text: // Licensed to the .NET Foundation under one or more agreements.
  // The .NET Foundation licenses this file to you under the MIT license.
  // See the LICENSE file in the project root for more information.
  
  /*=============================================================================
  **
  ** Source: test1.c
  **
  ** Purpose: Test to ensure that atanh return the correct values
  ** 
  ** Dependencies: PAL_Initialize
  **               PAL_Terminate
  **               Fail
  **               fabs
  **
  **===========================================================================*/
  
  #include <palsuite.h>
  
  // binary64 (double) has a machine epsilon of 2^-52 (approx. 2.22e-16). However, this 
  // is slightly too accurate when writing tests meant to run against libm implementations
  // for various platforms. 2^-50 (approx. 8.88e-16) seems to be as accurate as we can get.
  //
  // The tests themselves will take PAL_EPSILON and adjust it according to the expected result
  // so that the delta used for comparison will compare the most significant digits and ignore
  // any digits that are outside the double precision range (15-17 digits).
  
  // For example, a test with an expect result in the format of 0.xxxxxxxxxxxxxxxxx will use
  // PAL_EPSILON for the variance, while an expected result in the format of 0.0xxxxxxxxxxxxxxxxx
  // will use PAL_EPSILON / 10 and and expected result in the format of x.xxxxxxxxxxxxxxxx will
  // use PAL_EPSILON * 10.
  #define PAL_EPSILON 8.8817841970012523e-16
  
  #define PAL_NAN     sqrt(-1.0)
  #define PAL_POSINF -log(0.0)
  #define PAL_NEGINF  log(0.0)
  
  /**
   * Helper test structure
   */
  struct test
  {
      double value;     /* value to test the function with */
      double expected;  /* expected result */
      double variance;  /* maximum delta between the expected and actual result */
  };
  
  /**
   * validate
   *
   * test validation function
   */
  void __cdecl validate(double value, double expected, double variance)
  {
      double result = atanh(value);
  
      /*
       * The test is valid when the difference between result
       * and expected is less than or equal to variance
       */
      double delta = fabs(result - expected);
  
      if (delta > variance)
      {
          Fail("atanh(%g) returned %20.17g when it should have returned %20.17g",
               value, result, expected);
      }
  }
  
  /**
   * validate
   *
   * test validation function for values returning NaN
   */
  void __cdecl validate_isnan(double value)
  {
      double result = atanh(value);
  
      if (!_isnan(result))
      {
          Fail("atanh(%g) returned %20.17g when it should have returned %20.17g",
               value, result, PAL_NAN);
      }
  }
  
  /**
   * main
   * 
   * executable entry point
   */
  int __cdecl main(int argc, char **argv)
  {
      struct test tests[] = 
      {
          /* value                   expected                variance */
          {  0,                      0,                      PAL_EPSILON },
          {  0.30797791269089433,    0.31830988618379067,    PAL_EPSILON },       // expected:  1 / pi
          {  0.40890401183401433,    0.43429448190325183,    PAL_EPSILON },       // expected:  log10(e)
          {  0.56259360033158334,    0.63661977236758134,    PAL_EPSILON },       // expected:  2 / pi
          {  0.6,                    0.69314718055994531,    PAL_EPSILON },       // expected:  ln(2)
          {  0.60885936501391381,    0.70710678118654752,    PAL_EPSILON },       // expected:  1 / sqrt(2)
          {  0.65579420263267244,    0.78539816339744831,    PAL_EPSILON },       // expected:  pi / 4
          {  0.76159415595576489,    1,                      PAL_EPSILON * 10 },
          {  0.81046380599898809,    1.1283791670955126,     PAL_EPSILON * 10 },  // expected:  2 / sqrt(pi)
          {  0.88838556158566054,    1.4142135623730950,     PAL_EPSILON * 10 },  // expected:  sqrt(2)
          {  0.89423894585503855,    1.4426950408889634,     PAL_EPSILON * 10 },  // expected:  log2(e)
          {  0.91715233566727435,    1.5707963267948966,     PAL_EPSILON * 10 },  // expected:  pi / 2
          {  0.98019801980198020,    2.3025850929940457,     PAL_EPSILON * 10 },  // expected:  ln(10)
          {  0.99132891580059984,    2.7182818284590452,     PAL_EPSILON * 10 },  // expected:  e
          {  0.99627207622074994,    3.1415926535897932,     PAL_EPSILON * 10 },  // expected:  pi
          {  1,                      PAL_POSINF,             PAL_EPSILON * 10 }
      };
  
      /* PAL initialization */
      if (PAL_Initialize(argc, argv) != 0)
      {
          return FAIL;
      }
  
      for (int i = 0; i < (sizeof(tests) / sizeof(struct test)); i++)
      {
          validate( tests[i].value,  tests[i].expected, tests[i].variance);
          validate(-tests[i].value, -tests[i].expected, tests[i].variance);
      }
  
      validate_isnan(PAL_NAN);
  
      PAL_Terminate();
      return PASS;
  }
  