/*

  Copyright 2006-2012 by

  Laboratoire de l'Informatique du Parallelisme,
  UMR CNRS - ENS Lyon - UCB Lyon 1 - INRIA 5668,

  and by

  Laboratoire d'Informatique de Paris 6, equipe PEQUAN,
  UPMC Universite Paris 06 - CNRS - UMR 7606 - LIP6, Paris, France,

  Contributors Ch. Lauter, S. Chevillard

  christoph.lauter@christoph-lauter.org
  sylvain.chevillard@ens-lyon.org

  This software is a computer program whose purpose is to provide an
  environment for safe floating-point code development. It is
  particularly targeted to the automated implementation of
  mathematical floating-point libraries (libm). Amongst other features,
  it offers a certified infinity norm, an automatic polynomial
  implementer and a fast Remez algorithm.

  This software is governed by the CeCILL-C license under French law and
  abiding by the rules of distribution of free software.  You can  use,
  modify and/ or redistribute the software under the terms of the CeCILL-C
  license as circulated by CEA, CNRS and INRIA at the following URL
  "http://www.cecill.info".

  As a counterpart to the access to the source code and  rights to copy,
  modify and redistribute granted by the license, users are provided only
  with a limited warranty  and the software's author,  the holder of the
  economic rights,  and the successive licensors  have only  limited
  liability.

  In this respect, the user's attention is drawn to the risks associated
  with loading,  using,  modifying and/or developing or reproducing the
  software by the user in light of its specific status of free software,
  that may mean  that it is complicated to manipulate,  and  that  also
  therefore means  that it is reserved for developers  and  experienced
  professionals having in-depth computer knowledge. Users are therefore
  encouraged to load and test the software's suitability as regards their
  requirements in conditions enabling the security of their systems and/or
  data to be ensured and,  more generally, to use and operate it in the
  same conditions as regards security.

  The fact that you are presently reading this means that you have had
  knowledge of the CeCILL-C license and that you accept its terms.

  This program is distributed WITHOUT ANY WARRANTY; without even the
  implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

*/

#include <mpfr.h>
#include <gmp.h>
#include "worstcase.h"
#include <stdio.h> /* fprinft, fopen, fclose, */
#include <stdlib.h> /* exit, free, mktemp */
#include <string.h>
#include <errno.h>
#include "general.h"
#include "infnorm.h"
#include "double.h"

int mpfrToInt(int *res, mpfr_t val) {
  mpfr_t verg;


  if (!mpfr_integer_p(val)) {
    printMessage(1,SOLLYA_MSG_EXPR_DOES_NOT_EVALUATE_TO_INTEGER,"Warning: an expression given in this context does not evaluate to integer.\n");
    *res = 0;
    return 0;
  }

  *res = mpfr_get_si(val,GMP_RNDN);

  mpfr_init2(verg,mpfr_get_prec(val));

  if (mpfr_set_si(verg,*res,GMP_RNDN) != 0) {
    printMessage(1,SOLLYA_MSG_ROUNDING_ON_CONVERTING_A_MACHINE_INTEGER,"Warning: rounding occurred on reconverting back an integer variable.\n");
    *res = 0;
    mpfr_clear(verg);
    return 0;
  }

  if (mpfr_cmp(verg,val) != 0) {
    printMessage(1,SOLLYA_MSG_EXPR_DOES_NOT_EVALUATE_TO_MACHINE_INTEGER,"Warning: an expression given in this context does not evaluate to a machine integer.\n");
    *res = 0;
    mpfr_clear(verg);
    return 0;
  }

  mpfr_clear(verg);
  return 1;
}


void printWorstCases(node *func,
		     mpfr_t inputprec, rangetype inputExponRange,
		     mpfr_t outputprec, mpfr_t epsilon, mp_prec_t prec, FILE *fd) {
  int inputprecision, outputprecision, firstexponent, lastexponent;
  mpfr_t temp, temp2, x, y, yR, xL;
  double eps;
  long long int i;

