• In 1985, the IEEE 754 Standard for Floating-Point Arithmetic was established, and since the 1990s, the most commonly encountered representations are those defined by the IEEE. (wikipedia.org)
  • Date: Fri, 8 Oct 93 17:49:27 -0700 Subject: Comments on IEEE Arithmetic Comments on IEEE Arithmetic Jim Demmel Computer Science Division and Math Dept. University of California Berkeley, CA 94720 [email protected] This is in response to the various comments on IEEE arithmetic in the last few NA-Digests. (netlib.org)
  • This confusion, which is still much better than the pre-IEEE situation of different roundings, etc., has motivated some people to try to standardize language bindings in a proposed Language Independent Arithmetic (LIA) ISO standard. (netlib.org)
  • Most machines today use floating point arithmetic that conform to IEEE 754. (bayesserver.com)
  • As many of you have been aware it has been a long practice for software using IEEE 754 floating-point arithmetic run on MIPS processors to use an encoding of Not-a-Number (NaN) data different to one used by software run on other processors. (sourceware.org)
  • This C source fragment is part of the SoftFloat IEC/IEEE Floating-point Arithmetic Package, Release 2b. (linaro.org)
  • The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the typical case where the rounding mode is half-even. (kites-kw.com)
  • Values entered in hexadecimal need to conform to IEEE-754 format. (missouristate.edu)
  • IEEE 754 specifies additional floating-point formats, including 32-bit base-2 single precision and, more recently, base-10 representations ( decimal floating point ). (wikipedia.org)
  • If a decimal string with at most 15 significant digits is converted to the IEEE 754 double-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string. (wikipedia.org)
  • If an IEEE 754 double-precision number is converted to a decimal string with at least 17 significant digits, and then converted back to double-precision representation, the final result must match the original number. (wikipedia.org)
  • The details of this represntation are slightly different from the 128 bit decimal floating point in IEEE 754-2008. (open-std.org)
  • Most decimal values work this way in IEEE 754. (sqlite.org)
  • The size of a float is platform-dependent, although a maximum of ~1.8e308 with a precision of roughly 14 decimal digits is a common value (the 64 bit IEEE format). (moodle.org)
  • The precision provided by IEEE 754 Binary64 is sufficient for most computations. (sqlite.org)
  • ¹ Exception: The R-Tree extension stores information as 32-bit floating point or integer values. (sqlite.org)
  • IEEE 32-bit and 64-bit binary floating-point types have no more than one representation of each nonzero finite number, and each representation has only one encoding . (diploid.ca)
  • And as of IEEE 754-2008 revision [1] this encoding does not follow one recommended in the standard, as specified in section 6.2.1, where it is stated that quiet NaNs should have the first bit (d1) of their significand set to 1 while signalling NaNs should have that bit set to 0, but MIPS software interprets the two bits in the opposite manner. (sourceware.org)
  • Meanwhile, guidance is provided by the second and third paragraphs of 14.8, which state "The inquiry function IEEE_SUPPORT_NAN is provided to inquire whether the processor supports IEEE NaNs. (j3-fortran.org)
  • These binding were not part of the standard, because the committee members felt that writing a standard demanding simultaneous changes in hardware, languages, compilers, and perhaps operating systems (for exception handling) was unlikely to to be accepted, or if accepted, implemented correctly. (netlib.org)
  • This behavior is specified by the IEEE 754 standard and is common to many languages. (diploid.ca)
  • Dividing 0.0 by 0.0 is considered "invalid" and the result of that operation is NaN, as specified by the IEEE 754 standard. (diploid.ca)
  • The IEEE 754 standard requires that NaN compare not equal to any value, including itself. (diploid.ca)
  • Because most bits available to encode a floating-point value are not necessary to indicate that the value is NaN, the IEEE 754 standard specifies that unused bits can encode a payload , which can represent diagnostic information or can be put to some other use that is entirely left to the user's discretion. (diploid.ca)
  • Taking advantage of features in the IEEE-754 standard for floating point, MATLAB returns appropriate values on divide by zero ( 1 / 0 yields positive infinity, -1 / 0 yields negative infinity, and 0 / 0 yields Not a Number . (scholarpedia.org)
  • As the NaN encoding format is a property of GCC code generation that is both a user-selected GCC configuration default and can be overridden with GCC options, code that needs to know what NaN encoding standard it has been configured for checks for the __mips_nan2008 macro that is defined internally by GCC whenever the 2008-NaN mode has been selected. (sourceware.org)
  • NUMBER: F03/0042 TITLE: IEEE funny values and Standard real generic instrinsic procedures KEYWORDS: IEEE-754, real math library DEFECT TYPE: Erratum STATUS: For consideration QUESTION: Is an infinite result from an infinite argument to a real math function exceptional (raises an exception)? (j3-fortran.org)
