Java Code Examples for sun.misc.DoubleConsts#SIGNIF_BIT_MASK
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sun.misc.DoubleConsts#SIGNIF_BIT_MASK .
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Example 1
Source File: Math.java From JDKSourceCode1.8 with MIT License | 5 votes |
/** * Returns the closest {@code long} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Long.MIN_VALUE}, the result is * equal to the value of {@code Long.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Long.MAX_VALUE}, the result is * equal to the value of {@code Long.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to a * {@code long}. * @return the value of the argument rounded to the nearest * {@code long} value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { long longBits = Double.doubleToRawLongBits(a); long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 + DoubleConsts.EXP_BIAS) - biasedExp; if ((shift & -64) == 0) { // shift >= 0 && shift < 64 // a is a finite number such that pow(2,-64) <= ulp(a) < 1 long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) | (DoubleConsts.SIGNIF_BIT_MASK + 1)); if (longBits < 0) { r = -r; } // In the comments below each Java expression evaluates to the value // the corresponding mathematical expression: // (r) evaluates to a / ulp(a) // (r >> shift) evaluates to floor(a * 2) // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) return ((r >> shift) + 1) >> 1; } else { // a is either // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer // - an infinity or NaN return (long) a; } }
Example 2
Source File: Math.java From Java8CN with Apache License 2.0 | 5 votes |
/** * Returns the closest {@code long} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Long.MIN_VALUE}, the result is * equal to the value of {@code Long.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Long.MAX_VALUE}, the result is * equal to the value of {@code Long.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to a * {@code long}. * @return the value of the argument rounded to the nearest * {@code long} value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { long longBits = Double.doubleToRawLongBits(a); long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 + DoubleConsts.EXP_BIAS) - biasedExp; if ((shift & -64) == 0) { // shift >= 0 && shift < 64 // a is a finite number such that pow(2,-64) <= ulp(a) < 1 long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) | (DoubleConsts.SIGNIF_BIT_MASK + 1)); if (longBits < 0) { r = -r; } // In the comments below each Java expression evaluates to the value // the corresponding mathematical expression: // (r) evaluates to a / ulp(a) // (r >> shift) evaluates to floor(a * 2) // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) return ((r >> shift) + 1) >> 1; } else { // a is either // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer // - an infinity or NaN return (long) a; } }
Example 3
Source File: Math.java From jdk8u60 with GNU General Public License v2.0 | 5 votes |
/** * Returns the closest {@code long} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Long.MIN_VALUE}, the result is * equal to the value of {@code Long.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Long.MAX_VALUE}, the result is * equal to the value of {@code Long.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to a * {@code long}. * @return the value of the argument rounded to the nearest * {@code long} value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { long longBits = Double.doubleToRawLongBits(a); long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 + DoubleConsts.EXP_BIAS) - biasedExp; if ((shift & -64) == 0) { // shift >= 0 && shift < 64 // a is a finite number such that pow(2,-64) <= ulp(a) < 1 long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) | (DoubleConsts.SIGNIF_BIT_MASK + 1)); if (longBits < 0) { r = -r; } // In the comments below each Java expression evaluates to the value // the corresponding mathematical expression: // (r) evaluates to a / ulp(a) // (r >> shift) evaluates to floor(a * 2) // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) return ((r >> shift) + 1) >> 1; } else { // a is either // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer // - an infinity or NaN return (long) a; } }
Example 4
Source File: Math.java From jdk8u_jdk with GNU General Public License v2.0 | 5 votes |
