path: root/contrib/bc/manuals/bcl.3

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.TH "BCL" "3" "June 2021" "Gavin D. Howard" "Libraries Manual"
.SH NAME
.PP
bcl - library of arbitrary precision decimal arithmetic
.SH SYNOPSIS
.SS Use
.PP
\f[I]#include <bcl.h>\f[R]
.PP
Link with \f[I]-lbcl\f[R].
.SS Signals
.PP
This procedure will allow clients to use signals to interrupt
computations running in bcl(3).
.PP
\f[B]void bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]bool bcl_running(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.SS Setup
.PP
These items allow clients to set up bcl(3).
.PP
\f[B]BclError bcl_init(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_free(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]bool bcl_abortOnFatalError(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_setAbortOnFatalError(bool\f[R] \f[I]abrt\f[R]\f[B]);\f[R]
.PP
\f[B]bool bcl_leadingZeroes(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_setLeadingZeroes(bool\f[R]
\f[I]leadingZeroes\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_gc(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.SS Contexts
.PP
These items will allow clients to handle contexts, which are isolated
from each other.
This allows more than one client to use bcl(3) in the same program.
.PP
\f[B]struct BclCtxt;\f[R]
.PP
\f[B]typedef struct BclCtxt* BclContext;\f[R]
.PP
\f[B]BclContext bcl_ctxt_create(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_ctxt_free(BclContext\f[R] \f[I]ctxt\f[R]\f[B]);\f[R]
.PP
\f[B]BclError bcl_pushContext(BclContext\f[R] \f[I]ctxt\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_popContext(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]BclContext bcl_context(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_ctxt_freeNums(BclContext\f[R] \f[I]ctxt\f[R]\f[B]);\f[R]
.PP
\f[B]size_t bcl_ctxt_scale(BclContext\f[R] \f[I]ctxt\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_ctxt_setScale(BclContext\f[R] \f[I]ctxt\f[R]\f[B],
size_t\f[R] \f[I]scale\f[R]\f[B]);\f[R]
.PP
\f[B]size_t bcl_ctxt_ibase(BclContext\f[R] \f[I]ctxt\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_ctxt_setIbase(BclContext\f[R] \f[I]ctxt\f[R]\f[B],
size_t\f[R] \f[I]ibase\f[R]\f[B]);\f[R]
.PP
\f[B]size_t bcl_ctxt_obase(BclContext\f[R] \f[I]ctxt\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_ctxt_setObase(BclContext\f[R] \f[I]ctxt\f[R]\f[B],
size_t\f[R] \f[I]obase\f[R]\f[B]);\f[R]
.SS Errors
.PP
These items allow clients to handle errors.
.PP
\f[B]typedef enum BclError BclError;\f[R]
.PP
\f[B]BclError bcl_err(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.SS Numbers
.PP
These items allow clients to manipulate and query the
arbitrary-precision numbers managed by bcl(3).
.PP
\f[B]typedef struct { size_t i; } BclNumber;\f[R]
.PP
\f[B]BclNumber bcl_num_create(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_num_free(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.PP
\f[B]bool bcl_num_neg(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_num_setNeg(BclNumber\f[R] \f[I]n\f[R]\f[B], bool\f[R]
\f[I]neg\f[R]\f[B]);\f[R]
.PP
\f[B]size_t bcl_num_scale(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.PP
\f[B]BclError bcl_num_setScale(BclNumber\f[R] \f[I]n\f[R]\f[B],
size_t\f[R] \f[I]scale\f[R]\f[B]);\f[R]
.PP
\f[B]size_t bcl_num_len(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.SS Conversion
.PP
These items allow clients to convert numbers into and from strings and
integers.
.PP
\f[B]BclNumber bcl_parse(const char *restrict\f[R]
\f[I]val\f[R]\f[B]);\f[R]
.PP
\f[B]char* bcl_string(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.PP
\f[B]BclError bcl_bigdig(BclNumber\f[R] \f[I]n\f[R]\f[B], BclBigDig
*\f[R]\f[I]result\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_bigdig2num(BclBigDig\f[R] \f[I]val\f[R]\f[B]);\f[R]
.SS Math
.PP
These items allow clients to run math on numbers.
.PP
\f[B]BclNumber bcl_add(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_sub(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_mul(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_div(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_mod(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_pow(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_lshift(BclNumber\f[R] \f[I]a\f[R]\f[B],
BclNumber\f[R] \f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_rshift(BclNumber\f[R] \f[I]a\f[R]\f[B],
BclNumber\f[R] \f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_sqrt(BclNumber\f[R] \f[I]a\f[R]\f[B]);\f[R]
.PP
\f[B]BclError bcl_divmod(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B], BclNumber *\f[R]\f[I]c\f[R]\f[B], BclNumber
*\f[R]\f[I]d\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_modexp(BclNumber\f[R] \f[I]a\f[R]\f[B],
BclNumber\f[R] \f[I]b\f[R]\f[B], BclNumber\f[R] \f[I]c\f[R]\f[B]);\f[R]
.SS Miscellaneous
.PP
These items are miscellaneous.
.PP
\f[B]void bcl_zero(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.PP
\f[B]void bcl_one(BclNumber\f[R] \f[I]n\f[R]\f[B]);\f[R]
.PP
\f[B]ssize_t bcl_cmp(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R]
\f[I]b\f[R]\f[B]);\f[R]
.PP
\f[B]BclError bcl_copy(BclNumber\f[R] \f[I]d\f[R]\f[B], BclNumber\f[R]
\f[I]s\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_dup(BclNumber\f[R] \f[I]s\f[R]\f[B]);\f[R]
.SS Pseudo-Random Number Generator
.PP
These items allow clients to manipulate the seeded pseudo-random number
generator in bcl(3).
