The decNumber Library, version 3.68
Copyright (c) IBM Corporation, 2010. All rights reserved. ©
| 23 Jan 2010 |
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The decFloats modules are decSingle, decDouble, and decQuad.
These are based on the 32-bit, 64-bit, and 128-bit decimal types in
the IEEE 754 Standard for Floating Point Arithmetic.
In contrast to the arbitrary-precision decNumber module, these
modules work directly from the decimal-encoded formats designed by
the IEEE 754 committee, which are also now implemented in IBM System z
(z9 and z10) and IBM System p (POWER6) processors, and in SAP NetWeaver 7.1.[1]
Conversions to and from the decNumber internal format are not needed
(typically the numbers are represented internally in
‘unpacked’ BCD or in a base of some other power of ten), and no
memory allocation is necessary, so these modules are much faster than
using decNumber for implementing the types.
Like the decNumber module, the decFloats modules
- need only 32-bit integer support; 64-bit integers are not
required and binary floating-point is not used
- support both big-endian and little-endian encodings and platforms
- support both ASCII/UTF8 and EBCDIC strings
- are reentrant and use only aligned integers and strict aliasing
- use only ANSI C.
The modules should therefore be usable on any platform
with an ANSI C compiler that supports 32-bit integers.
The decFloats modules define the data structures and a large set of
functions for working directly with the same compressed formats as
decimal32, decimal64, and decimal128. The names are different to
allow them to be used stand-alone or with the decNumber module, as
illustrated in Examples 7 and 8 in the User’s
Guide.
These three modules all share many of the same functions (working on
the different sizes of the formats). The decQuad module has all the
same functions as decDouble except for two functions which would
convert to or from a wider format. The decSingle module is a limited
(‘storage’) format which has a only a few conversion and
miscellaneous functions; it is intended that any computation be
carried out in a wider format.
The remainder of this section therefore describes only the decDouble
format – in the list of functions, assume that there is a
corresponding decQuad format function unless stated and assume there
is not a corresponding decSingle format function unless
stated.
In this implementation each format is represented as an array of
unsigned bytes.
There is therefore just one field in the decDouble structure:
- bytes
-
The bytes field represents the eight bytes of a decDouble
number, using Densely Packed Decimal encoding for the coefficient.
As of decNumber 3.56 the structure has been changed to a union of the
bytes array with arrays of larger integers; see the header
file for each type for details.[2]
The storage of a number in the bytes array is assumed to follow
the byte ordering (‘endianness’) of the computing platform
(if big-endian, then bytes[0] contains the sign bit of the
format). The code in these modules requires that
the DECLITEND tuning parameter be set to
match the endianness of the platform.
The decSingle and decDouble modules both require that the next wider
format be included in a program compilation (so that conversion to
and from that wider format can be effected), hence the decQuad module
is always needed.[3]
It, therefore, contains the constant lookup tables from the
the decDPD.h header file which are shared by all three
modules. These tables are automatically generated and should not
need altering.
Most of the code for these modules is included from the shared source
files decCommon.c and decBasic.c. The former contains
the functions available in all three modules[4]
and the latter the functions available only in decDouble and decQuad.
Definitions
The decDouble.h header file defines the decDouble data structure
described above.
It includes the decContext.h and and decQuad.h header
files, which are both required for use.[5]
If more than one of the three decFloats formats are used in
a program, it is only necessary to include the smaller or smallest.
The decDouble.h header file also contains:
- Constants defining aspects of decDouble numbers, including the
maximum precision, the minimum and maximum (adjusted) exponent
supported, the bias applied to the exponent, the length of the number in
bytes, and the maximum number of characters in the string form of the
number (including terminator)
-
Definitions of the public functions in the decDouble module
-
Macros defining conversions to and from the decNumber format. These
are macros in order to avoid a compile-time dependency on the decNumber
module; they use decimal64 as a proxy, and their usage is shown in
Example 8 in the User’s Guide.