/** * Returns the closest {@code long} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Long.MIN_VALUE}, the result is * equal to the value of {@code Long.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Long.MAX_VALUE}, the result is * equal to the value of {@code Long.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to a * {@code long}. * @return the value of the argument rounded to the nearest * {@code long} value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { long longBits = Double.doubleToRawLongBits(a); long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 + DoubleConsts.EXP_BIAS) - biasedExp; if ((shift & -64) == 0) { // shift >= 0 && shift < 64 // a is a finite number such that pow(2,-64) <= ulp(a) < 1 long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) | (DoubleConsts.SIGNIF_BIT_MASK + 1)); if (longBits < 0) { r = -r; } // In the comments below each Java expression evaluates to the value // the corresponding mathematical expression: // (r) evaluates to a / ulp(a) // (r >> shift) evaluates to floor(a * 2) // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) return ((r >> shift) + 1) >> 1; } else { // a is either // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer // - an infinity or NaN return (long) a; } }
Example 5
Source File: Math.java From openjdk-8-source with GNU General Public License v2.0 | 5 votes |
/** * Returns the closest {@code long} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Long.MIN_VALUE}, the result is * equal to the value of {@code Long.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Long.MAX_VALUE}, the result is * equal to the value of {@code Long.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to a * {@code long}. * @return the value of the argument rounded to the nearest * {@code long} value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { long longBits = Double.doubleToRawLongBits(a); long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 + DoubleConsts.EXP_BIAS) - biasedExp; if ((shift & -64) == 0) { // shift >= 0 && shift < 64 // a is a finite number such that pow(2,-64) <= ulp(a) < 1 long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) | (DoubleConsts.SIGNIF_BIT_MASK + 1)); if (longBits < 0) { r = -r; } // In the comments below each Java expression evaluates to the value // the corresponding mathematical expression: // (r) evaluates to a / ulp(a) // (r >> shift) evaluates to floor(a * 2) // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) return ((r >> shift) + 1) >> 1; } else { // a is either // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer // - an infinity or NaN return (long) a; } }
Example 6
Source File: Math.java From openjdk-8 with GNU General Public License v2.0 | 5 votes |
/** * Returns the closest {@code long} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Long.MIN_VALUE}, the result is * equal to the value of {@code Long.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Long.MAX_VALUE}, the result is * equal to the value of {@code Long.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to a * {@code long}. * @return the value of the argument rounded to the nearest * {@code long} value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { long longBits = Double.doubleToRawLongBits(a); long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 + DoubleConsts.EXP_BIAS) - biasedExp; if ((shift & -64) == 0) { // shift >= 0 && shift < 64 // a is a finite number such that pow(2,-64) <= ulp(a) < 1 long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) | (DoubleConsts.SIGNIF_BIT_MASK + 1)); if (longBits < 0) { r = -r; } // In the comments below each Java expression evaluates to the value // the corresponding mathematical expression: // (r) evaluates to a / ulp(a) // (r >> shift) evaluates to floor(a * 2) // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) return ((r >> shift) + 1) >> 1; } else { // a is either // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer // - an infinity or NaN return (long) a; } }
Example 7
Source File: BigInteger.java From jdk8u-jdk with GNU General Public License v2.0 | 4 votes |
/** * Converts this BigInteger to a {@code double}. This * conversion is similar to the * <i>narrowing primitive conversion</i> from {@code double} to * {@code float} as defined in section 5.1.3 of * <cite>The Java™ Language Specification</cite>: * if this BigInteger has too great a magnitude * to 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 BigInteger value. * * @return this BigInteger converted to a {@code double}. */ public double doubleValue() { 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); }
Example 8
Source File: FpUtils.java From javaide with GNU General Public License v3.0 | 4 votes |
