text: /*
   * RELIC is an Efficient LIbrary for Cryptography
   * Copyright (c) 2009 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 integer arithmetic squaring
   * functions.
   *
   * @ingroup fp
   */
  
  #include "relic_core.h"
  #include "relic_fp_low.h"
  #include "relic_bn_low.h"
  
  /*============================================================================*/
  /* Private definitions                                                        */
  /*============================================================================*/
  
  #if FP_KARAT > 0 || !defined(STRIP)
  
  /**
   * Computes the square of a multiple precision integer using recursive Karatsuba
   * squaring.
   *
   * @param[out] c			- the result.
   * @param[in] a				- the prime field element to square.
   * @param[in] size			- the number of digits to square.
   * @param[in] level			- the number of Karatsuba steps to apply.
   */
  static void fp_sqr_karat_imp(dv_t c, const fp_t a, int size, int level) {
  	int i, h, h1;
  	dv_t t0, t1, a0a0, a1a1;
  	dig_t carry;
  
  	/* Compute half the digits of a or b. */
  	h = size >> 1;
  	h1 = size - h;
  
  	dv_null(t0);
  	dv_null(t1);
  	dv_null(a0a0);
  	dv_null(a1a1);
  
  	RLC_TRY {
  		/* Allocate the temp variables. */
  		dv_new(t0);
  		dv_new(t1);
  		dv_new(a0a0);
  		dv_new(a1a1);
  		dv_zero(t0, 2 * h1);
  		dv_zero(t1, 2 * (h1 + 1));
  		dv_zero(a0a0, 2 * h);
  		dv_zero(a1a1, 2 * h1);
  
  		if (level <= 1) {
  			/* a0a0 = a0 * a0 and a1a1 = a1 * a1 */
  #if FP_SQR == BASIC
  			for (i = 0; i < h - 1; i++) {
  				a0a0[h + i + 1] = bn_sqra_low(a0a0 + 2 * i, a + i, h - i);
  			}
  			bn_sqra_low(a0a0 + 2 * i, a + i, 1);
  			for (i = 0; i < h1 - 1; i++) {
  				a1a1[h1 + i + 1] = bn_sqra_low(a1a1 + 2 * i, a + h + i, h1 - i);
  			}
  			bn_sqra_low(a1a1 + 2 * i, a + h + i, 1);
  #elif FP_SQR == COMBA || FP_SQR == INTEG
  			bn_sqrn_low(a0a0, a, h);
  			bn_sqrn_low(a1a1, a + h, h1);
  #elif FP_SQR == MULTP
  			bn_muln_low(a0a0, a, a, h);
  			bn_muln_low(a1a1, a + h, a + h, h1);
  #endif
  		} else {
  			fp_sqr_karat_imp(a0a0, a, h, level - 1);
  			fp_sqr_karat_imp(a1a1, a + h, h1, level - 1);
  		}
  
  		/* t2 = a1 * a1 << 2*h digits + a0 * a0. */
  		for (i = 0; i < 2 * h; i++) {
  			c[i] = a0a0[i];
  		}
  		for (i = 0; i < 2 * h1; i++) {
  			c[2 * h + i] = a1a1[i];
  		}
  
  		/* t = (a1 + a0) */
  		carry = bn_addn_low(t0, a, a + h, h);
  		carry = bn_add1_low(t0 + h, t0 + h, carry, 2);
  		if (h1 > h) {
  			carry = bn_add1_low(t0 + h, t0 + h, *(a + 2 * h), 2);
  		}
  
  		if (level <= 1) {
  			/* a1a1 = (a1 + a0)*(a1 + a0) */
  #if FP_SQR == BASIC
  			for (i = 0; i < h1; i++) {
  				t1[h1 + i + 2] = bn_sqra_low(t1 + (2 * i), t0 + i, h1 + 1 - i);
  			}
  			bn_sqra_low(t1 + (2 * i), t0 + i, 1);
  #elif FP_SQR == COMBA || FP_SQR == INTEG
  			bn_sqrn_low(t1, t0, h1 + 1);
  #elif FP_SQR == MULTP
  			bn_muln_low(t1, t0, t0, h1 + 1);
  #endif
  		} else {
  			fp_sqr_karat_imp(t1, t0, h1 + 1, level - 1);
  		}
  