.PP
\f[B]#define BCL_SEED_ULONGS\f[R]
.PP
\f[B]#define BCL_SEED_SIZE\f[R]
.PP
\f[B]typedef unsigned long BclBigDig;\f[R]
.PP
\f[B]typedef unsigned long BclRandInt;\f[R]
.PP
\f[B]BclNumber bcl_irand(BclNumber\f[R] \f[I]a\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_frand(size_t\f[R] \f[I]places\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_ifrand(BclNumber\f[R] \f[I]a\f[R]\f[B], size_t\f[R]
\f[I]places\f[R]\f[B]);\f[R]
.PP
\f[B]BclError bcl_rand_seedWithNum(BclNumber\f[R]
\f[I]n\f[R]\f[B]);\f[R]
.PP
\f[B]BclError bcl_rand_seed(unsigned char\f[R]
\f[I]seed\f[R]\f[B][\f[R]\f[I]BCL_SEED_SIZE\f[R]\f[B]]);\f[R]
.PP
\f[B]void bcl_rand_reseed(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]BclNumber bcl_rand_seed2num(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]BclRandInt bcl_rand_int(\f[R]\f[I]void\f[R]\f[B]);\f[R]
.PP
\f[B]BclRandInt bcl_rand_bounded(BclRandInt\f[R]
\f[I]bound\f[R]\f[B]);\f[R]
.SH DESCRIPTION
.PP
bcl(3) is a library that implements arbitrary-precision decimal math, as
standardized by
POSIX (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
in bc(1).
.PP
bcl(3) is async-signal-safe if
\f[B]bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R] is used properly.
(See the \f[B]SIGNAL HANDLING\f[R] section.)
.PP
bcl(3) assumes that it is allowed to use the \f[B]bcl\f[R],
\f[B]Bcl\f[R], \f[B]bc\f[R], and \f[B]Bc\f[R] prefixes for symbol names
without collision.
.PP
All of the items in its interface are described below.
See the documentation for each function for what each function can
return.
.SS Signals
.TP
\f[B]void bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R]
An async-signal-safe function that can be called from a signal handler.
If called from a signal handler on the same thread as any executing
bcl(3) functions, it will interrupt the functions and force them to
return early.
It is undefined behavior if this function is called from a thread that
is \f[I]not\f[R] executing any bcl(3) functions while any bcl(3)
functions are executing.
.RS
.PP
If execution \f[I]is\f[R] interrupted,
\f[B]bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R] does \f[I]not\f[R]
return to its caller.
.PP
See the \f[B]SIGNAL HANDLING\f[R] section.
.RE
.TP
\f[B]bool bcl_running(\f[R]\f[I]void\f[R]\f[B])\f[R]
An async-signal-safe function that can be called from a signal handler.
It will return \f[B]true\f[R] if any bcl(3) procedures are running,
which means it is safe to call
\f[B]bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R].
Otherwise, it returns \f[B]false\f[R].
.RS
.PP
See the \f[B]SIGNAL HANDLING\f[R] section.
.RE
.SS Setup
.TP
\f[B]BclError bcl_init(\f[R]\f[I]void\f[R]\f[B])\f[R]
Initializes this library.
This function can be called multiple times, but each call must be
matched by a call to \f[B]bcl_free(\f[R]\f[I]void\f[R]\f[B])\f[R].
This is to make it possible for multiple libraries and applications to
initialize bcl(3) without problem.
.RS
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.PP
This function must be the first one clients call.
Calling any other function without calling this one first is undefined
behavior.
.RE
.TP
\f[B]void bcl_free(\f[R]\f[I]void\f[R]\f[B])\f[R]
Decrements bcl(3)\[cq]s reference count and frees the data associated
with it if the reference count is \f[B]0\f[R].
.RS
.PP
This function must be the last one clients call.
Calling this function before calling any other function is undefined
behavior.
.RE
.TP
\f[B]bool bcl_abortOnFatalError(\f[R]\f[I]void\f[R]\f[B])\f[R]
Queries and returns the current state of calling \f[B]abort()\f[R] on
fatal errors.
If \f[B]true\f[R] is returned, bcl(3) will cause a \f[B]SIGABRT\f[R] if
a fatal error occurs.
.RS
.PP
If activated, clients do not need to check for fatal errors.
.PP
The default is \f[B]false\f[R].
.RE
.TP
\f[B]void bcl_setAbortOnFatalError(bool\f[R] \f[I]abrt\f[R]\f[B])\f[R]
Sets the state of calling \f[B]abort()\f[R] on fatal errors.
If \f[I]abrt\f[R] is \f[B]false\f[R], bcl(3) will not cause a
\f[B]SIGABRT\f[R] on fatal errors after the call.
If \f[I]abrt\f[R] is \f[B]true\f[R], bcl(3) will cause a
\f[B]SIGABRT\f[R] on fatal errors after the call.
.RS
.PP
If activated, clients do not need to check for fatal errors.
.RE
.TP
\f[B]bool bcl_leadingZeroes(\f[R]\f[I]void\f[R]\f[B])\f[R]
Queries and returns the state of whether leading zeroes are added to
strings returned by \f[B]bcl_string()\f[R] when numbers are greater than
\f[B]-1\f[R], less than \f[B]1\f[R], and not equal to \f[B]0\f[R].
If \f[B]true\f[R] is returned, then leading zeroes will be added.
.RS
.PP
The default is \f[B]false\f[R].