/** * Returns unbiased exponent of a <code>double</code>; for * subnormal values, the number is treated as if it were * normalized. That is for all finite, non-zero, positive numbers * <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is * always in the range [1, 2). * <p> * Special cases: * <ul> * <li> If the argument is NaN, then the result is 2<sup>30</sup>. * <li> If the argument is infinite, then the result is 2<sup>28</sup>. * <li> If the argument is zero, then the result is -(2<sup>28</sup>). * </ul> * * @param d floating-point number whose exponent is to be extracted * @return unbiased exponent of the argument. * @author Joseph D. Darcy */ public static int ilogb(double d) { int exponent = getExponent(d); switch (exponent) { case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity if( isNaN(d) ) return (1<<30); // 2^30 else // infinite value return (1<<28); // 2^28 // break; case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal if(d == 0.0) { return -(1<<28); // -(2^28) } else { long transducer = Double.doubleToRawLongBits(d); /* * To avoid causing slow arithmetic on subnormals, * the scaling to determine when d's significand * is normalized is done in integer arithmetic. * (there must be at least one "1" bit in the * significand since zero has been screened out. */ // isolate significand bits transducer &= DoubleConsts.SIGNIF_BIT_MASK; assert(transducer != 0L); // This loop is simple and functional. We might be // able to do something more clever that was faster; // e.g. number of leading zero detection on // (transducer << (# exponent and sign bits). while (transducer < (1L << (DoubleConsts.SIGNIFICAND_WIDTH - 1))) { transducer *= 2; exponent--; } exponent++; assert( exponent >= DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1) && exponent < DoubleConsts.MIN_EXPONENT); return exponent; } // break; default: assert( exponent >= DoubleConsts.MIN_EXPONENT && exponent <= DoubleConsts.MAX_EXPONENT); return exponent; // break; } }
Example 9
Source File: BigInteger.java From j2objc with Apache License 2.0 | 4 votes |
/** * Converts this BigInteger to a {@code double}. This * conversion is similar to the * <i>narrowing primitive conversion</i> from {@code double} to * {@code float} as defined in section 5.1.3 of * <cite>The Java™ Language Specification</cite>: * if this BigInteger has too great a magnitude * to 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 BigInteger value. * * @return this BigInteger converted to a {@code double}. */ public double doubleValue() { 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); }
Example 10
Source File: FpUtils.java From openjdk-8 with GNU General Public License v2.0 | 4 votes |
/** * Returns unbiased exponent of a {@code double}; for * subnormal values, the number is treated as if it were * normalized. That is for all finite, non-zero, positive numbers * <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is * always in the range [1, 2). * <p> * Special cases: * <ul> * <li> If the argument is NaN, then the result is 2<sup>30</sup>. * <li> If the argument is infinite, then the result is 2<sup>28</sup>. * <li> If the argument is zero, then the result is -(2<sup>28</sup>). * </ul> * * @param d floating-point number whose exponent is to be extracted * @return unbiased exponent of the argument. * @author Joseph D. Darcy */ public static int ilogb(double d) { int exponent = getExponent(d); switch (exponent) { case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity if( isNaN(d) ) return (1<<30); // 2^30 else // infinite value return (1<<28); // 2^28 case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal if(d == 0.0) { return -(1<<28); // -(2^28) } else { long transducer = Double.doubleToRawLongBits(d); /* * To avoid causing slow arithmetic on subnormals, * the scaling to determine when d's significand * is normalized is done in integer arithmetic. * (there must be at least one "1" bit in the * significand since zero has been screened out. */ // isolate significand bits transducer &= DoubleConsts.SIGNIF_BIT_MASK; assert(transducer != 0L); // This loop is simple and functional. We might be // able to do something more clever that was faster; // e.g. number of leading zero detection on // (transducer << (# exponent and sign bits). while (transducer < (1L << (DoubleConsts.SIGNIFICAND_WIDTH - 1))) { transducer *= 2; exponent--; } exponent++; assert( exponent >= DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1) && exponent < DoubleConsts.MIN_EXPONENT); return exponent; } default: assert( exponent >= DoubleConsts.MIN_EXPONENT && exponent <= DoubleConsts.MAX_EXPONENT); return exponent; } }
Example 11
Source File: BigInteger.java From Java8CN with Apache License 2.0 | 4 votes |
