--- old/src/java.base/share/classes/java/math/BigDecimal.java	2016-05-11 10:37:28.126558223 -0700
+++ new/src/java.base/share/classes/java/math/BigDecimal.java	2016-05-11 10:37:27.730558229 -0700
@@ -346,6 +346,16 @@
     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
 
     /**
@@ -1995,6 +2005,219 @@
         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 floor(this.scale()/2.0)}. 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 equal to {@code ZERO}.
+     * </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.
+     * @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 follow, 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.
+
+            BigDecimal zeroWithFinalPreferredScale = valueOf(0L, this.scale()/2);
+
+            // 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 (BigInteger.ONE.equals(stripped.unscaledValue()) &&
+                strippedScale % 2 == 0) {
+                BigDecimal result = valueOf(1L, strippedScale/2);
+                // Adjust to requested precision and preferred scale as possible
+                return result.add(zeroWithFinalPreferredScale, mc);
+            }
+
+            System.out.println("\tStarting: " + this); // DEBUG
+            System.out.println("\tStripped: " + stripped); // DEBUG
+
+
+            // 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 as so
+            // that the significand portion is to right of the decimal
+            // point, roughly:
+            //
+            // (unscaledValue * (10^-precision) * 10^(-scale)) * (10^precision)
+            //
+            // so that
+            //
+            // sqrt(unscaledValue * (10^-precision) * 10^(-scale) * (10^precision)) =
+            //
+            // sqrt(unscaledValue * (10^-precision) * 10^(-scale)) * 10^(precision/2)
+            //
+            // Therefore, this adjustment occurs for by 10^-precision is precision is even or 
+            // (adjust as needed, +/-1
+            //
+            // (A double value might have as much as 17 decimal digits
+            // of precision; it depends on the relative density of
+            // binary and decimal numbers at different points of the
+            // number line.)
+
+            // 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;
+                stripped = stripped.divide(TEN);
+            }
+
+            // At least document potential exponent overflow issues here???
+            BigDecimal working = stripped.scaleByPowerOfTen(scaleAdjust);
+            System.out.println("\tWorking2: " + working + "\tscale: " + working.scale()); // DEBUG
+
+            // Verify 1 <= working < 10 (verify range)
+            assert working.compareTo(ONE) >= 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.
+            BigDecimal guess = new BigDecimal(Math.sqrt(working.doubleValue()));
+            int guessPrecision = 15;
+            int targetPrecision = mc.getPrecision();
+            RoundingMode rm = mc.getRoundingMode();
+
+            // When setting the precision to use inside the 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 {
+                System.out.println(approx); // DEBUG
+                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 = approx.round(mc);
+
+            // TODO: need code for Round.UNNECESSARY. Probably also
+            // need additinal checking for HALF_EVEN since we are only
+            // using two extra precision digits.
+
+            // For now, skip the rounding up / down fix up
+
+            // Read through "What every ..." for 2p + 2 discussion...
+
+            // Handle 1/2 ulp, 1 ulp, and unnecessary rounding separately?
+            // UP, DOWN,
+            // CEILING (equiv to UP), FLOOR (equiv to DOWN), 
+            //
+            // HALF_UP, HALF_DOWN, HALF_EVEN -- look up 2p + 2 derivation
+            // -- same for decimal as well as binary?
+
+            // Could use direct definition to test adjacent values to
+            // target precision -- need to lookup if Newton's iteration
+            // converges from above or below to avoid checking three values...
+
+            // UNNECESSARY
+
+            // Unnecessary rounding -- in the worst case, only need about
+            // (1/2 + 1) digits to produce an exact output, sqrt(100) =
+            // 10, sqrt(10_000) = 100, etc.. How to handle cases that are
+            // powers of 10 with trailing zeros?
+
+            // Normalize to a range [.1, 1] or [1, 10] -- presunmably this
+            // is open on one end to account for exact square roots...
+            // 
+
+
+            // Convert to double and take double sqrt -- easy way to get
+            // (at least) 15 digits of a decimal approximation :-)
+
+            // If did more work, could make sure came in from uniformly
+            // above / below the root?
+
+            // Final answer: rescale fraction and then add a zero with the
+            // preferred scale with a rounding precision equal to the
+            // target precision.
+            
+            result = result.scaleByPowerOfTen(-scaleAdjust/2);
+            return result.add(zeroWithFinalPreferredScale,
+                              new MathContext(mc.getPrecision(), RoundingMode.UNNECESSARY));
+        } 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");
+            }
+        }
+    }
+
     /**
      * Returns a {@code BigDecimal} whose value is
      * <code>(this<sup>n</sup>)</code>, The power is computed exactly, to
--- /dev/null	2016-04-30 12:24:07.320478178 -0700
+++ new/test/java/math/BigDecimal/SquareRootTests.java	2016-05-11 10:37:28.902558211 -0700
@@ -0,0 +1,192 @@
+/*
+ * Copyright (c) 2016, 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.
+ *
+ * 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.
+ */
+
+/*
+ * @test
+ * @bug 4851777
+ * @summary Tests of BigDecimal.sqrt().