.RE
.TP
\f[B]void bcl_setLeadingZeroes(bool\f[R] \f[I]leadingZeroes\f[R]\f[B])\f[R]
Sets the state of whether leading zeroes are added to strings returned
by \f[B]bcl_string()\f[R] when numbers are greater than \f[B]-1\f[R],
less than \f[B]1\f[R], and not equal to \f[B]0\f[R].
If \f[I]leadingZeroes\f[R] is \f[B]true\f[R], leading zeroes will be
added to strings returned by \f[B]bcl_string()\f[R].
.TP
\f[B]void bcl_gc(\f[R]\f[I]void\f[R]\f[B])\f[R]
Garbage collects cached instances of arbitrary-precision numbers.
This only frees the memory of numbers that are \f[I]not\f[R] in use, so
it is safe to call at any time.
.SS Contexts
.PP
All procedures that take a \f[B]BclContext\f[R] parameter a require a
valid context as an argument.
.TP
\f[B]struct BclCtxt\f[R]
A forward declaration for a hidden \f[B]struct\f[R] type.
Clients cannot access the internals of the \f[B]struct\f[R] type
directly.
All interactions with the type are done through pointers.
See \f[B]BclContext\f[R] below.
.TP
\f[B]BclContext\f[R]
A typedef to a pointer of \f[B]struct BclCtxt\f[R].
This is the only handle clients can get to \f[B]struct BclCtxt\f[R].
.RS
.PP
A \f[B]BclContext\f[R] contains the values \f[B]scale\f[R],
\f[B]ibase\f[R], and \f[B]obase\f[R], as well as a list of numbers.
.PP
\f[B]scale\f[R] is a value used to control how many decimal places
calculations should use.
A value of \f[B]0\f[R] means that calculations are done on integers
only, where applicable, and a value of 20, for example, means that all
applicable calculations return results with 20 decimal places.
The default is \f[B]0\f[R].
.PP
\f[B]ibase\f[R] is a value used to control the input base.
The minimum \f[B]ibase\f[R] is \f[B]2\f[R], and the maximum is
\f[B]36\f[R].
If \f[B]ibase\f[R] is \f[B]2\f[R], numbers are parsed as though they are
in binary, and any digits larger than \f[B]1\f[R] are clamped.
Likewise, a value of \f[B]10\f[R] means that numbers are parsed as
though they are decimal, and any larger digits are clamped.
The default is \f[B]10\f[R].
.PP
\f[B]obase\f[R] is a value used to control the output base.
The minimum \f[B]obase\f[R] is \f[B]0\f[R] and the maximum is
\f[B]BC_BASE_MAX\f[R] (see the \f[B]LIMITS\f[R] section).
.PP
Numbers created in one context are not valid in another context.
It is undefined behavior to use a number created in a different context.
Contexts are meant to isolate the numbers used by different clients in
the same application.
.RE
.TP
\f[B]BclContext bcl_ctxt_create(\f[R]\f[I]void\f[R]\f[B])\f[R]
Creates a context and returns it.
Returns \f[B]NULL\f[R] if there was an error.
.TP
\f[B]void bcl_ctxt_free(BclContext\f[R] \f[I]ctxt\f[R]\f[B])\f[R]
Frees \f[I]ctxt\f[R], after which it is no longer valid.
It is undefined behavior to attempt to use an invalid context.
.TP
\f[B]BclError bcl_pushContext(BclContext\f[R] \f[I]ctxt\f[R]\f[B])\f[R]
Pushes \f[I]ctxt\f[R] onto bcl(3)\[cq]s stack of contexts.
\f[I]ctxt\f[R] must have been created with
\f[B]bcl_ctxt_create(\f[R]\f[I]void\f[R]\f[B])\f[R].
.RS
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.PP
There \f[I]must\f[R] be a valid context to do any arithmetic.
.RE
.TP
\f[B]void bcl_popContext(\f[R]\f[I]void\f[R]\f[B])\f[R]
Pops the current context off of the stack, if one exists.
.TP
\f[B]BclContext bcl_context(\f[R]\f[I]void\f[R]\f[B])\f[R]
Returns the current context, or \f[B]NULL\f[R] if no context exists.
.TP
\f[B]void bcl_ctxt_freeNums(BclContext\f[R] \f[I]ctxt\f[R]\f[B])\f[R]
Frees all numbers in use that are associated with \f[I]ctxt\f[R].
It is undefined behavior to attempt to use a number associated with
\f[I]ctxt\f[R] after calling this procedure unless such numbers have
been created with \f[B]bcl_num_create(\f[R]\f[I]void\f[R]\f[B])\f[R]
after calling this procedure.
.TP
\f[B]size_t bcl_ctxt_scale(BclContext\f[R] \f[I]ctxt\f[R]\f[B])\f[R]
Returns the \f[B]scale\f[R] for given context.
.TP
\f[B]void bcl_ctxt_setScale(BclContext\f[R] \f[I]ctxt\f[R]\f[B], size_t\f[R] \f[I]scale\f[R]\f[B])\f[R]
Sets the \f[B]scale\f[R] for the given context to the argument
\f[I]scale\f[R].
.TP
\f[B]size_t bcl_ctxt_ibase(BclContext\f[R] \f[I]ctxt\f[R]\f[B])\f[R]
Returns the \f[B]ibase\f[R] for the given context.
.TP
\f[B]void bcl_ctxt_setIbase(BclContext\f[R] \f[I]ctxt\f[R]\f[B], size_t\f[R] \f[I]ibase\f[R]\f[B])\f[R]
Sets the \f[B]ibase\f[R] for the given context to the argument
\f[I]ibase\f[R].
