#include "g_libntptest.h" #include "g_timestructs.h" extern "C" { #include "ntp_fp.h" } #include #include #include #include class lfpTest : public libntptest { // nothing new right now }; struct lfp_hl { uint32_t h, l; }; //---------------------------------------------------------------------- // OO-wrapper for 'l_fp' //---------------------------------------------------------------------- class LFP { public: ~LFP(); LFP(); LFP(const LFP& rhs); LFP(int32 i, u_int32 f); LFP operator+ (const LFP &rhs) const; LFP& operator+=(const LFP &rhs); LFP operator- (const LFP &rhs) const; LFP& operator-=(const LFP &rhs); LFP& operator=(const LFP &rhs); LFP operator-() const; bool operator==(const LFP &rhs) const; LFP neg() const; LFP abs() const; int signum() const; bool l_isgt (const LFP &rhs) const { return L_ISGT(&_v, &rhs._v); } bool l_isgtu(const LFP &rhs) const { return L_ISGTU(&_v, &rhs._v); } bool l_ishis(const LFP &rhs) const { return L_ISHIS(&_v, &rhs._v); } bool l_isgeq(const LFP &rhs) const { return L_ISGEQ(&_v, &rhs._v); } bool l_isequ(const LFP &rhs) const { return L_ISEQU(&_v, &rhs._v); } int ucmp(const LFP & rhs) const; int scmp(const LFP & rhs) const; std::string toString() const; std::ostream& toStream(std::ostream &oo) const; operator double() const; explicit LFP(double); protected: LFP(const l_fp &rhs); static int cmp_work(u_int32 a[3], u_int32 b[3]); l_fp _v; }; static std::ostream& operator<<(std::ostream &oo, const LFP& rhs) { return rhs.toStream(oo); } //---------------------------------------------------------------------- // reference comparision // This is implementad as a full signed MP-subtract in 3 limbs, where // the operands are zero or sign extended before the subtraction is // executed. //---------------------------------------------------------------------- int LFP::scmp(const LFP & rhs) const { u_int32 a[3], b[3]; const l_fp &op1(_v), &op2(rhs._v); a[0] = op1.l_uf; a[1] = op1.l_ui; a[2] = 0; b[0] = op2.l_uf; b[1] = op2.l_ui; b[2] = 0; a[2] -= (op1.l_i < 0); b[2] -= (op2.l_i < 0); return cmp_work(a,b); } int LFP::ucmp(const LFP & rhs) const { u_int32 a[3], b[3]; const l_fp &op1(_v), &op2(rhs._v); a[0] = op1.l_uf; a[1] = op1.l_ui; a[2] = 0; b[0] = op2.l_uf; b[1] = op2.l_ui; b[2] = 0; return cmp_work(a,b); } int LFP::cmp_work(u_int32 a[3], u_int32 b[3]) { u_int32 cy, idx, tmp; for (cy = idx = 0; idx < 3; ++idx) { tmp = a[idx]; cy = (a[idx] -= cy ) > tmp; tmp = a[idx]; cy |= (a[idx] -= b[idx]) > tmp; } if (a[2]) return -1; return a[0] || a[1]; } //---------------------------------------------------------------------- // imlementation of the LFP stuff // This should be easy enough... //---------------------------------------------------------------------- LFP::~LFP() { // NOP } LFP::LFP() { _v.l_ui = 0; _v.l_uf = 0; } LFP::LFP(int32 i, u_int32 f) { _v.l_i = i; _v.l_uf = f; } LFP::LFP(const LFP &rhs) { _v = rhs._v; } LFP::LFP(const l_fp & rhs) { _v = rhs; } LFP& LFP::operator=(const LFP & rhs) { _v = rhs._v; return *this; } LFP& LFP::operator+=(const LFP & rhs) { L_ADD(&_v, &rhs._v); return *this; } LFP& LFP::operator-=(const LFP & rhs) { L_SUB(&_v, &rhs._v); return *this; } LFP LFP::operator+(const LFP &rhs) const { LFP tmp(*this); return tmp += rhs; } LFP LFP::operator-(const LFP &rhs) const { LFP tmp(*this); return tmp -= rhs; } LFP LFP::operator-() const { LFP tmp(*this); L_NEG(&tmp._v); return tmp; } LFP LFP::neg() const { LFP tmp(*this); L_NEG(&tmp._v); return tmp; } LFP LFP::abs() const { LFP tmp(*this); if (L_ISNEG(&tmp._v)) L_NEG(&tmp._v); return tmp; } int LFP::signum() const { if (_v.l_ui & 0x80000000u) return -1; return (_v.l_ui || _v.l_uf); } std::string LFP::toString() const { std::ostringstream oss; toStream(oss); return oss.str(); } std::ostream& LFP::toStream(std::ostream &os) const { return os << mfptoa(_v.l_ui, _v.l_uf, 9) << " [$" << std::setw(8) << std::setfill('0') << std::hex << _v.l_ui << ':' << std::setw(8) << std::setfill('0') << std::hex << _v.l_uf << ']'; } bool LFP::operator==(const LFP &rhs) const { return L_ISEQU(&_v, &rhs._v); } LFP::operator double() const { double res; LFPTOD(&_v, res); return res; } LFP::LFP(double rhs) { DTOLFP(rhs, &_v); } //---------------------------------------------------------------------- // testing the relational macros works better with proper predicate // formatting functions; it slows down the tests a bit, but makes for // readable failure messages. //---------------------------------------------------------------------- testing::AssertionResult isgt_p( const LFP &op1, const LFP &op2) { if (op1.l_isgt(op2)) return testing::AssertionSuccess() << "L_ISGT(" << op1 << "," << op2 << ") is true"; else return testing::AssertionFailure() << "L_ISGT(" << op1 << "," << op2 << ") is false"; } testing::AssertionResult isgeq_p( const LFP &op1, const LFP &op2) { if (op1.l_isgeq(op2)) return testing::AssertionSuccess() << "L_ISGEQ(" << op1 << "," << op2 << ") is true"; else return testing::AssertionFailure() << "L_ISGEQ(" << op1 << "," << op2 << ") is false"; } testing::AssertionResult isgtu_p( const LFP &op1, const LFP &op2) { if (op1.l_isgtu(op2)) return testing::AssertionSuccess() << "L_ISGTU(" << op1 << "," << op2 << ") is true"; else return testing::AssertionFailure() << "L_ISGTU(" << op1 << "," << op2 << ") is false"; } testing::AssertionResult ishis_p( const LFP &op1, const LFP &op2) { if (op1.l_ishis(op2)) return testing::AssertionSuccess() << "L_ISHIS(" << op1 << "," << op2 << ") is true"; else return testing::AssertionFailure() << "L_ISHIS(" << op1 << "," << op2 << ") is false"; } testing::AssertionResult isequ_p( const LFP &op1, const LFP &op2) { if (op1.l_isequ(op2)) return testing::AssertionSuccess() << "L_ISEQU(" << op1 << "," << op2 << ") is true"; else return testing::AssertionFailure() << "L_ISEQU(" << op1 << "," << op2 << ") is false"; } //---------------------------------------------------------------------- // test data table for add/sub and compare //---------------------------------------------------------------------- static const lfp_hl addsub_tab[][3] = { // trivial idendity: {{0 ,0 }, { 0,0 }, { 0,0}}, // with carry from fraction and sign change: {{-1,0x80000000}, { 0,0x80000000}, { 0,0}}, // without carry from fraction {{ 1,0x40000000}, { 1,0x40000000}, { 2,0x80000000}}, // with carry from fraction: {{ 1,0xC0000000}, { 1,0xC0000000}, { 3,0x80000000}}, // with carry from fraction and sign change: {{0x7FFFFFFF, 