Functions
The decDouble.c source file contains the public functions
defined in the header file. These comprise conversions to and from
strings and other formats, arithmetic and logical operations, and
utilities.
The functions are described briefly, below. More details of the
operation of each function can be found in the description of the
corresponding function in the decNumber module and details of the
underlying model and arithmetic can be found in
the General Decimal Arithmetic Specification.[6]
In the descriptions below, many parameters are defined as one of the
following:
- x, y, z
- (const decDouble *) decimal input arguments to a function
- r
- (decDouble *) a decimal result argument to a function
(which may be the same as an input argument); unless stated otherwise
this is also the return value from the function, and the result will be
canonical
- set
- (decContext *) the context for a function. Only two
fields of the context structure are used: round (the
rounding mode) and status (the bits in which are used to
indicate any error, etc.).
Note that the trap field in the context is not used; the
decDouble functions do not check for traps after every operation
to avoid the overhead that would incur.
The decContextSetStatus function can be
used to explicitly test status to trap.
Note also that the only informational flag set by decNumber
is DEC_Inexact; the others are never set by the
decFloats module in order to improve performance and also to avoid
the need for passing a context to many functions.[7]
In the following list, every function has corresponding decQuad
format function (for example, decQuadAbs(r, x, set)) unless
stated, and does not have a corresponding decSingle format
function unless stated.
Returns the absolute value of x.
This has the same effect as decDoublePlus unless x is negative,
in which case it has the same effect as decDoubleMinus. The effect
is also the same as decDoubleCopyAbs except that NaNs are handled
normally (the sign of a NaN is not affected, and an sNaN will
set DEC_Invalid_operation) and the result
will be canonical.
Adds x and y and places the result in r.
Carries out the digit-wise logical And of x and y and
places the result in r.
The operands must be zero or positive (sign=0), an integer (finite
with exponent=0) and comprise only zeros and/or ones; if
not, DEC_Invalid_operation is set.
This copies x to r, ensuring that the encoding of
r is canonical.
This returns the class (enum decClass) of the argument
x.
This returns a description of the class of the argument x as a
string (const char *).
Compares x and y numerically and places the result in
r.
The result may be –1, 0, 1, or NaN (unordered); –1
indicates that x is less than y, 0 indicates that
they are numerically equal, and 1 indicates that x is greater
than y.
NaN is returned only if x or y is a NaN.
The same as decDoubleCompare, except that a quiet NaN argument is
treated like a signaling NaN
(causes DEC_Invalid_operation to be set).
Compares x and y using the IEEE 754 total ordering (which
takes into account the exponent) and places the result in
r. No status is set (a signaling NaN is ordered between
Infinity and NaN).
The result will be –1, 0, or 1.
The same as decDoubleCompareTotal except that the absolute values of
the two arguments are used (as though modified by decDoubleCopyAbs).
Copies x to r quietly (no status is set).
This is a bit-wise operation and so the result might not be canonical.
Copies x to r quietly and sets the sign of r to
0 (no status is set).
This is a bit-wise operation and so the result might not be canonical.
Copies x to r quietly and inverts the sign of r
(no status is set).
This is a bit-wise operation and so the result might not be canonical.
Copies x to r quietly with the sign of r
set to the sign of y (no status is set).
This is a bit-wise operation and so the result might not be canonical.
Returns the number of significant digits in x as an unsigned
32-bit integer (uint32_t).
If x is a zero or is infinite, 1 is returned. If x is a NaN
then the number of digits in the payload is returned.
Divides x by y and places the result in r.
Divides x by y and places the integer part of the
result (rounded towards zero) in r with exponent=0.
If the result would not fit in r (because it would have
more than DECDOUBLE_Pmax digits)
then DEC_Division_impossible is set.
Calculates the fused multiply-add x × y +
z and places the result in r. The multiply is carried
out first and is exact, so this operation has only the one, final,
rounding.
