Ichthyostega
32fbfa7909
These two helpers ''just happen to work'' in the full domain, and also for unsigned types. I can not recall that I actually was aware of that, but it's nice. Thus add some test cases to cover the bounds of the domain
331 lines
11 KiB
C++
331 lines
11 KiB
C++
/*
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UtilFloordiv(Test) - verify integer rounding function
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Copyright (C)
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2011, Hermann Vosseler <Ichthyostega@web.de>
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**Lumiera** is free software; you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by the
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Free Software Foundation; either version 2 of the License, or (at your
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option) any later version. See the file COPYING for further details.
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* *****************************************************************/
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/** @file util-floordiv-test.cpp
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** unit test \ref UtilFloordiv_test
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*/
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#include "test/run.hpp"
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#include "lib/util-quant.hpp"
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#include "lib/util.hpp"
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#include "lib/format-cout.hpp"
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#include "lib/format-string.hpp"
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#include <cmath>
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#include <time.h>
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#include <vector>
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using ::Test;
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using util::isnil;
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using util::_Fmt;
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using std::integral;
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namespace util {
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namespace test {
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namespace{ // Test data and operations
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const uint NUM_ELMS_PERFORMANCE_TEST = 50000000;
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const uint NUMBER_LIMIT = 1 << 30;
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template<typename NUM>
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constexpr NUM _MAX = std::numeric_limits<NUM>::max();
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template<typename NUM>
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constexpr NUM _MIN = std::numeric_limits<NUM>::lowest();
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typedef std::vector<int> VecI;
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VecI
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buildTestNumberz (uint cnt)
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{
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VecI data;
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for (uint i=0; i<cnt; ++i)
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{
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int someNumber = -int(NUMBER_LIMIT)+rani(2*NUMBER_LIMIT);
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if (!someNumber) someNumber -= 1 + rani(NUMBER_LIMIT);
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data.push_back (someNumber);
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}
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return data;
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}
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/** the built-in integer division operator,
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* packaged as inline function for timing comparison
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*/
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inline long
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integerDiv (long num, long den)
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{
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return num / den;
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}
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/** an alternate formulation,
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* which turned out to perform slightly worse
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*/
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inline long
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floordiv_alternate (long num, long den)
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{
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ldiv_t res = ldiv(num,den);
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return (0 >= res.quot and res.rem)? res.quot-1
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: res.quot;
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}
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} // (End) test data and operations
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/******************************************************************//**
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* @test Evaluate a custom built integer floor function.
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* Also known as Knuth's floor division.
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* This function is crucial for Lumiera's rule of quantisation
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* of time values into frame intervals. This rule requires time
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* points to be rounded towards the next lower frame border always,
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* irrespective of the relation to the actual time origin.
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* Contrast this to the built-in integer division operator, which
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* truncates towards zero.
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*
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* @note if invoked with an non empty parameter, this test performs
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* some interesting timing comparisons, which initially were
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* used to tweak the implementation a bit.
