Created
February 9, 2020 11:25
-
-
Save mizar/4e39959272a3ed974dd46cc1c289ae75 to your computer and use it in GitHub Desktop.
イロレーティング計算テスト
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| #include <iostream> | |
| #include <limits> | |
| #include <boost/math/constants/constants.hpp> | |
| #include <boost/math/special_functions/gamma.hpp> | |
| #include <boost/math/special_functions/erf.hpp> | |
| #include <boost/multiprecision/cpp_dec_float.hpp> | |
| template<typename T> | |
| class Logit { | |
| private: | |
| T value{ 0.0 }; | |
| static T ln1mexp(T x) { | |
| if (x >= 0.0l) { | |
| return std::numeric_limits<T>::quiet_NaN(); | |
| } | |
| else if (x >= boost::math::constants::ln_two<T>()) { | |
| return log(-expm1(x)); | |
| } | |
| else { | |
| return log1p(-exp(x)); | |
| } | |
| } | |
| static T ln1pexp(T x) { | |
| if (x <= 0.0) { | |
| return log1p(exp(x)); | |
| } | |
| else { | |
| return x + log1p(exp(-x)); | |
| } | |
| } | |
| static T enlogit(T x) { | |
| if (x <= 0.0) { | |
| return -std::numeric_limits<T>::infinity(); | |
| } | |
| else if (x >= 1.0) { | |
| return std::numeric_limits<T>::infinity(); | |
| } | |
| else { | |
| return log(x) - log1p(-x); | |
| } | |
| } | |
| static T expenlogit(T x) { | |
| if (x >= 0.0) { | |
| return std::numeric_limits<T>::infinity(); | |
| } | |
| return x - ln1mexp(x); | |
| } | |
| static T delogit(T x) { | |
| if (x >= 0.0) { | |
| T nexp = exp(-x); | |
| return 1.0 / (nexp + 1.0); | |
| } | |
| else { | |
| T pexp = exp(x); | |
| return pexp / (pexp + 1.0); | |
| } | |
| } | |
| static T logdelogit(T x) { | |
| if (x >= 0.0) { | |
| return -log1p(exp(-x)); | |
| } | |
| else { | |
| return x - log1p(exp(x)); | |
| } | |
| } | |
| static T near_ipow2(T x) { | |
| return exp2(-round(log2(x))); | |
| } | |
| static T betaln(T a, T b) { | |
| return lgamma(a) + lgamma(b) - lgamma(a + b); | |
| } | |
| static T betacf(T x, T a, T b) { | |
| T eps = std::numeric_limits<T>::epsilon(); | |
| T qab = a + b; | |
| T qap = a + 1.0; | |
| T qam = a - 1.0; | |
| T m0 = 1.0; | |
| T m2 = 1.0; | |
| T m1 = 1.0; | |
| T m3 = 1.0 - x * qab / qap; | |
| for (int ni = 1; ni < 1024; ni++) { | |
| T n = ni; | |
| T n2 = n + n; | |
| T t1 = m1; | |
| T t3 = m3; | |
| T d0 = x * n * (b - n) / ((qam + n2) * (a + n2)); | |
| m0 *= d0; | |
| m2 *= d0; | |
| T d1 = 1.0 - x * (a + n) * (qab + n) / ((a + n2) * (qap + n2)); | |
| m1 = m0 + t1 * d1; | |
| m3 = m2 + t3 * d1; | |
| m0 += t1; | |
| m2 += t3; | |
| T tx = near_ipow2(m3); | |
| m0 *= tx; | |
| m2 *= tx; | |
| m1 *= tx; | |
| m3 *= tx; | |
| T r = m0 * m3; | |
| if (d0 == 0.0 || abs(r - m1 * m2) < abs(eps * r)) { | |
| break; | |
| } | |
| } | |
| return m1 / m3; | |
| } | |
| public: | |
| Logit() {} | |
| Logit(T v): value(v) {} | |
| static Logit px(T x) { return Logit(enlogit(x)); } | |
| static Logit nx(T x) { return Logit(-enlogit(x)); } | |
| static Logit lnpx(T x) { return Logit(expenlogit(x)); } | |
| static Logit lnnx(T x) { return Logit(-expenlogit(x)); } | |
| T v() { return value; } | |
| T px() { return delogit(value); } | |
| T nx() { return delogit(-value); } | |
| T lnpx() { return logdelogit(value); } | |
| T lnnx() { return logdelogit(-value); } | |
| T elo() { return boost::math::constants::log10_e<T>() * 400.0 * value; } | |
| Logit operator-() const { return Logit(-value); } | |
| static T logitbetaln(Logit<T> x, T a, T b) { | |
| T px = x.px(); | |
| if (px < (a + 1.0) / (a + b + 2.0)) { | |
| if (px == 0.0) { | |
| return -std::numeric_limits<T>::infinity(); | |
| } | |
| return a * x.lnpx() + b * x.lnnx() - betaln(a, b) + log(betacf(px, a, b) / a); | |
| } | |
| else { | |
| T nx = x.nx(); | |
| if (nx == 0.0) { | |
| return 0.0; | |
| } | |
| return ln1mexp(a * x.lnpx() + b * x.lnnx() - betaln(a, b) + log(betacf(nx, b, a) / b)); | |
| } | |
| } | |
| static Logit<T> ibetainvlogit(T p, T a, T b) { | |
| if (p <= 0.0) { | |
| return Logit<T>::px(0.0); | |
| } | |
| if (p >= 1.0) { | |
| return Logit<T>::nx(0.0); | |
| } | |
| Logit<T> x; | |
| if (a >= 1.0 && b >= 1.0) { | |
| T pp = p < 0.5 ? p : 1.0 - p; | |
| T t = sqrt(-2.0 * log(pp)); | |
| T u; | |
| if (p < 0.5) { | |
| u = t - (t * 0.27061 + 2.30753) / (t * (0.99229 + t * 0.04481) + 1.0); | |
| } | |
| else { | |
| u = (t * 0.27061 + 2.30753) / (t * (0.99229 + t * 0.04481) + 1.0) - t; | |
| } | |
| T al = (u * u - 3.0) / 6.0; | |
| T h = 2.0 / (1.0 / (2.0 * a - 1.0) + 1.0 / (2.0 * b - 1.0)); | |
| T w = (u * sqrt(al + h) / h) - (1.0 / (2.0 * b - 1.0) - 1.0 / (2.0 * a - 1.0)) * (al + 5.0 / 6.0 - 2.0 / (3.0 * h)); | |
| x = Logit<T>::px(a / (a + b * exp(2.0 * w))); | |
| } | |
| else { | |
| T lna = log(a / (a + b)); | |
| T lnb = log(b / (a + b)); | |
| T t = exp(a * lna) / a; | |
| T u = exp(b * lnb) / b; | |
| T w = t + u; | |
| if (p < t / w) { | |
| x = Logit<T>::lnpx(log(a * w * p) / a); | |
| } | |
| else { | |
| x = Logit<T>::lnnx(log(b * w * (1.0 - p)) / b); | |
| } | |
| } | |
| T eps = std::numeric_limits<T>::epsilon(); | |
| T afacmln2 = betaln(a, b) + boost::math::constants::ln_two<T>(); | |
| T ph = 0.5 * (log(p) - log1p(-p)); | |
| for (int j = 0; j < 20; j++) { | |
| if (!isfinite(x.v())) { | |
| break; | |
| } | |
| T lnbeta1 = logitbetaln(x, a, b); | |
| T lnbeta2 = logitbetaln(-x, b, a); | |
| T err = 0.5 * (lnbeta1 - lnbeta2) - ph; | |
| T grad = exp(x.lnpx() * a + x.lnnx() * b - afacmln2 - lnbeta1 - lnbeta2); | |
| T t = err / grad; | |
| /* | |
| std::cout | |
| << std::noshowpos | |
| << std::defaultfloat | |
| << std::setprecision(std::numeric_limits<T>::digits10) | |
| << " j:" << j | |
| << " x:" << x.v() | |
| << " lnbeta1:" << lnbeta1 | |
| << " lnbeta2:" << lnbeta2 | |
| << " err:" << err | |
