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1528 lines
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HTML
1528 lines
54 KiB
HTML
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<HTML>
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<HEAD>
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<TITLE>Berkeley SoftFloat Library Interface</TITLE>
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</HEAD>
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<BODY>
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<H1>Berkeley SoftFloat Release 3e: Library Interface</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>Contents</H2>
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<BLOCKQUOTE>
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<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
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<COL WIDTH=25>
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<COL WIDTH=*>
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<TR><TD COLSPAN=2>1. Introduction</TD></TR>
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<TR><TD COLSPAN=2>2. Limitations</TD></TR>
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<TR><TD COLSPAN=2>3. Acknowledgments and License</TD></TR>
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<TR><TD COLSPAN=2>4. Types and Functions</TD></TR>
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<TR><TD></TD><TD>4.1. Boolean and Integer Types</TD></TR>
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<TR><TD></TD><TD>4.2. Floating-Point Types</TD></TR>
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<TR><TD></TD><TD>4.3. Supported Floating-Point Functions</TD></TR>
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<TR>
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<TD></TD>
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<TD>4.4. Non-canonical Representations in <CODE>extFloat80_t</CODE></TD>
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</TR>
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<TR><TD></TD><TD>4.5. Conventions for Passing Arguments and Results</TD></TR>
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<TR><TD COLSPAN=2>5. Reserved Names</TD></TR>
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<TR><TD COLSPAN=2>6. Mode Variables</TD></TR>
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<TR><TD></TD><TD>6.1. Rounding Mode</TD></TR>
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<TR><TD></TD><TD>6.2. Underflow Detection</TD></TR>
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<TR>
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<TD></TD>
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<TD>6.3. Rounding Precision for the <NOBR>80-Bit</NOBR> Extended Format</TD>
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</TR>
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<TR><TD COLSPAN=2>7. Exceptions and Exception Flags</TD></TR>
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<TR><TD COLSPAN=2>8. Function Details</TD></TR>
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<TR><TD></TD><TD>8.1. Conversions from Integer to Floating-Point</TD></TR>
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<TR><TD></TD><TD>8.2. Conversions from Floating-Point to Integer</TD></TR>
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<TR><TD></TD><TD>8.3. Conversions Among Floating-Point Types</TD></TR>
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<TR><TD></TD><TD>8.4. Basic Arithmetic Functions</TD></TR>
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<TR><TD></TD><TD>8.5. Fused Multiply-Add Functions</TD></TR>
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<TR><TD></TD><TD>8.6. Remainder Functions</TD></TR>
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<TR><TD></TD><TD>8.7. Round-to-Integer Functions</TD></TR>
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<TR><TD></TD><TD>8.8. Comparison Functions</TD></TR>
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<TR><TD></TD><TD>8.9. Signaling NaN Test Functions</TD></TR>
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<TR><TD></TD><TD>8.10. Raise-Exception Function</TD></TR>
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<TR><TD COLSPAN=2>9. Changes from SoftFloat <NOBR>Release 2</NOBR></TD></TR>
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<TR><TD></TD><TD>9.1. Name Changes</TD></TR>
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<TR><TD></TD><TD>9.2. Changes to Function Arguments</TD></TR>
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<TR><TD></TD><TD>9.3. Added Capabilities</TD></TR>
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<TR><TD></TD><TD>9.4. Better Compatibility with the C Language</TD></TR>
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<TR><TD></TD><TD>9.5. New Organization as a Library</TD></TR>
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<TR><TD></TD><TD>9.6. Optimization Gains (and Losses)</TD></TR>
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<TR><TD COLSPAN=2>10. Future Directions</TD></TR>
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<TR><TD COLSPAN=2>11. Contact Information</TD></TR>
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</TABLE>
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</BLOCKQUOTE>
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<H2>1. Introduction</H2>
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<P>
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Berkeley SoftFloat is a software implementation of binary floating-point that
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conforms to the IEEE Standard for Floating-Point Arithmetic.
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The current release supports five binary formats: <NOBR>16-bit</NOBR>
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half-precision, <NOBR>32-bit</NOBR> single-precision, <NOBR>64-bit</NOBR>
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double-precision, <NOBR>80-bit</NOBR> double-extended-precision, and
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<NOBR>128-bit</NOBR> quadruple-precision.
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The following functions are supported for each format:
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<UL>
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<LI>
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addition, subtraction, multiplication, division, and square root;
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<LI>
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fused multiply-add as defined by the IEEE Standard, except for
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<NOBR>80-bit</NOBR> double-extended-precision;
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<LI>
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remainder as defined by the IEEE Standard;
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<LI>
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round to integral value;
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<LI>
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comparisons;
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<LI>
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conversions to/from other supported formats; and
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<LI>
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conversions to/from <NOBR>32-bit</NOBR> and <NOBR>64-bit</NOBR> integers,
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signed and unsigned.
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</UL>
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All operations required by the original 1985 version of the IEEE Floating-Point
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Standard are implemented, except for conversions to and from decimal.
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</P>
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<P>
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This document gives information about the types defined and the routines
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implemented by SoftFloat.
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It does not attempt to define or explain the IEEE Floating-Point Standard.
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Information about the standard is available elsewhere.
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</P>
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<P>
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The current version of SoftFloat is <NOBR>Release 3e</NOBR>.
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This release modifies the behavior of the rarely used <I>odd</I> rounding mode
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(<I>round to odd</I>, also known as <I>jamming</I>), and also adds some new
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specialization and optimization examples for those compiling SoftFloat.
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</P>
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<P>
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The previous <NOBR>Release 3d</NOBR> fixed bugs that were found in the square
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root functions for the <NOBR>64-bit</NOBR>, <NOBR>80-bit</NOBR>, and
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<NOBR>128-bit</NOBR> floating-point formats.
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(Thanks to Alexei Sibidanov at the University of Victoria for reporting an
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incorrect result.)
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The bugs affected all prior <NOBR>Release-3</NOBR> versions of SoftFloat
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<NOBR>through 3c</NOBR>.
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The flaw in the <NOBR>64-bit</NOBR> floating-point square root function was of
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very minor impact, causing a <NOBR>1-ulp</NOBR> error (<NOBR>1 unit</NOBR> in
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the last place) a few times out of a billion.
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The bugs in the <NOBR>80-bit</NOBR> and <NOBR>128-bit</NOBR> square root
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functions were more serious.
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Although incorrect results again occurred only a few times out of a billion,
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when they did occur a large portion of the less-significant bits could be
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wrong.
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</P>
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<P>
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Among earlier releases, 3b was notable for adding support for the
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<NOBR>16-bit</NOBR> half-precision format.
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For more about the evolution of SoftFloat releases, see
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<A HREF="SoftFloat-history.html"><NOBR><CODE>SoftFloat-history.html</CODE></NOBR></A>.
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</P>
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<P>
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The functional interface of SoftFloat <NOBR>Release 3</NOBR> and later differs
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in many details from the releases that came before.
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For specifics of these differences, see <NOBR>section 9</NOBR> below,
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<I>Changes from SoftFloat <NOBR>Release 2</NOBR></I>.
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</P>
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<H2>2. Limitations</H2>
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<P>
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SoftFloat assumes the computer has an addressable byte size of 8 or
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<NOBR>16 bits</NOBR>.
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(Nearly all computers in use today have <NOBR>8-bit</NOBR> bytes.)
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</P>
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<P>
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SoftFloat is written in C and is designed to work with other C code.
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The C compiler used must conform at a minimum to the 1989 ANSI standard for the
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C language (same as the 1990 ISO standard) and must in addition support basic
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arithmetic on <NOBR>64-bit</NOBR> integers.
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Earlier releases of SoftFloat included implementations of <NOBR>32-bit</NOBR>
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single-precision and <NOBR>64-bit</NOBR> double-precision floating-point that
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did not require <NOBR>64-bit</NOBR> integers, but this option is not supported
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starting with <NOBR>Release 3</NOBR>.
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Since 1999, ISO standards for C have mandated compiler support for
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<NOBR>64-bit</NOBR> integers.
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A compiler conforming to the 1999 C Standard or later is recommended but not
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strictly required.
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</P>
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<P>
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Most operations not required by the original 1985 version of the IEEE
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Floating-Point Standard but added in the 2008 version are not yet supported in
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SoftFloat <NOBR>Release 3e</NOBR>.
