; // store remainder in long |
| qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1; |
| if (r != 0) { |
| boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r); |
| return increment ? q + qsign : q; |
| } else { |
| return q; |
| } |
| } |
| |
| /** |
| * Shared logic of need increment computation. |
| */ |
| private static boolean commonNeedIncrement(int roundingMode, int qsign, |
| int cmpFracHalf, boolean oddQuot) { |
| switch(roundingMode) { |
| case ROUND_UNNECESSARY: |
| throw new ArithmeticException("Rounding necessary"); |
| |
| case ROUND_UP: // Away from zero |
| return true; |
| |
| case ROUND_DOWN: // Towards zero |
| return false; |
| |
| case ROUND_CEILING: // Towards +infinity |
| return qsign > 0; |
| |
| case ROUND_FLOOR: // Towards -infinity |
| return qsign < 0; |
| |
| default: // Some kind of half-way rounding |
| assert roundingMode >= ROUND_HALF_UP && |
| roundingMode <= ROUND_HALF_EVEN: "Unexpected rounding mode" + RoundingMode.valueOf(roundingMode); |
| |
| if (cmpFracHalf < 0 ) // We're closer to higher digit |
| return false; |
| else if (cmpFracHalf > 0 ) // We're closer to lower digit |
| return true; |
| else { // half-way |
| assert cmpFracHalf == 0; |
| |
| switch(roundingMode) { |
| case ROUND_HALF_DOWN: |
| return false; |
| |
| case ROUND_HALF_UP: |
| return true; |
| |
| case ROUND_HALF_EVEN: |
| return oddQuot; |
| |
| default: |
| throw new AssertionError("Unexpected rounding mode" + roundingMode); |
| } |
| } |
| } |
| } |
| |
| /** |
| * Tests if quotient has to be incremented according the roundingMode |
| */ |
| private static boolean needIncrement(long ldivisor, int roundingMode, |
| int qsign, long q, long r) { |
| assert r != 0L; |
| |
| int cmpFracHalf; |
| if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) { |
| cmpFracHalf = 1; // 2 * r can't fit into long |
| } else { |
| cmpFracHalf = longCompareMagnitude(2 * r, ldivisor); |
| } |
| |
| return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, (q & 1L) != 0L); |
| } |
| |
| /** |
| * Divides {@code BigInteger} value by {@code long} value and |
| * do rounding based on the passed in roundingMode. |
| */ |
| private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) { |
| // Descend into mutables for faster remainder checks |
| MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); |
| // store quotient |
| MutableBigInteger mq = new MutableBigInteger(); |
| // store quotient & remainder in long |
| long r = mdividend.divide(ldivisor, mq); |
| // record remainder is zero or not |
| boolean isRemainderZero = (r == 0); |
| // quotient sign |
| int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum; |
| if (!isRemainderZero) { |
| if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) { |
| mq.add(MutableBigInteger.ONE); |
| } |
| } |
| return mq.toBigInteger(qsign); |
| } |
| |
| /** |
| * Internally used for division operation for division {@code BigInteger} |
| * by {@code long}. |
| * The returned {@code BigDecimal} object is the quotient whose scale is set |
| * to the passed in scale. If the remainder is not zero, it will be rounded |
| * based on the passed in roundingMode. Also, if the remainder is zero and |
| * the last parameter, i.e. preferredScale is NOT equal to scale, the |
| * trailing zeros of the result is stripped to match the preferredScale. |
| */ |
| private static BigDecimal divideAndRound(BigInteger bdividend, |
| long ldivisor, int scale, int roundingMode, int preferredScale) { |
| // Descend into mutables for faster remainder checks |
| MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); |
| // store quotient |
| MutableBigInteger mq = new MutableBigInteger(); |
| // store quotient & remainder in long |
| long r = mdividend.divide(ldivisor, mq); |
| // record remainder is zero or not |
| boolean isRemainderZero = (r == 0); |
| // quotient sign |
| int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum; |
| if (!isRemainderZero) { |
| if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) { |
| mq.add(MutableBigInteger.ONE); |
| } |
| return mq.toBigDecimal(qsign, scale); |
| } else { |
| if (preferredScale != scale) { |
| long compactVal = mq.toCompactValue(qsign); |
| if(compactVal!=INFLATED) { |
| return createAndStripZerosToMatchScale(compactVal, scale, preferredScale); |
| } |
| BigInteger intVal = mq.toBigInteger(qsign); |
| return createAndStripZerosToMatchScale(intVal,scale, preferredScale); |
| } else { |
| return mq.toBigDecimal(qsign, scale); |
| } |
| } |
| } |
| |
| /** |
| * Tests if quotient has to be incremented according the roundingMode |
| */ |
| private static boolean needIncrement(long ldivisor, int roundingMode, |
| int qsign, MutableBigInteger mq, long r) { |
| assert r != 0L; |
| |
| int cmpFracHalf; |
| if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) { |
| cmpFracHalf = 1; // 2 * r can't fit into long |
| } else { |
| cmpFracHalf = longCompareMagnitude(2 * r, ldivisor); |