| << " grad:" << grad | |
| << " p:" << p | |
| << " a:" << a | |
| << " b:" << b | |
| << std::endl; | |
| */ | |
| x = Logit<T>::Logit(x.v() - t); | |
| if (abs(t) < abs(eps * x.v()) && j > 0) { | |
| break; | |
| } | |
| } | |
| return x; | |
| } | |
| }; | |
| template <typename T> | |
| static void do_calc(long long w, long long d, long long l) { | |
| T one = boost::lexical_cast<T>(1.0); | |
| T wd = boost::lexical_cast<T>(w) + boost::lexical_cast<T>(0.5) * boost::lexical_cast<T>(d); | |
| T ld = boost::lexical_cast<T>(l) + boost::lexical_cast<T>(0.5) * boost::lexical_cast<T>(d); | |
| T wd1 = wd + one; | |
| T ld1 = ld + one; | |
| T p_ary[] = { | |
| boost::lexical_cast<T>("0.375"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 0.5) * 0.5, | |
| boost::lexical_cast<T>("0.25"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 1.0) * 0.5, | |
| boost::lexical_cast<T>("0.125"), | |
| boost::lexical_cast<T>("0.1"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 1.5) * 0.5, | |
| boost::lexical_cast<T>("0.05"), | |
| boost::lexical_cast<T>("0.025"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 2.0) * 0.5, | |
| boost::lexical_cast<T>("0.01"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 2.5) * 0.5, | |
| boost::lexical_cast<T>("0.005"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 3.0) * 0.5, | |
| boost::lexical_cast<T>("0.001"), | |
| boost::lexical_cast<T>("0.0005"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 3.5) * 0.5, | |
| boost::lexical_cast<T>("0.0001"), | |
| boost::lexical_cast<T>("0.00005"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 4.0) * 0.5, | |
| boost::lexical_cast<T>("0.00001"), | |
| boost::lexical_cast<T>("0.000005"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 4.5) * 0.5, | |
| boost::lexical_cast<T>("0.000001"), | |
| boost::lexical_cast<T>("0.0000005"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 5.0) * 0.5, | |
| boost::lexical_cast<T>("0.0000001"), | |
| boost::lexical_cast<T>("0.00000005"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 5.5) * 0.5, | |
| boost::lexical_cast<T>("0.00000001"), | |
| boost::lexical_cast<T>("0.000000005"), | |
| boost::lexical_cast<T>("0.000000001"), | |
| erfc(boost::math::constants::one_div_root_two<T>() * 6.0) * 0.5, | |
| boost::lexical_cast<T>("0.0000000005"), | |
| }; | |
| std::cout | |
| << typeid(T).name() << std::endl | |
| << std::noshowpos | |
| << std::defaultfloat | |
| << std::setprecision(std::numeric_limits<T>::digits10) | |
| << "W-D-L:" << w << "-" << d << "-" << l << std::endl | |
| << std::endl | |
| << std::string(6, ' ') | |
| << "x" | |
| << std::string(12, ' ') | |
| << "p" | |
| << std::string(6, ' ') | |
| << "(sigma) |" | |
| << std::string(19, ' ') | |
| << "elorating" | |
| << std::string(19, ' ') | |
| << "| error_lower error_upper" | |
| << std::endl | |
| << std::string(34, '-') | |
| << "+" | |
| << std::string(47, '-') | |
| << "+" | |
| << std::string(24, '-') | |
| << std::endl; | |
| for(auto & p: p_ary) { | |
| std::cout | |
| << std::noshowpos | |
| << std::setprecision(10) | |
| << std::fixed | |
| << -p * 2.0 + 1.0 | |
| << " " | |
| << std::noshowpos | |
| << std::setprecision(10) | |
| << std::fixed | |
| << p | |
| << std::setprecision(3) | |
| << " (" << boost::math::erfc_inv(p * 2.0) * boost::math::constants::root_two<T>() | |
| << ") | "; | |
| auto lx_l = Logit<T>::ibetainvlogit(p, wd, ld1); | |
| std::cout | |
| << std::showpos | |
| << std::fixed | |
| << std::setprecision(4) | |
| << std::setw(11) | |
| << lx_l.elo() | |
| << std::noshowpos | |
| << std::fixed | |
| << std::setprecision(2) | |
| << " (" << std::setw(6) << lx_l.px() * 100.0 << "%)" | |
| << " - "; | |
| auto lx_u = -Logit<T>::ibetainvlogit(p, ld, wd1); | |
| std::cout | |
| << std::showpos | |
| << std::fixed | |
| << std::setprecision(4) | |
| << std::setw(11) | |
| << lx_u.elo() | |
| << std::noshowpos | |
| << std::fixed | |
| << std::setprecision(2) | |
| << " (" << std::setw(6) << lx_u.px() * 100.0 << "%)" | |
| << " |"; | |
| T error_l = exp(Logit<T>::logitbetaln(lx_l, wd, ld1)) - p; | |
| T error_u = exp(Logit<T>::logitbetaln(-lx_u, ld, wd1)) - p; | |
| std::cout | |
| << std::showpos | |
| << std::scientific | |
| << std::setprecision(3) | |
| << std::setw(12) | |
| << error_l | |
| << std::showpos | |
| << std::scientific | |
| << std::setprecision(3) | |
| << std::setw(12) | |
| << error_u | |
| << std::noshowpos | |
| << std::defaultfloat | |
| << std::setprecision(std::numeric_limits<T>::digits10) | |
| << std::endl; | |
| } | |
| std::cout << std::endl; | |
| } | |
| void do_calcset(long long w, long long d, long long l) { | |
| do_calc<double>(w, d, l); | |
| do_calc<boost::multiprecision::cpp_dec_float_50>(w, d, l); | |
| do_calc<boost::multiprecision::cpp_dec_float_100>(w, d, l); | |
| } | |
| int main() { | |
| do_calcset(120, 0, 80); | |
| do_calcset(987654321098765, 0, 123456789012345); | |
| do_calcset(987654321098765, 1, 0); | |
| } |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| double | |
| W-D-L:120-0-80 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +60.5521 ( 58.63%) - +80.1240 ( 61.33%) | -4.996e-16 +6.661e-16 | |
| 0.3829249225 0.3085375387 (0.500) | +56.0317 ( 57.99%) - +84.6895 ( 61.95%) | -2.276e-15 +8.327e-16 | |
| 0.5000000000 0.2500000000 (0.674) | +51.6889 ( 57.38%) - +89.0906 ( 62.55%) | +1.338e-14 -5.551e-17 | |
| 0.6826894921 0.1586552539 (1.000) | +43.6024 ( 56.24%) - +97.3249 ( 63.65%) | +1.971e-15 -6.717e-15 | |
| 0.7500000000 0.1250000000 (1.150) | +39.8735 ( 55.71%) - +101.1393 ( 64.16%) | +6.189e-15 -1.082e-15 | |
| 0.8000000000 0.1000000000 (1.282) | +36.6224 ( 55.25%) - +104.4739 ( 64.60%) | -5.135e-16 -8.327e-16 | |
