374 lines
16 KiB
Plaintext
374 lines
16 KiB
Plaintext
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$NetBSD: softfloat.txt,v 1.1 2000/06/06 08:15:10 bjh21 Exp $
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$FreeBSD$
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SoftFloat Release 2a General Documentation
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John R. Hauser
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1998 December 13
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-------------------------------------------------------------------------------
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Introduction
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SoftFloat is a software implementation of floating-point that conforms to
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the IEC/IEEE Standard for Binary Floating-Point Arithmetic. As many as four
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formats are supported: single precision, double precision, extended double
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precision, and quadruple precision. All operations required by the standard
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are implemented, except for conversions to and from decimal.
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This document gives information about the types defined and the routines
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implemented by SoftFloat. It does not attempt to define or explain the
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IEC/IEEE Floating-Point Standard. Details about the standard are available
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elsewhere.
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-------------------------------------------------------------------------------
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Limitations
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SoftFloat is written in C and is designed to work with other C code. The
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SoftFloat header files assume an ISO/ANSI-style C compiler. No attempt
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has been made to accomodate compilers that are not ISO-conformant. In
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particular, the distributed header files will not be acceptable to any
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compiler that does not recognize function prototypes.
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Support for the extended double-precision and quadruple-precision formats
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depends on a C compiler that implements 64-bit integer arithmetic. If the
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largest integer format supported by the C compiler is 32 bits, SoftFloat is
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limited to only single and double precisions. When that is the case, all
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references in this document to the extended double precision, quadruple
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precision, and 64-bit integers should be ignored.
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-------------------------------------------------------------------------------
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Contents
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Introduction
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Limitations
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Contents
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Legal Notice
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Types and Functions
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Rounding Modes
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Extended Double-Precision Rounding Precision
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Exceptions and Exception Flags
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Function Details
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Conversion Functions
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Standard Arithmetic Functions
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Remainder Functions
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Round-to-Integer Functions
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Comparison Functions
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Signaling NaN Test Functions
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Raise-Exception Function
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Contact Information
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-------------------------------------------------------------------------------
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Legal Notice
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SoftFloat was written by John R. Hauser. This work was made possible in
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part by the International Computer Science Institute, located at Suite 600,
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1947 Center Street, Berkeley, California 94704. Funding was partially
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provided by the National Science Foundation under grant MIP-9311980. The
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original version of this code was written as part of a project to build
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a fixed-point vector processor in collaboration with the University of
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California at Berkeley, overseen by Profs. Nelson Morgan and John Wawrzynek.
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
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has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
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TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
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PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
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AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
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-------------------------------------------------------------------------------
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Types and Functions
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When 64-bit integers are supported by the compiler, the `softfloat.h' header
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file defines four types: `float32' (single precision), `float64' (double
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precision), `floatx80' (extended double precision), and `float128'
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(quadruple precision). The `float32' and `float64' types are defined in
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terms of 32-bit and 64-bit integer types, respectively, while the `float128'
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type is defined as a structure of two 64-bit integers, taking into account
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the byte order of the particular machine being used. The `floatx80' type
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is defined as a structure containing one 16-bit and one 64-bit integer, with
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the machine's byte order again determining the order of the `high' and `low'
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fields.
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When 64-bit integers are _not_ supported by the compiler, the `softfloat.h'
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header file defines only two types: `float32' and `float64'. Because
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ISO/ANSI C guarantees at least one built-in integer type of 32 bits,
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the `float32' type is identified with an appropriate integer type. The
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`float64' type is defined as a structure of two 32-bit integers, with the
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machine's byte order determining the order of the fields.
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In either case, the types in `softfloat.h' are defined such that if a system
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implements the usual C `float' and `double' types according to the IEC/IEEE
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Standard, then the `float32' and `float64' types should be indistinguishable
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in memory from the native `float' and `double' types. (On the other hand,
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when `float32' or `float64' values are placed in processor registers by
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the compiler, the type of registers used may differ from those used for the
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native `float' and `double' types.)
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SoftFloat implements the following arithmetic operations:
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-- Conversions among all the floating-point formats, and also between
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integers (32-bit and 64-bit) and any of the floating-point formats.
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-- The usual add, subtract, multiply, divide, and square root operations
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for all floating-point formats.
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-- For each format, the floating-point remainder operation defined by the
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IEC/IEEE Standard.