Sets r from an exponent exp (which may indicate a NaN or
infinity), a BCD array bcd, and a sign.
exp (int32_t) is an in-range unbiased
exponent or a special value in the form returned by
decDoubleGetExponent (listed in decQuad.h).
bcd (const uint8_t *) is an array
of DECDOUBLE_Pmax elements, one digit in each byte
(BCD8 encoding); the first (most significant) digit is ignored if the
result will be a NaN; all are ignored if the result is infinite. All
bytes must be in the range 0–9.
sign (int32_t) is an integer which must
be DECFLOAT_Sign to set the sign bit of r to
1, or 0 to set it to 0.
For speed, the arguments are not checked; no status is set by this
function. The content of r is undefined if the arguments are
invalid or out of range (that is, could not be produced by
decDoubleToBCD).
(This function is also available in the decSingle module.)
Sets r from the signed 32-bit integer i
(int32_t).
The result is exact; no error is possible.
This function is implemented as a macro and sets r from a
decNumber, dn, using a decimal64 as a proxy as illustrated in
Example 8 in the User’s Guide.
To use this macro, the decimal64.h header file must be
included (see the text following the example for more details about
compilation).
(This function is also available in the decSingle module.)
Sets r from an exponent exp (which may indicate a
special value) and a packed BCD array, pack.
exp (int32_t) is an in-range unbiased
exponent or a special value in the form returned by
decDoubleGetExponent (listed in decQuad.h).
pack (const uint8_t *) is an array
of DECDOUBLE_Pmax packed decimal digits
(one digit per four-bit nibble) followed by a sign nibble, and (for
decDouble and decQuad only) prefixed with an extra pad nibble (which is
ignored); the sign nibble must be any of the six sign codes listed
in decQuad.h and described for the decPacked
module, and digit nibbles must be in the range 0–9.
Like the decDoubleFromBCD function, the first nibble of
pack (after the pad nibble, if any) is ignored if the result
will be a NaN, and all are ignored if the result is infinite.
For speed, the arguments are not checked; no status is set by this
function. The content of r is undefined if the
arguments are invalid or out of range (that is, could not be produced
by decNumberToPacked, except that all six sign codes are permitted).
(This function is also available in the decSingle module.)
Sets r from an exponent exp (which may indicate a
special value) and a packed BCD array, pack, with the input
values fully checked.
exp (int32_t) must be an in-range unbiased
exponent or a special value in the form returned by
decDoubleGetExponent (listed in decQuad.h).
pack (const uint8_t *) is an array
of DECDOUBLE_Pmax packed decimal digits
(one digit per four-bit nibble) followed by a sign nibble, and (for
decDouble and decQuad only) prefixed with an extra pad nibble (which
must be zero);
the sign nibble must be one of the six sign codes listed
in decQuad.h and described for the decPacked
module, and digit nibbles must be in the range 0–9.
The first nibble of pack (after the pad nibble, if any) must
be zero if the result will be a NaN, and all digit nibbles must be
zero if the result is infinite.
No status is set by this function. NULL is returned instead
of r if an argument is invalid or out of range (that is, could
not be produced by decNumberToPacked, except that all six sign codes
are permitted).
(This function is also available in the decSingle module.)
Sets r from a character string, string (const char
*).
The length of the coefficient and the size of the exponent are
checked by this routine, so rounding will be applied if necessary,
and this may set
status flags (underflow,
overflow) will be reported, or rounding applied, as necessary.
There is no limit to the coefficient length for finite inputs;
NaN payloads must be integers with no more
than DECDOUBLE_Pmax–1 digits.
Exponents may have up to nine significant digits.
The syntax of the string is fully checked; if it is not valid,
the result will be a quiet NaN and an error flag will be set.
(This function is also available in the decSingle module.)
Sets r from the unsigned 32-bit integer u
(uint32_t).
The result is exact and no error is possible.
