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diff --git a/src/libs/softfloat-3e/doc/SoftFloat.html b/src/libs/softfloat-3e/doc/SoftFloat.html new file mode 100644 index 00000000..b72b407f --- /dev/null +++ b/src/libs/softfloat-3e/doc/SoftFloat.html @@ -0,0 +1,1527 @@ + +<HTML> + +<HEAD> +<TITLE>Berkeley SoftFloat Library Interface</TITLE> +</HEAD> + +<BODY> + +<H1>Berkeley SoftFloat Release 3e: Library Interface</H1> + +<P> +John R. Hauser<BR> +2018 January 20<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. Types and Functions</TD></TR> +<TR><TD></TD><TD>4.1. Boolean and Integer Types</TD></TR> +<TR><TD></TD><TD>4.2. Floating-Point Types</TD></TR> +<TR><TD></TD><TD>4.3. Supported Floating-Point Functions</TD></TR> +<TR> + <TD></TD> + <TD>4.4. Non-canonical Representations in <CODE>extFloat80_t</CODE></TD> +</TR> +<TR><TD></TD><TD>4.5. Conventions for Passing Arguments and Results</TD></TR> +<TR><TD COLSPAN=2>5. Reserved Names</TD></TR> +<TR><TD COLSPAN=2>6. Mode Variables</TD></TR> +<TR><TD></TD><TD>6.1. Rounding Mode</TD></TR> +<TR><TD></TD><TD>6.2. Underflow Detection</TD></TR> +<TR> + <TD></TD> + <TD>6.3. Rounding Precision for the <NOBR>80-Bit</NOBR> Extended Format</TD> +</TR> +<TR><TD COLSPAN=2>7. Exceptions and Exception Flags</TD></TR> +<TR><TD COLSPAN=2>8. Function Details</TD></TR> +<TR><TD></TD><TD>8.1. Conversions from Integer to Floating-Point</TD></TR> +<TR><TD></TD><TD>8.2. Conversions from Floating-Point to Integer</TD></TR> +<TR><TD></TD><TD>8.3. Conversions Among Floating-Point Types</TD></TR> +<TR><TD></TD><TD>8.4. Basic Arithmetic Functions</TD></TR> +<TR><TD></TD><TD>8.5. Fused Multiply-Add Functions</TD></TR> +<TR><TD></TD><TD>8.6. Remainder Functions</TD></TR> +<TR><TD></TD><TD>8.7. Round-to-Integer Functions</TD></TR> +<TR><TD></TD><TD>8.8. Comparison Functions</TD></TR> +<TR><TD></TD><TD>8.9. Signaling NaN Test Functions</TD></TR> +<TR><TD></TD><TD>8.10. Raise-Exception Function</TD></TR> +<TR><TD COLSPAN=2>9. Changes from SoftFloat <NOBR>Release 2</NOBR></TD></TR> +<TR><TD></TD><TD>9.1. Name Changes</TD></TR> +<TR><TD></TD><TD>9.2. Changes to Function Arguments</TD></TR> +<TR><TD></TD><TD>9.3. Added Capabilities</TD></TR> +<TR><TD></TD><TD>9.4. Better Compatibility with the C Language</TD></TR> +<TR><TD></TD><TD>9.5. New Organization as a Library</TD></TR> +<TR><TD></TD><TD>9.6. Optimization Gains (and Losses)</TD></TR> +<TR><TD COLSPAN=2>10. Future Directions</TD></TR> +<TR><TD COLSPAN=2>11. Contact Information</TD></TR> +</TABLE> +</BLOCKQUOTE> + + +<H2>1. Introduction</H2> + +<P> +Berkeley SoftFloat is a software implementation of binary floating-point that +conforms to the IEEE Standard for Floating-Point Arithmetic. +The current release supports five binary formats: <NOBR>16-bit</NOBR> +half-precision, <NOBR>32-bit</NOBR> single-precision, <NOBR>64-bit</NOBR> +double-precision, <NOBR>80-bit</NOBR> double-extended-precision, and +<NOBR>128-bit</NOBR> quadruple-precision. +The following functions are supported for each format: +<UL> +<LI> +addition, subtraction, multiplication, division, and square root; +<LI> +fused multiply-add as defined by the IEEE Standard, except for +<NOBR>80-bit</NOBR> double-extended-precision; +<LI> +remainder as defined by the IEEE Standard; +<LI> +round to integral value; +<LI> +comparisons; +<LI> +conversions to/from other supported formats; and +<LI> +conversions to/from <NOBR>32-bit</NOBR> and <NOBR>64-bit</NOBR> integers, +signed and unsigned. +</UL> +All operations required by the original 1985 version of the IEEE Floating-Point +Standard are implemented, except for conversions to and from decimal. +</P> + +<P> +This document gives information about the types defined and the routines +implemented by SoftFloat. +It does not attempt to define or explain the IEEE Floating-Point Standard. +Information about the standard is available elsewhere. +</P> + +<P> +The current version of SoftFloat is <NOBR>Release 3e</NOBR>. +This release modifies the behavior of the rarely used <I>odd</I> rounding mode +(<I>round to odd</I>, also known as <I>jamming</I>), and also adds some new +specialization and optimization examples for those compiling SoftFloat. +</P> + +<P> +The previous <NOBR>Release 3d</NOBR> fixed bugs that were found in the square +root functions for the <NOBR>64-bit</NOBR>, <NOBR>80-bit</NOBR>, and +<NOBR>128-bit</NOBR> floating-point formats. +(Thanks to Alexei Sibidanov at the University of Victoria for reporting an +incorrect result.) +The bugs affected all prior <NOBR>Release-3</NOBR> versions of SoftFloat +<NOBR>through 3c</NOBR>. +The flaw in