Class Double

• If the argument is NaN, the result is the string "NaN".
• Otherwise, the result is a string that represents the sign and magnitude (absolute value) of the argument. If the sign is negative, the first character of the result is '-' ('\u002D'); if the sign is positive, no sign character appears in the result. As for the magnitude m:
  • If m is infinity, it is represented by the characters "Infinity"; thus, positive infinity produces the result "Infinity" and negative infinity produces the result "-Infinity".
  • If m is zero, it is represented by the characters "0.0"; thus, negative zero produces the result "-0.0" and positive zero produces the result "0.0".
  • Otherwise m is positive and finite. It is converted to a string in two stages:
    • Selection of a decimal: A well-defined decimal d_m is selected to represent m. This decimal is (almost always) the shortest one that rounds to m according to the round to nearest rounding policy of IEEE 754 floating-point arithmetic.
    • Formatting as a string: The decimal d_m is formatted as a string, either in plain or in computerized scientific notation, depending on its value.

A decimal is a number of the form s×10ⁱ for some (unique) integers s > 0 and i such that s is not a multiple of 10. These integers are the significand and the exponent, respectively, of the decimal. The length of the decimal is the (unique) positive integer n meeting 10^n-1 ≤ s < 10ⁿ.

The decimal d_m for a finite positive m is defined as follows:

• Let R be the set of all decimals that round to m according to the usual round to nearest rounding policy of IEEE 754 floating-point arithmetic.
• Let p be the minimal length over all decimals in R.
• When p ≥ 2, let T be the set of all decimals in R with length p. Otherwise, let T be the set of all decimals in R with length 1 or 2.
• Define d_m as the decimal in T that is closest to m. Or if there are two such decimals in T, select the one with the even significand.

The (uniquely) selected decimal d_m is then formatted. Let s, i and n be the significand, exponent and length of d_m, respectively. Further, let e = n + i - 1 and let s₁…s_n be the usual decimal expansion of s. Note that s₁ ≠ 0 and s_n ≠ 0. Below, the decimal point '.' is '\u002E' and the exponent indicator 'E' is '\u0045'.

• Case -3 ≤ e < 0: d_m is formatted as 0.0…0s₁…s_n, where there are exactly -(n + i) zeroes between the decimal point and s₁. For example, 123 × 10^-4 is formatted as 0.0123.
• Case 0 ≤ e < 7:
  • Subcase i ≥ 0: d_m is formatted as s₁…s_n0…0.0, where there are exactly i zeroes between s_n and the decimal point. For example, 123 × 10² is formatted as 12300.0.
  • Subcase i < 0: d_m is formatted as s₁…s_n+i.s_n+i+1…s_n, where there are exactly -i digits to the right of the decimal point. For example, 123 × 10^-1 is formatted as 12.3.
• Case e < -3 or e ≥ 7: computerized scientific notation is used to format d_m. Here e is formatted as by Integer.toString(int).
  • Subcase n = 1: d_m is formatted as s₁.0Ee. For example, 1 × 10²³ is formatted as 1.0E23.
  • Subcase n > 1: d_m is formatted as s₁.s₂…s_nEe. For example, 123 × 10^-21 is formatted as 1.23E-19.

To create localized string representations of a floating-point value, use subclasses of NumberFormat.

• If the argument is NaN, the result is the string "NaN".
• Otherwise, the result is a string that represents the sign and magnitude of the argument. If the sign is negative, the first character of the result is '-' ('\u002D'); if the sign is positive, no sign character appears in the result. As for the magnitude m:
  • If m is infinity, it is represented by the string "Infinity"; thus, positive infinity produces the result "Infinity" and negative infinity produces the result "-Infinity".
  • If m is zero, it is represented by the string "0x0.0p0"; thus, negative zero produces the result "-0x0.0p0" and positive zero produces the result "0x0.0p0".
  • If m is a double value with a normalized representation, substrings are used to represent the significand and exponent fields. The significand is represented by the characters "0x1." followed by a lowercase hexadecimal representation of the rest of the significand as a fraction. Trailing zeros in the hexadecimal representation are removed unless all the digits are zero, in which case a single zero is used. Next, the exponent is represented by "p" followed by a decimal string of the unbiased exponent as if produced by a call to Integer.toString on the exponent value.
  • If m is a double value with a subnormal representation, the significand is represented by the characters "0x0." followed by a hexadecimal representation of the rest of the significand as a fraction. Trailing zeros in the hexadecimal representation are removed. Next, the exponent is represented by "p-1022". Note that there must be at least one nonzero digit in a subnormal significand.

If s is null, then a NullPointerException is thrown.

Leading and trailing whitespace characters in s are ignored. Whitespace is removed as if by the String.trim() method; that is, both ASCII space and control characters are removed. The rest of s should constitute a FloatValue as described by the lexical syntax rules:

FloatValue:

Sign_opt NaN

Sign_opt Infinity

Sign_opt FloatingPointLiteral

Sign_opt HexFloatingPointLiteral

SignedInteger

HexFloatingPointLiteral:

HexSignificand BinaryExponent FloatTypeSuffix_opt

HexSignificand:

HexNumeral

HexNumeral .

0x HexDigits_opt . HexDigits

0X HexDigits_opt . HexDigits

BinaryExponent:

BinaryExponentIndicator SignedInteger

BinaryExponentIndicator:

p

P

Note that trailing format specifiers, specifiers that determine the type of a floating-point literal (1.0f is a float value; 1.0d is a double value), do not influence the results of this method. In other words, the numerical value of the input string is converted directly to the target floating-point type. The two-step sequence of conversions, string to float followed by float to double, is not equivalent to converting a string directly to double. For example, the float literal 0.1f is equal to the double value 0.10000000149011612; the float literal 0.1f represents a different numerical value than the double literal 0.1. (The numerical value 0.1 cannot be exactly represented in a binary floating-point number.)

