07-Jan-2022 17:55:14 C8LIB_TEST MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2. Test c8lib() C8_ABS_TEST C8_ABS computes the absolute value of a C8. C1=C8_UNIFORM_01 R2=C8_ABS(C1) R3=ABS(C1)) --------------------- --------------------- --------------------- ( 0.749055 -0.503627) 0.902620 0.902620 ( 0.304860 -0.184519) 0.356352 0.356352 ( 0.650485 0.457415) 0.795210 0.795210 ( -0.504999 -0.153212) 0.527729 0.527729 ( 0.954807 -0.214127) 0.978523 0.978523 ( 0.390247 -0.072938) 0.397005 0.397005 ( -0.974222 0.089772) 0.978349 0.978349 ( 0.562020 0.695999) 0.894584 0.894584 ( 0.560515 -0.328001) 0.649432 0.649432 ( 0.861387 -0.224097) 0.890060 0.890060 C8_ACOS_TEST C8_ACOS computes the inverse cosine of a C8. C1=C8_UNIFORM_01 C2 = C8_ACOS(C1) C3 = C8_COS(C2) --------------------- --------------------- --------------------- ( 0.789478 0.180180) ( 0.706385 -0.274142) ( 0.789478 0.180180) ( 0.843363 -0.371307) ( 0.739662 0.526242) ( 0.843363 -0.371307) ( 0.040050 -0.822880) ( 1.539871 0.750739) ( 0.040050 -0.822880) ( -0.671846 0.540144) ( 2.168156 -0.613969) ( -0.671846 0.540144) ( 0.384735 0.712360) ( 1.257736 -0.692149) ( 0.384735 0.712360) ( 0.823514 0.166945) ( 0.653267 -0.271336) ( 0.823514 0.166945) ( 0.504246 0.150530) ( 1.050857 -0.172594) ( 0.504246 0.150530) ( 0.138793 -0.279049) ( 1.436798 0.277979) ( 0.138793 -0.279049) ( -0.341111 0.760574) ( 1.841845 -0.724365) ( -0.341111 0.760574) ( 0.952051 0.209332) ( 0.506918 -0.418829) ( 0.952051 0.209332) C8_ACOSH_TEST C8_ACOSH computes the inverse hyperbolic cosine of a C8. C1=C8_UNIFORM_01 C2 = C8_ACOSH(C1) C3 = C8_COSH(C2) --------------------- --------------------- --------------------- ( -0.487269 0.448679) ( 0.479943 2.022028) ( -0.487269 0.448679) ( 0.245155 -0.839890) ( -0.774939 1.383355) ( 0.245155 -0.839890) ( -0.431394 0.027782) ( 0.030787 2.016607) ( -0.431394 0.027782) ( -0.404764 -0.530803) ( -0.540424 1.930595) ( -0.404764 -0.530803) ( 0.024798 -0.841873) ( -0.765149 1.551826) ( 0.024798 -0.841873) ( -0.224584 -0.474960) ( -0.467724 1.774272) ( -0.224584 -0.474960) ( 0.422416 0.690408) ( 0.680524 1.223364) ( 0.422416 0.690408) ( -0.344942 0.003546) ( 0.003778 1.922971) ( -0.344942 0.003546) ( -0.526934 0.825884) ( 0.807213 1.973710) ( -0.526934 0.825884) ( 0.125314 0.754695) ( 0.699921 1.470787) ( 0.125314 0.754695) C8_ADD_TEST C8_ADD computes the sum of two C8's. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 C3 = C1+C2 --------------------- --------------------- --------------------- ( -0.027743 0.866313) ( -0.223727 -0.675206) ( -0.251470 0.191106) ( 0.913169 -0.238800) ( 0.476437 0.565883) ( 1.389606 0.327083) ( -0.018221 0.385956) ( -0.024667 0.916574) ( -0.042888 1.302530) ( 0.036702 0.901631) ( -0.566536 0.779937) ( -0.529834 1.681567) ( -0.003020 0.443380) ( -0.773857 0.131111) ( -0.776877 0.574491) ( 0.288386 -0.518163) ( -0.727992 -0.235142) ( -0.439606 -0.753305) ( -0.213840 0.933523) ( 0.020387 -0.869934) ( -0.193454 0.063590) ( -0.561642 -0.254959) ( 0.259744 0.091583) ( -0.301898 -0.163376) ( 0.132772 -0.716358) ( 0.661990 0.704116) ( 0.794762 -0.012242) ( -0.740298 0.144159) ( -0.056782 0.093155) ( -0.797081 0.237314) C8_ARG_TEST C8_ARG computes the argument of a C8. C1=random ARG=C8_ARG(C1) 0.110615 -0.387229 -1.292548 -0.548925 -0.099479 -2.962314 -0.326265 -0.243310 -2.500821 -0.290690 -0.422458 -2.173485 -0.009642 -0.830133 -1.582410 0.580265 0.337393 0.526665 0.409311 -0.247874 -0.544517 0.179001 -0.346896 -1.094424 0.733502 -0.017818 -0.024286 -0.261660 0.098538 2.781430 C8_ASIN_TEST C8_ASIN computes the inverse sine of a C8. C1=C8_UNIFORM_01 C2 = C8_ASIN(C1) C3 = C8_SIN(C2) --------------------- --------------------- --------------------- ( 0.317263 -0.077438) ( 0.321734 -0.081536) ( 0.317263 -0.077438) ( 0.010611 -0.067243) ( 0.010588 -0.067196) ( 0.010611 -0.067243) ( 0.613438 -0.664076) ( 0.510006 -0.701851) ( 0.613438 -0.664076) ( -0.234849 0.171119) ( -0.233413 0.174994) ( -0.234849 0.171119) ( 0.157738 -0.484757) ( 0.142142 -0.471976) ( 0.157738 -0.484757) ( 0.556000 -0.349683) ( 0.540798 -0.397351) ( 0.556000 -0.349683) ( -0.036937 0.424833) ( -0.034000 0.413218) ( -0.036937 0.424833) ( 0.250361 0.287852) ( 0.242397 0.292338) ( 0.250361 0.287852) ( -0.817864 -0.447650) ( -0.767645 -0.587705) ( -0.817864 -0.447650) ( 0.454653 0.585791) ( 0.394030 0.598103) ( 0.454653 0.585791) C8_ASINH_TEST C8_ASINH computes the inverse hyperbolic sine of a C8. C1=C8_UNIFORM_01 C2 = C8_ASINH(C1) C3 = C8_SINH(C2) --------------------- --------------------- --------------------- ( -0.665053 -0.640886) ( -0.710466 -0.532119) ( -0.665053 -0.640886) ( -0.590361 -0.049261) ( -0.560999 -0.042423) ( -0.590361 -0.049261) ( 0.563036 0.291202) ( 0.553127 0.254442) ( 0.563036 0.291202) ( 0.349989 0.342672) ( 0.361665 0.327230) ( 0.349989 0.342672) ( 0.027055 0.427990) ( 0.029928 0.442056) ( 0.027055 0.427990) ( 0.614778 0.198279) ( 0.589014 0.169045) ( 0.614778 0.198279) ( 0.893513 -0.323035) ( 0.823577 -0.240043) ( 0.893513 -0.323035) ( -0.699020 0.047275) ( -0.652294 0.038747) ( -0.699020 0.047275) ( 0.470265 -0.341424) ( 0.475819 -0.311107) ( 0.470265 -0.341424) ( 0.465267 0.390862) ( 0.478253 0.357635) ( 0.465267 0.390862) C8_ATAN_TEST C8_ATAN computes the inverse tangent of a C8. C1=C8_UNIFORM_01 C2 = C8_ATAN(C1) C3 = C8_TAN(C2) --------------------- --------------------- --------------------- ( -0.679684 0.564165) ( -0.705264 0.373874) ( -0.679684 0.564165) ( -0.404712 0.279105) ( -0.408996 0.242072) ( -0.404712 0.279105) ( 0.209777 0.229015) ( 0.217359 0.222474) ( 0.209777 0.229015) ( 0.933961 -0.264136) ( 0.769891 -0.139521) ( 0.933961 -0.264136) ( 0.705552 0.278218) ( 0.639195 0.184574) ( 0.705552 0.278218) ( -0.292529 0.386273) ( -0.326378 0.367122) ( -0.292529 0.386273) ( 0.901957 0.087567) ( 0.735999 0.048231) ( 0.901957 0.087567) ( 0.101078 0.181127) ( 0.104092 0.181192) ( 0.101078 0.181127) ( -0.092322 -0.800370) ( -0.242203 -1.051843) ( -0.092322 -0.800370) ( -0.766866 0.244259) ( -0.672520 0.152826) ( -0.766866 0.244259) C8_ATANH_TEST C8_ATANH computes the inverse hyperbolic tangent of a C8. C1=C8_UNIFORM_01 C2 = C8_ATANH(C1) C3 = C8_TANH(C2) --------------------- --------------------- --------------------- ( -0.212229 0.708497) ( -0.140793 0.630690) ( -0.212229 0.708497) ( 0.322936 0.800253) ( 0.194323 0.706306) ( 0.322936 0.800253) ( 0.336224 0.757449) ( 0.211027 0.683453) ( 0.336224 0.757449) ( -0.427563 -0.430900) ( -0.366478 -0.469201) ( -0.427563 -0.430900) ( 0.771017 0.431000) ( 0.658829 0.660579) ( 0.771017 0.431000) ( 0.155072 -0.951493) ( 0.081077 -0.766853) ( 0.155072 -0.951493) ( -0.641807 0.273634) ( -0.653167 0.408752) ( -0.641807 0.273634) ( -0.231743 0.626960) ( -0.166022 0.577647) ( -0.231743 0.626960) ( -0.711465 -0.048225) ( -0.883455 -0.096889) ( -0.711465 -0.048225) ( 0.251352 -0.868591) ( 0.141983 -0.733099) ( 0.251352 -0.868591) C8_CONJ_TEST C8_CONJ computes the complex conjugate of a C8. C1=C8_UNIFORM_01 C2 = C8_CONJ(C1) C3 = C8_CONJ(C2) --------------------- --------------------- --------------------- ( -0.580316 0.554574) ( -0.580316 -0.554574) ( -0.580316 0.554574) ( -0.881784 -0.184491) ( -0.881784 0.184491) ( -0.881784 -0.184491) ( 0.549256 -0.221462) ( 0.549256 0.221462) ( 0.549256 -0.221462) ( -0.889827 -0.290089) ( -0.889827 0.290089) ( -0.889827 -0.290089) ( -0.673885 -0.410310) ( -0.673885 0.410310) ( -0.673885 -0.410310) ( -0.144236 0.432363) ( -0.144236 -0.432363) ( -0.144236 0.432363) ( 0.083920 0.681088) ( 0.083920 -0.681088) ( 0.083920 0.681088) ( 0.312534 0.864078) ( 0.312534 -0.864078) ( 0.312534 0.864078) ( 0.227128 0.417534) ( 0.227128 -0.417534) ( 0.227128 0.417534) ( -0.438727 0.187572) ( -0.438727 -0.187572) ( -0.438727 0.187572) C8_COS_TEST C8_COS computes the cosine of a C8. C1=C8_UNIFORM_01 C2 = C8_COS(C1) C3 = C8_ACOS(C1) --------------------- --------------------- --------------------- ( 0.494369 -0.258267) ( 0.909790 0.123908) ( 0.494369 -0.258267) ( 0.261185 0.601656) ( 1.146280 -0.164907) ( 0.261185 0.601656) ( 0.943562 -0.120715) ( 0.591189 0.097975) ( 0.943562 -0.120715) ( 0.507462 0.425855) ( 0.954435 -0.213261) ( 0.507462 0.425855) ( -0.426716 0.275642) ( 0.945132 0.115534) ( 0.426716 -0.275642) ( -0.059122 0.769026) ( 1.308274 0.050053) ( 0.059122 -0.769026) ( -0.187340 -0.753490) ( 1.274858 -0.153996) ( 0.187340 0.753490) ( 0.348456 0.316741) ( 0.987444 -0.109968) ( 0.348456 0.316741) ( -0.228123 0.494607) ( 1.095690 0.116472) ( 0.228123 -0.494607) ( -0.650487 -0.032144) ( 0.796200 -0.019469) ( 0.650487 0.032144) C8_COSH_TEST C8_COSH computes the hyperbolic cosine of a C8. C1=C8_UNIFORM_01 C2 = C8_COSH(C1) C3 = C8_ACOSH(C1) --------------------- --------------------- --------------------- ( -0.022911 0.291532) ( 0.958056 -0.006586) ( -0.022911 0.291532) ( 0.879952 0.163396) ( 1.393976 0.162343) ( 0.879952 0.163396) ( -0.118804 -0.956420) ( 0.580522 0.097308) ( 0.118804 0.956420) ( -0.615638 -0.331058) ( 1.130646 0.212991) ( 0.615638 0.331058) ( -0.470925 0.124551) ( 1.104328 -0.060689) ( -0.470925 0.124551) ( -0.939237 -0.284468) ( 1.415220 0.304095) ( 0.939237 0.284468) ( 0.083298 0.717075) ( 0.756347 0.054806) ( 0.083298 0.717075) ( -0.497329 -0.491489) ( 0.992926 0.244505) ( 0.497329 0.491489) ( -0.652796 0.502984) ( 1.069554 -0.337506) ( -0.652796 0.502984) ( 0.604438 -0.045729) ( 1.187060 -0.029344) ( -0.604438 0.045729) C8_CUBE_ROOT_TEST