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Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -8,22 +8,37 @@ #define TYPE float #define SUFFIX f #define EPS FLT_EPSILON #define CLOSE_ATOL 3 #define CLOSE_RTOL 1e-5 #define FMT "%.8e" #define NPY_PI_2 1.570796326794896619231321691639751442f #define NPY_PI 3.141592653589793238462643383279502884f #define NPY_LOG2E 1.442695040888963407359924681001892137f #define NPY_SQRT2 1.414213562373095048801688724209698079f #else #ifdef DOUBLE #define TYPE double #define SUFFIX #define EPS DBL_EPSILON #define CLOSE_ATOL 0 #define CLOSE_RTOL 1e-12 #define FMT "%.16e" #define NPY_PI_2 1.570796326794896619231321691639751442 #define NPY_PI 3.141592653589793238462643383279502884 #define NPY_LOG2E 1.442695040888963407359924681001892137 #define NPY_SQRT2 1.414213562373095048801688724209698079 #else #ifdef LONGDOUBLE #define TYPE long double #define SUFFIX l #define EPS 50*LDBL_EPSILON #define CLOSE_ATOL 0 #define CLOSE_RTOL 1e-12 #define FMT "%.18Le" #define NPY_PI_2 1.570796326794896619231321691639751442L #define NPY_PI 3.141592653589793238462643383279502884L #define NPY_LOG2E 1.442695040888963407359924681001892137L #define NPY_SQRT2 1.414213562373095048801688724209698079L #else #error "Define FLOAT or DOUBLE or LONGDOUBLE" #endif @@ -39,127 +54,191 @@ const TYPE NZERO = -1.0 * 0.0; #define ADDSUFFIX_INT(A, B) CONCAT(A, B) #define ADDSUFFIX(A) ADDSUFFIX_INT(A, SUFFIX) #define TEST_PRINTF(func, xr, xi, er, ei, rr, ri) \ printf("%d: " STRINGIZE(func) STRINGIZE(SUFFIX) "(" FMT " + " FMT "j): " \ "expected: " FMT " + " FMT "j: received: " FMT " + " FMT "j\n", \ __LINE__, xr, xi, er, ei, rr, ri) #define TEST_INT(func, xr, xi, er, ei, rtest, itest) \ do { \ TYPE dxr = xr; \ TYPE dxi = xi; \ TYPE der = er; \ TYPE dei = ei; \ TYPE complex x = cpack(dxr, dxi); \ TYPE complex r = ADDSUFFIX(func)(x); \ TYPE rr = ADDSUFFIX(creal)(r); \ TYPE ri = ADDSUFFIX(cimag)(r); \ if (!(rtest(rr, der) && itest(ri, dei))) { \ ret = 0; \ TEST_PRINTF(func, dxr, dxi, der, dei, rr, ri); \ } \ } \ while(0) #define TEST_EE(func, xr, xi, er, ei) \ TEST_INT(func, xr, xi, er, ei, isequal, isequal) #define TEST_EC(func, xr, xi, er, ei) \ TEST_INT(func, xr, xi, er, ei, isequal, isclose) #define TEST_CE(func, xr, xi, er, ei) \ TEST_INT(func, xr, xi, er, ei, isclose, isequal) #define TEST_CC(func, xr, xi, er, ei) \ TEST_INT(func, xr, xi, er, ei, isclose, isclose) #define TEST_UNSPECIFIED2(func, xr, xi, er1, ei1, er2, ei2) \ do { \ TYPE dxr = xr; \ TYPE dxi = xi; \ TYPE der1 = er1; \ TYPE dei1 = ei1; \ TYPE der2 = er2; \ TYPE dei2 = ei2; \ TYPE complex x = cpack(dxr, dxi); \ TYPE complex r = ADDSUFFIX(func)(x); \ TYPE rr = ADDSUFFIX(creal)(r); \ TYPE ri = ADDSUFFIX(cimag)(r); \ if (!((isequal(rr, der1) && isequal(ri, dei1)) || \ (isequal(rr, der2) && isequal(ri, dei2)))) { \ ret = 0; \ TEST_PRINTF(func, dxr, dxi, der1, dei1, rr, ri); \ printf("or"); \ TEST_PRINTF(func, dxr, dxi, der2, dei2, rr, ri); \ } \ } \ while(0) #define TEST_UNSPECIFIED4(func, xr, xi, er1, ei1, er2, ei2, er3, ei3, er4, ei4)\ do { \ TYPE dxr = xr; \ TYPE dxi = xi; \ TYPE der1 = er1; \ TYPE dei1 = ei1; \ TYPE der2 = er2; \ TYPE dei2 = ei2; \ TYPE der3 = er3; \ TYPE dei3 = ei3; \ TYPE der4 = er4; \ TYPE dei4 = ei4; \ TYPE complex x = cpack(dxr, dxi); \ TYPE complex r = func(x); \ TYPE rr = ADDSUFFIX(creal)(r); \ TYPE ri = ADDSUFFIX(cimag)(r); \ if (!((isequal(rr, der1) && isequal(ri, dei1)) || \ (isequal(rr, der2) && isequal(ri, dei2)) || \ (isequal(rr, der3) && isequal(ri, dei3)) || \ (isequal(rr, der4) && isequal(ri, dei4)))) { \ ret = 0; \ TEST_PRINTF(func, dxr, dxi, der1, dei1, rr, ri); \ printf("or"); \ TEST_PRINTF(func, dxr, dxi, der2, dei2, rr, ri); \ printf("or"); \ TEST_PRINTF(func, dxr, dxi, der3, dei3, rr, ri); \ printf("or"); \ TEST_PRINTF(func, dxr, dxi, der4, dei4, rr, ri); \ } \ } \ while(0) #define TEST_CPOW_INT(xr, xi, yr, yi, er, ei, test) \ do { \ TYPE dxr = xr; \ TYPE dxi = xi; \ TYPE dyr = yr; \ TYPE dyi = yi; \ TYPE der = er; \ TYPE dei = ei; \ TYPE complex x = cpack(xr, xi); \ TYPE complex y = cpack(yr, yi); \ TYPE complex r = ADDSUFFIX(cpow)(x, y); \ TYPE rr = ADDSUFFIX(creal)(r); \ TYPE ri = ADDSUFFIX(cimag)(r); \ if (!(test(rr, der) && test(ri, dei))) { \ ret = 0; \ printf("%d: " STRINGIZE(cpow) STRINGIZE(SUFFIX) "(" FMT " + " FMT \ "j, " FMT " + " FMT "j): expected: " FMT " + " FMT \ "j: received: " FMT " + " FMT "j\n", __LINE__, dxr, dxi, \ dyr, dyi, der, dei, rr, ri); \ } \ } \ while(0) #define TEST_CPOW_EE(xr, xi, yr, yi, er, ei) \ TEST_CPOW_INT(xr, xi, yr, yi, er, ei, isequal) #define TEST_CPOW_CC(xr, xi, yr, yi, er, ei) \ TEST_CPOW_INT(xr, xi, yr, yi, er, ei, isclose) #define TEST_RAISES(func, xr, xi, er, ei, fpe) \ do { \ int except; \ TYPE dxr = xr; \ TYPE dxi = xi; \ TYPE der = er; \ TYPE dei = ei; \ TYPE complex r; \ TYPE complex x = cpack(xr, xi); \ TYPE rr, ri; \ feclearexcept(FE_ALL_EXCEPT); \ r = ADDSUFFIX(func)(x); \ except = fetestexcept(fpe); \ rr = ADDSUFFIX(creal)(r); \ ri = ADDSUFFIX(cimag)(r); \ if (!(except & fpe && isequal(rr, der) && isequal(ri, dei))) { \ ret = 0; \ TEST_PRINTF(func, dxr, dxi, der, dei, rr, ri); \ } \ } \ while(0) #define TEST_RAISES_UNSPECIFIED2(func, xr, xi, er1, ei1, er2, ei2, fpe) \ do { \ int except; \ TYPE dxr = xr; \ TYPE dxi = xi; \ TYPE der1 = er1; \ TYPE dei1 = ei1; \ TYPE der2 = er2; \ TYPE dei2 = ei2; \ TYPE complex r; \ TYPE complex x = cpack(xr, xi); \ TYPE rr, ri; \ feclearexcept(FE_ALL_EXCEPT); \ r = ADDSUFFIX(func)(x); \ except = fetestexcept(fpe); \ rr = ADDSUFFIX(creal)(r); \ ri = ADDSUFFIX(cimag)(r); \ if (!