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