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* @see lib/util.hpp
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* @see QuantiserBasics_test
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*/
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class UtilFloordiv_test : public Test
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{
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virtual void
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run (Arg arg)
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{
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seedRand();
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verifyBehaviour();
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verifyIntegerTypes<int>();
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verifyIntegerTypes<long>();
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verifyIntegerTypes<short>();
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verifyIntegerTypes<int64_t>();
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verifyIntegerTypes<llong>();
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verifyBounds();
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if (not isnil (arg))
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runPerformanceTest();
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}
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void
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verifyBehaviour ()
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{
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CHECK ( 3 == floordiv ( 12,4));
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CHECK ( 2 == floordiv ( 11,4));
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CHECK ( 2 == floordiv ( 10,4));
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CHECK ( 2 == floordiv ( 9,4));
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CHECK ( 2 == floordiv ( 8,4));
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CHECK ( 1 == floordiv ( 7,4));
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CHECK ( 1 == floordiv ( 6,4));
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CHECK ( 1 == floordiv ( 5,4));
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CHECK ( 1 == floordiv ( 4,4));
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CHECK ( 0 == floordiv ( 3,4));
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CHECK ( 0 == floordiv ( 2,4));
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CHECK ( 0 == floordiv ( 1,4));
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CHECK ( 0 == floordiv ( 0,4));
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CHECK (-1 == floordiv (- 1,4));
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CHECK (-1 == floordiv (- 2,4));
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CHECK (-1 == floordiv (- 3,4));
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CHECK (-1 == floordiv (- 4,4));
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CHECK (-2 == floordiv (- 5,4));
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CHECK (-2 == floordiv (- 6,4));
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CHECK (-2 == floordiv (- 7,4));
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CHECK (-2 == floordiv (- 8,4));
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CHECK (-3 == floordiv (- 9,4));
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CHECK (-3 == floordiv (-10,4));
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CHECK (-3 == floordiv (-11,4));
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CHECK (-3 == floordiv (-12,4));
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}
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template<typename I>
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void
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verifyIntegerTypes()
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{
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I n,d,expectedRes;
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for (int i=-12; i <= 12; ++i)
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{
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n = i;
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d = 4;
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expectedRes = floordiv (i,4);
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CHECK (floordiv(n,d) == expectedRes);
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}
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}
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void
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verifyBounds()
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{
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auto verify = []<integral I>(I num, I den, I expect_quot, I expect_rem)
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{
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auto res = floorwrap (num,den);
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CHECK (res.quot == expect_quot, "quotient mismatch");
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CHECK (res.rem == expect_rem , "remainder mismatch");
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CHECK (res.quot == floordiv (num,den), "floordiv diverges");
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};
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//----- num | den | quotient | remainder
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verify (_MAX<int>, 1, _MAX<int> , 0);
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verify (_MAX<int>, 2, _MAX<int>/2 , 1);
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verify (_MAX<int>, 5, _MAX<int>/5 , 2);
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verify (_MIN<int>, 1, _MIN<int> , 0);
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verify (_MIN<int>, 2, _MIN<int>/2 , 0);
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verify (_MIN<int>, 5, _MIN<int>/5 -1, 2); // _MIN<int> ≡ -2147483648 /5 ≡ -429496729 -1 step ≡ -429496730 · 5 ≡ -2147483650 ⟹ Δ = +2
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verify (_MAX<int>,-1, -_MAX<int> , 0);
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verify (_MAX<int>,-2, -_MAX<int>/2 -1,-1);
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verify (_MAX<int>,-5, -_MAX<int>/5 -1,-3); // Δ ≡ -3 here since -_MAX<int> ≡ _MIN<int> + 1
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verify (_MAX<uint>, 1u, _MAX<uint> ,0u);
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verify (_MAX<uint>, 2u, _MAX<uint>/2 ,1u);
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verify (_MAX<uint>, 5u, _MAX<uint>/5 ,0u);
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verify (_MIN<int64_t>, int64_t(1), _MIN<int64_t> , int64_t(0));
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verify (_MIN<int64_t>, int64_t(2), _MIN<int64_t>/2 , int64_t(0));
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verify (_MIN<int64_t>, int64_t(5), _MIN<int64_t>/5 -1, int64_t(2)); // 2^63 / 5 ≡ 1844674407370955161.6 ; 1844674407370955162 · 5 ⟹ Δ = +2
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verify (_MIN<int8_t>, int8_t(1), int8_t(-128) , int8_t(0));
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verify (_MIN<int8_t>, int8_t(2), int8_t(-64 ) , int8_t(0));
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verify (_MIN<int8_t>, int8_t(5), int8_t(-26 ) , int8_t(2)); // 2^7 / 5 ≡ 25.6 ; 26 · 5 ≡ 130 ⟹ Δ = +2
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verify (_MAX<int8_t>, int8_t(5), int8_t( 25 ) , int8_t(2)); // (2^7-1) / 5 ≡ 25.4 ; 25 · 5 ≡ 125 ⟹ Δ = +2
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}
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/** @test timing measurements to compare implementation details.