(except & fpe && ((isequal(rr, der1) && isequal(ri, dei1)) \ || (isequal(rr, der2) && isequal(ri, dei2))))) {\ ret = 0; \ TEST_PRINTF(func, dxr, dxi, der1, dei1, rr, ri); \ printf("or"); \ TEST_PRINTF(func, dxr, dxi, der2, dei2, rr, ri); \ } \ } \ while(0) #define TEST_BRANCH_CUT(func, xr, xi, dxr, dxi, rsign, isign, cksignzero) \ do { \ TYPE vxr = xr; \ TYPE vxi = xi; \ TYPE vdxr = dxr; \ TYPE vdxi = dxi; \ int vrsign = rsign; \ int visign = isign; \ int vcksignzero = cksignzero; \ TYPE complex x = cpack(vxr, vxi); \ TYPE complex dx = cpack(vdxr, vdxi); \ int q = check_branch_cut(ADDSUFFIX(func), x, dx, \ vrsign, visign, vcksignzero); \ if (!q) { \ ret = 0; \ printf(STRINGIZE(func) STRINGIZE(SUFFIX) ": branch cut failure: " \ "x = " FMT " + " FMT "j, dx = " FMT " + " FMT "j, rsign = %d, " \ "isign = %d, check_sign_zero = %d\n", vxr, vxi, \ vdxr, vdxi, vrsign, visign, vcksignzero); \ } \ } \ while(0) @@ -193,34 +272,32 @@ int isclose(TYPE a, TYPE b) const TYPE atol = CLOSE_ATOL; const TYPE rtol = CLOSE_RTOL; if (isfinite(a) && isfinite(b)) { return (ADDSUFFIX(fabs)(a - b) <= (atol + rtol*ADDSUFFIX(fabs)(b))); } return 0; } int isequal(TYPE a, TYPE b) { if (isfinite(a) && isfinite(b)) { if (a == 0 && b == 0) { TYPE signa = ADDSUFFIX(copysign)(1.0, a); TYPE signb = ADDSUFFIX(copysign)(1.0, b); return signa == signb; } else { return a == b; } } else if (isnan(a) && isnan(b)) { return 1; } else {/* infs */ return a == b; } } typedef TYPE complex (*complexfunc)(TYPE complex); typedef TYPE (*realfunc)(TYPE); @@ -308,18 +385,18 @@ int check_near_crossover(complexfunc cfunc, const char* fname) if ( diff > 2*EPS || czp == czm) { printf(fname); printf(": Loss of precision: j = %d, k = %d\n", j, k); printf("zp = (" FMT " + " FMT "j) -> (" FMT " + " FMT "j)\n", \ ADDSUFFIX(creal)(zp), ADDSUFFIX(cimag)(zp), \ ADDSUFFIX(creal)(czp), ADDSUFFIX(cimag)(czp)); printf("zm = (" FMT " + " FMT "j) -> (" FMT " + " FMT "j)\n", \ ADDSUFFIX(creal)(zm), ADDSUFFIX(cimag)(zm), \ ADDSUFFIX(creal)(czm), ADDSUFFIX(cimag)(czm)); printf("diff = " FMT ", exact match = %d\n", diff, czp == czm); ret = 0; } } } return ret; } int clp_internal(complexfunc cfunc, realfunc rfunc, int real, TYPE x) @@ -366,8 +443,8 @@ int check_loss_of_precision(complexfunc cfunc, realfunc rfunc, int real, if (ratio > rtol) { printf(fname); printf(": Loss of precision vs real:\n"); printf("x = " FMT "\n", x); printf("ratio = " FMT "\n", ratio); ret = 0; } } @@ -378,8 +455,8 @@ int check_loss_of_precision(complexfunc cfunc, realfunc rfunc, int real, if (ratio > rtol) { printf(fname); printf(": Loss of precision vs. real:\n"); printf("x = " FMT "\n", x); printf("ratio = " FMT "\n", ratio); ret = 0; } } @@ -391,52 +468,52 @@ int test_cacos() { int ret = 1; /* cacos(conj(z)) = conj(cacos(z)) */ TEST_CE(cacos, 0, 0, NPY_PI_2, NZERO); TEST_CE(cacos, 0, NZERO, NPY_PI_2, 0); TEST_CE(cacos, NZERO, 0, NPY_PI_2, NZERO); TEST_CE(cacos, NZERO, NZERO, NPY_PI_2, 0); TEST_CE(cacos, 0, NAN, NPY_PI_2, NAN); TEST_CE(cacos, NZERO, NAN, NPY_PI_2, NAN); TEST_CE(cacos, 2.0, INFINITY, NPY_PI_2, -INFINITY); TEST_CE(cacos, 2.0, -INFINITY, NPY_PI_2, INFINITY); /* can raise FE_INVALID or not */ TEST_EE(cacos, 2.0, NAN, NAN, NAN); TEST_CE(cacos, -INFINITY, 2.0, NPY_PI, -INFINITY); TEST_CE(cacos, -INFINITY, -2.0, NPY_PI, INFINITY); TEST_EE(cacos, INFINITY, 2.0, 0, -INFINITY); TEST_EE(cacos, INFINITY, -2.0, 0, INFINITY); TEST_CE(cacos, -INFINITY, INFINITY, 0.75 * NPY_PI, -INFINITY); TEST_CE(cacos, -INFINITY, -INFINITY, 0.75 * NPY_PI, INFINITY); TEST_CE(cacos, INFINITY, INFINITY, 0.25 * NPY_PI, -INFINITY); TEST_CE(cacos, INFINITY, -INFINITY, 0.25 * NPY_PI, -INFINITY); /* sign of imaginary part is unspecified. */ TEST_UNSPECIFIED2(cacos, INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST_UNSPECIFIED2(cacos, -INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); /* can raise FE_INVALID or not */ TEST_EE(cacos, NAN, 2.0, NAN, NAN); TEST_EE(cacos, NAN, -2.0, NAN, NAN); TEST_EE(cacos, NAN, INFINITY, NAN, -INFINITY); TEST_EE(cacos, NAN, -INFINITY, NAN, INFINITY); TEST_EE(cacos, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(cacos, -2, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(cacos, 2, 0, 0, -1, 1, -1, 1); TEST_BRANCH_CUT(cacos, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(cacos, 0, 2, 1, 0, 1, 1, 1); TEST_CC(cacos, 0.5, 0.0, ADDSUFFIX(acos)(0.5), 0.0); return ret; } @@ -448,56 +525,56 @@ int test_casin() int ret = 1; /* casin(conj(z)) = conj(casin(z)) and casin is odd */ TEST_EE(casin, 0, 0, 0, 0); TEST_EE(casin, 0, NZERO, 0, NZERO); TEST_EE(casin, NZERO, 0, NZERO, 0); TEST_EE(casin, NZERO, NZERO, NZERO, NZERO); TEST_CE(casin, -INFINITY, 2.0, -NPY_PI_2, INFINITY); TEST_CE(casin, INFINITY, 2.0, NPY_PI_2, INFINITY); TEST_CE(casin, -INFINITY, -2.0, -NPY_PI_2, -INFINITY); TEST_CE(casin, INFINITY, -2.0, NPY_PI_2, -INFINITY); /* can raise FE_INVALID or not */ TEST_EE(casin, NAN, -2.0, NAN, NAN); TEST_EE(casin, NAN, 2.0, NAN, NAN); TEST_EE(casin, -2.0, INFINITY, NZERO, INFINITY); TEST_EE(casin, 2.0, INFINITY, 0, INFINITY); TEST_EE(casin, -2.0, -INFINITY, NZERO, -INFINITY); TEST_EE(casin, 2.0, -INFINITY, 