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<TITLE>Berkeley SoftFloat Source Documentation</TITLE>
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<H1>Berkeley SoftFloat Release 3: Source Documentation</H1>

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


<H2>Contents</H2>

<BLOCKQUOTE>
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<COL WIDTH=25>
<COL WIDTH=*>
<TR><TD COLSPAN=2>1. Introduction</TD></TR>
<TR><TD COLSPAN=2>2. Limitations</TD></TR>
<TR><TD COLSPAN=2>3. Acknowledgments and License</TD></TR>
<TR><TD COLSPAN=2>4. SoftFloat Package Directory Structure</TD></TR>
<TR><TD COLSPAN=2>5. Issues for Porting SoftFloat to a New Target</TD></TR>
<TR>
  <TD></TD>
  <TD>5.1. Standard Headers <CODE>&lt;stdbool.h&gt;</CODE> and
    <CODE>&lt;stdint.h&gt;</CODE></TD>
</TR>
<TR><TD></TD><TD>5.2. Specializing Floating-Point Behavior</TD></TR>
<TR><TD></TD><TD>5.3. Macros for Build Options</TD></TR>
<TR><TD></TD><TD>5.4. Adapting a Template Target Directory</TD></TR>
<TR>
  <TD></TD><TD>5.5. Target-Specific Optimization of Primitive Functions</TD>
</TR>
<TR><TD COLSPAN=2>6. Testing SoftFloat</TD></TR>
<TR>
  <TD COLSPAN=2>7. Providing SoftFloat as a Common Library for Applications</TD>
</TR>
<TR><TD COLSPAN=2>8. Contact Information</TD></TR>
</TABLE>
</BLOCKQUOTE>


<H2>1. Introduction</H2>

<P>
This document gives information needed for compiling and/or porting Berkeley
SoftFloat, a library of C functions implementing binary floating-point
conforming to the IEEE Standard for Floating-Point Arithmetic.
For basic documentation about SoftFloat refer to
<A HREF="SoftFloat.html"><CODE>SoftFloat.html</CODE></A>.
</P>

<P>
The source code for SoftFloat is intended to be relatively machine-independent
and should be compilable with any ISO-Standard C compiler that also supports
<NOBR>64-bit</NOBR> integers.
SoftFloat has been successfully compiled with the GNU C Compiler
(<CODE>gcc</CODE>) for several platforms.
</P>

<P>
<NOBR>Release 3</NOBR> of SoftFloat is a complete rewrite relative to
<NOBR>Release 2</NOBR> or earlier.
Changes to the interface of SoftFloat functions are documented in
<A HREF="SoftFloat.html"><CODE>SoftFloat.html</CODE></A>.
</P>


<H2>2. Limitations</H2>

<P>
SoftFloat assumes the computer has an addressable byte size of either 8 or
<NOBR>16 bits</NOBR>.
(Nearly all computers in use today have <NOBR>8-bit</NOBR> bytes.)
</P>

<P>
SoftFloat is written in C and is designed to work with other C code.
The C compiler used must conform at a minimum to the 1989 ANSI standard for the
C language (same as the 1990 ISO standard) and must in addition support basic
arithmetic on <NOBR>64-bit</NOBR> integers.
Earlier releases of SoftFloat included implementations of <NOBR>32-bit</NOBR>
single-precision and <NOBR>64-bit</NOBR> double-precision floating-point that
did not require <NOBR>64-bit</NOBR> integers, but this option is not supported
with <NOBR>Release 3</NOBR>.
Since 1999, ISO standards for C have mandated compiler support for
<NOBR>64-bit</NOBR> integers.
A compiler conforming to the 1999 C Standard or later is recommended but not
strictly required.
</P>

<P>
<NOBR>C Standard</NOBR> header files <CODE>&lt;stdbool.h&gt;</CODE> and
<CODE>&lt;stdint.h&gt;</CODE> are required for defining standard Boolean and
integer types.
If these headers are not supplied with the C compiler, minimal substitutes must
be provided.
SoftFloat&rsquo;s dependence on these headers is detailed later in
<NOBR>section 5.1</NOBR>, <I>Standard Headers &lt;stdbool.h&gt; and
&lt;stdint.h&gt;</I>.
</P>