Sets r from an instance, dq, of the next-wider
format (const decQuad *).
This narrowing function can cause rounding, overflow, etc., but not
Invalid operation (sNaNs are copied and do not signal).
(This function is also available in the decSingle module, but
is not available in the decQuad module.)
Extracts the coefficient of x as a BCD integer into the array
bcd (uint8_t *) and returns the sign as a
signed 32-bit integer (int32_t). The returned value
will be DECFLOAT_Sign if x has sign=1 or
otherwise will be 0.
The digits of the coefficent are written, one digit per byte,
into DECDOUBLE_Pmax elements of the bcd
array.
If x is a NaN the first byte will be zero (the remainder will
be the payload), and if it is infinite then all of bcd will be
zero.
(This function is also available in the decSingle module.)
Returns the exponent of x as a 32-bit integer
(int32_t).
If x is infinite or is a NaN (a special value) the first seven
bits of the decDouble are returned, padded with 25 zero bits on the
right and with the most significant (sign) bit set to 0.
For example, –sNaN would return 0x7e000000
(DECFLOAT_sNaN).
The possible return values for infinities and NaNs are listed
in decQuad.h.
(This function is also available in the decSingle module.)
Carries out the digit-wise logical inversion of x and
places the result in r.
The operand must be zero or positive (sign=0), an integer (finite
with exponent=0) and comprise only zeros and/or ones; if
not, DEC_Invalid_operation is set.
Returns an unsigned integer (uint32_t) which will
be 1 if the encoding of x is canonical, or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is neither infinite nor a NaN, or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if the encoding of x is an infinity, or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is finite and has exponent=0, or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is a valid argument for logical operations (that is,
x is zero or positive (sign=0), an integer (finite
with exponent=0) and comprises only zeros and/or ones), or 0
otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is a NaN (quiet or signaling), or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is less than zero and not a NaN, or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is a normal number (that is, is finite, non-zero, and
not subnormal), or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is greater than zero and not a NaN, or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is a signaling NaN, or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is a signaling NaN, or 0 otherwise.
(This is an alternative spelling of decDoubleIsSignaling.)
Returns an unsigned integer (uint32_t) which will
be 1 if x has sign=1, or 0 otherwise. Note that zeros and
NaNs may have sign=1.
Returns an unsigned integer (uint32_t) which will
be 1 if x is subnormal (that is, finite, non-zero, and with
magnitude less than 10emin), or 0 otherwise.
Returns an unsigned integer (uint32_t) which will
be 1 if x is a zero, or 0 otherwise.
Returns the adjusted exponent of x, according to IEEE 754 rules.
That is, the exponent returned is calculated as if the decimal point
followed the first significant digit (so, for example, if x
were 123 then the result would be 2).
If x is infinite, the result is +Infinity.
If x is a zero, the result is –Infinity,
and the DEC_Division_by_zero
flag is set.
If x is less than zero, the absolute value of x is
used.
If x=1, the result is 0.
NaNs are handled (propagated) as for arithmetic operations.
If both arguments are numeric (not NaNs) this returns the larger of
x and y (compared using decDoubleCompareTotal, to give
a well-defined result).
If either (but not both of) x or y is a quiet NaN then
the other argument is the result; otherwise NaNs are handled as for
arithmetic operations.
The same as decDoubleMax except that the absolute values of
the two arguments are used (as though modified by decDoubleCopyAbs).
If both arguments are numeric (not NaNs) this returns the smaller of
x and y (compared using decDoubleCompareTotal, to give
a well-defined result).
If either (but not both of) x or y is a quiet NaN then
the other argument is the result; otherwise NaNs are handled as for
arithmetic operations.
The same as decDoubleMin except that the absolute values of
the two arguments are used (as though modified by decDoubleCopyAbs).
This has the same effect as 0–x where the exponent of
the zero is the same as that of x (if x is finite).
