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lol/test/unit/real.cpp

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  1. //

  2. // Lol Engine

  3. //

  4. // Copyright: (c) 2010-2011 Sam Hocevar <sam@hocevar.net>

  5. //   This program is free software; you can redistribute it and/or

  6. //   modify it under the terms of the Do What The Fuck You Want To

  7. //   Public License, Version 2, as published by Sam Hocevar. See

  8. //   http://www.wtfpl.net/ for more details.

  9. //

  10. 

  11. #if defined HAVE_CONFIG_H

  12. #   include "config.h"

  13. #endif

  14. 

  15. #include <cmath>

  16. 

  17. #include "core.h"

  18. #include "lol/unit.h"

  19. 

  20. namespace lol

  21. {

  22. 

  23. LOLUNIT_FIXTURE(RealTest)

  24. {

  25.     LOLUNIT_TEST(Constants)

  26.     {

  27.         double a0 = real::R_0();

  28.         double a1 = real::R_1();

  29.         double a2 = real::R_2();

  30.         double a10 = real::R_10();

  31. 

  32.         LOLUNIT_ASSERT_EQUAL(a0, 0.0);

  33.         LOLUNIT_ASSERT_EQUAL(a1, 1.0);

  34.         LOLUNIT_ASSERT_EQUAL(a2, 2.0);

  35.         LOLUNIT_ASSERT_EQUAL(a10, 10.0);

  36. 

  37.         double b1 = log(real::R_E());

  38.         double b2 = log2(real::R_2());

  39.         LOLUNIT_ASSERT_EQUAL(b1, 1.0);

  40.         LOLUNIT_ASSERT_EQUAL(b2, 1.0);

  41. 

  42.         double c1 = exp(re(real::R_LOG2E()));

  43.         double c2 = log(exp2(real::R_LOG2E()));

  44.         LOLUNIT_ASSERT_EQUAL(c1, 2.0);

  45.         LOLUNIT_ASSERT_EQUAL(c2, 1.0);

  46. 

  47.         double d1 = exp(re(real::R_LOG10E()));

  48.         LOLUNIT_ASSERT_EQUAL(d1, 10.0);

  49. 

  50.         double e1 = exp(real::R_LN2());

  51.         LOLUNIT_ASSERT_EQUAL(e1, 2.0);

  52. 

  53.         double f1 = exp(real::R_LN10());

  54.         LOLUNIT_ASSERT_EQUAL(f1, 10.0);

  55. 

  56.         double g1 = sin(real::R_PI());

  57.         double g2 = cos(real::R_PI());

  58.         LOLUNIT_ASSERT_DOUBLES_EQUAL(g1, 0.0, 1e-100);

  59.         LOLUNIT_ASSERT_EQUAL(g2, -1.0);

  60. 

  61.         double h1 = sin(real::R_PI_2());

  62.         double h2 = cos(real::R_PI_2());

  63.         LOLUNIT_ASSERT_EQUAL(h1, 1.0);

  64.         LOLUNIT_ASSERT_DOUBLES_EQUAL(h2, 0.0, 1e-100);

  65. 

  66.         double i1 = sin(real::R_PI_4()) * sin(real::R_PI_4());

  67.         double i2 = cos(real::R_PI_4()) * cos(real::R_PI_4());

  68.         LOLUNIT_ASSERT_EQUAL(i1, 0.5);

  69.         LOLUNIT_ASSERT_EQUAL(i2, 0.5);

  70.     }

  71. 

  72.     LOLUNIT_TEST(FloatToReal)

  73.     {

  74.         float a1 = real(0.0f);

  75.         float a2 = real(-0.0f);

  76.         float a3 = real(1.0f);

  77.         float a4 = real(-1.0f);

  78.         float a5 = real(1.5f);

  79.         float a6 = real(12345678.0f);

  80. 

  81.         LOLUNIT_ASSERT_EQUAL(a1, 0.0f);

  82.         LOLUNIT_ASSERT_EQUAL(a2, -0.0f);

  83.         LOLUNIT_ASSERT_EQUAL(a3, 1.0f);

  84.         LOLUNIT_ASSERT_EQUAL(a4, -1.0f);

  85.         LOLUNIT_ASSERT_EQUAL(a5, 1.5f);

  86.         LOLUNIT_ASSERT_EQUAL(a6, 12345678.0f);

  87.     }

  88. 