| 0.8663855975 0.0668072013 (1.500) | +31.2152 ( 54.48%) - +110.0387 ( 65.33%) | -1.249e-16 -1.166e-15 | |
| 0.9000000000 0.0500000000 (1.645) | +27.6332 ( 53.97%) - +113.7378 ( 65.81%) | +1.492e-15 -9.714e-16 | |
| 0.9500000000 0.0250000000 (1.960) | +19.8502 ( 52.85%) - +121.8109 ( 66.85%) | +2.325e-16 +2.984e-16 | |
| 0.9544997361 0.0227501319 (2.000) | +18.8621 ( 52.71%) - +122.8393 ( 66.98%) | -6.523e-16 +3.400e-16 | |
| 0.9800000000 0.0100000000 (2.326) | +10.8140 ( 51.56%) - +131.2451 ( 68.04%) | -5.204e-18 -2.186e-16 | |
| 0.9875806693 0.0062096653 (2.500) | +6.5353 ( 50.94%) - +135.7353 ( 68.60%) | -3.487e-16 -9.541e-17 | |
| 0.9900000000 0.0050000000 (2.576) | +4.6676 ( 50.67%) - +137.7000 ( 68.84%) | -7.373e-17 +3.296e-17 | |
| 0.9973002039 0.0013498980 (3.000) | -5.7731 ( 49.17%) - +148.7356 ( 70.19%) | -4.337e-19 -2.320e-17 | |
| 0.9980000000 0.0010000000 (3.090) | -7.9930 ( 48.85%) - +151.0934 ( 70.47%) | +1.626e-17 +1.453e-17 | |
| 0.9990000000 0.0005000000 (3.291) | -12.9196 ( 48.14%) - +156.3407 ( 71.09%) | -9.758e-18 -3.036e-18 | |
| 0.9995347418 0.0002326291 (3.500) | -18.0709 ( 47.40%) - +161.8488 ( 71.74%) | +4.255e-18 +1.789e-18 | |
| 0.9998000000 0.0001000000 (3.719) | -23.4564 ( 46.63%) - +167.6308 ( 72.41%) | -2.223e-18 +2.399e-18 | |
| 0.9999000000 0.0000500000 (3.891) | -27.6754 ( 46.03%) - +172.1772 ( 72.93%) | -1.118e-18 +4.811e-19 | |
| 0.9999366575 0.0000316712 (4.000) | -30.3658 ( 45.64%) - +175.0841 ( 73.26%) | +1.220e-19 -4.743e-20 | |
| 0.9999800000 0.0000100000 (4.265) | -36.8809 ( 44.71%) - +182.1485 ( 74.05%) | +8.640e-20 -7.454e-20 | |
| 0.9999900000 0.0000050000 (4.417) | -40.6274 ( 44.18%) - +186.2269 ( 74.50%) | -7.284e-20 +1.050e-19 | |
| 0.9999932047 0.0000033977 (4.500) | -42.6656 ( 43.89%) - +188.4506 ( 74.74%) | -3.007e-20 +2.414e-20 | |
| 0.9999980000 0.0000010000 (4.753) | -48.9039 ( 43.01%) - +195.2783 ( 75.48%) | -1.376e-20 +4.023e-21 | |
| 0.9999990000 0.0000005000 (4.892) | -52.3079 ( 42.53%) - +199.0177 ( 75.87%) | +3.812e-21 -6.035e-21 | |
| 0.9999994267 0.0000002867 (5.000) | -54.9777 ( 42.15%) - +201.9574 ( 76.18%) | -5.823e-22 +2.965e-21 | |
| 0.9999998000 0.0000001000 (5.199) | -59.8914 ( 41.47%) - +207.3834 ( 76.74%) | -5.029e-21 -1.840e-21 | |
| 0.9999999000 0.0000000500 (5.327) | -63.0334 ( 41.03%) - +210.8636 ( 77.10%) | -4.765e-22 -1.012e-21 | |
| 0.9999999620 0.0000000190 (5.500) | -67.3098 ( 40.43%) - +215.6138 ( 77.58%) | +2.051e-22 -4.037e-22 | |
| 0.9999999800 0.0000000100 (5.612) | -70.0758 ( 40.05%) - +218.6944 ( 77.88%) | +1.952e-22 -1.241e-22 | |
| 0.9999999900 0.0000000050 (5.731) | -73.0094 ( 39.65%) - +221.9688 ( 78.21%) | +1.059e-22 -7.114e-23 | |
| 0.9999999980 0.0000000010 (5.998) | -79.6153 ( 38.74%) - +229.3686 ( 78.92%) | +1.840e-23 -2.068e-23 | |
| 0.9999999980 0.0000000010 (6.000) | -79.6696 ( 38.73%) - +229.4295 ( 78.93%) | +3.516e-24 +0.000e+00 | |
| 0.9999999990 0.0000000005 (6.109) | -82.3785 ( 38.36%) - +232.4748 ( 79.22%) | -1.654e-23 +1.137e-24 | |
| class boost::multiprecision::number<class boost::multiprecision::backends::cpp_dec_float<50,int,void>,1> | |
| W-D-L:120-0-80 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +60.5521 ( 58.63%) - +80.1240 ( 61.33%) | +2.469e-51 +2.469e-51 | |
| 0.3829249225 0.3085375387 (0.500) | +56.0317 ( 57.99%) - +84.6895 ( 61.95%) | +2.752e-51 +2.752e-51 | |
| 0.5000000000 0.2500000000 (0.674) | +51.6889 ( 57.38%) - +89.0906 ( 62.55%) | +1.519e-57 +1.519e-57 | |
| 0.6826894921 0.1586552539 (1.000) | +43.6024 ( 56.24%) - +97.3249 ( 63.65%) | +1.701e-51 +1.701e-51 | |
| 0.7500000000 0.1250000000 (1.150) | +39.8735 ( 55.71%) - +101.1393 ( 64.16%) | +7.597e-58 +7.597e-58 | |
| 0.8000000000 0.1000000000 (1.282) | +36.6224 ( 55.25%) - +104.4739 ( 64.60%) | +4.866e-51 +4.866e-51 | |
| 0.8663855975 0.0668072013 (1.500) | +31.2152 ( 54.48%) - +110.0387 ( 65.33%) | +2.294e-52 +2.294e-52 | |
| 0.9000000000 0.0500000000 (1.645) | +27.6332 ( 53.97%) - +113.7378 ( 65.81%) | +2.568e-51 +2.568e-51 | |
| 0.9500000000 0.0250000000 (1.960) | +19.8502 ( 52.85%) - +121.8109 ( 66.85%) | +1.318e-51 +1.318e-51 | |
| 0.9544997361 0.0227501319 (2.000) | +18.8621 ( 52.71%) - +122.8393 ( 66.98%) | +1.153e-51 +1.153e-51 | |
| 0.9800000000 0.0100000000 (2.326) | +10.8140 ( 51.56%) - +131.2451 ( 68.04%) | -9.301e-52 -9.301e-52 | |
| 0.9875806693 0.0062096653 (2.500) | +6.5353 ( 50.94%) - +135.7353 ( 68.60%) | +3.842e-52 +3.842e-52 | |
| 0.9900000000 0.0050000000 (2.576) | +4.6676 ( 50.67%) - +137.7000 ( 68.84%) | -4.674e-52 -4.674e-52 | |
| 0.9973002039 0.0013498980 (3.000) | -5.7731 ( 49.17%) - +148.7356 ( 70.19%) | +2.406e-52 +2.406e-52 | |
| 0.9980000000 0.0010000000 (3.090) | -7.9930 ( 48.85%) - +151.0934 ( 70.47%) | +8.295e-54 +8.295e-54 | |
| 0.9990000000 0.0005000000 (3.291) | -12.9196 ( 48.14%) - +156.3407 ( 71.09%) | +4.150e-54 +4.150e-54 | |
| 0.9995347418 0.0002326291 (3.500) | -18.0709 ( 47.40%) - +161.8488 ( 71.74%) | +5.471e-55 +5.471e-55 | |
| 0.9998000000 0.0001000000 (3.719) | -23.4564 ( 46.63%) - +167.6308 ( 72.41%) | +5.491e-54 +5.491e-54 | |
| 0.9999000000 0.0000500000 (3.891) | -27.6754 ( 46.03%) - +172.1772 ( 72.93%) | +2.746e-54 +2.746e-54 | |
| 0.9999366575 0.0000316712 (4.000) | -30.3658 ( 45.64%) - +175.0841 ( 73.26%) | +3.925e-55 +3.925e-55 | |
| 0.9999800000 0.0000100000 (4.265) | -36.8809 ( 44.71%) - +182.1485 ( 74.05%) | +1.651e-54 +1.651e-54 | |
| 0.9999900000 0.0000050000 (4.417) | -40.6274 ( 44.18%) - +186.2269 ( 74.50%) | +8.256e-55 +8.256e-55 | |
| 0.9999932047 0.0000033977 (4.500) | -42.6656 ( 43.89%) - +188.4506 ( 74.74%) | +6.554e-56 +6.554e-56 | |
| 0.9999980000 0.0000010000 (4.753) | -48.9039 ( 43.01%) - +195.2783 ( 75.48%) | -6.347e-57 -6.347e-57 | |