C8_CUBE_ROOT computes the principal cube root of a C8. C1=random C2=C8_CUBE_ROOT(C1) C3=C2*C2*C2 0.145856 -0.128316 0.562490 -0.137951 -0.004102 -0.006077 0.273440 -0.915706 0.896608 -0.407813 -0.667407 0.562436 -0.023413 0.313312 0.580111 0.354442 0.006882 -0.030241 -0.247464 -0.523563 0.652932 -0.518113 0.188349 0.047332 -0.066442 -0.363509 0.598725 -0.395577 0.026045 0.043219 -0.185762 -0.268802 0.515461 -0.456830 0.033856 -0.008405 0.127608 -0.691296 0.795644 -0.396933 -0.180870 0.296593 0.695535 -0.480904 0.926470 -0.189394 -0.146088 -0.586721 -0.476199 0.814959 0.750343 0.631837 0.840827 0.013151 0.269226 0.791368 0.862313 0.379196 -0.486305 -0.323524 C8_DIV_TEST C8_DIV computes C3 = C1 / C2. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 C3=C8_DIV(C1,C2) C4=C1/C2 --------------------- --------------------- --------------------- --------------------- -0.0065 -0.1746 -0.7015 0.0890 -0.0219 0.2462 -0.0219 0.2462 -0.7334 -0.6057 0.4988 -0.6073 0.0032 -1.2103 0.0032 -1.2103 -0.7952 -0.4161 0.0270 0.4268 -1.0884 1.7941 -1.0884 1.7941 0.9263 0.1687 0.3452 0.6089 0.8623 -1.0325 0.8623 -1.0325 -0.2298 -0.9622 -0.6958 0.1278 0.0737 1.3965 0.0737 1.3965 -0.1012 -0.2222 0.1856 0.0894 -0.9108 -0.7586 -0.9108 -0.7586 0.5929 0.4124 0.3725 -0.8243 -0.1456 0.7851 -0.1456 0.7851 0.5002 0.6872 -0.8066 -0.0947 -0.7103 -0.7686 -0.7103 -0.7686 -0.5848 -0.7943 -0.8572 0.2561 0.3722 1.0379 0.3722 1.0379 0.2997 -0.5853 0.1935 0.2145 -0.8093 -2.1273 -0.8093 -2.1273 C8_DIV_R8_TEST C8_DIV_R8 computes C3 = C1 / R2. C1=C8_UNIFORM_01 R2=RAND(1,1) C3=C8_DIV_R8(C1,R2) C4=C1/R2 --------------------- --------------------- --------------------- --------------------- -0.3224 0.2635 0.8314 -0.3878 0.3170 -0.3878 0.3170 0.8324 0.3324 0.3993 2.0848 0.8326 2.0848 0.8326 -0.6289 0.3624 0.6569 -0.9575 0.5517 -0.9575 0.5517 -0.2066 0.7650 0.4317 -0.4787 1.7723 -0.4787 1.7723 0.1238 -0.0124 0.1672 0.7407 -0.0744 0.7407 -0.0744 -0.2267 0.2342 0.1981 -1.1441 1.1820 -1.1441 1.1820 -0.3731 0.5920 0.9516 -0.3920 0.6221 -0.3920 0.6221 0.9073 0.3118 0.7379 1.2296 0.4225 1.2296 0.4225 -0.4590 0.2418 0.5479 -0.8378 0.4413 -0.8378 0.4413 -0.8441 0.4798 0.9831 -0.8587 0.4880 -0.8587 0.4880 C8_EXP_TEST C8_EXP computes the exponential of a C8. C1=C8_UNIFORM_01 C2=C8_EXP(C1) C3=C8_LOG(C2)) --------------------- --------------------- --------------------- ( -0.166057 -0.523336) ( 0.733633 -0.423306) ( -0.166057 -0.523336) ( -0.791753 -0.198662) ( 0.444139 -0.089413) ( -0.791753 -0.198662) ( -0.418394 -0.723223) ( 0.493364 -0.435535) ( -0.418394 -0.723223) ( 0.292734 0.304038) ( 1.278624 0.401189) ( 0.292734 0.304038) ( 0.475350 0.879274) ( 1.025807 1.239049) ( 0.475350 0.879274) ( -0.167372 -0.067731) ( 0.843946 -0.057249) ( -0.167372 -0.067731) ( -0.456662 -0.820565) ( 0.431854 -0.463348) ( -0.456662 -0.820565) ( -0.296555 0.320138) ( 0.705605 0.233939) ( -0.296555 0.320138) ( 0.674256 -0.078137) ( 1.956583 -0.153194) ( 0.674256 -0.078137) ( 0.243418 -0.311693) ( 1.214138 -0.391190) ( 0.243418 -0.311693) C8_I_TEST C8_I computes the imaginary unit I. C1 = C8_I ( ) = (0,1) C2 = C1 * C1 = (-1,0) C8_IMAG_TEST C8_IMAG computes the imaginary part of a C8. C1=C8_UNIFORM_01 R2=C8_IMAG(C1) R3=IMAG(C1)) --------------------- --------------------- --------------------- ( -0.572308 0.563230) 0.563230 0.563230 ( -0.393297 0.190372) 0.190372 0.190372 ( 0.504277 0.477207) 0.477207 0.477207 ( 0.114447 0.759216) 0.759216 0.759216 ( -0.537763 -0.308917) -0.308917 -0.308917 ( -0.126139 0.485690) 0.485690 0.485690 ( -0.075307 0.781933) 0.781933 0.781933 ( 0.902570 -0.098707) -0.098707 -0.098707 ( -0.475327 0.710150) 0.710150 0.710150 ( 0.595631 0.478846) 0.478846 0.478846 C8_INV_TEST C8_INV computes the inverse of a C8. C1=C8_UNIFORM_01 C2 = C8_INV(C1) C3 = C8_INV(C2) --------------------- --------------------- --------------------- ( 0.692560 -0.653199) ( 0.764155 0.720725) ( 0.692560 -0.653199) ( -0.060909 0.902248) ( -0.074483 -1.103315) ( -0.060909 0.902248) ( 0.763245 0.108687) ( 1.284154 -0.182866) ( 0.763245 0.108687) ( -0.250384 0.602136) ( -0.588778 -1.415926) ( -0.250384 0.602136) ( 0.173914 0.362269) ( 1.076967 -2.243363) ( 0.173914 0.362269) ( 0.539611 0.362912) ( 1.276022 -0.858181) ( 0.539611 0.362912) ( -0.760769 0.140551) ( -1.271076 -0.234829) ( -0.760769 0.140551) ( -0.258352 -0.793224) ( -0.371223 1.139772) ( -0.258352 -0.793224) ( 0.781336 0.167467) ( 1.223646 -0.262269) ( 0.781336 0.167467) ( -0.111089 0.237625) ( -1.614516 -3.453539) ( -0.111089 0.237625) C8_LE_L1_TEST C8_LE_L1 evalues (C1 <= C2) using the L1 norm. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 L3=C8_LE_L1(C1,C2) --------------------- --------------------- --------------------- -0.4116, -0.6012 0.2718, -0.5777 0 0.8312, -0.1659 -0.3315, 0.6492 0 -0.2492, -0.2087 -0.7824, 0.4083 1 -0.0311, 0.2998 -0.0759, 0.3846 1 -0.6538, -0.1126 0.4794, -0.4771 1 0.6751, -0.2497 0.7705, -0.2098 1 -0.2196, -0.4387 -0.2536, -0.4741 1 0.7588, 0.3455 0.0820, 0.4981 0 0.4568, -0.6776 0.1119, -0.5762 0 0.8211, 0.0347 -0.5878, 0.5067 1 C8_LE_L2_TEST C8_LE_L2 evalues (C1 <= C2) using the L2 norm. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 L3=C8_LE_L2(C1,C2) --------------------- --------------------- --------------------- 0.9570, 0.0069 -0.6046, 0.3112 0 0.0858, -0.6735 0.1230, -0.5544 0 0.6693, 0.1530 -0.0740, -0.4128 0 0.3949, 0.5635 -0.4561, -0.3649 0 -0.0318, -0.4367 0.4279, -0.2444 1 0.0504, -0.5163 -0.1014, 0.4224 0 -0.2679, -0.1391 -0.7915, -0.2386 1 -0.4017, -0.5142 -0.3471, -0.7260 1 0.7505, -0.2693 -0.1157, -0.4422 0 0.3556, 0.3314 -0.7414, 0.2402 1 C8_LE_LI_TEST C8_LE_LI evalues (C1 <= C2) using the Loo norm. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 L3=C8_LE_LI(C1,C2) --------------------- --------------------- --------------------- -0.3559, -0.5762 -0.5168, 0.7093 1 -0.7033, 0.4091 0.4567, -0.7958 1 -0.3831, -0.3312 -0.7382, -0.1932 1 -0.0865, 0.9287 0.4130, 0.3840 0 -0.5915, -0.7681 -0.4437, -0.5316 0 -0.4438, -0.5897 -0.1334, -0.7253 1 0.7223, -0.0286 0.3681, 0.2885 0 0.3051, 0.1288 -0.6029, 0.2027 1 0.0513, -0.6027 0.1091, -0.7849 1 0.9517, -0.1646 0.2817, 0.3357 0 C8_LOG_TEST C8_LOG computes the logarithm of a C8. C1=C8_UNIFORM_01 C2=C8_LOG(C1) C3=C8_EXP(C2)) --------------------- --------------------- --------------------- ( 0.693596 0.463887) ( -0.181012 0.589489) ( 0.693596 0.463887) ( -0.711713 -0.137363) ( -0.321794 -2.950934) ( -0.711713 -0.137363) ( -0.923777 0.088182) ( -0.074749 3.046423) ( -0.923777 0.088182) ( -0.297230 -0.552368) ( -0.466393 -2.064459) ( -0.297230 -0.552368) ( -0.854139 -0.108189) ( -0.149703 -3.015599) ( -0.854139 -0.108189) ( 0.346609 0.477048) ( -0.528189 0.942461) ( 0.346609 0.477048) ( -0.058365 0.763338) ( -0.267139 1.647108) ( -0.058365 0.763338) ( 0.006534 -0.210740) ( -1.556649 -1.539800) ( 0.006534 -0.210740) ( -0.460817 0.174451) ( -0.707789 2.779696) ( -0.460817 0.174451) ( -0.525533 0.641569) ( -0.187131 2.257097) ( -0.525533 0.641569) C8_MAG_TEST C8_MAG computes the magnitude of a C8. C1=C8_UNIFORM_01 R2=C8_MAG(C1) R3=ABS(C1)) --------------------- --------------------- --------------------- ( -0.677066 0.527182) 0.858103 0.858103 ( -0.235386 -0.792470) 0.826690 0.826690 ( 0.660035 0.081603) 0.665060 0.665060 ( -0.511371 0.263358) 0.575202 0.575202 ( 0.169775 0.491372) 0.519875 0.519875 ( -0.820025 0.386369) 0.906488 0.906488 ( -0.730434 0.595178) 0.942216 0.942216 ( -0.698966 0.529680) 0.876992 0.876992 ( 0.028679 -0.898717) 0.899174 0.899174 ( 0.130170 0.600376) 0.614325 0.614325 C8_MUL_TEST C8_MUL computes C3 = C1 * C2. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 C3=C8_MUL(C1,C2) C4=C1*C2 --------------------- --------------------- --------------------- --------------------- 0.8443 -0.2784 -0.2717 -0.5037 -0.3697 -0.3496 -0.3697 -0.3496 0.3318 -0.5732 0.4356 0.7610 0.5807 0.0028 0.5807 0.0028 0.9265 -0.0590 0.5359 -0.4767 0.4684 -0.4734 0.4684 -0.4734 0.4320 0.6336 -0.3728 0.2467 -0.3174 -0.1296 -0.3174 -0.1296 0.3957 -0.7695 -0.3710 0.8077 0.4748 0.6050 0.4748 0.6050 0.6172 0.3914 0.2190 0.2525 0.0363 0.2415 0.0363 0.2415 -0.8234 0.0250 -0.4353 0.0137 0.3581 -0.0221 0.3581 -0.0221 0.3615 0.1301 -0.8564 -0.3425 -0.2650 -0.2352 -0.2650 -0.2352 -0.3171 -0.9105 0.3049 -0.6999 -0.7339 -0.0557 -0.7339 -0.0557 0.9353 -0.0653 0.0152 -0.0171 0.0131 -0.0170 0.0131 -0.0170 C8_NINT_TEST C8_NINT computes the nearest integer to a C8. C1=10*C8_UNIFORM_01 C2=C8_NINT(C1) --------------------- --------------------- ( 7.811064 -0.493884) ( 8.000000 0.000000) ( -7.204120 0.932019) ( -7.000000 1.000000) ( 1.242221 8.865193) ( 1.000000 9.000000) ( 5.731840 -4.117699) ( 6.000000 -4.000000) ( 4.267969 -6.265027) ( 4.000000 -6.000000) ( -7.370303 -4.420708) ( -7.000000 -4.000000) ( -2.490385 -4.297841) ( -2.000000 -4.000000) ( -2.030714 -2.055355) ( -2.000000 -2.000000) ( -1.031515 -8.064145) ( -1.000000 -8.000000) ( 9.379683 -1.047266) ( 9.000000 -1.000000) C8_NORM_L1_TEST C8_NORM_L1 computes the L1 norm of a C8. C1=C8_UNIFORM_01 R2=C8_NORM_L1(C1) --------------------- --------------------- -0.764600, -0.429437 1.194037 -0.844049, -0.464644 1.308693 0.094515, 0.089721 0.184236 -0.924305, 0.091496 1.015801 0.231912, 0.889423 1.121335 -0.509127, -0.541370 1.050497 -0.134378, -0.118041 0.252419 0.573086, 0.184348 0.757434 0.247281, 0.654540 0.901821 0.096833, 0.337205 0.434038 C8_NORM_L2_TEST C8_NORM_L2 computes