/** * Converts this BigInteger to a {@code double}. This * conversion is similar to the * <i>narrowing primitive conversion</i> from {@code double} to * {@code float} as defined in section 5.1.3 of * <cite>The Java™ Language Specification</cite>: * if this BigInteger has too great a magnitude * to 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 BigInteger value. * * @return this BigInteger converted to a {@code double}. */ public double doubleValue() { 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); }
Example 12
Source File: FpUtils.java From java-n-IDE-for-Android with Apache License 2.0 | 4 votes |
/** * Returns unbiased exponent of a <code>double</code>; for * subnormal values, the number is treated as if it were * normalized. That is for all finite, non-zero, positive numbers * <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is * always in the range [1, 2). * <p> * Special cases: * <ul> * <li> If the argument is NaN, then the result is 2<sup>30</sup>. * <li> If the argument is infinite, then the result is 2<sup>28</sup>. * <li> If the argument is zero, then the result is -(2<sup>28</sup>). * </ul> * * @param d floating-point number whose exponent is to be extracted * @return unbiased exponent of the argument. * @author Joseph D. Darcy */ public static int ilogb(double d) { int exponent = getExponent(d); switch (exponent) { case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity if( isNaN(d) ) return (1<<30); // 2^30 else // infinite value return (1<<28); // 2^28 // break; case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal if(d == 0.0) { return -(1<<28); // -(2^28) } else { long transducer = Double.doubleToRawLongBits(d); /* * To avoid causing slow arithmetic on subnormals, * the scaling to determine when d's significand * is normalized is done in integer arithmetic. * (there must be at least one "1" bit in the * significand since zero has been screened out. */ // isolate significand bits transducer &= DoubleConsts.SIGNIF_BIT_MASK; assert(transducer != 0L); // This loop is simple and functional. We might be // able to do something more clever that was faster; // e.g. number of leading zero detection on // (transducer << (# exponent and sign bits). while (transducer < (1L << (DoubleConsts.SIGNIFICAND_WIDTH - 1))) { transducer *= 2; exponent--; } exponent++; assert( exponent >= DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1) && exponent < DoubleConsts.MIN_EXPONENT); return exponent; } // break; default: assert( exponent >= DoubleConsts.MIN_EXPONENT && exponent <= DoubleConsts.MAX_EXPONENT); return exponent; // break; } }
Example 13
Source File: BigInteger.java From dragonwell8_jdk with GNU General Public License v2.0 | 4 votes |
/** * Converts this BigInteger to a {@code double}. This * conversion is similar to the * <i>narrowing primitive conversion</i> from {@code double} to * {@code float} as defined in section 5.1.3 of * <cite>The Java™ Language Specification</cite>: * if this BigInteger has too great a magnitude * to 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 BigInteger value. * * @return this BigInteger converted to a {@code double}. */ public double doubleValue() { 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); }
Example 14
Source File: FpUtils.java From openjdk-jdk8u with GNU General Public License v2.0 | 4 votes |
/** * Returns unbiased exponent of a {@code double}; for * subnormal values, the number is treated as if it were * normalized. That is for all finite, non-zero, positive numbers * <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is * always in the range [1, 2). * <p> * Special cases: * <ul> * <li> If the argument is NaN, then the result is 2<sup>30</sup>. * <li> If the argument is infinite, then the result is 2<sup>28</sup>. * <li> If the argument is zero, then the result is -(2<sup>28</sup>). * </ul> * * @param d floating-point number whose exponent is to be extracted * @return unbiased exponent of the argument. * @author Joseph D. Darcy */ public static int ilogb(double d) { int exponent = getExponent(d); switch (exponent) { case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity if( isNaN(d) ) return (1<<30); // 2^30 else // infinite value return (1<<28); // 2^28 case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal if(d == 0.0) { return -(1<<28); // -(2^28) } else { long transducer = Double.doubleToRawLongBits(d); /* * To avoid causing slow arithmetic on subnormals, * the scaling to determine when d's significand * is normalized is done in integer arithmetic. * (there must be at least one "1" bit in the * significand since zero has been screened out. */ // isolate significand bits transducer &= DoubleConsts.SIGNIF_BIT_MASK; assert(transducer != 0L); // This loop is simple and functional. We might be // able to do something more clever that was faster; // e.g. number of leading zero detection on // (transducer << (# exponent and sign bits). while (transducer < (1L << (DoubleConsts.SIGNIFICAND_WIDTH - 1))) { transducer *= 2; exponent--; } exponent++; assert( exponent >= DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1) && exponent < DoubleConsts.MIN_EXPONENT); return exponent; } default: assert( exponent >= DoubleConsts.MIN_EXPONENT && exponent <= DoubleConsts.MAX_EXPONENT); return exponent; } }