<H2>3. Acknowledgments and License</H2>

<P>
The SoftFloat package was written by me, <NOBR>John R.</NOBR> Hauser.
<NOBR>Release 3</NOBR> of SoftFloat is a completely new implementation
supplanting earlier releases.
This project (<NOBR>Release 3</NOBR> only, not earlier releases) was done in
the employ of the University of California, Berkeley, within the Department of
Electrical Engineering and Computer Sciences, first for the Parallel Computing
Laboratory (Par Lab) and then for the ASPIRE Lab.
The work was officially overseen by Prof. Krste Asanovic, with funding provided
by these sources:
<BLOCKQUOTE>
<TABLE>
<COL>
<COL WIDTH=10>
<COL>
<TR>
<TD VALIGN=TOP><NOBR>Par Lab:</NOBR></TD>
<TD></TD>
<TD>
Microsoft (Award #024263), Intel (Award #024894), and U.C. Discovery
(Award #DIG07-10227), with additional support from Par Lab affiliates Nokia,
NVIDIA, Oracle, and Samsung.
</TD>
</TR>
<TR>
<TD VALIGN=TOP><NOBR>ASPIRE Lab:</NOBR></TD>
<TD></TD>
<TD>
DARPA PERFECT program (Award #HR0011-12-2-0016), with additional support from
ASPIRE industrial sponsor Intel and ASPIRE affiliates Google, Nokia, NVIDIA,
Oracle, and Samsung.
</TD>
</TR>
</TABLE>
</BLOCKQUOTE>
</P>

<P>
The following applies to the whole of SoftFloat <NOBR>Release 3</NOBR> as well
as to each source file individually.
</P>

<P>
Copyright 2011, 2012, 2013, 2014, 2015 The Regents of the University of
California (Regents).
All Rights Reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
</P>

<P>
Redistributions of source code must retain the above copyright notice, this
list of conditions, and the following two paragraphs of disclaimer.
Redistributions in binary form must reproduce the above copyright notice, this
list of conditions, and the following two paragraphs of disclaimer in the
documentation and/or other materials provided with the distribution.
Neither the name of the Regents nor the names of its contributors may be used
to endorse or promote products derived from this software without specific
prior written permission.
</P>

<P>
IN NO EVENT SHALL REGENTS BE LIABLE TO ANY PARTY FOR DIRECT, INDIRECT, SPECIAL,
INCIDENTAL, OR CONSEQUENTIAL DAMAGES, INCLUDING LOST PROFITS, ARISING OUT OF
THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF REGENTS HAS BEEN
ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
</P>

<P>
REGENTS SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
THE SOFTWARE AND ACCOMPANYING DOCUMENTATION, IF ANY, PROVIDED HEREUNDER IS
PROVIDED "<NOBR>AS IS</NOBR>".
REGENTS HAS NO OBLIGATION TO PROVIDE MAINTENANCE, SUPPORT, UPDATES,
ENHANCEMENTS, OR MODIFICATIONS.
</P>


<H2>4. SoftFloat Package Directory Structure</H2>

<P>
Because SoftFloat is targeted to multiple platforms, its source code is
slightly scattered between target-specific and target-independent directories
and files.
The supplied directory structure is as follows:
<BLOCKQUOTE>
<PRE>
doc
source
    include
    8086
    8086-SSE
build
    template-FAST_INT64
    template-not-FAST_INT64
    Linux-386-GCC
    Linux-386-SSE2-GCC
    Linux-x86_64-GCC
    Win32-MinGW
    Win32-SSE2-MinGW
    Win64-MinGW-w64
</PRE>
</BLOCKQUOTE>
The majority of the SoftFloat sources are provided in the <CODE>source</CODE>
directory.
The <CODE>include</CODE> subdirectory of <CODE>source</CODE> contains several
header files (unsurprisingly), while the <CODE>8086</CODE> and
<NOBR><CODE>8086-SSE</CODE></NOBR> subdirectories contain source files that
specialize the floating-point behavior to match the Intel x86 line of
processors.
The files in directory <CODE>8086</CODE> give floating-point behavior
consistent solely with Intel&rsquo;s older, 8087-derived floating-point, while
those in <NOBR><CODE>8086-SSE</CODE></NOBR> update the behavior of the
non-extended formats (<CODE>float32_t</CODE>, <CODE>float64_t</CODE>, and
<CODE>float128_t</CODE>) to mirror Intel&rsquo;s more recent Streaming SIMD
Extensions (SSE) and other compatible extensions.
If other specializations are attempted, these would be expected to be other
subdirectories of <CODE>source</CODE> alongside <CODE>8086</CODE> and
<NOBR><CODE>8086-SSE</CODE></NOBR>.
Specialization is covered later, in <NOBR>section 5.2</NOBR>, <I>Specializing
Floating-Point Behavior</I>.
</P>

