Class Float

Method Details

• toString

  public static String toString(float f)

  Returns a string representation of the float argument. All characters mentioned below are ASCII characters.

  • 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.

  Parameters:

  f - the float to be converted.

  Returns:

  a string representation of the argument.

• toHexString

  public static String toHexString(float f)

  Returns a hexadecimal string representation of the float argument. All characters mentioned below are ASCII characters.

  • 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 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 float 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 float 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-126". Note that there must be at least one nonzero digit in a subnormal significand.

  Examples

  Floating-point Value	Hexadecimal String
  1.0	0x1.0p0
  -1.0	-0x1.0p0
  2.0	0x1.0p1
  3.0	0x1.8p1
  0.5	0x1.0p-1
  0.25	0x1.0p-2
  Float.MAX_VALUE	0x1.fffffep127
  Minimum Normal Value	0x1.0p-126
  Maximum Subnormal Value	0x0.fffffep-126
  Float.MIN_VALUE	0x0.000002p-126

  Parameters:

  f - the float to be converted.

  Returns:

  a hex string representation of the argument.

  Since:

  1.5

• valueOf

  public static Float valueOf(String s) throws NumberFormatException

  Returns a Float object holding the float value represented by the argument string s.

  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

  where Sign, FloatingPointLiteral, HexNumeral, HexDigits, SignedInteger and FloatTypeSuffix are as defined in the lexical structure sections of The Java Language Specification, except that underscores are not accepted between digits. If s does not have the form of a FloatValue, then a NumberFormatException is thrown. Otherwise, s is regarded as representing an exact decimal value in the usual "computerized scientific notation" or as an exact hexadecimal value; this exact numerical value is then conceptually converted to an "infinitely precise" binary value that is then rounded to type float by the usual round-to-nearest rule of IEEE 754 floating-point arithmetic, which includes preserving the sign of a zero value. Note that the round-to-nearest rule also implies overflow and underflow behaviour; if the exact value of s is large enough in magnitude (greater than or equal to (MAX_VALUE + ulp(MAX_VALUE)/2), rounding to float will result in an infinity and if the exact value of s is small enough in magnitude (less than or equal to MIN_VALUE/2), rounding to float will result in a zero. Finally, after rounding a Float object representing this float value is returned.

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

  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. In general, the two-step sequence of conversions, string to double followed by double to float, is not equivalent to converting a string directly to float. For example, if first converted to an intermediate double and then to float, the string
  "1.00000017881393421514957253748434595763683319091796875001d"
  results in the float value 1.0000002f; if the string is converted directly to float, 1.0000001f results.

  To avoid calling this method on an invalid string and having a NumberFormatException be thrown, the documentation for Double.valueOf lists a regular expression which can be used to screen the input.

  Parameters:

  s - the string to be parsed.

  Returns:

  a Float object holding the value represented by the String argument.

  Throws:

  NumberFormatException - if the string does not contain a parsable number.

• valueOf

  public static Float valueOf(float f)

  Returns a Float instance representing the specified float value. If a new Float instance is not required, this method should generally be used in preference to the constructor Float(float), as this method is likely to yield significantly better space and time performance by caching frequently requested values.

  Parameters:

  f - a float value.

  Returns:

  a Float instance representing f.

  Since:

  1.5

• parseFloat

  public static float parseFloat(String s) throws NumberFormatException

  Returns a new float initialized to the value represented by the specified String, as performed by the valueOf method of class Float.

  Parameters:

  s - the string to be parsed.

  Returns:

  the float value represented by the string argument.

  Throws:

  NullPointerException - if the string is null

  NumberFormatException - if the string does not contain a parsable float.

  Since:

  1.2

  See Also:

  • valueOf(String)

• isNaN

  public static boolean isNaN(float v)

  Returns true if the specified number is a Not-a-Number (NaN) value, false otherwise.

  API Note:

  This method corresponds to the isNaN operation defined in IEEE 754.

  Parameters:

  v - the value to be tested.

  Returns:

  true if the argument is NaN; false otherwise.

• isInfinite

  public static boolean isInfinite(float v)

  Returns true if the specified number is infinitely large in magnitude, false otherwise.

