text: /*
   * RELIC is an Efficient LIbrary for Cryptography
   * Copyright (C) 2007-2019 RELIC Authors
   *
   * This file is part of RELIC. RELIC is legal property of its developers,
   * whose names are not listed here. Please refer to the COPYRIGHT file
   * for contact information.
   *
   * RELIC is free software; you can redistribute it and/or modify it under the
   * terms of the version 2.1 (or later) of the GNU Lesser General Public License
   * as published by the Free Software Foundation; or version 2.0 of the Apache
   * License as published by the Apache Software Foundation. See the LICENSE files
   * for more details.
   *
   * RELIC is distributed in the hope that it will be useful, but WITHOUT ANY
   * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
   * A PARTICULAR PURPOSE. See the LICENSE files for more details.
   *
   * You should have received a copy of the GNU Lesser General Public or the
   * Apache License along with RELIC. If not, see <https://www.gnu.org/licenses/>
   * or <https://www.apache.org/licenses/>.
   */
  
  /**
   * @file
   *
   * Implementation of the multiple precision addition and subtraction functions.
   *
   * @ingroup bn
   */
  
  #include "relic_core.h"
  #include "relic_bn_low.h"
  
  /*============================================================================*/
  /* Private definitions                                                        */
  /*============================================================================*/
  
  /**
   * Adds two multiple precision integers, where a >= b.
   *
   * @param[out] c        - the result.
   * @param[in] a         - the first multiple precision integer to add.
   * @param[in] b         - the second multiple precision integer to add.
   */
  static void bn_add_imp(bn_t c, const bn_t a, const bn_t b) {
  	int max, min;
  	dig_t carry;
  
  	max = a->used;
  	min = b->used;
  
  	/* Grow the result. */
  	bn_grow(c, max);
  
  	if (min == 0) {
  		bn_copy(c, a);
  		return;
  	}
  
  	if (a->used == b->used) {
  		carry = bn_addn_low(c->dp, a->dp, b->dp, max);
  	} else {
  		carry = bn_addn_low(c->dp, a->dp, b->dp, min);
  		carry = bn_add1_low(c->dp + min, a->dp + min, carry, max - min);
  	}
  	if (carry) {
  		bn_grow(c, max + 1);
  		c->dp[max] = carry;
  	}
  	c->used = max + carry;
  	bn_trim(c);
  }
  
  /**
   * Subtracts two multiple precision integers, where a >= b.
   *
   * @param[out] c        - the result.
   * @param[in] a         - the first multiple precision integer to subtract.
   * @param[in] b         - the second multiple precision integer to subtract.
   */
  static void bn_sub_imp(bn_t c, const bn_t a, const bn_t b) {
  	int max, min;
  	dig_t carry;
  
  	max = a->used;
  	min = b->used;
  
  	if (min == 0) {
  		bn_copy(c, a);
  		return;
  	}
  
  	/* Grow the destination to accomodate the result. */
  	bn_grow(c, max);
  
  	if (a->used == b->used) {
  		carry = bn_subn_low(c->dp, a->dp, b->dp, min);
  	} else {
  		carry = bn_subn_low(c->dp, a->dp, b->dp, min);
  		carry = bn_sub1_low(c->dp + min, a->dp + min, carry, max - min);
  	}
  	c->used = max;
  	bn_trim(c);
  }
  
  /*============================================================================*/
  /* Public definitions                                                         */
  /*============================================================================*/
  
  void bn_add(bn_t c, const bn_t a, const bn_t b) {
  	int sa, sb;
  
  	sa = a->sign;
  	sb = b->sign;
  
  	if (sa == sb) {
  		/* If the signs are equal, copy the sign and add. */
  		c->sign = sa;
  		if (bn_cmp_abs(a, b) == RLC_LT) {
  			bn_add_imp(c, b, a);
  		} else {
  			bn_add_imp(c, a, b);
  		}
  	} else {
  		/* If the signs are different, subtract. */
  		if (bn_cmp_abs(a, b) == RLC_LT) {
  			bn_sub_imp(c, b, a);
  			c->sign = sb;
  		} else {
  			bn_sub_imp(c, a, b);
  			c->sign = sa;
  		}
  	}
  }
  
  void bn_add_dig(bn_t c, const bn_t a, dig_t b) {
  	dig_t carry;
  
  	bn_grow(c, a->used);
  
  	if (a->sign == RLC_POS) {
  		carry = bn_add1_low(c->dp, a->dp, b, a->used);
  		if (carry) {
  			bn_grow(c, a->used + 1);
  			c->dp[a->used] = carry;
  		}
  		c->used = a->used + carry;
  		c->sign = RLC_POS;
  	} else {
  		/* If a < 0 && |a| >= b, compute c = -(|a| - b). */
  		if (a->used > 1 || a->dp[0] >= b) {
  			carry = bn_sub1_low(c->dp, a->dp, b, a->used);
  			c->used = a->used;
  			c->sign = RLC_NEG;
  		} else {
  			/* If a < 0 && |a| < b. */
  			if (a->used == 1) {
  				c->dp[0] = b - a->dp[0];
  			} else {
  				c->dp[0] = b;
  			}
  			c->used = 1;
  			c->sign = RLC_POS;
  		}
  	}
  	bn_trim(c);
  }
  
  void bn_sub(bn_t c, const bn_t a, const bn_t b) {
  	int sa, sb;
  
  	sa = a->sign;
  	sb = b->sign;
  
  	if (sa != sb) {
  		/* If the signs are different, copy the sign of the first number and
  		 * add. */
  		c->sign = sa;
  		if (bn_cmp_abs(a, b) == RLC_LT) {
  			bn_add_imp(c, b, a);
  		} else {
  			bn_add_imp(c, a, b);
  		}
  	} else {
  		/* If the signs are equal, adjust the sign and subtract. */
  		if (bn_cmp_abs(a, b) != RLC_LT) {
  			bn_sub_imp(c, a, b);
  			c->sign = sa;
  		} else {
  			bn_sub_imp(c, b, a);
  			c->sign = (sa == RLC_POS) ? RLC_NEG : RLC_POS;
  		}
  	}
  }
  
  void bn_sub_dig(bn_t c, const bn_t a, dig_t b) {
  	dig_t carry;
  
  	bn_grow(c, a->used);
  
  	/* If a < 0, compute c = -(|a| + b). */
  	if (a->sign == RLC_NEG) {
  		carry = bn_add1_low(c->dp, a->dp, b, a->used);
  		if (carry) {
  			bn_grow(c, a->used + 1);
  			c->dp[a->used] = carry;
  		}
  		c->used = a->used + carry;
  		c->sign = RLC_NEG;
  	} else {
  		/* If a > 0 && |a| >= b, compute c = (|a| - b). */
  		if (a->used > 1 || a->dp[0] >= b) {
  			carry = bn_sub1_low(c->dp, a->dp, b, a->used);
  			c->used = a->used;
  			c->sign = RLC_POS;
  		} else {
  			/* If a > 0 && a < b. */
  			if (a->used == 1) {
  				c->dp[0] = b - a->dp[0];
  			} else {
  				c->dp[0] = b;
  			}
  			c->used = 1;
  			c->sign = RLC_NEG;
  		}
  	}
  	bn_trim(c);
  }
  