| } |
| |
| return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd()); |
| } |
| |
| /** |
| * Divides {@code BigInteger} value by {@code BigInteger} value and |
| * do rounding based on the passed in roundingMode. |
| */ |
| private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) { |
| boolean isRemainderZero; // record remainder is zero or not |
| int qsign; // quotient sign |
| // Descend into mutables for faster remainder checks |
| MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); |
| MutableBigInteger mq = new MutableBigInteger(); |
| MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag); |
| MutableBigInteger mr = mdividend.divide(mdivisor, mq); |
| isRemainderZero = mr.isZero(); |
| qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1; |
| if (!isRemainderZero) { |
| if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) { |
| mq.add(MutableBigInteger.ONE); |
| } |
| } |
| return mq.toBigInteger(qsign); |
| } |
| |
| /** |
| * Internally used for division operation for division {@code BigInteger} |
| * by {@code BigInteger}. |
| * The returned {@code BigDecimal} object is the quotient whose scale is set |
| * to the passed in scale. If the remainder is not zero, it will be rounded |
| * based on the passed in roundingMode. Also, if the remainder is zero and |
| * the last parameter, i.e. preferredScale is NOT equal to scale, the |
| * trailing zeros of the result is stripped to match the preferredScale. |
| */ |
| private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode, |
| int preferredScale) { |
| boolean isRemainderZero; // record remainder is zero or not |
| int qsign; // quotient sign |
| // Descend into mutables for faster remainder checks |
| MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); |
| MutableBigInteger mq = new MutableBigInteger(); |
| MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag); |
| MutableBigInteger mr = mdividend.divide(mdivisor, mq); |
| isRemainderZero = mr.isZero(); |
| qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1; |
| if (!isRemainderZero) { |
| if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) { |
| mq.add(MutableBigInteger.ONE); |
| } |
| return mq.toBigDecimal(qsign, scale); |
| } else { |
| if (preferredScale != scale) { |
| long compactVal = mq.toCompactValue(qsign); |
| if (compactVal != INFLATED) { |
| return createAndStripZerosToMatchScale(compactVal, scale, preferredScale); |
| } |
| BigInteger intVal = mq.toBigInteger(qsign); |
| return createAndStripZerosToMatchScale(intVal, scale, preferredScale); |
| } else { |
| return mq.toBigDecimal(qsign, scale); |
| } |
| } |
| } |
| |
| /** |
| * Tests if quotient has to be incremented according the roundingMode |
| */ |
| private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode, |
| int qsign, MutableBigInteger mq, MutableBigInteger mr) { |
| assert !mr.isZero(); |
| int cmpFracHalf = mr.compareHalf(mdivisor); |
| return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd()); |
| } |
| |
| /** |
| * Remove insignificant trailing zeros from this |
| * {@code BigInteger} value until the preferred scale is reached or no |
| * more zeros can be removed. If the preferred scale is less than |
| * Integer.MIN_VALUE, all the trailing zeros will be removed. |
| * |
| * @return new {@code BigDecimal} with a scale possibly reduced |
| * to be closed to the preferred scale. |
| */ |
| private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) { |
| BigInteger qr[]; // quotient-remainder pair |
| while (intVal.compareMagnitude(BigInteger.TEN) >= 0 |
| && scale > preferredScale) { |
| if (intVal.testBit(0)) |
| break; // odd number cannot end in 0 |
| qr = intVal.divideAndRemainder(BigInteger.TEN); |
| if (qr[1].signum() != 0) |
| break; // non-0 remainder |
| intVal = qr[0]; |
| scale = checkScale(intVal,(long) scale - 1); // could Overflow |
| } |
| return valueOf(intVal, scale, 0); |
| } |
| |
| /** |
| * Remove insignificant trailing zeros from this |
| * {@code long} value until the preferred scale is reached or no |
| * more zeros can be removed. If the preferred scale is less than |
| * Integer.MIN_VALUE, all the trailing zeros will be removed. |
| * |
| * @return new {@code BigDecimal} with a scale possibly reduced |
| * to be closed to the preferred scale. |
| */ |
| private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) { |
| while (Math.abs(compactVal) >= 10L && scale > preferredScale) { |
| if ((compactVal & 1L) != 0L) |
| break; // odd number cannot end in 0 |
| long r = compactVal % 10L; |
| if (r != 0L) |
| break; // non-0 remainder |
| compactVal /= 10; |
| scale = checkScale(compactVal, (long) scale - 1); // could Overflow |
| } |
| return valueOf(compactVal, scale); |
| } |
| |
| private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) { |
| if(intCompact!=INFLATED) { |
| return createAndStripZerosToMatchScale(intCompact, scale, preferredScale); |
