validate.c

任意精度的数学库

xarray[8]  = 6.319e-6;      yarray[8]  = 3.17;
xarray[9]  = 2.108e9;       yarray[9]  = -2.0;
xarray[10] = 8.417e-3;      yarray[10] = 0.5;
xarray[11] = 5.347e7;       yarray[11] = 1.0;
xarray[12] = 10.0;          yarray[12] = -17.0;
xarray[13] = 10.0;          yarray[13] = 2.33e1;
xarray[14] = 9.0e2;         yarray[14] = 0.0;
xarray[15] = 2.0;           yarray[15] = -3.62;

for (i=1; i <= 15; i++)     
  {
   xx1 = xarray[i];
   xx2 = yarray[i];
   yy  = pow(xx1, xx2);
               
   m_apm_set_double(aa_mapm, xx1);
   m_apm_set_double(bb_mapm, xx2);
   m_apm_pow(cc_mapm, DECIMAL_PLACES, aa_mapm, bb_mapm);
   m_apm_to_string(buffer, DECIMAL_PLACES, cc_mapm);
   yy_mapm_lib = atof(buffer);
               
   ydiff = (yy_mapm_lib - yy) / yy;
               
   if (fabs(ydiff) > tolerance)
     {
      pass = FALSE;
      total_pass = FALSE;
            
      fprintf(stdout,
      "x1 = %10.3E  x2 = %10.3E  C-math-lib = %.15E \n",xx1,xx2,yy);
       fprintf(stdout,
      "DIFF = %17.10E          M_APM_LIB  = %s \n",ydiff,buffer);
     }
  }

if (pass)
  fprintf(stdout,"... POW function passes\n");
  

/*
 *
 */

numdigits = 70;

fprintf(stdout,
   "\nVerify Some Known Quantities to 70 Digits ...\n");

m_apm_sqrt(ee_mapm, (numdigits + 4), MM_Two);
m_apm_divide(dd_mapm, (numdigits + 4), ee_mapm, MM_Two);
m_apm_round(aa_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"SQRT(2) / 2 = \n[%s]\n",buffer);

m_apm_set_long(ee_mapm, 4L);
m_apm_divide(dd_mapm, (numdigits + 4), MM_PI, ee_mapm);
m_apm_sin(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"SIN(PI / 4) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: SQRT(2) / 2 == SIN(PI / 4)\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: SQRT(2) / 2 != SIN(PI / 4)\n");
  }

m_apm_cos(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"COS(PI / 4) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: SQRT(2) / 2 == COS(PI / 4)\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: SQRT(2) / 2 != COS(PI / 4)\n");
  }


m_apm_set_string(aa_mapm, "0.5");

m_apm_set_long(ee_mapm, 6L);
m_apm_divide(dd_mapm, (numdigits + 4), MM_PI, ee_mapm);
m_apm_sin(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"SIN(PI / 6) = [%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: SIN(PI / 6) == 0.5\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: SIN(PI / 6) != 0.5\n");
  }


m_apm_set_string(ee_mapm, "0.75");
m_apm_sqrt(aa_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"SQRT(0.75) = \n[%s]\n",buffer);

m_apm_set_long(ee_mapm, 6L);
m_apm_divide(dd_mapm, (numdigits + 4), MM_PI, ee_mapm);
m_apm_cos(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"COS(PI / 6) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: COS(PI / 6) == SQRT(0.75)\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: COS(PI / 6) != SQRT(0.75)\n");
  }


m_apm_set_string(ee_mapm, "3");
m_apm_sqrt(dd_mapm, (numdigits + 4), ee_mapm);
m_apm_add(ee_mapm, MM_Two, dd_mapm);
m_apm_round(aa_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"2 + SQRT(3) = \n[%s]\n",buffer);

m_apm_set_long(ee_mapm, 5L);
m_apm_set_long(dd_mapm, 12L);
m_apm_multiply(cc_mapm, MM_PI, ee_mapm);
m_apm_divide(ee_mapm, (numdigits + 4), cc_mapm, dd_mapm);
m_apm_tan(bb_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"TAN(5 * PI / 12) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: TAN(5 * PI / 12) == 2 + SQRT(3)\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: TAN(5 * PI / 12) != 2 + SQRT(3)\n");
  }


