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HP-UX Floating-Point Guide: HP 9000 Computers

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HP Part Number: B3906-90005

Edition: Edition 4

Published: May 1997

© Copyright 1997 Hewlett-Packard Company.

Table of Contents

Printing History

Conventions

In This Book

1 Introduction

Overview of Floating-Point Principles

Overview of HP-UX Math Libraries

Math Libraries and System Architecture
Selecting Different Versions of the Math Libraries
Locations of the Math Libraries at Release 10.30

2 Floating-Point Principles and the IEEE Standard for Binary Floating-Point Arithmetic

What Is the IEEE Standard?

Floating-Point Formats

Single-Precision, Double-Precision, and Quad-Precision Formats
Normalized and Denormalized Values
Infinity
Not-a-Number (NaN)
Zeros
Complex Data Types
IEEE Representation Summary

Exception Conditions

Inexact Result (Rounding)
Overflow Conditions
Underflow Conditions
Invalid Operation Conditions
Division by Zero Conditions

Exception Processing

Floating-Point Operations

Comparison
Conversion Between Operand Formats
The Remainder Operation

Recommended Functions

3 Factors that Affect the Results of Floating-Point Computations

How Basic Operations Affect Application Results

How Mathematical Library Functions Affect Application Results

How Exceptions and Library Errors Affect Application Results

Other System-Related Factors that Affect Application Results

Conversions Between Binary and Decimal
Compiler Behavior and Compiler Version
Compiler Options
Architecture Type of Run-Time System
Operating System Release of Build-Time System
Operating System Release of Run-Time System
Values of Certain Modifiable Hardware Status Register Fields

Floating-Point Coding Practices that Affect Application Results

Testing Floating-Point Values for Equality
Taking the Difference of Similar Values
Adding Values with Very Different Magnitudes
Unintentional Underflow
Truncation to an Integer Value
Ill-Conditioned Computations

4 HP-UX Math Libraries on HP 9000 Systems

HP-UX Library Basics

Math Library Basics

Anatomy of a Math Library Function Call
Math Library Error Handling for C
Math Library Error Handling for Fortran

Contents of the HP-UX Math Libraries

Scalar Math Libraries (libm and libcl)
The BLAS Library (libblas)
The Vector Library (libvec) (Obsolete)

Calling C Library Functions from Fortran

5 Manipulating the Floating-Point Status Register

Run-Time Mode Control: The fenv(5) Suite

The PA-RISC Floating-Point Status Register
Rounding Mode: fegetround and fesetround
Exception Bits
Manipulating the Floating-Point Environment: fegetenv, fesetenv, feupdateenv, feholdexcept
Underflow Mode: fegetflushtozero and fesetflushtozero

Command-Line Mode Control: The +FP Compiler Option

6 Floating-Point Trap Handling

Enabling Traps

Using the +FP Compiler Option
Using the fesettrapenable Function
Using the +fp_exception or +T Compiler Option (Fortran only)

Handling Traps

Using the ON Statement (Fortran only)
Using the sigaction(2) Function (C only)

Detecting Exceptions without Enabling Traps

Handling Integer Exceptions

Handling Integer Division by Zero
Handling Integer Overflow

7 Performance Tuning

Identifying and Removing Performance Bottlenecks

Inefficient Code

Optimizing Your Program
Specifying the Architecture Type
Including Debugging Information
Producing Position-Independent Code
Using Profile-Based Optimization
Creating and Zeroing Static Data (Fortran only)
Writing Routines in Assembly Language

BLAS Library Versions

Shared Libraries versus Archive Libraries

Denormalized Operands

Mixed-Precision Expressions

Matrix Operations

Data Alignment

Cache Aliasing

Static Variables

Quad-Precision Computations

A The C Math Library

C Math Library Tables

B The Fortran Math Library

C Floating-Point Problem Checklist

Results Different from Those Produced Previously
Incorrect or Imprecise Results
Compiling and Linking Errors

List of Figures

1-1 Math Library Directory Hierarchy at Release 10.30
2-1 IEEE Single-Precision Format
2-2 IEEE Double-Precision Format
2-3 IEEE Quad-Precision Format
2-4 IEEE Single-Precision Format: Example
3-1 Taking the Difference of Similar Values
3-2 Adding Values with Very Different Magnitudes
3-3 Unintentional Underflow
4-1 Anatomy of a Math Library Call
4-2 C Math Library Error Handling for the sqrt Function
4-3 Fortran 77 Math Library Error Handling
4-4 Fortran 90 Math Library Error Handling
5-1 PA-RISC Floating-Point Status Register (fr0L)

List of Tables

1-1 HP-UX Math Libraries
1-2 Math Library Path Names
2-1 IEEE Representations of Floating-Point Values
2-2 Minimum and Maximum Positive Denormalized Values
2-3 Arithmetic Properties of Infinity
2-4 Properties of NaNs
2-5 Operations With Zero
2-6 IEEE Single-Precision Value Summary (Hexadecimal Values)
2-7 IEEE Single-Precision Value Summary (Decimal Values)
2-8 IEEE Double-Precision Value Summary (Hexadecimal Values)
2-9 IEEE Double-Precision Value Summary (Decimal Values)
2-10 Approximate Maximum Representable Floating-Point Values
2-11 Overflow Results Based on Rounding Mode
2-12 HP-UX Support for IEEE Recommended Functions
3-1 Effects of Floating-Point Exceptions and Library Errors
4-1 fpclassify Values
5-1 IEEE Exception Bits
5-2 Rounding Modes
5-3 +FP Option Arguments
7-1 Typical Instruction Cache Aliasing Situation
A-1 The C Math Library (By Category)
A-2 The C Math Library (Alphabetical Listing)

List of Examples

1-1 Sample Program: get_arch.c
3-1 Sample Program: rounderr.f
3-2 Sample Program: flophex.f
3-3 Sample Program: flophex.c
3-4 Sample Program: fpeq.c
3-5 Sample Program: roundeps.f
3-6 Sample Program: diffmag1.f
3-7 Sample Program: diffmag2.f
3-8 Sample Program: trunc.c
3-9 Sample Program: sloppy_tangent.f
4-1 Sample Program: liberr77.f
4-2 Sample Program: liberr90.f
4-3 Sample Function: print_class.c
4-4 Sample Program: bessel.f
5-1 Sample Program: fe_round.c
5-2 Sample Program: fe_round.c (cont.)
5-3 Sample Program: fe_flags.c
5-4 Sample Program: fe_flags.c (cont.)
5-5 Sample Program: fe_traps.c
5-6 Sample Program: fe_traps.c (cont.)
5-7 Sample Program: fe_env.c
5-8 Sample Program: fe_env.c (cont.)
5-9 Sample Program: fe_update.c
5-10 Sample Program: fe_update.c (cont.)
5-11 Sample Program: fe_flush.c
6-1 Sample Program: overflow.f
6-2 Sample Program: overflow_trap.f
6-3 Sample Program: overflow_on.f
6-4 Sample Program: underflow_on.f
6-5 Sample Program: overflow_sig.c
6-6 Sample Program: overflow_sig.c (Cont.)

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© 1997 Hewlett-Packard Development Company, L.P.