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265 lines
8.9 KiB
265 lines
8.9 KiB
/*
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* *****************************************************************************
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*
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* Copyright (c) 2018-2021 Gavin D. Howard and contributors.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* * Redistributions of source code must retain the above copyright notice, this
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* list of conditions and the following disclaimer.
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*
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* * Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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* *****************************************************************************
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*
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* Definitions for the num type.
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*
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*/
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#ifndef BC_NUM_H
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#define BC_NUM_H
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#include <limits.h>
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#include <stdbool.h>
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#include <stddef.h>
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#include <stdint.h>
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#include <sys/types.h>
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#include <status.h>
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#include <vector.h>
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#include <bcl.h>
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#ifndef BC_ENABLE_EXTRA_MATH
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#define BC_ENABLE_EXTRA_MATH (1)
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#endif // BC_ENABLE_EXTRA_MATH
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#define BC_BASE (10)
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typedef unsigned long ulong;
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typedef BclBigDig BcBigDig;
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#if BC_LONG_BIT >= 64
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#define BC_NUM_BIGDIG_MAX ((BcBigDig) UINT64_MAX)
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#define BC_BASE_DIGS (9)
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#define BC_BASE_POW (1000000000)
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#define BC_NUM_BIGDIG_C UINT64_C
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typedef int_least32_t BcDig;
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#elif BC_LONG_BIT >= 32
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#define BC_NUM_BIGDIG_MAX ((BcBigDig) UINT32_MAX)
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#define BC_BASE_DIGS (4)
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#define BC_BASE_POW (10000)
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#define BC_NUM_BIGDIG_C UINT32_C
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typedef int_least16_t BcDig;
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#else
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#error BC_LONG_BIT must be at least 32
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#endif // BC_LONG_BIT >= 64
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#define BC_NUM_DEF_SIZE (8)
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typedef struct BcNum {
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BcDig *restrict num;
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size_t rdx;
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size_t scale;
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size_t len;
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size_t cap;
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} BcNum;
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#if BC_ENABLE_EXTRA_MATH
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#ifndef BC_ENABLE_RAND
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#define BC_ENABLE_RAND (1)
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#endif // BC_ENABLE_RAND
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#if BC_ENABLE_RAND
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// Forward declaration
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struct BcRNG;
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#endif // BC_ENABLE_RAND
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#endif // BC_ENABLE_EXTRA_MATH
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#define BC_NUM_MIN_BASE (BC_NUM_BIGDIG_C(2))
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#define BC_NUM_MAX_POSIX_IBASE (BC_NUM_BIGDIG_C(16))
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#define BC_NUM_MAX_IBASE (BC_NUM_BIGDIG_C(36))
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// This is the max base allowed by bc_num_parseChar().
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#define BC_NUM_MAX_LBASE (BC_NUM_BIGDIG_C('Z' + BC_BASE + 1))
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#define BC_NUM_PRINT_WIDTH (BC_NUM_BIGDIG_C(69))
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#ifndef BC_NUM_KARATSUBA_LEN
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#define BC_NUM_KARATSUBA_LEN (BC_NUM_BIGDIG_C(32))
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#elif BC_NUM_KARATSUBA_LEN < 16
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#error BC_NUM_KARATSUBA_LEN must be at least 16.
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#endif // BC_NUM_KARATSUBA_LEN
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// A crude, but always big enough, calculation of
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// the size required for ibase and obase BcNum's.
