path: root/testfloat/testfloat.txt

TestFloat Release 2a General Documentation

John R. Hauser
1998 December 16


-------------------------------------------------------------------------------
Introduction

TestFloat is a program for testing that a floating-point implementation
conforms to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
All standard operations supported by the system can be tested, except for
conversions to and from decimal.  Any of the following machine formats can
be tested:  single precision, double precision, extended double precision,
and/or quadruple precision.

TestFloat actually comes in two variants:  one is a program for testing
a machine's floating-point, and the other is a program for testing
the SoftFloat software implementation of floating-point.  (Information
about SoftFloat can be found at the SoftFloat Web page, `http://
HTTP.CS.Berkeley.EDU/~jhauser/arithmetic/SoftFloat.html'.)  The version that
tests SoftFloat is expected to be of interest only to people compiling the
SoftFloat sources.  However, because the two versions share much in common,
they are discussed together in all the TestFloat documentation.

This document explains how to use the TestFloat programs.  It does not
attempt to define or explain the IEC/IEEE Standard for floating-point.
Details about the standard are available elsewhere.

The first release of TestFloat (Release 1) was called _FloatTest_.  The old
name has been obsolete for some time.


-------------------------------------------------------------------------------
Limitations

TestFloat's output is not always easily interpreted.  Detailed knowledge
of the IEC/IEEE Standard and its vagaries is needed to use TestFloat
responsibly.

TestFloat performs relatively simple tests designed to check the fundamental
soundness of the floating-point under test.  TestFloat may also at times
manage to find rarer and more subtle bugs, but it will probably only find
such bugs by accident.  Software that purposefully seeks out various kinds
of subtle floating-point bugs can be found through links posted on the
TestFloat Web page (`http://HTTP.CS.Berkeley.EDU/~jhauser/arithmetic/
TestFloat.html').


-------------------------------------------------------------------------------
Contents

    Introduction
    Limitations
    Contents
    Legal Notice
    What TestFloat Does
    Executing TestFloat
    Functions Tested by TestFloat
        Conversion Functions
        Standard Arithmetic Functions
        Remainder and Round-to-Integer Functions
        Comparison Functions
    Interpreting TestFloat Output
    Variations Allowed by the IEC/IEEE Standard
        Underflow
        NaNs
        Conversions to Integer
    TestFloat Options
        -help
        -list
        -level <num>
        -errors <num>
        -errorstop
        -forever
        -checkNaNs
        -precision32, -precision64, -precision80
        -nearesteven, -tozero, -down, -up
        -tininessbefore, -tininessafter
    Function Sets
    Contact Information



-------------------------------------------------------------------------------
Legal Notice

TestFloat was written by John R. Hauser.

THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort
has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
TIMES RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO
PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.


-------------------------------------------------------------------------------
What TestFloat Does

TestFloat tests a system's floating-point by comparing its behavior with
that of TestFloat's own internal floating-point implemented in software.
For each operation tested, TestFloat generates a large number of test cases,
made up of simple pattern tests intermixed with weighted random inputs.
The cases generated should be adequate for testing carry chain propagations,
plus the rounding of adds, subtracts, multiplies, and simple operations like
conversions.  TestFloat makes a point of checking all boundary cases of the
arithmetic, including underflows, overflows, invalid operations, subnormal
inputs, zeros (positive and negative), infinities, and NaNs.  For the
interesting operations like adds and multiplies, literally millions of test
cases can be checked.

TestFloat is not remarkably good at testing difficult rounding cases for
divisions and square roots.  It also makes no attempt to find bugs specific
to SRT divisions and the like (such as the infamous Pentium divide bug).
Software that tests for such failures can be found through links on the
TestFloat Web page, `http://HTTP.CS.Berkeley.EDU/~jhauser/arithmetic/
TestFloat.html'.

NOTE!
It is the responsibility of the user to verify that the discrepancies
TestFloat finds actually represent faults in the system being tested.
Advice to help with this task is provided later in this document.
Furthermore, even if TestFloat finds no fault with a floating-point
implementation, that in no way guarantees that the implementation is bug-
free.