  API Note:

  This method corresponds to the isInfinite operation defined in IEEE 754.

  Parameters:

  v - the value to be tested.

  Returns:

  true if the argument is positive infinity or negative infinity; false otherwise.

• isFinite

  public static boolean isFinite(float f)

  Returns true if the argument is a finite floating-point value; returns false otherwise (for NaN and infinity arguments).

  API Note:

  This method corresponds to the isFinite operation defined in IEEE 754.

  Parameters:

  f - the float value to be tested

  Returns:

  true if the argument is a finite floating-point value, false otherwise.

  Since:

  1.8

• isNaN

  public boolean isNaN()

  Returns true if this Float value is a Not-a-Number (NaN), false otherwise.

  Returns:

  true if the value represented by this object is NaN; false otherwise.

• isInfinite

  public boolean isInfinite()

  Returns true if this Float value is infinitely large in magnitude, false otherwise.

  Returns:

  true if the value represented by this object is positive infinity or negative infinity; false otherwise.

• toString

  public String toString()

  Returns a string representation of this Float object. The primitive float value represented by this object is converted to a String exactly as if by the method toString of one argument.

  Overrides:

  toString in class Object

  Returns:

  a String representation of this object.

  See Also:

  • toString(float)

• byteValue

  public byte byteValue()

  Returns the value of this Float as a byte after a narrowing primitive conversion.

  Overrides:

  byteValue in class Number

  Returns:

  the float value represented by this object converted to type byte

  See Java Language Specification:

  5.1.3 Narrowing Primitive Conversion
  

• shortValue

  public short shortValue()

  Returns the value of this Float as a short after a narrowing primitive conversion.

  Overrides:

  shortValue in class Number

  Returns:

  the float value represented by this object converted to type short

  See Java Language Specification:

  5.1.3 Narrowing Primitive Conversion
  

  Since:

  1.1

• intValue

  public int intValue()

  Returns the value of this Float as an int after a narrowing primitive conversion.

  Specified by:

  intValue in class Number

  Returns:

  the float value represented by this object converted to type int

  See Java Language Specification:

  5.1.3 Narrowing Primitive Conversion
  

• longValue

  public long longValue()

  Returns value of this Float as a long after a narrowing primitive conversion.

  Specified by:

  longValue in class Number

  Returns:

  the float value represented by this object converted to type long

  See Java Language Specification:

  5.1.3 Narrowing Primitive Conversion
  

• floatValue

  public float floatValue()

  Returns the float value of this Float object.

  Specified by:

  floatValue in class Number

  Returns:

  the float value represented by this object

• doubleValue

  public double doubleValue()

  Returns the value of this Float as a double after a widening primitive conversion.

  Specified by:

  doubleValue in class Number

  API Note:

  This method corresponds to the convertFormat operation defined in IEEE 754.

  Returns:

  the float value represented by this object converted to type double

  See Java Language Specification:

  5.1.2 Widening Primitive Conversion
  

• hashCode

  public int hashCode()

  Returns a hash code for this Float object. The result is the integer bit representation, exactly as produced by the method floatToIntBits(float), of the primitive float value represented by this Float object.

  Overrides:

  hashCode in class Object

  Returns:

  a hash code value for this object.

  See Also:

  • Object.equals(java.lang.Object)
  • System.identityHashCode(java.lang.Object)

• hashCode

  public static int hashCode(float value)

  Returns a hash code for a float value; compatible with Float.hashCode().

  Parameters:

  value - the value to hash

  Returns:

  a hash code value for a float value.

  Since:

  1.8

• equals

  public boolean equals(Object obj)

  Compares this object against the specified object. The result is true if and only if the argument is not null and is a Float object that represents a float with the same value as the float represented by this object. For this purpose, two float values are considered to be the same if and only if the method floatToIntBits(float) returns the identical int value when applied to each.

  Overrides:

  equals in class Object

  API Note:

  This method is defined in terms of floatToIntBits(float) rather than the == operator on float values since the == operator does not define an equivalence relation and to satisfy the equals contract an equivalence relation must be implemented; see this discussion for details of floating-point equality and equivalence.

