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-$NetBSD: softfloat.txt,v 1.2 2006/11/24 19:46:58 christos Exp $
-
-SoftFloat Release 2a General Documentation
-
-John R. Hauser
-1998 December 13
-
-
--------------------------------------------------------------------------------
-Introduction
-
-SoftFloat is a software implementation of floating-point that conforms to
-the IEC/IEEE Standard for Binary Floating-Point Arithmetic. As many as four
-formats are supported: single precision, double precision, extended double
-precision, and quadruple precision. All operations required by the standard
-are implemented, except for conversions to and from decimal.
-
-This document gives information about the types defined and the routines
-implemented by SoftFloat. It does not attempt to define or explain the
-IEC/IEEE Floating-Point Standard. Details about the standard are available
-elsewhere.
-
-
--------------------------------------------------------------------------------
-Limitations
-
-SoftFloat is written in C and is designed to work with other C code. The
-SoftFloat header files assume an ISO/ANSI-style C compiler. No attempt
-has been made to accommodate compilers that are not ISO-conformant. In
-particular, the distributed header files will not be acceptable to any
-compiler that does not recognize function prototypes.
-
-Support for the extended double-precision and quadruple-precision formats
-depends on a C compiler that implements 64-bit integer arithmetic. If the
-largest integer format supported by the C compiler is 32 bits, SoftFloat is
-limited to only single and double precisions. When that is the case, all
-references in this document to the extended double precision, quadruple
-precision, and 64-bit integers should be ignored.
-
-
--------------------------------------------------------------------------------
-Contents
-
- Introduction
- Limitations
- Contents
- Legal Notice
- Types and Functions
- Rounding Modes
- Extended Double-Precision Rounding Precision
- Exceptions and Exception Flags
- Function Details
- Conversion Functions
- Standard Arithmetic Functions
- Remainder Functions
- Round-to-Integer Functions
- Comparison Functions
- Signaling NaN Test Functions
- Raise-Exception Function
- Contact Information
-
-
-
--------------------------------------------------------------------------------
-Legal Notice
-
-SoftFloat was written by John R. Hauser. This work was made possible in
-part by the International Computer Science Institute, located at Suite 600,
-1947 Center Street, Berkeley, California 94704. Funding was partially
-provided by the National Science Foundation under grant MIP-9311980. The
-original version of this code was written as part of a project to build
-a fixed-point vector processor in collaboration with the University of
-California at Berkeley, overseen by Profs. Nelson Morgan and John Wawrzynek.
-
-THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
-has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
-TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
-PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
-AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
-
-
--------------------------------------------------------------------------------
-Types and Functions
-
-When 64-bit integers are supported by the compiler, the `softfloat.h' header
-file defines four types: `float32' (single precision), `float64' (double
-precision), `floatx80' (extended double precision), and `float128'
-(quadruple precision). The `float32' and `float64' types are defined in
-terms of 32-bit and 64-bit integer types, respectively, while the `float128'
-type is defined as a structure of two 64-bit integers, taking into account
-the byte order of the particular machine being used. The `floatx80' type
-is defined as a structure containing one 16-bit and one 64-bit integer, with
-the machine's byte order again determining the order of the `high' and `low'
-fields.
-
-When 64-bit integers are _not_ supported by the compiler, the `softfloat.h'
-header file defines only two types: `float32' and `float64'. Because
-ISO/ANSI C guarantees at least one built-in integer type of 32 bits,
-the `float32' type is identified with an appropriate integer type. The
-`float64' type is defined as a structure of two 32-bit integers, with the
-machine's byte order determining the order of the fields.
-
-In either case, the types in `softfloat.h' are defined such that if a system
-implements the usual C `float' and `double' types according to the IEC/IEEE
-Standard, then the `float32' and `float64' types should be indistinguishable
-in memory from the native `float' and `double' types. (On the other hand,
-when `float32' or `float64' values are placed in processor registers by
-the compiler, the type of registers used may differ from those used for the
-native `float' and `double' types.)
-
-SoftFloat implements the following arithmetic operations:
-
--- Conversions among all the floating-point formats, and also between
- integers (32-bit and 64-bit) and any of the floating-point formats.
-
--- The usual add, subtract, multiply, divide, and square root operations
- for all floating-point formats.
-
--- For each format, the floating-point remainder operation defined by the
- IEC/IEEE Standard.
-
--- For each floating-point format, a ``round to integer'' operation that
- rounds to the nearest integer value in the same format. (The floating-
- point formats can hold integer values, of course.)
-
--- Comparisons between two values in the same floating-point format.
