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368 lines
14 KiB
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<HTML>
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<TITLE>testfloat_gen</TITLE>
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<BODY>
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<H1>Berkeley TestFloat Release 3e: <CODE>testfloat_gen</CODE></H1>
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<P>
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John R. Hauser<BR>
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2018 January 20<BR>
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</P>
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<H2>Overview</H2>
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<P>
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The <CODE>testfloat_gen</CODE> program generates test cases for testing that an
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implementation of floating-point arithmetic conforms to the IEEE Standard for
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Binary Floating-Point Arithmetic.
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<CODE>testfloat_gen</CODE> is part of the Berkeley TestFloat package, a small
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collection of programs for performing such tests.
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For general information about TestFloat, see file
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<A HREF="TestFloat-general.html"><NOBR><CODE>TestFloat-general.html</CODE></NOBR></A>.
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</P>
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<P>
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A single execution of <CODE>testfloat_gen</CODE> generates test cases for only
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a single floating-point operation and associated options.
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The <CODE>testfloat_gen</CODE> program must be repeatedly executed to generate
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test cases for each operation to be tested.
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</P>
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<P>
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The <CODE>testfloat_gen</CODE> program writes the test cases it generates to
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standard output.
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This output can either be captured in a file through redirection, or be piped
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to another program that exercises a floating-point operation using the test
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cases as they are supplied.
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Depending on use, the total output from <CODE>testfloat_gen</CODE> can be
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large, so piping to another program may be the best choice to avoid using
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inordinate file space.
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The format of <CODE>testfloat_gen</CODE>’s output is raw hexadecimal
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text, described in the section below titled <I>Output Format</I>.
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</P>
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<H2>Command Syntax</H2>
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<P>
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The <CODE>testfloat_gen</CODE> program is executed as a command in one of these
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forms:
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<BLOCKQUOTE>
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<PRE>
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testfloat_gen [<<I>option</I>>...] <<I>type</I>>
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testfloat_gen [<<I>option</I>>...] <<I>function</I>>
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</PRE>
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</BLOCKQUOTE>
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Square brackets (<CODE>[ ]</CODE>) denote optional arguments, and
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<CODE><<I>option</I>></CODE> is a supported option, documented below.
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A <CODE>testfloat_gen</CODE> command expects either a
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<CODE><<I>type</I>></CODE> specifying the type and number of outputs or a
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<CODE><<I>function</I>></CODE> naming a floating-point operation.
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If <CODE>testfloat_gen</CODE> is executed without any arguments, a summary of
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usage is written.
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</P>
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<P>
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A <CODE><<I>type</I>></CODE> can be one of the following:
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<BLOCKQUOTE>
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<TABLE CELLSPACING=0 CELLPADDING=0>
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<TR>
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<TD><CODE>ui32</CODE></TD>
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<TD>unsigned <NOBR>32-bit</NOBR> integers</TD>
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</TR>
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<TR>
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<TD><CODE>ui64</CODE></TD>
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<TD>unsigned <NOBR>64-bit</NOBR> integers</TD>
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</TR>
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<TR>
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<TD><CODE>i32</CODE></TD>
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<TD>signed <NOBR>32-bit</NOBR> integers</TD>
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</TR>
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<TR>
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<TD><CODE>i64</CODE></TD>
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<TD>signed <NOBR>64-bit</NOBR> integers</TD>
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</TR>
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<TR>
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<TD><CODE>f16 [<<I>num</I>>]</CODE></TD>
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<TD>one or more <NOBR>16-bit</NOBR> half-precision floating-point values</TD>
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</TR>
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<TR>
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<TD><CODE>f32 [<<I>num</I>>]</CODE></TD>
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<TD>one or more <NOBR>32-bit</NOBR> single-precision floating-point values</TD>
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</TR>
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<TR>
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<TD><CODE>f64 [<<I>num</I>>]</CODE></TD>
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<TD>one or more <NOBR>64-bit</NOBR> double-precision floating-point values</TD>
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</TR>
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<TR>
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<TD><CODE>extF80 [<<I>num</I>>] </CODE></TD>
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<TD>one or more <NOBR>80-bit</NOBR> double-extended-precision floating-point
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values</TD>
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</TR>
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<TR>
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<TD><CODE>f128 [<<I>num</I>>]</CODE></TD>
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<TD>one or more <NOBR>128-bit</NOBR> quadruple-precision floating-point
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values</TD>
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</TR>
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</TABLE>
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</BLOCKQUOTE>
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Optional <CODE><<I>num</I>></CODE> is one of 1, 2, <NOBR>or 3</NOBR>.