Example 15
Source File: BigInteger.java From openjdk-jdk8u-backup with GNU General Public License v2.0 | 4 votes |
/** * Converts this BigInteger to a {@code double}. This * conversion is similar to the * <i>narrowing primitive conversion</i> from {@code double} to * {@code float} as defined in section 5.1.3 of * <cite>The Java™ Language Specification</cite>: * if this BigInteger has too great a magnitude * to 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 BigInteger value. * * @return this BigInteger converted to a {@code double}. */ public double doubleValue() { 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); }
Example 16
Source File: Double.java From openjdk-jdk8u-backup with GNU General Public License v2.0 | 3 votes |
/** * Returns a representation of the specified floating-point value * according to the IEEE 754 floating-point "double * format" bit layout. * * <p>Bit 63 (the bit that is selected by the mask * {@code 0x8000000000000000L}) represents the sign of the * floating-point number. Bits * 62-52 (the bits that are selected by the mask * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 * (the bits that are selected by the mask * {@code 0x000fffffffffffffL}) represent the significand * (sometimes called the mantissa) of the floating-point number. * * <p>If the argument is positive infinity, the result is * {@code 0x7ff0000000000000L}. * * <p>If the argument is negative infinity, the result is * {@code 0xfff0000000000000L}. * * <p>If the argument is NaN, the result is * {@code 0x7ff8000000000000L}. * * <p>In all cases, the result is a {@code long} integer that, when * given to the {@link #longBitsToDouble(long)} method, will produce a * floating-point value the same as the argument to * {@code doubleToLongBits} (except all NaN values are * collapsed to a single "canonical" NaN value). * * @param value a {@code double} precision floating-point number. * @return the bits that represent the floating-point number. */ public static long doubleToLongBits(double value) { long result = doubleToRawLongBits(value); // Check for NaN based on values of bit fields, maximum // exponent and nonzero significand. if ( ((result & DoubleConsts.EXP_BIT_MASK) == DoubleConsts.EXP_BIT_MASK) && (result & DoubleConsts.SIGNIF_BIT_MASK) != 0L) result = 0x7ff8000000000000L; return result; }
Example 17
Source File: Double.java From jdk8u-jdk with GNU General Public License v2.0 | 3 votes |
/** * Returns a representation of the specified floating-point value * according to the IEEE 754 floating-point "double * format" bit layout. * * <p>Bit 63 (the bit that is selected by the mask * {@code 0x8000000000000000L}) represents the sign of the * floating-point number. Bits * 62-52 (the bits that are selected by the mask * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 * (the bits that are selected by the mask * {@code 0x000fffffffffffffL}) represent the significand * (sometimes called the mantissa) of the floating-point number. * * <p>If the argument is positive infinity, the result is * {@code 0x7ff0000000000000L}. * * <p>If the argument is negative infinity, the result is * {@code 0xfff0000000000000L}. * * <p>If the argument is NaN, the result is * {@code 0x7ff8000000000000L}. * * <p>In all cases, the result is a {@code long} integer that, when * given to the {@link #longBitsToDouble(long)} method, will produce a * floating-point value the same as the argument to * {@code doubleToLongBits} (except all NaN values are * collapsed to a single "canonical" NaN value). * * @param value a {@code double} precision floating-point number. * @return the bits that represent the floating-point number. */ public static long doubleToLongBits(double value) { long result = doubleToRawLongBits(value); // Check for NaN based on values of bit fields, maximum // exponent and nonzero significand. if ( ((result & DoubleConsts.EXP_BIT_MASK) == DoubleConsts.EXP_BIT_MASK) && (result & DoubleConsts.SIGNIF_BIT_MASK) != 0L) result = 0x7ff8000000000000L; return result; }
Example 18
Source File: Double.java From jdk8u_jdk with GNU General Public License v2.0 | 3 votes |