The effect is also the same as decFloatCopyNegate except that NaNs
are handled as for arithmetic operations (the sign of a NaN is not
affected, and an sNaN will signal), the result is canonical, and a
zero result has sign=0.
Multiplies x by y and places the result in r.
Returns the ‘next’ decDouble to x in the direction of
–Infinity according to IEEE 754 rules for nextDown.
The only status possible is DEC_Invalid_operation
(from an sNaN).
Returns the ‘next’ decDouble to x in the direction of
+Infinity according to IEEE 754 rules for nextUp.
The only status possible is DEC_Invalid_operation
(from an sNaN).
Returns the ‘next’ decDouble to x in the direction of
y according to proposed IEEE 754 rules for nextAfter.[8]
If x=y the result is decDoubleCopySign(r, x, y).
If either operand is a NaN the result is as for arithmetic
operations.
Otherwise (the operands are numeric and different) the result of
adding (or subtracting) an infinitesimal positive amount to x
and rounding towards +Infinity (or –Infinity) is returned,
depending on whether y is larger (or smaller) than x.
The addition will set flags, except that if the result is normal (finite,
non-zero, and not subnormal) no flags are set.
Carries out the digit-wise logical inclusive Or of x and
y and places the result in r.
The operands must be zero or positive (sign=0), an integer (finite
with exponent=0) and comprise only zeros and/or ones; if
not, DEC_Invalid_operation is set.
This has the same effect as 0+x where the exponent of
the zero is the same as that of x (if x is finite).
The effect is also the same as decFloatCopy except that NaNs
are handled as for arithmetic operations (the sign of a NaN is not
affected, and an sNaN will signal), the result is canonical, and a
zero result has sign=0.
Returns x set to have the same quantum as y, if
possible (that is, numerically the same value but rounded or padded
if necessary to have the same exponent as y, for example to
round a monetary quantity to cents). More details and an example are
given with the decNumberQuantize function.
Returns an unsigned integer (uint32_t) set to the
base used for arithmetic in this module (always ten).
(This function is also available in the decSingle module.)
Returns a copy of x with its coefficient reduced to its
shortest possible form without changing the value of the result.
This removes all possible trailing zeros from the coefficient
(some may remain when the number is very close to the most positive
or most negative number).
Infinities and NaNs are unchanged and no status is set unless
x is an sNaN.
If x is a zero the result exponent is 0.
Integer-divides x by y and places the remainder from the
division in r.
That is, if the same x and y
were given to the decDoubleDivideInteger and
decDoubleRemainder functions, resulting in int
and rem respectively, then the identity
x = (int × y) + rem
holds.
Note that, as for decDoubleDivideInteger, it must be possible to express
the intermediate result (int) as an integer. That is, it must
have no more than DECDOUBLE_Pmax digits. If it has
too many then DEC_Division_impossible
is raised.
This is the same as decDoubleRemainder except that the nearest
integer (or the nearest even integer if the remainder is equidistant
from two) is used for int instead of the result from
decDoubleDivideInteger. Again, that integer must fit.
The result is a copy of x with the digits of the coefficient
rotated to the left (if y is positive) or to the right (if
y is negative) without adjusting the exponent or the sign of
x.
y is the count of positions to rotate and must be a finite
integer (with exponent=0) in the range
–DECDOUBLE_Pmax through
+DECDOUBLE_Pmax.
NaNs are propagated as usual.
If x is infinite the result is Infinity of the same sign.
No status is set unless y is invalid or an operand is an sNaN.
Returns an unsigned integer (uint32_t) which will
be 1 if the operands have the same exponent or are both NaNs (quiet
or signaling) or both infinite. In all other cases, 0 is
returned. No error or status is possible.
This calculates x × 10y and places
the result in r.
y must be an integer (finite with exponent=0) in the
range ±2 × (DECDOUBLE_Pmax
+ DECDOUBLE_Emax), typically resulting from
decDoubleLogB.