  89.     LOLUNIT_TEST(DoubleToReal)

  90.     {

  91.         double a1 = real(0.0);

  92.         double a2 = real(-0.0);

  93.         double a3 = real(1.0);

  94.         double a4 = real(-1.0);

  95.         double a5 = real(1.5);

  96.         double a6 = real(1234567876543210.0);

  97. 

  98.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a1, 0.0, 0.0);

  99.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a2, -0.0, 0.0);

  100.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a3, 1.0, 0.0);

  101.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a4, -1.0, 0.0);

  102.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a5, 1.5, 0.0);

  103.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a6, 1234567876543210.0, 0.0);

  104.     }

  105. 

  106.     LOLUNIT_TEST(Init)

  107.     {

  108.         real r;

  109.         float f1 = (float)r;

  110. 

  111.         LOLUNIT_ASSERT_EQUAL(f1, 0.0f);

  112. 

  113.         rcmplx q;

  114.         float f2 = (float)q.x;

  115.         float f3 = (float)q.y;

  116. 

  117.         LOLUNIT_ASSERT_EQUAL(f2, 0.0f);

  118.         LOLUNIT_ASSERT_EQUAL(f3, 0.0f);

  119.     }

  120. 

  121.     LOLUNIT_TEST(StringToReal)

  122.     {

  123.         float a1 = real("0");

  124.         float a2 = real("1");

  125.         float a3 = real("-1");

  126.         /* 2^-128 * 2^128 */

  127.         float a4 = real("0.0000000000000000000000000000000000000029387358770"

  128.                         "557187699218413430556141945466638919302188037718792"

  129.                         "6569604314863681793212890625")

  130.                  * real("340282366920938463463374607431768211456");

  131. 

  132.         LOLUNIT_ASSERT_EQUAL(a1, 0.0f);

  133.         LOLUNIT_ASSERT_EQUAL(a2, 1.0f);

  134.         LOLUNIT_ASSERT_EQUAL(a3, -1.0f);

  135.         LOLUNIT_ASSERT_EQUAL(a4, 1.0f);

  136.     }

  137. 

  138.     LOLUNIT_TEST(UnaryMinus)

  139.     {

  140.         float a1 = - real(1.0f);

  141.         float a2 = - real(-1.0f);

  142.         float a3 = - real(0.0f);

  143.         float a4 = - real(-0.0f);

  144. 

  145.         LOLUNIT_ASSERT_EQUAL(a1, -1.0f);

  146.         LOLUNIT_ASSERT_EQUAL(a2, 1.0f);

  147.         LOLUNIT_ASSERT_EQUAL(a3, -0.0f);

  148.         LOLUNIT_ASSERT_EQUAL(a4, 0.0f);

  149.     }

  150. 

  151.     LOLUNIT_TEST(Comparison)

  152.     {

  153.         LOLUNIT_ASSERT(real(1.0f) > real(0.5f));

  154.         LOLUNIT_ASSERT(real(1.0f) >= real(0.5f));

  155.         LOLUNIT_ASSERT(real(1.0f) >= real(1.0f));

  156. 

  157.         LOLUNIT_ASSERT(real(-1.0f) < real(-0.5f));

  158.         LOLUNIT_ASSERT(real(-1.0f) <= real(-0.5f));

  159.         LOLUNIT_ASSERT(real(-1.0f) <= real(-1.0f));

  160. 

  161.         LOLUNIT_ASSERT(real(-1.0f) < real(0.5f));

  162.         LOLUNIT_ASSERT(real(-0.5f) < real(1.0f));

  163.         LOLUNIT_ASSERT(real(-1.0f) <= real(0.5f));

  164.         LOLUNIT_ASSERT(real(-0.5f) <= real(1.0f));

  165. 

  166.         LOLUNIT_ASSERT(real(1.0f) > real(-0.5f));

  167.         LOLUNIT_ASSERT(real(0.5f) > real(-1.0f));

  168.         LOLUNIT_ASSERT(real(1.0f) >= real(-0.5f));

  169.         LOLUNIT_ASSERT(real(0.5f) >= real(-1.0f));

  170.     }

  171. 

  172.     LOLUNIT_TEST(Addition)

  173.     {

  174.         float a1 = real(1.0f) + real(0.0f);

  175.         float a2 = real(0.0f) + real(1.0f);

  176.         float a3 = real(1.0f) + real(1.0f);

  177.         float a4 = real(-1.0f) + real(-1.0f);

  178.         float a5 = real(1.0f) + real(0.125f);

  179.         double a6 = real(3.13609818956293918)

  180.                   + real(0.00005972154828114);

  181.         float a7 = real(1.0f) + real(-0.125f);

  182.         double a8 = real(0.10000000002) + real(-2.0e-11);

  183. 