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If a <CODE><<I>type</I>></CODE> is given without
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<CODE><<I>num</I>></CODE> (such as <CODE>ui32</CODE> or
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<CODE>f64</CODE>), <CODE>testfloat_gen</CODE> outputs a list of values of the
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specified type, one value per line, appropriate for testing a floating-point
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operation with exactly one operand of the given type.
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If a floating-point type and number are given (such as
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<NOBR><CODE>f32</CODE> <CODE>2</CODE></NOBR> or
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<NOBR><CODE>extF80</CODE> <CODE>1</CODE></NOBR>), <CODE>testfloat_gen</CODE>
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outputs the specified number of values per line, appropriate for testing a
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floating-point operation with that number of operands.
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Although the exact operation being tested is not specified, the test cases
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output by <CODE>testfloat_gen</CODE> cover all standard floating-point
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operations, to the degree explained in
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<A HREF="TestFloat-general.html"><NOBR><CODE>TestFloat-general.html</CODE></NOBR></A>.
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</P>
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<P>
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If a <CODE><<I>function</I>></CODE> operation name is given, then each
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line of output from <CODE>testfloat_gen</CODE> contains not only the operands
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for that operation (as would be generated by an appropriate
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<CODE><<I>type</I>></CODE> argument) but also the expected results as
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determined by <CODE>testfloat_gen</CODE>’s internal floating-point
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emulation (Berkeley SoftFloat).
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The available operation names are listed in
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<A HREF="TestFloat-general.html"><NOBR><CODE>TestFloat-general.html</CODE></NOBR></A>.
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In all cases, floating-point operations have two results:
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first, a value, which may be floating-point, integer, or Boolean, and, second,
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the floating-point exception flags raised by the operation.
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If the output from a tested floating-point operation does not match the
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expected output specified by <CODE>testfloat_gen</CODE>, this may or may not
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indicate an error in the floating-point operation.
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For further explanation, see
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<A HREF="TestFloat-general.html"><NOBR><CODE>TestFloat-general.html</CODE></NOBR></A>,
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especially the section titled <I>Variations Allowed by the IEEE Floating-Point
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Standard</I>.
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</P>
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<H2>Options</H2>
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<P>
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The <CODE>testfloat_gen</CODE> program accepts several command options.
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If mutually contradictory options are given, the last one has priority.
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</P>
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<H3><CODE>-help</CODE></H3>
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<P>
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The <CODE>-help</CODE> option causes a summary of program usage to be written,
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after which the program exits.
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</P>
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<H3><CODE>-prefix <<I>text</I>></CODE></H3>
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<P>
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The <CODE>-prefix</CODE> option causes <CODE>testfloat_gen</CODE> to write the
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supplied text argument verbatim as the first line of output before any test
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cases.
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This can be used, for example, to indicate to a downstream program what kind of
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test to perform for the test cases that follow.
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</P>
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<H3><CODE>-seed <<I>num</I>></CODE></H3>
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<P>
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The <CODE>-seed</CODE> option sets the seed for the pseudo-random number
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generator used for generating test cases.
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The argument to <CODE>-seed</CODE> is a nonnegative integer.
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Executing the same <CODE>testfloat_gen</CODE> program with the same arguments
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(including the same pseudo-random number seed) should always generate the same
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sequence of test cases, whereas changing the pseudo-random number seed should
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result in a different sequence of test cases.
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The default seed number <NOBR>is 1</NOBR>.