| } else { |
| return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal, |
| scale, preferredScale); |
| } |
| } |
| |
| /* |
| * returns INFLATED if oveflow |
| */ |
| private static long add(long xs, long ys){ |
| long sum = xs + ys; |
| // See "Hacker's Delight" section 2-12 for explanation of |
| // the overflow test. |
| if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed |
| return sum; |
| } |
| return INFLATED; |
| } |
| |
| private static BigDecimal add(long xs, long ys, int scale){ |
| long sum = add(xs, ys); |
| if (sum!=INFLATED) |
| return BigDecimal.valueOf(sum, scale); |
| return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale); |
| } |
| |
| private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) { |
| long sdiff = (long) scale1 - scale2; |
| if (sdiff == 0) { |
| return add(xs, ys, scale1); |
| } else if (sdiff < 0) { |
| int raise = checkScale(xs,-sdiff); |
| long scaledX = longMultiplyPowerTen(xs, raise); |
| if (scaledX != INFLATED) { |
| return add(scaledX, ys, scale2); |
| } else { |
| BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys); |
| return ((xs^ys)>=0) ? // same sign test |
| new BigDecimal(bigsum, INFLATED, scale2, 0) |
| : valueOf(bigsum, scale2, 0); |
| } |
| } else { |
| int raise = checkScale(ys,sdiff); |
| long scaledY = longMultiplyPowerTen(ys, raise); |
| if (scaledY != INFLATED) { |
| return add(xs, scaledY, scale1); |
| } else { |
| BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs); |
| return ((xs^ys)>=0) ? |
| new BigDecimal(bigsum, INFLATED, scale1, 0) |
| : valueOf(bigsum, scale1, 0); |
| } |
| } |
| } |
| |
| private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) { |
| int rscale = scale1; |
| long sdiff = (long)rscale - scale2; |
| boolean sameSigns = (Long.signum(xs) == snd.signum); |
| BigInteger sum; |
| if (sdiff < 0) { |
| int raise = checkScale(xs,-sdiff); |
| rscale = scale2; |
| long scaledX = longMultiplyPowerTen(xs, raise); |
| if (scaledX == INFLATED) { |
| sum = snd.add(bigMultiplyPowerTen(xs,raise)); |
| } else { |
| sum = snd.add(scaledX); |
| } |
| } else { //if (sdiff > 0) { |
| int raise = checkScale(snd,sdiff); |
| snd = bigMultiplyPowerTen(snd,raise); |
| sum = snd.add(xs); |
| } |
| return (sameSigns) ? |
| new BigDecimal(sum, INFLATED, rscale, 0) : |
| valueOf(sum, rscale, 0); |
| } |
| |
| private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) { |
| int rscale = scale1; |
| long sdiff = (long)rscale - scale2; |
| if (sdiff != 0) { |
| if (sdiff < 0) { |
| int raise = checkScale(fst,-sdiff); |
| rscale = scale2; |
| fst = bigMultiplyPowerTen(fst,raise); |
| } else { |
| int raise = checkScale(snd,sdiff); |
| snd = bigMultiplyPowerTen(snd,raise); |
| } |
| } |
| BigInteger sum = fst.add(snd); |
| return (fst.signum == snd.signum) ? |
| new BigDecimal(sum, INFLATED, rscale, 0) : |
| valueOf(sum, rscale, 0); |
| } |
| |
| private static BigInteger bigMultiplyPowerTen(long value, int n) { |
| if (n <= 0) |
| return BigInteger.valueOf(value); |
| return bigTenToThe(n).multiply(value); |
| } |
| |
| private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) { |
| if (n <= 0) |
| return value; |
| if(n<LONG_TEN_POWERS_TABLE.length) { |
| return value.multiply(LONG_TEN_POWERS_TABLE[n]); |
| } |
| return value.multiply(bigTenToThe(n)); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (xs / |
| * ys)}, with rounding according to the context settings. |
| * |
| * Fast path - used only when (xscale <= yscale && yscale < 18 |
| * && mc.presision<18) { |
| */ |
| private static BigDecimal divideSmallFastPath(final long xs, int xscale, |
| final long ys, int yscale, |
| long preferredScale, MathContext mc) { |
| int mcp = mc.precision; |
| int roundingMode = mc.roundingMode.oldMode; |
| |
| assert (xscale <= yscale) && (yscale < 18) && (mcp < 18); |
| int xraise = yscale - xscale; // xraise >=0 |
| long scaledX = (xraise==0) ? xs : |
| longMultiplyPowerTen(xs, xraise); // can't overflow here! |
| BigDecimal quotient; |
| |
| int cmp = longCompareMagnitude(scaledX, ys); |
| if(cmp > 0) { // satisfy constraint (b) |
| yscale -= 1; // [that is, divisor *= 10] |
| int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); |
| if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { |
| // assert newScale >= xscale |
| int raise = checkScaleNonZero((long) mcp + yscale - xscale); |
| long scaledXs; |
| if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) { |
| quotient = null; |
| if((mcp-1) >=0 && (mcp-1)<LONG_TEN_POWERS_TABLE.length) { |
| quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp-1], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } |
| if(quotient==null) { |
| BigInteger rb = bigMultiplyPowerTen(scaledX,mcp-1); |
| quotient = divideAndRound(rb, ys, |
| scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } |
| } else { |
| quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } |
| } else { |