If the argument \f[I]ibase\f[R] is invalid, it clamped, so an
\f[I]ibase\f[R] of \f[B]0\f[R] or \f[B]1\f[R] is clamped to \f[B]2\f[R],
and any values above \f[B]36\f[R] are clamped to \f[B]36\f[R].
.TP
\f[B]size_t bcl_ctxt_obase(BclContext\f[R] \f[I]ctxt\f[R]\f[B])\f[R]
Returns the \f[B]obase\f[R] for the given context.
.TP
\f[B]void bcl_ctxt_setObase(BclContext\f[R] \f[I]ctxt\f[R]\f[B], size_t\f[R] \f[I]obase\f[R]\f[B])\f[R]
Sets the \f[B]obase\f[R] for the given context to the argument
\f[I]obase\f[R].
.SS Errors
.TP
\f[B]BclError\f[R]
An \f[B]enum\f[R] of possible error codes.
See the \f[B]ERRORS\f[R] section for a complete listing the codes.
.TP
\f[B]BclError bcl_err(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Checks for errors in a \f[B]BclNumber\f[R].
All functions that can return a \f[B]BclNumber\f[R] can encode an error
in the number, and this function will return the error, if any.
If there was no error, it will return \f[B]BCL_ERROR_NONE\f[R].
.RS
.PP
There must be a valid current context.
.RE
.SS Numbers
.PP
All procedures in this section require a valid current context.
.TP
\f[B]BclNumber\f[R]
A handle to an arbitrary-precision number.
The actual number type is not exposed; the \f[B]BclNumber\f[R] handle is
the only way clients can refer to instances of arbitrary-precision
numbers.
.TP
\f[B]BclNumber bcl_num_create(\f[R]\f[I]void\f[R]\f[B])\f[R]
Creates and returns a \f[B]BclNumber\f[R].
.RS
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]void bcl_num_free(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Frees \f[I]n\f[R].
It is undefined behavior to use \f[I]n\f[R] after calling this function.
.TP
\f[B]bool bcl_num_neg(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Returns \f[B]true\f[R] if \f[I]n\f[R] is negative, \f[B]false\f[R]
otherwise.
.TP
\f[B]void bcl_num_setNeg(BclNumber\f[R] \f[I]n\f[R]\f[B], bool\f[R] \f[I]neg\f[R]\f[B])\f[R]
Sets \f[I]n\f[R]\[cq]s sign to \f[I]neg\f[R], where \f[B]true\f[R] is
negative, and \f[B]false\f[R] is positive.
.TP
\f[B]size_t bcl_num_scale(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Returns the \f[I]scale\f[R] of \f[I]n\f[R].
.RS
.PP
The \f[I]scale\f[R] of a number is the number of decimal places it has
after the radix (decimal point).
.RE
.TP
\f[B]BclError bcl_num_setScale(BclNumber\f[R] \f[I]n\f[R]\f[B], size_t\f[R] \f[I]scale\f[R]\f[B])\f[R]
Sets the \f[I]scale\f[R] of \f[I]n\f[R] to the argument \f[I]scale\f[R].
If the argument \f[I]scale\f[R] is greater than the \f[I]scale\f[R] of
\f[I]n\f[R], \f[I]n\f[R] is extended.
If the argument \f[I]scale\f[R] is less than the \f[I]scale\f[R] of
\f[I]n\f[R], \f[I]n\f[R] is truncated.
.RS
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]size_t bcl_num_len(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Returns the number of \f[I]significant decimal digits\f[R] in
\f[I]n\f[R].
.SS Conversion
.PP
All procedures in this section require a valid current context.
.PP
All procedures in this section consume the given \f[B]BclNumber\f[R]
arguments that are not given to pointer arguments.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.TP
\f[B]BclNumber bcl_parse(const char *restrict\f[R] \f[I]val\f[R]\f[B])\f[R]
Parses a number string according to the current context\[cq]s
\f[B]ibase\f[R] and returns the resulting number.
.RS
.PP
\f[I]val\f[R] must be non-\f[B]NULL\f[R] and a valid string.
See \f[B]BCL_ERROR_PARSE_INVALID_STR\f[R] in the \f[B]ERRORS\f[R]
section for more information.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_PARSE_INVALID_STR\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]char* bcl_string(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Returns a string representation of \f[I]n\f[R] according the the current
context\[cq]s \f[B]ibase\f[R].
The string is dynamically allocated and must be freed by the caller.
.RS
.PP
\f[I]n\f[R] is consumed; it cannot be used after the call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.RE
.TP
\f[B]BclError bcl_bigdig(BclNumber\f[R] \f[I]n\f[R]\f[B], BclBigDig *\f[R]\f[I]result\f[R]\f[B])\f[R]
Converts \f[I]n\f[R] into a \f[B]BclBigDig\f[R] and returns the result
in the space pointed to by \f[I]result\f[R].
.RS
.PP
\f[I]a\f[R] must be smaller than \f[B]BC_OVERFLOW_MAX\f[R].
See the \f[B]LIMITS\f[R] section.
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_OVERFLOW\f[R]
.PP
\f[I]n\f[R] is consumed; it cannot be used after the call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.RE
.TP
\f[B]BclNumber bcl_bigdig2num(BclBigDig\f[R] \f[I]val\f[R]\f[B])\f[R]
Creates a \f[B]BclNumber\f[R] from \f[I]val\f[R].
.RS
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.SS Math
.PP
All procedures in this section require a valid current context.
.PP
All procedures in this section can return the following errors:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.TP
\f[B]BclNumber bcl_add(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Adds \f[I]a\f[R] and \f[I]b\f[R] and returns the result.