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</P>
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<H2>3. Acknowledgments and License</H2>
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<P>
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The SoftFloat package was written by me, <NOBR>John R.</NOBR> Hauser.
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<NOBR>Release 3</NOBR> of SoftFloat was a completely new implementation
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supplanting earlier releases.
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The project to create <NOBR>Release 3</NOBR> (now <NOBR>through 3e</NOBR>) was
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done in the employ of the University of California, Berkeley, within the
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Department of Electrical Engineering and Computer Sciences, first for the
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Parallel Computing Laboratory (Par Lab) and then for the ASPIRE Lab.
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The work was officially overseen by Prof. Krste Asanovic, with funding provided
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by these sources:
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<BLOCKQUOTE>
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<TABLE>
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<COL>
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<COL WIDTH=10>
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<COL>
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<TR>
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<TD VALIGN=TOP><NOBR>Par Lab:</NOBR></TD>
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<TD></TD>
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<TD>
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Microsoft (Award #024263), Intel (Award #024894), and U.C. Discovery
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(Award #DIG07-10227), with additional support from Par Lab affiliates Nokia,
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NVIDIA, Oracle, and Samsung.
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</TD>
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</TR>
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<TR>
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<TD VALIGN=TOP><NOBR>ASPIRE Lab:</NOBR></TD>
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<TD></TD>
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<TD>
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DARPA PERFECT program (Award #HR0011-12-2-0016), with additional support from
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ASPIRE industrial sponsor Intel and ASPIRE affiliates Google, Nokia, NVIDIA,
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Oracle, and Samsung.
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</TD>
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</TR>
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</TABLE>
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</BLOCKQUOTE>
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</P>
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<P>
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The following applies to the whole of SoftFloat <NOBR>Release 3e</NOBR> as well
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as to each source file individually.
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</P>
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<P>
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Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Regents of the
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University of California.
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All rights reserved.
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</P>
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<P>
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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<OL>
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<LI>
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<P>
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Redistributions of source code must retain the above copyright notice, this
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list of conditions, and the following disclaimer.
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</P>
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<LI>
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<P>
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Redistributions in binary form must reproduce the above copyright notice, this
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list of conditions, and the following disclaimer in the documentation and/or
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other materials provided with the distribution.
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</P>
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<LI>
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<P>
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Neither the name of the University nor the names of its contributors may be
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used to endorse or promote products derived from this software without specific
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prior written permission.
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</P>
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</OL>
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</P>
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<P>
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THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS “AS IS”,
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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
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DISCLAIMED.
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IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
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INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE
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OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
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ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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</P>
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<H2>4. Types and Functions</H2>
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<P>
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The types and functions of SoftFloat are declared in header file
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<CODE>softfloat.h</CODE>.
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</P>
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<H3>4.1. Boolean and Integer Types</H3>
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<P>
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Header file <CODE>softfloat.h</CODE> depends on standard headers
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<CODE><stdbool.h></CODE> and <CODE><stdint.h></CODE> to define type
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<CODE>bool</CODE> and several integer types.
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These standard headers have been part of the ISO C Standard Library since 1999.
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With any recent compiler, they are likely to be supported, even if the compiler
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does not claim complete conformance to the latest ISO C Standard.
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For older or nonstandard compilers, a port of SoftFloat may have substitutes
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for these headers.
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Header <CODE>softfloat.h</CODE> depends only on the name <CODE>bool</CODE> from
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<CODE><stdbool.h></CODE> and on these type names from
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<CODE><stdint.h></CODE>:
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<BLOCKQUOTE>
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<PRE>
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uint16_t
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uint32_t
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uint64_t
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int32_t
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int64_t
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uint_fast8_t
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uint_fast32_t
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uint_fast64_t
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int_fast32_t
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int_fast64_t
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</PRE>
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</BLOCKQUOTE>
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</P>
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<H3>4.2. Floating-Point Types</H3>
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<P>
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The <CODE>softfloat.h</CODE> header defines five floating-point types:
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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>float16_t</CODE></TD>
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<TD><NOBR>16-bit</NOBR> half-precision binary format</TD>
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</TR>
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<TR>
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<TD><CODE>float32_t</CODE></TD>
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<TD><NOBR>32-bit</NOBR> single-precision binary format</TD>
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</TR>
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<TR>
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<TD><CODE>float64_t</CODE></TD>
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<TD><NOBR>64-bit</NOBR> double-precision binary format</TD>
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</TR>
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<TR>
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<TD><CODE>extFloat80_t </CODE></TD>
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<TD><NOBR>80-bit</NOBR> double-extended-precision binary format (old Intel or
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Motorola format)</TD>
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</TR>
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<TR>
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<TD><CODE>float128_t</CODE></TD>
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<TD><NOBR>128-bit</NOBR> quadruple-precision binary format</TD>
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</TR>
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</TABLE>
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</BLOCKQUOTE>
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The non-extended types are each exactly the size specified:
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<NOBR>16 bits</NOBR> for <CODE>float16_t</CODE>, <NOBR>32 bits</NOBR> for
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<CODE>float32_t</CODE>, <NOBR>64 bits</NOBR> for <CODE>float64_t</CODE>, and
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<NOBR>128 bits</NOBR> for <CODE>float128_t</CODE>.
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Aside from these size requirements, the definitions of all these types may
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differ for different ports of SoftFloat to specific systems.
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A given port of SoftFloat may or may not define some of the floating-point
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types as aliases for the C standard types <CODE>float</CODE>,
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<CODE>double</CODE>, and <CODE>long</CODE> <CODE>double</CODE>.
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</P>
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<P>
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Header file <CODE>softfloat.h</CODE> also defines a structure,
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<CODE>struct</CODE> <CODE>extFloat80M</CODE>, for the representation of
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<NOBR>80-bit</NOBR> double-extended-precision floating-point values in memory.
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This structure is the same size as type <CODE>extFloat80_t</CODE> and contains
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at least these two fields (not necessarily in this order):
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<BLOCKQUOTE>
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<PRE>
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uint16_t signExp;
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uint64_t signif;
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</PRE>
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</BLOCKQUOTE>
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Field <CODE>signExp</CODE> contains the sign and exponent of the floating-point
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value, with the sign in the most significant bit (<NOBR>bit 15</NOBR>) and the
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encoded exponent in the other <NOBR>15 bits</NOBR>.
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Field <CODE>signif</CODE> is the complete <NOBR>64-bit</NOBR> significand of
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the floating-point value.
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(In the usual encoding for <NOBR>80-bit</NOBR> extended floating-point, the
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leading <NOBR>1 bit</NOBR> of normalized numbers is not implicit but is stored
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in the most significant bit of the significand.)
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</P>
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<H3>4.3. Supported Floating-Point Functions</H3>
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<P>
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SoftFloat implements these arithmetic operations for its floating-point types:
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<UL>
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<LI>
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conversions between any two floating-point formats;
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<LI>
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for each floating-point format, conversions to and from signed and unsigned
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<NOBR>32-bit</NOBR> and <NOBR>64-bit</NOBR> integers;
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<LI>
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for each format, the usual addition, subtraction, multiplication, division, and
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square root operations;
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<LI>
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for each format except <CODE>extFloat80_t</CODE>, the fused multiply-add
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operation defined by the IEEE Standard;
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<LI>
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for each format, the floating-point remainder operation defined by the IEEE
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Standard;
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<LI>
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for each format, a “round to integer” operation that rounds to the
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nearest integer value in the same format; and
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<LI>
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comparisons between two values in the same floating-point format.
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</UL>
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</P>
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<P>
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The following operations required by the 2008 IEEE Floating-Point Standard are
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not supported in SoftFloat <NOBR>Release 3e</NOBR>:
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<UL>
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<LI>
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<B>nextUp</B>, <B>nextDown</B>, <B>minNum</B>, <B>maxNum</B>, <B>minNumMag</B>,
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<B>maxNumMag</B>, <B>scaleB</B>, and <B>logB</B>;
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<LI>
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conversions between floating-point formats and decimal or hexadecimal character
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sequences;
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<LI>
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all “quiet-computation” operations (<B>copy</B>, <B>negate</B>,
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<B>abs</B>, and <B>copySign</B>, which all involve only simple copying and/or
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manipulation of the floating-point sign bit); and
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<LI>
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all “non-computational” operations other than <B>isSignaling</B>
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(which is supported).