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-- For each floating-point format, a ``round to integer'' operation that
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rounds to the nearest integer value in the same format. (The floating-
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point formats can hold integer values, of course.)
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-- Comparisons between two values in the same floating-point format.
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The only functions required by the IEC/IEEE Standard that are not provided
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are conversions to and from decimal.
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-------------------------------------------------------------------------------
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Rounding Modes
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All four rounding modes prescribed by the IEC/IEEE Standard are implemented
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for all operations that require rounding. The rounding mode is selected
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by the global variable `float_rounding_mode'. This variable may be set
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to one of the values `float_round_nearest_even', `float_round_to_zero',
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`float_round_down', or `float_round_up'. The rounding mode is initialized
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to nearest/even.
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-------------------------------------------------------------------------------
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Extended Double-Precision Rounding Precision
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For extended double precision (`floatx80') only, the rounding precision
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of the standard arithmetic operations is controlled by the global variable
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`floatx80_rounding_precision'. The operations affected are:
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floatx80_add floatx80_sub floatx80_mul floatx80_div floatx80_sqrt
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When `floatx80_rounding_precision' is set to its default value of 80, these
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operations are rounded (as usual) to the full precision of the extended
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double-precision format. Setting `floatx80_rounding_precision' to 32
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or to 64 causes the operations listed to be rounded to reduced precision
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equivalent to single precision (`float32') or to double precision
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(`float64'), respectively. When rounding to reduced precision, additional
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bits in the result significand beyond the rounding point are set to zero.
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The consequences of setting `floatx80_rounding_precision' to a value other
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than 32, 64, or 80 is not specified. Operations other than the ones listed
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above are not affected by `floatx80_rounding_precision'.
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-------------------------------------------------------------------------------
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Exceptions and Exception Flags
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All five exception flags required by the IEC/IEEE Standard are
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implemented. Each flag is stored as a unique bit in the global variable
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`float_exception_flags'. The positions of the exception flag bits within
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this variable are determined by the bit masks `float_flag_inexact',
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`float_flag_underflow', `float_flag_overflow', `float_flag_divbyzero', and
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`float_flag_invalid'. The exception flags variable is initialized to all 0,
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meaning no exceptions.
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An individual exception flag can be cleared with the statement
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float_exception_flags &= ~ float_flag_<exception>;
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where `<exception>' is the appropriate name. To raise a floating-point
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exception, the SoftFloat function `float_raise' should be used (see below).
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In the terminology of the IEC/IEEE Standard, SoftFloat can detect tininess
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for underflow either before or after rounding. The choice is made by
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the global variable `float_detect_tininess', which can be set to either
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`float_tininess_before_rounding' or `float_tininess_after_rounding'.
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Detecting tininess after rounding is better because it results in fewer
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spurious underflow signals. The other option is provided for compatibility
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with some systems. Like most systems, SoftFloat always detects loss of
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accuracy for underflow as an inexact result.
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-------------------------------------------------------------------------------
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Function Details
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Conversion Functions
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All conversions among the floating-point formats are supported, as are all
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conversions between a floating-point format and 32-bit and 64-bit signed
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integers. The complete set of conversion functions is:
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int32_to_float32 int64_to_float32
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int32_to_float64 int64_to_float32
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int32_to_floatx80 int64_to_floatx80
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int32_to_float128 int64_to_float128
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float32_to_int32 float32_to_int64
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float32_to_int32 float64_to_int64
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floatx80_to_int32 floatx80_to_int64
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float128_to_int32 float128_to_int64
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float32_to_float64 float32_to_floatx80 float32_to_float128
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float64_to_float32 float64_to_floatx80 float64_to_float128
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floatx80_to_float32 floatx80_to_float64 floatx80_to_float128
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float128_to_float32 float128_to_float64 float128_to_floatx80
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Each conversion function takes one operand of the appropriate type and
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returns one result. Conversions from a smaller to a larger floating-point
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format are always exact and so require no rounding. Conversions from 32-bit
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integers to double precision and larger formats are also exact, and likewise
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for conversions from 64-bit integers to extended double and quadruple
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precisions.
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Conversions from floating-point to integer raise the invalid exception if
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the source value cannot be rounded to a representable integer of the desired
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size (32 or 64 bits). If the floating-point operand is a NaN, the largest
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positive integer is returned. Otherwise, if the conversion overflows, the
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largest integer with the same sign as the operand is returned.
