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<H1>Berkeley TestFloat Release 3: <CODE>testfloat_ver</CODE></H1>

<P>
John R. Hauser<BR>
2015 Jan 9<BR>
</P>


<H2>Overview</H2>

<P>
The <CODE>testfloat_ver</CODE> program takes test-case results obtained from
exercising an implementation of floating-point arithmetic and verifies that
those results conform to the IEEE Standard for Binary Floating-Point
Arithmetic.
<CODE>testfloat_ver</CODE> is part of the Berkeley TestFloat package, a small
collection of programs for performing such tests.
For general information about TestFloat, see file
<A HREF="TestFloat-general.html"><NOBR><CODE>TestFloat-general.html</CODE></NOBR></A>.
</P>

<P>
A single execution of <CODE>testfloat_ver</CODE> verifies results for only a
single floating-point operation and associated options.
The <CODE>testfloat_ver</CODE> program must be repeatedly executed to verify
results for each operation to be tested.
</P>

<P>
The test cases to be verified are read by <CODE>testfloat_ver</CODE> from
standard input.
This input will typically be piped from another program that, for each test
case, invokes the floating-point operation and writes out the results.
The format of <CODE>testfloat_ver</CODE>&rsquo;s input is raw hexadecimal text,
described in the section below titled <I>Input Format</I>.
</P>

<P>
For each test case given to it, <CODE>testfloat_ver</CODE> examines the
computed results and reports any unexpected results as likely errors.

For more about the operation of <CODE>testfloat_ver</CODE> and how to interpret
its output, refer to
<A HREF="TestFloat-general.html"><NOBR><CODE>TestFloat-general.html</CODE></NOBR></A>.
</P>


<H2>Command Syntax</H2>

<P>
The <CODE>testfloat_ver</CODE> program is executed as a command with this
syntax:
<BLOCKQUOTE>
<PRE>
testfloat_ver [&lt;option&gt;...] &lt;function&gt;
</PRE>
</BLOCKQUOTE>
Square brackets (<CODE>[ ]</CODE>) denote optional arguments,
<CODE>&lt;option&gt;</CODE> is a supported option, and
<CODE>&lt;function&gt;</CODE> is the name of a testable operation.
The available options are documented below.
The testable operation names are listed in
<A HREF="TestFloat-general.html"><NOBR><CODE>TestFloat-general.html</CODE></NOBR></A>.
If <CODE>testfloat_ver</CODE> is executed without any arguments, a summary of
usage is written.
</P>


<H2>Options</H2>

<P>
The <CODE>testfloat_ver</CODE> program accepts several command options.
If mutually contradictory options are given, the last one has priority.
</P>

<H3><CODE>-help</CODE></H3>

<P>
The <CODE>-help</CODE> option causes a summary of program usage to be written,
after which the program exits.
</P>

<H3><CODE>-errors &lt;num&gt;</CODE></H3>

<P>
The <CODE>-errors</CODE> option instructs <CODE>testfloat_ver</CODE> to report
no more than the specified number of errors.
The argument to <CODE>-errors</CODE> must be a nonnegative decimal integer.
Once the specified number of error reports has been generated, the program
exits.
The default is <NOBR><CODE>-errors</CODE> <CODE>20</CODE></NOBR>.
</P>

<P>
Against intuition, <NOBR><CODE>-errors</CODE> <CODE>0</CODE></NOBR> causes
<CODE>testfloat_ver</CODE> to continue for any number of errors.
</P>

<H3><CODE>-checkNaNs</CODE></H3>

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

<H3><CODE>-precision32, -precision64, -precision80</CODE></H3>

<P>
When <CODE>&lt;function&gt;</CODE> is an <NOBR>80-bit</NOBR>
double-extended-precision operation affected by rounding precision control, the
<CODE>-precision32</CODE> option indicates that the rounding precision should
be <NOBR>32 bits</NOBR>, equivalent to <NOBR>32-bit</NOBR> single-precision.
Likewise, <CODE>-precision64</CODE> indicates that the rounding precision
should be <NOBR>64 bits</NOBR>, equivalent to <NOBR>64-bit</NOBR>
double-precision, and <CODE>-precision80</CODE> indicates that the rounding
precision should be the full <NOBR>80 bits</NOBR> of the
double-extended-precision format.
All these options are ignored for operations not affected by rounding precision
control.
When rounding precision is applicable but not specified, the default assumption
is the full <NOBR>80 bits</NOBR>, same as <CODE>-precision80</CODE>.
</P>