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#define BC_NUM_BIGDIG_LOG10 (BC_NUM_DEF_SIZE)
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#define BC_NUM_NONZERO(n) ((n)->len)
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#define BC_NUM_ZERO(n) (!BC_NUM_NONZERO(n))
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#define BC_NUM_ONE(n) ((n)->len == 1 && (n)->rdx == 0 && (n)->num[0] == 1)
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#define BC_NUM_NUM_LETTER(c) ((c) - 'A' + BC_BASE)
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#define BC_NUM_KARATSUBA_ALLOCS (6)
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#define BC_NUM_ROUND_POW(s) (bc_vm_growSize((s), BC_BASE_DIGS - 1))
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#define BC_NUM_RDX(s) (BC_NUM_ROUND_POW(s) / BC_BASE_DIGS)
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#define BC_NUM_RDX_VAL(n) ((n)->rdx >> 1)
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#define BC_NUM_RDX_VAL_NP(n) ((n).rdx >> 1)
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#define BC_NUM_RDX_SET(n, v) \
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((n)->rdx = (((v) << 1) | ((n)->rdx & (BcBigDig) 1)))
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#define BC_NUM_RDX_SET_NP(n, v) \
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((n).rdx = (((v) << 1) | ((n).rdx & (BcBigDig) 1)))
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#define BC_NUM_RDX_SET_NEG(n, v, neg) \
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((n)->rdx = (((v) << 1) | (neg)))
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#define BC_NUM_RDX_VALID(n) \
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(BC_NUM_ZERO(n) || BC_NUM_RDX_VAL(n) * BC_BASE_DIGS >= (n)->scale)
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#define BC_NUM_RDX_VALID_NP(n) \
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((!(n).len) || BC_NUM_RDX_VAL_NP(n) * BC_BASE_DIGS >= (n).scale)
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#define BC_NUM_NEG(n) ((n)->rdx & ((BcBigDig) 1))
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#define BC_NUM_NEG_NP(n) ((n).rdx & ((BcBigDig) 1))
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#define BC_NUM_NEG_CLR(n) ((n)->rdx &= ~((BcBigDig) 1))
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#define BC_NUM_NEG_CLR_NP(n) ((n).rdx &= ~((BcBigDig) 1))
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#define BC_NUM_NEG_SET(n) ((n)->rdx |= ((BcBigDig) 1))
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#define BC_NUM_NEG_TGL(n) ((n)->rdx ^= ((BcBigDig) 1))
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#define BC_NUM_NEG_TGL_NP(n) ((n).rdx ^= ((BcBigDig) 1))
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#define BC_NUM_NEG_VAL(n, v) (((n)->rdx & ~((BcBigDig) 1)) | (v))
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#define BC_NUM_NEG_VAL_NP(n, v) (((n).rdx & ~((BcBigDig) 1)) | (v))
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#define BC_NUM_SIZE(n) ((n) * sizeof(BcDig))
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#if BC_DEBUG_CODE
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#define BC_NUM_PRINT(x) fprintf(stderr, "%s = %lu\n", #x, (unsigned long)(x))
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#define DUMP_NUM bc_num_dump
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#else // BC_DEBUG_CODE
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#undef DUMP_NUM
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#define DUMP_NUM(x,y)
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#define BC_NUM_PRINT(x)
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#endif // BC_DEBUG_CODE
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typedef void (*BcNumBinaryOp)(BcNum*, BcNum*, BcNum*, size_t);
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typedef void (*BcNumBinOp)(BcNum*, BcNum*, BcNum* restrict, size_t);
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typedef size_t (*BcNumBinaryOpReq)(const BcNum*, const BcNum*, size_t);
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typedef void (*BcNumDigitOp)(size_t, size_t, bool);
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typedef void (*BcNumShiftAddOp)(BcDig* restrict, const BcDig* restrict, size_t);
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void bc_num_init(BcNum *restrict n, size_t req);
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void bc_num_setup(BcNum *restrict n, BcDig *restrict num, size_t cap);
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void bc_num_copy(BcNum *d, const BcNum *s);
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void bc_num_createCopy(BcNum *d, const BcNum *s);
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void bc_num_createFromBigdig(BcNum *n, BcBigDig val);
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void bc_num_clear(BcNum *restrict n);
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void bc_num_free(void *num);
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size_t bc_num_scale(const BcNum *restrict n);
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size_t bc_num_len(const BcNum *restrict n);
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void bc_num_bigdig(const BcNum *restrict n, BcBigDig *result);
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void bc_num_bigdig2(const BcNum *restrict n, BcBigDig *result);
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void bc_num_bigdig2num(BcNum *restrict n, BcBigDig val);
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#if BC_ENABLE_EXTRA_MATH && BC_ENABLE_RAND
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void bc_num_irand(const BcNum *restrict a, BcNum *restrict b,
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struct BcRNG *restrict rng);