  184.         LOLUNIT_ASSERT_EQUAL(a1, 1.0f);

  185.         LOLUNIT_ASSERT_EQUAL(a2, 1.0f);

  186.         LOLUNIT_ASSERT_EQUAL(a3, 2.0f);

  187.         LOLUNIT_ASSERT_EQUAL(a4, -2.0f);

  188.         LOLUNIT_ASSERT_EQUAL(a5, 1.125f);

  189.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a6, 3.1361579, 0.000001);

  190.         LOLUNIT_ASSERT_EQUAL(a7, 0.875f);

  191.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a8, 0.1, 1.0e-13);

  192.     }

  193. 

  194.     LOLUNIT_TEST(Subtraction)

  195.     {

  196.         float a1 = real(1.0f) + real(1e20f) - real(1e20f);

  197. 

  198.         LOLUNIT_ASSERT_EQUAL(a1, 1.0f);

  199.     }

  200. 

  201.     LOLUNIT_TEST(Multiplication)

  202.     {

  203.         real x(1.25f);

  204.         real y(1.5f);

  205.         real z(1.99999f);

  206.         real w(-1.5f);

  207. 

  208.         float m1 = x * x;

  209.         float m2 = y * y;

  210.         float m3 = z * z;

  211.         float m4 = w * w;

  212. 

  213.         LOLUNIT_ASSERT_EQUAL(m1, 1.25f * 1.25f);

  214.         LOLUNIT_ASSERT_EQUAL(m2, 1.5f * 1.5f);

  215.         LOLUNIT_ASSERT_EQUAL(m3, 1.99999f * 1.99999f);

  216.         LOLUNIT_ASSERT_EQUAL(m4, -1.5f * -1.5f);

  217.     }

  218. 

  219.     LOLUNIT_TEST(ExactDivision)

  220.     {

  221.         float m1 = real::R_1() / real::R_1();

  222.         float m2 = real::R_2() / real::R_1();

  223.         float m3 = real::R_1() / real::R_2();

  224.         float m4 = real::R_2() / real::R_2();

  225.         float m5 = real::R_1() / -real::R_2();

  226. 

  227.         LOLUNIT_ASSERT_EQUAL(m1, 1.0f);

  228.         LOLUNIT_ASSERT_EQUAL(m2, 2.0f);

  229.         LOLUNIT_ASSERT_EQUAL(m3, 0.5f);

  230.         LOLUNIT_ASSERT_EQUAL(m4, 1.0f);

  231.         LOLUNIT_ASSERT_EQUAL(m5, -0.5f);

  232.     }

  233. 

  234.     LOLUNIT_TEST(InexactDivision)

  235.     {

  236.         /* 1 / 3 * 3 should be close to 1... check that it does not differ

  237.          * by more than 2^-k where k is the number of bits in the mantissa. */

  238.         real a = real::R_1() / real::R_3() * real::R_3();

  239.         real b = ldexp(real::R_1() - a, real::BIGITS * real::BIGIT_BITS);

  240. 

  241.         LOLUNIT_ASSERT_LEQUAL((double)fabs(b), 1.0);

  242.     }

  243. 

  244.     LOLUNIT_TEST(LoadExp)

  245.     {

  246.         real a1(1.5);

  247.         real a2(-1.5);

  248.         real a3(0.0);

  249. 

  250.         LOLUNIT_ASSERT_EQUAL((double)ldexp(a1, 7), 192.0);

  251.         LOLUNIT_ASSERT_EQUAL((double)ldexp(a1, -7), 0.01171875);

  252. 

  253.         LOLUNIT_ASSERT_EQUAL((double)ldexp(a2, 7), -192.0);

  254.         LOLUNIT_ASSERT_EQUAL((double)ldexp(a2, -7), -0.01171875);

  255. 

  256.         LOLUNIT_ASSERT_EQUAL((double)ldexp(a3, 7), 0.0);

  257.         LOLUNIT_ASSERT_EQUAL((double)ldexp(a3, -7), 0.0);

  258.     }

  259. 

  260.     LOLUNIT_TEST(Ulp)

  261.     {

  262.         real a1 = real::R_PI();

  263. 

