27-Jul-2022 09:08:58 toms743_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test toms743(). Number of bits in mantissa - 1 = 52 toms743_test01() Compare wapr() to stored values. Wp results for x near -exp(-1) Offset x W(x) (WAPR) W(x) (EXACT) Digits Correct 1e-40 -1 -1 16 2e-40 -1 -1 16 3e-40 -1 -1 16 4e-40 -1 -1 16 5e-40 -1 -1 16 6e-40 -1 -1 16 7e-40 -1 -1 16 8e-40 -1 -1 16 9e-40 -1 -1 16 1e-39 -1 -1 16 1e-30 -1 -1 16 2e-30 -1 -1 16 3e-30 -1 -1 16 4e-30 -1 -1 16 5e-30 -1 -1 16 6e-30 -1 -1 16 7e-30 -1 -1 16 8e-30 -1 -1 16 9e-30 -1 -1 16 1e-29 -1 -1 16 1e-20 -1 -1 16 2e-20 -1 -1 16 3e-20 -1 -1 16 4e-20 -1 -1 16 5e-20 -1 -1 16 6e-20 -1 -1 16 7e-20 -1 -1 16 8e-20 -1 -1 16 9e-20 -1 -1 16 1e-19 -1 -1 16 1e-10 -0.99997668 -0.99997668 16 2e-10 -0.99996703 -0.99996703 16 3e-10 -0.99995962 -0.99995962 16 4e-10 -0.99995337 -0.99995337 16 5e-10 -0.99994786 -0.99994786 16 6e-10 -0.99994289 -0.99994289 16 7e-10 -0.99993831 -0.99993831 16 8e-10 -0.99993405 -0.99993405 16 9e-10 -0.99993005 -0.99993005 16 1e-09 -0.99992627 -0.99992627 16 1e-05 -0.99264476 -0.99264476 16 2e-05 -0.98960864 -0.98960864 16 3e-05 -0.98728311 -0.98728311 16 4e-05 -0.98532539 -0.98532539 16 5e-05 -0.98360272 -0.98360272 16 6e-05 -0.982047 -0.982047 16 7e-05 -0.9806178 -0.9806178 16 8e-05 -0.97928875 -0.97928875 16 9e-05 -0.97804155 -0.97804155 16 0.0001 -0.97686287 -0.97686287 16 0.0002 -0.96738263 -0.96738263 15 0.0003 -0.96014854 -0.96014854 15 0.0004 -0.95407687 -0.95407687 15 0.0005 -0.94874787 -0.94874787 15 0.0006 -0.94394629 -0.94394629 15 0.0007 -0.93954428 -0.93954428 15 0.0008 -0.93545853 -0.93545853 15 0.0009 -0.9316312 -0.9316312 15 0.001 -0.92802015 -0.92802015 15 0.002 -0.89918577 -0.89918577 15 0.003 -0.87742872 -0.87742872 15 0.004 -0.8593275 -0.8593275 16 0.005 -0.843558 -0.843558 15 0.006 -0.82944169 -0.82944169 16 0.007 -0.81657581 -0.81657581 16 0.008 -0.80469816 -0.80469816 15 0.009 -0.79362675 -0.79362675 16 0.01 -0.7832292 -0.7832292 16 Wp results for x near 0 x W(x) (WAPR) W(x) (EXACT) Digits Correct 1e-09 1e-09 1e-09 16 2e-09 2e-09 2e-09 16 3e-09 3e-09 3e-09 16 4e-09 4e-09 4e-09 16 5e-09 5e-09 5e-09 16 6e-09 6e-09 6e-09 16 7e-09 7e-09 7e-09 16 8e-09 7.9999999e-09 7.9999999e-09 16 9e-09 8.9999999e-09 8.9999999e-09 16 1e-08 9.9999999e-09 9.9999999e-09 16 0.01 0.0099014738 0.0099014738 16 0.02 0.019611589 0.019611589 16 0.03 0.029138459 0.029138459 16 0.04 0.038489666 0.038489666 16 0.05 0.047672309 0.047672309 16 0.06 0.056693044 0.056693044 16 0.07 0.065558123 0.065558123 16 0.08 0.074273425 0.074273425 16 0.09 0.082844486 0.082844486 16 0.1 0.091276527 0.091276527 16 -1e-09 -1e-09 -1e-09 16 -2e-09 -2e-09 -2e-09 16 -3e-09 -3e-09 -3e-09 16 -4e-09 -4e-09 -4e-09 16 -5e-09 -5e-09 -5e-09 16 -6e-09 -6e-09 -6e-09 16 -7e-09 -7e-09 -7e-09 16 -8e-09 -8.0000001e-09 -8.0000001e-09 16 -9e-09 -9.0000001e-09 -9.0000001e-09 16 -1e-08 -1e-08 -1e-08 16 -0.01 -0.010101527 -0.010101527 16 -0.02 -0.020412444 -0.020412444 16 -0.03 -0.030942795 -0.030942795 16 -0.04 -0.041703408 -0.041703408 16 -0.05 -0.052705984 -0.052705984 16 -0.06 -0.063963189 -0.063963189 16 -0.07 -0.075488779 -0.075488779 16 -0.08 -0.087297721 -0.087297721 16 -0.09 -0.099406353 -0.099406353 16 -0.1 -0.11183256 -0.11183256 16 Other Wp results x W(x) (WAPR) W(x) (EXACT) Digits Correct 10 1.745528 1.745528 16 100 3.3856301 3.3856301 16 1000 5.2496029 5.2496029 16 10000 7.231846 7.231846 16 100000 9.2845714 9.2845714 16 1000000 11.383358 11.383358 16 10000000 13.514344 13.514344 16 1e+08 15.668997 15.668997 16 1e+09 17.841726 17.841726 16 1e+10 20.028685 20.028685 16 Wm results for x near 0 x W(x) (WAPR) W(x) (EXACT) Digits Correct 1e-40 -1 -1 16 2e-40 -1 -1 16 3e-40 -1 -1 16 4e-40 -1 -1 16 5e-40 -1 -1 16 6e-40 -1 -1 16 7e-40 -1 -1 16 8e-40 -1 -1 16 9e-40 -1 -1 16 1e-39 -1 -1 16 1e-30 -1 -1 16 2e-30 -1 -1 16 3e-30 -1 -1 16 4e-30 -1 -1 16 5e-30 -1 -1 16 6e-30 -1 -1 16 7e-30 -1 -1 16 8e-30 -1 -1 16 9e-30 -1 -1 16 1e-29 -1 -1 16 1e-20 -1 -1 16 2e-20 -1 -1 16 3e-20 -1 -1 16 4e-20 -1 -1 16 5e-20 -1 -1 16 6e-20 -1 -1 16 7e-20 -1 -1 16 8e-20 -1 -1 16 9e-20 -1 -1 16 1e-19 -1 -1 16 1e-10 -1.0000233 -1.0000233 16 2e-10 -1.000033 -1.000033 16 3e-10 -1.0000404 -1.0000404 16 4e-10 -1.0000466 -1.0000466 16 5e-10 -1.0000521 -1.0000521 16 6e-10 -1.0000571 -1.0000571 16 7e-10 -1.0000617 -1.0000617 16 8e-10 -1.000066 -1.000066 16 9e-10 -1.00007 -1.00007 16 1e-09 -1.0000737 -1.0000737 16 1e-05 -1.0073915 -1.0073915 16 2e-05 -1.0104638 -1.0104638 16 3e-05 -1.0128256 -1.0128256 16 4e-05 -1.0148196 -1.0148196 16 5e-05 -1.0165785 -1.0165785 16 6e-05 -1.0181705 -1.0181705 16 7e-05 -1.0196359 -1.0196359 16 8e-05 -1.0210012 -1.0210012 16 9e-05 -1.0222847 -1.0222847 16 0.0001 -1.0234996 -1.0234996 16 0.0002 -1.0333424 -1.0333424 15 0.0003 -1.0409392 -1.0409392 15 0.0004 -1.0473736 -1.0473736 15 0.0005 -1.0530655 -1.0530655 14 0.0006 -1.05823 -1.05823 15 0.0007 -1.0629951 -1.0629951 15 0.0008 -1.067444 -1.067444 16 0.0009 -1.0716346 -1.0716346 15 0.001 -1.0756089 -1.0756089 15 0.002 -1.1080819 -1.1080819 15 0.003 -1.133487 -1.133487 15 0.004 -1.1552459 -1.1552459 16 0.005 -1.1746826 -1.1746826 15 0.006 -1.1924759 -1.1924759 15 0.007 -1.2090284 -1.2090284 16 0.008 -1.2246024 -1.2246024 16 0.009 -1.2393801 -1.2393801 15 0.01 -1.2534938 -1.2534938 15 Wm results for x near -exp(-1) Offset x W(x) (WAPR) W(x) (EXACT) Digits Correct -1e-40 -96.674756 -96.674756 16 -2e-40 -95.974337 -95.974337 16 -3e-40 -95.564594 -95.564594 16 -4e-40 -95.273865 -95.273865 16 -5e-40 -95.048352 -95.048352 16 -6e-40 -94.864089 -94.864089 16 -7e-40 -94.708295 -94.708295 16 -8e-40 -94.573338 -94.573338 16 -9e-40 -94.454295 -94.454295 16 -1e-39 -94.347807 -94.347807 16 -1e-30 -73.37311 -73.37311 16 -2e-30 -72.670339 -72.670339 16 -3e-30 -72.2592 -72.2592 16 -4e-30 -71.967473 -71.967473 16 -5e-30 -71.74118 -71.74118 16 -6e-30 -71.556278 -71.556278 16 -7e-30 -71.39994 -71.39994 16 -8e-30 -71.26451 -71.26451 16 -9e-30 -71.145049 -71.145049 16 -1e-29 -71.038185 -71.038185 16 -1e-20 -49.962984 -49.962984 16 -2e-20 -49.255577 -49.255577 16 -3e-20 -48.841673 -48.841673 16 -4e-20 -48.54796 -48.54796 16 -5e-20 -48.320112 -48.320112 16 -6e-20 -48.13393 -48.13393 16 -7e-20 -47.976503 -47.976503 16 -8e-20 -47.840125 -47.840125 16 -9e-20 -47.719824 -47.719824 16 -1e-19 -47.612206 -47.612206 16 -1e-10 -26.295239 -26.295239 16 -2e-10 -25.574291 -25.574291 16 -3e-10 -25.152183 -25.152183 16 -4e-10 -24.852516 -24.852516 16 -5e-10 -24.619971 -24.619971 16 -6e-10 -24.429899 -24.429899 16 -7e-10 -24.269147 -24.269147 16 -8e-10 -24.129859 -24.129859 16 -9e-10 -24.006971 -24.006971 16 -1e-09 -23.89702 -23.89702 16 -1e-05 -14.163601 -14.163601 16 -2e-05 -13.416245 -13.416245 16 -3e-05 -12.977533 -12.977533 16 -4e-05 -12.665514 -12.665514 16 -5e-05 -12.42304 -12.42304 16 -6e-05 -12.224618 -12.224618 16 -7e-05 -12.05663 -12.05663 16 -8e-05 -11.910941 -11.910941 16 -9e-05 -11.782299 -11.782299 16 -0.0001 -11.667115 -11.667115 16 -0.0002 -10.906557 -10.906557 16 -0.0003 -10.459211 -10.459211 16 -0.0004 -10.140592 -10.140592 16 -0.0005 -9.8926995 -9.8926995 16 -0.0006 -9.689638 -9.689638 16 -0.0007 -9.5175698 -9.5175698 16 -0.0008 -9.3682222 -9.3682222 16 -0.0009 -9.236252 -9.236252 16 -0.001 -9.1180065 -9.1180065 16 -0.002 -8.3350814 -8.3350814 16 -0.003 -7.8725214 -7.8725214 16 -0.004 -7.5419404 -7.5419404 16 -0.005 -7.2839971 -7.2839971 16 -0.006 -7.072162 -7.072162 16 -0.007 -6.8922415 -6.8922415 16 -0.008 -6.7357417 -6.7357417 16 -0.009 -6.5971717 -6.5971717 16 -0.01 -6.4727751 -6.4727751 16 toms743_test02(): Test wapr() when input X is the offset from -exp(-1). Both branches of the W function will be checked. Results for Wp(x): Offset x W(x) (WAPR) W(x) (BISECT) Digits Correct 1e-09 -0.99992627 -0.99992627 14 2e-09 -0.99989573 -0.99989573 12 3e-09 -0.9998723 -0.9998723 12 4e-09 -0.99985254 -0.99985254 13 5e-09 -0.99983514 -0.99983514 12 6e-09 -0.9998194 -0.9998194 13 7e-09 -0.99980493 -0.99980493 13 8e-09 -0.99979147 -0.99979147 12 9e-09 -0.99977882 -0.99977882 12 1e-08 -0.99976685 -0.99976685 12 1.1e-08 -0.99975548 -0.99975548 13 Results for Wm(x): Offset x W(x) (WAPR) W(x) (BISECT) Digits Correct 1e-09 -1.0000737 -1.0000737 12 2e-09 -1.0001043 -1.0001043 13 3e-09 -1.0001277 -1.0001277 13 4e-09 -1.0001475 -1.0001475 13 5e-09 -1.0001649 -1.0001649 12 6e-09 -1.0001806 -1.0001806 13 7e-09 -1.0001951 -1.0001951 12 8e-09 -1.0002086 -1.0002086 12 9e-09 -1.0002212 -1.0002212 12 1e-08 -1.0002332 -1.0002332 12 1.1e-08 -1.0002446 -1.0002446 13 xmax = 1.0000e+20 toms743_test03(): Test wapr(x) when input X is the argument. Wp has been selected (maximum x is > 0) Results for Wp(x): x W(x) (WAPR) W(x) (BISECT) Digits Correct 0 0 0 16 5e+18 39.382644 39.382644 16 1e+19 40.058769 40.058769 16 1.5e+19 40.454406 40.454406 16 2e+19 40.735172 40.735172 16 2.5e+19 40.952983 40.952983 16 3e+19 41.130968 41.130968 16 3.5e+19 41.281466 41.281466 16 4e+19 41.411844 41.411844 16 4.5e+19 41.526854 41.526854 16 5e+19 41.62974 41.62974 16 5.5e+19 41.722817 41.722817 16 6e+19 41.807793 41.807793 16 6.5e+19 41.885968 41.885968 16 7e+19 41.958349 41.958349 16 7.5e+19 42.025738 42.025738 16 8e+19 42.088777 42.088777 16 8.5e+19 42.147996 42.147996 16 9e+19 42.20383 42.20383 16 9.5e+19 42.256647 42.256647 16 1e+20 42.306755 42.306755 16 toms743_test(): Normal end of execution. 27-Jul-2022 09:08:58