/** * Returns a representation of the specified floating-point value * according to the IEEE 754 floating-point "double * format" bit layout. * * <p>Bit 63 (the bit that is selected by the mask * {@code 0x8000000000000000L}) represents the sign of the * floating-point number. Bits * 62-52 (the bits that are selected by the mask * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 * (the bits that are selected by the mask * {@code 0x000fffffffffffffL}) represent the significand * (sometimes called the mantissa) of the floating-point number. * * <p>If the argument is positive infinity, the result is * {@code 0x7ff0000000000000L}. * * <p>If the argument is negative infinity, the result is * {@code 0xfff0000000000000L}. * * <p>If the argument is NaN, the result is * {@code 0x7ff8000000000000L}. * * <p>In all cases, the result is a {@code long} integer that, when * given to the {@link #longBitsToDouble(long)} method, will produce a * floating-point value the same as the argument to * {@code doubleToLongBits} (except all NaN values are * collapsed to a single "canonical" NaN value). * * @param value a {@code double} precision floating-point number. * @return the bits that represent the floating-point number. */ public static long doubleToLongBits(double value) { long result = doubleToRawLongBits(value); // Check for NaN based on values of bit fields, maximum // exponent and nonzero significand. if ( ((result & DoubleConsts.EXP_BIT_MASK) == DoubleConsts.EXP_BIT_MASK) && (result & DoubleConsts.SIGNIF_BIT_MASK) != 0L) result = 0x7ff8000000000000L; return result; }
Example 19
Source File: Double.java From AndroidComponentPlugin with Apache License 2.0 | 3 votes |
/** * Returns a representation of the specified floating-point value * according to the IEEE 754 floating-point "double * format" bit layout. * * <p>Bit 63 (the bit that is selected by the mask * {@code 0x8000000000000000L}) represents the sign of the * floating-point number. Bits * 62-52 (the bits that are selected by the mask * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 * (the bits that are selected by the mask * {@code 0x000fffffffffffffL}) represent the significand * (sometimes called the mantissa) of the floating-point number. * * <p>If the argument is positive infinity, the result is * {@code 0x7ff0000000000000L}. * * <p>If the argument is negative infinity, the result is * {@code 0xfff0000000000000L}. * * <p>If the argument is NaN, the result is * {@code 0x7ff8000000000000L}. * * <p>In all cases, the result is a {@code long} integer that, when * given to the {@link #longBitsToDouble(long)} method, will produce a * floating-point value the same as the argument to * {@code doubleToLongBits} (except all NaN values are * collapsed to a single "canonical" NaN value). * * @param value a {@code double} precision floating-point number. * @return the bits that represent the floating-point number. */ public static long doubleToLongBits(double value) { long result = doubleToRawLongBits(value); // Check for NaN based on values of bit fields, maximum // exponent and nonzero significand. if ( ((result & DoubleConsts.EXP_BIT_MASK) == DoubleConsts.EXP_BIT_MASK) && (result & DoubleConsts.SIGNIF_BIT_MASK) != 0L) result = 0x7ff8000000000000L; return result; }
Example 20
Source File: Double.java From openjdk-jdk8u with GNU General Public License v2.0 | 3 votes |
/** * Returns a representation of the specified floating-point value * according to the IEEE 754 floating-point "double * format" bit layout. * * <p>Bit 63 (the bit that is selected by the mask * {@code 0x8000000000000000L}) represents the sign of the * floating-point number. Bits * 62-52 (the bits that are selected by the mask * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 * (the bits that are selected by the mask * {@code 0x000fffffffffffffL}) represent the significand * (sometimes called the mantissa) of the floating-point number. * * <p>If the argument is positive infinity, the result is * {@code 0x7ff0000000000000L}. * * <p>If the argument is negative infinity, the result is * {@code 0xfff0000000000000L}. * * <p>If the argument is NaN, the result is * {@code 0x7ff8000000000000L}. * * <p>In all cases, the result is a {@code long} integer that, when * given to the {@link #longBitsToDouble(long)} method, will produce a * floating-point value the same as the argument to * {@code doubleToLongBits} (except all NaN values are * collapsed to a single "canonical" NaN value). * * @param value a {@code double} precision floating-point number. * @return the bits that represent the floating-point number. */ public static long doubleToLongBits(double value) { long result = doubleToRawLongBits(value); // Check for NaN based on values of bit fields, maximum // exponent and nonzero significand. if ( ((result & DoubleConsts.EXP_BIT_MASK) == DoubleConsts.EXP_BIT_MASK) && (result & DoubleConsts.SIGNIF_BIT_MASK) != 0L) result = 0x7ff8000000000000L; return result; }