0, -INFINITY); TEST_CE(casin, -INFINITY, INFINITY, -0.25*NPY_PI, INFINITY); TEST_CE(casin, INFINITY, INFINITY, 0.25*NPY_PI, INFINITY); TEST_CE(casin, -INFINITY, -INFINITY, -0.25*NPY_PI, -INFINITY); TEST_CE(casin, INFINITY, -INFINITY, 0.25*NPY_PI, -INFINITY); TEST_EE(casin, NAN, INFINITY, NAN, INFINITY); TEST_EE(casin, NAN, -INFINITY, NAN, -INFINITY); TEST_EE(casin, 0, NAN, 0, NAN); TEST_EE(casin, NZERO, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST_EE(casin, -2.0, NAN, NAN, NAN); TEST_EE(casin, 2.0, NAN, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(casin, -INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST_UNSPECIFIED2(casin, INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST_EE(casin, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(casin, asin, 0); TEST_CC(casin, 1e-5, 1e-5, 9.999999999666666667e-6, 1.0000000000333333333e-5); TEST_BRANCH_CUT(casin, -2, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(casin, 2, 0, 0, -1, 1, -1, 1); TEST_BRANCH_CUT(casin, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(casin, 0, 2, 1, 0, 1, 1, 1); TEST_CC(casin, 0.5, 0, ADDSUFFIX(asin)(0.5), 0); return ret; } @@ -508,61 +585,61 @@ int test_catan() { int ret = 1; /* catan(conj(z)) = conj(catan(z)) and catan is odd */ TEST_EE(catan, 0, 0, 0, 0); TEST_EE(catan, 0, NZERO, 0, NZERO); TEST_EE(catan, NZERO, 0, NZERO, 0); TEST_EE(catan, NZERO, NZERO, NZERO, NZERO); TEST_EE(catan, NAN, 0, NAN, 0); TEST_EE(catan, NAN, NZERO, NAN, NZERO); TEST_RAISES(catan, NZERO, 1, NZERO, INFINITY, FE_DIVBYZERO); TEST_RAISES(catan, 0, 1, 0, INFINITY, FE_DIVBYZERO); TEST_RAISES(catan, NZERO, -1, NZERO, -INFINITY, FE_DIVBYZERO); TEST_RAISES(catan, 0, -1, 0, -INFINITY, FE_DIVBYZERO); TEST_CE(catan, -INFINITY, 2.0, -NPY_PI_2, 0); TEST_CE(catan, INFINITY, 2.0, NPY_PI_2, 0); TEST_CE(catan, -INFINITY, -2.0, -NPY_PI_2, NZERO); TEST_CE(catan, INFINITY, -2.0, NPY_PI_2, NZERO); /* can raise FE_INVALID or not */ TEST_EE(catan, NAN, -2.0, NAN, NAN); TEST_EE(catan, NAN, 2.0, NAN, NAN); TEST_CE(catan, -2.0, INFINITY, -NPY_PI_2, 0); TEST_CE(catan, 2.0, INFINITY, NPY_PI_2, 0); TEST_CE(catan, -2.0, -INFINITY, -NPY_PI_2, NZERO); TEST_CE(catan, 2.0, -INFINITY, NPY_PI_2, NZERO); TEST_CE(catan, -INFINITY, INFINITY, -NPY_PI_2, 0); TEST_CE(catan, INFINITY, INFINITY, NPY_PI_2, 0); TEST_CE(catan, -INFINITY, -INFINITY, -NPY_PI_2, NZERO); TEST_CE(catan, INFINITY, -INFINITY, NPY_PI_2, NZERO); TEST_EE(catan, NAN, INFINITY, NAN, 0); TEST_EE(catan, NAN, -INFINITY, NAN, NZERO); /* can raise FE_INVALID or not */ TEST_EE(catan, -2.0, NAN, NAN, NAN); TEST_EE(catan, 2.0, NAN, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(catan, -INFINITY, NAN, -NPY_PI_2, 0, -NPY_PI_2, NZERO); TEST_UNSPECIFIED2(catan, INFINITY, NAN, NPY_PI_2, 0, NPY_PI_2, NZERO); TEST_EE(catan, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(catan, atan, 0); TEST_CC(catan, 1e-5, 1e-5, 1.000000000066666666e-5, 9.999999999333333333e-6); TEST_BRANCH_CUT(catan, 0, -2, 1, 0, -1, 1, 1); TEST_BRANCH_CUT(catan, 0, 2, -1, 0, -1, 1, 1); TEST_BRANCH_CUT(catan, -2, 0, 0, 1, 1, 1, 1); TEST_BRANCH_CUT(catan, 2, 0, 0, 1, 1, 1, 1); TEST_CC(catan, 0.5, 0, ADDSUFFIX(catan)(0.5), 0); return ret; } @@ -573,49 +650,49 @@ int test_cacosh() { int ret = 1; /* cacosh(conj(z)) = conj(cacosh(z)) */ TEST_EC(cacosh, 0, 0, 0, NPY_PI_2); TEST_EC(cacosh, 0, NZERO, 0, -NPY_PI_2); TEST_EC(cacosh, NZERO, 0, 0, NPY_PI_2); TEST_EC(cacosh, NZERO, NZERO, 0, -NPY_PI_2); TEST_EC(cacosh, 2.0, INFINITY, INFINITY, NPY_PI_2); TEST_EC(cacosh, 2.0, -INFINITY, INFINITY, -NPY_PI_2); /* can raise FE_INVALID or not */ TEST_EE(cacosh, 2.0, NAN, NAN, NAN); TEST_EC(cacosh, -INFINITY, 2.0, INFINITY, NPY_PI); TEST_EC(cacosh, -INFINITY, -2.0, INFINITY, -NPY_PI); TEST_EE(cacosh, INFINITY, 2.0, INFINITY, 0); TEST_EE(cacosh, INFINITY, -2.0, INFINITY, NZERO); TEST_EC(cacosh, -INFINITY, INFINITY, INFINITY, 0.75*NPY_PI); TEST_EC(cacosh, -INFINITY, -INFINITY, INFINITY, -0.75*NPY_PI); TEST_EC(cacosh, INFINITY, INFINITY, INFINITY, 0.25*NPY_PI); TEST_EC(cacosh, INFINITY, -INFINITY, INFINITY, -0.25*NPY_PI); TEST_EE(cacosh, INFINITY, NAN, INFINITY, NAN); TEST_EE(cacosh, -INFINITY, NAN, INFINITY, NAN); /* can raise FE_INVALID or not */ TEST_EE(cacosh, NAN, 2.0, NAN, NAN); TEST_EE(cacosh, NAN, -2.0, NAN, NAN); TEST_EE(cacosh, NAN, INFINITY, INFINITY, NAN); TEST_EE(cacosh, NAN, -INFINITY, INFINITY, NAN); TEST_EE(cacosh, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(cacosh, -1, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(cacosh, 0.5, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(cacosh, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(cacosh, 0, 2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(cacosh, 2, 0, 0, 1, 1, 1, 1); TEST_CC(cacosh, 1.5, 0, ADDSUFFIX(acosh)(1.5), 0); return ret; } #endif @@ -625,57 +702,57 @@ int test_casinh() { int ret = 1; /* casinh(conj(z)) = conj(casinh(z)) and casinh is odd */ TEST_EE(casinh, 0, 0, 0, 0); TEST_EE(casinh, 0, NZERO, 0, NZERO); TEST_EE(casinh, NZERO, 0, NZERO, 0); TEST_EE(casinh, NZERO, NZERO, NZERO, NZERO); TEST_EC(casinh, 2.0, INFINITY, INFINITY, NPY_PI_2); TEST_EC(casinh, 2.0, -INFINITY, INFINITY, -NPY_PI_2); TEST_EC(casinh, -2.0, INFINITY, -INFINITY, NPY_PI_2); TEST_EC(casinh, -2.0, -INFINITY, -INFINITY, -NPY_PI_2); /* can raise FE_INVALID or not */ TEST_EE(casinh, 