m_apm_set_string(ee_mapm, "0.5");
m_apm_arcsin(aa_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"ARC-SIN(0.5) = \n[%s]\n",buffer);

m_apm_set_long(ee_mapm, 6L);
m_apm_divide(dd_mapm, (numdigits + 4), MM_PI, ee_mapm);
m_apm_round(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"PI / 6 = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: ARC-SIN(0.5) == PI / 6\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: ARC-SIN(0.5) != PI / 6\n");
  }


m_apm_set_string(ee_mapm, "0.75");
m_apm_sqrt(dd_mapm, (numdigits + 4), ee_mapm);
m_apm_arccos(aa_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"ARC-COS(SQRT(0.75)) = \n[%s]\n",buffer);

m_apm_set_long(ee_mapm, 6L);
m_apm_divide(dd_mapm, (numdigits + 4), MM_PI, ee_mapm);
m_apm_round(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"PI / 6 = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: ARC-COS(SQRT(0.75)) == PI / 6\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: ARC-COS(SQRT(0.75)) != PI / 6\n");
  }


m_apm_arctan(aa_mapm, numdigits, MM_One);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"ARC-TAN(1.0) = \n[%s]\n",buffer);

m_apm_set_long(ee_mapm, 4L);
m_apm_divide(dd_mapm, (numdigits + 4), MM_PI, ee_mapm);
m_apm_round(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"PI / 4 = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: ARC-TAN(1.0) == PI / 4\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: ARC-TAN(1.0) != PI / 4\n");
  }


m_apm_exp(aa_mapm, numdigits, MM_One);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"EXP(1.0) = \n[%s]\n",buffer);

m_apm_round(bb_mapm, numdigits, MM_E);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"E = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: EXP(1.0) == E\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: EXP(1.0) != E\n");
  }


m_apm_set_string(ee_mapm, "0.5");
m_apm_exp(aa_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"EXP(0.5) = \n[%s]\n",buffer);

m_apm_sqrt(bb_mapm, numdigits, MM_E);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"SQRT(E) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: EXP(0.5) == SQRT(E)\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: EXP(0.5) != SQRT(E)\n");
  }


m_apm_copy(ee_mapm, MM_One);

for (i=1; i <= 15; i++)
  {
   m_apm_multiply(dd_mapm, ee_mapm, MM_E);
   m_apm_copy(ee_mapm, dd_mapm);
  }

m_apm_round(bb_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"E ^ 15 = \n[%s]\n",buffer);

m_apm_set_string(ee_mapm, "15.0");
m_apm_exp(aa_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"EXP(15) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: EXP(15) == E ^ 15\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: EXP(15) != E ^ 15\n");
  }

m_apm_integer_pow(cc_mapm, numdigits, MM_E, 15);
m_apm_to_string(buffer, -1, cc_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"INTEGER_POW (E^15) = \n[%s]\n",buffer);

k = m_apm_compare(bb_mapm, cc_mapm);
if (k == 0)
   fprintf(stdout,"PASS: INTEGER_POW E ^15 == E ^ 15\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: INTEGER_POW E ^15 != E ^ 15\n");
  }


m_apm_copy(ee_mapm, MM_One);

for (i=1; i <= 26; i++)
  {
   m_apm_multiply(dd_mapm, ee_mapm, MM_PI);
   m_apm_copy(ee_mapm, dd_mapm);
  }

m_apm_divide(dd_mapm, (numdigits + 8), MM_One, ee_mapm);
m_apm_round(bb_mapm, numdigits, dd_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"1 / (PI ^ 26) = \n[%s]\n",buffer);

m_apm_integer_pow(cc_mapm, numdigits, MM_PI, -26);
m_apm_to_string(buffer, -1, cc_mapm);

fprintf(stdout,"INTEGER_POW (PI ^ -26) = \n[%s]\n",buffer);

k = m_apm_compare(bb_mapm, cc_mapm);
if (k == 0)
   fprintf(stdout,"PASS: INTEGER_POW PI ^ -26 == PI ^ -26\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: INTEGER_POW PI ^ -26 != PI ^ -26\n");
  }


