/* * ***************************************************************************** * * SPDX-License-Identifier: BSD-2-Clause * * Copyright (c) 2018-2021 Gavin D. Howard and contributors. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * * Redistributions of source code must retain the above copyright notice, this * list of conditions and the following disclaimer. * * * Redistributions in binary form must reproduce the above copyright notice, * this list of conditions and the following disclaimer in the documentation * and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. * * ***************************************************************************** * * Definitions for the num type. * */ #ifndef BC_NUM_H #define BC_NUM_H #include #include #include #include #include #include #include #include #ifndef BC_ENABLE_EXTRA_MATH #define BC_ENABLE_EXTRA_MATH (1) #endif // BC_ENABLE_EXTRA_MATH /// Everything in bc is base 10.. #define BC_BASE (10) /// Alias. typedef unsigned long ulong; /// This is here because BcBigDig came first, but when I created bcl, it's /// definition has to be defined first. typedef BclBigDig BcBigDig; #if BC_LONG_BIT >= 64 /// The biggest number held by a BcBigDig. #define BC_NUM_BIGDIG_MAX ((BcBigDig) UINT64_MAX) /// The number of decimal digits in one limb. #define BC_BASE_DIGS (9) /// The max number + 1 that one limb can hold. #define BC_BASE_POW (1000000000) /// An alias for portability. #define BC_NUM_BIGDIG_C UINT64_C /// The actual limb type. typedef int_least32_t BcDig; #elif BC_LONG_BIT >= 32 /// The biggest number held by a BcBigDig. #define BC_NUM_BIGDIG_MAX ((BcBigDig) UINT32_MAX) /// The number of decimal digits in one limb. #define BC_BASE_DIGS (4) /// The max number + 1 that one limb can hold. #define BC_BASE_POW (10000) /// An alias for portability. #define BC_NUM_BIGDIG_C UINT32_C /// The actual limb type. typedef int_least16_t BcDig; #else /// LONG_BIT must be at least 32 on POSIX. We depend on that. #error BC_LONG_BIT must be at least 32 #endif // BC_LONG_BIT >= 64 /// The default (and minimum) number of limbs when allocating a number. #define BC_NUM_DEF_SIZE (8) /// The actual number struct. This is where the magic happens. typedef struct BcNum { /// The limb array. It is restrict because *no* other item should own the /// array. For more information, see the development manual /// (manuals/development.md#numbers). BcDig *restrict num; /// The number of limbs before the decimal (radix) point. This also stores /// the negative bit in the least significant bit since it uses at least two /// bits less than scale. It is also used less than scale. See the /// development manual (manuals/development.md#numbers) for more info. size_t rdx; /// The actual scale of the number. This is different from rdx because there /// are multiple digits in one limb, and in the last limb, only some of the /// digits may be part of the scale. However, scale must always match rdx /// (except when the number is 0), or there is a bug. For more information, /// see the development manual (manuals/development.md#numbers). size_t scale; /// The number of valid limbs in the array. If this is 0, then the number is /// 0 as well. size_t len; /// The capacity of the limbs array. This is how many limbs the number could /// expand to without reallocation. size_t cap; } BcNum; #if BC_ENABLE_EXTRA_MATH // Forward declaration struct BcRNG; #endif // BC_ENABLE_EXTRA_MATH /// The minimum obase. #define BC_NUM_MIN_BASE (BC_NUM_BIGDIG_C(2)) /// The maximum ibase allowed by POSIX. #define BC_NUM_MAX_POSIX_IBASE (BC_NUM_BIGDIG_C(16)) /// The actual ibase supported by this implementation. #define BC_NUM_MAX_IBASE (BC_NUM_BIGDIG_C(36)) /// The max base allowed by bc_num_parseChar(). #define BC_NUM_MAX_LBASE (BC_NUM_BIGDIG_C('Z' + BC_BASE + 1)) /// The default number of characters to print before a backslash newline. #define BC_NUM_PRINT_WIDTH (BC_NUM_BIGDIG_C(69)) /// The base for printing streams from numbers. #define BC_NUM_STREAM_BASE (256) // This sets a default for the Karatsuba length. #ifndef BC_NUM_KARATSUBA_LEN #define BC_NUM_KARATSUBA_LEN (BC_NUM_BIGDIG_C(32)) #elif BC_NUM_KARATSUBA_LEN < 16 #error BC_NUM_KARATSUBA_LEN