the <NOBR>64-bit</NOBR> floating-point square root function was of +very minor impact, causing a <NOBR>1-ulp</NOBR> error (<NOBR>1 unit</NOBR> in +the last place) a few times out of a billion. +The bugs in the <NOBR>80-bit</NOBR> and <NOBR>128-bit</NOBR> square root +functions were more serious. +Although incorrect results again occurred only a few times out of a billion, +when they did occur a large portion of the less-significant bits could be +wrong. +</P> + +<P> +Among earlier releases, 3b was notable for adding support for the +<NOBR>16-bit</NOBR> half-precision format. +For more about the evolution of SoftFloat releases, see +<A HREF="SoftFloat-history.html"><NOBR><CODE>SoftFloat-history.html</CODE></NOBR></A>. +</P> + +<P> +The functional interface of SoftFloat <NOBR>Release 3</NOBR> and later differs +in many details from the releases that came before. +For specifics of these differences, see <NOBR>section 9</NOBR> below, +<I>Changes from SoftFloat <NOBR>Release 2</NOBR></I>. +</P> + + +<H2>2. Limitations</H2> + +<P> +SoftFloat assumes the computer has an addressable byte size of 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 +starting 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> +Most operations not required by the original 1985 version of the IEEE +Floating-Point Standard but added in the 2008 version are not yet supported in +SoftFloat <NOBR>Release 3e</NOBR>. +</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 was a completely new implementation +supplanting earlier releases. +The project to create <NOBR>Release 3</NOBR> (now <NOBR>through 3e</NOBR>) 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 3e</NOBR> as well +as to each source file individually. +</P> + +<P> +Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Regents of the +University of California. +All rights reserved. +</P> + +<P> +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: +<OL> + +<LI> +<P> +Redistributions of source code must retain the above copyright notice, this +list of conditions, and the following disclaimer. +</P> + +<LI> +<P> +Redistributions in binary form must reproduce the above copyright notice, this +list of conditions, and the following disclaimer in the documentation and/or +other materials provided with the distribution. +</P> + +<LI> +<P> +Neither the name of the University nor the names of its contributors may be +used to endorse or promote products derived from this software without specific +prior written permission. +</P> + +</OL> +</P> + +<P> +THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS “AS IS”, +AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE +DISCLAIMED. +IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, +INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE +OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +</P> + + +<H2>4. Types and Functions</H2> + +<P> +The types and functions of SoftFloat are declared in header file +<CODE>softfloat.h</CODE>. +</P> + +<H3>4.1. Boolean and Integer Types</H3> + +<P> +Header file <CODE>softfloat.h</CODE> depends on standard headers +<CODE><stdbool.h></CODE> and <CODE><stdint.h></CODE> to define type +<CODE>bool</CODE> and several integer types. +These standard headers have been part of the ISO C Standard Library since 1999. +With any recent compiler, they 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, a port of SoftFloat may have substitutes +for these headers. +Header <CODE>softfloat.h</CODE> depends only on the name <CODE>bool</CODE> from +<CODE><stdbool.h></CODE> and on these type names from +<CODE><stdint.h></CODE>: +<BLOCKQUOTE> +<PRE> +uint16_t +uint32_t +uint64_t +int32_t +int64_t +uint_fast8_t +uint_fast32_t +uint_fast64_t +int_fast32_t +int_fast64_t +</PRE> +</BLOCKQUOTE> +</P> + + +<H3>4.2. Floating-Point Types</H3> + +<P> +The <CODE>softfloat.h</CODE> header defines five floating-point types: +<BLOCKQUOTE> +<TABLE CELLSPACING=0 CELLPADDING=0> +<TR> +<TD><CODE>float16_t</CODE></TD> +<TD><NOBR>16-bit</NOBR> half-precision binary format</TD> +</TR> +<TR> +<TD><CODE>float32_t</CODE></TD> +<TD><NOBR>32-bit</NOBR> single-precision binary format</TD> +</TR> +<TR> +<TD><CODE>float64_t</CODE></TD> +<TD><NOBR>64-bit</NOBR> double-precision binary format</TD> +</TR> +<TR> +<TD><CODE>extFloat80_t </CODE></TD> +<TD><NOBR>80-bit</NOBR> double-extended-precision binary format (old Intel or +Motorola format)</TD> +</TR> +<TR> +<TD><CODE>float128_t</CODE></TD> +<TD><NOBR>128-bit</NOBR> quadruple-precision binary format</TD> +</TR> +</TABLE> +</BLOCKQUOTE> +The non-extended types are each exactly the size specified: +<NOBR>16 bits</NOBR> for <CODE>float16_t</CODE>, <NOBR>32 bits</NOBR> for +<CODE>float32_t</CODE>, <NOBR>64 bits</NOBR> for <CODE>float64_t</CODE>, and +<NOBR>128 bits</NOBR> for <CODE>float128_t</CODE>. +Aside from these size requirements, the definitions of all these types may +differ for different ports of SoftFloat to specific systems. +A given port of SoftFloat may or may not define some of the floating-point +types as aliases for the C standard types <CODE>float</CODE>, +<CODE>double</CODE>, and <CODE>long</CODE> <CODE>double</CODE>. +</P> + +<P> +Header file <CODE>softfloat.h</CODE> also defines a structure, +<CODE>struct</CODE> <CODE>extFloat80M</CODE>, for the representation of +<NOBR>80-bit</NOBR> double-extended-precision floating-point values in memory. +This structure is the same size as type <CODE>extFloat80_t</CODE> and contains +at least these two fields (not necessarily in this order): +<BLOCKQUOTE> +<PRE> +uint16_t signExp; +uint64_t signif; +</PRE> +</BLOCKQUOTE> +Field <CODE>signExp</CODE> contains the sign and exponent of the floating-point +value, with the sign in the most significant bit (<NOBR>bit 15</NOBR>) and the +encoded exponent in the other <NOBR>15 bits</NOBR>. +Field <CODE>signif</CODE> is the complete <NOBR>64-bit</NOBR> significand of +the floating-point value. +(In the usual encoding for <NOBR>80-bit</NOBR> extended floating-point, the +leading <NOBR>1 bit</NOBR> of normalized numbers is not implicit but is stored +in the most significant bit of the significand.) +</P> + +<H3>4.3. Supported Floating-Point Functions</H3> + +<P> +SoftFloat implements these arithmetic operations for its floating-point types: +<UL> +<LI> +conversions between any two floating-point formats; +<LI> +for each floating-point format, conversions to and from signed and unsigned +<NOBR>32-bit</NOBR> and <NOBR>64-bit</NOBR> integers; +<LI> +for each format, the usual addition, subtraction, multiplication, division, and +square root operations; +<LI> +for each format except <CODE>extFloat80_t</CODE>, the fused multiply-add +operation defined by the IEEE Standard; +<LI> +for each format, the floating-point remainder operation defined by the IEEE +Standard; +<LI> +for each format, a “round to integer” operation that rounds to the +nearest integer value in the same format; and +<LI> +comparisons between two values in the same floating-point format. +</UL> +</P> + +<P> +The following operations required by the 2008 IEEE Floating-Point Standard are +not supported in SoftFloat <NOBR>Release 3e</NOBR>: +<UL> +<LI> +<B>nextUp</B>, <B>nextDown</B>, <B>minNum</B>, <B>maxNum</B>, <B>minNumMag</B>, +<B>maxNumMag</B>, <B>scaleB</B>, and <B>logB</B>; +<LI> +conversions between floating-point formats and decimal or hexadecimal character +sequences; +<LI> +all “quiet-computation” operations (<B>copy</B>, <B>negate</B>, +<B>abs</B>, and <B>copySign</B>, which all involve only simple copying and/or +manipulation of the floating-point sign bit); and +<LI> +all “non-computational” operations other than <B>isSignaling</B> +(which is supported). +</UL> +</P> + +<H3>4.4. Non-canonical Representations in <CODE>extFloat80_t</CODE></H3> + +<P> +Because the <NOBR>80-bit</NOBR> double-extended-precision format, +<CODE>extFloat80_t</CODE>, stores an explicit leading significand bit, many +finite floating-point numbers are encodable in this type in multiple equivalent +forms. +Of these multiple encodings, there is always a unique one with the least +encoded exponent value, and this encoding is considered the <I>canonical</I> +representation of the floating-point number. +Any other equivalent representations (having a higher encoded exponent value) +are <I>non-canonical</I>. +For a value in the subnormal range (including zero), the canonical +representation always has an encoded exponent of zero and a leading significand +bit <NOBR>of 0</NOBR>. +For finite values outside the subnormal range, the canonical representation +always has an encoded exponent that is nonzero and a leading significand bit +<NOBR>of 1</NOBR>. +</P> + +<P> +For an infinity or NaN, the leading significand bit is similarly expected to +<NOBR>be 1</NOBR>. +An infinity or NaN with a leading significand bit <NOBR>of 0</NOBR> is again +considered non-canonical. +Hence, altogether, to be canonical, a value of type <CODE>extFloat80_t</CODE> +must have a leading significand bit <NOBR>of 1</NOBR>, unless the value is +subnormal or zero, in which case the leading significand bit and the encoded +exponent must both be zero. +</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> + |