m_apm_multiply(ee_mapm, MM_E, MM_E);
m_apm_round(bb_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"E ^ 2 = \n[%s]\n",buffer);

m_apm_exp(aa_mapm, numdigits, MM_Two);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"EXP(2) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: EXP(2) == E ^ 2\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: EXP(2) != E ^ 2\n");
  }


m_apm_copy(ee_mapm, MM_One);

for (i=1; i <= 13; i++)
  {
   m_apm_multiply(dd_mapm, ee_mapm, MM_E);
   m_apm_copy(ee_mapm, dd_mapm);
  }

m_apm_sqrt(dd_mapm, (numdigits + 4), ee_mapm);
m_apm_divide(ee_mapm, (numdigits + 4), MM_One, dd_mapm);
m_apm_round(bb_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"1 / SQRT(E ^ 13) = \n[%s]\n",buffer);

m_apm_set_string(ee_mapm, "-6.5");
m_apm_exp(aa_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"EXP(-6.5) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: EXP(-6.5) == 1 / SQRT(E ^ 13)\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: EXP(-6.5) != 1 / SQRT(E ^ 13)\n");
  }


m_apm_copy(ee_mapm, MM_One);

for (i=1; i <= 85; i++)
  {
   m_apm_multiply(dd_mapm, ee_mapm, MM_E);
   m_apm_round(ee_mapm, (numdigits + 4), dd_mapm);
  }

m_apm_sqrt(bb_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"SQRT(E ^ 85) = \n[%s]\n",buffer);

m_apm_set_string(ee_mapm, "42.5");
m_apm_exp(aa_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"EXP(42.5) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: EXP(42.5) == SQRT(E ^ 85)\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: EXP(42.5) != SQRT(E ^ 85)\n");
  }


m_apm_round(aa_mapm, numdigits, MM_LOG_10_BASE_E);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"LOG_10_BASE_E = \n[%s]\n",buffer);

m_apm_log(bb_mapm, numdigits, MM_Ten);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"LOG(10) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: LOG(10) == LOG_10_BASE_E\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: LOG(10) != LOG_10_BASE_E\n");
  }


m_apm_round(aa_mapm, numdigits, MM_LOG_E_BASE_10);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"LOG_E_BASE_10 = \n[%s]\n",buffer);

m_apm_log10(bb_mapm, numdigits, MM_E);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"LOG10(E) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: LOG10(E) == LOG_E_BASE_10\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: LOG10(E) != LOG_E_BASE_10\n");
  }


m_apm_round(aa_mapm, numdigits, MM_LOG_2_BASE_E);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"LOG_2_BASE_E = \n[%s]\n",buffer);

m_apm_log(bb_mapm, numdigits, MM_Two);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"LOG(2) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: LOG(2) == LOG_2_BASE_E\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: LOG(2) != LOG_2_BASE_E\n");
  }


m_apm_round(aa_mapm, numdigits, MM_LOG_3_BASE_E);
m_apm_to_string(buffer, -1, aa_mapm);

fprintf(stdout,"\n");
fprintf(stdout,"LOG_3_BASE_E = \n[%s]\n",buffer);

m_apm_set_long(ee_mapm, 3L);
m_apm_log(bb_mapm, numdigits, ee_mapm);
m_apm_to_string(buffer, -1, bb_mapm);

fprintf(stdout,"LOG(3) = \n[%s]\n",buffer);

k = m_apm_compare(aa_mapm, bb_mapm);
if (k == 0)
   fprintf(stdout,"PASS: LOG(3) == LOG_3_BASE_E\n");
else
  {
   total_pass = FALSE;
   fprintf(stdout,"FAIL: LOG(3) != LOG_3_BASE_E\n");
  }


if (total_pass)
  fprintf(stdout,"\nvalidate : PASS\n\n");
else
  fprintf(stdout,"\nvalidate : FAIL\n\n");

m_apm_free(aa_mapm);
m_apm_free(bb_mapm);
m_apm_free(cc_mapm);
m_apm_free(dd_mapm);
m_apm_free(ee_mapm);

free(num1);
free(num2);
free(answer);

exit(0);
}