The \f[I]scale\f[R] of the result is the max of the \f[I]scale\f[R]s of
\f[I]a\f[R] and \f[I]b\f[R].
.RS
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_sub(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Subtracts \f[I]b\f[R] from \f[I]a\f[R] and returns the result.
The \f[I]scale\f[R] of the result is the max of the \f[I]scale\f[R]s of
\f[I]a\f[R] and \f[I]b\f[R].
.RS
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_mul(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Multiplies \f[I]a\f[R] and \f[I]b\f[R] and returns the result.
If \f[I]ascale\f[R] is the \f[I]scale\f[R] of \f[I]a\f[R] and
\f[I]bscale\f[R] is the \f[I]scale\f[R] of \f[I]b\f[R], the
\f[I]scale\f[R] of the result is equal to
\f[B]min(ascale+bscale,max(scale,ascale,bscale))\f[R], where
\f[B]min()\f[R] and \f[B]max()\f[R] return the obvious values.
.RS
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_div(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Divides \f[I]a\f[R] by \f[I]b\f[R] and returns the result.
The \f[I]scale\f[R] of the result is the \f[I]scale\f[R] of the current
context.
.RS
.PP
\f[I]b\f[R] cannot be \f[B]0\f[R].
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_DIVIDE_BY_ZERO\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_mod(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Divides \f[I]a\f[R] by \f[I]b\f[R] to the \f[I]scale\f[R] of the current
context, computes the modulus \f[B]a-(a/b)*b\f[R], and returns the
modulus.
.RS
.PP
\f[I]b\f[R] cannot be \f[B]0\f[R].
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_DIVIDE_BY_ZERO\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_pow(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Calculates \f[I]a\f[R] to the power of \f[I]b\f[R] to the
\f[I]scale\f[R] of the current context.
\f[I]b\f[R] must be an integer, but can be negative.
If it is negative, \f[I]a\f[R] must be non-zero.
.RS
.PP
\f[I]b\f[R] must be an integer.
If \f[I]b\f[R] is negative, \f[I]a\f[R] must not be \f[B]0\f[R].
.PP
\f[I]a\f[R] must be smaller than \f[B]BC_OVERFLOW_MAX\f[R].
See the \f[B]LIMITS\f[R] section.
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NON_INTEGER\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_OVERFLOW\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_DIVIDE_BY_ZERO\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_lshift(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Shifts \f[I]a\f[R] left (moves the radix right) by \f[I]b\f[R] places
and returns the result.
This is done in decimal.
\f[I]b\f[R] must be an integer.
.RS
.PP
\f[I]b\f[R] must be an integer.
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NON_INTEGER\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_rshift(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Shifts \f[I]a\f[R] right (moves the radix left) by \f[I]b\f[R] places
and returns the result.
This is done in decimal.
\f[I]b\f[R] must be an integer.
.RS
.PP
\f[I]b\f[R] must be an integer.
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]a\f[R] and \f[I]b\f[R] can be the same number.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NON_INTEGER\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_sqrt(BclNumber\f[R] \f[I]a\f[R]\f[B])\f[R]
Calculates the square root of \f[I]a\f[R] and returns the result.
The \f[I]scale\f[R] of the result is equal to the \f[B]scale\f[R] of the
current context.
.RS
.PP
\f[I]a\f[R] cannot be negative.
.PP
\f[I]a\f[R] is consumed; it cannot be used after the call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NEGATIVE\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclError bcl_divmod(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B], BclNumber *\f[R]\f[I]c\f[R]\f[B], BclNumber *\f[R]\f[I]d\f[R]\f[B])\f[R]
Divides \f[I]a\f[R] by \f[I]b\f[R] and returns the quotient in a new
number which is put into the space pointed to by \f[I]c\f[R], and puts
the modulus in a new number which is put into the space pointed to by
\f[I]d\f[R].
.RS
.PP
\f[I]b\f[R] cannot be \f[B]0\f[R].
.PP
\f[I]a\f[R] and \f[I]b\f[R] are consumed; they cannot be used after the
call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
\f[I]c\f[R] and \f[I]d\f[R] cannot point to the same place, nor can they
point to the space occupied by \f[I]a\f[R] or \f[I]b\f[R].
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_DIVIDE_BY_ZERO\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_modexp(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B], BclNumber\f[R] \f[I]c\f[R]\f[B])\f[R]
Computes a modular exponentiation where \f[I]a\f[R] is the base,
\f[I]b\f[R] is the exponent, and \f[I]c\f[R] is the modulus, and returns
the result.
The \f[I]scale\f[R] of the result is equal to the \f[B]scale\f[R] of the
current context.
.RS
.PP
\f[I]a\f[R], \f[I]b\f[R], and \f[I]c\f[R] must be integers.
\f[I]c\f[R] must not be \f[B]0\f[R].
\f[I]b\f[R] must not be negative.
.PP
\f[I]a\f[R], \f[I]b\f[R], and \f[I]c\f[R] are consumed; they cannot be
used after the call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NEGATIVE\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NON_INTEGER\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_DIVIDE_BY_ZERO\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.SS Miscellaneous
.TP
\f[B]void bcl_zero(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Sets \f[I]n\f[R] to \f[B]0\f[R].
.TP
\f[B]void bcl_one(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Sets \f[I]n\f[R] to \f[B]1\f[R].
.TP
\f[B]ssize_t bcl_cmp(BclNumber\f[R] \f[I]a\f[R]\f[B], BclNumber\f[R] \f[I]b\f[R]\f[B])\f[R]
Compares \f[I]a\f[R] and \f[I]b\f[R] and returns \f[B]0\f[R] if
\f[I]a\f[R] and \f[I]b\f[R] are equal, \f[B]<0\f[R] if \f[I]a\f[R] is
less than \f[I]b\f[R], and \f[B]>0\f[R] if \f[I]a\f[R] is greater than
\f[I]b\f[R].