| int newScale = checkScaleNonZero((long) xscale - mcp); |
| // assert newScale >= yscale |
| if (newScale == yscale) { // easy case |
| quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } else { |
| int raise = checkScaleNonZero((long) newScale - yscale); |
| long scaledYs; |
| if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) { |
| BigInteger rb = bigMultiplyPowerTen(ys,raise); |
| quotient = divideAndRound(BigInteger.valueOf(xs), |
| rb, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } else { |
| quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } |
| } |
| } |
| } else { |
| // abs(scaledX) <= abs(ys) |
| // result is "scaledX * 10^msp / ys" |
| int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); |
| if(cmp==0) { |
| // abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign |
| quotient = roundedTenPower(((scaledX < 0) == (ys < 0)) ? 1 : -1, mcp, scl, checkScaleNonZero(preferredScale)); |
| } else { |
| // abs(scaledX) < abs(ys) |
| long scaledXs; |
| if ((scaledXs = longMultiplyPowerTen(scaledX, mcp)) == INFLATED) { |
| quotient = null; |
| if(mcp<LONG_TEN_POWERS_TABLE.length) { |
| quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } |
| if(quotient==null) { |
| BigInteger rb = bigMultiplyPowerTen(scaledX,mcp); |
| quotient = divideAndRound(rb, ys, |
| scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } |
| } else { |
| quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } |
| } |
| } |
| // doRound, here, only affects 1000000000 case. |
| return doRound(quotient,mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (xs / |
| * ys)}, with rounding according to the context settings. |
| */ |
| private static BigDecimal divide(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) { |
| int mcp = mc.precision; |
| if(xscale <= yscale && yscale < 18 && mcp<18) { |
| return divideSmallFastPath(xs, xscale, ys, yscale, preferredScale, mc); |
| } |
| if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b) |
| yscale -= 1; // [that is, divisor *= 10] |
| } |
| int roundingMode = mc.roundingMode.oldMode; |
| // In order to find out whether the divide generates the exact result, |
| // we avoid calling the above divide method. 'quotient' holds the |
| // return BigDecimal object whose scale will be set to 'scl'. |
| int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); |
| BigDecimal quotient; |
| if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { |
| int raise = checkScaleNonZero((long) mcp + yscale - xscale); |
| long scaledXs; |
| if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) { |
| BigInteger rb = bigMultiplyPowerTen(xs,raise); |
| quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } else { |
| quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } |
| } else { |
| int newScale = checkScaleNonZero((long) xscale - mcp); |
| // assert newScale >= yscale |
| if (newScale == yscale) { // easy case |
| quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } else { |
| int raise = checkScaleNonZero((long) newScale - yscale); |
| long scaledYs; |
| if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) { |
| BigInteger rb = bigMultiplyPowerTen(ys,raise); |
| quotient = divideAndRound(BigInteger.valueOf(xs), |
| rb, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } else { |
| quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } |
| } |
| } |
| // doRound, here, only affects 1000000000 case. |
| return doRound(quotient,mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (xs / |
| * ys)}, with rounding according to the context settings. |
| */ |
| private static BigDecimal divide(BigInteger xs, int xscale, long ys, int yscale, long preferredScale, MathContext mc) { |
| // Normalize dividend & divisor so that both fall into [0.1, 0.999...] |
| if ((-compareMagnitudeNormalized(ys, yscale, xs, xscale)) > 0) {// satisfy constraint (b) |
| yscale -= 1; // [that is, divisor *= 10] |
| } |
| int mcp = mc.precision; |
| int roundingMode = mc.roundingMode.oldMode; |
| |
| // In order to find out whether the divide generates the exact result, |
| // we avoid calling the above divide method. 'quotient' holds the |
| // return BigDecimal object whose scale will be set to 'scl'. |
| BigDecimal quotient; |
| int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); |
| if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { |
| int raise = checkScaleNonZero((long) mcp + yscale - xscale); |
| BigInteger rb = bigMultiplyPowerTen(xs,raise); |
| quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } else { |
| int newScale = checkScaleNonZero((long) xscale - mcp); |
| // assert newScale >= yscale |
| if (newScale == yscale) { // easy case |
| quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } else { |
| int raise = checkScaleNonZero((long) newScale - yscale); |
| long scaledYs; |
| if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) { |