<P>
The <CODE>build</CODE> directory is intended to contain a subdirectory for each
target platform for which a build of the SoftFloat library may be created.
For each build target, the target&rsquo;s subdirectory is where all derived
object files and the completed SoftFloat library (typically
<CODE>softfloat.a</CODE> or <CODE>libsoftfloat.a</CODE>) are created.
The two <CODE>template</CODE> subdirectories are not actual build targets but
contain sample files for creating new target directories.
(The meaning of <CODE>FAST_INT64</CODE> will be explained later.)
</P>

<P>
Ignoring the <CODE>template</CODE> directories, the supplied target directories
are intended to follow a naming system of
<NOBR><CODE>&lt;execution-environment&gt;-&lt;compiler&gt;</CODE></NOBR>.
For the example targets,
<NOBR><CODE>&lt;execution-environment&gt;</CODE></NOBR> is
<NOBR><CODE>Linux-386</CODE></NOBR>, <NOBR><CODE>Linux-386-SSE2</CODE></NOBR>,
<NOBR><CODE>Linux-x86_64</CODE></NOBR>, <CODE>Win32</CODE>,
<NOBR><CODE>Win32-SSE2</CODE></NOBR>, or <CODE>Win64</CODE>, and
<NOBR><CODE>&lt;compiler&gt;</CODE></NOBR> is <CODE>GCC</CODE>,
<CODE>MinGW</CODE>, or <NOBR><CODE>MinGW-w64</CODE></NOBR>.
</P>

<P>
As supplied, each target directory contains two files:
<BLOCKQUOTE>
<PRE>
Makefile
platform.h
</PRE>
</BLOCKQUOTE>
The provided <CODE>Makefile</CODE> is written for GNU <CODE>make</CODE>.
A build of SoftFloat for the specific target is begun by executing the
<CODE>make</CODE> command with the target directory as the current directory.
A completely different build tool can be used if an appropriate
<CODE>Makefile</CODE> equivalent is created.
</P>

<P>
The <CODE>platform.h</CODE> header file exists to provide a location for
additional C declarations specific to the build target.
Every C source file of SoftFloat contains a <CODE>#include</CODE> for
<CODE>platform.h</CODE>.
In many cases, the contents of <CODE>platform.h</CODE> can be as simple as one
or two lines of code.
At the other extreme, to get maximal performance from SoftFloat, it may be
desirable to include in header <CODE>platform.h</CODE> (directly or via
<CODE>#include</CODE>) declarations for numerous target-specific optimizations.
Such possibilities are discussed in the next section, <I>Issues for Porting
SoftFloat to a New Target</I>.
If the target&rsquo;s compiler or library has bugs or other shortcomings,
workarounds for these issues may also be possible with target-specific
declarations in <CODE>platform.h</CODE>, avoiding the need to modify the main
SoftFloat sources.
</P>


<H2>5. Issues for Porting SoftFloat to a New Target</H2>

<H3>5.1. Standard Headers <CODE>&lt;stdbool.h&gt;</CODE> and <CODE>&lt;stdint.h&gt;</CODE></H3>

<P>
The SoftFloat sources make use of standard headers
<CODE>&lt;stdbool.h&gt;</CODE> and <CODE>&lt;stdint.h&gt;</CODE>, which have
been part of the ISO C Standard Library since 1999.
With any recent compiler, these standard headers are likely to be supported,
even if the compiler does not claim complete conformance to the latest ISO C
Standard.
For older or nonstandard compilers, substitutes for
<CODE>&lt;stdbool.h&gt;</CODE> and <CODE>&lt;stdint.h&gt;</CODE> may need to be
created.
SoftFloat depends on these names from <CODE>&lt;stdbool.h&gt;</CODE>:
<BLOCKQUOTE>
<PRE>
bool
true
false
</PRE>
</BLOCKQUOTE>
and on these names from <CODE>&lt;stdint.h&gt;</CODE>:
<BLOCKQUOTE>
<PRE>
uint16_t
uint32_t
uint64_t
int32_t
int64_t
UINT64_C
INT64_C
uint_least8_t
uint_fast8_t
uint_fast16_t
uint_fast32_t
uint_fast64_t
int_fast8_t
int_fast16_t
int_fast32_t
int_fast64_t
</PRE>
</BLOCKQUOTE>
</P>


<H3>5.2. Specializing Floating-Point Behavior</H3>

<P>
The IEEE Floating-Point Standard allows for some flexibility in a conforming
implementation, particularly concerning NaNs.
The SoftFloat <CODE>source</CODE> directory is supplied with some
<I>specialization</I> subdirectories containing possible definitions for this
implementation-specific behavior.
For example, the <CODE>8086</CODE> and <NOBR><CODE>8086-SSE</CODE></NOBR>
subdirectories have source files that specialize SoftFloat&rsquo;s behavior to
match that of Intel&rsquo;s x86 line of processors.
The files in a specialization subdirectory must determine:
<UL>
<LI>
whether tininess for underflow is detected before or after rounding by default;
<LI>
what (if anything) special happens when exceptions are raised;
<LI>
how signaling NaNs are distinguished from quiet NaNs;
<LI>
the default generated quiet NaNs; and
<LI>
how NaNs are propagated from function inputs to output.
</UL>
</P>