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</UL>
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</P>
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<H3>4.4. Non-canonical Representations in <CODE>extFloat80_t</CODE></H3>
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<P>
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Because the <NOBR>80-bit</NOBR> double-extended-precision format,
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<CODE>extFloat80_t</CODE>, stores an explicit leading significand bit, many
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finite floating-point numbers are encodable in this type in multiple equivalent
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forms.
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Of these multiple encodings, there is always a unique one with the least
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encoded exponent value, and this encoding is considered the <I>canonical</I>
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representation of the floating-point number.
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Any other equivalent representations (having a higher encoded exponent value)
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are <I>non-canonical</I>.
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For a value in the subnormal range (including zero), the canonical
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representation always has an encoded exponent of zero and a leading significand
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bit <NOBR>of 0</NOBR>.
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For finite values outside the subnormal range, the canonical representation
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always has an encoded exponent that is nonzero and a leading significand bit
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<NOBR>of 1</NOBR>.
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</P>
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<P>
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For an infinity or NaN, the leading significand bit is similarly expected to
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<NOBR>be 1</NOBR>.
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An infinity or NaN with a leading significand bit <NOBR>of 0</NOBR> is again
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considered non-canonical.
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Hence, altogether, to be canonical, a value of type <CODE>extFloat80_t</CODE>
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must have a leading significand bit <NOBR>of 1</NOBR>, unless the value is
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subnormal or zero, in which case the leading significand bit and the encoded
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exponent must both be zero.
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</P>
|
|
|
|
<P>
|
|
SoftFloat’s functions are not guaranteed to operate as expected when
|
|
inputs of type <CODE>extFloat80_t</CODE> are non-canonical.
|
|
Assuming all of a function’s <CODE>extFloat80_t</CODE> inputs (if any)
|
|
are canonical, function outputs of type <CODE>extFloat80_t</CODE> will always
|
|
be canonical.
|
|
</P>
|
|
|
|
<H3>4.5. Conventions for Passing Arguments and Results</H3>
|
|
|
|
<P>
|
|
Values that are at most <NOBR>64 bits</NOBR> in size (i.e., not the
|
|
<NOBR>80-bit</NOBR> or <NOBR>128-bit</NOBR> floating-point formats) are in all
|
|
cases passed as function arguments by value.
|
|
Likewise, when an output of a function is no more than <NOBR>64 bits</NOBR>, it
|
|
is always returned directly as the function result.
|
|
Thus, for example, the SoftFloat function for adding two <NOBR>64-bit</NOBR>
|
|
floating-point values has this simple signature:
|
|
<BLOCKQUOTE>
|
|
<CODE>float64_t f64_add( float64_t, float64_t );</CODE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<P>
|
|
The story is more complex when function inputs and outputs are
|
|
<NOBR>80-bit</NOBR> and <NOBR>128-bit</NOBR> floating-point.
|
|
For these types, SoftFloat always provides a function that passes these larger
|
|
values into or out of the function indirectly, via pointers.
|
|
For example, for adding two <NOBR>128-bit</NOBR> floating-point values,
|
|
SoftFloat supplies this function:
|
|
<BLOCKQUOTE>
|
|
<CODE>void f128M_add( const float128_t *, const float128_t *, float128_t * );</CODE>
|
|
</BLOCKQUOTE>
|
|
The first two arguments point to the values to be added, and the last argument
|
|
points to the location where the sum will be stored.
|
|
The <CODE>M</CODE> in the name <CODE>f128M_add</CODE> is mnemonic for the fact
|
|
that the <NOBR>128-bit</NOBR> inputs and outputs are “in memory”,
|
|
pointed to by pointer arguments.
|
|
</P>
|
|
|
|
<P>
|
|
All ports of SoftFloat implement these <I>pass-by-pointer</I> functions for
|
|
types <CODE>extFloat80_t</CODE> and <CODE>float128_t</CODE>.
|
|
At the same time, SoftFloat ports may also implement alternate versions of
|
|
these same functions that pass <CODE>extFloat80_t</CODE> and
|
|
<CODE>float128_t</CODE> by value, like the smaller formats.
|
|
Thus, besides the function with name <CODE>f128M_add</CODE> shown above, a
|
|
SoftFloat port may also supply an equivalent function with this signature:
|
|
<BLOCKQUOTE>
|
|
<CODE>float128_t f128_add( float128_t, float128_t );</CODE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<P>
|
|
As a general rule, on computers where the machine word size is
|
|
<NOBR>32 bits</NOBR> or smaller, only the pass-by-pointer versions of functions
|
|
(e.g., <CODE>f128M_add</CODE>) are provided for types <CODE>extFloat80_t</CODE>
|
|
and <CODE>float128_t</CODE>, because passing such large types directly can have
|
|
significant extra cost.
|
|
On computers where the word size is <NOBR>64 bits</NOBR> or larger, both
|
|
function versions (<CODE>f128M_add</CODE> and <CODE>f128_add</CODE>) are
|
|
provided, because the cost of passing by value is then more reasonable.
|
|
Applications that must be portable accross both classes of computers must use
|
|
the pointer-based functions, as these are always implemented.
|
|
However, if it is known that SoftFloat includes the by-value functions for all
|
|
platforms of interest, programmers can use whichever version they prefer.
|
|
</P>
|
|
|
|
|
|
<H2>5. Reserved Names</H2>
|
|
|
|
<P>
|
|
In addition to the variables and functions documented here, SoftFloat defines
|
|
some symbol names for its own private use.
|
|
These private names always begin with the prefix
|
|
‘<CODE>softfloat_</CODE>’.
|
|
When a program includes header <CODE>softfloat.h</CODE> or links with the
|
|
SoftFloat library, all names with prefix ‘<CODE>softfloat_</CODE>’
|
|
are reserved for possible use by SoftFloat.
|
|
Applications that use SoftFloat should not define their own names with this
|
|
prefix, and should reference only such names as are documented.
|
|
</P>
|
|
|
|
|
|
<H2>6. Mode Variables</H2>
|
|
|
|
<P>
|
|
The following global variables control rounding mode, underflow detection, and
|
|
the <NOBR>80-bit</NOBR> extended format’s rounding precision:
|
|
<BLOCKQUOTE>
|
|
<CODE>softfloat_roundingMode</CODE><BR>
|
|
<CODE>softfloat_detectTininess</CODE><BR>
|
|
<CODE>extF80_roundingPrecision</CODE>
|
|
</BLOCKQUOTE>
|
|
These mode variables are covered in the next several subsections.
|
|
For some SoftFloat ports, these variables may be <I>per-thread</I> (declared
|
|
<CODE>thread_local</CODE>), meaning that different execution threads have their
|
|
own separate copies of the variables.
|
|
</P>
|
|
|
|
<H3>6.1. Rounding Mode</H3>
|
|
|
|
<P>
|
|
All five rounding modes defined by the 2008 IEEE Floating-Point Standard are
|
|
implemented for all operations that require rounding.
|
|
Some ports of SoftFloat may also implement the <I>round-to-odd</I> mode.
|
|
</P>
|
|
|
|
<P>
|
|
The rounding mode is selected by the global variable
|
|
<BLOCKQUOTE>
|
|
<CODE>uint_fast8_t softfloat_roundingMode;</CODE>
|
|
</BLOCKQUOTE>
|
|
This variable may be set to one of the values
|
|
<BLOCKQUOTE>
|
|
<TABLE CELLSPACING=0 CELLPADDING=0>
|
|
<TR>
|
|
<TD><CODE>softfloat_round_near_even</CODE></TD>
|
|
<TD>round to nearest, with ties to even</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>softfloat_round_near_maxMag </CODE></TD>
|
|
<TD>round to nearest, with ties to maximum magnitude (away from zero)</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>softfloat_round_minMag</CODE></TD>
|
|
<TD>round to minimum magnitude (toward zero)</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>softfloat_round_min</CODE></TD>
|
|
<TD>round to minimum (down)</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>softfloat_round_max</CODE></TD>
|
|
<TD>round to maximum (up)</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>softfloat_round_odd</CODE></TD>
|
|
<TD>round to odd (jamming), if supported by the SoftFloat port</TD>
|
|
</TR>
|
|
</TABLE>
|
|
</BLOCKQUOTE>
|
|
Variable <CODE>softfloat_roundingMode</CODE> is initialized to
|
|
<CODE>softfloat_round_near_even</CODE>.