| BigInteger rb = bigMultiplyPowerTen(ys,raise); |
| quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } else { |
| quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } |
| } |
| } |
| // doRound, here, only affects 1000000000 case. |
| return doRound(quotient, mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (xs / |
| * ys)}, with rounding according to the context settings. |
| */ |
| private static BigDecimal divide(long xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) { |
| // Normalize dividend & divisor so that both fall into [0.1, 0.999...] |
| if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b) |
| yscale -= 1; // [that is, divisor *= 10] |
| } |
| int mcp = mc.precision; |
| int roundingMode = mc.roundingMode.oldMode; |
| |
| // In order to find out whether the divide generates the exact result, |
| // we avoid calling the above divide method. 'quotient' holds the |
| // return BigDecimal object whose scale will be set to 'scl'. |
| BigDecimal quotient; |
| int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); |
| if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { |
| int raise = checkScaleNonZero((long) mcp + yscale - xscale); |
| BigInteger rb = bigMultiplyPowerTen(xs,raise); |
| quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } else { |
| int newScale = checkScaleNonZero((long) xscale - mcp); |
| int raise = checkScaleNonZero((long) newScale - yscale); |
| BigInteger rb = bigMultiplyPowerTen(ys,raise); |
| quotient = divideAndRound(BigInteger.valueOf(xs), rb, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } |
| // doRound, here, only affects 1000000000 case. |
| return doRound(quotient, mc); |
| } |
| |
| /** |
| * Returns a {@code BigDecimal} whose value is {@code (xs / |
| * ys)}, with rounding according to the context settings. |
| */ |
| private static BigDecimal divide(BigInteger xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) { |
| // Normalize dividend & divisor so that both fall into [0.1, 0.999...] |
| if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b) |
| yscale -= 1; // [that is, divisor *= 10] |
| } |
| int mcp = mc.precision; |
| int roundingMode = mc.roundingMode.oldMode; |
| |
| // In order to find out whether the divide generates the exact result, |
| // we avoid calling the above divide method. 'quotient' holds the |
| // return BigDecimal object whose scale will be set to 'scl'. |
| BigDecimal quotient; |
| int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); |
| if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { |
| int raise = checkScaleNonZero((long) mcp + yscale - xscale); |
| BigInteger rb = bigMultiplyPowerTen(xs,raise); |
| quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); |
| } else { |
| int newScale = checkScaleNonZero((long) xscale - mcp); |
| int raise = checkScaleNonZero((long) newScale - yscale); |
| BigInteger rb = bigMultiplyPowerTen(ys,raise); |
| quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale)); |
| } |
| // doRound, here, only affects 1000000000 case. |
| return doRound(quotient, mc); |
| } |
| |
| /* |
| * performs divideAndRound for (dividend0*dividend1, divisor) |
| * returns null if quotient can't fit into long value; |
| */ |
| private static BigDecimal multiplyDivideAndRound(long dividend0, long dividend1, long divisor, int scale, int roundingMode, |
| int preferredScale) { |
| int qsign = Long.signum(dividend0)*Long.signum(dividend1)*Long.signum(divisor); |
| dividend0 = Math.abs(dividend0); |
| dividend1 = Math.abs(dividend1); |
| divisor = Math.abs(divisor); |
| // multiply dividend0 * dividend1 |
| long d0_hi = dividend0 >>> 32; |
| long d0_lo = dividend0 & LONG_MASK; |
| long d1_hi = dividend1 >>> 32; |
| long d1_lo = dividend1 & LONG_MASK; |
| long product = d0_lo * d1_lo; |
| long d0 = product & LONG_MASK; |
| long d1 = product >>> 32; |
| product = d0_hi * d1_lo + d1; |
| d1 = product & LONG_MASK; |
| long d2 = product >>> 32; |
| product = d0_lo * d1_hi + d1; |
| d1 = product & LONG_MASK; |
| d2 += product >>> 32; |
| long d3 = d2>>>32; |
| d2 &= LONG_MASK; |
| product = d0_hi*d1_hi + d2; |
| d2 = product & LONG_MASK; |
| d3 = ((product>>>32) + d3) & LONG_MASK; |
| final long dividendHi = make64(d3,d2); |
| final long dividendLo = make64(d1,d0); |
| // divide |
| return divideAndRound128(dividendHi, dividendLo, divisor, qsign, scale, roundingMode, preferredScale); |
| } |
| |
| private static final long DIV_NUM_BASE = (1L<<32); // Number base (32 bits). |
| |
| /* |
| * divideAndRound 128-bit value by long divisor. |
| * returns null if quotient can't fit into long value; |
| * Specialized version of Knuth's division |
| */ |
| private static BigDecimal divideAndRound128(final long dividendHi, final long dividendLo, long divisor, int sign, |
| int scale, int roundingMode, int preferredScale) { |
| if (dividendHi >= divisor) { |
| return null; |
| } |
| |
| final int shift = Long.numberOfLeadingZeros(divisor); |