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On conversions to integer, if the floating-point operand is not already an
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integer value, the operand is rounded according to the current rounding
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mode as specified by `float_rounding_mode'. Because C (and perhaps other
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languages) require that conversions to integers be rounded toward zero, the
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following functions are provided for improved speed and convenience:
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float32_to_int32_round_to_zero float32_to_int64_round_to_zero
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float64_to_int32_round_to_zero float64_to_int64_round_to_zero
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floatx80_to_int32_round_to_zero floatx80_to_int64_round_to_zero
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float128_to_int32_round_to_zero float128_to_int64_round_to_zero
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These variant functions ignore `float_rounding_mode' and always round toward
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zero.
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Standard Arithmetic Functions
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The following standard arithmetic functions are provided:
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float32_add float32_sub float32_mul float32_div float32_sqrt
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float64_add float64_sub float64_mul float64_div float64_sqrt
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floatx80_add floatx80_sub floatx80_mul floatx80_div floatx80_sqrt
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float128_add float128_sub float128_mul float128_div float128_sqrt
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Each function takes two operands, except for `sqrt' which takes only one.
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The operands and result are all of the same type.
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Rounding of the extended double-precision (`floatx80') functions is affected
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by the `floatx80_rounding_precision' variable, as explained above in the
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section _Extended_Double-Precision_Rounding_Precision_.
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Remainder Functions
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For each format, SoftFloat implements the remainder function according to
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the IEC/IEEE Standard. The remainder functions are:
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float32_rem
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float64_rem
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floatx80_rem
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float128_rem
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Each remainder function takes two operands. The operands and result are all
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of the same type. Given operands x and y, the remainder functions return
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the value x - n*y, where n is the integer closest to x/y. If x/y is exactly
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halfway between two integers, n is the even integer closest to x/y. The
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remainder functions are always exact and so require no rounding.
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Depending on the relative magnitudes of the operands, the remainder
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functions can take considerably longer to execute than the other SoftFloat
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functions. This is inherent in the remainder operation itself and is not a
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flaw in the SoftFloat implementation.
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Round-to-Integer Functions
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For each format, SoftFloat implements the round-to-integer function
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specified by the IEC/IEEE Standard. The functions are:
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float32_round_to_int
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float64_round_to_int
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floatx80_round_to_int
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float128_round_to_int
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Each function takes a single floating-point operand and returns a result of
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the same type. (Note that the result is not an integer type.) The operand
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is rounded to an exact integer according to the current rounding mode, and
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the resulting integer value is returned in the same floating-point format.
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Comparison Functions
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The following floating-point comparison functions are provided:
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float32_eq float32_le float32_lt
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float64_eq float64_le float64_lt
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floatx80_eq floatx80_le floatx80_lt
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float128_eq float128_le float128_lt
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Each function takes two operands of the same type and returns a 1 or 0
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representing either _true_ or _false_. The abbreviation `eq' stands for
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``equal'' (=); `le' stands for ``less than or equal'' (<=); and `lt' stands
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for ``less than'' (<).
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The standard greater-than (>), greater-than-or-equal (>=), and not-equal
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(!=) functions are easily obtained using the functions provided. The
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not-equal function is just the logical complement of the equal function.
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The greater-than-or-equal function is identical to the less-than-or-equal
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function with the operands reversed; and the greater-than function can be
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obtained from the less-than function in the same way.
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The IEC/IEEE Standard specifies that the less-than-or-equal and less-than
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functions raise the invalid exception if either input is any kind of NaN.
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The equal functions, on the other hand, are defined not to raise the invalid
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exception on quiet NaNs. For completeness, SoftFloat provides the following
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additional functions:
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float32_eq_signaling float32_le_quiet float32_lt_quiet
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float64_eq_signaling float64_le_quiet float64_lt_quiet
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floatx80_eq_signaling floatx80_le_quiet floatx80_lt_quiet
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float128_eq_signaling float128_le_quiet float128_lt_quiet
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The `signaling' equal functions are identical to the standard functions
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except that the invalid exception is raised for any NaN input. Likewise,
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the `quiet' comparison functions are identical to their counterparts except
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that the invalid exception is not raised for quiet NaNs.
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Signaling NaN Test Functions
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The following functions test whether a floating-point value is a signaling
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NaN:
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|
||
|
|
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'.
|
||
|
|
|
||
|
|
|