|
|
</P>
|
|
|
|
<P>
|
|
When <CODE>softfloat_round_odd</CODE> is the rounding mode for a function that
|
|
rounds to an integer value (either conversion to an integer format or a
|
|
‘<CODE>roundToInt</CODE>’ function), if the input is not already an
|
|
integer, the rounded result is the closest <EM>odd</EM> integer.
|
|
For other operations, this rounding mode acts as though the floating-point
|
|
result is first rounded to minimum magnitude, the same as
|
|
<CODE>softfloat_round_minMag</CODE>, and then, if the result is inexact, the
|
|
least-significant bit of the result is set <NOBR>to 1</NOBR>.
|
|
Rounding to odd is also known as <EM>jamming</EM>.
|
|
</P>
|
|
|
|
<H3>6.2. Underflow Detection</H3>
|
|
|
|
<P>
|
|
In the terminology of the IEEE Standard, SoftFloat can detect tininess for
|
|
underflow either before or after rounding.
|
|
The choice is made by the global variable
|
|
<BLOCKQUOTE>
|
|
<CODE>uint_fast8_t softfloat_detectTininess;</CODE>
|
|
</BLOCKQUOTE>
|
|
which can be set to either
|
|
<BLOCKQUOTE>
|
|
<CODE>softfloat_tininess_beforeRounding</CODE><BR>
|
|
<CODE>softfloat_tininess_afterRounding</CODE>
|
|
</BLOCKQUOTE>
|
|
Detecting tininess after rounding is usually better because it results in fewer
|
|
spurious underflow signals.
|
|
The other option is provided for compatibility with some systems.
|
|
Like most systems (and as required by the newer 2008 IEEE Standard), SoftFloat
|
|
always detects loss of accuracy for underflow as an inexact result.
|
|
</P>
|
|
|
|
<H3>6.3. Rounding Precision for the <NOBR>80-Bit</NOBR> Extended Format</H3>
|
|
|
|
<P>
|
|
For <CODE>extFloat80_t</CODE> only, the rounding precision of the basic
|
|
arithmetic operations is controlled by the global variable
|
|
<BLOCKQUOTE>
|
|
<CODE>uint_fast8_t extF80_roundingPrecision;</CODE>
|
|
</BLOCKQUOTE>
|
|
The operations affected are:
|
|
<BLOCKQUOTE>
|
|
<CODE>extF80_add</CODE><BR>
|
|
<CODE>extF80_sub</CODE><BR>
|
|
<CODE>extF80_mul</CODE><BR>
|
|
<CODE>extF80_div</CODE><BR>
|
|
<CODE>extF80_sqrt</CODE>
|
|
</BLOCKQUOTE>
|
|
When <CODE>extF80_roundingPrecision</CODE> is set to its default value of 80,
|
|
these operations are rounded to the full precision of the <NOBR>80-bit</NOBR>
|
|
double-extended-precision format, like occurs for other formats.
|
|
Setting <CODE>extF80_roundingPrecision</CODE> to 32 or to 64 causes the
|
|
operations listed to be rounded to <NOBR>32-bit</NOBR> precision (equivalent to
|
|
<CODE>float32_t</CODE>) or to <NOBR>64-bit</NOBR> precision (equivalent to
|
|
<CODE>float64_t</CODE>), respectively.
|
|
When rounding to reduced precision, additional bits in the result significand
|
|
beyond the rounding point are set to zero.
|
|
The consequences of setting <CODE>extF80_roundingPrecision</CODE> to a value
|
|
other than 32, 64, or 80 is not specified.
|
|
Operations other than the ones listed above are not affected by
|
|
<CODE>extF80_roundingPrecision</CODE>.
|
|
</P>
|
|
|
|
|
|
<H2>7. Exceptions and Exception Flags</H2>
|
|
|
|
<P>
|
|
All five exception flags required by the IEEE Floating-Point Standard are
|
|
implemented.
|
|
Each flag is stored as a separate bit in the global variable
|
|
<BLOCKQUOTE>
|
|
<CODE>uint_fast8_t softfloat_exceptionFlags;</CODE>
|
|
</BLOCKQUOTE>
|
|
The positions of the exception flag bits within this variable are determined by
|
|
the bit masks
|
|
<BLOCKQUOTE>
|
|
<CODE>softfloat_flag_inexact</CODE><BR>
|
|
<CODE>softfloat_flag_underflow</CODE><BR>
|
|
<CODE>softfloat_flag_overflow</CODE><BR>
|
|
<CODE>softfloat_flag_infinite</CODE><BR>
|
|
<CODE>softfloat_flag_invalid</CODE>
|
|
</BLOCKQUOTE>
|
|
Variable <CODE>softfloat_exceptionFlags</CODE> is initialized to all zeros,
|
|
meaning no exceptions.
|
|
</P>
|
|
|
|
<P>
|
|
For some SoftFloat ports, <CODE>softfloat_exceptionFlags</CODE> may be
|
|
<I>per-thread</I> (declared <CODE>thread_local</CODE>), meaning that different
|
|
execution threads have their own separate instances of it.
|
|
</P>
|
|
|
|
<P>
|
|
An individual exception flag can be cleared with the statement
|
|
<BLOCKQUOTE>
|
|
<CODE>softfloat_exceptionFlags &= ~softfloat_flag_<<I>exception</I>>;</CODE>
|
|
</BLOCKQUOTE>
|
|
where <CODE><<I>exception</I>></CODE> is the appropriate name.
|
|
To raise a floating-point exception, function <CODE>softfloat_raiseFlags</CODE>
|
|
should normally be used.
|
|
</P>
|
|
|
|
<P>
|
|
When SoftFloat detects an exception other than <I>inexact</I>, it calls
|
|
<CODE>softfloat_raiseFlags</CODE>.
|
|
The default version of this function simply raises the corresponding exception
|
|
flags.
|
|
Particular ports of SoftFloat may support alternate behavior, such as exception
|
|
traps, by modifying the default <CODE>softfloat_raiseFlags</CODE>.
|
|
A program may also supply its own <CODE>softfloat_raiseFlags</CODE> function to
|
|
override the one from the SoftFloat library.
|
|
</P>
|
|
|
|
<P>
|
|
Because inexact results occur frequently under most circumstances (and thus are
|
|
hardly exceptional), SoftFloat does not ordinarily call
|
|
<CODE>softfloat_raiseFlags</CODE> for <I>inexact</I> exceptions.
|
|
It does always raise the <I>inexact</I> exception flag as required.
|
|
</P>
|
|
|
|
|
|
<H2>8. Function Details</H2>
|
|
|
|
<P>
|
|
In this section, <CODE><<I>float</I>></CODE> appears in function names as
|
|
a substitute for one of these abbreviations:
|
|
<BLOCKQUOTE>
|
|
<TABLE CELLSPACING=0 CELLPADDING=0>
|
|
<TR>
|
|
<TD><CODE>f16</CODE></TD>
|
|
<TD>indicates <CODE>float16_t</CODE>, passed by value</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>f32</CODE></TD>
|
|
<TD>indicates <CODE>float32_t</CODE>, passed by value</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>f64</CODE></TD>
|
|
<TD>indicates <CODE>float64_t</CODE>, passed by value</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>extF80M </CODE></TD>
|
|
<TD>indicates <CODE>extFloat80_t</CODE>, passed indirectly via pointers</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>extF80</CODE></TD>
|
|
<TD>indicates <CODE>extFloat80_t</CODE>, passed by value</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>f128M</CODE></TD>
|
|
<TD>indicates <CODE>float128_t</CODE>, passed indirectly via pointers</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>f128</CODE></TD>
|
|
<TD>indicates <CODE>float128_t</CODE>, passed by value</TD>
|
|
</TR>
|
|
</TABLE>
|
|
</BLOCKQUOTE>
|
|
The circumstances under which values of floating-point types
|
|
<CODE>extFloat80_t</CODE> and <CODE>float128_t</CODE> may be passed either by
|
|
value or indirectly via pointers was discussed earlier in
|
|
<NOBR>section 4.5</NOBR>, <I>Conventions for Passing Arguments and Results</I>.
