05-Dec-2018 21:28:22 C8LIB_TEST MATLAB version Test the C8LIB library. C8_ABS_TEST C8_ABS computes the absolute value of a C8. C1=C8_UNIFORM_01 R2=C8_ABS(C1) R3=ABS(C1)) --------------------- --------------------- --------------------- ( -0.287314 0.367424) 0.466422 0.466422 ( -0.567465 -0.797059) 0.978427 0.978427 ( 0.038567 -0.525981) 0.527393 0.527393 ( 0.007082 -0.188614) 0.188747 0.188747 ( 0.594470 -0.537153) 0.801204 0.801204 ( 0.193014 -0.675087) 0.702137 0.702137 ( 0.351515 -0.201470) 0.405158 0.405158 ( 0.258528 0.892305) 0.929002 0.929002 ( -0.632219 0.014884) 0.632394 0.632394 ( -0.607431 -0.407965) 0.731715 0.731715 C8_ACOS_TEST C8_ACOS computes the inverse cosine of a C8. C1=C8_UNIFORM_01 C2 = C8_ACOS(C1) C3 = C8_COS(C2) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( 1.842579 -0.372734) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( 2.010654 0.794610) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 1.536661 0.504600) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 1.563837 0.187518) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 1.041719 0.587792) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 1.410789 0.639362) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 1.219948 0.212927) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 1.378315 -0.815611) ( 0.258528 0.892305) ( -0.632219 0.014884) ( 2.255060 -0.019207) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( 2.148513 0.469554) ( -0.607431 -0.407965) 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) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( 0.372734 1.842579) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.794610 2.010654) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( -0.504600 1.536661) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( -0.187518 1.563837) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( -0.587792 1.041719) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( -0.639362 1.410789) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( -0.212927 1.219948) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.815611 1.378315) ( 0.258528 0.892305) ( -0.632219 0.014884) ( 0.019207 2.255060) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.469554 2.148513) ( -0.607431 -0.407965) C8_ADD_TEST C8_ADD computes the sum of two C8's. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 C3 = C1+C2 --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.854779 -0.429635) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.045649 -0.714595) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.787484 -1.212240) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.610043 0.690835) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -1.239650 -0.393081) ( -0.557291 -0.455610) ( -0.113356 -0.856649) ( -0.670647 -1.312258) ( -0.513617 0.268282) ( 0.099216 -0.946423) ( -0.414402 -0.678141) ( -0.738137 0.319551) ( 0.775767 -0.211283) ( 0.037630 0.108268) ( 0.337929 0.784052) ( 0.234194 0.389924) ( 0.572123 1.173976) ( 0.303308 -0.934921) ( -0.420641 -0.463573) ( -0.117333 -1.398495) C8_ARG_TEST C8_ARG computes the argument of a C8. C1=random ARG=C8_ARG(C1) -0.287314 0.367424 2.234446 -0.567465 -0.797059 4.093689 0.038567 -0.525981 4.785582 0.007082 -0.188614 4.749920 0.594470 -0.537153 5.548394 0.193014 -0.675087 4.990870 0.351515 -0.201470 5.762744 0.258528 0.892305 1.288788 -0.632219 0.014884 3.118054 -0.607431 -0.407965 3.733020 C8_ASIN_TEST C8_ASIN computes the inverse sine of a C8. C1=C8_UNIFORM_01 C2 = C8_ASIN(C1) C3 = C8_SIN(C2) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.271783 0.372734) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.439858 -0.794610) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.034136 -0.504600) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.006960 -0.187518) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.529077 -0.587792) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.160007 -0.639362) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.350848 -0.212927) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.192481 0.815611) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.684263 0.019207) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.577717 -0.469554) ( -0.607431 -0.407965) 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) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.302245 0.358914) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.684544 -0.695711) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.045313 -0.553234) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.007212 -0.189746) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.623497 -0.463797) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.252489 -0.713026) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.350776 -0.190837) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.432450 0.952575) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.596298 0.012581) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.608336 -0.349676) ( -0.607431 -0.407965) C8_ATAN_TEST C8_ATAN computes the inverse tangent of a C8. C1=C8_UNIFORM_01 C2 = C8_ATAN(C1) C3 = C8_TAN(C2) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.316720 0.349353) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.766603 -0.570037) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( -3.088367 -0.583083) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( -3.134249 -0.190889) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( -2.502459 -0.391387) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( -2.816216 -0.747767) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( -2.791941 -0.180516) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( -2.485658 0.959893) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.563845 0.010634) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.602766 -0.296054) ( -0.607431 -0.407965) 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) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.256291 0.377017) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.331110 2.369578) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.030211 2.656896) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.006839 2.955160) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.458118 2.517057) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.132282 2.535803) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.349630 2.916991) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.142503 0.747102) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.744716 0.024784) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.537357 2.615003) ( -0.607431 -0.407965) C8_CONJ_TEST C8_CONJ computes the complex conjugate of a C8. C1=C8_UNIFORM_01 C2 = C8_CONJ(C1) C3 = C8_CONJ(C2) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.287314 -0.367424) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.567465 0.797059) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.038567 0.525981) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.007082 0.188614) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.594470 0.537153) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.193014 0.675087) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.351515 0.201470) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.258528 -0.892305) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.632219 -0.014884) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.607431 0.407965) ( -0.607431 -0.407965) C8_COS_TEST C8_COS computes the cosine of a C8. C1=C8_UNIFORM_01 C2 = C8_COS(C1) C3 = C8_ACOS(C1) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( 1.024473 0.106478) ( 0.287314 -0.367424) ( -0.567465 -0.797059) ( 1.125616 -0.475241) ( 0.567465 0.797059) ( 0.038567 -0.525981) ( 1.140698 0.021229) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 1.017815 0.001344) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.950864 0.315521) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 1.213694 0.139557) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.957971 0.069840) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 1.377866 -0.259626) ( 0.258528 0.892305) ( -0.632219 0.014884) ( 0.806808 0.008796) ( 0.632219 -0.014884) ( -0.607431 -0.407965) ( 0.890402 -0.239363) ( 0.607431 0.407965) C8_COSH_TEST C8_COSH computes the hyperbolic cosine of a C8. C1=C8_UNIFORM_01 C2 = C8_COSH(C1) C3 = C8_ACOSH(C1) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( 0.972041 -0.104633) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( 0.814380 0.428048) ( 0.567465 0.797059) ( 0.038567 -0.525981) ( 0.865475 -0.019368) ( -0.038567 0.525981) ( 0.007082 -0.188614) ( 0.982290 -0.001328) ( -0.007082 0.188614) ( 0.594470 -0.537153) ( 1.015505 -0.322421) ( -0.594470 0.537153) ( 0.193014 -0.675087) ( 0.795239 -0.121378) ( -0.193014 0.675087) ( 0.351515 -0.201470) ( 1.040931 -0.071799) ( -0.351515 0.201470) ( 0.258528 0.892305) ( 0.648710 0.203519) ( 0.258528 0.892305) ( -0.632219 0.014884) ( 1.206463 -0.010049) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( 1.092547 0.256089) ( 0.607431 0.407965) 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 -0.287314 0.367424 0.570173 0.525675 0.092645 0.041390 -0.567465 -0.797059 0.739888 -0.661915 0.898802 -0.263624 0.038567 -0.525981 0.709342 -0.386780 -0.031952 0.143169 0.007082 -0.188614 0.500321 -0.280574 -0.000755 0.006682 0.594470 -0.537153 0.901063 -0.225220 -0.304492 -0.414494 0.193014 -0.675087 0.807609 -0.371141 -0.256704 0.232215 0.351515 -0.201470 0.728853 -0.127726 0.000630 -0.066505 0.258528 0.892305 0.887088 0.406404 -0.600248 -0.531545 -0.632219 0.014884 0.434993 0.739960 -0.252278 0.017845 -0.607431 -0.407965 0.594684 -0.677024 0.079169 -0.383683 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 --------------------- --------------------- --------------------- --------------------- 0.4499 -0.1267 -0.8432 -0.3443 -0.4047 0.3155 -0.4047 0.3155 0.5896 0.2601 0.3911 0.3234 1.2219 -0.3453 1.2219 -0.3453 -0.1395 -0.1561 -0.2361 0.0775 0.3374 0.7721 0.3374 0.7721 0.0186 -0.6332 0.8928 0.0103 0.0126 -0.7094 0.0126 -0.7094 -0.5605 0.7638 0.3064 0.0263 -1.6038 2.6307 -1.6038 2.6307 0.5008 -0.7799 0.3505 0.0166 1.3209 -2.2878 1.3209 -2.2878 0.4350 -0.2666 -0.2009 0.2707 -1.4040 -0.5646 -1.4040 -0.5646 -0.0975 0.9019 -0.7702 -0.3143 -0.3011 -1.0480 -0.3011 -1.0480 -0.8892 0.2657 -0.7799 -0.5512 0.5998 -0.7646 0.5998 -0.7646 0.0314 -0.4336 0.2491 0.5787 -0.6124 -0.3178 -0.6124 -0.3178 C8_DIV_R8_TEST C8_DIV_R8 computes C3 = C1 / R2. C1=C8_UNIFORM_01 R2=R8_UNIFORM_01 C3=C8_DIV_R8(C1,R2) C4=C1/R2 --------------------- --------------------- --------------------- --------------------- 0.4499 -0.1267 0.8295 0.5423 -0.1527 0.5423 -0.1527 -0.8432 -0.3443 0.4153 -2.0303 -0.8290 -2.0303 -0.8290 0.5896 0.2601 0.2576 2.2891 1.0098 2.2891 1.0098 0.3911 0.3234 0.0438 8.9242 7.3787 8.9242 7.3787 -0.1395 -0.1561 0.0617 -2.2594 -2.5294 -2.2594 -2.5294 -0.2361 0.0775 0.4013 -0.5882 0.1930 -0.5882 0.1930 0.0186 -0.6332 0.7973 0.0233 -0.7942 0.0233 -0.7942 0.8928 0.0103 0.8975 0.9948 0.0115 0.9948 0.0115 -0.5605 0.7638 0.0945 -5.9280 8.0787 -5.9280 8.0787 0.3064 0.0263 0.8591 0.3566 0.0306 0.3566 0.0306 C8_EXP_TEST C8_EXP computes the exponential of a C8. C1=C8_UNIFORM_01 C2=C8_EXP(C1) C3=C8_LOG(C2)) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( 0.700200 0.269508) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( 0.396200 -0.405549) ( -0.567465 5.486127) ( 0.038567 -0.525981) ( 0.898837 -0.521803) ( 0.038567 5.757204) ( 0.007082 -0.188614) ( 0.989246 -0.188830) ( 0.007082 6.094571) ( 0.594470 -0.537153) ( 1.556874 -0.927222) ( 0.594470 5.746032) ( 0.193014 -0.675087) ( 0.946854 -0.758020) ( 0.193014 5.608099) ( 0.351515 -0.201470) ( 1.392473 -0.284400) ( 0.351515 6.081715) ( 0.258528 0.892305) ( 0.812781 1.008202) ( 0.258528 0.892305) ( -0.632219 0.014884) ( 0.531352 0.007909) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( 0.500041 -0.216125) ( -0.607431 5.875220) 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)) --------------------- --------------------- --------------------- ( -0.287314 0.367424) 0.367424 0.367424 ( -0.567465 -0.797059) -0.797059 -0.797059 ( 0.038567 -0.525981) -0.525981 -0.525981 ( 0.007082 -0.188614) -0.188614 -0.188614 ( 0.594470 -0.537153) -0.537153 -0.537153 ( 0.193014 -0.675087) -0.675087 -0.675087 ( 0.351515 -0.201470) -0.201470 -0.201470 ( 0.258528 0.892305) 0.892305 0.892305 ( -0.632219 0.014884) 0.014884 0.014884 ( -0.607431 -0.407965) -0.407965 -0.407965 C8_INV_TEST C8_INV computes the inverse of a C8. C1=C8_UNIFORM_01 C2 = C8_INV(C1) C3 = C8_INV(C2) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -1.320683 -1.688920) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.592765 0.832595) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.138659 1.891041) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.198796 5.294369) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.926069 0.836781) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.391513 1.369354) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 2.141387 1.227331) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.299553 -1.033903) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -1.580854 -0.037218) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -1.134520 0.761971) ( -0.607431 -0.407965) 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) --------------------- --------------------- --------------------- 0.4499, -0.1267 -0.8432, -0.3443 1 0.5896, 0.2601 0.3911, 0.3234 0 -0.1395, -0.1561 -0.2361, 0.0775 1 0.0186, -0.6332 0.8928, 0.0103 1 -0.5605, 0.7638 0.3064, 0.0263 0 0.5008, -0.7799 0.3505, 0.0166 0 0.4350, -0.2666 -0.2009, 0.2707 0 -0.0975, 0.9019 -0.7702, -0.3143 1 -0.8892, 0.2657 -0.7799, -0.5512 1 0.0314, -0.4336 0.2491, 0.5787 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) --------------------- --------------------- --------------------- 0.4499, -0.1267 -0.8432, -0.3443 1 0.5896, 0.2601 0.3911, 0.3234 0 -0.1395, -0.1561 -0.2361, 0.0775 1 0.0186, -0.6332 0.8928, 0.0103 1 -0.5605, 0.7638 0.3064, 0.0263 0 0.5008, -0.7799 0.3505, 0.0166 0 0.4350, -0.2666 -0.2009, 0.2707 0 -0.0975, 0.9019 -0.7702, -0.3143 0 -0.8892, 0.2657 -0.7799, -0.5512 1 0.0314, -0.4336 0.2491, 0.5787 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) --------------------- --------------------- --------------------- 0.4499, -0.1267 -0.8432, -0.3443 1 0.5896, 0.2601 0.3911, 0.3234 0 -0.1395, -0.1561 -0.2361, 0.0775 1 0.0186, -0.6332 0.8928, 0.0103 1 -0.5605, 0.7638 0.3064, 0.0263 0 0.5008, -0.7799 0.3505, 0.0166 0 0.4350, -0.2666 -0.2009, 0.2707 0 -0.0975, 0.9019 -0.7702, -0.3143 0 -0.8892, 0.2657 -0.7799, -0.5512 0 0.0314, -0.4336 0.2491, 0.5787 1 C8_LOG_TEST C8_LOG computes the logarithm of a C8. C1=C8_UNIFORM_01 C2=C8_LOG(C1) C3=C8_EXP(C2)) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.762664 2.234446) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.021810 4.093689) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( -0.639809 4.785582) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( -1.667348 4.749920) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( -0.221640 5.548394) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( -0.353626 4.990870) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( -0.903479 5.762744) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( -0.073644 1.288788) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.458242 3.118054) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.312364 3.733020) ( -0.607431 -0.407965) C8_MAG_TEST