2.0, NAN, NAN, NAN); TEST_EE(casinh, -2.0, NAN, NAN, NAN); TEST_EE(casinh, INFINITY, 2.0, INFINITY, 0); TEST_EE(casinh, INFINITY, -2.0, INFINITY, NZERO); TEST_EE(casinh, -INFINITY, 2.0, -INFINITY, 0); TEST_EE(casinh, -INFINITY, -2.0, -INFINITY, NZERO); TEST_EC(casinh, INFINITY, INFINITY, INFINITY, 0.25*NPY_PI); TEST_EC(casinh, INFINITY, -INFINITY, INFINITY, -0.25*NPY_PI); TEST_EC(casinh, -INFINITY, INFINITY, -INFINITY, 0.25*NPY_PI); TEST_EC(casinh, -INFINITY, -INFINITY, -INFINITY, -0.25*NPY_PI); TEST_EE(casinh, INFINITY, NAN, INFINITY, NAN); TEST_EE(casinh, -INFINITY, NAN, -INFINITY, NAN); TEST_EE(casinh, NAN, 0, NAN, 0); TEST_EE(casinh, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST_EE(casinh, NAN, 2.0, NAN, NAN); TEST_EE(casinh, NAN, -2.0, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(casinh, NAN, INFINITY, INFINITY, NAN, -INFINITY, NAN); TEST_UNSPECIFIED2(casinh, NAN, -INFINITY, INFINITY, NAN, -INFINITY, NAN); TEST_EE(casinh, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(casinh, asinh, 1); TEST_CC(casinh, 1e-5, 1e-5, 1.0000000000333333333e-5, 9.999999999666666667e-6); TEST_BRANCH_CUT(casinh, 0, -2, -1, 0, -1, 1, 1); TEST_BRANCH_CUT(casinh, 0, 2, 1, 0, -1, 1, 1); TEST_BRANCH_CUT(casinh, -2, 0, 0, 1, 1, 1, 1); TEST_BRANCH_CUT(casinh, 2, 0, 0, 1, 1, 1, 1); TEST_BRANCH_CUT(casinh, 0, 0, 1, 0, 1, 1, 1); TEST_CC(casinh, 0.5, 0, ADDSUFFIX(asinh)(0.5), 0); return ret; } @@ -686,63 +763,63 @@ int test_catanh() { int ret = 1; /* catanh(conj(z)) = conj(catanh(z)) and catanh is odd */ TEST_EE(catanh, 0, 0, 0, 0); TEST_EE(catanh, 0, NZERO, 0, NZERO); TEST_EE(catanh, NZERO, 0, NZERO, 0); TEST_EE(catanh, NZERO, NZERO, NZERO, NZERO); TEST_EE(catanh, 0, NAN, 0, NAN); TEST_EE(catanh, NZERO, NAN, NZERO, NAN); TEST_RAISES(catanh, 1, 0, INFINITY, 0, FE_DIVBYZERO); TEST_RAISES(catanh, 1, NZERO, INFINITY, NZERO, FE_DIVBYZERO); TEST_RAISES(catanh, -1, 0, -INFINITY, 0, FE_DIVBYZERO); TEST_RAISES(catanh, -1, NZERO, -INFINITY, NZERO, FE_DIVBYZERO); TEST_EC(catanh, 2.0, INFINITY, 0, NPY_PI_2); TEST_EC(catanh, 2.0, -INFINITY, 0, -NPY_PI_2); TEST_EC(catanh, -2.0, INFINITY, NZERO, NPY_PI_2); TEST_EC(catanh, -2.0, -INFINITY, NZERO, -NPY_PI_2); /* can raise FE_INVALID or not */ TEST_EE(catanh, 2.0, NAN, NAN, NAN); TEST_EE(catanh, -2.0, NAN, NAN, NAN); TEST_EC(catanh, INFINITY, 2.0, 0, NPY_PI_2); TEST_EC(catanh, INFINITY, -2.0, 0, -NPY_PI_2); TEST_EC(catanh, -INFINITY, 2.0, NZERO, NPY_PI_2); TEST_EC(catanh, -INFINITY, -2.0, NZERO, -NPY_PI_2); TEST_EC(catanh, INFINITY, INFINITY, 0, NPY_PI_2); TEST_EC(catanh, INFINITY, -INFINITY, 0, -NPY_PI_2); TEST_EC(catanh, -INFINITY, INFINITY, NZERO, NPY_PI_2); TEST_EC(catanh, -INFINITY, -INFINITY, NZERO, -NPY_PI_2); TEST_EE(catanh, INFINITY, NAN, 0, NAN); TEST_EE(catanh, -INFINITY, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST_EE(catanh, NAN, 2.0, NAN, NAN); TEST_EE(catanh, NAN, -2.0, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(catanh, NAN, INFINITY, 0, NPY_PI_2, NZERO, NPY_PI_2); TEST_UNSPECIFIED2(catanh, NAN, -INFINITY, 0, -NPY_PI_2, NZERO, -NPY_PI_2); /* TEST(catanh, NAN, INFINITY, 0, NPY_PI_2); */ TEST_EE(catanh, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(catanh, atanh, 1); TEST_CC(catanh, 1e-5, 1e-5, 9.999999999333333333e-6, 1.000000000066666666e-5); TEST_BRANCH_CUT(catanh, -2, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(catanh, 2, 0, 0, -1, 1, -1, 1); TEST_BRANCH_CUT(catanh, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(catanh, 0, 2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(catanh, 0, 0, 0, 1, 1, 1, 1); TEST_CC(catanh, 0.5, 0, ADDSUFFIX(atanh)(0.5), 0); return ret; } @@ -753,10 +830,10 @@ int test_ccos() { int ret = 1; /* ccos(conj(z)) = conj(ccos(z)) and ccos is even */ TEST_EE(ccos, NZERO, 0, 1, 0); TEST_EE(ccos, 0, 0, 1, NZERO); TEST_EE(ccos, NZERO, NZERO, 1, NZERO); TEST_EE(ccos, 0, NZERO, 1, 0); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccos, -INFINITY, 0, NAN, 0, \ @@ -772,49 +849,49 @@ int test_ccos() TEST_RAISES(ccos, INFINITY, -2.0, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST_EE(ccos, NAN, 2.0, NAN, NAN); TEST_EE(ccos, NAN, -2.0, NAN, NAN); TEST_EE(ccos, NZERO, INFINITY, INFINITY, 0); TEST_EE(ccos, 0, INFINITY, INFINITY, NZERO); TEST_EE(ccos, NZERO, -INFINITY, INFINITY, NZERO); TEST_EE(ccos, 0, -INFINITY, INFINITY, 0); TEST_EE(ccos, -1.0, INFINITY, INFINITY, INFINITY); TEST_EE(ccos, 1.0, INFINITY, INFINITY, -INFINITY); TEST_EE(ccos, -1.0, -INFINITY, INFINITY, -INFINITY); TEST_EE(ccos, 1.0, -INFINITY, INFINITY, INFINITY); TEST_EE(ccos, -2.0, INFINITY, -INFINITY, INFINITY); TEST_EE(ccos, 2.0, INFINITY, -INFINITY, -INFINITY); TEST_EE(ccos, -2.0, -INFINITY, -INFINITY, -INFINITY); TEST_EE(ccos, 2.0, -INFINITY, -INFINITY, INFINITY); TEST_EE(ccos, -4.0, INFINITY, -INFINITY, -INFINITY); TEST_EE(ccos, 4.0, INFINITY, -INFINITY, INFINITY); TEST_EE(ccos, -4.0, -INFINITY, -INFINITY, INFINITY); TEST_EE(ccos, 4.0, -INFINITY, -INFINITY, -INFINITY); TEST_EE(ccos, -5.0, INFINITY, INFINITY, -INFINITY); TEST_EE(ccos, 5.0, INFINITY, INFINITY, INFINITY); TEST_EE(ccos, -5.0, -INFINITY, INFINITY, INFINITY); TEST_EE(ccos, 5.0, -INFINITY, INFINITY, -INFINITY); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccos, -INFINITY, INFINITY, INFINITY, NAN, \ -INFINITY, NAN, FE_INVALID); TEST_EE(ccos, NAN, INFINITY, INFINITY, NAN); TEST_EE(ccos, NAN, -INFINITY, INFINITY, NAN); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccos, 