To avoid calling this method on an invalid string and having a NumberFormatException be thrown, the regular expression below can be used to screen the input string:

 final String Digits     = "(\\p{Digit}+)";
 final String HexDigits  = "(\\p{XDigit}+)";
 // an exponent is 'e' or 'E' followed by an optionally
 // signed decimal integer.
 final String Exp        = "[eE][+-]?"+Digits;
 final String fpRegex    =
     ("[\\x00-\\x20]*"+  // Optional leading "whitespace"
      "[+-]?(" + // Optional sign character
      "NaN|" +           // "NaN" string
      "Infinity|" +      // "Infinity" string

      // A decimal floating-point string representing a finite positive
      // number without a leading sign has at most five basic pieces:
      // Digits . Digits ExponentPart FloatTypeSuffix
      //
      // Since this method allows integer-only strings as input
      // in addition to strings of floating-point literals, the
      // two sub-patterns below are simplifications of the grammar
      // productions from section 3.10.2 of
      // The Java Language Specification.

      // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
      "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+

      // . Digits ExponentPart_opt FloatTypeSuffix_opt
      "(\\.("+Digits+")("+Exp+")?)|"+

      // Hexadecimal strings
      "((" +
       // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
       "(0[xX]" + HexDigits + "(\\.)?)|" +

       // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
       "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +

       ")[pP][+-]?" + Digits + "))" +
      "[fFdD]?))" +
      "[\\x00-\\x20]*");// Optional trailing "whitespace"
 if (Pattern.matches(fpRegex, myString))
     Double.valueOf(myString); // Will not throw NumberFormatException
 else {
     // Perform suitable alternative action
 }

(int)(v^(v>>>32))

long v = Double.doubleToLongBits(this.doubleValue());

Bit 63 (the bit that is selected by the mask 0x8000000000000000L) represents the sign of the floating-point number. Bits 62-52 (the bits that are selected by the mask 0x7ff0000000000000L) represent the exponent. Bits 51-0 (the bits that are selected by the mask 0x000fffffffffffffL) represent the significand (sometimes called the mantissa) of the floating-point number.

If the argument is positive infinity, the result is 0x7ff0000000000000L.

If the argument is negative infinity, the result is 0xfff0000000000000L.

If the argument is NaN, the result is 0x7ff8000000000000L.

In all cases, the result is a long integer that, when given to the longBitsToDouble(long) method, will produce a floating-point value the same as the argument to doubleToLongBits (except all NaN values are collapsed to a single "canonical" NaN value).

Bit 63 (the bit that is selected by the mask 0x8000000000000000L) represents the sign of the floating-point number. Bits 62-52 (the bits that are selected by the mask 0x7ff0000000000000L) represent the exponent. Bits 51-0 (the bits that are selected by the mask 0x000fffffffffffffL) represent the significand (sometimes called the mantissa) of the floating-point number.

If the argument is positive infinity, the result is 0x7ff0000000000000L.

If the argument is negative infinity, the result is 0xfff0000000000000L.

If the argument is NaN, the result is the long integer representing the actual NaN value. Unlike the doubleToLongBits method, doubleToRawLongBits does not collapse all the bit patterns encoding a NaN to a single "canonical" NaN value.

In all cases, the result is a long integer that, when given to the longBitsToDouble(long) method, will produce a floating-point value the same as the argument to doubleToRawLongBits.

If the argument is 0x7ff0000000000000L, the result is positive infinity.

If the argument is 0xfff0000000000000L, the result is negative infinity.

If the argument is any value in the range 0x7ff0000000000001L through 0x7fffffffffffffffL or in the range 0xfff0000000000001L through 0xffffffffffffffffL, the result is a NaN. No IEEE 754 floating-point operation provided by Java can distinguish between two NaN values of the same type with different bit patterns. Distinct values of NaN are only distinguishable by use of the Double.doubleToRawLongBits method.

In all other cases, let s, e, and m be three values that can be computed from the argument:

int s = ((bits >> 63) == 0) ? 1 : -1;
int e = (int)((bits >> 52) & 0x7ffL);
long m = (e == 0) ?
                (bits & 0xfffffffffffffL) << 1 :
                (bits & 0xfffffffffffffL) | 0x10000000000000L;

Note that this method may not be able to return a double NaN with exactly same bit pattern as the long argument. IEEE 754 distinguishes between two kinds of NaNs, quiet NaNs and signaling NaNs. The differences between the two kinds of NaN are generally not visible in Java. Arithmetic operations on signaling NaNs turn them into quiet NaNs with a different, but often similar, bit pattern. However, on some processors merely copying a signaling NaN also performs that conversion. In particular, copying a signaling NaN to return it to the calling method may perform this conversion. So longBitsToDouble may not be able to return a double with a signaling NaN bit pattern. Consequently, for some long values, doubleToRawLongBits(longBitsToDouble(start)) may not equal start. Moreover, which particular bit patterns represent signaling NaNs is platform dependent; although all NaN bit patterns, quiet or signaling, must be in the NaN range identified above.

• A NaN is unordered with respect to other values and unequal to itself under the comparison operators. This method chooses to define Double.NaN to be equal to itself and greater than all other double values (including Double.POSITIVE_INFINITY).
• Positive zero and negative zero compare equal numerically, but are distinct and distinguishable values. This method chooses to define positive zero (+0.0d), to be greater than negative zero (-0.0d).

   Double.valueOf(d1).compareTo(Double.valueOf(d2))