| 0.9999990000 0.0000005000 (4.892) | -52.3079 ( 42.53%) - +199.0177 ( 75.87%) | -3.173e-57 -3.173e-57 | |
| 0.9999994267 0.0000002867 (5.000) | -54.9777 ( 42.15%) - +201.9574 ( 76.18%) | +2.260e-56 +2.260e-56 | |
| 0.9999998000 0.0000001000 (5.199) | -59.8914 ( 41.47%) - +207.3834 ( 76.74%) | +5.356e-57 +5.356e-57 | |
| 0.9999999000 0.0000000500 (5.327) | -63.0334 ( 41.03%) - +210.8636 ( 77.10%) | +2.678e-57 +2.678e-57 | |
| 0.9999999620 0.0000000190 (5.500) | -67.3098 ( 40.43%) - +215.6138 ( 77.58%) | -4.334e-57 -4.334e-57 | |
| 0.9999999800 0.0000000100 (5.612) | -70.0758 ( 40.05%) - +218.6944 ( 77.88%) | +6.735e-57 +6.735e-57 | |
| 0.9999999900 0.0000000050 (5.731) | -73.0094 ( 39.65%) - +221.9688 ( 78.21%) | +3.368e-57 +3.368e-57 | |
| 0.9999999980 0.0000000010 (5.998) | -79.6153 ( 38.74%) - +229.3686 ( 78.92%) | +6.180e-59 +6.180e-59 | |
| 0.9999999980 0.0000000010 (6.000) | -79.6696 ( 38.73%) - +229.4295 ( 78.93%) | -3.454e-59 -3.454e-59 | |
| 0.9999999990 0.0000000005 (6.109) | -82.3785 ( 38.36%) - +232.4748 ( 79.22%) | +3.090e-59 +3.090e-59 | |
| class boost::multiprecision::number<class boost::multiprecision::backends::cpp_dec_float<100,int,void>,1> | |
| W-D-L:120-0-80 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +60.5521 ( 58.63%) - +80.1240 ( 61.33%) | +5.651e-101 +5.651e-101 | |
| 0.3829249225 0.3085375387 (0.500) | +56.0317 ( 57.99%) - +84.6895 ( 61.95%) | -2.081e-101 -2.081e-101 | |
| 0.5000000000 0.2500000000 (0.674) | +51.6889 ( 57.38%) - +89.0906 ( 62.55%) | -1.053e-105 -1.053e-105 | |
| 0.6826894921 0.1586552539 (1.000) | +43.6024 ( 56.24%) - +97.3249 ( 63.65%) | -2.206e-101 -2.206e-101 | |
| 0.7500000000 0.1250000000 (1.150) | +39.8735 ( 55.71%) - +101.1393 ( 64.16%) | -2.632e-106 -2.632e-106 | |
| 0.8000000000 0.1000000000 (1.282) | +36.6224 ( 55.25%) - +104.4739 ( 64.60%) | +1.118e-101 +1.118e-101 | |
| 0.8663855975 0.0668072013 (1.500) | +31.2152 ( 54.48%) - +110.0387 ( 65.33%) | -1.240e-102 -1.240e-102 | |
| 0.9000000000 0.0500000000 (1.645) | +27.6332 ( 53.97%) - +113.7378 ( 65.81%) | +2.972e-101 +2.972e-101 | |
| 0.9500000000 0.0250000000 (1.960) | +19.8502 ( 52.85%) - +121.8109 ( 66.85%) | +1.525e-101 +1.525e-101 | |
| 0.9544997361 0.0227501319 (2.000) | +18.8621 ( 52.71%) - +122.8393 ( 66.98%) | +9.842e-102 +9.842e-102 | |
| 0.9800000000 0.0100000000 (2.326) | +10.8140 ( 51.56%) - +131.2451 ( 68.04%) | -7.917e-102 -7.917e-102 | |
| 0.9875806693 0.0062096653 (2.500) | +6.5353 ( 50.94%) - +135.7353 ( 68.60%) | +5.572e-102 +5.572e-102 | |
| 0.9900000000 0.0050000000 (2.576) | +4.6676 ( 50.67%) - +137.7000 ( 68.84%) | -3.978e-102 -3.978e-102 | |
| 0.9973002039 0.0013498980 (3.000) | -5.7731 ( 49.17%) - +148.7356 ( 70.19%) | +3.763e-102 +3.763e-102 | |
| 0.9980000000 0.0010000000 (3.090) | -7.9930 ( 48.85%) - +151.0934 ( 70.47%) | -2.494e-104 -2.494e-104 | |
| 0.9990000000 0.0005000000 (3.291) | -12.9196 ( 48.14%) - +156.3407 ( 71.09%) | -1.248e-104 -1.248e-104 | |
| 0.9995347418 0.0002326291 (3.500) | -18.0709 ( 47.40%) - +161.8488 ( 71.74%) | +2.273e-104 +2.273e-104 | |
| 0.9998000000 0.0001000000 (3.719) | -23.4564 ( 46.63%) - +167.6308 ( 72.41%) | +4.587e-104 +4.587e-104 | |
| 0.9999000000 0.0000500000 (3.891) | -27.6754 ( 46.03%) - +172.1772 ( 72.93%) | +2.294e-104 +2.294e-104 | |
| 0.9999366575 0.0000316712 (4.000) | -30.3658 ( 45.64%) - +175.0841 ( 73.26%) | -3.129e-105 -3.129e-105 | |
| 0.9999800000 0.0000100000 (4.265) | -36.8809 ( 44.71%) - +182.1485 ( 74.05%) | +1.427e-104 +1.427e-104 | |
| 0.9999900000 0.0000050000 (4.417) | -40.6274 ( 44.18%) - +186.2269 ( 74.50%) | +7.135e-105 +7.135e-105 | |
| 0.9999932047 0.0000033977 (4.500) | -42.6656 ( 43.89%) - +188.4506 ( 74.74%) | +3.058e-105 +3.058e-105 | |
| 0.9999980000 0.0000010000 (4.753) | -48.9039 ( 43.01%) - +195.2783 ( 75.48%) | -3.857e-107 -3.857e-107 | |
| 0.9999990000 0.0000005000 (4.892) | -52.3079 ( 42.53%) - +199.0177 ( 75.87%) | -1.928e-107 -1.928e-107 | |
| 0.9999994267 0.0000002867 (5.000) | -54.9777 ( 42.15%) - +201.9574 ( 76.18%) | -5.881e-106 -5.881e-106 | |
| 0.9999998000 0.0000001000 (5.199) | -59.8914 ( 41.47%) - +207.3834 ( 76.74%) | +1.853e-106 +1.853e-106 | |
| 0.9999999000 0.0000000500 (5.327) | -63.0334 ( 41.03%) - +210.8636 ( 77.10%) | +9.264e-107 +9.264e-107 | |
| 0.9999999620 0.0000000190 (5.500) | -67.3098 ( 40.43%) - +215.6138 ( 77.58%) | +2.146e-107 +2.146e-107 | |
| 0.9999999800 0.0000000100 (5.612) | -70.0758 ( 40.05%) - +218.6944 ( 77.88%) | +5.916e-107 +5.916e-107 | |
| 0.9999999900 0.0000000050 (5.731) | -73.0094 ( 39.65%) - +221.9688 ( 78.21%) | +2.958e-107 +2.958e-107 | |
| 0.9999999980 0.0000000010 (5.998) | -79.6153 ( 38.74%) - +229.3686 ( 78.92%) | +4.553e-109 +4.553e-109 | |
| 0.9999999980 0.0000000010 (6.000) | -79.6696 ( 38.73%) - +229.4295 ( 78.93%) | +8.597e-110 +8.597e-110 | |
| 0.9999999990 0.0000000005 (6.109) | -82.3785 ( 38.36%) - +232.4748 ( 79.22%) | +2.277e-109 +2.277e-109 | |
| double | |
| W-D-L:987654321098765-0-123456789012345 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | +2.213e-02 +nan | |
| 0.3829249225 0.3085375387 (0.500) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | -2.431e-02 +nan | |
| 0.5000000000 0.2500000000 (0.674) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | +5.918e-03 +nan | |
| 0.6826894921 0.1586552539 (1.000) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | -1.776e-03 +nan | |
| 0.7500000000 0.1250000000 (1.150) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | +7.987e-03 +nan | |
| 0.8000000000 0.1000000000 (1.282) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | -1.705e-03 +nan | |
| 0.8663855975 0.0668072013 (1.500) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | +5.969e-04 +nan | |