.TP
\f[B]BclError bcl_copy(BclNumber\f[R] \f[I]d\f[R]\f[B], BclNumber\f[R] \f[I]s\f[R]\f[B])\f[R]
Copies \f[I]s\f[R] into \f[I]d\f[R].
.RS
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_dup(BclNumber\f[R] \f[I]s\f[R]\f[B])\f[R]
Creates and returns a new \f[B]BclNumber\f[R] that is a copy of
\f[I]s\f[R].
.RS
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.SS Pseudo-Random Number Generator
.PP
The pseudo-random number generator in bcl(3) is a \f[I]seeded\f[R] PRNG.
Given the same seed twice, it will produce the same sequence of
pseudo-random numbers twice.
.PP
By default, bcl(3) attempts to seed the PRNG with data from
\f[B]/dev/urandom\f[R].
If that fails, it seeds itself with by calling \f[B]libc\f[R]\[cq]s
\f[B]srand(time(NULL))\f[R] and then calling \f[B]rand()\f[R] for each
byte, since \f[B]rand()\f[R] is only guaranteed to return \f[B]15\f[R]
bits.
.PP
This should provide fairly good seeding in the standard case while also
remaining fairly portable.
.PP
If necessary, the PRNG can be reseeded with one of the following
functions:
.IP \[bu] 2
\f[B]bcl_rand_seedWithNum(BclNumber)\f[R]
.IP \[bu] 2
\f[B]bcl_rand_seed(unsigned
char[\f[R]\f[I]BCL_SEED_SIZE\f[R]\f[B]])\f[R]
.IP \[bu] 2
\f[B]bcl_rand_reseed(\f[R]\f[I]void\f[R]\f[B])\f[R]
.PP
The following items allow clients to use the pseudo-random number
generator.
All procedures require a valid current context.
.TP
\f[B]BCL_SEED_ULONGS\f[R]
The number of \f[B]unsigned long\f[R]\[cq]s in a seed for bcl(3)\[cq]s
random number generator.
.TP
\f[B]BCL_SEED_SIZE\f[R]
The size, in \f[B]char\f[R]\[cq]s, of a seed for bcl(3)\[cq]s random
number generator.
.TP
\f[B]BclBigDig\f[R]
bcl(3)\[cq]s overflow type (see the \f[B]PERFORMANCE\f[R] section).
.TP
\f[B]BclRandInt\f[R]
An unsigned integer type returned by bcl(3)\[cq]s random number
generator.
.TP
\f[B]BclNumber bcl_irand(BclNumber\f[R] \f[I]a\f[R]\f[B])\f[R]
Returns a random number that is not larger than \f[I]a\f[R] in a new
number.
If \f[I]a\f[R] is \f[B]0\f[R] or \f[B]1\f[R], the new number is equal to
\f[B]0\f[R].
The bound is unlimited, so it is not bound to the size of
\f[B]BclRandInt\f[R].
This is done by generating as many random numbers as necessary,
multiplying them by certain exponents, and adding them all together.
.RS
.PP
\f[I]a\f[R] must be an integer and non-negative.
.PP
\f[I]a\f[R] is consumed; it cannot be used after the call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
This procedure requires a valid current context.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NEGATIVE\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NON_INTEGER\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_frand(size_t\f[R] \f[I]places\f[R]\f[B])\f[R]
Returns a random number between \f[B]0\f[R] (inclusive) and \f[B]1\f[R]
(exclusive) that has \f[I]places\f[R] decimal digits after the radix
(decimal point).
There are no limits on \f[I]places\f[R].
.RS
.PP
This procedure requires a valid current context.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclNumber bcl_ifrand(BclNumber\f[R] \f[I]a\f[R]\f[B], size_t\f[R] \f[I]places\f[R]\f[B])\f[R]
Returns a random number less than \f[I]a\f[R] with \f[I]places\f[R]
decimal digits after the radix (decimal point).
There are no limits on \f[I]a\f[R] or \f[I]places\f[R].
.RS
.PP
\f[I]a\f[R] must be an integer and non-negative.
.PP
\f[I]a\f[R] is consumed; it cannot be used after the call.
See the \f[B]Consumption and Propagation\f[R] subsection below.
.PP
This procedure requires a valid current context.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NEGATIVE\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_MATH_NON_INTEGER\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclError bcl_rand_seedWithNum(BclNumber\f[R] \f[I]n\f[R]\f[B])\f[R]
Seeds the PRNG with \f[I]n\f[R].
.RS
.PP
\f[I]n\f[R] is \f[I]not\f[R] consumed.
.PP
This procedure requires a valid current context.
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_NUM\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.PP
Note that if \f[B]bcl_rand_seed2num(\f[R]\f[I]void\f[R]\f[B])\f[R] or
\f[B]bcl_rand_seed2num_err(BclNumber)\f[R] are called right after this
function, they are not guaranteed to return a number equal to
\f[I]n\f[R].
.RE
.TP
\f[B]BclError bcl_rand_seed(unsigned char\f[R] \f[I]seed\f[R]\f[B][\f[R]\f[I]BCL_SEED_SIZE\f[R]\f[B]])\f[R]
Seeds the PRNG with the bytes in \f[I]seed\f[R].
.RS
.PP
If there was no error, \f[B]BCL_ERROR_NONE\f[R] is returned.