  sollyaPrintf("prec = %d\n",(int) prec);

  if (!(mpfrToInt(&inputprecision, inputprec) &&
	mpfrToInt(&outputprecision, outputprec) &&
	mpfrToInt(&firstexponent, *(inputExponRange.a)) &&
	mpfrToInt(&lastexponent, *(inputExponRange.b)))) {
    printMessage(1,SOLLYA_MSG_HARMLESS_ERROR_OCCURRED_COMMAND_NOT_EXECUTED,"Warning: an error occurred. The last command will not succeed. This is harmless.\n");
    return;
  }

  if ((inputprecision < 10) || (outputprecision < 10)) {
    printMessage(1,SOLLYA_MSG_INPUT_AND_OUTPUT_PRECISION_MUST_BE_GREATER_TEN,"Warning: input and outputprecision must be greater or equal to 10.\n");
    printMessage(1,SOLLYA_MSG_CONTINUATION,"Warning: an error occurred. The last command will not succeed. This is harmless.\n");
    return;
  }

  if ((prec < (mp_prec_t) inputprecision) || (prec < (mp_prec_t) outputprecision)) {
    printMessage(1,SOLLYA_MSG_INTERNAL_PREC_LESS_THAN_IN_AND_OUT_PREC,"Warning: the internal precision is less than the input or output precision.\n");
    printMessage(1,SOLLYA_MSG_CONTINUATION,"Try to increase the tool's precision.\n");
    printMessage(1,SOLLYA_MSG_CONTINUATION,"Warning: an error occurred. The last command will not succeed. This is harmless.\n");
    return;
  }

  mpfr_init2(temp,prec);
  mpfr_init2(temp2,prec);

  mpfr_mul_2ui(temp,epsilon,(unsigned int) (outputprecision + 1),GMP_RNDN);
  mpfr_set_d(temp2,1.0,GMP_RNDN);

  if (mpfr_cmp(temp,temp2) >= 0) {
    printMessage(1,SOLLYA_MSG_EPS_SPECIFIED_GREATER_THAN_HALFULP_OF_OUT_PREC,"Warning: the epsilon asked is greater than half an ulp of a %d bit format.\n",
		 outputprecision);
    printMessage(1,SOLLYA_MSG_CONTINUATION,"Warning: an error occurred. The last command will not succeed. This is harmless.\n");
    mpfr_clear(temp);
    mpfr_clear(temp2);
    return;
  }

  if (mpfr_sgn(epsilon) < 0) {
    printMessage(1,SOLLYA_MSG_GIVEN_EPS_MUST_BE_POSITIVE_TAKING_ABS,"Warning: the epsilon given is negative. Will take its absolute value.\n");
    mpfr_abs(epsilon,epsilon,GMP_RNDN);
  }

  mpfr_init2(x,inputprecision);
  mpfr_init2(xL,inputprecision);
  mpfr_init2(yR,outputprecision);
  mpfr_init2(y,prec);

  mpfr_set_d(x,1.0,GMP_RNDN);
  mpfr_mul_2si(x,x,firstexponent,GMP_RNDN);

  mpfr_set_d(xL,1.0,GMP_RNDN);
  mpfr_mul_2si(xL,xL,lastexponent-1,GMP_RNDN);
  mpfr_nextbelow(x);

  if (mpfr_cmp(x,xL) > 0) {
    mpfr_swap(x,xL);
  }


  i = 0;
  while (mpfr_cmp(x,xL) <= 0) {
    if (verbosity >= 2) {
      if ((i % 1000) == 0) printMessage(2,SOLLYA_MSG_CERTAIN_AMOUNT_OF_CASES_HANDLED,"Information: %d cases handled.\n",i);
      i++;
    }

    mpfr_set(temp,x,GMP_RNDN);

    evaluate(y,func,temp,prec);