| 0.9000000000 0.0500000000 (1.645) | +361.2360 ( 88.89%) - -nan(ind) (-nan(ind)%) | -3.372e-03 +nan | |
| 0.9500000000 0.0250000000 (1.960) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +9.547e-04 +3.039e-04 | |
| 0.9544997361 0.0227501319 (2.000) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +1.473e-03 -6.243e-04 | |
| 0.9800000000 0.0100000000 (2.326) | +361.2360 ( 88.89%) - +361.2361 ( 88.89%) | -2.904e-04 -2.212e-04 | |
| 0.9875806693 0.0062096653 (2.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -2.084e-04 -9.618e-05 | |
| 0.9900000000 0.0050000000 (2.576) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +2.000e-04 -3.269e-04 | |
| 0.9973002039 0.0013498980 (3.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.908e-05 -3.098e-05 | |
| 0.9980000000 0.0010000000 (3.090) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -4.792e-05 -5.232e-05 | |
| 0.9990000000 0.0005000000 (3.291) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.281e-05 +2.235e-05 | |
| 0.9995347418 0.0002326291 (3.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.549e-06 +2.025e-05 | |
| 0.9998000000 0.0001000000 (3.719) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +5.498e-06 +1.312e-06 | |
| 0.9999000000 0.0000500000 (3.891) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -2.104e-06 -6.428e-07 | |
| 0.9999366575 0.0000316712 (4.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +2.707e-06 -3.865e-07 | |
| 0.9999800000 0.0000100000 (4.265) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -8.088e-08 -2.778e-07 | |
| 0.9999900000 0.0000050000 (4.417) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.620e-07 -2.436e-07 | |
| 0.9999932047 0.0000033977 (4.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.186e-07 +4.026e-08 | |
| 0.9999980000 0.0000010000 (4.753) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.439e-08 +5.083e-09 | |
| 0.9999990000 0.0000005000 (4.892) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +3.003e-08 +2.766e-08 | |
| 0.9999994267 0.0000002867 (5.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -8.274e-09 -9.134e-09 | |
| 0.9999998000 0.0000001000 (5.199) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -7.217e-09 -7.111e-09 | |
| 0.9999999000 0.0000000500 (5.327) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.760e-09 +2.047e-09 | |
| 0.9999999620 0.0000000190 (5.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +7.584e-10 -3.338e-10 | |
| 0.9999999800 0.0000000100 (5.612) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -2.548e-10 -1.884e-10 | |
| 0.9999999900 0.0000000050 (5.731) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.210e-10 -1.441e-10 | |
| 0.9999999980 0.0000000010 (5.998) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -3.343e-11 -7.989e-11 | |
| 0.9999999980 0.0000000010 (6.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.922e-11 -6.297e-12 | |
| 0.9999999990 0.0000000005 (6.109) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +9.259e-12 -1.416e-11 | |
| class boost::multiprecision::number<class boost::multiprecision::backends::cpp_dec_float<50,int,void>,1> | |
| W-D-L:987654321098765-0-123456789012345 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +5.799e-48 -2.388e-50 | |
| 0.3829249225 0.3085375387 (0.500) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -7.923e-49 +4.204e-50 | |
| 0.5000000000 0.2500000000 (0.674) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -3.819e-49 -5.379e-50 | |
| 0.6826894921 0.1586552539 (1.000) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -4.382e-49 -2.909e-51 | |
| 0.7500000000 0.1250000000 (1.150) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -3.038e-49 +1.005e-50 | |
| 0.8000000000 0.1000000000 (1.282) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +1.032e-49 +8.469e-51 | |
| 0.8663855975 0.0668072013 (1.500) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +3.175e-50 +1.040e-51 | |
| 0.9000000000 0.0500000000 (1.645) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +2.894e-49 -1.023e-51 | |
| 0.9500000000 0.0250000000 (1.960) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +1.247e-50 +2.231e-51 | |
| 0.9544997361 0.0227501319 (2.000) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +4.288e-50 +7.133e-51 | |
| 0.9800000000 0.0100000000 (2.326) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -2.269e-50 -4.932e-52 | |
| 0.9875806693 0.0062096653 (2.500) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +6.918e-51 -1.443e-51 | |
| 0.9900000000 0.0050000000 (2.576) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +8.322e-50 -1.967e-51 | |
| 0.9973002039 0.0013498980 (3.000) | +361.2359 ( 88.89%) - +361.2360 ( 88.89%) | -1.193e-51 +4.526e-52 | |
| 0.9980000000 0.0010000000 (3.090) | +361.2359 ( 88.89%) - +361.2360 ( 88.89%) | -8.412e-52 +2.360e-52 | |
| 0.9990000000 0.0005000000 (3.291) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +2.013e-51 +9.915e-53 | |
| 0.9995347418 0.0002326291 (3.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -3.108e-52 +7.156e-53 | |
| 0.9998000000 0.0001000000 (3.719) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -6.595e-53 -7.218e-53 | |
| 0.9999000000 0.0000500000 (3.891) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +2.726e-53 +4.233e-54 | |
| 0.9999366575 0.0000316712 (4.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +2.858e-53 +3.052e-54 | |
| 0.9999800000 0.0000100000 (4.265) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -5.447e-54 -3.641e-55 | |
| 0.9999900000 0.0000050000 (4.417) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +3.797e-54 +5.391e-55 | |
