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@@ -19,120 +19,28 @@ |
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using namespace lol; |
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using namespace std; |
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float adjustf(float f, int i) __attribute__((noinline)); |
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float adjustf(float f, int i) |
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mat4 multiply_copy(mat4 m1, mat4 m2, mat4 m3) |
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{ |
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union { float f; uint32_t x; } u = { f }; |
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u.x += i; |
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return u.f; |
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return m1 * m2 * m3; |
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} |
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double adjust(double f, int i) __attribute__((noinline)); |
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double adjust(double f, int i) |
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mat4 multiply_ref(mat4 const &m1, mat4 const &m2, mat4 const &m3) |
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{ |
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union { double f; uint64_t x; } u = { f }; |
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u.x += i; |
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return u.f; |
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} |
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static void inspect(float f) |
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{ |
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union { float f; uint32_t x; } u = { f }; |
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printf("%08x %14.12g -- ", u.x, u.f); |
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int i = (u.x & 0x7fffffu) | 0x800000u; |
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int j = 23 - ((u.x >> 23) & 0xff) + ((1 << 7) - 1); |
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if (u.f <= 0) |
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i = -i; |
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printf("%i / 2^%i = %14.12g\n", i, j, (float)i / (1LLu << j)); |
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} |
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//#define float double |
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#if 1 |
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static float const a0 = 1.0; |
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static float const a1 = -0.1666666666663036; |
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static float const a2 = 0.008333333325075758; |
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static float const a3 = -0.0001984126372689299; |
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static float const a4 = 2.755533925906394e-06; |
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static float const a5 = -2.476042626296988e-08; |
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static float const a6 = 0.0; |
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#elif 0 |
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static float const a0 = adjust(0.9999999999999376, 0); |
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static float const a1 = adjust(-0.1666666666643236, 0); |
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static float const a2 = adjust(0.008333333318766562, 0); |
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static float const a3 = adjust(-0.0001984126641174625, 0); |
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static float const a4 = adjust(2.755693193297308e-006, 0); |
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static float const a5 = adjust(-2.502951900290311e-008, 0); |
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static float const a6 = adjust(1.540117123154927e-010, 0); |
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#elif 0 |
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static float const a0 = adjust(1.0, 0); |
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static float const a1 = adjust(-0.1666666666372165, 0); |
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static float const a2 = adjust(0.008333332748323419, 0); |
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static float const a3 = adjust(-0.0001984108245332497, 0); |
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static float const a4 = adjust(2.753619853326498e-06, 0); |
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static float const a5 = adjust(-2.407483949485896e-08, 0); |
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static float const a6 = 0.0; |
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#else |
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static float const a0 = adjust(0.9999999946887117, 0); |
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static float const a1 = adjust(-0.1666665668590824, 0); |
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static float const a2 = adjust(0.008333025160523476, 0); |
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static float const a3 = adjust(-0.0001980741944205014, 0); |
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static float const a4 = adjust(2.60190356966559e-06, 0); // -900 in floats |
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static float const a5 = 0.0; |
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static float const a6 = 0.0; |
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#endif |
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static float floatsin(float f) |
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{ |
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return lol_sin(f); |
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//static float const k = (float)real::R_2_PI(); |
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//f *= k; |
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float f2 = f * f; |
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float f4 = f2 * f2; |
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return f * (a0 + f4 * (a2 + f4 * (a4 + f4 * a6)) + f2 * (a1 + f4 * (a3 + f4 * a5))); |
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//return f * (a0 + f2 * (a1 + f2 * (a2 + f2 * (a3 + f2 * (a4 + f2 * (a5 + f2 * a6)))))); |
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//return f * (a0 + a1 * f2 + a2 * f2 * f2 + a3 * f2 * f2 * f2 + a4 * f2 * f2 * f2 * f2 + a5 * f2 * f2 * f2 * f2 * f2 + a6 * f2 * f2 * f2 * f2 * f2 * f2); |
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#undef float |
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return m1 * m2 * m3; |
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} |
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int main(int argc, char **argv) |
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{ |
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UNUSED(argc, argv); |
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typedef union { float f; uint32_t x; } flint; |
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int error[5] = { 0 }; |
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inspect(a0); |
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inspect(a1); |
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inspect(a2); |
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inspect(a3); |
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inspect(a4); |
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inspect(a5); |
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for (flint u = { (float)real::R_PI_2() }; u.f > 1e-30; u.x -= 1) |
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{ |
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union { float f; uint32_t x; } s1 = { sinf(adjustf(u.f, 0)) }; |
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union { float f; uint32_t x; } s2 = { floatsin(adjustf(u.f, 0)) }; |
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int e = lol::abs((int)(s1.x - s2.x)); |
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switch (e) |
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{ |
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case 3: |
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case 2: |
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case 1: |
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if (lol::abs((double)s1.f - (double)s2.f) > 1e-10 * lol::abs(s1.f)) |
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printf("%15.13g %08x: %15.13g %15.13g %08x %08x\n", u.f, u.x, s1.f, s2.f, s1.x, s2.x); |
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case 0: |
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error[e]++; |
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break; |
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default: |
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error[4]++; |
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break; |
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} |
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} |
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mat4 a = mat4::rotate(0.1f, vec3(1.f, 1.f, 0.f)); |
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mat4 b = mat4::rotate(0.1f, vec3(0.f, 0.f, 1.f)); |
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mat4 m = mat4(1.f); |
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printf("exact: %i off by 1: %i by 2: %i by 3: %i error: %i\n", |
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error[0], error[1], error[2], error[3], error[4]); |
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for (int i = 0; i < 40000000; ++i) |
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//m = multiply_copy(a, m, b); |
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m = multiply_ref(a, m, b); |
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m.printf(); |
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return EXIT_SUCCESS; |
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} |
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