must be at least 16. #endif // BC_NUM_KARATSUBA_LEN // A crude, but always big enough, calculation of // the size required for ibase and obase BcNum's. #define BC_NUM_BIGDIG_LOG10 (BC_NUM_DEF_SIZE) /** * Returns non-zero if the BcNum @a n is non-zero. * @param n The number to test. * @return Non-zero if @a n is non-zero, zero otherwise. */ #define BC_NUM_NONZERO(n) ((n)->len) /** * Returns true if the BcNum @a n is zero. * @param n The number to test. * @return True if @a n is zero, false otherwise. */ #define BC_NUM_ZERO(n) (!BC_NUM_NONZERO(n)) /** * Returns true if the BcNum @a n is one with no scale. * @param n The number to test. * @return True if @a n equals 1 with no scale, false otherwise. */ #define BC_NUM_ONE(n) ((n)->len == 1 && (n)->rdx == 0 && (n)->num[0] == 1) /** * Converts the letter @a c into a number. * @param c The letter to convert. * @return The number corresponding to the letter. */ #define BC_NUM_NUM_LETTER(c) ((c) - 'A' + BC_BASE) /// The number of allocations done by bc_num_k(). If you change the number of /// allocations, you must change this. This is done in order to allocate them /// all as one allocation and just give them all pointers to different parts. /// Works pretty well, but you have to be careful. #define BC_NUM_KARATSUBA_ALLOCS (6) /** * Rounds @a s (scale) up to the next power of BC_BASE_DIGS. This also check for * overflow and gives a fatal error if that happens because we just can't go * over the limits we have imposed. * @param s The scale to round up. * @return @a s rounded up to the next power of BC_BASE_DIGS. */ #define BC_NUM_ROUND_POW(s) (bc_vm_growSize((s), BC_BASE_DIGS - 1)) /** * Returns the equivalent rdx for the scale @a s. * @param s The scale to convert. * @return The rdx for @a s. */ #define BC_NUM_RDX(s) (BC_NUM_ROUND_POW(s) / BC_BASE_DIGS) /** * Returns the actual rdx of @a n. (It removes the negative bit.) * @param n The number. * @return The real rdx of @a n. */ #define BC_NUM_RDX_VAL(n) ((n)->rdx >> 1) /** * Returns the actual rdx of @a n, where @a n is not a pointer. (It removes the * negative bit.) * @param n The number. * @return The real rdx of @a n. */ #define BC_NUM_RDX_VAL_NP(n) ((n).rdx >> 1) /** * Sets the rdx of @a n to @a v. * @param n The number. * @param v The value to set the rdx to. */ #define BC_NUM_RDX_SET(n, v) \ ((n)->rdx = (((v) << 1) | ((n)->rdx & (BcBigDig) 1))) /** * Sets the rdx of @a n to @a v, where @a n is not a pointer. * @param n The number. * @param v The value to set the rdx to. */ #define BC_NUM_RDX_SET_NP(n, v) \ ((n).rdx = (((v) << 1) | ((n).rdx & (BcBigDig) 1))) /** * Sets the rdx of @a n to @a v and the negative bit to @a neg. * @param n The number. * @param v The value to set the rdx to. * @param neg The value to set the negative bit to. */ #define BC_NUM_RDX_SET_NEG(n, v, neg) \ ((n)->rdx = (((v) << 1) | (neg))) /** * Returns true if the rdx and scale for @a n match. * @param n The number to test. * @return True if the rdx and scale of @a n match, false otherwise. */ #define BC_NUM_RDX_VALID(n) \ (BC_NUM_ZERO(n) || BC_NUM_RDX_VAL(n) * BC_BASE_DIGS >= (n)->scale) /** * Returns true if the rdx and scale for @a n match, where @a n is not a * pointer. * @param n The number to test. * @return True if the rdx and scale of @a n match, false otherwise. */ #define BC_NUM_RDX_VALID_NP(n) \ ((!(n).len) || BC_NUM_RDX_VAL_NP(n) * BC_BASE_DIGS >= (n).scale) /** * Returns true if @a n is negative, false otherwise. * @param n The number to test. * @return True if @a n is negative, false otherwise. */ #define BC_NUM_NEG(n) ((n)->rdx & ((BcBigDig) 1)) /** * Returns true if @a n is negative, false otherwise, where @a n is not a * pointer. * @param n The number to test. * @return True if @a n is negative, false otherwise. */ #define BC_NUM_NEG_NP(n) ((n).rdx & ((BcBigDig) 1)) /** * Clears the negative bit on @a n. * @param n The number. */ #define BC_NUM_NEG_CLR(n) ((n)->rdx &= ~((BcBigDig) 1)) /** * Clears the negative bit on @a n, where @a n is not a pointer. * @param n The number. */ #define BC_NUM_NEG_CLR_NP(n) ((n).rdx &= ~((BcBigDig) 1)) /** * Sets the negative bit on @a n. * @param n The number. */ #define BC_NUM_NEG_SET(n) ((n)->rdx |= ((BcBigDig) 1)) /** * Toggles the negative bit on @a n. * @param n The number. */ #define BC_NUM_NEG_TGL(n) ((n)->rdx ^= ((BcBigDig) 1)) /** * Toggles the negative bit on @a n, where @a n is not a pointer. * @param n The number. */ #define BC_NUM_NEG_TGL_NP(n) ((n).rdx ^= ((BcBigDig) 1)) /** * Returns the rdx val for @a n if the negative bit is set to @a v. * @param n The number. * @param v The value for the negative bit. * @return The value of the rdx of @a n if the negative bit were set to @a v. */ #define BC_NUM_NEG_VAL(n, v) (((n)->rdx & ~((BcBigDig) 1)) | (v)) /** * Returns the rdx val for @a n if the negative bit is set to @a v, where @a n * is not a pointer. * @param n The number. * @param v The value for the negative bit. * @return The value of the rdx of @a n if the negative bit were set to @a v. */ #define BC_NUM_NEG_VAL_NP(n, v) (((n).rdx & ~((BcBigDig) 1)) | (v)) /** * Returns the size, in bytes, of limb array with @a n limbs. * @param n The number. * @return The size, in bytes, of a limb array with @a n limbs. */ #define BC_NUM_SIZE(n) ((n) * sizeof(BcDig)) // These are for debugging only. #if BC_DEBUG_CODE #define BC_NUM_PRINT(x) fprintf(stderr, "%s = %lu\n", #x, (unsigned long)(x)) #define DUMP_NUM bc_num_dump #else // BC_DEBUG_CODE #undef DUMP_NUM #define DUMP_NUM(x,y) #define BC_NUM_PRINT(x) #endif // BC_DEBUG_CODE /** * A function type for binary operators. * @param a The first parameter. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ typedef void (*BcNumBinaryOp)(BcNum* a, BcNum* b, BcNum* c, size_t scale); /** * A function type for binary operators *after* @a c has been properly * allocated. At this point, *nothing* should be pointing to @a c (in any way * that matters, anyway). * @param a The first operand. * @param b The second operand. * @param c The return parameter. * @param scale The current scale. */ typedef void (*BcNumBinOp)(BcNum* a, BcNum* b, BcNum* restrict c, size_t scale); /** * A function type for getting the allocation size needed for a binary operator. * Any function used for this *must* return enough space for *all* possible * invocations of the operator. * @param a The first parameter. * @param b The second parameter. * @param scale The current scale. * @return The size of allocation needed for the result of the operator * with @a a, @a b, and @a scale. */ typedef size_t (*BcNumBinaryOpReq)(const BcNum* a, const BcNum* b, size_t scale); /** * A function type for printing a "digit." Functions of this type will print one * digit in a number. Digits are printed differently based on the base, which is * why there is more than one implementation of this function type. * @param n The "digit" to print. * @param len The "length" of the digit, or number of characters that will * need to be printed for the digit. * @param rdx True if a decimal (radix) point should be printed. * @param bslash True if a backslash+newline should be printed if the character * limit for the line is reached, false otherwise. */ typedef void (*BcNumDigitOp)(size_t n, size_t len, bool rdx, bool bslash); /** * A function type to run an operator on @a a and @a b and store the result in * @a a. This is used in karatsuba for faster adds and subtracts at the end. * @param a The first parameter and return value. * @param b The second parameter. * @param len The minimum length of both arrays. */ typedef void (*BcNumShiftAddOp)(BcDig* restrict a, const BcDig* restrict b, size_t len); /** * Initializes @a n with @a req limbs in its array. * @param n The number to initialize. * @param req The number of limbs @a n must have in its limb array. */ void bc_num_init(BcNum *restrict n, size_t req); /** * Initializes (sets up) @a n with the preallocated limb array @a num that has * size @a cap. This is called by @a bc_num_init(), but it is also used by parts * of bc that use statically allocated limb arrays. * @param n The number to initialize. * @param num The preallocated limb array. * @param cap The capacity of @a num. */ void bc_num_setup(BcNum *restrict n, BcDig *restrict num, size_t cap); /** * Copies @a s into @a d. This does a deep copy and requires that @a d is * already a valid and allocated BcNum. * @param