the L2 norm of a C8. C1=C8_UNIFORM_01 R2=C8_NORM_L2(C1) --------------------- --------------------- 0.142980, 0.355066 0.382773 -0.136384, -0.155086 0.206525 -0.515376, -0.127493 0.530911 -0.833752, 0.004631 0.833764 -0.688995, 0.247158 0.731984 -0.351394, 0.021316 0.352040 0.648653, -0.657455 0.923579 0.134156, 0.502291 0.519898 -0.477985, -0.580095 0.751651 0.176362, 0.621229 0.645778 C8_NORM_LI_TEST C8_NORM_LI computes the Loo norm of a C8. C1=C8_UNIFORM_01 R2=C8_NORM_LI(C1) --------------------- --------------------- 0.847012, 0.480107 0.847012 0.204016, 0.253154 0.253154 -0.295728, -0.281079 0.295728 0.717248, 0.243445 0.717248 -0.128991, -0.956328 0.956328 0.791710, 0.333221 0.791710 0.849926, -0.371574 0.849926 0.627321, -0.768679 0.768679 -0.883189, -0.074410 0.883189 -0.338735, 0.250722 0.338735 C8_NORMAL_01_TEST C8_NORMAL_01 generates unit pseudonormal complex values. 1.967559 0.386741 -0.112268 0.336116 -0.777320 1.354148 -0.736534 -0.989989 1.485237 -2.270167 0.656172 -0.855882 -1.370438 0.483425 1.067474 2.165454 -0.441055 0.792471 0.340940 0.312807 -0.147850 -0.037944 0.832872 -0.002660 -1.355985 0.807428 0.108409 -1.233034 0.511971 0.373059 -1.180784 1.434008 -2.373171 -0.328412 0.665106 1.319023 1.464530 -0.993229 -0.868630 0.174381 C8_ONE_TEST C8_ONE returns one as a C8. C1 = C8_ONE ( ) = (1,0) C2 = C1 + C1 = (2,0) C8_PRINT_TEST C8_PRINT prints a C8. Zero: ( 0, 0 ) One: ( 1, 0 ) Pi: ( 3.14159, 0 ) i: ( 0, 1 ) 1+2i: ( 1, 2 ) -12.34 + 56.78i: ( -12.34, 56.78 ) 1E-3 + 2E-6i ( 0.001, 2e-06 ) 3E8 - 4.5E9i: ( 3e+08, -4.5e+09 ) C8_REAL_TEST C8_REAL computes the real part of a C8. C1=C8_UNIFORM_01 R2=C8_REAL(C1) R3=REAL(C1)) --------------------- --------------------- --------------------- ( 0.758263 0.580663) 0.758263 0.758263 ( -0.074410 -0.860238) -0.074410 -0.074410 ( 0.301171 0.686409) 0.301171 0.301171 ( -0.238516 0.735066) -0.238516 -0.238516 ( 0.085267 0.356164) 0.085267 0.085267 ( 0.852266 0.410590) 0.852266 0.852266 ( 0.464608 0.163173) 0.464608 0.464608 ( 0.662308 0.055405) 0.662308 0.662308 ( 0.311551 0.894498) 0.311551 0.311551 ( -0.107771 0.285930) -0.107771 -0.107771 C8_SIN_TEST C8_SIN computes the sine of a C8. C1=C8_UNIFORM_01 C2 = C8_SIN(C1) C3 = C8_ASIN(C1) --------------------- --------------------- --------------------- ( 0.542152 0.402652) ( 0.558377 0.354308) ( 0.542152 0.402652) ( -0.492097 0.867889) ( -0.661869 0.864616) ( -0.492097 0.867889) ( 0.504381 0.207235) ( 0.493680 0.182730) ( 0.504381 0.207235) ( 0.523120 0.156809) ( 0.505740 0.136395) ( 0.523120 0.156809) ( 0.050995 -0.709103) ( 0.064334 -0.769041) ( 0.050995 -0.709103) ( 0.671023 0.425204) ( 0.678849 0.343139) ( 0.671023 0.425204) ( 0.048434 -0.280208) ( 0.050328 -0.283557) ( 0.048434 -0.280208) ( -0.930047 -0.200368) ( -0.817794 -0.120582) ( -0.930047 -0.200368) ( 0.151486 -0.293609) ( 0.157458 -0.294435) ( 0.151486 -0.293609) ( -0.158616 0.559409) ( -0.183318 0.581651) ( -0.158616 0.559409) C8_SINH_TEST C8_SINH computes the hyperbolic sine of a C8. C1=C8_UNIFORM_01 C2 = C8_SINH(C1) C3 = C8_ASINH(C1) --------------------- --------------------- --------------------- ( 0.862073 0.056068) ( 0.971361 0.078183) ( 0.862073 0.056068) ( -0.108554 -0.191477) ( -0.106779 -0.191431) ( -0.108554 -0.191477) ( -0.766408 -0.126835) ( -0.836894 -0.165500) ( -0.766408 -0.126835) ( -0.226684 -0.823604) ( -0.155373 -0.752529) ( -0.226684 -0.823604) ( -0.208930 0.858909) ( -0.137482 0.773716) ( -0.208930 0.858909) ( -0.779986 -0.290092) ( -0.825519 -0.377552) ( -0.779986 -0.290092) ( 0.583133 0.237648) ( 0.599414 0.276590) ( 0.583133 0.237648) ( -0.461907 0.752873) ( -0.349181 0.757985) ( -0.461907 0.752873) ( -0.042823 -0.778481) ( -0.030498 -0.702842) ( -0.042823 -0.778481) ( 0.224733 0.233042) ( 0.220503 0.236794) ( 0.224733 0.233042) C8_SQRT_TEST C8_SQRT computes the principal square root of a C8. C1=random C2=C8_SQRT(C1) C3=C2*C2 -0.738120 0.068700 0.039938 0.860067 0.540101 -0.101417 0.285735 -0.899350 0.784023 -0.573548 -0.727187 -0.513952 0.812751 0.271619 0.913698 0.148637 0.586787 0.441517 0.229274 0.142543 0.499623 0.142651 0.032248 0.065363 0.836828 -0.313161 0.930143 -0.168340 0.602211 -0.524124 0.558095 0.610119 0.832156 0.366590 -0.060775 0.681009 0.653833 0.543348 0.867169 0.313288 0.132270 0.710518 -0.217298 -0.265093 0.250474 -0.529183 -0.023056 0.115208 -0.325843 -0.471848 0.351838 -0.670547 -0.116467 0.307497 -0.749967 -0.432067 0.240372 -0.898746 0.375768 0.648071 C8_SUB_TEST C8_SUB computes the difference of two C8's. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 C3 = C1-C2 --------------------- --------------------- --------------------- ( 0.081888 0.856345) ( 0.842710 -0.157473) ( -0.760822 1.013818) ( 0.797729 0.480166) ( -0.412157 0.443354) ( 1.209886 0.036812) ( -0.675830 -0.477789) ( -0.598577 0.656559) ( -0.077253 -1.134348) ( 0.388253 0.235134) ( 0.241543 0.844743) ( 0.146710 -0.609609) ( -0.590428 -0.199163) ( -0.300483 -0.372375) ( -0.289945 0.173212) ( 0.402569 0.567819) ( 0.713404 0.522482) ( -0.310835 0.045337) ( 0.042978 0.540573) ( 0.611482 0.396184) ( -0.568504 0.144389) ( 0.503424 0.389717) ( 0.071921 -0.327279) ( 0.431503 0.716996) ( -0.429693 -0.327007) ( -0.895006 0.404212) ( 0.465312 -0.731220) ( 0.042399 -0.832439) ( -0.368009 -0.545171) ( 0.410408 -0.287268) C8_TAN_TEST C8_TAN computes the tangent of a C8. C1=C8_UNIFORM_01 C2 = C8_TAN(C1) C3 = C8_ATAN(C1) --------------------- --------------------- --------------------- ( 0.303011 -0.133937) ( 0.306565 -0.145903) ( 0.303011 -0.133937) ( -0.043937 0.430732) ( -0.036709 0.406588) ( -0.043937 0.430732) ( -0.890505 0.069500) ( -1.220947 0.174091) ( -0.890505 0.069500) ( -0.696275 0.533066) ( -0.546287 0.710446) ( -0.696275 0.533066) ( 0.508203 0.121113) ( 0.546448 0.157209) ( 0.508203 0.121113) ( -0.741493 0.351402) ( -0.740631 0.566622) ( -0.741493 0.351402) ( -0.518258 -0.427958) ( -0.453340 -0.507954) ( -0.518258 -0.427958) ( -0.097935 0.223186) ( -0.093470 0.221569) ( -0.097935 0.223186) ( -0.290308 -0.829725) ( -0.154107 -0.711650) ( -0.290308 -0.829725) ( 0.242100 0.258302) ( 0.230276 0.267077) ( 0.242100 0.258302) C8_TANH_TEST C8_TANH computes the hyperbolic sine of a C8. C1=C8_UNIFORM_01 C2 = C8_TANH(C1) C3 = C8_ATANH(C1) --------------------- --------------------- --------------------- ( 0.303528 0.014926) ( 0.294598 0.013632) ( 0.303528 0.014926) ( -0.363678 -0.539303) ( -0.453534 -0.503902) ( -0.363678 -0.539303) ( -0.833954 -0.165662) ( -0.692653 -0.088145) ( -0.833954 -0.165662) ( -0.223133 -0.242960) ( -0.232299 -0.235218) ( -0.223133 -0.242960) ( 0.236373 0.265758) ( 0.248271 0.256514) ( 0.236373 0.265758) ( 0.197051 0.244469) ( 0.206160 0.239453) ( 0.197051 0.244469) ( 0.135912 0.387013) ( 0.157044 0.398922) ( 0.135912 0.387013) ( -0.228408 0.515082) ( -0.291743 0.528973) ( -0.228408 0.515082) ( -0.003053 0.466427) ( -0.003827 0.503473) ( -0.003053 0.466427) ( -0.273745 -0.904426) ( -0.626747 -1.058787) ( -0.273745 -0.904426) C8_TO_CARTESIAN_TEST C8_TO_CARTESIAN converts C8 to (X,Y). C1=C8_UNIFORM_01 (X2,Y2)=C8_TO_CARTESIAN(C1) C3=CARTESIAN_TO_C8(X2,Y2) ---------------------- ---------------------- ----------------------- ( 0.298498 0.683108) 0.298498 0.683108 ( 0.298498 0.683108) ( 0.407153 0.215075) 0.407153 0.215075 ( 0.407153 0.215075) ( -0.256787 -0.920793) -0.256787 -0.920793 ( -0.256787 -0.920793) ( -0.289831 0.688322) -0.289831 0.688322 ( -0.289831 0.688322) ( -0.292771 -0.283705) -0.292771 -0.283705 ( -0.292771 -0.283705) ( 0.476473 0.872301) 0.476473 0.872301 ( 0.476473 0.872301) ( -0.404680 0.306637) -0.404680 0.306637 ( -0.404680 0.306637) ( -0.109448 -0.249030) -0.109448 -0.249030 ( -0.109448 -0.249030) ( 0.630655 -0.068281) 0.630655 -0.068281 ( 0.630655 -0.068281) ( -0.460460 -0.436074) -0.460460 -0.436074 ( -0.460460 -0.436074) C8_TO_POLAR_TEST C8_TO_POLAR converts C8 to polar form. C1=C8_UNIFORM_01 (R2,T2)=C8_TO_POLAR(C1) C3=POLAR_TO_C8(R2,T2) ---------------------- ---------------------- ----------------------- ( -0.288674 0.266528) 0.392899 2.396063 ( -0.288674 0.266528) ( 0.020452 -0.400894) 0.401415 -1.519824 ( 0.020452 -0.400894) ( -0.552278 0.752396) 0.933333 2.203995 ( -0.552278 0.752396) ( -0.226740 0.796319) 0.827971 1.848190 ( -0.226740 0.796319) ( 0.360609 -0.632922) 0.728443 -1.052915 ( 0.360609 -0.632922) ( -0.394777 0.664561) 0.772975 2.106823 ( -0.394777 0.664561) ( -0.522926 0.160540) 0.547015 2.843723 ( -0.522926 0.160540) ( -0.413157 0.501943) 0.650112 2.259473 ( -0.413157 0.501943) ( -0.034986 -0.746388) 0.747208 -1.617635 ( -0.034986 -0.746388) ( -0.588286 0.279740) 0.651410 2.697722 ( -0.588286 0.279740) C8_UNIFORM_01_TEST C8_UNIFORM_01 returns a uniformly random "unit" C8. C1=C8_UNIFORM_01 --------------------- ( 0.349217 0.054038) ( -0.221742 0.490934) ( 0.779094 -0.216107) ( -0.933664 0.252987) ( 0.042768 -0.488517) ( -0.051174 -0.869890) ( 0.678341 0.532487) ( -0.803668 0.188886) ( 0.375146 0.267261) ( 0.411951 0.808623) C8_ZERO_TEST C8_ZERO returns zero as a C8 C1 = C8_ZERO ( ) = (0,0) C8MAT_IDENTITY_TEST C8MAT_IDENTITY returns the complex identity matrix. The identity matrix: Col: 1 2 3 4 Row --- 1: 1.000000 0.0 0.0 0.0 2: 0.0 1.000000 0.0 0.0 3: 0.0 0.0 1.000000 0.0 4: 0.0 0.0 0.0 1.000000 C8MAT_INDICATOR_TEST C8MAT_INDICATOR returns the complex indicator matrix. The indicator matrix: Col: 1 2 3 Row --- 1: 1.000000 1.000000 1.000000 2.000000 1.000000 3.000000 