For each operation, TestFloat can test all four rounding modes required
by the IEC/IEEE Standard.  TestFloat verifies not only that the numeric
results of an operation are correct, but also that the proper floating-point
exception flags are raised.  All five exception flags are tested, including
the inexact flag.  TestFloat does not attempt to verify that the floating-
point exception flags are actually implemented as sticky flags.

For machines that implement extended double precision with rounding
precision control (such as Intel's 80x86), TestFloat can test the add,
subtract, multiply, divide, and square root functions at all the standard
rounding precisions.  The rounding precision can be set equivalent to single
precision, to double precision, or to the full extended double precision.
Rounding precision control can only be applied to the extended double-
precision format and only for the five standard arithmetic operations:  add,
subtract, multiply, divide, and square root.  Other functions can be tested
only at full precision.

As a rule, TestFloat is not particular about the bit patterns of NaNs that
appear as function results.  Any NaN is considered as good a result as
another.  This laxness can be overridden so that TestFloat checks for
particular bit patterns within NaN results.  See the sections _Variations_
_Allowed_by_the_IEC/IEEE_Standard_ and _TestFloat_Options_ for details.

Not all IEC/IEEE Standard functions are supported by all machines.
TestFloat can only test functions that exist on the machine.  But even if
a function is supported by the machine, TestFloat may still not be able
to test the function if it is not accessible through standard ISO C (the
programming language in which TestFloat is written) and if the person who
compiled TestFloat did not provide an alternate means for TestFloat to
invoke the machine function.

TestFloat compares a machine's floating-point against the SoftFloat software
implementation of floating-point, also written by me.  SoftFloat is built
into the TestFloat executable and does not need to be supplied by the user.
If SoftFloat is wanted for some other reason (to compile a new version
of TestFloat, for instance), it can be found separately at the Web page
`http://HTTP.CS.Berkeley.EDU/~jhauser/arithmetic/SoftFloat.html'.

For testing SoftFloat itself, the TestFloat package includes a program that
compares SoftFloat's floating-point against _another_ software floating-
point implementation.  The second software floating-point is simpler and
slower than SoftFloat, and is completely independent of SoftFloat.  Although
the second software floating-point cannot be guaranteed to be bug-free, the
chance that it would mimic any of SoftFloat's bugs is remote.  Consequently,
an error in one or the other floating-point version should appear as an
unexpected discrepancy between the two implementations.  Note that testing
SoftFloat should only be necessary when compiling a new TestFloat executable
or when compiling SoftFloat for some other reason.


-------------------------------------------------------------------------------
Executing TestFloat

TestFloat is intended to be executed from a command line interpreter.  The
`testfloat' program is invoked as follows:

    testfloat [<option>...] <function>

Here square brackets ([]) indicate optional items, while angled brackets
(<>) denote parameters to be filled in.

The `<function>' argument is a name like `float32_add' or `float64_to_int32'.
The complete list of function names is given in the next section,
_Functions_Tested_by_TestFloat_.  It is also possible to test all machine
functions in a single invocation.  The various options to TestFloat are
detailed in the section _TestFloat_Options_ later in this document.  If
`testfloat' is executed without any arguments, a summary of TestFloat usage
is written.

TestFloat will ordinarily test a function for all four rounding modes, one
after the other.  If the rounding mode is not supposed to have any affect
on the results--for instance, some operations do not require rounding--only
the nearest/even rounding mode is checked.  For extended double-precision
operations affected by rounding precision control, TestFloat also tests all
three rounding precision modes, one after the other.  Testing can be limited
to a single rounding mode and/or rounding precision with appropriate options
(see _TestFloat_Options_).

As it executes, TestFloat writes status information to the standard error
output, which should be the screen by default.  In order for this status to
be displayed properly, the standard error stream should not be redirected
to a file.  The discrepancies TestFloat finds are written to the standard
output stream, which is easily redirected to a file if desired.  Ordinarily,
the errors TestFloat reports and the ongoing status information appear
intermixed on the same screen.

