int log2 = DoubleMath.log2(d, FLOOR);
      assertTrue(StrictMath.pow(2.0, log2) <= d);
      assertTrue(StrictMath.pow(2.0, log2 + 1) > d);
    }
  }

  @GwtIncompatible // DoubleMath.log2(double, RoundingMode), StrictMath
  public void testRoundLog2Ceiling() {
    for (double d : POSITIVE_FINITE_DOUBLE_CANDIDATES) {
      int log2 = DoubleMath.log2(d, CEILING);

      int log2 = DoubleMath.log2(d, FLOOR);
      assertTrue(StrictMath.pow(2.0, log2) <= d);
      assertTrue(StrictMath.pow(2.0, log2 + 1) > d);
    }
  }

  @GwtIncompatible // DoubleMath.log2(double, RoundingMode), StrictMath
  public void testRoundLog2Ceiling() {
    for (double d : POSITIVE_FINITE_DOUBLE_CANDIDATES) {
      int log2 = DoubleMath.log2(d, CEILING);

     *
     * The key idea is that based on the number of leading zeros (equivalently, floor(log2(x))), we
     * can narrow the possible floor(log10(x)) values to two. For example, if floor(log2(x)) is 6,
     * then 64 <= x < 128, so floor(log10(x)) is either 1 or 2.
     */
    int y = maxLog10ForLeadingZeros[Integer.numberOfLeadingZeros(x)];
    /*

     *
     * The key idea is that based on the number of leading zeros (equivalently, floor(log2(x))), we
     * can narrow the possible floor(log10(x)) values to two. For example, if floor(log2(x)) is 6,
     * then 64 <= x < 128, so floor(log10(x)) is either 1 or 2.
     */
    int y = maxLog10ForLeadingZeros[Long.numberOfLeadingZeros(x)];
    /*

    // This is an extremely fast implementation of BigInteger.doubleValue(). JDK patch pending.
    BigInteger absX = x.abs();
    int exponent = absX.bitLength() - 1;
    // exponent == floor(log2(abs(x)))
    if (exponent < Long.SIZE - 1) {
      return x.longValue();
    } else if (exponent > MAX_EXPONENT) {
      return x.signum() * POSITIVE_INFINITY;
    }

    /*

    }
  }

  // Relies on the correctness of log2(BigInteger, {HALF_UP,HALF_DOWN}).
  public void testLog2HalfEven() {
    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
      int halfEven = BigIntegerMath.log2(x, HALF_EVEN);
      // Now figure out what rounding mode we should behave like (it depends if FLOOR was
      // odd/even).
      boolean floorWasEven = (BigIntegerMath.log2(x, FLOOR) & 1) == 0;

import static com.google.common.base.Preconditions.checkPositionIndexes;
import static com.google.common.base.Preconditions.checkState;
import static com.google.common.math.IntMath.divide;
import static com.google.common.math.IntMath.log2;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.math.RoundingMode.CEILING;
import static java.math.RoundingMode.FLOOR;
import static java.math.RoundingMode.UNNECESSARY;

errors.New("input overflows the modulus") } return x, nil } // SetOverflowingBytes assigns x = b, where b is a slice of big-endian bytes. // SetOverflowingBytes returns an error if b has a longer bit length than m, but // reduces overflowing values up to 2^⌈log2(m)⌉ - 1. // // The output will be resized to the size of m and overwritten. func (x *Nat) SetOverflowingBytes(b []byte, m *Modulus) (*Nat, error) { x.resetFor(m) if err := x.setBytes(b); err != nil { return nil, err } // setBytes would have returned...