  		/* t = t - (a0*a0 << h digits) */
  		carry = bn_subn_low(t1, t1, a0a0, 2 * h);
  		bn_sub1_low(t1 + 2 * h, t1 + 2 * h, carry, 2 * (h1 + 1) - 2 * h);
  
  		/* t = t - (a1*a1 << h digits) */
  		carry = bn_subn_low(t1, t1, a1a1, 2 * h1);
  		bn_sub1_low(t1 + 2 * h, t1 + 2 * h, carry, 2 * (h1 + 1) - 2 * h);
  
  		/* c = c + [(a1 + a0)*(a1 + a0) << digits] */
  		c += h;
  		carry = bn_addn_low(c, c, t1, 2 * (h1 + 1));
  		c += 2 * (h1 + 1);
  		carry = bn_add1_low(c, c, carry, 2 * size - h - 2 * (h1 + 1));
  	}
  	RLC_CATCH_ANY {
  		RLC_THROW(ERR_CAUGHT);
  	}
  	RLC_FINALLY {
  		dv_free(t0);
  		dv_free(t1);
  		dv_free(a0a0);
  		dv_free(a1a1);
  	}
  }
  #endif
  
  /*============================================================================*/
  /* Public definitions                                                         */
  /*============================================================================*/
  
  #if FP_SQR == BASIC || !defined(STRIP)
  
  void fp_sqr_basic(fp_t c, const fp_t a) {
  	int i;
  	dv_t t;
  
  	dv_null(t);
  
  	RLC_TRY {
  		dv_new(t);
  		dv_zero(t, 2 * RLC_FP_DIGS);
  
  		for (i = 0; i < RLC_FP_DIGS - 1; i++) {
  			t[RLC_FP_DIGS + i + 1] =
  					bn_sqra_low(t + 2 * i, a + i, RLC_FP_DIGS - i);
  		}
  		bn_sqra_low(t + 2 * i, a + i, 1);
  
  		fp_rdc(c, t);
  	}
  	RLC_CATCH_ANY {
  		RLC_THROW(ERR_CAUGHT);
  	}
  	RLC_FINALLY {
  		fp_free(t);
  	}
  }
  
  #endif
  
  #if FP_SQR == COMBA || !defined(STRIP)
  
  void fp_sqr_comba(fp_t c, const fp_t a) {
  	dv_t t;
  
  	dv_null(t);
  
  	RLC_TRY {
  		dv_new(t);
  
  		fp_sqrn_low(t, a);
  
  		fp_rdc(c, t);
  	} RLC_CATCH_ANY {
  		RLC_THROW(ERR_CAUGHT);
  	}
  	RLC_FINALLY {
  		fp_free(t);
  	}
  }
  
  #endif
  
  #if FP_SQR == INTEG || !defined(STRIP)
  
  void fp_sqr_integ(fp_t c, const fp_t a) {
  	fp_sqrm_low(c, a);
  }
  
  #endif
  
  #if FP_KARAT > 0 || !defined(STRIP)
  
  void fp_sqr_karat(fp_t c, const fp_t a) {
  	dv_t t;
  
  	dv_null(t);
  
  	RLC_TRY {
  		dv_new(t);
  		dv_zero(t, 2 * RLC_FP_DIGS);
  
  		if (RLC_FP_DIGS > 1) {
  			fp_sqr_karat_imp(t, a, RLC_FP_DIGS, FP_KARAT);
  		} else {
  			fp_sqrn_low(t, a);
  		}
  
  
  		fp_rdc(c, t);
  	} RLC_CATCH_ANY {
  		RLC_THROW(ERR_CAUGHT);
  	}
  	RLC_FINALLY {
  		dv_free(t);
  	}
  }
  
  #endif
  