| divisor <<= shift; |
| |
| final long v1 = divisor >>> 32; |
| final long v0 = divisor & LONG_MASK; |
| |
| long tmp = dividendLo << shift; |
| long u1 = tmp >>> 32; |
| long u0 = tmp & LONG_MASK; |
| |
| tmp = (dividendHi << shift) | (dividendLo >>> 64 - shift); |
| long u2 = tmp & LONG_MASK; |
| long q1, r_tmp; |
| if (v1 == 1) { |
| q1 = tmp; |
| r_tmp = 0; |
| } else if (tmp >= 0) { |
| q1 = tmp / v1; |
| r_tmp = tmp - q1 * v1; |
| } else { |
| long[] rq = divRemNegativeLong(tmp, v1); |
| q1 = rq[1]; |
| r_tmp = rq[0]; |
| } |
| |
| while(q1 >= DIV_NUM_BASE || unsignedLongCompare(q1*v0, make64(r_tmp, u1))) { |
| q1--; |
| r_tmp += v1; |
| if (r_tmp >= DIV_NUM_BASE) |
| break; |
| } |
| |
| tmp = mulsub(u2,u1,v1,v0,q1); |
| u1 = tmp & LONG_MASK; |
| long q0; |
| if (v1 == 1) { |
| q0 = tmp; |
| r_tmp = 0; |
| } else if (tmp >= 0) { |
| q0 = tmp / v1; |
| r_tmp = tmp - q0 * v1; |
| } else { |
| long[] rq = divRemNegativeLong(tmp, v1); |
| q0 = rq[1]; |
| r_tmp = rq[0]; |
| } |
| |
| while(q0 >= DIV_NUM_BASE || unsignedLongCompare(q0*v0,make64(r_tmp,u0))) { |
| q0--; |
| r_tmp += v1; |
| if (r_tmp >= DIV_NUM_BASE) |
| break; |
| } |
| |
| if((int)q1 < 0) { |
| // result (which is positive and unsigned here) |
| // can't fit into long due to sign bit is used for value |
| MutableBigInteger mq = new MutableBigInteger(new int[]{(int)q1, (int)q0}); |
| if (roundingMode == ROUND_DOWN && scale == preferredScale) { |
| return mq.toBigDecimal(sign, scale); |
| } |
| long r = mulsub(u1, u0, v1, v0, q0) >>> shift; |
| if (r != 0) { |
| if(needIncrement(divisor >>> shift, roundingMode, sign, mq, r)){ |
| mq.add(MutableBigInteger.ONE); |
| } |
| return mq.toBigDecimal(sign, scale); |
| } else { |
| if (preferredScale != scale) { |
| BigInteger intVal = mq.toBigInteger(sign); |
| return createAndStripZerosToMatchScale(intVal,scale, preferredScale); |
| } else { |
| return mq.toBigDecimal(sign, scale); |
| } |
| } |
| } |
| |
| long q = make64(q1,q0); |
| q*=sign; |
| |
| if (roundingMode == ROUND_DOWN && scale == preferredScale) |
| return valueOf(q, scale); |
| |
| long r = mulsub(u1, u0, v1, v0, q0) >>> shift; |
| if (r != 0) { |
| boolean increment = needIncrement(divisor >>> shift, roundingMode, sign, q, r); |
| return valueOf((increment ? q + sign : q), scale); |
| } else { |
| if (preferredScale != scale) { |
| return createAndStripZerosToMatchScale(q, scale, preferredScale); |
| } else { |
| return valueOf(q, scale); |
| } |
| } |
| } |
| |
| /* |
| * calculate divideAndRound for ldividend*10^raise / divisor |
| * when abs(dividend)==abs(divisor); |
| */ |
| private static BigDecimal roundedTenPower(int qsign, int raise, int scale, int preferredScale) { |
| if (scale > preferredScale) { |
| int diff = scale - preferredScale; |
| if(diff < raise) { |
| return scaledTenPow(raise - diff, qsign, preferredScale); |
| } else { |
| return valueOf(qsign,scale-raise); |
| } |
| } else { |
| return scaledTenPow(raise, qsign, scale); |
| } |
| } |
| |
| static BigDecimal scaledTenPow(int n, int sign, int scale) { |
| if (n < LONG_TEN_POWERS_TABLE.length) |
| return valueOf(sign*LONG_TEN_POWERS_TABLE[n],scale); |
| else { |
| BigInteger unscaledVal = bigTenToThe(n); |
| if(sign==-1) { |
| unscaledVal = unscaledVal.negate(); |
| } |
| return new BigDecimal(unscaledVal, INFLATED, scale, n+1); |
| } |
| } |
| |
| /** |
| * Calculate the quotient and remainder of dividing a negative long by |
| * another long. |
| * |
| * @param n the numerator; must be negative |
| * @param d the denominator; must not be unity |
| * @return a two-element {@long} array with the remainder and quotient in |
| * the initial and final elements, respectively |
| */ |
| private static long[] divRemNegativeLong(long n, long d) { |
| assert n < 0 : "Non-negative numerator " + n; |
| assert d != 1 : "Unity denominator"; |
| |
| // Approximate the quotient and remainder |
| long q = (n >>> 1) / (d >>> 1); |
| long r = n - q * d; |
| |
| // Correct the approximation |
| while (r < 0) { |
| r += d; |
| q--; |
| } |
| while (r >= d) { |
| r -= d; |
| q++; |
| } |
| |
| // n - q*d == r && 0 <= r < d, hence we're done. |
| return new long[] {r, q}; |
| } |
| |
| private static long make64(long hi, long lo) { |
| return hi<<32 | lo; |
| } |
| |
| private static long mulsub(long u1, long u0, final long v1, final long v0, long q0) { |
| long tmp = u0 - q0*v0; |
| return make64(u1 + (tmp>>>32) - q0*v1,tmp & LONG_MASK); |
| } |
| |
| private static boolean unsignedLongCompare(long one, long two) { |
| return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE); |
| } |
| |
| private static boolean unsignedLongCompareEq(long one, long two) { |
| return (one+Long.MIN_VALUE) >= (two+Long.MIN_VALUE); |
| } |
| |
| |
| // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...] |
| private static int compareMagnitudeNormalized(long xs, int xscale, long ys, int yscale) { |
| // assert xs!=0 && ys!=0 |