0, NAN, NAN, 0, NAN, NZERO); TEST_UNSPECIFIED2(ccos, NZERO, NAN, NAN, 0, NAN, NZERO); /* can raise FE_INVALID or not */ TEST_EE(ccos, -2.0, NAN, NAN, NAN); TEST_EE(ccos, 2.0, NAN, NAN, NAN); TEST_EE(ccos, NAN, NAN, NAN, NAN); TEST_CC(ccos, 0.5, 0, ADDSUFFIX(cos)(0.5), 0); return ret; } @@ -825,10 +902,10 @@ int test_csin() { int ret = 1; /* csin(conj(z)) = conj(csin(z)) and csin is odd */ TEST_EE(csin, 0, 0, 0, 0); TEST_EE(csin, 0, NZERO, 0, NZERO); TEST_EE(csin, NZERO, 0, NZERO, 0); TEST_EE(csin, NZERO, NZERO, NZERO, NZERO); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(csin, -INFINITY, 0, NAN, 0, \ @@ -844,30 +921,30 @@ int test_csin() TEST_RAISES(csin, INFINITY, -2.0, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST_EE(csin, NAN, 2.0, NAN, NAN); TEST_EE(csin, NAN, -2.0, NAN, NAN); TEST_EE(csin, NZERO, INFINITY, NZERO, INFINITY); TEST_EE(csin, 0, INFINITY, 0, INFINITY); TEST_EE(csin, NZERO, -INFINITY, NZERO, -INFINITY); TEST_EE(csin, 0, -INFINITY, 0, -INFINITY); TEST_EE(csin, -1.0, INFINITY, -INFINITY, INFINITY); TEST_EE(csin, 1.0, INFINITY, INFINITY, INFINITY); TEST_EE(csin, -1.0, -INFINITY, -INFINITY, -INFINITY); TEST_EE(csin, 1.0, -INFINITY, INFINITY, -INFINITY); TEST_EE(csin, -2.0, INFINITY, -INFINITY, -INFINITY); TEST_EE(csin, 2.0, INFINITY, INFINITY, -INFINITY); TEST_EE(csin, -2.0, -INFINITY, -INFINITY, INFINITY); TEST_EE(csin, 2.0, -INFINITY, INFINITY, INFINITY); TEST_EE(csin, -4.0, INFINITY, INFINITY, -INFINITY); TEST_EE(csin, 4.0, INFINITY, -INFINITY, -INFINITY); TEST_EE(csin, -4.0, -INFINITY, INFINITY, INFINITY); TEST_EE(csin, 4.0, -INFINITY, -INFINITY, INFINITY); TEST_EE(csin, -5.0, INFINITY, INFINITY, INFINITY); TEST_EE(csin, 5.0, INFINITY, -INFINITY, INFINITY); TEST_EE(csin, -5.0, -INFINITY, INFINITY, -INFINITY); TEST_EE(csin, 5.0, -INFINITY, -INFINITY, -INFINITY); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(csin, -INFINITY, INFINITY, NAN, INFINITY, \ @@ -877,16 +954,16 @@ int test_csin() TEST_UNSPECIFIED2(csin, NAN, INFINITY, NAN, INFINITY, NAN, -INFINITY); TEST_UNSPECIFIED2(csin, NAN, -INFINITY, NAN, INFINITY, NAN, -INFINITY); TEST_EE(csin, 0, NAN, 0, NAN); TEST_EE(csin, NZERO, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST_EE(csin, -2.0, NAN, NAN, NAN); TEST_EE(csin, 2.0, NAN, NAN, NAN); TEST_EE(csin, NAN, NAN, NAN, NAN); TEST_CC(csin, 0.5, 0, ADDSUFFIX(sin)(0.5), 0); return ret; } @@ -897,26 +974,26 @@ int test_ctan() { int ret = 1; /* ctan(conj(z)) = conj(ctan(z)) and ctan is odd */ TEST_EE(ctan, 0, 0, 0, 0); TEST_EE(ctan, 0, NZERO, 0, NZERO); TEST_EE(ctan, NZERO, 0, NZERO, 0); TEST_EE(ctan, NZERO, NZERO, NZERO, NZERO); TEST_RAISES(ctan, -INFINITY, 2.0, NAN, NAN, FE_INVALID); TEST_RAISES(ctan, -INFINITY, -2.0, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST_EE(ctan, NAN, 2.0, NAN, NAN); TEST_EE(ctan, NAN, -2.0, NAN, NAN); TEST_EE(ctan, -1.0, INFINITY, NZERO, 1.0); TEST_EE(ctan, 1.0, INFINITY, 0, 1.0); TEST_EE(ctan, -1.0, -INFINITY, NZERO, -1.0); TEST_EE(ctan, 1.0, -INFINITY, 0, -1.0); TEST_EE(ctan, -2.0, INFINITY, 0, 1); TEST_EE(ctan, 2.0, INFINITY, NZERO, 1); TEST_EE(ctan, -2.0, -INFINITY, 0, -1); TEST_EE(ctan, 2.0, -INFINITY, NZERO, -1); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(ctan, INFINITY, INFINITY, 0, 1, NZERO, 1); @@ -928,19 +1005,19 @@ int test_ctan() TEST_UNSPECIFIED2(ctan, NAN, INFINITY, 0, 1, NZERO, 1); TEST_UNSPECIFIED2(ctan, NAN, -INFINITY, 0, -1, NZERO, -1); TEST_EE(ctan, 0, NAN, 0, NAN); TEST_EE(ctan, NZERO, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST_EE(ctan, 2.0, NAN, NAN, NAN); TEST_EE(ctan, -2.0, NAN, NAN, NAN); TEST_EE(ctan, NAN, NAN, NAN, NAN); TEST_CC(ctan, 0.5, 0, ADDSUFFIX(tan)(0.5), 0); TEST_CC(ctan, 0, 1000, 0, 1); TEST_CC(ctan, 0, -1000, 0, -1); return ret; } @@ -951,10 +1028,10 @@ int test_ccosh() { int ret = 1; /* ccosh(conj(z)) = conj(ccosh(z)) and ccosh is even */ TEST_EE(ccosh, 0, 0, 1, 0); TEST_EE(ccosh, 0, NZERO, 1, NZERO); TEST_EE(ccosh, NZERO, 0, 1, NZERO); TEST_EE(ccosh, NZERO, NZERO, 1, 0); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccosh, 0, INFINITY, NAN, 0, \ @@ -970,49 +1047,49 @@ int test_ccosh() TEST_RAISES(ccosh, -2.0, -INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST_EE(ccosh, 2.0, NAN, NAN, NAN); TEST_EE(ccosh, -2.0, NAN, NAN, NAN); TEST_EE(ccosh, INFINITY, 0, INFINITY, 0); TEST_EE(ccosh, INFINITY, NZERO, INFINITY, NZERO); TEST_EE(ccosh, -INFINITY, 0, INFINITY, NZERO); TEST_EE(ccosh, -INFINITY, NZERO, INFINITY, 0); TEST_EE(ccosh, INFINITY, 1.0, INFINITY, INFINITY); TEST_EE(ccosh, INFINITY, -1.0, INFINITY, -INFINITY); TEST_EE(ccosh, -INFINITY, 1.0, INFINITY, -INFINITY); TEST_EE(ccosh, -INFINITY, -1.0, INFINITY, INFINITY); TEST_EE(ccosh, INFINITY, 2.0, -INFINITY, INFINITY); TEST_EE(ccosh, INFINITY, -2.0, -INFINITY, -INFINITY); TEST_EE(ccosh, -INFINITY, 2.0, -INFINITY, -INFINITY); TEST_EE(ccosh, -INFINITY, -2.0, -INFINITY, INFINITY); TEST_EE(ccosh, INFINITY, 4.0, -INFINITY, -INFINITY); TEST_EE(ccosh, INFINITY, -4.0, -INFINITY, INFINITY); TEST_EE(ccosh, -INFINITY, 4.0, -INFINITY, INFINITY); TEST_EE(ccosh, -INFINITY, -4.0, -INFINITY, -INFINITY); TEST_EE(ccosh, INFINITY, 5.0, INFINITY, -INFINITY); TEST_EE(ccosh, INFINITY, -5.0, INFINITY, INFINITY); TEST_EE(ccosh, -INFINITY, 5.0, INFINITY, INFINITY); TEST_EE(ccosh, -INFINITY, -5.0, INFINITY, -INFINITY); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccosh, INFINITY, INFINITY, INFINITY, NAN, \ -INFINITY, NAN, FE_INVALID); TEST_EE(ccosh, INFINITY, NAN, INFINITY, NAN); TEST_EE(ccosh, -INFINITY, NAN, INFINITY, NAN); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccosh, NAN, 0, NAN, 0, NAN, NZERO); TEST_UNSPECIFIED2(ccosh, NAN, NZERO, NAN, 0, NAN, NZERO); /* can raise FE_INVALID or not */ TEST_EE(ccosh, NAN, 2.0, NAN, NAN); TEST_EE(ccosh, NAN, -2.0, NAN, NAN); TEST_EE(ccosh, NAN, NAN, NAN, NAN); TEST_CC(ccosh, 0.5, 0, ADDSUFFIX(cosh)(0.5), 0); return ret; } @@ -1023,10 +1100,10 @@ int test_csinh() { int ret = 1; /* csinh(conj(z)) = conj(csinh(z)) and csinh is odd */ TEST_EE(csinh, 0, 0, 0, 0); TEST_EE(csinh, 0, NZERO, 0, NZERO); TEST_EE(csinh, NZERO, 0, NZERO, 0); TEST_EE(csinh, NZERO, NZERO, NZERO, NZERO); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(csinh, 0, INFINITY, 0, NAN, \ @@ -1042,30 +1119,30 @@ int test_csinh() TEST_RAISES(csinh, -2.0, -INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST_EE(csinh, 2.0, NAN, NAN, NAN); TEST_EE(csinh, -2.0, NAN, NAN, NAN); TEST_EE(csinh, INFINITY, 0, INFINITY, 0); TEST_EE(csinh, INFINITY, NZERO, INFINITY, NZERO); TEST_EE(csinh, -INFINITY, 0, -INFINITY, 0); TEST_EE(csinh, -INFINITY, NZERO, -INFINITY, NZERO); TEST_EE(csinh, INFINITY, 1.0, INFINITY, INFINITY); TEST_EE(csinh, INFINITY, -1.0, INFINITY, -INFINITY); TEST_EE(csinh, -INFINITY, 1.0, -INFINITY, INFINITY); TEST_EE(csinh, -INFINITY, -1.0, -INFINITY, -INFINITY); TEST_EE(csinh, INFINITY, 2.0, -INFINITY, INFINITY); TEST_EE(csinh, INFINITY, -2.0, -INFINITY, -INFINITY); TEST_EE(csinh, -INFINITY, 2.0, INFINITY, INFINITY); TEST_EE(csinh, -INFINITY, -2.0, INFINITY, -INFINITY); TEST_EE(csinh, INFINITY, 4.0, -INFINITY, -INFINITY); TEST_EE(csinh, INFINITY, -4.0, -INFINITY, INFINITY); TEST_EE(csinh, -INFINITY, 4.0, INFINITY, -INFINITY); TEST_EE(csinh, -INFINITY, -4.0, INFINITY, INFINITY); TEST_EE(csinh, INFINITY, 5.0, INFINITY, -INFINITY); TEST_EE(csinh, INFINITY, -5.0, INFINITY, INFINITY); TEST_EE(csinh, -INFINITY, 5.0, -INFINITY, -INFINITY); TEST_EE(csinh, -INFINITY, -5.0, -INFINITY, INFINITY); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(csinh, INFINITY, INFINITY, INFINITY, NAN, \ @@ -1075,16 +1152,16 @@ int test_csinh() TEST_UNSPECIFIED2(csinh, INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); TEST_UNSPECIFIED2(csinh, -INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); TEST_EE(csinh, NAN, 0, NAN, 0); TEST_EE(csinh, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST_EE(csinh, NAN, 2.0, NAN, NAN); TEST_EE(csinh, NAN, -2.0, NAN, NAN); TEST_EE(csinh, NAN, NAN, NAN, NAN); TEST_CC(csinh, 0.5, 0, ADDSUFFIX(sinh)(0.5), 0); return ret; } @@ -1095,26 +1172,26 @@ int test_ctanh() { int ret = 1; /* ctanh(conj(z)) = conj(ctanh(z)) and ctanh is odd */ TEST_EE(ctanh, 0, 0, 0, 0); TEST_EE(ctanh, 0, NZERO, 0, NZERO); TEST_EE(ctanh, NZERO, 0, NZERO, 0); TEST_EE(ctanh, NZERO, NZERO, NZERO, NZERO); TEST_RAISES(ctanh, 2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(ctanh, -2.0, INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST_EE(ctanh, 2.0, NAN, NAN, NAN); TEST_EE(ctanh, -2.0, NAN, NAN, NAN); TEST_EE(ctanh, INFINITY, 1.0, 1.0, 0); TEST_EE(ctanh, INFINITY, -1.0, 1.0, NZERO); TEST_EE(ctanh, -INFINITY, 1.0, -1.0, 0); TEST_EE(ctanh, -INFINITY, -1.0, -1.0, NZERO); TEST_EE(ctanh, INFINITY, 2.0, 1.0, NZERO); TEST_EE(ctanh, INFINITY, -2.0, 1.0, 0); TEST_EE(ctanh, -INFINITY, 2.0, -1.0, NZERO); TEST_EE(ctanh, -INFINITY, -2.0, -1.0, 0); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ctanh, INFINITY, INFINITY, 1, 0, 1, NZERO); @@ -1126,19 +1203,19 @@ int test_ctanh() TEST_UNSPECIFIED2(ctanh, INFINITY, NAN, 1, 0, 1, NZERO); TEST_UNSPECIFIED2(ctanh, -INFINITY, NAN, -1, 0, -1, NZERO); TEST_EE(ctanh, NAN, 0, NAN, 0); TEST_EE(ctanh, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST_EE(ctanh, NAN, 2.0, NAN, NAN); TEST_EE(ctanh, NAN, -2.0, NAN, NAN); TEST_EE(ctanh, NAN, NAN, NAN, NAN); TEST_CC(ctanh, 0.5, 0, ADDSUFFIX(tanh)(0.5), 0); TEST_CC(ctanh, 1000, 0, 1, 0); TEST_CC(ctanh, -1000, 0, -1, 0); return ret; } @@ -1149,38 +1226,38 @@ int test_cexp() { int ret = 1; /* cexp(conj(z)) = conj(cexp(z)) */ TEST_EE(cexp, 0, 0, 1, 0); TEST_EE(cexp, 0, NZERO, 1, NZERO); TEST_EE(cexp, NZERO, 0, 1, 0); TEST_EE(cexp, NZERO, NZERO, 1, NZERO); TEST_RAISES(cexp, 2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(cexp, 2.0, -INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST_EE(cexp, 42.0, NAN, NAN, NAN); TEST_EE(cexp, INFINITY, 0, INFINITY, 0); TEST_EE(cexp, INFINITY, NZERO, INFINITY, NZERO); TEST_EE(cexp, -INFINITY, 1.0, 0, 0); TEST_EE(cexp, -INFINITY, -1.0, 0, NZERO); TEST_EE(cexp, -INFINITY, 2.0, NZERO, 0); TEST_EE(cexp, -INFINITY, -2.0, NZERO, NZERO); TEST_EE(cexp, -INFINITY, 4.0, NZERO, NZERO); TEST_EE(cexp, -INFINITY, -4.0, NZERO, 0); TEST_EE(cexp, -INFINITY, 5.0, 0, NZERO); TEST_EE(cexp, -INFINITY, -5.0, 0, 0); TEST_EE(cexp, INFINITY, 1.0, INFINITY, INFINITY); TEST_EE(cexp, INFINITY, -1.0, INFINITY, -INFINITY); TEST_EE(cexp, INFINITY, 2.0, -INFINITY, INFINITY); TEST_EE(cexp, INFINITY, -2.0, -INFINITY, -INFINITY); TEST_EE(cexp, INFINITY, 4.0, -INFINITY, -INFINITY); TEST_EE(cexp, INFINITY, -4.0, -INFINITY, INFINITY); TEST_EE(cexp, INFINITY, 5.0, INFINITY, -INFINITY); TEST_EE(cexp, INFINITY, -5.0, INFINITY, INFINITY); /* signs of both parts are unspecified */ TEST_UNSPECIFIED4(cexp, -INFINITY, INFINITY, 0, 0, NZERO, 0, \ @@ -1199,21 +1276,20 @@ int test_cexp() /* sign of real part is unspecified */ TEST_UNSPECIFIED2(cexp, INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); TEST_EE(cexp, NAN, 0, NAN, 0); TEST_EE(cexp, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST_EE(cexp, NAN, 2.0, NAN, NAN); TEST_EE(cexp, NAN, -2.0, NAN, NAN); TEST_EE(cexp, NAN, NAN, NAN, NAN); TEST_CC(cexp, 0.5, 0, ADDSUFFIX(exp)(0.5), 0); TEST_CC(cexp, 1, 0, M_E, 0); TEST_CC(cexp, 0, 1, ADDSUFFIX(cos)(1), ADDSUFFIX(sin)(1)); TEST_CC(cexp, 1, 1, M_E*ADDSUFFIX(cos)(1), M_E*ADDSUFFIX(sin)(1)); return ret; } @@ -1224,48 +1300,48 @@ int test_clog() { int ret = 1; /* clog(conj(z)) = conj(clog(z)) */ TEST_RAISES(clog, NZERO, 0, -INFINITY, NPY_PI, FE_DIVBYZERO); TEST_RAISES(clog, NZERO, NZERO, -INFINITY, -NPY_PI, FE_DIVBYZERO); TEST_RAISES(clog, 0, 0, -INFINITY, 0, FE_DIVBYZERO); TEST_RAISES(clog, 0, NZERO, -INFINITY, NZERO, FE_DIVBYZERO); TEST_EC(clog, 2.0, INFINITY, INFINITY, NPY_PI_2); TEST_EC(clog, 2.0, -INFINITY, INFINITY, -NPY_PI_2); /* can raise FE_INVALID or not */ TEST_EE(clog, 2.0, NAN, NAN, NAN); TEST_EC(clog, -INFINITY, 2.0, INFINITY, NPY_PI); TEST_EC(clog, -INFINITY, -2.0, INFINITY, -NPY_PI); TEST_EE(clog, INFINITY, 2.0, INFINITY, 0); TEST_EE(clog, INFINITY, -2.0, INFINITY, NZERO); TEST_EC(clog, -INFINITY, INFINITY, INFINITY, 0.75 * NPY_PI); TEST_EC(clog, -INFINITY, -INFINITY, INFINITY, -0.75 * NPY_PI); TEST_EC(clog, INFINITY, INFINITY, INFINITY, 0.25 * NPY_PI); TEST_EC(clog, INFINITY, -INFINITY, INFINITY, -0.25 * NPY_PI); TEST_EE(clog, INFINITY, NAN, INFINITY, NAN); TEST_EE(clog, -INFINITY, NAN, INFINITY, NAN); /* can raise FE_INVALID or not */ TEST_EE(clog, NAN, 2.0, NAN, NAN); TEST_EE(clog, NAN, -2.0, NAN, NAN); TEST_EE(clog, NAN, INFINITY, INFINITY, NAN); TEST_EE(clog, NAN, -INFINITY, INFINITY, NAN); TEST_EE(clog, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(clog, -0.5, 0, 0, 1, 1, -1, 1); TEST_CC(clog, 0.5, 0, ADDSUFFIX(log)(0.5), 0); TEST_CC(clog, 1, 0, 0, 0); TEST_CC(clog, 1, 2, 0.80471895621705014, 1.1071487177940904); return ret; } @@ -1280,78 +1356,78 @@ int test_cpow() /* We can check for branch cuts in here */ /* tests from test_umath.py: TestPower: test_power_complex */ TEST_CPOW_CC(1, 2, 0, 0, 1, 0); TEST_CPOW_CC(2, 3, 0, 0, 1, 0); TEST_CPOW_CC(3, 4, 0, 0, 1, 0); TEST_CPOW_CC(1, 2, 1, 0, 1, 2); TEST_CPOW_CC(2, 3, 1, 0, 2, 3); TEST_CPOW_CC(3, 4, 1, 0, 3, 4); TEST_CPOW_CC(1, 2, 2, 0, -3, 4); TEST_CPOW_CC(2, 3, 2, 0, -5, 12); TEST_CPOW_CC(3, 4, 2, 0, -7, 24); TEST_CPOW_CC(1, 2, 3, 0, -11, -2); TEST_CPOW_CC(2, 3, 3, 0, -46, 9); TEST_CPOW_CC(3, 4, 3, 0, -117, 44); TEST_CPOW_CC(1, 2, 4, 0, -7, -24); TEST_CPOW_CC(2, 3, 4, 0, -119, -120); TEST_CPOW_CC(3, 4, 4, 0, -527, -336); TEST_CPOW_CC(1, 2, -1, 0, 1.0/5.0, -2.0/5.0); TEST_CPOW_CC(2, 3, -1, 0, 2.0/13.0, -3.0/13.0); TEST_CPOW_CC(3, 4, -1, 0, 3.0/25.0, -4.0/25.0); TEST_CPOW_CC(1, 2, -2, 0, -3.0/25.0, -4.0/25.0); TEST_CPOW_CC(2, 3, -2, 0, -5.0/169.0, -12.0/169.0); TEST_CPOW_CC(3, 4, -2, 0, -7.0/625.0, -24.0/625.0); TEST_CPOW_CC(1, 2, -3, 0, -11.0/125.0, 2.0/125.0); TEST_CPOW_CC(2, 3, -3, 0, -46.0/2197.0, -9.0/2197.0); TEST_CPOW_CC(3, 4, -3, 0, -117.0/15625.0, -44.0/15625.0); TEST_CPOW_CC(1, 2, 0.5, 0, 1.272019649514069, 0.7861513777574233); TEST_CPOW_CC(2, 3, 0.5, 0, 1.6741492280355401, 0.895977476129838); TEST_CPOW_CC(3, 4, 0.5, 0, 2, 1); TEST_CPOW_CC(1, 2, 14, 0, -76443, 16124); TEST_CPOW_CC(2, 3, 14, 0, 23161315, 58317492); TEST_CPOW_CC(3, 4, 14, 0, 5583548873, 2465133864); TEST_CPOW_EE(0, INFINITY, 1, 0, 0, INFINITY); TEST_CPOW_EE(0, INFINITY, 2, 0, -INFINITY, NAN); TEST_CPOW_EE(0, INFINITY, 3, 0, NAN, NAN); TEST_CPOW_EE(1, INFINITY, 1, 0, 1, INFINITY); TEST_CPOW_EE(1, INFINITY, 2, 0, -INFINITY, INFINITY); TEST_CPOW_EE(1, INFINITY, 3, 0, -INFINITY, NAN); /* tests from test_umath.py: TestPower: test_power_zero */ TEST_CPOW_CC(0, 0, 0.33, 0, 0, 0); TEST_CPOW_CC(0, 0, 0.5, 0, 0, 0); TEST_CPOW_CC(0, 0, 1.0, 0, 0, 0); TEST_CPOW_CC(0, 0, 1.5, 0, 0, 0); TEST_CPOW_CC(0, 0, 2.0, 0, 0, 0); TEST_CPOW_CC(0, 0, 3.0, 0, 0, 0); TEST_CPOW_CC(0, 0, 4.0, 0, 0, 0); TEST_CPOW_CC(0, 0, 5.0, 0, 0, 0); TEST_CPOW_CC(0, 0, 6.6, 0, 0, 0); TEST_CPOW_EE(0, 0, 0, 0, 1, 0); TEST_CPOW_EE(0, 0, 0, 1, NAN, NAN); TEST_CPOW_EE(0, 0, -0.33, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -0.5, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -1.0, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -1.5, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -2.0, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -3.0, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -4.0, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -5.0, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -6.6, 0, NAN, NAN); TEST_CPOW_EE(0, 0, -1, 0.2, NAN, NAN); /* tests from test_umath_complex.py: TestCpow: test_simple * --- skip, duplicating existing tests --- @@ -1360,40 +1436,40 @@ int test_cpow() /* tests from test_umath_complex.py: TestCpow: test_scalar, test_array * these tests are equilvent for this level. */ TEST_CPOW_CC(1, 0, 1, 0, 1, 0); TEST_CPOW_CC(1, 0, 0, 1, 1, 0); TEST_CPOW_CC(1, 0, -0.5, 1.5, 1, 0); TEST_CPOW_CC(1, 0, 2, 0, 1, 0); TEST_CPOW_CC(1, 0, 3, 0, 1, 0); TEST_CPOW_CC(0, 1, 1, 0, 0, 1); TEST_CPOW_CC(0, 1, 0, 1, ADDSUFFIX(exp)(-NPY_PI_2), 0); TEST_CPOW_CC(0, 1, -0.5, 1.5, 