  264.         LOLUNIT_ASSERT_NOT_EQUAL((double)(a1 + ulp(a1) - a1), 0.0);

  265.         LOLUNIT_ASSERT_EQUAL((double)(a1 + ulp(a1) / 2 - a1), 0.0);

  266.     }

  267. 

  268.     LOLUNIT_TEST(Bool)

  269.     {

  270.         real a = 0.0;

  271.         LOLUNIT_ASSERT(!a);

  272. 

  273.         a = -0.0;

  274.         LOLUNIT_ASSERT(!a);

  275. 

  276.         a = 1234.0;

  277.         LOLUNIT_ASSERT(a);

  278.         LOLUNIT_ASSERT(!!a);

  279. 

  280.         a = -1234.0;

  281.         LOLUNIT_ASSERT(a);

  282.         LOLUNIT_ASSERT(!!a);

  283.     }

  284. 

  285.     LOLUNIT_TEST(AsinAcos)

  286.     {

  287.         double tests[] =

  288.         {

  289.             -1024.0, -1023.0, -513.0, -512.0, -511.0, -1.0, -0.0,

  290.             0.0, 1.0, 511.0, 512.0, 513.0, 1023.0, 1024.0

  291.         };

  292. 

  293.         for (double test : tests)

  294.         {

  295.             double a = test / 1024;

  296.             double b = sin(asin((real)a));

  297.             double c = cos(acos((real)a));

  298. 

  299.             LOLUNIT_SET_CONTEXT(a);

  300.             LOLUNIT_ASSERT_DOUBLES_EQUAL(b, a, 1e-100);

  301.             LOLUNIT_ASSERT_DOUBLES_EQUAL(c, a, 1e-100);

  302.         }

  303.     }

  304. 

  305.     LOLUNIT_TEST(FloorCeilEtc)

  306.     {

  307.         double tests[] =

  308.         {

  309.             -2.0,  -2.0, -2.0,  -2.0,

  310.             -1.5,  -2.0, -1.0,  -2.0,

  311.             -1.0,  -1.0, -1.0,  -1.0,

  312.             -0.0,  -0.0, -0.0,  -0.0,

  313.              0.0,   0.0,  0.0,   0.0,

  314.              0.25,  0.0,  1.0,   0.0,

  315.              0.375, 0.0,  1.0,   0.0,

  316.              0.5,   0.0,  1.0,   1.0,

  317.              1.0,   1.0,  1.0,   1.0,

  318.              1.5,   1.0,  2.0,   2.0,

  319.              2.0,   2.0,  2.0,   2.0,

  320.              2.5,   2.0,  3.0,   3.0,

  321.              3.0,   3.0,  3.0,   3.0,

  322.             8192.0,     8192.0, 8192.0, 8192.0,

  323.             8192.03125, 8192.0, 8193.0, 8192.0,

  324.             8192.5,     8192.0, 8193.0, 8193.0,

  325.             8193.0,     8193.0, 8193.0, 8193.0,

  326.             549755813888.0,     549755813888.0, 549755813888.0, 549755813888.0,

  327.             549755813888.03125, 549755813888.0, 549755813889.0, 549755813888.0,

  328.             549755813888.5,     549755813888.0, 549755813889.0, 549755813889.0,

  329.             549755813889.0,     549755813889.0, 549755813889.0, 549755813889.0,

  330.         };

  331. 

  332.         for (unsigned int n = 0; n < sizeof(tests) / sizeof(*tests); n += 4)

  333.         {

  334.             double a0 = floor((real)tests[n]);

  335.             double b0 = tests[n + 1];

  336.             double a1 = ceil((real)tests[n]);

  337.             double b1 = tests[n + 2];

  338.             double a2 = round((real)tests[n]);

  339.             double b2 = tests[n + 3];

  340. 

  341.             LOLUNIT_ASSERT_EQUAL(b0, a0);

  342.             LOLUNIT_ASSERT_EQUAL(b1, a1);

  343.             LOLUNIT_ASSERT_EQUAL(b2, a2);

  344.         }

  345.     }

  346. 

  347.     LOLUNIT_TEST(Pow)

  348.     {

  349.         double a1 = pow(-real::R_2(), real::R_2());

  350.         double b1 = 4.0;

  351.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a1, b1, 1.0e-13);

  352. 

  353.         double a2 = pow(-real::R_2(), real::R_3());

  354.         double b2 = -8.0;

  355.         LOLUNIT_ASSERT_DOUBLES_EQUAL(a2, b2, 1.0e-13);

  356.     }

  357. };

  358. 

  359. } /* namespace lol */