| int sdiff = xscale - yscale; |
| if (sdiff != 0) { |
| if (sdiff < 0) { |
| xs = longMultiplyPowerTen(xs, -sdiff); |
| } else { // sdiff > 0 |
| ys = longMultiplyPowerTen(ys, sdiff); |
| } |
| } |
| if (xs != INFLATED) |
| return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1; |
| else |
| return 1; |
| } |
| |
| // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...] |
| private static int compareMagnitudeNormalized(long xs, int xscale, BigInteger ys, int yscale) { |
| // assert "ys can't be represented as long" |
| if (xs == 0) |
| return -1; |
| int sdiff = xscale - yscale; |
| if (sdiff < 0) { |
| if (longMultiplyPowerTen(xs, -sdiff) == INFLATED ) { |
| return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys); |
| } |
| } |
| return -1; |
| } |
| |
| // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...] |
| private static int compareMagnitudeNormalized(BigInteger xs, int xscale, BigInteger ys, int yscale) { |
| int sdiff = xscale - yscale; |
| if (sdiff < 0) { |
| return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys); |
| } else { // sdiff >= 0 |
| return xs.compareMagnitude(bigMultiplyPowerTen(ys, sdiff)); |
| } |
| } |
| |
| private static long multiply(long x, long y){ |
| long product = x * y; |
| long ax = Math.abs(x); |
| long ay = Math.abs(y); |
| if (((ax | ay) >>> 31 == 0) || (y == 0) || (product / y == x)){ |
| return product; |
| } |
| return INFLATED; |
| } |
| |
| private static BigDecimal multiply(long x, long y, int scale) { |
| long product = multiply(x, y); |
| if(product!=INFLATED) { |
| return valueOf(product,scale); |
| } |
| return new BigDecimal(BigInteger.valueOf(x).multiply(y),INFLATED,scale,0); |
| } |
| |
| private static BigDecimal multiply(long x, BigInteger y, int scale) { |
| if(x==0) { |
| return zeroValueOf(scale); |
| } |
| return new BigDecimal(y.multiply(x),INFLATED,scale,0); |
| } |
| |
| private static BigDecimal multiply(BigInteger x, BigInteger y, int scale) { |
| return new BigDecimal(x.multiply(y),INFLATED,scale,0); |
| } |
| |
| /** |
| * Multiplies two long values and rounds according {@code MathContext} |
| */ |
| private static BigDecimal multiplyAndRound(long x, long y, int scale, MathContext mc) { |
| long product = multiply(x, y); |
| if(product!=INFLATED) { |
| return doRound(product, scale, mc); |
| } |
| // attempt to do it in 128 bits |
| int rsign = 1; |
| if(x < 0) { |
| x = -x; |
| rsign = -1; |
| } |
| if(y < 0) { |
| y = -y; |
| rsign *= -1; |
| } |
| // multiply dividend0 * dividend1 |
| long m0_hi = x >>> 32; |
| long m0_lo = x & LONG_MASK; |
| long m1_hi = y >>> 32; |
| long m1_lo = y & LONG_MASK; |
| product = m0_lo * m1_lo; |
| long m0 = product & LONG_MASK; |
| long m1 = product >>> 32; |
| product = m0_hi * m1_lo + m1; |
| m1 = product & LONG_MASK; |
| long m2 = product >>> 32; |
| product = m0_lo * m1_hi + m1; |
| m1 = product & LONG_MASK; |
| m2 += product >>> 32; |
| long m3 = m2>>>32; |
| m2 &= LONG_MASK; |
| product = m0_hi*m1_hi + m2; |
| m2 = product & LONG_MASK; |
| m3 = ((product>>>32) + m3) & LONG_MASK; |
| final long mHi = make64(m3,m2); |
| final long mLo = make64(m1,m0); |
| BigDecimal res = doRound128(mHi, mLo, rsign, scale, mc); |
| if(res!=null) { |
| return res; |
| } |
| res = new BigDecimal(BigInteger.valueOf(x).multiply(y*rsign), INFLATED, scale, 0); |
| return doRound(res,mc); |
| } |
| |
| private static BigDecimal multiplyAndRound(long x, BigInteger y, int scale, MathContext mc) { |
| if(x==0) { |
| return zeroValueOf(scale); |
| } |
| return doRound(y.multiply(x), scale, mc); |
| } |
| |
| private static BigDecimal multiplyAndRound(BigInteger x, BigInteger y, int scale, MathContext mc) { |
| return doRound(x.multiply(y), scale, mc); |
| } |
| |
| /** |
| * rounds 128-bit value according {@code MathContext} |
| * returns null if result can't be repsented as compact BigDecimal. |
| */ |
| private static BigDecimal doRound128(long hi, long lo, int sign, int scale, MathContext mc) { |
| int mcp = mc.precision; |
| int drop; |
| BigDecimal res = null; |
| if(((drop = precision(hi, lo) - mcp) > 0)&&(drop<LONG_TEN_POWERS_TABLE.length)) { |
| scale = checkScaleNonZero((long)scale - drop); |
| res = divideAndRound128(hi, lo, LONG_TEN_POWERS_TABLE[drop], sign, scale, mc.roundingMode.oldMode, scale); |
| } |
| if(res!=null) { |
| return doRound(res,mc); |
| } |
| return null; |
| } |
| |
| private static final long[][] LONGLONG_TEN_POWERS_TABLE = { |
| { 0L, 0x8AC7230489E80000L }, //10^19 |
| { 0x5L, 0x6bc75e2d63100000L }, //10^20 |
| { 0x36L, 0x35c9adc5dea00000L }, //10^21 |
| { 0x21eL, 0x19e0c9bab2400000L }, //10^22 |
| { 0x152dL, 0x02c7e14af6800000L }, //10^23 |
| { 0xd3c2L, 0x1bcecceda1000000L }, //10^24 |
| { 0x84595L, 0x161401484a000000L }, //10^25 |
| { 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26 |
| { 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27 |
| { 0x204fce5eL, 0x3e25026110000000L }, //10^28 |