2: 2.000000 1.000000 2.000000 2.000000 2.000000 3.000000 3: 3.000000 1.000000 3.000000 2.000000 3.000000 3.000000 4: 4.000000 1.000000 4.000000 2.000000 4.000000 3.000000 5: 5.000000 1.000000 5.000000 2.000000 5.000000 3.000000 C8MAT_NORM_FRO_TEST C8MAT_NORM_FRO returns the Frobenius norm of a C8MAT. The indicator matrix: Col: 1 2 3 4 Row --- 1: 1.000000 1.000000 1.000000 2.000000 1.000000 3.000000 1.000000 4.000000 2: 2.000000 1.000000 2.000000 2.000000 2.000000 3.000000 2.000000 4.000000 3: 3.000000 1.000000 3.000000 2.000000 3.000000 3.000000 3.000000 4.000000 4: 4.000000 1.000000 4.000000 2.000000 4.000000 3.000000 4.000000 4.000000 5: 5.000000 1.000000 5.000000 2.000000 5.000000 3.000000 5.000000 4.000000 Frobenius norm = 19.2354 C8MAT_NORM_L1_TEST C8MAT_NORM_L1 returns the L1 norm of a C8MAT. The indicator matrix: Col: 1 2 3 4 Row --- 1: 1.000000 1.000000 1.000000 2.000000 1.000000 3.000000 1.000000 4.000000 2: 2.000000 1.000000 2.000000 2.000000 2.000000 3.000000 2.000000 4.000000 3: 3.000000 1.000000 3.000000 2.000000 3.000000 3.000000 3.000000 4.000000 4: 4.000000 1.000000 4.000000 2.000000 4.000000 3.000000 4.000000 4.000000 5: 5.000000 1.000000 5.000000 2.000000 5.000000 3.000000 5.000000 4.000000 L1 norm = 25.6552 C8MAT_NORM_LI_TEST C8MAT_NORM_LI returns the Loo norm of a C8MAT. The indicator matrix: Col: 1 2 3 4 Row --- 1: 1.000000 1.000000 1.000000 2.000000 1.000000 3.000000 1.000000 4.000000 2: 2.000000 1.000000 2.000000 2.000000 2.000000 3.000000 2.000000 4.000000 3: 3.000000 1.000000 3.000000 2.000000 3.000000 3.000000 3.000000 4.000000 4: 4.000000 1.000000 4.000000 2.000000 4.000000 3.000000 4.000000 4.000000 5: 5.000000 1.000000 5.000000 2.000000 5.000000 3.000000 5.000000 4.000000 Loo norm = 22.7183 C8MAT_UNIFORM_01_TEST C8MAT_UNIFORM_01 computes a "random" complex matrix. The matrix: Col: 1 2 3 4 Row --- 1: -0.203712 -0.349387 -0.007806 -0.899524 0.127138 -0.066118 0.115871 0.859372 2: -0.940608 -0.098214 -0.342396 -0.054330 0.737122 -0.332190 0.027532 -0.251851 3: 0.477302 0.689119 -0.546680 -0.164239 0.355684 -0.192358 -0.177650 -0.799777 4: -0.944411 -0.248083 -0.543807 0.321176 -0.788097 -0.416606 -0.699852 0.390215 5: 0.802799 0.187743 -0.014386 0.424889 -0.031722 0.662593 0.252364 -0.571904 C8VEC_INDICATOR_TEST C8VEC_INDICATOR sets A = (1-1i,2-2i,...,N-Ni) The "indicator" vector: 1: 1-1i 2: 2-2i 3: 3-3i 4: 4-4i 5: 5-5i 6: 6-6i 7: 7-7i 8: 8-8i 9: 9-9i 10: 10-10i C8VEC_NINT_TEST C8VEC_NINT rounds a C8VEC The initial vector: 1: 2.6644-1.9218i 2: 4.7949-1.9589i 3: -0.73411-4.0808i 4: -5.5854-1.0646i 5: 1.366-0.41781i The rounded vector: 1: 3-2i 2: 5-2i 3: -1-4i 4: -6-1i 5: 1 C8VEC_NORM_L1_TEST C8VEC_NORM_L1 computes the L1 norm of a C8VEC. The "indicator" vector: 1: 1-1i 2: 2-2i 3: 3-3i 4: 4-4i 5: 5-5i L1 norm = 21.2132 C8VEC_NORM_L2_TEST C8VEC_NORM_L2 computes the L2 norm of a C8VEC. The "indicator" vector: 1: 1-1i 2: 2-2i 3: 3-3i 4: 4-4i 5: 5-5i L2 norm = 10.4881 C8VEC_NORM_LI_TEST C8VEC_NORM_LI computes the Loo norm of a C8VEC. The "indicator" vector: 1: 1-1i 2: 2-2i 3: 3-3i 4: 4-4i 5: 5-5i Loo norm = 7.07107 C8VEC_PRINT_TEST C8VEC_PRINT prints a C8VEC The "indicator" vector: 1: 1-1i 2: 2-2i 3: 3-3i 4: 4-4i 5: 5-5i C8VEC_PRINT_PART_TEST C8VEC_PRINT_PART prints part of a C8VEC Part of the vector: 1 1-1i 2 2-2i 3 3-3i 4 4-4i 5 5-5i 6 6-6i 7 7-7i 8 8-8i ...... .............. .............. 100 100-100i C8VEC_SORT_A_L1_TEST C8VEC_SORT_A_L1 sorts a C8VEC by L1 norm. The unsorted vector: 1: -0.48723+0.62753i 2: 0.16133+0.98538i 3: -0.63827-0.49503i 4: 0.39004+0.48489i 5: -0.13946+0.075405i 6: -0.065056-0.42411i 7: 0.33111-0.51062i 8: -0.77295-0.36983i 9: 0.40556-0.11127i 10: 0.45833-0.23506i I, A(I), ||A(I)|| 1 -0.13946+0.075405i 0.214865 2 -0.065056-0.42411i 0.489165 3 0.40556-0.11127i 0.51682 4 0.45833-0.23506i 0.693391 5 0.33111-0.51062i 0.841727 6 0.39004+0.48489i 0.874925 7 -0.48723+0.62753i 1.11476 8 -0.63827-0.49503i 1.13331 9 -0.77295-0.36983i 1.14278 10 0.16133+0.98538i 1.14671 C8VEC_SORT_A_L2_TEST C8VEC_SORT_A_L2 sorts a C8VEC by L2 norm. The unsorted vector: 1: -0.33146+0.3375i 2: -0.18839-0.22806i 3: 0.40808+0.1187i 4: -0.48871+0.69594i 5: -0.60584+0.54182i 6: 0.78474+0.10741i 7: 0.29806-0.90649i 8: 0.33356-0.79661i 9: -0.4585-0.41604i 10: -0.74513-0.14239i I, A(I), ||A(I)|| 1 -0.18839-0.22806i 0.295805 2 0.40808+0.1187i 0.42499 3 -0.33146+0.3375i 0.473044 4 -0.4585-0.41604i 0.619117 5 -0.74513-0.14239i 0.758614 6 0.78474+0.10741i 0.792052 7 -0.60584+0.54182i 0.812783 8 -0.48871+0.69594i 0.850396 9 0.33356-0.79661i 0.863625 10 0.29806-0.90649i 0.954238 C8VEC_SORT_A_LI_TEST C8VEC_SORT_A_LI sorts a C8VEC by Loo norm. The unsorted vector: 1: 0.004518+0.52445i 2: 