The version of TestFloat for testing SoftFloat is called `testsoftfloat'.
It is invoked the same as `testfloat',

    testsoftfloat [<option>...] <function>

and operates similarly.


-------------------------------------------------------------------------------
Functions Tested by TestFloat

TestFloat tests all operations required by the IEC/IEEE Standard except for
conversions to and from decimal.  The operations are

-- Conversions among the supported floating-point formats, and also between
   integers (32-bit and 64-bit) and any of the floating-point formats.

-- The usual add, subtract, multiply, divide, and square root operations
   for all supported floating-point formats.

-- For each format, the floating-point remainder operation defined by the
   IEC/IEEE Standard.

-- For each floating-point format, a ``round to integer'' operation that
   rounds to the nearest integer value in the same format.  (The floating-
   point formats can hold integer values, of course.)

-- Comparisons between two values in the same floating-point format.

Detailed information about these functions is given below.  In the function
names used by TestFloat, single precision is called `float32', double
precision is `float64', extended double precision is `floatx80', and
quadruple precision is `float128'.  TestFloat uses the same names for
functions as SoftFloat.

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Conversion Functions

All conversions among the floating-point formats and all conversion between
a floating-point format and 32-bit and 64-bit signed integers can be tested.
The conversion functions are:

   int32_to_float32      int64_to_float32
   int32_to_float64      int64_to_float32
   int32_to_floatx80     int64_to_floatx80
   int32_to_float128     int64_to_float128

   float32_to_int32      float32_to_int64
   float32_to_int32      float64_to_int64
   floatx80_to_int32     floatx80_to_int64
   float128_to_int32     float128_to_int64

   float32_to_float64    float32_to_floatx80   float32_to_float128
   float64_to_float32    float64_to_floatx80   float64_to_float128
   floatx80_to_float32   floatx80_to_float64   floatx80_to_float128
   float128_to_float32   float128_to_float64   float128_to_floatx80

These conversions all round according to the current rounding mode as
necessary.  Conversions from a smaller to a larger floating-point format are
always exact and so require no rounding.  Conversions from 32-bit integers
to double precision or to any larger floating-point format are also exact,
and likewise for conversions from 64-bit integers to extended double and
quadruple precisions.

ISO/ANSI C requires that conversions to integers be rounded toward zero.
Such conversions can be tested with the following functions that ignore any
rounding mode:

   float32_to_int32_round_to_zero    float32_to_int64_round_to_zero
   float64_to_int32_round_to_zero    float64_to_int64_round_to_zero
   floatx80_to_int32_round_to_zero   floatx80_to_int64_round_to_zero
   float128_to_int32_round_to_zero   float128_to_int64_round_to_zero

TestFloat assumes that conversions from floating-point to integer should
raise the invalid exception if the source value cannot be rounded to a
representable integer of the desired size (32 or 64 bits).  If such a
conversion overflows, TestFloat expects the largest integer with the same
sign as the operand to be returned.  If the floating-point operand is a NaN,
TestFloat allows either the largest postive or largest negative integer to
be returned.

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Standard Arithmetic Functions

The following standard arithmetic functions can be tested:

   float32_add    float32_sub    float32_mul    float32_div    float32_sqrt
   float64_add    float64_sub    float64_mul    float64_div    float64_sqrt
   floatx80_add   floatx80_sub   floatx80_mul   floatx80_div   floatx80_sqrt
   float128_add   float128_sub   float128_mul   float128_div   float128_sqrt

The extended double-precision (`floatx80') functions can be rounded to
reduced precision under rounding precision control.

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Remainder and Round-to-Integer Functions

For each format, TestFloat can test the IEC/IEEE Standard remainder and
round-to-integer functions.  The remainder functions are:

   float32_rem
   float64_rem
   floatx80_rem
   float128_rem

The round-to-integer functions are:

   float32_round_to_int
   float64_round_to_int
   floatx80_round_to_int
   float128_round_to_int

The remainder functions are always exact and so do not require rounding.