    mpfr_set(yR,y,GMP_RNDN);
    mpfr_sub(temp2,y,yR,GMP_RNDN);
    mpfr_abs(temp2,temp2,GMP_RNDN);
    if (mpfr_zero_p(y)) {
      printMessage(1,SOLLYA_MSG_FUNC_EVALUATED_TO_ZERO_TAKING_ABSOLUTE_ERROR,"Warning: the given function evaluates to 0 on %v\nThe rounding error will be considered as an absolute one.\n",x);
    } else {
      mpfr_div(temp2,temp2,y,GMP_RNDN);
    }

    if (mpfr_cmp(temp2,epsilon) <= 0) {
      sollyaPrintf("%s = ",((variablename == NULL) ? "_x_" : variablename));
      printValue(&x);
      sollyaPrintf("\t\tf(%s) = ",((variablename == NULL) ? "_x_" : variablename));
      printValue(&yR);
      sollyaPrintf("\t\teps = ");
      printValue(&temp2);
      mpfr_log2(temp,temp2,GMP_RNDN);
      eps = sollya_mpfr_get_d(temp,GMP_RNDN);
      sollyaPrintf(" = 2^(%f) \n",eps);
      if (fd != NULL) {
	sollyaFprintf(fd,"%s = ",((variablename == NULL) ? "_x_" : variablename));
	fprintValue(fd,x);
	sollyaFprintf(fd,"\tf(%s) = ",((variablename == NULL) ? "_x_" : variablename));
	fprintValue(fd,yR);
	sollyaFprintf(fd,"\teps = ");
	fprintValue(fd,temp2);
	sollyaFprintf(fd," = 2^(%f) ",eps);
	if (mpfr_zero_p(y)) {
	  sollyaFprintf(fd,"ABSOLUTE");
	}
	sollyaFprintf(fd,"\n");
      }
    }

    mpfr_nextabove(x);
  }

  mpfr_clear(temp);
  mpfr_clear(temp2);
  mpfr_clear(x);
  mpfr_clear(xL);
  mpfr_clear(y);
  mpfr_clear(yR);
}


int searchGalValue(chain *funcs, mpfr_t foundValue, mpfr_t startValue, mp_prec_t searchPrec, int steps,
                   chain *imageFormats, chain *epsilons, mp_prec_t prec) {
  mpfr_t currLeft, currRight;
  mpfr_t yCurrLeft, yCurrRight;
  mpfr_t yCurrLeftRound, yCurrRightRound;
  mpfr_t errorLeft, errorRight;
  mp_prec_t p;
  mpfr_t t, one;
  int res;
  int numberFuncs, numberFormats, numberEpsilons;
  chain *myFuncs;
  chain *currFunc, *currFormat, *currEpsilon;

  if (steps > 63) {
    printMessage(1,SOLLYA_MSG_CANNOT_PERFORM_MORE_THAN_63_STEPS,"Warning: cannot perform more than 63 steps. Will decrease step number to 63.\n");
    steps = 63;
  }

  p = prec;
  if (searchPrec > p) p = searchPrec;
  if (p < 165) p = 165;

  if (mpfr_get_prec(foundValue) < searchPrec) {
    printMessage(1,SOLLYA_MSG_SEARCH_PREC_HIGHER_THAN_TOOL_PREC,"Warning: the search precision is higher than the current precision of the tool.\nNo search is possible.\n");
    return 0;
  }

  numberFuncs = lengthChain(funcs);
  numberFormats = lengthChain(imageFormats);
  numberEpsilons = lengthChain(epsilons);

  if ((numberFuncs != numberFormats) ||
      (numberFuncs != numberEpsilons)) {
    printMessage(1,SOLLYA_MSG_NUMBERS_OF_FUNCS_AND_FORMATS_DIFFER,"Warning: the numbers of the given functions, formats and accuracies differ.\nNo search is possible.\n");
    return 0;
  }

  myFuncs = copyChain(funcs, copyTreeOnVoid);