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void bc_num_rng(const BcNum *restrict n, struct BcRNG *rng);
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void bc_num_createFromRNG(BcNum *restrict n, struct BcRNG *rng);
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#endif // BC_ENABLE_EXTRA_MATH && BC_ENABLE_RAND
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void bc_num_add(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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void bc_num_sub(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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void bc_num_mul(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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void bc_num_div(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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void bc_num_mod(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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void bc_num_pow(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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#if BC_ENABLE_EXTRA_MATH
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void bc_num_places(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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void bc_num_lshift(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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void bc_num_rshift(BcNum *a, BcNum *b, BcNum *c, size_t scale);
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#endif // BC_ENABLE_EXTRA_MATH
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void bc_num_sqrt(BcNum *restrict a, BcNum *restrict b, size_t scale);
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void bc_num_sr(BcNum *restrict a, BcNum *restrict b, size_t scale);
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void bc_num_divmod(BcNum *a, BcNum *b, BcNum *c, BcNum *d, size_t scale);
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size_t bc_num_addReq(const BcNum* a, const BcNum* b, size_t scale);
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size_t bc_num_mulReq(const BcNum *a, const BcNum *b, size_t scale);
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size_t bc_num_divReq(const BcNum *a, const BcNum *b, size_t scale);
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size_t bc_num_powReq(const BcNum *a, const BcNum *b, size_t scale);
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#if BC_ENABLE_EXTRA_MATH
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size_t bc_num_placesReq(const BcNum *a, const BcNum *b, size_t scale);
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#endif // BC_ENABLE_EXTRA_MATH
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void bc_num_truncate(BcNum *restrict n, size_t places);
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void bc_num_extend(BcNum *restrict n, size_t places);
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void bc_num_shiftRight(BcNum *restrict n, size_t places);
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ssize_t bc_num_cmp(const BcNum *a, const BcNum *b);
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#if DC_ENABLED
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void bc_num_modexp(BcNum *a, BcNum *b, BcNum *c, BcNum *restrict d);
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#endif // DC_ENABLED
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void bc_num_zero(BcNum *restrict n);
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void bc_num_one(BcNum *restrict n);
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ssize_t bc_num_cmpZero(const BcNum *n);
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#if !defined(NDEBUG) || BC_ENABLE_LIBRARY
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bool bc_num_strValid(const char *restrict val);
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#endif // !defined(NDEBUG) || BC_ENABLE_LIBRARY
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void bc_num_parse(BcNum *restrict n, const char *restrict val, BcBigDig base);
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void bc_num_print(BcNum *restrict n, BcBigDig base, bool newline);
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#if DC_ENABLED
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void bc_num_stream(BcNum *restrict n, BcBigDig base);
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#endif // DC_ENABLED
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#if BC_DEBUG_CODE
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void bc_num_printDebug(const BcNum *n, const char *name, bool emptyline);
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void bc_num_printDigs(const BcDig* n, size_t len, bool emptyline);
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void bc_num_printWithDigs(const BcNum *n, const char *name, bool emptyline);
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void bc_num_dump(const char *varname, const BcNum *n);
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#endif // BC_DEBUG_CODE
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extern const char bc_num_hex_digits[];
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extern const BcBigDig bc_num_pow10[BC_BASE_DIGS + 1];
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extern const BcDig bc_num_bigdigMax[];
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extern const BcDig bc_num_bigdigMax2[];
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extern const size_t bc_num_bigdigMax_size;
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extern const size_t bc_num_bigdigMax2_size;
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#endif // BC_NUM_H
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