Otherwise, this function can return:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.RE
.TP
\f[B]void bcl_rand_reseed(\f[R]\f[I]void\f[R]\f[B])\f[R]
Reseeds the PRNG with the default reseeding behavior.
First, it attempts to read data from \f[B]/dev/urandom\f[R] and falls
back to \f[B]libc\f[R]\[cq]s \f[B]rand()\f[R].
.RS
.PP
This procedure cannot fail.
.RE
.TP
\f[B]BclNumber bcl_rand_seed2num(\f[R]\f[I]void\f[R]\f[B])\f[R]
Returns the current seed of the PRNG as a \f[B]BclNumber\f[R].
.RS
.PP
This procedure requires a valid current context.
.PP
bcl(3) will encode an error in the return value, if there was one.
The error can be queried with \f[B]bcl_err(BclNumber)\f[R].
Possible errors include:
.IP \[bu] 2
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
.IP \[bu] 2
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
.RE
.TP
\f[B]BclRandInt bcl_rand_int(\f[R]\f[I]void\f[R]\f[B])\f[R]
Returns a random integer between \f[B]0\f[R] and \f[B]BC_RAND_MAX\f[R]
(inclusive).
.RS
.PP
This procedure cannot fail.
.RE
.TP
\f[B]BclRandInt bcl_rand_bounded(BclRandInt\f[R] \f[I]bound\f[R]\f[B])\f[R]
Returns a random integer between \f[B]0\f[R] and \f[I]bound\f[R]
(exclusive).
Bias is removed before returning the integer.
.RS
.PP
This procedure cannot fail.
.RE
.SS Consumption and Propagation
.PP
Some functions are listed as consuming some or all of their arguments.
This means that the arguments are freed, regardless of if there were
errors or not.
.PP
This is to enable compact code like the following:
.IP
.nf
\f[C]
BclNumber n = bcl_num_add(bcl_num_mul(a, b), bcl_num_div(c, d));
\f[R]
.fi
.PP
If arguments to those functions were not consumed, memory would be
leaked until reclaimed with \f[B]bcl_ctxt_freeNums(BclContext)\f[R].
.PP
When errors occur, they are propagated through.
The result should always be checked with \f[B]bcl_err(BclNumber)\f[R],
so the example above should properly be:
.IP
.nf
\f[C]
BclNumber n = bcl_num_add(bcl_num_mul(a, b), bcl_num_div(c, d));
if (bc_num_err(n) != BCL_ERROR_NONE) {
    // Handle the error.
}
\f[R]
.fi
.SH ERRORS
.PP
Most functions in bcl(3) return, directly or indirectly, any one of the
error codes defined in \f[B]BclError\f[R].
The complete list of codes is the following:
.TP
\f[B]BCL_ERROR_NONE\f[R]
Success; no error occurred.
.TP
\f[B]BCL_ERROR_INVALID_NUM\f[R]
An invalid \f[B]BclNumber\f[R] was given as a parameter.
.TP
\f[B]BCL_ERROR_INVALID_CONTEXT\f[R]
An invalid \f[B]BclContext\f[R] is being used.
.TP
\f[B]BCL_ERROR_SIGNAL\f[R]
A signal interrupted execution.
.TP
\f[B]BCL_ERROR_MATH_NEGATIVE\f[R]
A negative number was given as an argument to a parameter that cannot
accept negative numbers, such as for square roots.
.TP
\f[B]BCL_ERROR_MATH_NON_INTEGER\f[R]
A non-integer was given as an argument to a parameter that cannot accept
non-integer numbers, such as for the second parameter of
\f[B]bcl_num_pow()\f[R].
.TP
\f[B]BCL_ERROR_MATH_OVERFLOW\f[R]
A number that would overflow its result was given as an argument, such
as for converting a \f[B]BclNumber\f[R] to a \f[B]BclBigDig\f[R].
.TP
\f[B]BCL_ERROR_MATH_DIVIDE_BY_ZERO\f[R]
A divide by zero occurred.
.TP
\f[B]BCL_ERROR_PARSE_INVALID_STR\f[R]
An invalid number string was passed to a parsing function.
.RS
.PP
A valid number string can only be one radix (period).
In addition, any lowercase ASCII letters, symbols, or non-ASCII
characters are invalid.
It is allowed for the first character to be a dash.
In that case, the number is considered to be negative.
.PP
There is one exception to the above: one lowercase \f[B]e\f[R] is
allowed in the number, after the radix, if it exists.
If the letter \f[B]e\f[R] exists, the number is considered to be in
scientific notation, where the part before the \f[B]e\f[R] is the
number, and the part after, which must be an integer, is the exponent.
There can be a dash right after the \f[B]e\f[R] to indicate a negative
exponent.
.PP
\f[B]WARNING\f[R]: Both the number and the exponent in scientific
notation are interpreted according to the current \f[B]ibase\f[R], but
the number is still multiplied by \f[B]10\[ha]exponent\f[R] regardless
of the current \f[B]ibase\f[R].
For example, if \f[B]ibase\f[R] is \f[B]16\f[R] and bcl(3) is given the
number string \f[B]FFeA\f[R], the resulting decimal number will be
\f[B]2550000000000\f[R], and if bcl(3) is given the number string
\f[B]10e-4\f[R], the resulting decimal number will be \f[B]0.0016\f[R].
.RE
.TP
\f[B]BCL_ERROR_FATAL_ALLOC_ERR\f[R]
bcl(3) failed to allocate memory.
.RS
.PP
If clients call \f[B]bcl_setAbortOnFatalError()\f[R] with an
\f[B]true\f[R] argument, this error will cause bcl(3) to throw a
\f[B]SIGABRT\f[R].