  • Although it depends on the system, PHP typically uses the IEEE 754 double precision format, which will give a maximum relative error due to rounding in the order of 1.11e-16. (moodle.org)
  • An attempt to take the sqrt() of negative x raises an invalid exception and causes an NaN to be returned (except that the square root of -0 is valid and equal to -0. (unix.com)
  • Numeric values are, by default, two-dimensional arrays (matrices). (scholarpedia.org)
  • What is the rationale for all comparisons returning false for IEEE754 NaN values? (stackoverflow.com)
  • So-called "REAL" or floating point values are stored in the IEEE 754 Binary-64 format¹. (sqlite.org)
  • J3/05-121r1 Date: 2 Feb 2005 To: J3 From: John Reid Subject: Math library and IEEE funny values Here is a draft response for F03/0042, with thanks to Malcolm Cohen for his help. (j3-fortran.org)
  • The IEEE 754 special values of NaN, inf, and -inf will be handled according to IEEE rules. (kites-kw.com)
  • As from revision 3.50 [2][3] the MIPS Architecture provides for processors that support the IEEE 754-2008 preferred NaN encoding format. (sourceware.org)
  • IEEE 754-2008 features are controlled in the Floating-Point Control and Status (FCSR) register and updates are needed to floating environment support so that the 2008-NaN flag is set correctly and the kernel default, inferred from the 2008-NaN ELF file header flag at the time an executable is loaded, respected. (sourceware.org)
  • Revision: 104046 $' frozen expanded class interface REAL_64 create default_create -- Process instances of classes with no creation clause. (eiffel.org)
  • Is a NaN result from a NaN argument to a real math function exceptional (raises an exception)? (j3-fortran.org)
  • Many user complaints are a result of the IEEE floating point standards 754 and 854 specifying how systems "should appear" to the user, without specifying any specific language bindings. (netlib.org)
  • Reason: IEEE-754 mathematical operations on quiet NaN operands that produce a quiet NaN result are unexceptional. (j3-fortran.org)
  • Reason: IEEE-754 mathematical operations on infinity that produce an infinity are unexceptional. (j3-fortran.org)
  • This "act of cowardice" (in the words of W. Kahan) has unfortunately made it impossible to write portable software which uses features of IEEE like exception handling. (netlib.org)
  • Unfortunately, I believe the LIA still does not give adequate access to IEEE features, and indeed it was recently voted down for this reason by the US/ISO committee. (netlib.org)
  • Support for IEEE 754 floating point numbers and floating point Not-a-Number (NaN) . (python.org)
  • C11 compiler, IEEE 754 and NaN support are now required. (python.org)
  • I suppose this simplifies numerical computations in some way, but I couldn't find an explicitly stated reason, not even in the Lecture Notes on the Status of IEEE 754 by Kahan which discusses other design decisions in detail. (stackoverflow.com)
  • Additionally a type for functions and exceptions exists. (sparkslabs.com)
  • functions, perhaps, with a bold face IEEE sub-heading. (j3-fortran.org)
  • This function is defined in IEC 559 (and the appendix with recommended functions in IEEE 754/IEEE 854). (linuxhowtos.org)
  • In glibc version 2.5 and earlier, these functions do not raise an underflow floating-point ( FE_UNDERFLOW ) exception when an underflow occurs. (linuxhowtos.org)
  • It is available anytime execution is paused and at termination (even if terminated due to exception). (missouristate.edu)
  • DPROD(+/-0.0, +/-0.0) returns a zero with its sign being the XOR of the arguments, and raises no exceptions. (j3-fortran.org)
  • There is general agreement in the technical computing community that the main reasons for MATLAB's success are its intuitive, concise syntax, the use of complex matrices as the default numeric data object, the power of the built-in operators, easily used graphics, and its simple and friendly programming environment, allowing easy extension of the language. (scholarpedia.org)
  • Oracle can use two environment variables to specify default connections: ORACLE_SID and TWO_TASK. (debian.net)
  • NB: The usual description of IEEE 754 is more complex, and it is important to understand the added complexity if you really want to appreciate the details, merits, and limitations of IEEE 754. (sqlite.org)
  • When using Python 3, unlike in many other languages, calculations involving floating point numbers can raise exceptions. (bayesserver.com)
  • the error is less than half an ulp in the default mode (round-to-nearest). (unix.com)
  • If k is not specified or is None, then k defaults to n and the function returns n! (kites-kw.com)
  • [ citation needed ] Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language implementers. (wikipedia.org)
  • Better source information for datums When the `positions' reader option is on, as it is by default, Guile's reader will record source information for more kinds of datums. (gnu.org)
  • New in 4.4 If the setting for Self-Modifying Code is enabled (disabled by default, look in the Settings menu), text segment binary code can be modified using the same technique described above. (missouristate.edu)