d The destination BcNum. * @param s The source BcNum. */ void bc_num_copy(BcNum *d, const BcNum *s); /** * Creates @a d and copies @a s into @a d. This does a deep copy and requires * that @a d is *not* a valid or allocated BcNum. * @param d The destination BcNum. * @param s The source BcNum. */ void bc_num_createCopy(BcNum *d, const BcNum *s); /** * Creates (initializes) @a n and sets its value to the equivalent of @a val. * @a n must *not* be a valid or preallocated BcNum. * @param n The number to initialize and set. * @param val The value to set @a n's value to. */ void bc_num_createFromBigdig(BcNum *restrict n, BcBigDig val); /** * Makes @a n valid for holding strings. @a n must *not* be allocated; this * simply clears some fields, including setting the num field to NULL. * @param n The number to clear. */ void bc_num_clear(BcNum *restrict n); /** * Frees @a num, which is a BcNum as a void pointer. This is a destructor. * @param num The BcNum to free as a void pointer. */ void bc_num_free(void *num); /** * Returns the scale of @a n. * @param n The number. * @return The scale of @a n. */ size_t bc_num_scale(const BcNum *restrict n); /** * Returns the length (in decimal digits) of @a n. This is complicated. First, * if the number is zero, we always return at least one, but we also return the * scale if it exists. Then, If it is not zero, it opens a whole other can of * worms. Read the comments in the definition. * @param n The number. * @return The length of @a n. */ size_t bc_num_len(const BcNum *restrict n); /** * Convert a number to a BcBigDig (hardware integer). This version does error * checking, and if it finds an error, throws it. Otherwise, it calls * bc_num_bigdig2(). * @param n The number to convert. * @return The number as a hardware integer. */ BcBigDig bc_num_bigdig(const BcNum *restrict n); /** * Convert a number to a BcBigDig (hardware integer). This version does no error * checking. * @param n The number to convert. * @return The number as a hardware integer. */ BcBigDig bc_num_bigdig2(const BcNum *restrict n); /** * Sets @a n to the value of @a val. @a n is expected to be a valid and * allocated BcNum. * @param n The number to set. * @param val The value to set the number to. */ void bc_num_bigdig2num(BcNum *restrict n, BcBigDig val); #if BC_ENABLE_EXTRA_MATH /** * Generates a random arbitrary-size integer less than or equal to @a a and * returns it in @a b. This implements irand(). * @param a The limit for the integer to generate. * @param b The return value. * @param rng The pseudo-random number generator. */ void bc_num_irand(BcNum *restrict a, BcNum *restrict b, struct BcRNG *restrict rng); /** * Sets the seed for the PRNG @a rng from @a n. * @param n The new seed for the PRNG. * @param rng The PRNG to set the seed for. */ void bc_num_rng(const BcNum *restrict n, struct BcRNG *rng); /** * Sets @a n to the value produced by the PRNG. This implements rand(). * @param n The number to set. * @param rng The pseudo-random number generator. */ void bc_num_createFromRNG(BcNum *restrict n, struct BcRNG *rng); #endif // BC_ENABLE_EXTRA_MATH /** * The add function. This is a BcNumBinaryOp function. * @param a The first parameter. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_add(BcNum *a, BcNum *b, BcNum *c, size_t scale); /** * The subtract function. This is a BcNumBinaryOp function. * @param a The first parameter. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_sub(BcNum *a, BcNum *b, BcNum *c, size_t scale); /** * The multiply function. * @param a The first parameter. This is a BcNumBinaryOp function. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_mul(BcNum *a, BcNum *b, BcNum *c, size_t scale); /** * The division function. * @param a The first parameter. This is a BcNumBinaryOp function. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_div(BcNum *a, BcNum *b, BcNum *c, size_t scale); /** * The modulus function. * @param a The first parameter. This is a BcNumBinaryOp function. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_mod(BcNum *a, BcNum *b, BcNum *c, size_t scale); /** * The power function. * @param a The first parameter. This is a BcNumBinaryOp function. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_pow(BcNum *a, BcNum *b, BcNum *c, size_t scale); #if BC_ENABLE_EXTRA_MATH /** * The places function (@ operator). This is a BcNumBinaryOp function. * @param a The first parameter. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_places(BcNum *a, BcNum *b, BcNum *c, size_t scale); /** * The left shift function (<< operator). This is a BcNumBinaryOp function. * @param a The first parameter. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_lshift(BcNum *a, BcNum *b, BcNum *c, size_t scale); /** * The right shift function (>> operator). This is a BcNumBinaryOp function. * @param a The first parameter. * @param b The second parameter. * @param c The return value. * @param scale The current scale. */ void bc_num_rshift(BcNum *a, BcNum *b, BcNum *c, size_t scale); #endif // BC_ENABLE_EXTRA_MATH /** * Square root. * @param a The first parameter. * @param b The return value. * @param scale The current scale. */ void bc_num_sqrt(BcNum *restrict a, BcNum *restrict b, size_t scale); /** * Divsion and modulus together. This is a dc extension. * @param a The first parameter. * @param b The second parameter. * @param c The first return value (quotient). * @param d The second return value (modulus). * @param scale The current scale. */ void bc_num_divmod(BcNum *a, BcNum *b, BcNum *c, BcNum *d, size_t scale); /** * A function returning the required allocation size for an addition or a * subtraction. This is a BcNumBinaryOpReq function. * @param a The first parameter. * @param b The second parameter. * @param scale The current scale. * @return The size of allocation needed for the result of add or subtract * with @a a, @a b, and @a scale. */ size_t bc_num_addReq(const BcNum* a, const BcNum* b, size_t scale); /** * A function returning the required allocation size for a multiplication. This * is a BcNumBinaryOpReq function. * @param a The first parameter. * @param b The second parameter. * @param scale The current scale. * @return The size of allocation needed for the result of multiplication * with @a a, @a b, and @a scale. */ size_t bc_num_mulReq(const BcNum *a, const BcNum *b, size_t scale); /** * A function returning the required allocation size for a division or modulus. * This is a BcNumBinaryOpReq function. * @param a The first parameter. * @param b The second parameter. * @param scale The current scale. * @return The size of allocation needed for the result of division or * modulus with @a a, @a b, and @a scale. */ size_t bc_num_divReq(const BcNum *a, const BcNum *b, size_t scale); /** * A function returning the required allocation size for an exponentiation. This * is a BcNumBinaryOpReq function. * @param a The first parameter. * @param b The second parameter. * @param scale The current scale. * @return The size of allocation needed for the result of exponentiation * with @a a, @a b, and @a scale. */ size_t bc_num_powReq(const BcNum *a, const BcNum *b, size_t scale); #if BC_ENABLE_EXTRA_MATH /** * A function returning the required allocation size for a places, left shift, * or right shift. This is a BcNumBinaryOpReq function. * @param a The first parameter. * @param b The second parameter. * @param scale The current scale. * @return The size of allocation needed for the result of places, left * shift, or right shift with @a a, @a b, and @a scale. */ size_t bc_num_placesReq(const BcNum *a, const BcNum *b, size_t scale); #endif // BC_ENABLE_EXTRA_MATH /** * Truncate @a n *by* @a places decimal places. This only extends places *after* * the decimal point. * @param n The number to truncate. * @param places The number of places to truncate @a n by. */ void bc_num_truncate(BcNum *restrict n, size_t places); /** * Extend @a n *by* @a places decimal places. This only extends places *after* * the decimal point. * @param n The number to truncate. * @param places The number of places to extend @a n by. */ void bc_num_extend(BcNum *restrict n, size_t places); /** * Shifts @a n right by @a places decimal places. This is the workhorse of the * right shift operator, and would be static to src/num.c, except that * src/library.c uses it for efficiency when executing its frand. * @param n The number