<P>
As provided, the build process for a target expects to involve exactly
<EM>one</EM> specialization directory that defines <EM>all</EM> of these
implementation-specific details for the target.
A specialization directory such as <CODE>8086</CODE> is expected to contain a
header file called <CODE>specialize.h</CODE>, together with whatever other
source files are needed to complete the specialization.
</P>

<P>
A new build target may use an existing specialization, such as the ones
provided by the <CODE>8086</CODE> and <NOBR><CODE>8086-SSE</CODE></NOBR>
subdirectories.
If a build target needs a new specialization, different from any existing ones,
it is recommended that a new specialization subdirectory be created in the
<CODE>source</CODE> directory for this purpose.
The <CODE>specialize.h</CODE> header file from any of the provided
specialization subdirectories can be used as a model for what definitions are
needed.
</P>


<H3>5.3. Macros for Build Options</H3>

<P>
The SoftFloat source files adapt the floating-point implementation according to
a few C preprocessor macros:
<BLOCKQUOTE>
<DL>
<DT><CODE>LITTLEENDIAN</CODE>
<DD>
Must be defined for little-endian machines; must not be defined for big-endian
machines.
<DT><CODE>SOFTFLOAT_FAST_INT64</CODE>
<DD>
Can be defined to indicate that the build target&rsquo;s implementation of
<NOBR>64-bit</NOBR> arithmetic is efficient.
For newer <NOBR>64-bit</NOBR> processors, this macro should usually be defined.
For very small microprocessors whose buses and registers are <NOBR>8-bit</NOBR>
or <NOBR>16-bit</NOBR> in size, this macro should usually not be defined.
Whether this macro should be defined for a <NOBR>32-bit</NOBR> processor may
depend on the target machine and the applications that will use SoftFloat.
<DT><CODE>SOFTFLOAT_FAST_DIV64TO32</CODE>
<DD>
Can be defined to indicate that the target&rsquo;s division operator
<NOBR>in C</NOBR> (written as <CODE>/</CODE>) is reasonably efficient for
dividing a <NOBR>64-bit</NOBR> unsigned integer by a <NOBR>32-bit</NOBR>
unsigned integer.
Setting this macro may affect the performance of division, remainder, and
square root operations.
<DT><CODE>INLINE_LEVEL</CODE>
<DD>
Can be defined to an integer to determine the degree of inlining requested of
the compiler.
Larger numbers request that more inlining be done.
If this macro is not defined or is defined to a value less <NOBR>than 1</NOBR>
(zero or negative), no inlining is requested.
The maximum effective value is no higher <NOBR>than 5</NOBR>.
Defining this macro to a value greater than 5 is the same as defining it
<NOBR>to 5</NOBR>.
<DT><CODE>INLINE</CODE>
<DD>
Specifies the sequence of tokens used to indicate that a C function should be
inlined.
If macro <CODE>INLINE_LEVEL</CODE> is defined with a value of 1 or higher, this
macro must be defined; otherwise, this macro is ignored and need not be
defined.
For some compilers, this macro can be defined as the single keyword
<CODE>inline</CODE>.
Historically, the <CODE>gcc</CODE> compiler has required that this macro be
defined to <CODE>extern</CODE> <CODE>inline</CODE>.
</DL>
</BLOCKQUOTE>
</P>

<P>
Following the usual custom <NOBR>for C</NOBR>, for the first three macros (all
except <CODE>INLINE_LEVEL</CODE> and <CODE>INLINE</CODE>), the content of any
definition is irrelevant;
what matters is a macro&rsquo;s effect on <CODE>#ifdef</CODE> directives.
</P>

<P>
It is recommended that any definitions of macros <CODE>LITTLEENDIAN</CODE> and
<CODE>INLINE</CODE> be made in a build target&rsquo;s <CODE>platform.h</CODE>
header file, because these macros are expected to be determined inflexibly by
the target machine and compiler.
The other three macros control optimization and might be better located in the
target&rsquo;s Makefile (or its equivalent).
</P>