-
-The only functions required by the IEC/IEEE Standard that are not provided
-are conversions to and from decimal.
-
-
--------------------------------------------------------------------------------
-Rounding Modes
-
-All four rounding modes prescribed by the IEC/IEEE Standard are implemented
-for all operations that require rounding. The rounding mode is selected
-by the global variable `float_rounding_mode'. This variable may be set
-to one of the values `float_round_nearest_even', `float_round_to_zero',
-`float_round_down', or `float_round_up'. The rounding mode is initialized
-to nearest/even.
-
-
--------------------------------------------------------------------------------
-Extended Double-Precision Rounding Precision
-
-For extended double precision (`floatx80') only, the rounding precision
-of the standard arithmetic operations is controlled by the global variable
-`floatx80_rounding_precision'. The operations affected are:
-
- floatx80_add floatx80_sub floatx80_mul floatx80_div floatx80_sqrt
-
-When `floatx80_rounding_precision' is set to its default value of 80, these
-operations are rounded (as usual) to the full precision of the extended
-double-precision format. Setting `floatx80_rounding_precision' to 32
-or to 64 causes the operations listed to be rounded to reduced precision
-equivalent to single precision (`float32') or to double precision
-(`float64'), respectively. When rounding to reduced precision, additional
-bits in the result significand beyond the rounding point are set to zero.
-The consequences of setting `floatx80_rounding_precision' to a value other
-than 32, 64, or 80 is not specified. Operations other than the ones listed
-above are not affected by `floatx80_rounding_precision'.
-
-
--------------------------------------------------------------------------------
-Exceptions and Exception Flags
-
-All five exception flags required by the IEC/IEEE Standard are
-implemented. Each flag is stored as a unique bit in the global variable
-`float_exception_flags'. The positions of the exception flag bits within
-this variable are determined by the bit masks `float_flag_inexact',
-`float_flag_underflow', `float_flag_overflow', `float_flag_divbyzero', and
-`float_flag_invalid'. The exception flags variable is initialized to all 0,
-meaning no exceptions.
-
-An individual exception flag can be cleared with the statement
-
- float_exception_flags &= ~ float_flag_<exception>;
-
-where `<exception>' is the appropriate name. To raise a floating-point
-exception, the SoftFloat function `float_raise' should be used (see below).
-
-In the terminology of the IEC/IEEE Standard, SoftFloat can detect tininess
-for underflow either before or after rounding. The choice is made by
-the global variable `float_detect_tininess', which can be set to either
-`float_tininess_before_rounding' or `float_tininess_after_rounding'.
-Detecting tininess after rounding is better because it results in fewer
-spurious underflow signals. The other option is provided for compatibility
-with some systems. Like most systems, SoftFloat always detects loss of
-accuracy for underflow as an inexact result.
-
-
--------------------------------------------------------------------------------
-Function Details
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Conversion Functions
-
-All conversions among the floating-point formats are supported, as are all
-conversions between a floating-point format and 32-bit and 64-bit signed
-integers. The complete set of conversion functions is:
-
- int32_to_float32 int64_to_float32
- int32_to_float64 int64_to_float32
- int32_to_floatx80 int64_to_floatx80
- int32_to_float128 int64_to_float128
-
- float32_to_int32 float32_to_int64
- float32_to_int32 float64_to_int64
- floatx80_to_int32 floatx80_to_int64
- float128_to_int32 float128_to_int64
-
- float32_to_float64 float32_to_floatx80 float32_to_float128
- float64_to_float32 float64_to_floatx80 float64_to_float128
- floatx80_to_float32 floatx80_to_float64 floatx80_to_float128
- float128_to_float32 float128_to_float64 float128_to_floatx80
-
-Each conversion function takes one operand of the appropriate type and
-returns one result. Conversions from a smaller to a larger floating-point
-format are always exact and so require no rounding. Conversions from 32-bit
-integers to double precision and larger formats are also exact, and likewise
-for conversions from 64-bit integers to extended double and quadruple
-precisions.
-
-Conversions from floating-point to integer raise the invalid exception if
-the source value cannot be rounded to a representable integer of the desired
-size (32 or 64 bits). If the floating-point operand is a NaN, the largest
-positive integer is returned. Otherwise, if the conversion overflows, the
-largest integer with the same sign as the operand is returned.
-
-On conversions to integer, if the floating-point operand is not already an
-integer value, the operand is rounded according to the current rounding
-mode as specified by `float_rounding_mode'. Because C (and perhaps other
-languages) require that conversions to integers be rounded toward zero, the
-following functions are provided for improved speed and convenience:
-
- float32_to_int32_round_to_zero float32_to_int64_round_to_zero
- float64_to_int32_round_to_zero float64_to_int64_round_to_zero
- floatx80_to_int32_round_to_zero floatx80_to_int64_round_to_zero
- float128_to_int32_round_to_zero float128_to_int64_round_to_zero
-
-These variant functions ignore `float_rounding_mode' and always round toward
-zero.
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Standard Arithmetic Functions
-
-The following standard arithmetic functions are provided:
-
- float32_add float32_sub float32_mul float32_div float32_sqrt
- float64_add float64_sub float64_mul float64_div float64_sqrt
- floatx80_add floatx80_sub floatx80_mul floatx80_div floatx80_sqrt
- float128_add float128_sub float128_mul float128_div float128_sqrt
-
-Each function takes two operands, except for `sqrt' which takes only one.
-The operands and result are all of the same type.
-
-Rounding of the extended double-precision (`floatx80') functions is affected
-by the `floatx80_rounding_precision' variable, as explained above in the
-section _Extended_Double-Precision_Rounding_Precision_.
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Remainder Functions
-
-For each format, SoftFloat implements the remainder function according to
-the IEC/IEEE Standard. The remainder functions are:
-
- float32_rem
- float64_rem
- floatx80_rem
- float128_rem
-
-Each remainder function takes two operands. The operands and result are all
-of the same type. Given operands x and y, the remainder functions return
-the value x - n*y, where n is the integer closest to x/y. If x/y is exactly
-halfway between two integers, n is the even integer closest to x/y. The
-remainder functions are always exact and so require no rounding.
-
-Depending on the relative magnitudes of the operands, the remainder
-functions can take considerably longer to execute than the other SoftFloat
-functions. This is inherent in the remainder operation itself and is not a
-flaw in the SoftFloat implementation.
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Round-to-Integer Functions
-
-For each format, SoftFloat implements the round-to-integer function
-specified by the IEC/IEEE Standard. The functions are:
-
- float32_round_to_int
- float64_round_to_int
- floatx80_round_to_int
- float128_round_to_int
-
-Each function takes a single floating-point operand and returns a result of
-the same type. (Note that the result is not an integer type.) The operand
-is rounded to an exact integer according to the current rounding mode, and
-the resulting integer value is returned in the same floating-point format.
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Comparison Functions
-
-The following floating-point comparison functions are provided:
-
- float32_eq float32_le float32_lt
- float64_eq float64_le float64_lt
- floatx80_eq floatx80_le floatx80_lt
- float128_eq float128_le float128_lt
-
-Each function takes two operands of the same type and returns a 1 or 0
-representing either _true_ or _false_. The abbreviation `eq' stands for
-``equal'' (=); `le' stands for ``less than or equal'' (<=); and `lt' stands
-for ``less than'' (<).
-
-The standard greater-than (>), greater-than-or-equal (>=), and not-equal
-(!=) functions are easily obtained using 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 operands reversed; and the greater-than function can be
-obtained from the less-than function in the same way.
-
-The IEC/IEEE Standard specifies that the less-than-or-equal and less-than
-functions raise the invalid exception if either input is any kind of NaN.
-The equal functions, on the other hand, are defined not to raise the invalid
-exception on quiet NaNs. For completeness, SoftFloat provides the following
-additional functions:
-
- float32_eq_signaling float32_le_quiet float32_lt_quiet
- float64_eq_signaling float64_le_quiet float64_lt_quiet
- floatx80_eq_signaling floatx80_le_quiet floatx80_lt_quiet
- float128_eq_signaling float128_le_quiet float128_lt_quiet
-
-The `signaling' equal functions are identical to the standard functions
-except that the invalid exception is raised for any NaN input. Likewise,
-the `quiet' comparison functions are identical to their counterparts except
-that the invalid exception is not raised for quiet NaNs.
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Signaling NaN Test Functions
-
-The following functions test whether a floating-point value is a signaling
-NaN:
-
- float32_is_signaling_nan
- float64_is_signaling_nan
- floatx80_is_signaling_nan
- float128_is_signaling_nan
-
-The functions take one operand and return 1 if the operand is a signaling
-NaN and 0 otherwise.
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Raise-Exception Function
-
-SoftFloat provides a function for raising floating-point exceptions:
-
- float_raise
-
-The function takes a mask indicating the set of exceptions to raise. No
-result is returned. In addition to setting the specified exception flags,
-this function may cause a trap or abort appropriate for the current system.
-
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-
-
--------------------------------------------------------------------------------
-Contact Information
-
-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 `http://
-HTTP.CS.Berkeley.EDU/~jhauser/arithmetic/SoftFloat.html'.
-
-
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