  Parameters:

  obj - the object to be compared

  Returns:

  true if the objects are the same; false otherwise.

  See Java Language Specification:

  15.21.1 Numerical Equality Operators == and !=
  

  See Also:

  • floatToIntBits(float)

• floatToIntBits

  public static int floatToIntBits(float value)

  Returns a representation of the specified floating-point value according to the IEEE 754 floating-point "single format" bit layout.

  Bit 31 (the bit that is selected by the mask 0x80000000) represents the sign of the floating-point number. Bits 30-23 (the bits that are selected by the mask 0x7f800000) represent the exponent. Bits 22-0 (the bits that are selected by the mask 0x007fffff) represent the significand (sometimes called the mantissa) of the floating-point number.

  If the argument is positive infinity, the result is 0x7f800000.

  If the argument is negative infinity, the result is 0xff800000.

  If the argument is NaN, the result is 0x7fc00000.

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

  Parameters:

  value - a floating-point number.

  Returns:

  the bits that represent the floating-point number.

• floatToRawIntBits

  public static int floatToRawIntBits(float value)

  Returns a representation of the specified floating-point value according to the IEEE 754 floating-point "single format" bit layout, preserving Not-a-Number (NaN) values.

  Bit 31 (the bit that is selected by the mask 0x80000000) represents the sign of the floating-point number. Bits 30-23 (the bits that are selected by the mask 0x7f800000) represent the exponent. Bits 22-0 (the bits that are selected by the mask 0x007fffff) represent the significand (sometimes called the mantissa) of the floating-point number.

  If the argument is positive infinity, the result is 0x7f800000.

  If the argument is negative infinity, the result is 0xff800000.

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

  In all cases, the result is an integer that, when given to the intBitsToFloat(int) method, will produce a floating-point value the same as the argument to floatToRawIntBits.

  Parameters:

  value - a floating-point number.

  Returns:

  the bits that represent the floating-point number.

  Since:

  1.3

• intBitsToFloat

  public static float intBitsToFloat(int bits)

  Returns the float value corresponding to a given bit representation. The argument is considered to be a representation of a floating-point value according to the IEEE 754 floating-point "single format" bit layout.

  If the argument is 0x7f800000, the result is positive infinity.

  If the argument is 0xff800000, the result is negative infinity.

  If the argument is any value in the range 0x7f800001 through 0x7fffffff or in the range 0xff800001 through 0xffffffff, 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 Float.floatToRawIntBits method.

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

  Copy

  int s = ((bits >> 31) == 0) ? 1 : -1;
  int e = ((bits >> 23) & 0xff);
  int m = (e == 0) ?
                  (bits & 0x7fffff) << 1 :
                  (bits & 0x7fffff) | 0x800000;
  

  Then the floating-point result equals the value of the mathematical expression s·m·2^e-150.

  Note that this method may not be able to return a float NaN with exactly same bit pattern as the int 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 intBitsToFloat may not be able to return a float with a signaling NaN bit pattern. Consequently, for some int values, floatToRawIntBits(intBitsToFloat(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.

  Parameters:

  bits - an integer.

  Returns:

  the float floating-point value with the same bit pattern.

• float16ToFloat

  public static float float16ToFloat(short floatBinary16)

  Returns the float value closest to the numerical value of the argument, a floating-point binary16 value encoded in a short. The conversion is exact; all binary16 values can be exactly represented in float. Special cases:

  • If the argument is zero, the result is a zero with the same sign as the argument.
  • If the argument is infinite, the result is an infinity with the same sign as the argument.
  • If the argument is a NaN, the result is a NaN.

  IEEE 754 binary16 format

  The IEEE 754 standard defines binary16 as a 16-bit format, along with the 32-bit binary32 format (corresponding to the float type) and the 64-bit binary64 format (corresponding to the double type). The binary16 format is similar to the other IEEE 754 formats, except smaller, having all the usual IEEE 754 values such as NaN, signed infinities, signed zeros, and subnormals. The parameters (JLS 4.2.3) for the binary16 format are N = 11 precision bits, K = 5 exponent bits, E_max = 15, and E_min = -14.

