Overview: Intel® IEEE 754-2008 Binary Floating-Point Conformance Library
The Intel® IEEE 754-2008 Binary Floating-Point Conformance Library provides all operations mandated by the IEEE 754-2008 standard for binary32 and binary64 binary floating-point interchange formats. The minimum requirements for correct operation of the library are an Intel® Pentium® 4 processor and an operating system supporting Intel® Streaming SIMD Extensions 2 (Intel® SSE2) instructions.
The library supports all four rounding-direction attributes mandated by the IEEE 754-2008 standard for binary floating-point arithmetic:
roundTowardZero. The additional rounding-direction attribute,
roundTiesToAway, is not required by the standard, hence, not fully supported in this library. The default rounding-direction attribute is set as
The library also supports all mandated exceptions (invalid operation, division by zero, overflow, underflow, and inexact) and sets flags accordingly under default exception handling. Alternate exception handling, which is optional in the standard, is not supported.
bfp754.hheader file includes prototypes for the library functions. For a complete list of the functions available, refer to the . The user also needs to specify linker option
-lbfp754and floating-point semantics control option
-fp-model source -fp-model exceptin order to use the library.
Many routines in the
libbfp754Library are more optimized for Intel® microprocessors than for non-Intel microprocessors.
The IEEE standard 754-2008 defines four types of operations.
- General-computational operations that produce correctly rounded floating-point or integer results. These operations might signal the floating-point exceptions.
- Quiet-computational operations that produce floating-point results. These operations do not signal any floating-point exceptions.
- Signaling-computational operations that produce no floating-point results. These operations might signal floating-point exceptions.
- Non-computational operations that produce no floating-point results. These operations do not signal floating-point exceptions.
Produce no result
Might signal FP exception
Do not signal FP exception
The standard also distinguishes among operations by their floating-point operand formats and result format for general-computational operations:
- Homogenous general-computational operations whose floating-point operands and floating-point result are in the same format.
- formatOfgeneral-computational operations whose floating-point operands and floating-point result have different formats.The IEEE 754-2008 standard requires that allformatOfgeneral-computational operations be computed without any lost of precision before converting to the destination format. This may differ from how these operations are implemented on most hardware and software.For example, when all operands are in binary64 format and the destination format is binary32, most hardware and software implementations would first compute an intermediate result rounded in binary64 and then convert the intermediate result to binary32. This double rounding procedure may produce a result different from what is defined in the standard under certain rounding mode. For example:x = 0x3ff0000010000000 = 1.000000000000000000000001_2,y = 0x3ca0000000000000 = 1.0_2*2^(-53) x+y = 1.00000000000000000000000100000000000000000000000000001_2When the rounding-direction attribute is set toroundTiesToEven, using double rounding procedure, the addition result rounds to1.000000000000000000000001_2 (0x3ff0000010000000)in binary64, which would then round to1 (0x3f800000)in binary32. On the other hand, according to the standard, the addition result should round to1.00000000000000000000001_2 (0x3f800001)in binary32.
The following table correlates the names of the formats used in defining operations in the standard with their C99 types used in this library.
IEEE 754-2008 binary32 interchange format
IEEE 754-2008 binary64 interchange format
Integer operand formats
int, unsigned int, long long int, unsigned long long int
Signed 32-bit integer
Unsigned 32-bit integer
Signed 64-bit integer
long long int
Unsigned 64-bit integer
unsigned long long int
Boolean value represented by generic integer type
Enumerated values of floating-point class
Enumerated values of floating-point radix
Type for the destination of the
logBoperation and the scale exponent operand of the
Decimal character sequence
Hexadecimal-significand character sequence
Set of exceptions as a set of booleans
Set of status flags