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</P>
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<H3><CODE>-level <<I>num</I>></CODE></H3>
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<P>
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The <CODE>-level</CODE> option sets the level of testing.
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The argument to <CODE>-level</CODE> can be either 1 <NOBR>or 2</NOBR>.
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The default is <NOBR>level 1</NOBR>.
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<NOBR>Level 2</NOBR> causes many more test cases to be generated, with better
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coverage, than <NOBR>level 1</NOBR>.
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</P>
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<H3><CODE>-n <<I>num</I>></CODE></H3>
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<P>
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Option <CODE>-n</CODE> specifies the number of test cases to generate.
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For each <CODE><<I>type</I>></CODE> or
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<CODE><<I>function</I>></CODE> and each testing level (set by
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<CODE>-level</CODE>), there is a minimum value that <CODE>testfloat_gen</CODE>
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will accept for <CODE><<I>num</I>></CODE>.
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If no <CODE>-n</CODE> option is given, the number of test cases generated by
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<CODE>testfloat_gen</CODE> equals the minimum value acceptable for the
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<CODE>-n</CODE> argument.
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Option <CODE>-n</CODE> cannot be used to reduce this number, but can increase
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it, without changing the testing level.
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</P>
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<H3><CODE>-forever</CODE></H3>
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<P>
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The <CODE>-forever</CODE> option causes test cases to be generated
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indefinitely, without limit (until the program is terminated by some external
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cause).
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The testing level is set to 2 by this option.
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</P>
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<H3><CODE>-precision32, -precision64, -precision80</CODE></H3>
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<P>
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When a <CODE><<I>function</I>></CODE> is specified that is an
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<NOBR>80-bit</NOBR> double-extended-precision operation affected by rounding
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precision control, the <CODE>-precision32</CODE> option sets the rounding
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precision to <NOBR>32 bits</NOBR>, equivalent to <NOBR>32-bit</NOBR>
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single-precision.
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Likewise, <CODE>-precision64</CODE> sets the rounding precision to
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<NOBR>64 bits</NOBR>, equivalent to <NOBR>64-bit</NOBR> double-precision, and
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<CODE>-precision80</CODE> sets the rounding precision to the full
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<NOBR>80 bits</NOBR> of the double-extended-precision format.
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All these options are ignored for operations not affected by rounding precision
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control.
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When rounding precision is applicable but not specified, the default is the
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full <NOBR>80 bits</NOBR>, same as <CODE>-precision80</CODE>.
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</P>
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<H3><CODE>-rnear_even, -rnear_maxMag, -rminMag, -rmin, -rmax, -rodd</CODE></H3>
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<P>
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When a <CODE><<I>function</I>></CODE> is specified that requires
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rounding, the <CODE>-rnear_even</CODE> option sets the rounding mode to
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nearest/even;
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<CODE>-rnear_maxMag</CODE> sets rounding to nearest/maximum magnitude
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(nearest-away);
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<CODE>-rminMag</CODE> sets rounding to minimum magnitude (toward zero);
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<CODE>-rmin</CODE> sets rounding to minimum (down, toward negative infinity);
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<CODE>-rmax</CODE> sets rounding to maximum (up, toward positive infinity);
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and <CODE>-rodd</CODE>, if supported, sets rounding to odd.
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These options are ignored for operations that are exact and thus do not round.
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When rounding mode is relevant but not specified, the default is to round to
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nearest/even, same as <CODE>-rnear_even</CODE>.
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</P>
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<H3><CODE>-tininessbefore, -tininessafter</CODE></H3>
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<P>
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When a <CODE><<I>function</I>></CODE> is specified that requires
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rounding, the <CODE>-tininessbefore</CODE> option indicates that tininess on
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underflow will be detected before rounding, while <CODE>-tininessafter</CODE>
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indicates that tininess on underflow will be detected after rounding.
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These options are ignored for operations that are exact and thus do not round.
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When the method of tininess detection matters but is not specified, the default
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is to detect tininess on underflow after rounding, same as
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<CODE>-tininessafter</CODE>.