+ */
+
+import java.math.*;
+import java.util.*;
+
+public class SquareRootTests {
+
+    public static void main(String... args) {
+        int failures = 0;
+
+        failures += negativeTests();
+        failures += zeroTests();
+        failures += evenPowersOfTenTests();
+        failures += squareRootTwoTests();
+
+        // Add trickier rounding cases -- try to find examples of
+
+            // When setting the precision to use inside the loop, take
+            // care to avoid the case where the precision of the input
+            // exceeds the requested precision and rounding the input
+            // value too soon.
+
+
+        if (failures > 0 ) {
+            throw new RuntimeException("Incurred " + failures + " failures" +
+                                       " testing BigDecimal.sqrt().");
+        }
+    }
+
+    private static int negativeTests() {
+        int failures = 0;
+
+        for (long i = -10; i < 0; i++) {
+            for (int j = -5; j < 5; j++) {
+                try {
+                    BigDecimal input = BigDecimal.valueOf(i, j);
+                    BigDecimal result = input.sqrt(MathContext.DECIMAL64);
+                    System.err.println("Unexpected sqrt of negative: (" +
+                                       input + ").sqrt()  = " + result );
+                    failures += 1;
+                } catch (ArithmeticException e) {
+                    ; // Expected
+                }
+            }
+        }
+        
+        return failures;
+    }
+
+    private static int zeroTests() {
+        int failures = 0;
+
+        for (int i = -100; i < 100; i++) {
+            BigDecimal expected = BigDecimal.valueOf(0L, i/2);
+            // These results are independent of rounding mode
+            failures += compare(BigDecimal.valueOf(0L, i).sqrt(MathContext.UNLIMITED),
+                                expected, true, "zeros");
+
+            failures += compare(BigDecimal.valueOf(0L, i).sqrt(MathContext.DECIMAL64),
+                                expected, true, "zeros");
+        }
+
+        return failures;
+    }
+
+    /**
+     * sqrt(10^2N) is 10^N
+     * Both numerical value and representation should be verified
+     */
+    private static int evenPowersOfTenTests() {
+        int failures = 0;
+        MathContext oneDigitExactly = new MathContext(1, RoundingMode.UNNECESSARY);
+
+        for (int scale = -100; scale <= 100; scale++) {
+            BigDecimal testValue       = BigDecimal.valueOf(1, 2*scale);
+            BigDecimal expectedNumericalResult = BigDecimal.valueOf(1, scale);
+
+            BigDecimal result;
+
+
+            failures += equalNumerically(expectedNumericalResult,
+                                           result = testValue.sqrt(MathContext.DECIMAL64),
+                                           "Even powers of 10, DECIMAL64");
+
+            // Can round to one digit of precision exactly
+            failures += equalNumerically(expectedNumericalResult,
+                                           result = testValue.sqrt(oneDigitExactly),
+                                           "even powers of 10, 1 digit");
+            if (result.precision() > 1) {
+                failures += 1;
+                System.err.println("Excess precision for " + result);
+            }
+                
+
+            // If rounding to more than one digit, do precision / scale checking...
+
+        }
+
+        return failures;
+    }
+
+    private static int squareRootTwoTests() {
+        int failures = 0;
+        BigDecimal TWO = new BigDecimal(2);
+
+        // Square root of 2 truncated to 65 digits
+        BigDecimal highPrecisionRoot2 =
+            new BigDecimal("1.41421356237309504880168872420969807856967187537694807317667973799");
+
+
+        RoundingMode[] modes = {
+            RoundingMode.UP,       RoundingMode.DOWN,
+            RoundingMode.CEILING, RoundingMode.FLOOR,
+            RoundingMode.HALF_UP, RoundingMode.HALF_DOWN, RoundingMode.HALF_EVEN
+        };
+
+        // For each iteresting rounding mode, for precisions 1 to, say
+        // 63 numerically compare TWO.sqrt(mc) to
+        // highPrecisionRoot2.round(mc)
+        
+        for (RoundingMode mode : modes) {
+            for (int precision = 1; precision < 63; precision++) {
+                MathContext mc = new MathContext(precision, mode);
+                BigDecimal expected = highPrecisionRoot2.round(mc); 
+                BigDecimal computed = TWO.sqrt(mc);
+
+                equalNumerically(expected, computed, "sqrt(2)");
+            }
+        }
+
+        return failures;
+    }
+
+
+
+    private static int compare(BigDecimal a, BigDecimal b, boolean expected, String prefix) {
+        boolean result = a.equals(b);
+        int failed = (result==expected) ? 0 : 1;
+        if (failed == 1) {
+            System.err.println("Testing " + prefix + 
+                               "(" + a + ").compareTo(" + b + ") => " + result +
+                               "\n\tExpected " + expected);
+        }
+        return failed;
+    }
+
+    private static int equalNumerically(BigDecimal a, BigDecimal b,
+                                        String prefix) {
+        return compareNumerically(a, b, 0, prefix);
+    }
+
+
+    private static int compareNumerically(BigDecimal a, BigDecimal b,
+                                          int expected, String prefix) {
+        int result = a.compareTo(b);
+        int failed = (result==expected) ? 0 : 1;
+        if (failed == 1) {
+            System.err.println("Testing " + prefix + 
+                               "(" + a + ").compareTo(" + b + ") => " + result +
+                               "\n\tExpected " + expected);
+        }
+        return failed;
+    }
+
+}