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Comparison Functions

The following floating-point comparison functions can be tested:

   float32_eq    float32_le    float32_lt
   float64_eq    float64_le    float64_lt
   floatx80_eq   floatx80_le   floatx80_lt
   float128_eq   float128_le   float128_lt

The abbreviation `eq' stands for ``equal'' (=); `le' stands for ``less than
or equal'' (<=); and `lt' stands for ``less than'' (<).

The IEC/IEEE Standard specifies that the less-than-or-equal and less-than
functions raise the invalid exception if either input is any kind of NaN.
The equal functions, for their part, are defined not to raise the invalid
exception on quiet NaNs.  For completeness, the following additional
functions can be tested if supported:

   float32_eq_signaling    float32_le_quiet    float32_lt_quiet
   float64_eq_signaling    float64_le_quiet    float64_lt_quiet
   floatx80_eq_signaling   floatx80_le_quiet   floatx80_lt_quiet
   float128_eq_signaling   float128_le_quiet   float128_lt_quiet

The `signaling' equal functions are identical to the standard functions
except that the invalid exception should be raised for any NaN input.
Likewise, the `quiet' comparison functions should be identical to their
counterparts except that the invalid exception is not raised for quiet NaNs.

Obviously, no comparison functions ever require rounding.  Any rounding mode
is ignored.

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-------------------------------------------------------------------------------
Interpreting TestFloat Output

The ``errors'' reported by TestFloat may or may not really represent errors
in the system being tested.  For each test case tried, TestFloat performs
the same floating-point operation for the two implementations being compared
and reports any unexpected difference in the results.  The two results could
differ for several reasons:

-- The IEC/IEEE Standard allows for some variation in how conforming
   floating-point behaves.  Two implementations can occasionally give
   different results without either being incorrect.

-- The trusted floating-point emulation could be faulty.  This could be
   because there is a bug in the way the enulation is coded, or because a
   mistake was made when the code was compiled for the current system.

-- TestFloat may not work properly, reporting discrepancies that do not
   exist.

-- Lastly, the floating-point being tested could actually be faulty.

It is the responsibility of the user to determine the causes for the
discrepancies TestFloat reports.  Making this determination can require
detailed knowledge about the IEC/IEEE Standard.  Assuming TestFloat is
working properly, any differences found will be due to either the first or
last of these reasons.  Variations in the IEC/IEEE Standard that could lead
to false error reports are discussed in the section _Variations_Allowed_by_
_the_IEC/IEEE_Standard_.

For each error (or apparent error) TestFloat reports, a line of text
is written to the default output.  If a line would be longer than 79
characters, it is divided.  The first part of each error line begins in the
leftmost column, and any subsequent ``continuation'' lines are indented with
a tab.

Each error reported by `testfloat' is of the form:

    <inputs>  soft: <output-from-emulation>  syst: <output-from-system>

The `<inputs>' are the inputs to the operation.  Each output is shown as a
pair:  the result value first, followed by the exception flags.  The `soft'
label stands for ``software'' (or ``SoftFloat''), while `syst' stands for
``system,'' the machine's floating-point.

For example, two typical error lines could be

    800.7FFF00  87F.000100  soft: 001.000000 ....x  syst: 001.000000 ...ux
    081.000004  000.1FFFFF  soft: 001.000000 ....x  syst: 001.000000 ...ux

In the first line, the inputs are `800.7FFF00' and `87F.000100'.  The
internal emulation result is `001.000000' with flags `....x', and the
system result is the same but with flags `...ux'.  All the items composed of
hexadecimal digits and a single period represent floating-point values (here
single precision).  These cases were reported as errors because the flag
results differ.

In addition to the exception flags, there are seven data types that may
be represented.  Four are floating-point types:  single precision, double
precision, extended double precision, and quadruple precision.  The
remaining three types are 32-bit and 64-bit two's-complement integers and
Boolean values (the results of comparison operations).  Boolean values are
represented as a single character, either a `0' or a `1'.  32-bit integers
are written as 8 hexadecimal digits in two's-complement form.  Thus,
`FFFFFFFF' is -1, and `7FFFFFFF' is the largest positive 32-bit integer.
64-bit integers are the same except with 16 hexadecimal digits.

Floating-point values are written in a correspondingly primitive form.
Double-precision values are represented by 16 hexadecimal digits that give
the raw bits of the floating-point encoding.  A period separates the 3rd and
4th hexadecimal digits to mark the division between the exponent bits and
fraction bits.  Some notable double-precision values include:

    000.0000000000000    +0
    3FF.0000000000000     1
    400.0000000000000     2
    7FF.0000000000000    +infinity

    800.0000000000000    -0
    BFF.0000000000000    -1
    C00.0000000000000    -2
    FFF.0000000000000    -infinity

    3FE.FFFFFFFFFFFFF    largest representable number preceding +1

The following categories are easily distinguished (assuming the `x's are not
all 0):

    000.xxxxxxxxxxxxx    positive subnormal (denormalized) numbers
    7FF.xxxxxxxxxxxxx    positive NaNs
    800.xxxxxxxxxxxxx    negative subnormal numbers
    FFF.xxxxxxxxxxxxx    negative NaNs

Quadruple-precision values are written the same except with 4 hexadecimal
digits for the sign and exponent and 28 for the fraction.  Notable values
include:

    0000.0000000000000000000000000000    +0
    3FFF.0000000000000000000000000000     1
    4000.0000000000000000000000000000     2
    7FFF.0000000000000000000000000000    +infinity

    8000.0000000000000000000000000000    -0
    BFFF.0000000000000000000000000000    -1
    C000.0000000000000000000000000000    -2
    FFFF.0000000000000000000000000000    -infinity

    3FFE.FFFFFFFFFFFFFFFFFFFFFFFFFFFF    largest representable number
                                             preceding +1

Extended double-precision values are a little unusual in that the leading
significand bit is not hidden as with other formats.  When correctly
encoded, the leading significand bit of an extended double-precision value
will be 0 if the value is zero or subnormal, and will be 1 otherwise.
Hence, the same values listed above appear in extended double-precision as
follows (note the leading `8' digit in the significands):

    0000.0000000000000000    +0
    3FFF.8000000000000000     1
    4000.8000000000000000     2
    7FFF.8000000000000000    +infinity

    8000.0000000000000000    -0
    BFFF.8000000000000000    -1
    C000.8000000000000000    -2
    FFFF.8000000000000000    -infinity

    3FFE.FFFFFFFFFFFFFFFF    largest representable number preceding +1

The representation of single-precision values is unusual for a different
reason.  Because the subfields of standard single-precision do not fall
on neat 4-bit boundaries, single-precision outputs are slightly perturbed.
These are written as 9 hexadecimal digits, with a period separating the 3rd
and 4th hexadecimal digits.  Broken out into bits, the 9 hexademical digits
cover the single-precision subfields as follows:

    x000 .... ....  .  .... .... .... .... .... ....    sign       (1 bit)
    .... xxxx xxxx  .  .... .... .... .... .... ....    exponent   (8 bits)
    .... .... ....  .  0xxx xxxx xxxx xxxx xxxx xxxx    fraction  (23 bits)

As shown in this schematic, the first hexadecimal digit contains only
the sign, and will be either `0' or `8'.  The next two digits give the
biased exponent as an 8-bit integer.  This is followed by a period and
6 hexadecimal digits of fraction.  The most significant hexadecimal digit
of the fraction can be at most a `7'.

Notable single-precision values include:

    000.000000    +0
    07F.000000     1
    080.000000     2
    0FF.000000    +infinity

    800.000000    -0
    87F.000000    -1
    880.000000    -2
    8FF.000000    -infinity

    07E.7FFFFF    largest representable number preceding +1

Again, certain categories are easily distinguished (assuming the `x's are
not all 0):

    000.xxxxxx    positive subnormal (denormalized) numbers
    0FF.xxxxxx    positive NaNs
    800.xxxxxx    negative subnormal numbers
    8FF.xxxxxx    negative NaNs

Lastly, exception flag values are represented by five characters, one
character per flag.  Each flag is written as either a letter or a period
(`.') according to whether the flag was set or not by the operation.  A
period indicates the flag was not set.  The letter used to indicate a set
flag depends on the flag:

    v    invalid flag
    z    division-by-zero flag
    o    overflow flag
    u    underflow flag
    x    inexact flag

For example, the notation `...ux' indicates that the underflow and inexact
exception flags were set and that the other three flags (invalid, division-
by-zero, and overflow) were not set.  The exception flags are always shown
following the value returned as the result of the operation.

