#pragma once #include #include #include union Float_t { float f; int i; struct { uint32_t man : 23; uint32_t exp : 8; uint32_t sign : 1; } parts; }; inline float fround(float x, int32_t precision = 8) { auto power_of_10 = std::pow(10, precision); return std::round(x * power_of_10) / power_of_10; } inline bool almost_equal_eps(float a, float b, int ulp = 128) { auto eps = std::numeric_limits::epsilon() * (std::max(fabs(a), fabs(b)) * ulp); auto d = fabs(a - b); if (d > eps) { std::cout << "*** almost_equal_eps: d=" << d << ", eps=" << eps << std::endl; return false; } return true; } inline bool almost_equal_ulp(float a, float b, int32_t ulp = 6) { Float_t fa{a}, fb{b}; auto d = std::abs(fa.i - fb.i); if (d > ulp) { std::cout << "*** almost_equal_ulp: a=" << a << ", b=" << b << ", ulp=" << d << ", ia=" << std::hex << fa.i << ", ib=" << fb.i << std::endl; return false; } return true; } inline bool almost_equal(float a, float b) { if (a == b) return true; /*if (almost_equal_eps(a, b)) return true;*/ return almost_equal_ulp(a, b); } class ITestCase { public: ITestCase() {} virtual ~ITestCase() {} virtual void setup(int n, void* src1, void* src2) = 0; virtual int verify(int n, void* dst, const void* src1, const void* src2) = 0; }; class Test_IADD : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (int32_t*)src1; auto b = (int32_t*)src2; for (int i = 0; i < n; ++i) { a[i] = n/2 - i; b[i] = n/2 + i; } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (int32_t*)src1; auto b = (int32_t*)src2; auto c = (int32_t*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] + b[i]; if (c[i] != ref) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_IMUL : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (int32_t*)src1; auto b = (int32_t*)src2; for (int i = 0; i < n; ++i) { a[i] = n/2 - i; b[i] = n/2 + i; } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (int32_t*)src1; auto b = (int32_t*)src2; auto c = (int32_t*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] * b[i]; if (c[i] != ref) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_IDIV : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (int32_t*)src1; auto b = (int32_t*)src2; for (int i = 0; i < n; ++i) { a[i] = n/2 - i; b[i] = n/2 + i; } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (int32_t*)src1; auto b = (int32_t*)src2; auto c = (int32_t*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] / b[i]; if (c[i] != ref) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_IDIV_MUL : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (int32_t*)src1; auto b = (int32_t*)src2; for (int i = 0; i < n; ++i) { a[i] = n/2 - i; b[i] = n/2 + i; } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (int32_t*)src1; auto b = (int32_t*)src2; auto c = (int32_t*)dst; for (int i = 0; i < n; ++i) { auto x = a[i] / b[i]; auto y = a[i] * b[i]; auto ref = x + y; if (c[i] != ref) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FADD : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] + b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FSUB : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] - b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FMUL : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] * b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FMADD : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] * b[i] + b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FMSUB : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] * b[i] - b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FNMADD : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = -a[i] * b[i] - b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FNMSUB : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = -a[i] * b[i] + b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FNMADD_MADD : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto x = -a[i] * b[i] - b[i]; auto y = a[i] * b[i] + b[i]; auto ref = x + y; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FDIV : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = a[i] / b[i]; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FDIV2 : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n - i) * (1.0f/n)); b[i] = fround((n + i) * (1.0f/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto x = a[i] / b[i]; auto y = b[i] / a[i]; auto ref = x + y; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FSQRT : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { float q = 1.0f + (i % 64); a[i] = q; b[i] = q; } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto ref = sqrt(a[i] * b[i]); if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FTOI : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround((n/2 - i) + (float(i)/n)); b[i] = fround((n/2 - i) + (float(i)/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (int32_t*)dst; for (int i = 0; i < n; ++i) { auto x = a[i] + b[i]; auto ref = (int32_t)x; if (c[i] != ref) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_FTOU : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (float*)src1; auto b = (float*)src2; for (int i = 0; i < n; ++i) { a[i] = fround(i + (float(i)/n)); b[i] = fround(i + (float(i)/n)); } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (float*)src1; auto b = (float*)src2; auto c = (uint32_t*)dst; for (int i = 0; i < n; ++i) { auto x = a[i] + b[i]; auto ref = (uint32_t)x; if (c[i] != ref) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_ITOF : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (int32_t*)src1; auto b = (int32_t*)src2; for (int i = 0; i < n; ++i) { a[i] = n/2 - i; b[i] = n/2 - i; } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (int32_t*)src1; auto b = (int32_t*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto x = a[i] + b[i]; auto ref = (float)x; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } }; class Test_UTOF : public ITestCase { public: void setup(int n, void* src1, void* src2) override { auto a = (uint32_t*)src1; auto b = (uint32_t*)src2; for (int i = 0; i < n; ++i) { a[i] = i; b[i] = i; } } int verify(int n, void* dst, const void* src1, const void* src2) override { int errors = 0; auto a = (uint32_t*)src1; auto b = (uint32_t*)src2; auto c = (float*)dst; for (int i = 0; i < n; ++i) { auto x = a[i] + b[i]; auto ref = (float)x; if (!almost_equal(c[i], ref)) { std::cout << "error at result #" << i << ": expected=" << ref << ", actual=" << c[i] << ", a=" << a[i] << ", b=" << b[i] << std::endl; ++errors; } } return errors; } };