src/share/classes/java/math/BigInteger.java
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rev 7488 : 7131192: BigInteger.doubleValue() is depressingly slow
Summary: In doubleValue() and floatValue() replace converting to String and parsing to Double or Float with direct conversion into IEEE 754 bits.
Reviewed-by: bpb, drchase, martin
Contributed-by: Louis Wasserman <lowasser@google.com>
@@ -33,10 +33,12 @@
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.io.ObjectStreamField;
import java.util.Arrays;
import java.util.Random;
+import sun.misc.DoubleConsts;
+import sun.misc.FloatConsts;
/**
* Immutable arbitrary-precision integers. All operations behave as if
* BigIntegers were represented in two's-complement notation (like Java's
* primitive integer types). BigInteger provides analogues to all of Java's
@@ -3450,12 +3452,76 @@
* information about the precision of the BigInteger value.
*
* @return this BigInteger converted to a {@code float}.
*/
public float floatValue() {
- // Somewhat inefficient, but guaranteed to work.
- return Float.parseFloat(this.toString());
+ if (signum == 0) {
+ return 0.0f;
+ }
+
+ int exponent = ((mag.length - 1) << 5) + bitLengthForInt(mag[0]) - 1;
+
+ // exponent == floor(log2(abs(this)))
+ if (exponent < Long.SIZE - 1) {
+ return longValue();
+ } else if (exponent > Float.MAX_EXPONENT) {
+ return signum > 0 ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;
+ }
+
+ /*
+ * We need the top SIGNIFICAND_WIDTH bits, including the "implicit"
+ * one bit. To make rounding easier, we pick out the top
+ * SIGNIFICAND_WIDTH + 1 bits, so we have one to help us round up or
+ * down. twiceSignifFloor will contain the top SIGNIFICAND_WIDTH + 1
+ * bits, and signifFloor the top SIGNIFICAND_WIDTH.
+ *
+ * It helps to consider the real number signif = abs(this) *
+ * 2^(SIGNIFICAND_WIDTH - 1 - exponent).
+ */
+ int shift = exponent - FloatConsts.SIGNIFICAND_WIDTH;
+
+ int twiceSignifFloor;
+ // twiceSignifFloor will be == abs().shiftRight(shift).intValue()
+ // We do the shift into an int directly to improve performance.
+
+ int nBits = shift & 0x1f;
+ int nBits2 = 32 - nBits;
+
+ if (nBits == 0) {
+ twiceSignifFloor = mag[0];
+ } else {
+ twiceSignifFloor = mag[0] >>> nBits;
+ if (twiceSignifFloor == 0) {
+ twiceSignifFloor = (mag[0] << nBits2) | (mag[1] >>> nBits);
+ }
+ }
+
+ int signifFloor = twiceSignifFloor >> 1;
+ signifFloor &= FloatConsts.SIGNIF_BIT_MASK; // remove the implied bit
+
+ /*
+ * We round up if either the fractional part of signif is strictly
+ * greater than 0.5 (which is true if the 0.5 bit is set and any lower
+ * bit is set), or if the fractional part of signif is >= 0.5 and
+ * signifFloor is odd (which is true if both the 0.5 bit and the 1 bit
+ * are set). This is equivalent to the desired HALF_EVEN rounding.
+ */
+ boolean increment = (twiceSignifFloor & 1) != 0
+ && ((signifFloor & 1) != 0 || abs().getLowestSetBit() < shift);
+ int signifRounded = increment ? signifFloor + 1 : signifFloor;
+ int bits = ((exponent + FloatConsts.EXP_BIAS))
+ << (FloatConsts.SIGNIFICAND_WIDTH - 1);
+ bits += signifRounded;
+ /*
+ * If signifRounded == 2^24, we'd need to set all of the significand
+ * bits to zero and add 1 to the exponent. This is exactly the behavior
+ * we get from just adding signifRounded to bits directly. If the
+ * exponent is Float.MAX_EXPONENT, we round up (correctly) to
+ * Float.POSITIVE_INFINITY.