|
|
</P>
|
|
|
|
<H3>8.1. Conversions from Integer to Floating-Point</H3>
|
|
|
|
<P>
|
|
All conversions from a <NOBR>32-bit</NOBR> or <NOBR>64-bit</NOBR> integer,
|
|
signed or unsigned, to a floating-point format are supported.
|
|
Functions performing these conversions have these names:
|
|
<BLOCKQUOTE>
|
|
<CODE>ui32_to_<<I>float</I>></CODE><BR>
|
|
<CODE>ui64_to_<<I>float</I>></CODE><BR>
|
|
<CODE>i32_to_<<I>float</I>></CODE><BR>
|
|
<CODE>i64_to_<<I>float</I>></CODE>
|
|
</BLOCKQUOTE>
|
|
Conversions from <NOBR>32-bit</NOBR> integers to <NOBR>64-bit</NOBR>
|
|
double-precision and larger formats are always exact, and likewise conversions
|
|
from <NOBR>64-bit</NOBR> integers to <NOBR>80-bit</NOBR>
|
|
double-extended-precision and <NOBR>128-bit</NOBR> quadruple-precision are also
|
|
always exact.
|
|
</P>
|
|
|
|
<P>
|
|
Each conversion function takes one input of the appropriate type and generates
|
|
one output.
|
|
The following illustrates the signatures of these functions in cases when the
|
|
floating-point result is passed either by value or via pointers:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
float64_t i32_to_f64( int32_t <I>a</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void i32_to_f128M( int32_t <I>a</I>, float128_t *<I>destPtr</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<H3>8.2. Conversions from Floating-Point to Integer</H3>
|
|
|
|
<P>
|
|
Conversions from a floating-point format to a <NOBR>32-bit</NOBR> or
|
|
<NOBR>64-bit</NOBR> integer, signed or unsigned, are supported with these
|
|
functions:
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_to_ui32</CODE><BR>
|
|
<CODE><<I>float</I>>_to_ui64</CODE><BR>
|
|
<CODE><<I>float</I>>_to_i32</CODE><BR>
|
|
<CODE><<I>float</I>>_to_i64</CODE>
|
|
</BLOCKQUOTE>
|
|
The functions have signatures as follows, depending on whether the
|
|
floating-point input is passed by value or via pointers:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
int_fast32_t f64_to_i32( float64_t <I>a</I>, uint_fast8_t <I>roundingMode</I>, bool <I>exact</I> );
|
|
</PRE>
|
|
<PRE>
|
|
int_fast32_t
|
|
f128M_to_i32( const float128_t *<I>aPtr</I>, uint_fast8_t <I>roundingMode</I>, bool <I>exact</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<P>
|
|
The <CODE><I>roundingMode</I></CODE> argument specifies the rounding mode for
|
|
the conversion.
|
|
The variable that usually indicates rounding mode,
|
|
<CODE>softfloat_roundingMode</CODE>, is ignored.
|
|
Argument <CODE><I>exact</I></CODE> determines whether the <I>inexact</I>
|
|
exception flag is raised if the conversion is not exact.
|
|
If <CODE><I>exact</I></CODE> is <CODE>true</CODE>, the <I>inexact</I> flag may
|
|
be raised;
|
|
otherwise, it will not be, even if the conversion is inexact.
|
|
</P>
|
|
|
|
<P>
|
|
A conversion from floating-point to integer format raises the <I>invalid</I>
|
|
exception if the source value cannot be rounded to a representable integer of
|
|
the desired size (32 or 64 bits).
|
|
In such circumstances, the integer result returned is determined by the
|
|
particular port of SoftFloat, although typically this value will be either the
|
|
maximum or minimum value of the integer format.
|
|
The functions that convert to integer types never raise the floating-point
|
|
<I>overflow</I> exception.
|
|
</P>
|
|
|
|
<P>
|
|
Because languages such <NOBR>as C</NOBR> require that conversions to integers
|
|
be rounded toward zero, the following functions are provided for improved speed
|
|
and convenience:
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_to_ui32_r_minMag</CODE><BR>
|
|
<CODE><<I>float</I>>_to_ui64_r_minMag</CODE><BR>
|
|
<CODE><<I>float</I>>_to_i32_r_minMag</CODE><BR>
|
|
<CODE><<I>float</I>>_to_i64_r_minMag</CODE>
|
|
</BLOCKQUOTE>
|
|
These functions round only toward zero (to minimum magnitude).
|
|
The signatures for these functions are the same as above without the redundant
|
|
<CODE><I>roundingMode</I></CODE> argument:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
int_fast32_t f64_to_i32_r_minMag( float64_t <I>a</I>, bool <I>exact</I> );
|
|
</PRE>
|
|
<PRE>
|
|
int_fast32_t f128M_to_i32_r_minMag( const float128_t *<I>aPtr</I>, bool <I>exact</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<H3>8.3. Conversions Among Floating-Point Types</H3>
|
|
|
|
<P>
|
|
Conversions between floating-point formats are done by functions with these
|
|
names:
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_to_<<I>float</I>></CODE>
|
|
</BLOCKQUOTE>
|
|
All combinations of source and result type are supported where the source and
|
|
result are different formats.
|
|
There are four different styles of signature for these functions, depending on
|
|
whether the input and the output floating-point values are passed by value or
|
|
via pointers:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
float32_t f64_to_f32( float64_t <I>a</I> );
|
|
</PRE>
|
|
<PRE>
|
|
float32_t f128M_to_f32( const float128_t *<I>aPtr</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void f32_to_f128M( float32_t <I>a</I>, float128_t *<I>destPtr</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void extF80M_to_f128M( const extFloat80_t *<I>aPtr</I>, float128_t *<I>destPtr</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<P>
|
|
Conversions from a smaller to a larger floating-point format are always exact
|
|
and so require no rounding.
|
|
</P>
|
|
|
|
<H3>8.4. Basic Arithmetic Functions</H3>
|
|
|
|
<P>
|
|
The following basic arithmetic functions are provided:
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_add</CODE><BR>
|
|
<CODE><<I>float</I>>_sub</CODE><BR>
|
|
<CODE><<I>float</I>>_mul</CODE><BR>
|
|
<CODE><<I>float</I>>_div</CODE><BR>
|
|
<CODE><<I>float</I>>_sqrt</CODE>
|
|
</BLOCKQUOTE>
|
|
Each floating-point operation takes two operands, except for <CODE>sqrt</CODE>
|
|
(square root) which takes only one.
|
|
The operands and result are all of the same floating-point format.
|
|
Signatures for these functions take the following forms:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
float64_t f64_add( float64_t <I>a</I>, float64_t <I>b</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void
|
|
f128M_add(
|
|
const float128_t *<I>aPtr</I>, const float128_t *<I>bPtr</I>, float128_t *<I>destPtr</I> );
|
|
</PRE>
|
|
<PRE>
|
|
float64_t f64_sqrt( float64_t <I>a</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void f128M_sqrt( const float128_t *<I>aPtr</I>, float128_t *<I>destPtr</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
When floating-point values are passed indirectly through pointers, arguments
|
|
<CODE><I>aPtr</I></CODE> and <CODE><I>bPtr</I></CODE> point to the input
|
|
operands, and the last argument, <CODE><I>destPtr</I></CODE>, points to the
|
|
location where the result is stored.
|
|
</P>
|
|
|
|
<P>
|
|
Rounding of the <NOBR>80-bit</NOBR> double-extended-precision
|
|
(<CODE>extFloat80_t</CODE>) functions is affected by variable
|
|
<CODE>extF80_roundingPrecision</CODE>, as explained earlier in
|
|
<NOBR>section 6.3</NOBR>,
|
|
<I>Rounding Precision for the <NOBR>80-Bit</NOBR> Extended Format</I>.
|
|
</P>
|
|
|
|
<H3>8.5. Fused Multiply-Add Functions</H3>
|
|
|
|
<P>
|
|
The 2008 version of the IEEE Floating-Point Standard defines a <I>fused
|
|
multiply-add</I> operation that does a combined multiplication and addition
|
|
with only a single rounding.
|
|
SoftFloat implements fused multiply-add with functions
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_mulAdd</CODE>
|
|
</BLOCKQUOTE>
|
|
Unlike other operations, fused multiple-add is not supported for the
|
|
<NOBR>80-bit</NOBR> double-extended-precision format,
|
|
<CODE>extFloat80_t</CODE>.