| 0.9999932047 0.0000033977 (4.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -2.097e-54 -6.192e-55 | |
| 0.9999980000 0.0000010000 (4.753) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.575e-54 +7.690e-56 | |
| 0.9999990000 0.0000005000 (4.892) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +6.936e-57 -9.657e-56 | |
| 0.9999994267 0.0000002867 (5.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -9.856e-56 +3.279e-56 | |
| 0.9999998000 0.0000001000 (5.199) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -3.400e-57 +1.610e-56 | |
| 0.9999999000 0.0000000500 (5.327) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +3.115e-56 -3.093e-57 | |
| 0.9999999620 0.0000000190 (5.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.867e-56 -5.831e-58 | |
| 0.9999999800 0.0000000100 (5.612) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +2.461e-57 +2.635e-57 | |
| 0.9999999900 0.0000000050 (5.731) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.148e-57 +2.971e-57 | |
| 0.9999999980 0.0000000010 (5.998) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +2.439e-59 +3.901e-58 | |
| 0.9999999980 0.0000000010 (6.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.706e-58 +3.091e-58 | |
| 0.9999999990 0.0000000005 (6.109) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +5.320e-58 -1.931e-58 | |
| class boost::multiprecision::number<class boost::multiprecision::backends::cpp_dec_float<100,int,void>,1> | |
| W-D-L:987654321098765-0-123456789012345 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +2.983e-96 +3.128e-98 | |
| 0.3829249225 0.3085375387 (0.500) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +9.535e-97 -4.976e-99 | |
| 0.5000000000 0.2500000000 (0.674) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +8.181e-99 +2.553e-98 | |
| 0.6826894921 0.1586552539 (1.000) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +5.116e-98 -2.947e-98 | |
| 0.7500000000 0.1250000000 (1.150) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +1.102e-97 +2.223e-98 | |
| 0.8000000000 0.1000000000 (1.282) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -5.825e-98 +6.303e-100 | |
| 0.8663855975 0.0668072013 (1.500) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -1.219e-96 -3.776e-99 | |
| 0.9000000000 0.0500000000 (1.645) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | -7.247e-99 +7.077e-100 | |
| 0.9500000000 0.0250000000 (1.960) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +3.824e-98 +5.665e-100 | |
| 0.9544997361 0.0227501319 (2.000) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +1.993e-98 +4.408e-99 | |
| 0.9800000000 0.0100000000 (2.326) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +1.669e-98 -8.277e-100 | |
| 0.9875806693 0.0062096653 (2.500) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +1.147e-97 +2.847e-99 | |
| 0.9900000000 0.0050000000 (2.576) | +361.2360 ( 88.89%) - +361.2360 ( 88.89%) | +6.564e-99 +1.670e-99 | |
| 0.9973002039 0.0013498980 (3.000) | +361.2359 ( 88.89%) - +361.2360 ( 88.89%) | +1.308e-99 +4.076e-100 | |
| 0.9980000000 0.0010000000 (3.090) | +361.2359 ( 88.89%) - +361.2360 ( 88.89%) | +4.595e-99 -1.211e-100 | |
| 0.9990000000 0.0005000000 (3.291) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +4.477e-100 +1.438e-100 | |
| 0.9995347418 0.0002326291 (3.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.306e-99 -4.785e-101 | |
| 0.9998000000 0.0001000000 (3.719) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -3.850e-101 +1.030e-101 | |
| 0.9999000000 0.0000500000 (3.891) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.153e-99 +1.166e-101 | |
| 0.9999366575 0.0000316712 (4.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.642e-101 -2.166e-102 | |
| 0.9999800000 0.0000100000 (4.265) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -5.669e-102 +2.113e-102 | |
| 0.9999900000 0.0000050000 (4.417) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -2.825e-102 -1.580e-102 | |
| 0.9999932047 0.0000033977 (4.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.347e-102 -4.822e-103 | |
| 0.9999980000 0.0000010000 (4.753) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +9.926e-103 -1.400e-102 | |
| 0.9999990000 0.0000005000 (4.892) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +4.358e-103 -1.681e-103 | |
| 0.9999994267 0.0000002867 (5.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -2.076e-103 -9.822e-104 | |
| 0.9999998000 0.0000001000 (5.199) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -1.921e-104 +1.045e-104 | |
| 0.9999999000 0.0000000500 (5.327) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -3.574e-104 -7.448e-105 | |
| 0.9999999620 0.0000000190 (5.500) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -4.564e-105 +4.425e-105 | |
| 0.9999999800 0.0000000100 (5.612) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +3.519e-105 -1.062e-105 | |
| 0.9999999900 0.0000000050 (5.731) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +5.004e-105 +4.753e-107 | |
| 0.9999999980 0.0000000010 (5.998) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +1.962e-108 +4.458e-106 | |
| 0.9999999980 0.0000000010 (6.000) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | -4.294e-106 -2.398e-106 | |
| 0.9999999990 0.0000000005 (6.109) | +361.2359 ( 88.89%) - +361.2361 ( 88.89%) | +3.758e-106 -1.845e-107 | |
| double | |
| W-D-L:987654321098765-1-0 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +nan ( nan%) - +6070.8727 (100.00%) | +nan +6.661e-16 | |
| 0.3829249225 0.3085375387 (0.500) | +nan ( nan%) - +6166.6852 (100.00%) | +nan +2.220e-16 | |
| 0.5000000000 0.2500000000 (0.674) | +nan ( nan%) - +6256.0196 (100.00%) | +nan -3.331e-16 | |