<H3>5.4. Adapting a Template Target Directory</H3>

<P>
In the <CODE>build</CODE> directory, two <CODE>template</CODE> subdirectories
provide models for new target directories.
Two different templates exist because different functions are needed in the
SoftFloat library depending on whether macro <CODE>SOFTFLOAT_FAST_INT64</CODE>
is defined.
If macro <CODE>SOFTFLOAT_FAST_INT64</CODE> will be defined,
<NOBR><CODE>template-FAST_INT64</CODE></NOBR> is the template to use;
otherwise, <NOBR><CODE>template-not-FAST_INT64</CODE></NOBR> is the appropriate
template.
A new target directory can be created by copying the correct template directory
and editing the files inside.
To avoid confusion, it would be wise to refrain from editing the files within a
template directory directly.
</P>


<H3>5.5. Target-Specific Optimization of Primitive Functions</H3>

<P>
Header file <CODE>primitives.h</CODE> (in directory
<CODE>source/include</CODE>) declares macros and functions for numerous
underlying arithmetic operations upon which many of SoftFloat&rsquo;s
floating-point functions are ultimately built.
The SoftFloat sources include implementations of all of these functions/macros,
written as standard C code, so a complete and correct SoftFloat library can be
built using only the supplied code for all functions.
However, for many targets, SoftFloat&rsquo;s performance can be improved by
substituting target-specific implementations of some of the functions/macros
declared in <CODE>primitives.h</CODE>.
</P>

<P>
For example, <CODE>primitives.h</CODE> declares a function called
<CODE>softfloat_countLeadingZeros32</CODE> that takes an unsigned
<NOBR>32-bit</NOBR> integer as an argument and returns the maximal number of
the integer&rsquo;s most-significant bits that are all zeros.
While the SoftFloat sources include an implementation of this function written
in <NOBR>standard C</NOBR>, many processors can perform this same function
directly in only one or two machine instructions.
An alternative, target-specific implementation that maps to those instructions
is likely to be more efficient than the generic C code from the SoftFloat
package.
</P>

<P>
A build target can replace the supplied version of any function or macro of
<CODE>primitives.h</CODE> by defining a macro with the same name in the
target&rsquo;s <CODE>platform.h</CODE> header file.
For this purpose, it may be helpful for <CODE>platform.h</CODE> to
<CODE>#include</CODE> header file <CODE>primitiveTypes.h</CODE>, which defines
types used for arguments and results of functions declared in
<CODE>primitives.h</CODE>.
When a desired replacement implementation is a function, not a macro, it is
sufficient for <CODE>platform.h</CODE> to include the line
<BLOCKQUOTE>
<PRE>
#define &lt;function-name&gt; &lt;function-name&gt;
</PRE>
</BLOCKQUOTE>
where <NOBR><CODE>&lt;function-name&gt;</CODE></NOBR> is the name of the
function.
This technically defines <NOBR><CODE>&lt;function-name&gt;</CODE></NOBR> as a
macro, but one that resolves to the same name, which may then be a function.
(A preprocessor conforming to the C Standard must limit recursive macro
expansion from being applied more than once.)
</P>


<H2>6. Testing SoftFloat</H2>

<P>
SoftFloat can be tested using the <CODE>testsoftfloat</CODE> program by the
same author.
This program is part of the Berkeley TestFloat package available at the Web
page
<A HREF="http://www.jhauser.us/arithmetic/TestFloat.html"><CODE>http://www.jhauser.us/arithmetic/TestFloat.html</CODE></A>.
The TestFloat package also has a program called <CODE>timesoftfloat</CODE> that
measures the speed of SoftFloat&rsquo;s floating-point functions.
</P>


<H2>7. Providing SoftFloat as a Common Library for Applications</H2>

<P>
Header file <CODE>softfloat.h</CODE> defines the SoftFloat interface as seen by
clients.
If the SoftFloat library will be made a common library for programs on a
particular system, the supplied <CODE>softfloat.h</CODE> has a couple of
deficiencies for this purpose:
<UL>
<LI>
As supplied, <CODE>softfloat.h</CODE> depends on another header,
<CODE>softfloat_types.h</CODE>, that is not intended for public use but which
must also be visible to the programmer&rsquo;s compiler.
<LI>
More troubling, at the time <CODE>softfloat.h</CODE> is included in a C
source file, macro <CODE>SOFTFLOAT_FAST_INT64</CODE> must be defined, or not
defined, consistent with whether this macro was defined when the SoftFloat
library was built.
</UL>
In the situation that new programs may regularly <CODE>#include</CODE> header
file <CODE>softfloat.h</CODE>, it is recommended that a custom, self-contained
version of this header file be created that eliminates these issues.
</P>


<H2>8. 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"><CODE>http://www.jhauser.us/arithmetic/SoftFloat.html</CODE></A>.
</P>


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