|
|
</P>
|
|
|
|
<P>
|
|
Depending on whether floating-point values are passed by value or via pointers,
|
|
the fused multiply-add functions have signatures of these forms:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
float64_t f64_mulAdd( float64_t <I>a</I>, float64_t <I>b</I>, float64_t <I>c</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void
|
|
f128M_mulAdd(
|
|
const float128_t *<I>aPtr</I>,
|
|
const float128_t *<I>bPtr</I>,
|
|
const float128_t *<I>cPtr</I>,
|
|
float128_t *<I>destPtr</I>
|
|
);
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
The functions compute
|
|
<NOBR>(<CODE><I>a</I></CODE> × <CODE><I>b</I></CODE>)
|
|
+ <CODE><I>c</I></CODE></NOBR>
|
|
with a single rounding.
|
|
When floating-point values are passed indirectly through pointers, arguments
|
|
<CODE><I>aPtr</I></CODE>, <CODE><I>bPtr</I></CODE>, and
|
|
<CODE><I>cPtr</I></CODE> point to operands <CODE><I>a</I></CODE>,
|
|
<CODE><I>b</I></CODE>, and <CODE><I>c</I></CODE> respectively, and
|
|
<CODE><I>destPtr</I></CODE> points to the location where the result is stored.
|
|
</P>
|
|
|
|
<P>
|
|
If one of the multiplication operands <CODE><I>a</I></CODE> and
|
|
<CODE><I>b</I></CODE> is infinite and the other is zero, these functions raise
|
|
the invalid exception even if operand <CODE><I>c</I></CODE> is a quiet NaN.
|
|
</P>
|
|
|
|
<H3>8.6. Remainder Functions</H3>
|
|
|
|
<P>
|
|
For each format, SoftFloat implements the remainder operation defined by the
|
|
IEEE Floating-Point Standard.
|
|
The remainder functions have names
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_rem</CODE>
|
|
</BLOCKQUOTE>
|
|
Each remainder operation takes two floating-point operands of the same format
|
|
and returns a result in the same format.
|
|
Depending on whether floating-point values are passed by value or via pointers,
|
|
the remainder functions have signatures of these forms:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
float64_t f64_rem( float64_t <I>a</I>, float64_t <I>b</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void
|
|
f128M_rem(
|
|
const float128_t *<I>aPtr</I>, const float128_t *<I>bPtr</I>, float128_t *<I>destPtr</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
When floating-point values are passed indirectly through pointers, arguments
|
|
<CODE><I>aPtr</I></CODE> and <CODE><I>bPtr</I></CODE> point to operands
|
|
<CODE><I>a</I></CODE> and <CODE><I>b</I></CODE> respectively, and
|
|
<CODE><I>destPtr</I></CODE> points to the location where the result is stored.
|
|
</P>
|
|
|
|
<P>
|
|
The IEEE Standard remainder operation computes the value
|
|
<NOBR><CODE><I>a</I></CODE>
|
|
− <I>n</I> × <CODE><I>b</I></CODE></NOBR>,
|
|
where <I>n</I> is the integer closest to
|
|
<NOBR><CODE><I>a</I></CODE> ÷ <CODE><I>b</I></CODE></NOBR>.
|
|
If <NOBR><CODE><I>a</I></CODE> ÷ <CODE><I>b</I></CODE></NOBR> is exactly
|
|
halfway between two integers, <I>n</I> is the <EM>even</EM> integer closest to
|
|
<NOBR><CODE><I>a</I></CODE> ÷ <CODE><I>b</I></CODE></NOBR>.
|
|
The IEEE Standard’s remainder operation is always exact and so requires
|
|
no rounding.
|
|
</P>
|
|
|
|
<P>
|
|
Depending on the relative magnitudes of the operands, the remainder
|
|
functions can take considerably longer to execute than the other SoftFloat
|
|
functions.
|
|
This is an inherent characteristic of the remainder operation itself and is not
|
|
a flaw in the SoftFloat implementation.
|
|
</P>
|
|
|
|
<H3>8.7. Round-to-Integer Functions</H3>
|
|
|
|
<P>
|
|
For each format, SoftFloat implements the round-to-integer operation specified
|
|
by the IEEE Floating-Point Standard.
|
|
These functions are named
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_roundToInt</CODE>
|
|
</BLOCKQUOTE>
|
|
Each round-to-integer operation takes a single floating-point operand.
|
|
This operand is rounded to an integer according to a specified rounding mode,
|
|
and the resulting integer value is returned in the same floating-point format.
|
|
(Note that the result is not an integer type.)
|
|
</P>
|
|
|
|
<P>
|
|
The signatures of the round-to-integer functions are similar to those for
|
|
conversions to an integer type:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
float64_t f64_roundToInt( float64_t <I>a</I>, uint_fast8_t <I>roundingMode</I>, bool <I>exact</I> );
|
|
</PRE>
|
|
<PRE>
|
|
void
|
|
f128M_roundToInt(
|
|
const float128_t *<I>aPtr</I>,
|
|
uint_fast8_t <I>roundingMode</I>,
|
|
bool <I>exact</I>,
|
|
float128_t *<I>destPtr</I>
|
|
);
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
When floating-point values are passed indirectly through pointers,
|
|
<CODE><I>aPtr</I></CODE> points to the input operand and
|
|
<CODE><I>destPtr</I></CODE> points to the location where the result is stored.
|
|
</P>
|
|
|
|
<P>
|
|
The <CODE><I>roundingMode</I></CODE> argument specifies the rounding mode to
|
|
apply.
|
|
The variable that usually indicates rounding mode,
|
|
<CODE>softfloat_roundingMode</CODE>, is ignored.
|
|
Argument <CODE><I>exact</I></CODE> determines whether the <I>inexact</I>
|
|
exception flag is raised if the conversion is not exact.
|
|
If <CODE><I>exact</I></CODE> is <CODE>true</CODE>, the <I>inexact</I> flag may
|
|
be raised;
|
|
otherwise, it will not be, even if the conversion is inexact.
|
|
</P>
|
|
|
|
<H3>8.8. Comparison Functions</H3>
|
|
|
|
<P>
|
|
For each format, the following floating-point comparison functions are
|
|
provided:
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_eq</CODE><BR>
|
|
<CODE><<I>float</I>>_le</CODE><BR>
|
|
<CODE><<I>float</I>>_lt</CODE>
|
|
</BLOCKQUOTE>
|
|
Each comparison takes two operands of the same type and returns a Boolean.
|
|
The abbreviation <CODE>eq</CODE> stands for “equal” (=);
|
|
<CODE>le</CODE> stands for “less than or equal” (≤);
|
|
and <CODE>lt</CODE> stands for “less than” (<).
|
|
Depending on whether the floating-point operands are passed by value or via
|
|
pointers, the comparison functions have signatures of these forms:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
bool f64_eq( float64_t <I>a</I>, float64_t <I>b</I> );
|
|
</PRE>
|
|
<PRE>
|
|
bool f128M_eq( const float128_t *<I>aPtr</I>, const float128_t *<I>bPtr</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<P>
|
|
The usual greater-than (>), greater-than-or-equal (≥), and not-equal
|
|
(≠) comparisons are easily obtained from the functions provided.
|
|
The not-equal function is just the logical complement of the equal function.
|
|
The greater-than-or-equal function is identical to the less-than-or-equal
|
|
function with the arguments in reverse order, and likewise the greater-than
|
|
function is identical to the less-than function with the arguments reversed.
|
|
</P>
|
|
|
|
<P>
|
|
The IEEE Floating-Point Standard specifies that the less-than-or-equal and
|
|
less-than comparisons by default raise the <I>invalid</I> exception if either
|
|
operand is any kind of NaN.
|
|
Equality comparisons, on the other hand, are defined by default to raise the
|
|
<I>invalid</I> exception only for signaling NaNs, not quiet NaNs.
|
|
For completeness, SoftFloat provides these complementary functions:
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_eq_signaling</CODE><BR>
|
|
<CODE><<I>float</I>>_le_quiet</CODE><BR>
|
|
<CODE><<I>float</I>>_lt_quiet</CODE>
|
|
</BLOCKQUOTE>
|
|
The <CODE>signaling</CODE> equality comparisons are identical to the default
|
|
equality comparisons except that the <I>invalid</I> exception is raised for any
|
|
NaN input, not just for signaling NaNs.