| { 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29 |
| { 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30 |
| { 0x7e37be2022L, 0xc0914b2680000000L }, //10^31 |
| { 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32 |
| { 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33 |
| { 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34 |
| { 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35 |
| { 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36 |
| { 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37 |
| { 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38 |
| }; |
| |
| /* |
| * returns precision of 128-bit value |
| */ |
| private static int precision(long hi, long lo){ |
| if(hi==0) { |
| if(lo>=0) { |
| return longDigitLength(lo); |
| } |
| return (unsignedLongCompareEq(lo, LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19; |
| // 0x8AC7230489E80000L = unsigned 2^19 |
| } |
| int r = ((128 - Long.numberOfLeadingZeros(hi) + 1) * 1233) >>> 12; |
| int idx = r-19; |
| return (idx >= LONGLONG_TEN_POWERS_TABLE.length || longLongCompareMagnitude(hi, lo, |
| LONGLONG_TEN_POWERS_TABLE[idx][0], LONGLONG_TEN_POWERS_TABLE[idx][1])) ? r : r + 1; |
| } |
| |
| /* |
| * returns true if 128 bit number <hi0,lo0> is less than <hi1,lo1> |
| * hi0 & hi1 should be non-negative |
| */ |
| private static boolean longLongCompareMagnitude(long hi0, long lo0, long hi1, long lo1) { |
| if(hi0!=hi1) { |
| return hi0<hi1; |
| } |
| return (lo0+Long.MIN_VALUE) <(lo1+Long.MIN_VALUE); |
| } |
| |
| private static BigDecimal divide(long dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) { |
| if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { |
| int newScale = scale + divisorScale; |
| int raise = newScale - dividendScale; |
| if(raise<LONG_TEN_POWERS_TABLE.length) { |
| long xs = dividend; |
| if ((xs = longMultiplyPowerTen(xs, raise)) != INFLATED) { |
| return divideAndRound(xs, divisor, scale, roundingMode, scale); |
| } |
| BigDecimal q = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[raise], dividend, divisor, scale, roundingMode, scale); |
| if(q!=null) { |
| return q; |
| } |
| } |
| BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); |
| return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); |
| } else { |
| int newScale = checkScale(divisor,(long)dividendScale - scale); |
| int raise = newScale - divisorScale; |
| if(raise<LONG_TEN_POWERS_TABLE.length) { |
| long ys = divisor; |
| if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) { |
| return divideAndRound(dividend, ys, scale, roundingMode, scale); |
| } |
| } |
| BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); |
| return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale); |
| } |
| } |
| |
| private static BigDecimal divide(BigInteger dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) { |
| if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { |
| int newScale = scale + divisorScale; |
| int raise = newScale - dividendScale; |
| BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); |
| return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); |
| } else { |
| int newScale = checkScale(divisor,(long)dividendScale - scale); |
| int raise = newScale - divisorScale; |
| if(raise<LONG_TEN_POWERS_TABLE.length) { |
| long ys = divisor; |
| if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) { |
| return divideAndRound(dividend, ys, scale, roundingMode, scale); |
| } |
| } |
| BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); |
| return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale); |
| } |
| } |
| |
| private static BigDecimal divide(long dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) { |
| if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { |
| int newScale = scale + divisorScale; |
| int raise = newScale - dividendScale; |
| BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); |
| return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); |
| } else { |
| int newScale = checkScale(divisor,(long)dividendScale - scale); |
| int raise = newScale - divisorScale; |
| BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); |
| return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale); |
| } |
| } |
| |
| private static BigDecimal divide(BigInteger dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) { |
| if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { |
| int newScale = scale + divisorScale; |
| int raise = newScale - dividendScale; |
| BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); |
| return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); |
| } else { |
| int newScale = checkScale(divisor,(long)dividendScale - scale); |
| int raise = newScale - divisorScale; |
| BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); |
| return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale); |
| } |
| } |
| |
| } |