| 0.6826894921 0.1586552539 (1.000) | +nan ( nan%) - +6429.9068 (100.00%) | +nan +5.551e-17 | |
| 0.7500000000 0.1250000000 (1.150) | +nan ( nan%) - +6516.4537 (100.00%) | +nan -8.327e-17 | |
| 0.8000000000 0.1000000000 (1.282) | +nan ( nan%) - +6596.1101 (100.00%) | +nan +5.551e-17 | |
| 0.8663855975 0.0668072013 (1.500) | +nan ( nan%) - +6738.3063 (100.00%) | +nan -9.714e-17 | |
| 0.9000000000 0.0500000000 (1.645) | +nan ( nan%) - +6839.7082 (100.00%) | +nan -2.082e-17 | |
| 0.9500000000 0.0250000000 (1.960) | +nan ( nan%) - +7081.2148 (100.00%) | +nan -1.041e-17 | |
| 0.9544997361 0.0227501319 (2.000) | +nan ( nan%) - +7114.0186 (100.00%) | +nan -3.469e-18 | |
| 0.9800000000 0.0100000000 (2.326) | +5597.8789 (100.00%) - +7399.7571 (100.00%) | -1.197e-16 +3.469e-18 | |
| 0.9875806693 0.0062096653 (2.500) | +5589.0848 (100.00%) - +7565.3248 (100.00%) | -6.939e-18 -6.939e-18 | |
| 0.9900000000 0.0050000000 (2.576) | +5585.3728 (100.00%) - +7640.6083 (100.00%) | +1.396e-16 -6.939e-18 | |
| 0.9973002039 0.0013498980 (3.000) | +5564.5434 (100.00%) - +8095.5519 (100.00%) | +6.722e-18 +8.674e-19 | |
| 0.9980000000 0.0010000000 (3.090) | +5560.2997 (100.00%) - +8199.7930 (100.00%) | -1.128e-17 +1.084e-18 | |
| 0.9990000000 0.0005000000 (3.291) | +5550.4386 (100.00%) - +8440.6173 (100.00%) | -5.746e-18 +1.084e-19 | |
| 0.9995347418 0.0002326291 (3.500) | +5540.2471 (100.00%) - +8706.4621 (100.00%) | -1.752e-06 +5.421e-19 | |
| 0.9998000000 0.0001000000 (3.719) | +5529.6980 (100.00%) - +8999.7934 (100.00%) | -7.117e-07 +2.575e-19 | |
| 0.9999000000 0.0000500000 (3.891) | +5521.6290 (100.00%) - +9240.6174 (100.00%) | -1.030e-18 +4.066e-20 | |
| 0.9999366575 0.0000316712 (4.000) | +5516.3223 (100.00%) - +9399.2613 (100.00%) | -4.405e-19 +6.099e-20 | |
| 0.9999800000 0.0000100000 (4.265) | +5503.8996 (100.00%) - +9799.7934 (100.00%) | +1.525e-20 +1.525e-20 | |
| 0.9999900000 0.0000050000 (4.417) | +5496.9387 (100.00%) - +10040.6174 (100.00%) | -9.995e-20 -1.694e-21 | |
| 0.9999932047 0.0000033977 (4.500) | +5493.0201 (100.00%) - +10174.8481 (100.00%) | -2.414e-20 +0.000e+00 | |
| 0.9999980000 0.0000010000 (4.753) | +5481.4666 (100.00%) - +10599.7934 (100.00%) | +4.235e-22 +4.235e-22 | |
| 0.9999990000 0.0000005000 (4.892) | +5475.2419 (100.00%) - +10840.6174 (100.00%) | +7.306e-21 -6.353e-22 | |
| 0.9999994267 0.0000002867 (5.000) | +5470.5132 (100.00%) - +11033.9099 (100.00%) | -1.027e-20 -5.823e-22 | |
| 0.9999998000 0.0000001000 (5.199) | +5461.7091 (100.00%) - +11399.7934 (100.00%) | -7.676e-22 -5.294e-23 | |
| 0.9999999000 0.0000000500 (5.327) | +5456.1996 (100.00%) - +11640.6174 (100.00%) | +2.184e-21 +2.316e-22 | |
| 0.9999999620 0.0000000190 (5.500) | +5448.7602 (100.00%) - +11976.9814 (100.00%) | +3.309e-24 +3.309e-24 | |
| 0.9999999800 0.0000000100 (5.612) | +5444.0419 (100.00%) - +12199.7934 (100.00%) | +4.086e-22 -1.820e-23 | |
| 0.9999999900 0.0000000050 (5.731) | +5438.9981 (100.00%) - +12440.6174 (100.00%) | +3.557e-23 +0.000e+00 | |
| 0.9999999980 0.0000000010 (5.998) | +5427.9115 (100.00%) - +12999.7934 (100.00%) | +2.544e-23 +4.136e-24 | |
| 0.9999999980 0.0000000010 (6.000) | +5427.8180 (100.00%) - +13004.4848 (100.00%) | +4.549e-23 +3.516e-24 | |
| 0.9999999990 0.0000000005 (6.109) | +5423.3780 (100.00%) - +13240.6174 (100.00%) | -1.840e-23 +1.137e-24 | |
| class boost::multiprecision::number<class boost::multiprecision::backends::cpp_dec_float<50,int,void>,1> | |
| W-D-L:987654321098765-1-0 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +5921.1595 (100.00%) - +6366.9658 (100.00%) | +1.408e-51 +2.469e-51 | |
| 0.3829249225 0.3085375387 (0.500) | +5895.9317 (100.00%) - +6439.3343 (100.00%) | +5.703e-52 +2.752e-51 | |
| 0.5000000000 0.2500000000 (0.674) | +5872.7872 (100.00%) - +6515.6144 (100.00%) | -5.213e-52 -3.799e-58 | |
| 0.6826894921 0.1586552539 (1.000) | +5832.3122 (100.00%) - +6677.1284 (100.00%) | +1.701e-51 +1.701e-51 | |
| 0.7500000000 0.1250000000 (1.150) | +5814.7070 (100.00%) - +6760.8474 (100.00%) | +7.908e-58 +7.597e-58 | |
| 0.8000000000 0.1000000000 (1.282) | +5799.8634 (100.00%) - +6838.8926 (100.00%) | +4.866e-51 +4.866e-51 | |
| 0.8663855975 0.0668072013 (1.500) | +5776.1566 (100.00%) - +6979.5407 (100.00%) | +2.294e-52 +2.294e-52 | |
| 0.9000000000 0.0500000000 (1.645) | +5761.0884 (100.00%) - +7080.4024 (100.00%) | +2.568e-51 +2.568e-51 | |
| 0.9500000000 0.0250000000 (1.960) | +5729.9590 (100.00%) - +7321.3972 (100.00%) | +1.318e-51 +1.318e-51 | |
| 0.9544997361 0.0227501319 (2.000) | +5726.1560 (100.00%) - +7354.1718 (100.00%) | +1.153e-51 +1.153e-51 | |
| 0.9800000000 0.0100000000 (2.326) | +5696.3342 (100.00%) - +7639.7969 (100.00%) | -9.301e-52 -9.301e-52 | |
| 0.9875806693 0.0062096653 (2.500) | +5681.2684 (100.00%) - +7805.3480 (100.00%) | +3.842e-52 +3.842e-52 | |
| 0.9900000000 0.0050000000 (2.576) | +5674.8529 (100.00%) - +7880.6278 (100.00%) | -4.674e-52 -4.674e-52 | |
| 0.9973002039 0.0013498980 (3.000) | +5640.6641 (100.00%) - +8335.5651 (100.00%) | +2.406e-52 +2.406e-52 | |
| 0.9980000000 0.0010000000 (3.090) | +5633.7392 (100.00%) - +8439.8059 (100.00%) | +8.295e-54 +8.295e-54 | |
| 0.9990000000 0.0005000000 (3.291) | +5618.7705 (100.00%) - +8680.6300 (100.00%) | +4.150e-54 +4.150e-54 | |
| 0.9995347418 0.0002326291 (3.500) | +5603.6799 (100.00%) - +8946.4748 (100.00%) | +5.471e-55 +5.471e-55 | |
| 0.9998000000 0.0001000000 (3.719) | +5588.4792 (100.00%) - +9239.8060 (100.00%) | +5.491e-54 +5.491e-54 | |
| 0.9999000000 0.0000500000 (3.891) | +5576.9588 (100.00%) - +9480.6300 (100.00%) | +2.746e-54 +2.746e-54 | |
| 0.9999366575 0.0000316712 (4.000) | +5569.7818 (100.00%) - +9639.2740 (100.00%) | +3.925e-55 +3.925e-55 | |