0x7FFFFFFF}, {0x7FFFFFFF,0x7FFFFFFF}, {0xFFFFFFFE,0xFFFFFFFE}}, // two tests w/o carry (used for l_fp<-->double): {{0x55555555,0xAAAAAAAA}, {0x11111111,0x11111111}, {0x66666666,0xBBBBBBBB}}, {{0x55555555,0x55555555}, {0x11111111,0x11111111}, {0x66666666,0x66666666}}, // wide-range test, triggers compare trouble {{0x80000000,0x00000001}, {0xFFFFFFFF,0xFFFFFFFE}, {0x7FFFFFFF,0xFFFFFFFF}} }; static const size_t addsub_cnt(sizeof(addsub_tab)/sizeof(addsub_tab[0])); static const size_t addsub_tot(sizeof(addsub_tab)/sizeof(addsub_tab[0][0])); //---------------------------------------------------------------------- // epsilon estimation for the precision of a conversion double --> l_fp // // The error estimation limit is as follows: // * The 'l_fp' fixed point fraction has 32 bits precision, so we allow // for the LSB to toggle by clamping the epsilon to be at least 2^(-31) // // * The double mantissa has a precsion 54 bits, so the other minimum is // dval * (2^(-53)) // // The maximum of those two boundaries is used for the check. // // Note: once there are more than 54 bits between the highest and lowest // '1'-bit of the l_fp value, the roundtrip *will* create truncation // errors. This is an inherent property caused by the 54-bit mantissa of // the 'double' type. double eps(double d) { return std::max(ldexp(1.0, -31), ldexp(fabs(d), -53)); } //---------------------------------------------------------------------- // test addition //---------------------------------------------------------------------- TEST_F(lfpTest, AdditionLR) { for (size_t idx=0; idx < addsub_cnt; ++idx) { LFP op1(addsub_tab[idx][0].h, addsub_tab[idx][0].l); LFP op2(addsub_tab[idx][1].h, addsub_tab[idx][1].l); LFP exp(addsub_tab[idx][2].h, addsub_tab[idx][2].l); LFP res(op1 + op2); ASSERT_EQ(exp, res); } } TEST_F(lfpTest, AdditionRL) { for (size_t idx=0; idx < addsub_cnt; ++idx) { LFP op2(addsub_tab[idx][0].h, addsub_tab[idx][0].l); LFP op1(addsub_tab[idx][1].h, addsub_tab[idx][1].l); LFP exp(addsub_tab[idx][2].h, addsub_tab[idx][2].l); LFP res(op1 + op2); ASSERT_EQ(exp, res); } } //---------------------------------------------------------------------- // test subtraction //---------------------------------------------------------------------- TEST_F(lfpTest, SubtractionLR) { for (size_t idx=0; idx < addsub_cnt; ++idx) { LFP op2(addsub_tab[idx][0].h, addsub_tab[idx][0].l); LFP exp(addsub_tab[idx][1].h, addsub_tab[idx][1].l); LFP op1(addsub_tab[idx][2].h, addsub_tab[idx][2].l); LFP res(op1 - op2); ASSERT_EQ(exp, res); } } TEST_F(lfpTest, SubtractionRL) { for (size_t idx=0; idx < addsub_cnt; ++idx) { LFP exp(addsub_tab[idx][0].h, addsub_tab[idx][0].l); LFP op2(addsub_tab[idx][1].h, addsub_tab[idx][1].l); LFP op1(addsub_tab[idx][2].h, addsub_tab[idx][2].l); LFP res(op1 - op2); ASSERT_EQ(exp, res); } } //---------------------------------------------------------------------- // test negation //---------------------------------------------------------------------- TEST_F(lfpTest, Negation) { for (size_t idx=0; idx < addsub_cnt; ++idx) { LFP op1(addsub_tab[idx][0].h, addsub_tab[idx][0].l); LFP op2(-op1); LFP sum(op1 + op2); ASSERT_EQ(LFP(0,0), sum); } } //---------------------------------------------------------------------- // test