  API Note:

  This method corresponds to the convertFormat operation defined in IEEE 754 from the binary16 format to the binary32 format. The operation of this method is analogous to a primitive widening conversion (JLS 5.1.2).

  Parameters:

  floatBinary16 - the binary16 value to convert to float

  Returns:

  the float value closest to the numerical value of the argument, a floating-point binary16 value encoded in a short

  Since:

  20

• floatToFloat16

  public static short floatToFloat16(float f)

  Returns the floating-point binary16 value, encoded in a short, closest in value to the argument. The conversion is computed under the round to nearest even rounding mode. Special cases:

  • If the argument is zero, the result is a zero with the same sign as the argument.
  • If the argument is infinite, the result is an infinity with the same sign as the argument.
  • If the argument is a NaN, the result is a NaN.

  The binary16 format is discussed in more detail in the float16ToFloat(short) method.

  API Note:

  This method corresponds to the convertFormat operation defined in IEEE 754 from the binary32 format to the binary16 format. The operation of this method is analogous to a primitive narrowing conversion (JLS 5.1.3).

  Parameters:

  f - the float value to convert to binary16

  Returns:

  the floating-point binary16 value, encoded in a short, closest in value to the argument

  Since:

  20

• compareTo

  public int compareTo(Float anotherFloat)

  Compares two Float objects numerically. This method imposes a total order on Float objects with two differences compared to the incomplete order defined by the Java language numerical comparison operators (<, <=, ==, >=, >) on float values.

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

  This ensures that the natural ordering of Float objects imposed by this method is consistent with equals; see this discussion for details of floating-point comparison and ordering.

  Specified by:

  compareTo in interface Comparable<Float>

  Parameters:

  anotherFloat - the Float to be compared.

  Returns:

  the value 0 if anotherFloat is numerically equal to this Float; a value less than 0 if this Float is numerically less than anotherFloat; and a value greater than 0 if this Float is numerically greater than anotherFloat.

  See Java Language Specification:

  15.20.1 Numerical Comparison Operators <, <=, >, and >=
  

  Since:

  1.2

• compare

  public static int compare(float f1, float f2)

  Compares the two specified float values. The sign of the integer value returned is the same as that of the integer that would be returned by the call:

      Float.valueOf(f1).compareTo(Float.valueOf(f2))
   

  Parameters:

  f1 - the first float to compare.

  f2 - the second float to compare.

  Returns:

  the value 0 if f1 is numerically equal to f2; a value less than 0 if f1 is numerically less than f2; and a value greater than 0 if f1 is numerically greater than f2.

  Since:

  1.4

• sum

  public static float sum(float a, float b)

  Adds two float values together as per the + operator.

  API Note:

  This method corresponds to the addition operation defined in IEEE 754.

  Parameters:

  a - the first operand

  b - the second operand

  Returns:

  the sum of a and b

  See Java Language Specification:

  4.2.4 Floating-Point Operations
  

  Since:

  1.8

  See Also:

  • BinaryOperator

• max

  public static float max(float a, float b)

  Returns the greater of two float values as if by calling Math.max.

  API Note:

  This method corresponds to the maximum operation defined in IEEE 754.

  Parameters:

  a - the first operand

  b - the second operand

  Returns:

  the greater of a and b

  Since:

  1.8

  See Also:

  • BinaryOperator

• min

  public static float min(float a, float b)

  Returns the smaller of two float values as if by calling Math.min.

  API Note:

  This method corresponds to the minimum operation defined in IEEE 754.

  Parameters:

  a - the first operand

  b - the second operand

  Returns:

  the smaller of a and b

  Since:

  1.8

  See Also:

  • BinaryOperator

• describeConstable

  public Optional<Float> describeConstable()

  Returns an Optional containing the nominal descriptor for this instance, which is the instance itself.

  Specified by:

  describeConstable in interface Constable

  Returns:

  an Optional describing the Float instance

  Since:

  12

• resolveConstantDesc

  public Float resolveConstantDesc(MethodHandles.Lookup lookup)

  Resolves this instance as a ConstantDesc, the result of which is the instance itself.

  Specified by:

  resolveConstantDesc in interface ConstantDesc

  Parameters:

  lookup - ignored

  Returns:

  the Float instance

  Since:

  12