This behavior can also be turned off later by calling that same function
with a \f[B]false\f[R] argument.
By default, this behavior is off.
.PP
It is highly recommended that client libraries do \f[I]not\f[R] activate
this behavior.
.RE
.TP
\f[B]BCL_ERROR_FATAL_UNKNOWN_ERR\f[R]
An unknown error occurred.
.RS
.PP
If clients call \f[B]bcl_setAbortOnFatalError()\f[R] with an
\f[B]true\f[R] argument, this error will cause bcl(3) to throw a
\f[B]SIGABRT\f[R].
This behavior can also be turned off later by calling that same function
with a \f[B]false\f[R] argument.
By default, this behavior is off.
.PP
It is highly recommended that client libraries do \f[I]not\f[R] activate
this behavior.
.RE
.SH ATTRIBUTES
.PP
When \f[B]bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R] is used
properly, bcl(3) is async-signal-safe.
.PP
bcl(3) is \f[I]MT-Unsafe\f[R]: it is unsafe to call any functions from
more than one thread.
.SH PERFORMANCE
.PP
Most bc(1) implementations use \f[B]char\f[R] types to calculate the
value of \f[B]1\f[R] decimal digit at a time, but that can be slow.
bcl(3) does something different.
.PP
It uses large integers to calculate more than \f[B]1\f[R] decimal digit
at a time.
If built in a environment where \f[B]BC_LONG_BIT\f[R] (see the
\f[B]LIMITS\f[R] section) is \f[B]64\f[R], then each integer has
\f[B]9\f[R] decimal digits.
If built in an environment where \f[B]BC_LONG_BIT\f[R] is \f[B]32\f[R]
then each integer has \f[B]4\f[R] decimal digits.
This value (the number of decimal digits per large integer) is called
\f[B]BC_BASE_DIGS\f[R].
.PP
In addition, this bcl(3) uses an even larger integer for overflow
checking.
This integer type depends on the value of \f[B]BC_LONG_BIT\f[R], but is
always at least twice as large as the integer type used to store digits.
.SH LIMITS
.PP
The following are the limits on bcl(3):
.TP
\f[B]BC_LONG_BIT\f[R]
The number of bits in the \f[B]long\f[R] type in the environment where
bcl(3) was built.
This determines how many decimal digits can be stored in a single large
integer (see the \f[B]PERFORMANCE\f[R] section).
.TP
\f[B]BC_BASE_DIGS\f[R]
The number of decimal digits per large integer (see the
\f[B]PERFORMANCE\f[R] section).
Depends on \f[B]BC_LONG_BIT\f[R].
.TP
\f[B]BC_BASE_POW\f[R]
The max decimal number that each large integer can store (see
\f[B]BC_BASE_DIGS\f[R]) plus \f[B]1\f[R].
Depends on \f[B]BC_BASE_DIGS\f[R].
.TP
\f[B]BC_OVERFLOW_MAX\f[R]
The max number that the overflow type (see the \f[B]PERFORMANCE\f[R]
section) can hold.
Depends on \f[B]BC_LONG_BIT\f[R].
.TP
\f[B]BC_BASE_MAX\f[R]
The maximum output base.
Set at \f[B]BC_BASE_POW\f[R].
.TP
\f[B]BC_SCALE_MAX\f[R]
The maximum \f[B]scale\f[R].
Set at \f[B]BC_OVERFLOW_MAX-1\f[R].
.TP
\f[B]BC_NUM_MAX\f[R]
The maximum length of a number (in decimal digits), which includes
digits after the decimal point.
Set at \f[B]BC_OVERFLOW_MAX-1\f[R].
.TP
\f[B]BC_RAND_MAX\f[R]
The maximum integer (inclusive) returned by the \f[B]bcl_rand_int()\f[R]
function.
Set at \f[B]2\[ha]BC_LONG_BIT-1\f[R].
.TP
Exponent
The maximum allowable exponent (positive or negative).
Set at \f[B]BC_OVERFLOW_MAX\f[R].
.PP
These limits are meant to be effectively non-existent; the limits are so
large (at least on 64-bit machines) that there should not be any point
at which they become a problem.
In fact, memory should be exhausted before these limits should be hit.
.SH SIGNAL HANDLING
.PP
If a signal handler calls
\f[B]bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R] from the same
thread that there are bcl(3) functions executing in, it will cause all
execution to stop as soon as possible, interrupting long-running
calculations, if necessary and cause the function that was executing to
return.
If possible, the error code \f[B]BC_ERROR_SIGNAL\f[R] is returned.
.PP
If execution \f[I]is\f[R] interrupted,
\f[B]bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R] does \f[I]not\f[R]
return to its caller.
.PP
It is undefined behavior if
\f[B]bcl_handleSignal(\f[R]\f[I]void\f[R]\f[B])\f[R] is called from a
thread that is not executing bcl(3) functions, if bcl(3) functions are
executing.
.SH SEE ALSO
.PP
bc(1) and dc(1)
.SH STANDARDS
.PP
bcl(3) is compliant with the arithmetic defined in the IEEE Std
1003.1-2017
(\[lq]POSIX.1-2017\[rq]) (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
specification for bc(1).
.PP
Note that the specification explicitly says that bc(1) only accepts
numbers that use a period (\f[B].\f[R]) as a radix point, regardless of
the value of \f[B]LC_NUMERIC\f[R].
This is also true of bcl(3).
.SH BUGS
.PP
None are known.
Report bugs at https://git.yzena.com/gavin/bc.
.SH AUTHORS
.PP
Gavin D.
Howard <gavin@yzena.com> and contributors.