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* This test uses a sequence of random integers, where the values
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* used as denominator are ensured not to be zero.
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*
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* \par measurement results
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* My experiments (AMD Athlon-64 4200 X2) gave me
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* the following timing measurements in nanoseconds:
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*
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* Verification.......... 127.7
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* Integer_div........... 111.7
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* double_floor.......... 74.8
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* floordiv_int.......... 112.7
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* floordiv_long......... 119.8
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* floordiv_int64_t...... 121.4
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* floordiv_long_alt..... 122.7
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*
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* These figures are the average of 6 runs with 50 million
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* iterations each (as produced by this function)
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*
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* \par conclusions
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* The most significant result is the striking performance of the
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* fpu based calculation. Consequently, integer arithmetics should
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* only be used when necessary due to resolution requirements, as
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* is the case for int64_t based Lumiera Time values, which require
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* a precision beyond the 16 digits provided by double.
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* Besides that, we can conclude that the additional tests and
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* adjustment of the custom floordiv only creates a slight overhead
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* compared to the built-in integer div function. An oddity to note
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* is the slightly better performance of long over int64_t. Also,
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* the alternative formulation of the function, which uses the
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* \c fdiv() function also to divide the positive results,
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* performs only slightly worse. So this implementation
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* was chosen mainly because it seems to state its
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* intent more clearly in code.
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*/
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void
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runPerformanceTest ()
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{
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VecI testdata = buildTestNumberz (2*NUM_ELMS_PERFORMANCE_TEST);
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typedef VecI::const_iterator I;
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clock_t start(0), stop(0);
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_Fmt resultDisplay{"timings(%s)%|30T.|%5.3fsec\n"};
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#define START_TIMINGS start=clock();
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#define DISPLAY_TIMINGS(ID) \
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stop = clock(); \
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cout << resultDisplay % STRINGIFY (ID) % (double(stop-start)/CLOCKS_PER_SEC) ;
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START_TIMINGS
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for (I ii =testdata.begin(); ii!=testdata.end(); )
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{
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int num = *ii;
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++ii;
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int den = *ii;
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++ii;
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CHECK (floor(double(num)/den) == floordiv(num,den));
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}
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DISPLAY_TIMINGS (Verification)
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START_TIMINGS
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for (I ii =testdata.begin(); ii!=testdata.end(); )
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{
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integerDiv (*ii++, *ii++);
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}
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DISPLAY_TIMINGS (Integer_div)
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START_TIMINGS
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for (I ii =testdata.begin(); ii!=testdata.end(); )
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{
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floor (double(*ii++) / *ii++);
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}
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DISPLAY_TIMINGS (double_floor)
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START_TIMINGS
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for (I ii =testdata.begin(); ii!=testdata.end(); )
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{
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floordiv (*ii++, *ii++);
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}
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DISPLAY_TIMINGS (floordiv_int)
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START_TIMINGS
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for (I ii =testdata.begin(); ii!=testdata.end(); )
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{
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floordiv (long(*ii++), long(*ii++));
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}
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DISPLAY_TIMINGS (floordiv_long)
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START_TIMINGS
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for (I ii =testdata.begin(); ii!=testdata.end(); )
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{
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floordiv (int64_t(*ii++), int64_t(*ii++));
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}
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DISPLAY_TIMINGS (floordiv_int64_t)
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START_TIMINGS
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for (I ii =testdata.begin(); ii!=testdata.end(); )
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{
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floordiv_alternate (*ii++, *ii++);
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}
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DISPLAY_TIMINGS (floordiv_long_alt)
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}
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};
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LAUNCHER (UtilFloordiv_test, "unit common");
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}} // namespace util::test
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