|
|
Similarly, the <CODE>quiet</CODE> comparison functions are identical to their
|
|
default counterparts except that the <I>invalid</I> exception is not raised for
|
|
quiet NaNs.
|
|
</P>
|
|
|
|
<H3>8.9. Signaling NaN Test Functions</H3>
|
|
|
|
<P>
|
|
Functions for testing whether a floating-point value is a signaling NaN are
|
|
provided with these names:
|
|
<BLOCKQUOTE>
|
|
<CODE><<I>float</I>>_isSignalingNaN</CODE>
|
|
</BLOCKQUOTE>
|
|
The functions take one floating-point operand and return a Boolean indicating
|
|
whether the operand is a signaling NaN.
|
|
Accordingly, the functions have the forms
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
bool f64_isSignalingNaN( float64_t <I>a</I> );
|
|
</PRE>
|
|
<PRE>
|
|
bool f128M_isSignalingNaN( const float128_t *<I>aPtr</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<H3>8.10. Raise-Exception Function</H3>
|
|
|
|
<P>
|
|
SoftFloat provides a single function for raising floating-point exceptions:
|
|
<BLOCKQUOTE>
|
|
<PRE>
|
|
void softfloat_raiseFlags( uint_fast8_t <I>exceptions</I> );
|
|
</PRE>
|
|
</BLOCKQUOTE>
|
|
The <CODE><I>exceptions</I></CODE> argument is a mask indicating the set of
|
|
exceptions to raise.
|
|
(See earlier section 7, <I>Exceptions and Exception Flags</I>.)
|
|
In addition to setting the specified exception flags in variable
|
|
<CODE>softfloat_exceptionFlags</CODE>, the <CODE>softfloat_raiseFlags</CODE>
|
|
function may cause a trap or abort appropriate for the current system.
|
|
</P>
|
|
|
|
|
|
<H2>9. Changes from SoftFloat <NOBR>Release 2</NOBR></H2>
|
|
|
|
<P>
|
|
Apart from a change in the legal use license, <NOBR>Release 3</NOBR> of
|
|
SoftFloat introduced numerous technical differences compared to earlier
|
|
releases.
|
|
</P>
|
|
|
|
<H3>9.1. Name Changes</H3>
|
|
|
|
<P>
|
|
The most obvious and pervasive difference compared to <NOBR>Release 2</NOBR>
|
|
is that the names of most functions and variables have changed, even when the
|
|
behavior has not.
|
|
First, the floating-point types, the mode variables, the exception flags
|
|
variable, the function to raise exceptions, and various associated constants
|
|
have been renamed as follows:
|
|
<BLOCKQUOTE>
|
|
<TABLE>
|
|
<TR>
|
|
<TD>old name, Release 2:</TD>
|
|
<TD>new name, Release 3:</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float32</CODE></TD>
|
|
<TD><CODE>float32_t</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float64</CODE></TD>
|
|
<TD><CODE>float64_t</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>floatx80</CODE></TD>
|
|
<TD><CODE>extFloat80_t</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float128</CODE></TD>
|
|
<TD><CODE>float128_t</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_rounding_mode</CODE></TD>
|
|
<TD><CODE>softfloat_roundingMode</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_round_nearest_even</CODE></TD>
|
|
<TD><CODE>softfloat_round_near_even</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_round_to_zero</CODE></TD>
|
|
<TD><CODE>softfloat_round_minMag</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_round_down</CODE></TD>
|
|
<TD><CODE>softfloat_round_min</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_round_up</CODE></TD>
|
|
<TD><CODE>softfloat_round_max</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_detect_tininess</CODE></TD>
|
|
<TD><CODE>softfloat_detectTininess</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_tininess_before_rounding </CODE></TD>
|
|
<TD><CODE>softfloat_tininess_beforeRounding</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_tininess_after_rounding</CODE></TD>
|
|
<TD><CODE>softfloat_tininess_afterRounding</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>floatx80_rounding_precision</CODE></TD>
|
|
<TD><CODE>extF80_roundingPrecision</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_exception_flags</CODE></TD>
|
|
<TD><CODE>softfloat_exceptionFlags</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_flag_inexact</CODE></TD>
|
|
<TD><CODE>softfloat_flag_inexact</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_flag_underflow</CODE></TD>
|
|
<TD><CODE>softfloat_flag_underflow</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_flag_overflow</CODE></TD>
|
|
<TD><CODE>softfloat_flag_overflow</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_flag_divbyzero</CODE></TD>
|
|
<TD><CODE>softfloat_flag_infinite</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_flag_invalid</CODE></TD>
|
|
<TD><CODE>softfloat_flag_invalid</CODE></TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>float_raise</CODE></TD>
|
|
<TD><CODE>softfloat_raiseFlags</CODE></TD>
|
|
</TR>
|
|
</TABLE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<P>
|
|
Furthermore, <NOBR>Release 3</NOBR> adopted the following new abbreviations for
|
|
function names:
|
|
<BLOCKQUOTE>
|
|
<TABLE>
|
|
<TR>
|
|
<TD>used in names in Release 2:<CODE> </CODE></TD>
|
|
<TD>used in names in Release 3:</TD>
|
|
</TR>
|
|
<TR> <TD><CODE>int32</CODE></TD> <TD><CODE>i32</CODE></TD> </TR>
|
|
<TR> <TD><CODE>int64</CODE></TD> <TD><CODE>i64</CODE></TD> </TR>
|
|
<TR> <TD><CODE>float32</CODE></TD> <TD><CODE>f32</CODE></TD> </TR>
|
|
<TR> <TD><CODE>float64</CODE></TD> <TD><CODE>f64</CODE></TD> </TR>
|
|
<TR> <TD><CODE>floatx80</CODE></TD> <TD><CODE>extF80</CODE></TD> </TR>
|
|
<TR> <TD><CODE>float128</CODE></TD> <TD><CODE>f128</CODE></TD> </TR>
|
|
</TABLE>
|
|
</BLOCKQUOTE>
|
|
Thus, for example, the function to add two <NOBR>32-bit</NOBR> floating-point
|
|
numbers, previously called <CODE>float32_add</CODE> in <NOBR>Release 2</NOBR>,
|
|
is now <CODE>f32_add</CODE>.
|
|
Lastly, there have been a few other changes to function names:
|
|
<BLOCKQUOTE>
|
|
<TABLE>
|
|
<TR>
|
|
<TD>used in names in Release 2:<CODE> </CODE></TD>
|
|
<TD>used in names in Release 3:<CODE> </CODE></TD>
|
|
<TD>relevant functions:</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>_round_to_zero</CODE></TD>
|
|
<TD><CODE>_r_minMag</CODE></TD>
|
|
<TD>conversions from floating-point to integer (<NOBR>section 8.2</NOBR>)</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>round_to_int</CODE></TD>
|
|
<TD><CODE>roundToInt</CODE></TD>
|
|
<TD>round-to-integer functions (<NOBR>section 8.7</NOBR>)</TD>
|
|
</TR>
|
|
<TR>
|
|
<TD><CODE>is_signaling_nan </CODE></TD>
|
|
<TD><CODE>isSignalingNaN</CODE></TD>
|
|
<TD>signaling NaN test functions (<NOBR>section 8.9</NOBR>)</TD>
|
|
</TR>
|
|
</TABLE>
|
|
</BLOCKQUOTE>
|
|
</P>
|
|
|
|
<H3>9.2. Changes to Function Arguments</H3>
|
|
|
|
<P>
|
|
Besides simple name changes, some operations were given a different interface
|
|
in <NOBR>Release 3</NOBR> than they had in <NOBR>Release 2</NOBR>:
|
|
<UL>
|
|
|
|
<LI>
|
|
<P>
|
|
Since <NOBR>Release 3</NOBR>, integer arguments and results of functions have
|
|
standard types from header <CODE><stdint.h></CODE>, such as
|
|
<CODE>uint32_t</CODE>, whereas previously their types could be defined
|
|
differently for each port of SoftFloat, usually using traditional C types such
|
|
as <CODE>unsigned</CODE> <CODE>int</CODE>.
