Developer Guide and Reference

Contents

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:
roundTiesToEven
,
roundTowardPositive
,
roundTowardNegative
,
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
roundTiesToEven
.
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.
The
bfp754.h
header 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
-lbfp754
and floating-point semantics control option
-fp-model source -fp-model except
in order to use the library.
Many routines in the
libbfp754
Library are more optimized for Intel® microprocessors than for non-Intel microprocessors.

Operations

The IEEE standard 754-2008 defines four types of operations.
  1. General-computational operations that produce correctly rounded floating-point or integer results. These operations might signal the floating-point exceptions.
  2. Quiet-computational operations that produce floating-point results. These operations do not signal any floating-point exceptions.
  3. Signaling-computational operations that produce no floating-point results. These operations might signal floating-point exceptions.
  4. Non-computational operations that produce no floating-point results. These operations do not signal floating-point exceptions.
Produce result
Produce no result
Might signal FP exception
General-computational
Signaling-computational
Do not signal FP exception
Quiet-computational
Non-computational
The standard also distinguishes among operations by their floating-point operand formats and result format for general-computational operations:
  1. Homogenous general-computational operations whose floating-point operands and floating-point result are in the same format.
  2. formatOf
    general-computational operations whose floating-point operands and floating-point result have different formats.
    The IEEE 754-2008 standard requires that all
    formatOf
    general-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_2
    When the rounding-direction attribute is set to
    roundTiesToEven
    , using double rounding procedure, the addition result rounds to
    1.000000000000000000000001_2 (0x3ff0000010000000)
    in binary64, which would then round to
    1 (0x3f800000)
    in binary32. On the other hand, according to the standard, the addition result should round to
    1.00000000000000000000001_2 (0x3f800001)
    in binary32.

Data Types

The following table correlates the names of the formats used in defining operations in the standard with their C99 types used in this library.
Format Name
Definition
C99 Type
binary32
IEEE 754-2008 binary32 interchange format
float
binary64
IEEE 754-2008 binary64 interchange format
double
int
Integer operand formats
int, unsigned int, long long int, unsigned long long int
int32
Signed 32-bit integer
int
uint32
Unsigned 32-bit integer
unsigned int
int64
Signed 64-bit integer
long long int
uint64
Unsigned 64-bit integer
unsigned long long int
boolean
Boolean value represented by generic integer type
int
enum
Enumerated values of floating-point class
int
Enumerated values of floating-point radix
int
logBFormat
Type for the destination of the
logB
operation and the scale exponent operand of the
scaleB
operation
int
decimalCharacterSequence
Decimal character sequence
char*
hexCharacterSequence
Hexadecimal-significand character sequence
exceptionGroup
Set of exceptions as a set of booleans
int
flags
Set of status flags
int