Underflow and overflow might occur. NaNs propagate as usual.
Sets the coefficient of r from a BCD integer in the array
bcd (uint8_t *) and the signed 32-bit
integer (int32_t) sign.
bcd must have DECDOUBLE_Pmax elements in the
range 0–9, and sign must be DECFLOAT_Sign to
set the sign bit of r to 1, or 0 to set it to 0.
If r is a NaN the first byte of bcd will be ignored
(the remainder will be the payload), and if it is infinite then all
of bcd will be ignored (the coefficient will become zero).
For speed, the arguments are not checked; no status is set by this
function. The result is undefined if the arguments are invalid or out
of range (that is, could not have been produced by decDoubleGetCoefficient).
(This function is also available in the decSingle module.)
Sets the exponent of r from the signed 32-bit integer
(int32_t) exp. exp is either an
in-range exponent or a special code as returned by
decDoubleGetExponent. If r becomes infinite then its
coefficient is set to zero, if it becomes NaN then the first digit of
the coefficient is lost,[9]
otherwise the coefficient is unchanged.
For speed, exp is not checked; however, underflow or overflow
can result. The result is undefined if exp is not a value that
could have been produced by decDoubleGetExponent.
(This function is also available in the decSingle module.)
The result is a copy of x with the digits of the coefficient
shifted to the left (if y is positive) or to the right (if
y is negative) without adjusting the exponent or the sign of
x. Any digits ‘shifted in’ from the left or from the
right will be 0.
y is the count of positions to shift and must be a finite
integer (with exponent=0) in the range
–DECDOUBLE_Pmax through
+DECDOUBLE_Pmax.
NaNs are propagated as usual.
If x is infinite the result is Infinity of the same sign.
No status is set unless y is invalid or an operand is an sNaN.
This function uses printf to display a readable rendering of
x, showing both the encoding (in hexadecimal) and the value,
and returns nothing (void).
The string tag (const char *) is included in the
display and may be used as an identifier for the displayed data.
This function is intended as a debug aid. It is not a programming
interface – the format of the displayed data may change from
release to release.
(This function is also available in the decSingle module.)
Subtracts y from x and places the result in r.
Converts x into an exponent exp (int32_t *)
and a BCD array bcd (uint8_t *).
exp is set to the value that would be returned by
decDoubleGetExponent(x), and bcd and the returned integer
(int32_t) are as from decDoubleGetCoefficient(x,
bcd).
(This function is also available in the decSingle module.)
The same as decDoubleToString(x, string) except that if exponential
notation is used the exponent will be a multiple of 3 (‘engineering
notation’).
(This function is also available in the decSingle module.)
Returns a signed 32-bit integer (int32_t) which is the
value of x, rounded to an integer if necessary using the
explicit rounding mode round (enum rounding) instead of
the rounding mode in set.
If x is infinite, is a NaN, or after rounding is outside the
range of the result, then DEC_Invalid_operation
is set.
The DEC_Inexact flag is not set by this function,
even if rounding ocurred.
The same as decDoubleToInt32 except that if rounding removes
non-zero digits then the DEC_Inexact flag is set.
Returns the value of x, rounded to an integral value
using the rounding mode in set.
If x is infinite, Infinity of the same sign is returned.
If x is a NaN, the result is as for other arithmetic
operations. If rounding removes non-zero digits then
the DEC_Inexact flag is set.
Returns the value of x, rounded to an integral value
using the explicit rounding mode round (enum rounding)
instead of the rounding mode in set.
If x is infinite, Infinity of the same sign is returned.
If x is a NaN, the result is as for other arithmetic
operations.
The DEC_Inexact flag is not set by this function,
even if rounding ocurred.
This function is implemented as a macro and sets a decNumber,
dn, from x using a decimal64 as a proxy as illustrated
in Example 8 in the User’s Guide. The decNumber
must have sufficient space for the digits in x.