0.093802+0.66546i 3: 0.89349-0.07821i 4: -0.16885-0.038483i 5: 0.094867-0.27942i 6: 0.90786+0.40612i 7: 0.96291+0.11046i 8: 0.17398-0.80844i 9: 0.54931-0.48208i 10: -0.66649-0.67439i I, A(I), ||A(I)|| 1 -0.16885-0.038483i 0.168852 2 0.094867-0.27942i 0.279423 3 0.004518+0.52445i 0.524451 4 0.54931-0.48208i 0.549307 5 0.093802+0.66546i 0.665462 6 -0.66649-0.67439i 0.674388 7 0.17398-0.80844i 0.808437 8 0.89349-0.07821i 0.893495 9 0.90786+0.40612i 0.907862 10 0.96291+0.11046i 0.962911 C8VEC_SPIRAL_TEST C8VEC_SPIRAL returns N points on a spiral which includes M complete turns. The spiral points: 1: 5 2: 4.1858+2.4167i 3: 2.3333+4.0415i 4: 2.7555e-16+4.5i 5: -2.1667+3.7528i 6: -3.6084+2.0833i 7: -4+4.8986e-16i 8: -3.3198-1.9167i 9: -1.8333-3.1754i 10: -6.4294e-16-3.5i 11: 1.6667-2.8868i 12: 2.7424-1.5833i 13: 3-7.3479e-16i C8VEC_UNIFORM_01_TEST C8VEC_UNIFORM_01_TEST returns a random C8VEC The random C8VEC: 1: 0.074607+0.36373i 2: 0.41213+0.11086i 3: -0.24333-0.21848i 4: -0.59151+0.76797i 5: 0.63771-0.062912i C8VEC_UNITY_TEST C8VEC_UNITY sets A to the N roots of unity The N roots of unity: 1: 1 2: 0.86603+0.5i 3: 0.5+0.86603i 4: 6.1232e-17+1i 5: -0.5+0.86603i 6: -0.86603+0.5i 7: -1+1.2246e-16i 8: -0.86603-0.5i 9: -0.5-0.86603i 10: -1.837e-16-1i 11: 0.5-0.86603i 12: 0.86603-0.5i CARTESIAN_TO_C8_TEST CARTESIAN_TO_C8 converts (X,Y) to C8. X1,Y1=R8_UNIFORM_01 C2=CARTESIAN_TO_C8(X1,Y1) X3,Y3=C8_TO_CARTESIAN(C2) ---------------------- ---------------------- ----------------------- 0.945579 0.676645 ( 0.945579 0.676645) 0.945579 0.676645 0.988302 0.766831 ( 0.988302 0.766831) 0.988302 0.766831 0.336699 0.662382 ( 0.336699 0.662382) 0.336699 0.662382 0.244165 0.295507 ( 0.244165 0.295507) 0.244165 0.295507 0.680178 0.527847 ( 0.680178 0.527847) 0.680178 0.527847 0.411594 0.602638 ( 0.411594 0.602638) 0.411594 0.602638 0.750520 0.583533 ( 0.750520 0.583533) 0.750520 0.583533 0.551793 0.583571 ( 0.551793 0.583571) 0.551793 0.583571 0.511820 0.082593 ( 0.511820 0.082593) 0.511820 0.082593 0.719570 0.996156 ( 0.719570 0.996156) 0.719570 0.996156 polar_to_c8_test(): POLAR_TO_C8 converts polar form to C8. (R1,T1)=R8_UNIFORM_01() C2=POLAR_TO_C8(R1,T1) (R3,T3)=C8_TO_POLAR(C2) ---------------------- ---------------------- ----------------------- 0.354534 6.102599 ( 0.348769 -0.063677) 0.354534 -0.180586 0.346449 5.570319 ( 0.262085 -0.226579) 0.346449 -0.712866 0.454695 2.597640 ( -0.389069 0.235315) 0.454695 2.597640 0.217732 0.789511 ( 0.153325 0.154592) 0.217732 0.789511 0.308915 4.562249 ( -0.046206 -0.305439) 0.308915 -1.720937 0.782872 4.359196 ( -0.270792 -0.734548) 0.782872 -1.923989 0.009802 5.298066 ( 0.005418 -0.008169) 0.009802 -0.985120 0.922332 4.844048 ( 0.121083 -0.914350) 0.922332 -1.439137 0.042660 2.376214 ( -0.030763 0.029555) 0.042660 2.376214 0.704340 4.583666 ( -0.090415 -0.698512) 0.704340 -1.699520 R8_SIGN_TEST R8_SIGN returns the sign of an R8. R8 R8_SIGN(R8) -1.250000 -1.000000 -0.250000 -1.000000 0.000000 1.000000 0.500000 1.000000 9.000000 1.000000 R8POLY2_ROOT_TEST R8POLY2_ROOT finds quadratic equation roots. A B C R1 R2 2.000000 -2.000000 -24.000000 4.000000 -3.000000 1.000000 -20.000000 100.000000 10.000000 10.000000 1.000000 -2.000000 10.000000 1.000000 1.000000 R8POLY3_ROOT_TEST R8POLY3_ROOT finds roots of cubic equations. Polynomial coefficients: A = 1.000000, B = -6.000000, C = 11.000000, D = -6.000000 Roots: 1.000000 3.000000 2.000000 Polynomial coefficients: A = 9.000000, B = -36.000000, C = 54.000000, D = -27.000000 Roots: 1.000000 1.500000 1.500000 Polynomial coefficients: A = 1.000000, B = -5.000000, C = 8.000000, D = -4.000000 Roots: 1.000000 2.000000 2.000000 Polynomial coefficients: A = 1.000000, B = -8.000000, C = 25.000000, D = -26.000000 Roots: 2.000000 3.000000 3.000000 R8POLY4_ROOT_TEST R8POLY4_ROOT finds roots of quartic equations. A = 1.000000 B = -10.000000 C = 35.000000 D = -50.000000 E = 24.000000 Roots: 4.000000 1.000000 3.000000 2.000000 A = 1.000000 B = -5.000000 C = 1.000000 D = 21.000000 E = -18.000000 Roots: 3.000000 3.000000 1.000000 -2.000000 A = 1.000000 B = -22.000000 C = 141.000000 D = -220.000000 E = 100.000000 Roots: 10.000000 10.000000 1.000000 1.000000 A = 1.000000 B = -16.000000 C = 72.000000 D = -128.000000 E = 80.000000 Roots: 10.000000 2.000000 2.000000 2.000000 A = 1.000000 B = -20.000000 C = 150.000000 D = -500.000000 E = 625.000000 Roots: 5.000000 5.000000 5.000000 5.000000 A = 1.000000 B = 2.000000 C = 1.000000 D = 8.000000 E = -12.000000 Roots: -0.000000 -0.000000 1.000000 -3.000000 A = 1.000000 B = 0.000000 C = 13.000000 D = 0.000000 E = 36.000000 Roots: 0.000000 0.000000 0.000000 -0.000000 C8LIB_TEST Normal end of execution. 07-Jan-2022 17:55:15