The output from `testsoftfloat' is of the same form, except that the results
are labeled `true' and `soft':

    <inputs>  true: <simple-software-result>  soft: <SoftFloat-result>

The ``true'' result is from the simpler, slower software floating-point,
which, although not necessarily correct, is more likely to be right than
the SoftFloat (`soft') result.


-------------------------------------------------------------------------------
Variations Allowed by the IEC/IEEE Standard

The IEC/IEEE Standard admits some variation among conforming
implementations.  Because TestFloat expects the two implementations being
compared to deliver bit-for-bit identical results under most circumstances,
this leeway in the standard can result in false errors being reported if
the two implementations do not make the same choices everywhere the standard
provides an option.

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Underflow

The standard specifies that the underflow exception flag is to be raised
when two conditions are met simultaneously:  (1) _tininess_ and (2) _loss_
_of_accuracy_.  A result is tiny when its magnitude is nonzero yet smaller
than any normalized floating-point number.  The standard allows tininess to
be determined either before or after a result is rounded to the destination
precision.  If tininess is detected before rounding, some borderline cases
will be flagged as underflows even though the result after rounding actually
lies within the normal floating-point range.  By detecting tininess after
rounding, a system can avoid some unnecessary signaling of underflow.

Loss of accuracy occurs when the subnormal format is not sufficient
to represent an underflowed result accurately.  The standard allows
loss of accuracy to be detected either as an _inexact_result_ or as a
_denormalization_loss_.  If loss of accuracy is detected as an inexact
result, the underflow flag is raised whenever an underflowed quantity
cannot be exactly represented in the subnormal format (that is, whenever the
inexact flag is also raised).  A denormalization loss, on the other hand,
occurs only when the subnormal format is not able to represent the result
that would have been returned if the destination format had infinite range.
Some underflowed results are inexact but do not suffer a denormalization
loss.  By detecting loss of accuracy as a denormalization loss, a system can
once again avoid some unnecessary signaling of underflow.

The `-tininessbefore' and `-tininessafter' options can be used to control
whether TestFloat expects tininess on underflow to be detected before or
after rounding.  (See _TestFloat_Options_ below.)  One or the other is
selected as the default when TestFloat is compiled, but these command
options allow the default to be overridden.

Most (possibly all) systems detect loss of accuracy as an inexact result.
The current version of TestFloat can only test for this case.

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NaNs

The IEC/IEEE Standard gives the floating-point formats a large number of
NaN encodings and specifies that NaNs are to be returned as results under
certain conditions.  However, the standard allows an implementation almost
complete freedom over _which_ NaN to return in each situation.

By default, TestFloat does not check the bit patterns of NaN results.  When
the result of an operation should be a NaN, any NaN is considered as good
as another.  This laxness can be overridden with the `-checkNaNs' option.
(See _TestFloat_Options_ below.)  In order for this option to be sensible,
TestFloat must have been compiled so that its internal floating-point
implementation (SoftFloat) generates the proper NaN results for the system
being tested.

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Conversions to Integer

Conversion of a floating-point value to an integer format will fail if the
source value is a NaN or if it is too large.  The IEC/IEEE Standard does not
specify what value should be returned as the integer result in these cases.
Moreover, according to the standard, the invalid exception can be raised or
an unspecified alternative mechanism may be used to signal such cases.

TestFloat assumes that conversions to integer will raise the invalid
exception if the source value cannot be rounded to a representable integer.
When the conversion overflows, TestFloat expects the largest integer with
the same sign as the operand to be returned.  If the floating-point operand
is a NaN, TestFloat allows either the largest postive or largest negative
integer to be returned.  The current version of TestFloat provides no means
to alter these conventions.