| 0.9999800000 0.0000100000 (4.265) | +5552.9223 (100.00%) - +10039.8060 (100.00%) | +1.651e-54 +1.651e-54 | |
| 0.9999900000 0.0000050000 (4.417) | +5543.5450 (100.00%) - +10280.6300 (100.00%) | +8.256e-55 +8.256e-55 | |
| 0.9999932047 0.0000033977 (4.500) | +5538.5367 (100.00%) - +10414.8608 (100.00%) | +6.554e-56 +6.554e-56 | |
| 0.9999980000 0.0000010000 (4.753) | +5523.5976 (100.00%) - +10839.8060 (100.00%) | -6.347e-57 -6.347e-57 | |
| 0.9999990000 0.0000005000 (4.892) | +5515.6842 (100.00%) - +11080.6300 (100.00%) | -3.173e-57 -3.173e-57 | |
| 0.9999994267 0.0000002867 (5.000) | +5509.5905 (100.00%) - +11273.9226 (100.00%) | +2.260e-56 +2.260e-56 | |
| 0.9999998000 0.0000001000 (5.199) | +5498.6245 (100.00%) - +11639.8060 (100.00%) | +5.356e-57 +5.356e-57 | |
| 0.9999999000 0.0000000500 (5.327) | +5491.7759 (100.00%) - +11880.6300 (100.00%) | +2.678e-57 +2.678e-57 | |
| 0.9999999620 0.0000000190 (5.500) | +5482.6512 (100.00%) - +12216.9941 (100.00%) | -4.334e-57 -4.334e-57 | |
| 0.9999999800 0.0000000100 (5.612) | +5476.8663 (100.00%) - +12439.8060 (100.00%) | +6.735e-57 +6.735e-57 | |
| 0.9999999900 0.0000000050 (5.731) | +5470.8278 (100.00%) - +12680.6300 (100.00%) | +3.368e-57 +3.368e-57 | |
| 0.9999999980 0.0000000010 (5.998) | +5457.5828 (100.00%) - +13239.8060 (100.00%) | +6.180e-59 +6.180e-59 | |
| 0.9999999980 0.0000000010 (6.000) | +5457.4759 (100.00%) - +13244.4975 (100.00%) | -3.454e-59 -3.454e-59 | |
| 0.9999999990 0.0000000005 (6.109) | +5452.1816 (100.00%) - +13480.6300 (100.00%) | +3.090e-59 +3.090e-59 | |
| class boost::multiprecision::number<class boost::multiprecision::backends::cpp_dec_float<100,int,void>,1> | |
| W-D-L:987654321098765-1-0 | |
| x p (sigma) | elorating | error_lower error_upper | |
| ----------------------------------+-----------------------------------------------+------------------------ | |
| 0.2500000000 0.3750000000 (0.319) | +5921.1595 (100.00%) - +6366.9658 (100.00%) | +4.500e-101 +5.651e-101 | |
| 0.3829249225 0.3085375387 (0.500) | +5895.9317 (100.00%) - +6439.3343 (100.00%) | -4.586e-101 -2.081e-101 | |
| 0.5000000000 0.2500000000 (0.674) | +5872.7872 (100.00%) - +6515.6144 (100.00%) | -1.123e-101 -1.053e-105 | |
| 0.6826894921 0.1586552539 (1.000) | +5832.3122 (100.00%) - +6677.1284 (100.00%) | -2.206e-101 -2.206e-101 | |
| 0.7500000000 0.1250000000 (1.150) | +5814.7070 (100.00%) - +6760.8474 (100.00%) | -3.050e-108 +2.105e-105 | |
| 0.8000000000 0.1000000000 (1.282) | +5799.8634 (100.00%) - +6838.8926 (100.00%) | +1.118e-101 +1.118e-101 | |
| 0.8663855975 0.0668072013 (1.500) | +5776.1566 (100.00%) - +6979.5407 (100.00%) | -1.240e-102 -1.240e-102 | |
| 0.9000000000 0.0500000000 (1.645) | +5761.0884 (100.00%) - +7080.4024 (100.00%) | +2.972e-101 +2.972e-101 | |
| 0.9500000000 0.0250000000 (1.960) | +5729.9590 (100.00%) - +7321.3972 (100.00%) | +1.525e-101 +1.525e-101 | |
| 0.9544997361 0.0227501319 (2.000) | +5726.1560 (100.00%) - +7354.1718 (100.00%) | +9.842e-102 +9.842e-102 | |
| 0.9800000000 0.0100000000 (2.326) | +5696.3342 (100.00%) - +7639.7969 (100.00%) | -7.917e-102 -7.917e-102 | |
| 0.9875806693 0.0062096653 (2.500) | +5681.2684 (100.00%) - +7805.3480 (100.00%) | +5.572e-102 +5.572e-102 | |
| 0.9900000000 0.0050000000 (2.576) | +5674.8529 (100.00%) - +7880.6278 (100.00%) | -3.978e-102 -3.978e-102 | |
| 0.9973002039 0.0013498980 (3.000) | +5640.6641 (100.00%) - +8335.5651 (100.00%) | +3.763e-102 +3.763e-102 | |
| 0.9980000000 0.0010000000 (3.090) | +5633.7392 (100.00%) - +8439.8059 (100.00%) | -2.494e-104 -2.494e-104 | |
| 0.9990000000 0.0005000000 (3.291) | +5618.7705 (100.00%) - +8680.6300 (100.00%) | -1.248e-104 -1.248e-104 | |
| 0.9995347418 0.0002326291 (3.500) | +5603.6799 (100.00%) - +8946.4748 (100.00%) | +2.273e-104 +2.273e-104 | |
| 0.9998000000 0.0001000000 (3.719) | +5588.4792 (100.00%) - +9239.8060 (100.00%) | +4.587e-104 +4.587e-104 | |
| 0.9999000000 0.0000500000 (3.891) | +5576.9588 (100.00%) - +9480.6300 (100.00%) | +2.294e-104 +2.294e-104 | |
| 0.9999366575 0.0000316712 (4.000) | +5569.7818 (100.00%) - +9639.2740 (100.00%) | -3.129e-105 -3.129e-105 | |
| 0.9999800000 0.0000100000 (4.265) | +5552.9223 (100.00%) - +10039.8060 (100.00%) | +1.427e-104 +1.427e-104 | |
| 0.9999900000 0.0000050000 (4.417) | +5543.5450 (100.00%) - +10280.6300 (100.00%) | +7.135e-105 +7.135e-105 | |
| 0.9999932047 0.0000033977 (4.500) | +5538.5367 (100.00%) - +10414.8608 (100.00%) | +3.058e-105 +3.058e-105 | |
| 0.9999980000 0.0000010000 (4.753) | +5523.5976 (100.00%) - +10839.8060 (100.00%) | -3.857e-107 -3.857e-107 | |
| 0.9999990000 0.0000005000 (4.892) | +5515.6842 (100.00%) - +11080.6300 (100.00%) | -1.928e-107 -1.928e-107 | |
| 0.9999994267 0.0000002867 (5.000) | +5509.5905 (100.00%) - +11273.9226 (100.00%) | -5.881e-106 -5.881e-106 | |
| 0.9999998000 0.0000001000 (5.199) | +5498.6245 (100.00%) - +11639.8060 (100.00%) | +1.853e-106 +1.853e-106 | |
| 0.9999999000 0.0000000500 (5.327) | +5491.7759 (100.00%) - +11880.6300 (100.00%) | +9.264e-107 +9.264e-107 | |
| 0.9999999620 0.0000000190 (5.500) | +5482.6512 (100.00%) - +12216.9941 (100.00%) | +2.146e-107 +2.146e-107 | |
| 0.9999999800 0.0000000100 (5.612) | +5476.8663 (100.00%) - +12439.8060 (100.00%) | +5.916e-107 +5.916e-107 | |
| 0.9999999900 0.0000000050 (5.731) | +5470.8278 (100.00%) - +12680.6300 (100.00%) | +2.958e-107 +2.958e-107 | |
| 0.9999999980 0.0000000010 (5.998) | +5457.5828 (100.00%) - +13239.8060 (100.00%) | +4.553e-109 +4.553e-109 | |
| 0.9999999980 0.0000000010 (6.000) | +5457.4759 (100.00%) - +13244.4975 (100.00%) | +8.597e-110 +8.597e-110 | |
| 0.9999999990 0.0000000005 (6.109) | +5452.1816 (100.00%) - +13480.6300 (100.00%) | +2.277e-109 +2.277e-109 | |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment