ISO/IEC 60559:2020
Information technology — Microprocessor Systems — Floating-Point arithmetic
This standard specifies interchange and arithmetic formats and methods for binary and decimal floating-point arithmetic in computer programming environments. This standard specifies exception conditions and their default handling. An implementation of a floating-point system conforming to this standard may be realized entirely in software, entirely in hardware, or in any combination of software and hardware. For operations specified in the normative part of this standard, numerical results and exceptions are uniquely determined by the values of the input data, sequence of operations, and destination formats, all under user control.
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Contents
Participants
Introduction
1. Overview
1.1 Scope
1.2 Purpose
1.3 Inclusions
1.4 Exclusions
1.5 Programming environment considerations
1.6 Word usage
2. Definitions, abbreviations, and acronyms
2.1 Definitions
2.2 Abbreviations and acronyms
3. Floating-point formats
3.1 Overview
3.1.1 Formats
3.1.2 Conformance
3.2 Specification levels
3.3 Sets of floating-point data
3.4 Binary interchange format encodings
3.5 Decimal interchange format encodings
3.5.1 Cohorts
3.5.2 Encodings
3.6 Interchange format parameters
3.7 Extended and extendable precisions
4. Attributes and rounding
4.1 Attribute specification
4.2 Dynamic modes for attributes
4.3 Rounding-direction attributes
4.3.1 Rounding-direction attributes to nearest
4.3.2 Directed rounding attributes
4.3.3 Rounding attribute requirements
5. Operations
5.1 Overview
5.2 Decimal exponent calculation
5.3 Homogeneous general-computational operations
5.3.1 General operations
5.3.2 Decimal operations
5.3.3 logBFormat operations
5.4 formatOf general-computational operations
5.4.1 Arithmetic operations
5.4.2 Conversion operations for floating-point formats and decimal character sequences
5.4.3 Conversion operations for binary formats
5.5 Quiet-computational operations
5.5.1 Sign bit operations
5.5.2 Decimal re-encoding operations
5.6 Signaling-computational operations
5.6.1 Comparisons
5.7 Non-computational operations
5.7.1 Conformance predicates
5.7.2 General operations
5.7.3 Decimal operation
5.7.4 Operations on subsets of flags
5.8 Details of conversions from floating-point to integer formats
5.9 Details of operations to round a floating-point datum to integral value
5.10 Details of totalOrder predicate
5.11 Details of comparison predicates
5.12 Details of conversion between floating-point data and external character sequences
5.12.1 External character sequences representing zeros, infinities, and NaNs
5.12.2 External decimal character sequences representing finite numbers
5.12.3 External hexadecimal-significand character sequences representing finite numbers
6. Infinity, NaNs, and sign bit
6.1 Infinity arithmetic
6.2 Operations with NaNs
6.2.1 NaN encodings in binary interchange formats
6.2.2 NaN encodings in decimal interchange formats
6.2.3 NaN propagation
6.3 The sign bit
7. Exceptions and default exception handling
7.1 Overview: exceptions and flags
7.2 Invalid operation
7.3 Division by zero
7.4 Overflow
7.5 Underflow
7.6 Inexact
8. Alternate exception handling attributes
8.1 Overview
8.2 Resuming alternate exception handling attributes
8.3 Immediate and delayed alternate exception handling attributes
9. Recommended operations
9.1 Conforming language- and implementation-defined operations
9.2 Additional mathematical operations
9.2.1 Special values
9.2.2 Preferred exponents
9.3 Dynamic mode operations
9.3.1 Operations on individual dynamic modes
9.3.2 Operations on all dynamic modes
9.4 Reduction operations
9.5 Augmented arithmetic operations
9.6 Minimum and maximum operations
9.7 NaN payload operations
10. Expression evaluation
10.1 Expression evaluation rules
10.2 Assignments, parameters, and function values
10.3 preferredWidth attributes for expression evaluation
10.4 Literal meaning and value-changing optimizations
11. Reproducible floating-point results
Annex A (informative) Bibliography
Annex B (informative) Program debugging support
Annex C (informative) List of operations
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Contents
Participants
Introduction
1. Overview
1.1 Scope
1.2 Purpose
1.3 Inclusions
1.4 Exclusions
1.5 Programming environment considerations
1.6 Word usage
2. Definitions, abbreviations, and acronyms
2.1 Definitions
2.2 Abbreviations and acronyms
3. Floating-point formats
3.1 Overview
3.1.1 Formats
3.1.2 Conformance
3.2 Specification levels
3.3 Sets of floating-point data
3.4 Binary interchange format encodings
3.5 Decimal interchange format encodings
3.5.1 Cohorts
3.5.2 Encodings
3.6 Interchange format parameters
3.7 Extended and extendable precisions
4. Attributes and rounding
4.1 Attribute specification
4.2 Dynamic modes for attributes
4.3 Rounding-direction attributes
4.3.1 Rounding-direction attributes to nearest
4.3.2 Directed rounding attributes
4.3.3 Rounding attribute requirements
5. Operations
5.1 Overview
5.2 Decimal exponent calculation
5.3 Homogeneous general-computational operations
5.3.1 General operations
5.3.2 Decimal operations
5.3.3 logBFormat operations
5.4 formatOf general-computational operations
5.4.1 Arithmetic operations
5.4.2 Conversion operations for floating-point formats and decimal character sequences
5.4.3 Conversion operations for binary formats
5.5 Quiet-computational operations
5.5.1 Sign bit operations
5.5.2 Decimal re-encoding operations
5.6 Signaling-computational operations
5.6.1 Comparisons
5.7 Non-computational operations
5.7.1 Conformance predicates
5.7.2 General operations
5.7.3 Decimal operation
5.7.4 Operations on subsets of flags
5.8 Details of conversions from floating-point to integer formats
5.9 Details of operations to round a floating-point datum to integral value
5.10 Details of totalOrder predicate
5.11 Details of comparison predicates
5.12 Details of conversion between floating-point data and external character sequences
5.12.1 External character sequences representing zeros, infinities, and NaNs
5.12.2 External decimal character sequences representing finite numbers
5.12.3 External hexadecimal-significand character sequences representing finite numbers
6. Infinity, NaNs, and sign bit
6.1 Infinity arithmetic
6.2 Operations with NaNs
6.2.1 NaN encodings in binary interchange formats
6.2.2 NaN encodings in decimal interchange formats
6.2.3 NaN propagation
6.3 The sign bit
7. Exceptions and default exception handling
7.1 Overview: exceptions and flags
7.2 Invalid operation
7.3 Division by zero
7.4 Overflow
7.5 Underflow
7.6 Inexact
8. Alternate exception handling attributes
8.1 Overview
8.2 Resuming alternate exception handling attributes
8.3 Immediate and delayed alternate exception handling attributes
9. Recommended operations
9.1 Conforming language- and implementation-defined operations
9.2 Additional mathematical operations
9.2.1 Special values
9.2.2 Preferred exponents
9.3 Dynamic mode operations
9.3.1 Operations on individual dynamic modes
9.3.2 Operations on all dynamic modes
9.4 Reduction operations
9.5 Augmented arithmetic operations
9.6 Minimum and maximum operations
9.7 NaN payload operations
10. Expression evaluation
10.1 Expression evaluation rules
10.2 Assignments, parameters, and function values
10.3 preferredWidth attributes for expression evaluation
10.4 Literal meaning and value-changing optimizations
11. Reproducible floating-point results
Annex A (informative) Bibliography
Annex B (informative) Program debugging support
Annex C (informative) List of operations