absolute value //---------------------------------------------------------------------- TEST_F(lfpTest, Absolute) { for (size_t idx=0; idx < addsub_cnt; ++idx) { LFP op1(addsub_tab[idx][0].h, addsub_tab[idx][0].l); LFP op2(op1.abs()); ASSERT_TRUE(op2.signum() >= 0); if (op1.signum() >= 0) op1 -= op2; else op1 += op2; ASSERT_EQ(LFP(0,0), op1); } // There is one special case we have to check: the minimum // value cannot be negated, or, to be more precise, the // negation reproduces the original pattern. LFP minVal(0x80000000, 0x00000000); LFP minAbs(minVal.abs()); ASSERT_EQ(-1, minVal.signum()); ASSERT_EQ(minVal, minAbs); } //---------------------------------------------------------------------- // fp -> double -> fp rountrip test //---------------------------------------------------------------------- TEST_F(lfpTest, FDF_RoundTrip) { // since a l_fp has 64 bits in it's mantissa and a double has // only 54 bits available (including the hidden '1') we have to // make a few concessions on the roundtrip precision. The 'eps()' // function makes an educated guess about the avilable precision // and checks the difference in the two 'l_fp' values against // that limit. for (size_t idx=0; idx < addsub_cnt; ++idx) { LFP op1(addsub_tab[idx][0].h, addsub_tab[idx][0].l); double op2(op1); LFP op3(op2); // for manual checks only: // std::cout << std::setprecision(16) << op2 << std::endl; ASSERT_LE(fabs(op1-op3), eps(op2)); } } //---------------------------------------------------------------------- // test the compare stuff // // This uses the local compare and checks if the operations using the // macros in 'ntp_fp.h' produce mathing results. // ---------------------------------------------------------------------- TEST_F(lfpTest, SignedRelOps) { const lfp_hl * tv(&addsub_tab[0][0]); for (size_t lc=addsub_tot-1; lc; --lc,++tv) { LFP op1(tv[0].h,tv[0].l); LFP op2(tv[1].h,tv[1].l); int cmp(op1.scmp(op2)); switch (cmp) { case -1: std::swap(op1, op2); case 1: EXPECT_TRUE (isgt_p(op1,op2)); EXPECT_FALSE(isgt_p(op2,op1)); EXPECT_TRUE (isgeq_p(op1,op2)); EXPECT_FALSE(isgeq_p(op2,op1)); EXPECT_FALSE(isequ_p(op1,op2)); EXPECT_FALSE(isequ_p(op2,op1)); break; case 0: EXPECT_FALSE(isgt_p(op1,op2)); EXPECT_FALSE(isgt_p(op2,op1)); EXPECT_TRUE (isgeq_p(op1,op2)); EXPECT_TRUE (isgeq_p(op2,op1)); EXPECT_TRUE (isequ_p(op1,op2)); EXPECT_TRUE (isequ_p(op2,op1)); break; default: FAIL() << "unexpected SCMP result: " << cmp; } } } TEST_F(lfpTest, UnsignedRelOps) { const lfp_hl * tv(&addsub_tab[0][0]); for (size_t lc=addsub_tot-1; lc; --lc,++tv) { LFP op1(tv[0].h,tv[0].l); LFP op2(tv[1].h,tv[1].l); int cmp(op1.ucmp(op2)); switch (cmp) { case -1: std::swap(op1, op2); case 1: EXPECT_TRUE (isgtu_p(op1,op2)); EXPECT_FALSE(isgtu_p(op2,op1)); EXPECT_TRUE (ishis_p(op1,op2)); EXPECT_FALSE(ishis_p(op2,op1)); break; case 0: EXPECT_FALSE(isgtu_p(op1,op2)); EXPECT_FALSE(isgtu_p(op2,op1)); EXPECT_TRUE (ishis_p(op1,op2)); EXPECT_TRUE (ishis_p(op2,op1)); break; default: FAIL() << "unexpected UCMP result: " << cmp; } } } //---------------------------------------------------------------------- // that's all folks... but feel free to add things! //----------------------------------------------------------------------