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-------------------------------------------------------------------------------
TestFloat Options

The `testfloat' (and `testsoftfloat') program accepts several command
options.  If mutually contradictory options are given, the last one has
priority.

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-help

The `-help' option causes a summary of program usage to be written, after
which the program exits.

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-list

The `-list' option causes a list of testable functions to be written,
after which the program exits.  Some machines do not implement all of the
functions TestFloat can test, plus it may not be possible to test functions
that are inaccessible from the C language.

The `testsoftfloat' program does not have this option.  All SoftFloat
functions can be tested by `testsoftfloat'.

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-level <num>

The `-level' option sets the level of testing.  The argument to `-level' can
be either 1 or 2.  The default is level 1.  Level 2 performs many more tests
than level 1.  Testing at level 2 can take as much as a day (even longer for
`testsoftfloat'), but can reveal bugs not found by level 1.

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-errors <num>

The `-errors' option instructs TestFloat to report no more than the
specified number of errors for any combination of function, rounding mode,
etc.  The argument to `-errors' must be a nonnegative decimal number.  Once
the specified number of error reports has been generated, TestFloat ends the
current test and begins the next one, if any.  The default is `-errors 20'.

Against intuition, `-errors 0' causes TestFloat to report every error it
finds.

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-errorstop

The `-errorstop' option causes the program to exit after the first function
for which any errors are reported.

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-forever

The `-forever' option causes a single operation to be repeatedly tested.
Only one rounding mode and/or rounding precision can be tested in a single
invocation.  If not specified, the rounding mode defaults to nearest/even.
For extended double-precision operations, the rounding precision defaults
to full extended double precision.  The testing level is set to 2 by this
option.

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-checkNaNs

The `-checkNaNs' option causes TestFloat to verify the bitwise correctness
of NaN results.  In order for this option to be sensible, TestFloat must
have been compiled so that its internal floating-point implementation
(SoftFloat) generates the proper NaN results for the system being tested.

This option is not available to `testsoftfloat'.

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-precision32, -precision64, -precision80

For extended double-precision functions affected by rounding precision
control, the `-precision32' option restricts testing to only the cases
in which rounding precision is equivalent to single precision.  The other
rounding precision options are not tested.  Likewise, the `-precision64'
and `-precision80' options fix the rounding precision equivalent to double
precision or extended double precision, respectively.  These options are
ignored for functions not affected by rounding precision control.

These options are not available if extended double precision is not
supported by the machine or if extended double precision functions cannot be
tested.

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-nearesteven, -tozero, -down, -up

The `-nearesteven' option restricts testing to only the cases in which the
rounding mode is nearest/even.  The other rounding mode options are not
tested.  Likewise, `-tozero' forces rounding to zero; `-down' forces
rounding down; and `-up' forces rounding up.  These options are ignored for
functions that are exact and thus do not round.

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-tininessbefore, -tininessafter

The `-tininessbefore' option indicates that the system detects tininess
on underflow before rounding.  The `-tininessafter' option indicates that
tininess is detected after rounding.  TestFloat alters its expectations
accordingly.  These options override the default selected when TestFloat was
compiled.  Choosing the wrong one of these two options should cause error
reports for some (not all) functions.

For `testsoftfloat', these options operate more like the rounding precision
and rounding mode options, in that they restrict the tests performed by
`testsoftfloat'.  By default, `testsoftfloat' tests both cases for any
function for which there is a difference.

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-------------------------------------------------------------------------------
Function Sets

Just as TestFloat can test an operation for all four rounding modes in
sequence, multiple operations can be tested with a single invocation of
TestFloat.  Three sets are recognized:  `-all1', `-all2', and `-all'.  The
set `-all1' comprises all one-operand functions; `-all2' is all two-operand
functions; and `-all' is all functions.  A function set can be used in place
of a function name in the TestFloat command line, such as

    testfloat [<option>...] -all


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Contact Information

At the time of this writing, the most up-to-date information about
TestFloat and the latest release can be found at the Web page `http://
HTTP.CS.Berkeley.EDU/~jhauser/arithmetic/TestFloat.html'.