|
|
Likewise, functions in <NOBR>Release 3</NOBR> and later pass Booleans as
|
|
standard type <CODE>bool</CODE> from <CODE><stdbool.h></CODE>, whereas
|
|
previously these were again passed as a port-specific type (usually
|
|
<CODE>int</CODE>).
|
|
</P>
|
|
|
|
<LI>
|
|
<P>
|
|
As explained earlier in <NOBR>section 4.5</NOBR>, <I>Conventions for Passing
|
|
Arguments and Results</I>, SoftFloat functions in <NOBR>Release 3</NOBR> and
|
|
later may pass <NOBR>80-bit</NOBR> and <NOBR>128-bit</NOBR> floating-point
|
|
values through pointers, meaning that functions take pointer arguments and then
|
|
read or write floating-point values at the locations indicated by the pointers.
|
|
In <NOBR>Release 2</NOBR>, floating-point arguments and results were always
|
|
passed by value, regardless of their size.
|
|
</P>
|
|
|
|
<LI>
|
|
<P>
|
|
Functions that round to an integer have additional
|
|
<CODE><I>roundingMode</I></CODE> and <CODE><I>exact</I></CODE> arguments that
|
|
they did not have in <NOBR>Release 2</NOBR>.
|
|
Refer to sections 8.2 <NOBR>and 8.7</NOBR> for descriptions of these functions
|
|
since <NOBR>Release 3</NOBR>.
|
|
For <NOBR>Release 2</NOBR>, the rounding mode, when needed, was taken from the
|
|
same global variable that affects the basic arithmetic operations (now called
|
|
<CODE>softfloat_roundingMode</CODE> but previously known as
|
|
<CODE>float_rounding_mode</CODE>).
|
|
Also, for <NOBR>Release 2</NOBR>, if the original floating-point input was not
|
|
an exact integer value, and if the <I>invalid</I> exception was not raised by
|
|
the function, the <I>inexact</I> exception was always raised.
|
|
<NOBR>Release 2</NOBR> had no option to suppress raising <I>inexact</I> in this
|
|
case.
|
|
Applications using SoftFloat <NOBR>Release 3</NOBR> or later can get the same
|
|
effect as <NOBR>Release 2</NOBR> by passing variable
|
|
<CODE>softfloat_roundingMode</CODE> for argument
|
|
<CODE><I>roundingMode</I></CODE> and <CODE>true</CODE> for argument
|
|
<CODE><I>exact</I></CODE>.
|
|
</P>
|
|
|
|
</UL>
|
|
</P>
|
|
|
|
<H3>9.3. Added Capabilities</H3>
|
|
|
|
<P>
|
|
With <NOBR>Release 3</NOBR>, some new features have been added that were not
|
|
present in <NOBR>Release 2</NOBR>:
|
|
<UL>
|
|
|
|
<LI>
|
|
<P>
|
|
A port of SoftFloat can now define any of the floating-point types
|
|
<CODE>float32_t</CODE>, <CODE>float64_t</CODE>, <CODE>extFloat80_t</CODE>, and
|
|
<CODE>float128_t</CODE> as aliases for C’s standard floating-point types
|
|
<CODE>float</CODE>, <CODE>double</CODE>, and <CODE>long</CODE>
|
|
<CODE>double</CODE>, using either <CODE>#define</CODE> or <CODE>typedef</CODE>.
|
|
This potential convenience was not supported under <NOBR>Release 2</NOBR>.
|
|
</P>
|
|
|
|
<P>
|
|
(Note, however, that there may be a performance cost to defining
|
|
SoftFloat’s floating-point types this way, depending on the platform and
|
|
the applications using SoftFloat.
|
|
Ports of SoftFloat may choose to forgo the convenience in favor of better
|
|
speed.)
|
|
</P>
|
|
|
|
<P>
|
|
<LI>
|
|
As of <NOBR>Release 3b</NOBR>, <NOBR>16-bit</NOBR> half-precision,
|
|
<CODE>float16_t</CODE>, is supported.
|
|
</P>
|
|
|
|
<P>
|
|
<LI>
|
|
Functions have been added for converting between the floating-point types and
|
|
unsigned integers.
|
|
<NOBR>Release 2</NOBR> supported only signed integers, not unsigned.
|
|
</P>
|
|
|
|
<P>
|
|
<LI>
|
|
Fused multiply-add functions have been added for all floating-point formats
|
|
except <NOBR>80-bit</NOBR> double-extended-precision,
|
|
<CODE>extFloat80_t</CODE>.
|
|
</P>
|
|
|
|
<P>
|
|
<LI>
|
|
New rounding modes are supported:
|
|
<CODE>softfloat_round_near_maxMag</CODE> (round to nearest, with ties to
|
|
maximum magnitude, away from zero), and, as of <NOBR>Release 3c</NOBR>,
|
|
optional <CODE>softfloat_round_odd</CODE> (round to odd, also known as
|
|
jamming).
|
|
</P>
|
|
|
|
</UL>
|
|
</P>
|
|
|
|
<H3>9.4. Better Compatibility with the C Language</H3>
|
|
|
|
<P>
|
|
<NOBR>Release 3</NOBR> of SoftFloat was written to conform better to the ISO C
|
|
Standard’s rules for portability.
|
|
For example, older releases of SoftFloat employed type conversions in ways
|
|
that, while commonly practiced, are not fully defined by the C Standard.
|
|
Such problematic type conversions have generally been replaced by the use of
|
|
unions, the behavior around which is more strictly regulated these days.
|
|
</P>
|
|
|
|
<H3>9.5. New Organization as a Library</H3>
|
|
|
|
<P>
|
|
Starting with <NOBR>Release 3</NOBR>, SoftFloat now builds as a library.
|
|
Previously, SoftFloat compiled into a single, monolithic object file containing
|
|
all the SoftFloat functions, with the consequence that a program linking with
|
|
SoftFloat would get every SoftFloat function in its binary file even if only a
|
|
few functions were actually used.
|
|
With SoftFloat in the form of a library, a program that is linked by a standard
|
|
linker will include only those functions of SoftFloat that it needs and no
|
|
others.
|
|
</P>
|
|
|
|
<H3>9.6. Optimization Gains (and Losses)</H3>
|
|
|
|
<P>
|
|
Individual SoftFloat functions have been variously improved in
|
|
<NOBR>Release 3</NOBR> compared to earlier releases.
|
|
In particular, better, faster algorithms have been deployed for the operations
|
|
of division, square root, and remainder.
|
|
For functions operating on the larger <NOBR>80-bit</NOBR> and
|
|
<NOBR>128-bit</NOBR> formats, <CODE>extFloat80_t</CODE> and
|
|
<CODE>float128_t</CODE>, code size has also generally been reduced.
|
|
</P>
|
|
|
|
<P>
|
|
However, because <NOBR>Release 2</NOBR> compiled all of SoftFloat together as a
|
|
single object file, compilers could make optimizations across function calls
|
|
when one SoftFloat function calls another.
|
|
Now that the functions of SoftFloat are compiled separately and only afterward
|
|
linked together into a program, there is not usually the same opportunity to
|
|
optimize across function calls.
|
|
Some loss of speed has been observed due to this change.
|
|
</P>
|
|
|
|
|
|
<H2>10. Future Directions</H2>
|
|
|
|
<P>
|
|
The following improvements are anticipated for future releases of SoftFloat:
|
|
<UL>
|
|
<LI>
|
|
more functions from the 2008 version of the IEEE Floating-Point Standard;
|
|
<LI>
|
|
consistent, defined behavior for non-canonical representations of extended
|
|
format <CODE>extFloat80_t</CODE> (discussed in <NOBR>section 4.4</NOBR>,
|
|
<I>Non-canonical Representations in <CODE>extFloat80_t</CODE></I>).
|
|
|
|
</UL>
|
|
</P>
|
|
|
|
|
|
<H2>11. Contact Information</H2>
|
|
|
|
<P>
|
|
At the time of this writing, the most up-to-date information about SoftFloat
|
|
and the latest release can be found at the Web page
|
|
<A HREF="http://www.jhauser.us/arithmetic/SoftFloat.html"><NOBR><CODE>http://www.jhauser.us/arithmetic/SoftFloat.html</CODE></NOBR></A>.
|
|
</P>
|
|
|
|
|
|
</BODY>
|
|
|