  mpfr_init2(currLeft, searchPrec);
  mpfr_init2(currRight, searchPrec);
  mpfr_init2(yCurrLeft, p);
  mpfr_init2(yCurrRight, p);
  mpfr_init2(yCurrLeftRound, p);
  mpfr_init2(yCurrRightRound, p);
  mpfr_init2(errorLeft, p);
  mpfr_init2(errorRight, p);


  if ((mpfr_set(currLeft,startValue,GMP_RNDN) != 0) ||
      (mpfr_set(currRight,startValue,GMP_RNDN) != 0)) {
    printMessage(1,SOLLYA_MSG_START_POINT_TOO_PRECISE_FOR_GIVEN_INPUT_PREC,"Warning: the given start point is too precise for the given search precision.\nIt has been rounded to: %v",currLeft);
  }

  mpfr_init2(t,128);
  mpfr_init2(one,12);
  mpfr_set_si(t,1,GMP_RNDN);
  mpfr_set_si(one,1,GMP_RNDN);
  mpfr_mul_2ui(t,t,steps,GMP_RNDN);
  res = 1;
  while (mpfr_sgn(t) > 0) {
    res = 1;
    currFunc = myFuncs;
    currFormat = imageFormats;
    currEpsilon = epsilons;
    while ((currFunc != NULL) && (currFormat != NULL) && (currEpsilon != NULL)) {
      evaluateFaithful(yCurrLeft, (node *) (currFunc->value), currLeft, p);
      sollya_mpfr_round_to_format(yCurrLeftRound, yCurrLeft, *((int *) (currFormat->value)));
      mpfr_sub(errorLeft,yCurrLeftRound,yCurrLeft,GMP_RNDN);
      mpfr_div(errorLeft,errorLeft,yCurrLeft,GMP_RNDN);
      if (!(mpfr_number_p(errorLeft) && (mpfr_cmpabs(errorLeft,*((mpfr_t *) (currEpsilon->value))) <= 0))) {
	res = 0;
	break;
      }
      currFunc = currFunc->next;
      currFormat = currFormat->next;
      currEpsilon = currEpsilon->next;
    }
    if (res) {
      mpfr_set(foundValue,currLeft,GMP_RNDN);
      break;
    }
    res = 1;
    currFunc = myFuncs;
    currFormat = imageFormats;
    currEpsilon = epsilons;
    while ((currFunc != NULL) && (currFormat != NULL) && (currEpsilon != NULL)) {
      evaluateFaithful(yCurrRight, (node *) (currFunc->value), currRight, p);
      sollya_mpfr_round_to_format(yCurrRightRound, yCurrRight, *((int *) (currFormat->value)));
      mpfr_sub(errorRight,yCurrRightRound,yCurrRight,GMP_RNDN);
      mpfr_div(errorRight,errorRight,yCurrRight,GMP_RNDN);
      if (!(mpfr_number_p(errorRight) && (mpfr_cmpabs(errorRight,*((mpfr_t *) (currEpsilon->value))) <= 0))) {
	res = 0;
	break;
      }
      currFunc = currFunc->next;
      currFormat = currFormat->next;
      currEpsilon = currEpsilon->next;
    }
    if (res) {
      mpfr_set(foundValue,currRight,GMP_RNDN);
      break;
    }
    mpfr_nextbelow(currLeft);
    mpfr_nextabove(currRight);
    mpfr_sub(t,t,one,GMP_RNDN); /* exact*/
  }

  mpfr_clear(currLeft);
  mpfr_clear(currRight);
  mpfr_clear(yCurrLeft);
  mpfr_clear(yCurrRight);
  mpfr_clear(yCurrLeftRound);
  mpfr_clear(yCurrRightRound);
  mpfr_clear(errorLeft);
  mpfr_clear(errorRight);
  mpfr_clear(one);
  mpfr_clear(t);

  freeChain(myFuncs, freeMemoryOnVoid);

  return res;
}