C8_MAG computes the magnitude of a C8. C1=C8_UNIFORM_01 R2=C8_MAG(C1) R3=ABS(C1)) --------------------- --------------------- --------------------- ( -0.287314 0.367424) 0.466422 0.466422 ( -0.567465 -0.797059) 0.978427 0.978427 ( 0.038567 -0.525981) 0.527393 0.527393 ( 0.007082 -0.188614) 0.188747 0.188747 ( 0.594470 -0.537153) 0.801204 0.801204 ( 0.193014 -0.675087) 0.702137 0.702137 ( 0.351515 -0.201470) 0.405158 0.405158 ( 0.258528 0.892305) 0.929002 0.929002 ( -0.632219 0.014884) 0.632394 0.632394 ( -0.607431 -0.407965) 0.731715 0.731715 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 --------------------- --------------------- --------------------- --------------------- 0.4499 -0.1267 -0.8432 -0.3443 -0.4229 -0.0481 -0.4229 -0.0481 0.5896 0.2601 0.3911 0.3234 0.1465 0.2924 0.1465 0.2924 -0.1395 -0.1561 -0.2361 0.0775 0.0450 0.0261 0.0450 0.0261 0.0186 -0.6332 0.8928 0.0103 0.0231 -0.5652 0.0231 -0.5652 -0.5605 0.7638 0.3064 0.0263 -0.1918 0.2193 -0.1918 0.2193 0.5008 -0.7799 0.3505 0.0166 0.1884 -0.2651 0.1884 -0.2651 0.4350 -0.2666 -0.2009 0.2707 -0.0152 0.1713 -0.0152 0.1713 -0.0975 0.9019 -0.7702 -0.3143 0.3585 -0.6640 0.3585 -0.6640 -0.8892 0.2657 -0.7799 -0.5512 0.8399 0.2829 0.8399 0.2829 0.0314 -0.4336 0.2491 0.5787 0.2587 -0.0898 0.2587 -0.0898 C8_NINT_TEST C8_NINT computes the nearest integer to a C8. C1=10*C8_UNIFORM_01 C2=C8_NINT(C1) --------------------- --------------------- ( -2.873141 3.674237) ( -3.000000 4.000000) ( -5.674647 -7.970585) ( -6.000000 -8.000000) ( 0.385671 -5.259813) ( 0.000000 -5.000000) ( 0.070822 -1.886140) ( 0.000000 -2.000000) ( 5.944697 -5.371534) ( 6.000000 -5.000000) ( 1.930145 -6.750867) ( 2.000000 -7.000000) ( 3.515149 -2.014700) ( 4.000000 -2.000000) ( 2.585280 8.923053) ( 3.000000 9.000000) ( -6.322190 0.148845) ( -6.000000 0.000000) ( -6.074306 -4.079652) ( -6.000000 -4.000000) C8_NORM_L1_TEST C8_NORM_L1 computes the L1 norm of a C8. C1=C8_UNIFORM_01 R2=C8_NORM_L1(C1) --------------------- --------------------- 0.449860, -0.126667 0.576527 -0.843197, -0.344280 1.187477 0.589627, 0.260090 0.849717 0.391140, 0.323400 0.714540 -0.139466, -0.156136 0.295601 -0.236066, 0.077459 0.313526 0.018599, -0.633214 0.651814 0.892850, 0.010314 0.903163 -0.560465, 0.763795 1.324260 0.306357, 0.026275 0.332632 C8_NORM_L2_TEST C8_NORM_L2 computes the L2 norm of a C8. C1=C8_UNIFORM_01 R2=C8_NORM_L2(C1) --------------------- --------------------- 0.449860, -0.126667 0.467352 -0.843197, -0.344280 0.910774 0.589627, 0.260090 0.644443 0.391140, 0.323400 0.507521 -0.139466, -0.156136 0.209354 -0.236066, 0.077459 0.248450 0.018599, -0.633214 0.633487 0.892850, 0.010314 0.892909 -0.560465, 0.763795 0.947367 0.306357, 0.026275 0.307481 C8_NORM_LI_TEST C8_NORM_LI computes the Loo norm of a C8. C1=C8_UNIFORM_01 R2=C8_NORM_LI(C1) --------------------- --------------------- 0.449860, -0.126667 0.449860 -0.843197, -0.344280 0.843197 0.589627, 0.260090 0.589627 0.391140, 0.323400 0.391140 -0.139466, -0.156136 0.156136 -0.236066, 0.077459 0.236066 0.018599, -0.633214 0.633214 0.892850, 0.010314 0.892850 -0.560465, 0.763795 0.763795 0.306357, 0.026275 0.306357 C8_NORMAL_01_TEST C8_NORMAL_01 generates unit pseudonormal complex values. Using initial random number seed = 123456789 1.679040 -0.472769 -0.566060 -0.231124 1.212934 0.535037 1.269381 1.049543 -1.666087 -1.865228 -2.242464 0.735809 0.039675 -1.350736 0.673068 0.007775 -0.275127 0.374940 2.164005 0.185600 0.297785 -0.463758 2.044536 0.096577 1.398819 -0.857394 -1.242985 1.674516 -0.067084 0.620783 -0.794396 -0.324163 -0.523768 0.156483 -0.350567 -0.247757 0.131700 -1.820756 0.537380 1.248567 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)) --------------------- --------------------- --------------------- ( -0.287314 0.367424) -0.287314 -0.287314 ( -0.567465 -0.797059) -0.567465 -0.567465 ( 0.038567 -0.525981) 0.038567 0.038567 ( 0.007082 -0.188614) 0.007082 0.007082 ( 0.594470 -0.537153) 0.594470 0.594470 ( 0.193014 -0.675087) 0.193014 0.193014 ( 0.351515 -0.201470) 0.351515 0.351515 ( 0.258528 0.892305) 0.258528 0.258528 ( -0.632219 0.014884) -0.632219 -0.632219 ( -0.607431 -0.407965) -0.607431 -0.607431 C8_SIN_TEST C8_SIN computes the sine of a C8. C1=C8_UNIFORM_01 C2 = C8_SIN(C1) C3 = C8_ASIN(C1) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.302722 0.360344) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.717465 -0.745596) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.044015 -0.550162) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.007208 -0.189730) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.642831 -0.466713) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.237214 -0.714035) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.351332 -0.190433) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.364371 0.981771) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.591002 0.012008) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.618919 -0.344357) ( -0.607431 -0.407965) C8_SINH_TEST C8_SINH computes the hyperbolic sine of a C8. C1=C8_UNIFORM_01 C2 = C8_SINH(C1) C3 = C8_ASINH(C1) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.271842 0.374141) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.418180 -0.833597) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.033362 -0.502435) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.006957 -0.187502) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.541369 -0.604801) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.151615 -0.636643) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.351542 -0.212601) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.164071 0.804683) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.675110 0.017959) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.592505 -0.472214) ( -0.607431 -0.407965) C8_SQRT_TEST C8_SQRT computes the principal square root of a C8. C1=random C2=C8_SQRT(C1) C3=C2*C2 -0.287314 0.367424 0.299256 0.613896 -0.052451 -0.211132 -0.567465 -0.797059 -0.453300 0.879173 -0.313286 0.904605 0.038567 -0.525981 -0.531959 0.494382 -0.275169 -0.040571 0.007082 -0.188614 -0.312913 0.301384 -0.035525 -0.002672 0.594470 -0.537153 -0.835366 0.321508 0.064860 -0.638643 0.193014 -0.675087 -0.669011 0.504541 -0.418487 -0.260603 0.351515 -0.201470 -0.615091 0.163773 0.082973 -0.141639 0.258528 0.892305 0.770562 0.578997 -0.729372 0.461372 -0.632219 0.014884 0.009359 0.795177 0.399479 -0.018821 -0.607431 -0.407965 -0.249284 0.818274 0.202536 0.495621 C8_SUB_TEST C8_SUB computes the difference of two C8's. C1=C8_UNIFORM_01 C2=C8_UNIFORM_01 C3 = C1-C2 --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.567465 -0.797059) ( 0.280151 1.164482) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.031485 -0.337367) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.401455 0.137933) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( 0.092987 -1.093775) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.024788 0.422850) ( -0.557291 -0.455610) ( -0.113356 -0.856649) ( -0.443935 0.401039) ( -0.513617 0.268282) ( 0.099216 -0.946423) ( -0.612833 1.214706) ( -0.738137 0.319551) ( 0.775767 -0.211283) ( -1.513903 0.530834) ( 0.337929 0.784052) ( 0.234194 0.389924) ( 0.103735 0.394128) ( 0.303308 -0.934921) ( -0.420641 -0.463573) ( 0.723948 -0.471348) C8_TAN_TEST C8_TAN computes the tangent of a C8. C1=C8_UNIFORM_01 C2 = C8_TAN(C1) C3 = C8_ATAN(C1) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.256165 0.378361) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.303612 -0.790576) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.029600 -0.482854) ( -3.103026 -0.525981) ( 0.007082 -0.188614) ( 0.006836 -0.186418) ( -3.134510 -0.188614) ( 0.594470 -0.537153) ( 0.462278 -0.644226) ( -2.547123 -0.537153) ( 0.193014 -0.675087) ( 