to shift right. * @param places The number of decimal places to shift @a n right by. */ void bc_num_shiftRight(BcNum *restrict n, size_t places); /** * Compare a and b and return the result of their comparison as an ssize_t. * Returns >0 if @a a is greater than @a b, <0 if @a a is less than @a b, and =0 * if a == b. * @param a The first number. * @param b The second number. * @return The result of the comparison. */ ssize_t bc_num_cmp(const BcNum *a, const BcNum *b); /** * Modular exponentiation. * @param a The first parameter. * @param b The second parameter. * @param c The third parameter. * @param d The return value. */ void bc_num_modexp(BcNum *a, BcNum *b, BcNum *c, BcNum *restrict d); /** * Sets @a n to zero with a scale of zero. * @param n The number to zero. */ void bc_num_zero(BcNum *restrict n); /** * Sets @a n to one with a scale of zero. * @param n The number to set to one. */ void bc_num_one(BcNum *restrict n); /** * An efficient function to compare @a n to zero. * @param n The number to compare to zero. * @return The result of the comparison. */ ssize_t bc_num_cmpZero(const BcNum *n); #if !defined(NDEBUG) || BC_ENABLE_LIBRARY /** * Check a number string for validity and return true if it is, false otherwise. * The library needs this to check user-supplied strings, but in bc and dc, this * is only used for debug asserts because the parsers should get the numbers * parsed right, which should ensure they are always valid. * @param val The string to check. * @return True if the string is a valid number, false otherwise. */ bool bc_num_strValid(const char *restrict val); #endif // !defined(NDEBUG) || BC_ENABLE_LIBRARY /** * Parses a number string into the number @a n according to @a base. * @param n The number to set to the parsed value. * @param val The number string to parse. * @param base The base to parse the number string by. */ void bc_num_parse(BcNum *restrict n, const char *restrict val, BcBigDig base); /** * Prints the number @a n according to @a base. * @param n The number to print. * @param base The base to print the number by. * @param newline True if a newline should be inserted at the end, false * otherwise. */ void bc_num_print(BcNum *restrict n, BcBigDig base, bool newline); #if !BC_ENABLE_LIBRARY /** * Prints a number as a character stream. * @param n The number to print as a character stream. */ void bc_num_stream(BcNum *restrict n); #endif // !BC_ENABLE_LIBRARY #if BC_DEBUG_CODE /** * Print a number with a label. This is a debug-only function. * @param n The number to print. * @param name The label to print the number with. * @param emptyline True if there should be an empty line after the number. */ void bc_num_printDebug(const BcNum *n, const char *name, bool emptyline); /** * Print the limbs of @a n. This is a debug-only function. * @param n The number to print. * @param len The length of the number. * @param emptyline True if there should be an empty line after the number. */ void bc_num_printDigs(const BcDig* n, size_t len, bool emptyline); /** * Print debug info about @a n along with its limbs. * @param n The number to print. * @param name The label to print the number with. * @param emptyline True if there should be an empty line after the number. */ void bc_num_printWithDigs(const BcNum *n, const char *name, bool emptyline); /** * Dump debug info about a BcNum variable. * @param varname The variable name. * @param n The number. */ void bc_num_dump(const char *varname, const BcNum *n); #endif // BC_DEBUG_CODE /// A reference to an array of hex digits for easy conversion for printing. extern const char bc_num_hex_digits[]; /// An array of powers of 10 for easy conversion from number of digits to //powers. extern const BcBigDig bc_num_pow10[BC_BASE_DIGS + 1]; /// A reference to a constant array that is the max of a BigDig. extern const BcDig bc_num_bigdigMax[]; /// A reference to a constant size of the above array. extern const size_t bc_num_bigdigMax_size; /// A reference to a constant array that is 2 times the max of a BigDig. extern const BcDig bc_num_bigdigMax2[]; /// A reference to a constant size of the above array. extern const size_t bc_num_bigdigMax2_size; #endif // BC_NUM_H