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</P>
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<H3><CODE>-notexact, -exact</CODE></H3>
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<P>
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When a <CODE><<I>function</I>></CODE> is specified that rounds to an
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integer (either conversion to an integer type or a <CODE>roundToInt</CODE>
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operation), the <CODE>-notexact</CODE> option indicates that the <I>inexact</I>
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exception flag is never raised, while <CODE>-exact</CODE> indicates that the
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<I>inexact</I> exception flag is to be raised if the result is inexact.
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For other operations, these options are ignored.
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If neither option is specified, the default is not to raise the <I>inexact</I>
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exception flag when rounding to an integer, same as <CODE>-notexact</CODE>.
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</P>
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<H2>Output Format</H2>
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<P>
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For each test case generated, <CODE>testfloat_gen</CODE> writes a single line
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of text to standard output.
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When the <CODE>testfloat_gen</CODE> command is given a
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<CODE><<I>type</I>></CODE> argument, each test case consists of either
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one integer value or one, two, or three floating-point values.
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Each value is written to output as a raw hexadecimal number.
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When there is more than one value per line, they are separated by spaces.
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For example, output from executing
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<BLOCKQUOTE>
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<PRE>
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testfloat_gen f64 2
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</PRE>
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</BLOCKQUOTE>
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might look like this:
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<BLOCKQUOTE>
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<PRE>
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3F90EB5825D6851E C3E0080080000000
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41E3C00000000000 C182024F8AE474A8
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7FD80FFFFFFFFFFF 7FEFFFFFFFFFFF80
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3FFFED6A25C534BE 3CA1000000020000
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...
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</PRE>
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</BLOCKQUOTE>
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with each hexadecimal number being one <NOBR>64-bit</NOBR> floating-point
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value.
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Note that, for floating-point values, the sign and exponent are at the
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most-significant end of the number.
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Thus, for the first number on the first line above, the leading hexadecimal
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digits <CODE>3F9</CODE> are the sign and encoded exponent of the
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<NOBR>64-bit</NOBR> floating-point value, and the remaining digits are the
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encoded significand.
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</P>
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<P>
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When <CODE>testfloat_gen</CODE> is given a <CODE><<I>function</I>></CODE>
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operation name, each line of output has not only the operands for the operation
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but also the expected output, consisting of a result value and the exception
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flags that are raised.
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For example, the output from
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<BLOCKQUOTE>
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<PRE>
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testfloat_gen f64_add
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</PRE>
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</BLOCKQUOTE>
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could include these lines:
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<BLOCKQUOTE>
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<PRE>
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3F90EB5825D6851E C3E0080080000000 C3E0080080000000 01
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41E3C00000000000 C182024F8AE474A8 41E377F6C1D46E2D 01
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7FD80FFFFFFFFFFF 7FEFFFFFFFFFFF80 7FF0000000000000 05
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3FFFED6A25C534BE 3CA1000000020000 3FFFED6A25C534BF 01
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...
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</PRE>
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</BLOCKQUOTE>
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On each line, the first two numbers are the operands for the floating-point
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addition, and the third and fourth numbers are the expected floating-point
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result (the sum) and the exception flags raised.
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Exception flags are encoded with one bit per flag as follows:
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<BLOCKQUOTE>
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<TABLE CELLSPACING=0 CELLPADDING=0>
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<TR>
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<TD>bit 0<CODE> </CODE></TD>
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<TD><I>inexact</I> exception</TD>
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</TR>
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<TR><TD>bit 1</TD><TD><I>underflow</I> exception</TD></TR>
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<TR><TD>bit 2</TD><TD><I>overflow</I> exception</TD></TR>
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<TR>
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<TD>bit 3</TD>
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<TD><I>infinite</I> exception (“divide by zero”)</TD>
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</TR>
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<TR><TD>bit 4</TD><TD><I>invalid</I> exception</TD></TR>
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</TABLE>
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</BLOCKQUOTE>
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</P>
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</BODY>
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