+ */
+ bits |= signum & FloatConsts.SIGN_BIT_MASK;
+ return Float.intBitsToFloat(bits);
}
/**
* Converts this BigInteger to a {@code double}. This
* conversion is similar to the
@@ -3470,12 +3536,84 @@
* information about the precision of the BigInteger value.
*
* @return this BigInteger converted to a {@code double}.
*/
public double doubleValue() {
- // Somewhat inefficient, but guaranteed to work.
- return Double.parseDouble(this.toString());
+ if (signum == 0) {
+ return 0.0;
+ }
+
+ int exponent = ((mag.length - 1) << 5) + bitLengthForInt(mag[0]) - 1;
+
+ // exponent == floor(log2(abs(this))Double)
+ if (exponent < Long.SIZE - 1) {
+ return longValue();
+ } else if (exponent > Double.MAX_EXPONENT) {
+ return signum > 0 ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
+ }
+
+ /*
+ * We need the top SIGNIFICAND_WIDTH bits, including the "implicit"
+ * one bit. To make rounding easier, we pick out the top
+ * SIGNIFICAND_WIDTH + 1 bits, so we have one to help us round up or
+ * down. twiceSignifFloor will contain the top SIGNIFICAND_WIDTH + 1
+ * bits, and signifFloor the top SIGNIFICAND_WIDTH.
+ *
+ * It helps to consider the real number signif = abs(this) *
+ * 2^(SIGNIFICAND_WIDTH - 1 - exponent).
+ */
+ int shift = exponent - DoubleConsts.SIGNIFICAND_WIDTH;
+
+ long twiceSignifFloor;
+ // twiceSignifFloor will be == abs().shiftRight(shift).longValue()
+ // We do the shift into a long directly to improve performance.
+
+ int nBits = shift & 0x1f;
+ int nBits2 = 32 - nBits;
+
+ int highBits;
+ int lowBits;
+ if (nBits == 0) {
+ highBits = mag[0];
+ lowBits = mag[1];
+ } else {
+ highBits = mag[0] >>> nBits;
+ lowBits = (mag[0] << nBits2) | (mag[1] >>> nBits);
+ if (highBits == 0) {
+ highBits = lowBits;
+ lowBits = (mag[1] << nBits2) | (mag[2] >>> nBits);
+ }
+ }
+
+ twiceSignifFloor = ((highBits & LONG_MASK) << 32)
+ | (lowBits & LONG_MASK);
+
+ long signifFloor = twiceSignifFloor >> 1;
+ signifFloor &= DoubleConsts.SIGNIF_BIT_MASK; // remove the implied bit
+
+ /*
+ * We round up if either the fractional part of signif is strictly
+ * greater than 0.5 (which is true if the 0.5 bit is set and any lower
+ * bit is set), or if the fractional part of signif is >= 0.5 and
+ * signifFloor is odd (which is true if both the 0.5 bit and the 1 bit
+ * are set). This is equivalent to the desired HALF_EVEN rounding.
+ */
+ boolean increment = (twiceSignifFloor & 1) != 0
+ && ((signifFloor & 1) != 0 || abs().getLowestSetBit() < shift);
+ long signifRounded = increment ? signifFloor + 1 : signifFloor;
+ long bits = (long) ((exponent + DoubleConsts.EXP_BIAS))
+ << (DoubleConsts.SIGNIFICAND_WIDTH - 1);
+ bits += signifRounded;
+ /*
+ * If signifRounded == 2^53, we'd need to set all of the significand
+ * bits to zero and add 1 to the exponent. This is exactly the behavior
+ * we get from just adding signifRounded to bits directly. If the
+ * exponent is Double.MAX_EXPONENT, we round up (correctly) to
+ * Double.POSITIVE_INFINITY.
+ */
+ bits |= signum & DoubleConsts.SIGN_BIT_MASK;
+ return Double.longBitsToDouble(bits);
}
/**
* Returns a copy of the input array stripped of any leading zero bytes.
*/