To use this macro, the decimal64.h header file must be
included (see the text following the example for more details).
A pointer to dn is returned (decNumber *).
(This function is also available in the decSingle module.)
Converts x into an exponent exp (int32_t *)
and a Packed BCD array pack (uint8_t *).
exp is set to the value that would be returned by
decDoubleGetExponent(x).
pack receives DECDOUBLE_Pmax packed decimal
digits (one digit per four-bit nibble) followed by a sign nibble and
prefixed (for decDouble and decQuad only) with an extra pad nibble
(which is 0).
The sign nibble will be DECPMINUS if x has sign=1
or DECPPLUS otherwise.
The digit nibbles will be in the range 0–9.
A signed 32-bit integer (int32_t) is returned; it
will be DECFLOAT_Sign if x has sign=1 or
otherwise will be 0.
(This function is also available in the decSingle module.)
Converts x to a zero-terminated string in the character array
string (char *) and returns string.
string must have at least DECDOUBLE_String
elements (this count includes the terminator character).
Finite numbers will be converted to a string with exponential
notation if the exponent is positive or if the magnitude of x
is less than 1 and would require more than five zeros between the
decimal point and the first significant digit.
Note that strings which are not simply numbers (one of Infinity,
–Infinity, NaN, or sNaN) are possible. A
NaN string may have a leading – sign and/or following payload
digits. No digits follow the NaN string if the payload is 0.
(This function is also available in the decSingle module.)
Returns an unsigned 32-bit integer (uint32_t) which is the
value of x, rounded to an integer if necessary using the
explicit rounding mode round (enum rounding) instead of
the rounding mode in set.
If x is infinite, is a NaN, or after rounding is outside the
range of the result, then DEC_Invalid_operation
is set.
The DEC_Inexact flag is not set by this function,
even if rounding ocurred.
Note that –0 converts to 0 and is valid, but all negative
numbers are not valid.
The same as decDoubleToUInt32 except that if rounding removes
non-zero digits then the DEC_Inexact flag is set.
Converts x into a structure, dq, of the next-wider
format (decQuad *) and returns dq.
Widening is always exact; no status is set (sNaNs are copied and
do not signal). The result will be canonical if x is
canonical, but otherwise might not be.
(This function is also available in the decSingle module, but
is not available in the decQuad module.)
Returns a pointer to a character string (const char *) which
includes the name and the version of the decNumber package.
(This function is also available in the decSingle module.)
Carries out the digit-wise logical exclusive Or of x and y and
places the result in r.
The operands must be zero or positive (sign=0), an integer (finite
with exponent=0) and comprise only zeros and/or ones; if
not, DEC_Invalid_operation is set.
Sets r to the unsigned integer zero (that is, with
the coefficient, the exponent, and the sign all set to 0).
(This function is also available in the decSingle module.)
Footnotes:
| [1] |
IBM, the IBM logo, System p, System z, and POWER6 are trademarks of
International Business Machines Corporation in the United States,
other countries, or both.
SAP and SAP NetWeaver are trademarks of SAP AG, in Germany, other
countries, or both.
|
| [2] |
See
http://speleotrove.com/decimal/DPDecimal.html
for a summary of Densely Packed Decimal encoding.
|
| [3] |
This requirement is different from the decimal32, decimal64, and
decimal128 modules because they can convert to wider or narrower
formats using the decNumber format as an intermediate step.
|
| [4] |
Except that the widening and narrowing functions are not used by
decQuad.
|
| [5] |
The decSingle.h header file also includes decDouble.h,
but the decQuad.h header file only includes decContext.h.
|
| [6] |
See
http://speleotrove.com/decimal/#arithmetic
for details.
|
| [7] |
The DEC_Subnormal flag is particularly
expensive to maintain.
|
| [8] |
The nextAfter operation was dropped from the proposed standard during
the ballot process.
|
| [9] |
A NaN payload has one fewer digit than the coefficient of a finite
number.
|
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