0.126132 -0.602819) ( -2.948578 -0.675087) ( 0.351515 -0.201470) ( 0.350391 -0.224333) ( -2.790078 -0.201470) ( 0.258528 0.892305) ( 0.125723 0.736220) ( -2.883065 0.892305) ( -0.632219 0.014884) ( -0.732270 0.022867) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.551294 -0.534946) ( -0.607431 -0.407965) C8_TANH_TEST C8_TANH computes the hyperbolic sine of a C8. C1=C8_UNIFORM_01 C2 = C8_TANH(C1) C3 = C8_ATANH(C1) --------------------- --------------------- --------------------- ( -0.287314 0.367424) ( -0.317415 0.350735) ( -0.287314 0.367424) ( -0.567465 -0.797059) ( -0.823894 -0.590548) ( -0.567465 2.344534) ( 0.038567 -0.525981) ( 0.051514 -0.579379) ( 0.038567 2.615611) ( 0.007082 -0.188614) ( 0.007340 -0.190873) ( 0.007082 2.952979) ( 0.594470 -0.537153) ( 0.656060 -0.387269) ( 0.594470 2.604439) ( 0.193014 -0.675087) ( 0.305722 -0.753905) ( 0.193014 2.466506) ( 0.351515 -0.201470) ( 0.350140 -0.180090) ( 0.351515 2.940123) ( 0.258528 0.892305) ( 0.584544 1.057047) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.559663 0.010224) ( -0.632219 0.014884) ( -0.607431 -0.407965) ( -0.610105 -0.289208) ( -0.607431 2.733627) 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) ---------------------- ---------------------- ----------------------- ( 0.449860 -0.126667) 0.449860 -0.126667 ( 0.449860 -0.126667) ( -0.843197 -0.344280) -0.843197 -0.344280 ( -0.843197 -0.344280) ( 0.589627 0.260090) 0.589627 0.260090 ( 0.589627 0.260090) ( 0.391140 0.323400) 0.391140 0.323400 ( 0.391140 0.323400) ( -0.139466 -0.156136) -0.139466 -0.156136 ( -0.139466 -0.156136) ( -0.236066 0.077459) -0.236066 0.077459 ( -0.236066 0.077459) ( 0.018599 -0.633214) 0.018599 -0.633214 ( 0.018599 -0.633214) ( 0.892850 0.010314) 0.892850 0.010314 ( 0.892850 0.010314) ( -0.560465 0.763795) -0.560465 0.763795 ( -0.560465 0.763795) ( 0.306357 0.026275) 0.306357 0.026275 ( 0.306357 0.026275) 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) ---------------------- ---------------------- ----------------------- ( 0.449860 -0.126667) 0.467352 6.008721 ( 0.449860 -0.126667) ( -0.843197 -0.344280) 0.910774 3.529237 ( -0.843197 -0.344280) ( 0.589627 0.260090) 0.644443 0.415436 ( 0.589627 0.260090) ( 0.391140 0.323400) 0.507521 0.690879 ( 0.391140 0.323400) ( -0.139466 -0.156136) 0.209354 3.983324 ( -0.139466 -0.156136) ( -0.236066 0.077459) 0.248450 2.824537 ( -0.236066 0.077459) ( 0.018599 -0.633214) 0.633487 4.741753 ( 0.018599 -0.633214) ( 0.892850 0.010314) 0.892909 0.011551 ( 0.892850 0.010314) ( -0.560465 0.763795) 0.947367 2.203842 ( -0.560465 0.763795) ( 0.306357 0.026275) 0.307481 0.085557 ( 0.306357 0.026275) C8_UNIFORM_01_TEST C8_UNIFORM_01 returns a uniformly random "unit" C8. C1=C8_UNIFORM_01 --------------------- ( -0.287314 0.367424) ( -0.567465 -0.797059) ( 0.038567 -0.525981) ( 0.007082 -0.188614) ( 0.594470 -0.537153) ( 0.193014 -0.675087) ( 0.351515 -0.201470) ( 0.258528 0.892305) ( -0.632219 0.014884) ( -0.607431 -0.407965) 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: 0.449860 -0.126667 -0.236066 0.077459 0.500804 -0.779931 -0.770245 -0.314307 2: -0.843197 -0.344280 0.018599 -0.633214 0.350471 0.016555 -0.889181 0.265655 3: 0.589627 0.260090 0.892850 0.010314 0.434989 -0.266623 -0.779871 -0.551160 4: 0.391140 0.323400 -0.560465 0.763795 -0.200947 0.270711 0.031360 -0.433556 5: -0.139466 -0.156136 0.306357 0.026275 -0.097460 0.901881 0.249089 0.578743 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: 2.6293+0.71624i 2: -3.1831-4.251i 3: 2.1679+3.0693i 4: 0.9855+2.7904i 5: -0.22892-1.1991i The rounded vector: 1: 3+1i 2: -3-4i 3: 2+3i 4: 1+3i 5: 0-1i 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: 0.44986-0.12667i 2: -0.8432-0.34428i 3: 0.58963+0.26009i 4: 0.39114+0.3234i 5: -0.13947-0.15614i 6: -0.23607+0.077459i 7: 0.018599-0.63321i 8: 0.89285+0.010314i 9: -0.56047+0.7638i 10: 0.30636+0.026275i I, A(I), ||A(I)|| 1 -0.13947-0.15614i 0.295601 2 -0.23607+0.077459i 0.313526 3 0.30636+0.026275i 0.332632 4 0.44986-0.12667i 0.576527 5 0.018599-0.63321i 0.651814 6 0.39114+0.3234i 0.71454 7 0.58963+0.26009i 0.849717 8 0.89285+0.010314i 0.903163 9 -0.8432-0.34428i 1.18748 10 -0.56047+0.7638i 1.32426 C8VEC_SORT_A_L2_TEST C8VEC_SORT_A_L2 sorts a C8VEC by L2 norm. The unsorted vector: 1: 0.44986-0.12667i 2: -0.8432-0.34428i 3: 0.58963+0.26009i 4: 0.39114+0.3234i 5: -0.13947-0.15614i 6: -0.23607+0.077459i 7: 0.018599-0.63321i 8: 0.89285+0.010314i 9: -0.56047+0.7638i 10: 0.30636+0.026275i I, A(I), ||A(I)|| 1 -0.13947-0.15614i 0.209354 2 -0.23607+0.077459i 0.24845 3 0.30636+0.026275i 0.307481 4 0.44986-0.12667i 0.467352 5 0.39114+0.3234i 0.507521 6 0.018599-0.63321i 0.633487 7 0.58963+0.26009i 0.644443 8 0.89285+0.010314i 0.892909 9 -0.8432-0.34428i 0.910774 10 -0.56047+0.7638i 0.947367 C8VEC_SORT_A_LI_TEST C8VEC_SORT_A_LI sorts a C8VEC by Loo norm. The unsorted vector: 1: 0.44986-0.12667i 2: -0.8432-0.34428i 3: 0.58963+0.26009i 4: 0.39114+0.3234i 5: -0.13947-0.15614i 6: -0.23607+0.077459i 7: 0.018599-0.63321i 8: 0.89285+0.010314i 9: -0.56047+0.7638i 10: 0.30636+0.026275i I, A(I), ||A(I)|| 1 -0.13947-0.15614i 0.156136 2 -0.23607+0.077459i 0.236066 3 0.30636+0.026275i 0.306357 4 0.39114+0.3234i 0.39114 5 0.44986-0.12667i 0.44986 6 0.58963+0.26009i 0.589627 7 0.018599-0.63321i 0.633214 8 -0.56047+0.7638i 0.763795 9 -0.8432-0.34428i 0.843197 10 0.89285+0.010314i 0.89285 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: 0.44986-0.12667i 2: -0.8432-0.34428i 3: 0.58963+0.26009i 4: 0.39114+0.3234i 5: -0.13947-0.15614i 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) ---------------------- ---------------------- ----------------------- 0.218418 0.956318 ( 0.218418 0.956318) 0.218418 0.956318 0.829509 0.561695 ( 0.829509 0.561695) 0.829509 0.561695 0.415307 0.066119 ( 0.415307 0.066119) 0.415307 0.066119 0.257578 0.109957 ( 0.257578 0.109957) 0.257578 0.109957 0.043829 0.633966 ( 0.043829 0.633966) 0.043829 0.633966 0.061727 0.449539 ( 0.061727 0.449539) 0.061727 0.449539 0.401306 0.754673 ( 0.401306 0.754673) 0.401306 0.754673 0.797287 0.001838 ( 0.797287 0.001838) 0.797287 0.001838 0.897504 0.350752 ( 0.897504 0.350752) 0.897504 0.350752 0.094545 0.013617 ( 0.094545 0.013617) 0.094545 0.013617 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) ---------------------- ---------------------- ----------------------- 0.218418 6.008721 ( 0.210243 -0.059198) 0.218418 6.008721 0.829509 3.529237 ( -0.767962 -0.313561) 0.829509 3.529237 0.415307 0.415436 ( 0.379981 0.167613) 0.415307 0.415436 0.257578 0.690879 ( 0.198512 0.164132) 0.257578 0.690879 0.043829 3.983324 ( -0.029198 -0.032688) 0.043829 3.983324 0.061727 2.824537 ( -0.058651 0.019245) 0.061727 2.824537 0.401306 4.741753 ( 0.011782 -0.401133) 0.401306 4.741753 0.797287 0.011551 ( 0.797234 0.009209) 0.797287 0.011551 0.897504 2.203842 ( -0.530966 0.723594) 0.897504 2.203842 0.094545 0.085557 ( 0.094199 0.008079) 0.094545 0.085557 R8_ATAN_TEST R8_ATAN computes the arc-tangent given Y and X; ATAN2 is the system version of this routine. X Y ATAN2(Y,X) R8_ATAN(Y,X) 1.000000 0.000000 0.000000 0.000000 1.000000 1.000000 0.785398 0.785398 0.000000 1.000000 1.570796 1.570796 -1.000000 1.000000 2.356194 2.356194 -1.000000 0.000000 3.141593 3.141593 -1.000000 -1.000000 -2.356194 3.926991 0.000000 -1.000000 -1.570796 4.712389 1.000000 -1.000000 -0.785398 5.497787 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 R8_UNIFORM_01_TEST R8_UNIFORM_01 produces a sequence of random values. Using random seed 123456789 SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 Verify that the sequence can be restarted. Set the seed back to its original value, and see that we generate the same sequence. SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 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. 05-Dec-2018 21:28:22