<H3><CODE>-rnear_even, -rnear_maxMag, -rminMag, -rmin, -rmax</CODE></H3>

<P>
When <CODE>&lt;function&gt;</CODE> is an operation that requires rounding, the
<CODE>-rnear_even</CODE> option indicates that rounding should be to
nearest/even, <CODE>-rnear_maxMag</CODE> indicates rounding to nearest/maximum
magnitude (nearest-away), <CODE>-rminMag</CODE> indicates rounding to minimum
magnitude (toward zero), <CODE>-rmin</CODE> indicates rounding to minimum
(down, toward negative infinity), and <CODE>-rmax</CODE> indicates rounding to
maximum (up, toward positive infinity).
These options are ignored for operations that are exact and thus do not round.
When rounding mode is relevant but not specified, the default assumption is
rounding to nearest/even, same as <CODE>-rnear_even</CODE>.
</P>

<H3><CODE>-tininessbefore, -tininessafter</CODE></H3>

<P>
When <CODE>&lt;function&gt;</CODE> is an operation that requires rounding, the
<CODE>-tininessbefore</CODE> option indicates that tininess on underflow should
be detected before rounding, while <CODE>-tininessafter</CODE> indicates that
tininess on underflow should be detected after rounding.
These options are ignored for operations that are exact and thus do not round.
When the method of tininess detection matters but is not specified, the default
assumption is that tininess should be detected before rounding, same as
<CODE>-tininessbefore</CODE>.
</P>

<H3><CODE>-notexact, -exact</CODE></H3>

<P>
When <CODE>&lt;function&gt;</CODE> is an operation that rounds to an integer
(either conversion to an integer type or a <CODE>roundToInt</CODE> operation),
the <CODE>-notexact</CODE> option indicates that the <I>inexact</I> exception
flag should never be raised, while <CODE>-exact</CODE> indicates that the
<I>inexact</I> exception flag should be raised when the result is inexact.
For other operations, these options are ignored.
If neither option is specified, the default assumption is that the
<I>inexact</I> exception flag should not be raised when rounding to an integer,
same as <CODE>-notexact</CODE>.
</P>


<H2>Input Format</H2>

<P>
For a given <CODE>&lt;function&gt;</CODE> argument, the input format expected
by <CODE>testfloat_ver</CODE> is the same as the output generated by program
<A HREF="testfloat_gen.html"><NOBR><CODE>testfloat_gen</CODE></NOBR></A> for
the same argument.
</P>

<P>
Input to <CODE>testfloat_ver</CODE> is expected to be text, with each line
containing the data for one test case.
The number of input lines thus equals the number of test cases.
A single test case is organized as follows:  first are the operands for the
operation, next is the result value obtained, and last is a number indicating
the exception flags that were raised.
These values are all expected to be provided as raw hexadecimal numbers
separated on the line by spaces.
For example, for the command
<BLOCKQUOTE>
<PRE>
testfloat_ver f64_add
</PRE>
</BLOCKQUOTE>
valid input could include these lines:
<BLOCKQUOTE>
<PRE>
3F90EB5825D6851E C3E0080080000000 C3E0080080000000 01
41E3C00000000000 C182024F8AE474A8 41E377F6C1D46E2D 01
7FD80FFFFFFFFFFF 7FEFFFFFFFFFFF80 7FF0000000000000 05
3FFFED6A25C534BE 3CA1000000020000 3FFFED6A25C534BF 01
...
</PRE>
</BLOCKQUOTE>
On each line above, the first two hexadecimal numbers represent the
<NOBR>64-bit</NOBR> floating-point operands, the third hexadecimal number is
the <NOBR>64-bit</NOBR> floating-point result of the operation (the sum), and
the last hexadecimal number gives the exception flags that were raised by the
operation.
</P>

<P>
Note that, for floating-point values, the sign and exponent are at the
most-significant end of the number.
Thus, for the first number on the first line above, the leading hexadecimal
digits <CODE>3F9</CODE> are the sign and encoded exponent of the
<NOBR>64-bit</NOBR> floating-point value, and the remaining digits are the
encoded significand.
</P>

<P>
Exception flags are encoded with one bit per flag as follows:
<BLOCKQUOTE>
<TABLE CELLSPACING=0 CELLPADDING=0>
<TR>
  <TD>bit 0<CODE>&nbsp;&nbsp;&nbsp;</CODE></TD>
  <TD><I>inexact</I> exception</TD>
</TR>
<TR><TD>bit 1</TD><TD><I>underflow</I> exception</TD></TR>
<TR><TD>bit 2</TD><TD><I>overflow</I> exception</TD></TR>
<TR>
  <TD>bit 3</TD>
  <TD><I>infinite</I> exception (&ldquo;divide by zero&rdquo;)</TD>
</TR>
<TR><TD>bit 4</TD><TD><I>invalid</I> exception</TD></TR>
</TABLE>
</BLOCKQUOTE>
</P>


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