0.067019739708273365, 0.067019739708273365); TEST_CPOW_CC(0, 1, 2, 0, -1, 0); TEST_CPOW_CC(0, 1, 3, 0, 0, -1); TEST_CPOW_CC(2, 0, 1, 0, 2, 0); TEST_CPOW_CC(2, 0, 0, 1, ADDSUFFIX(cos)(NPY_LOG2E), ADDSUFFIX(sin)(NPY_LOG2E)); TEST_CPOW_CC(2, 0, 2, 0, 4, 0); TEST_CPOW_CC(2, 0, 3, 0, 8, 0); TEST_CPOW_CC(2.5, 0.375, 1, 0, 2.5, 0.375); TEST_CPOW_CC(2.5, 0.375, 0, 1, 0.51691507509598866, 0.68939360813851125); TEST_CPOW_CC(2.5, 0.375, -0.5, 1.5, 0.12646517347496394, 0.48690593271654437); TEST_CPOW_CC(2.5, 0.375, 2, 0, 391.0/64.0, 15.0/8.0); TEST_CPOW_CC(2.5, 0.375, 3, 0, 1865.0/128.0, 3573.0/512.0); TEST_CPOW_EE(INFINITY, 0, 1, 0, NAN, NAN); TEST_CPOW_EE(INFINITY, 0, 0, 1, NAN, NAN); TEST_CPOW_EE(INFINITY, 0, -0.5, 1.5, NAN, NAN); TEST_CPOW_EE(INFINITY, 0, 2, 0, NAN, NAN); TEST_CPOW_EE(INFINITY, 0, 3, 0, NAN, NAN); TEST_CPOW_EE(NAN, 0, 1, 0, NAN, NAN); TEST_CPOW_EE(NAN, 0, 0, 1, NAN, NAN); TEST_CPOW_EE(NAN, 0, -0.5, 1.5, NAN, NAN); TEST_CPOW_EE(NAN, 0, 2, 0, NAN, NAN); TEST_CPOW_EE(NAN, 0, 3, 0, NAN, NAN); return ret; } @@ -1404,53 +1480,53 @@ int test_csqrt() { int ret = 1; /* csqrt(conj(z)) = conj(csqrt(z)) */ TEST_EE(csqrt, 0, 0, 0, 0); TEST_EE(csqrt, 0, NZERO, 0, NZERO); TEST_EE(csqrt, NZERO, 0, 0, 0); TEST_EE(csqrt, NZERO, NZERO, 0, NZERO); TEST_EE(csqrt, 2.0, INFINITY, INFINITY, INFINITY); TEST_EE(csqrt, 2.0, -INFINITY, INFINITY, -INFINITY); TEST_EE(csqrt, NAN, INFINITY, INFINITY, INFINITY); TEST_EE(csqrt, NAN, -INFINITY, INFINITY, -INFINITY); TEST_EE(csqrt, INFINITY, INFINITY, INFINITY, INFINITY); TEST_EE(csqrt, INFINITY, -INFINITY, INFINITY, -INFINITY); TEST_EE(csqrt, -INFINITY, INFINITY, INFINITY, INFINITY); TEST_EE(csqrt, -INFINITY, -INFINITY, INFINITY, -INFINITY); /* can raise FE_INVALID or not */ TEST_EE(csqrt, 2.0, NAN, NAN, NAN); TEST_EE(csqrt, -INFINITY, 2.0, 0, INFINITY); TEST_EE(csqrt, -INFINITY, -2.0, 0, -INFINITY); TEST_EE(csqrt, INFINITY, 2.0, INFINITY, 0); TEST_EE(csqrt, INFINITY, -2.0, INFINITY, NZERO); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(csqrt, -INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST_EE(csqrt, INFINITY, NAN, INFINITY, NAN); /* can raise FE_INVALID or not */ TEST_EE(csqrt, NAN, 2.0, NAN, NAN); TEST_EE(csqrt, NAN, -2.0, NAN, NAN); TEST_EE(csqrt, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(csqrt, -0.5, 0, 0, 1, 1, -1, 1); TEST_CC(csqrt, 0.5, 0, ADDSUFFIX(sqrt)(0.5), 0); TEST_CC(csqrt, 1, 0, 1, 0); TEST_CC(csqrt, 0, 1, NPY_SQRT2/2.0, NPY_SQRT2/2.0); TEST_CC(csqrt, -1, 0, 0, 1); TEST_CC(csqrt, 1, 1, 1.0986841134678100, 0.4550898605622273); TEST_CC(csqrt, 1, -1, 1.0986841134678100, -0.4550898605622273); return ret; } @@ -1497,7 +1573,7 @@ int main(int argc, char** argv) #ifdef CEXP printf("cexp: %d\n\n", test_cexp()); #endif #ifdef CLOG printf("clog: %d\n\n", test_clog()); #endif #ifdef CPOW -
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Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -8,24 +8,29 @@ #define TYPE float #define SUFFIX f #define EPS FLT_EPSILON #define CLOSE_ATOL 0 #define CLOSE_RTOL 1e-5 #else #ifdef DOUBLE #define TYPE double #define SUFFIX #define EPS DBL_EPSILON #define CLOSE_ATOL 0 #define CLOSE_RTOL 1e-12 #else #ifdef LONGDOUBLE #define TYPE long double #define SUFFIX l #define EPS 50*LDBL_EPSILON #define CLOSE_ATOL 0 #define CLOSE_RTOL 1e-12 #else #error "Define FLOAT or DOUBLE or LONGDOUBLE" #endif #endif #endif const TYPE NZERO = -1.0 * 0.0; #define STRINGIZE_INT(A) #A #define STRINGIZE(A) STRINGIZE_INT(A) @@ -34,14 +39,18 @@ const float NZEROf = -1.0 * 0.0; #define ADDSUFFIX_INT(A, B) CONCAT(A, B) #define ADDSUFFIX(A) ADDSUFFIX_INT(A, SUFFIX) #define TEST_PRINTF(func, x, e, r) \ printf("%d: " STRINGIZE(func) STRINGIZE(SUFFIX) "(%.16e + %.16ej): " \ "expected: %.16e + %.16ej: received: %.16e + %.16ej\n", __LINE__, \ ADDSUFFIX(creal)(x), ADDSUFFIX(cimag)(x), ADDSUFFIX(creal)(e), \ ADDSUFFIX(cimag)(e), ADDSUFFIX(creal)(r), ADDSUFFIX(cimag)(r)) #define TEST(func, xr, xi, er, ei) \ do { \ TYPE complex x = cpack(xr, xi); \ TYPE complex e = cpack(er, ei); \ TYPE complex r = ADDSUFFIX(func)(x); \ if (!cisclose(r, e)) { \ ret = 0; \ TEST_PRINTF(func, x, e, r); \ } \ @@ -50,11 +59,11 @@ const float NZEROf = -1.0 * 0.0; #define TEST_UNSPECIFIED2(func, xr, xi, er1, ei1, er2, ei2) \ do { \ TYPE complex x = cpack(xr, xi); \ TYPE complex e1 = cpack(er1, ei1); \ TYPE complex e2 = cpack(er2, ei2); \ TYPE complex r = ADDSUFFIX(func)(x); \ if (!(cisclose(r, e1) || cisclose(r, e2))) { \ ret = 0; \ TEST_PRINTF(func, x, e1, r); \ printf("or"); \ @@ -65,14 +74,14 @@ const float NZEROf = -1.0 * 0.0; #define TEST_UNSPECIFIED4(func, xr, xi, er1, ei1, er2, ei2, er3, ei3, er4, ei4)\ do { \ TYPE complex x = cpack(xr, xi); \ TYPE complex e1 = cpack(er1, ei1); \ TYPE complex e2 = cpack(er2, ei2); \ TYPE complex e3 = cpack(er3, ei3); \ TYPE complex e4 = cpack(er4, ei4); \ TYPE complex r = func(x); \ if (!(cisclose(r, e1) || cisclose(r, e2) \ || cisclose(r, e3) || cisclose(r, e4))) { \ ret = 0; \ TEST_PRINTF(func, x, e1, r); \ printf("or"); \ @@ -85,65 +94,114 @@ const float NZEROf = -1.0 * 0.0; } \ while(0) #define TEST_CPOW(xr, xi, yr, yi, er, ei) \ do { \ TYPE complex x = cpack(xr, xi); \ TYPE complex y = cpack(yr, yi); \ TYPE complex e = cpack(er, ei); \ TYPE complex r = ADDSUFFIX(cpow)(x, y); \ if (!cisclose(r, e)) { \ ret = 0; \ printf("%d: " STRINGIZE(cpow) STRINGIZE(SUFFIX) "(%.16e + %.16ej," \ " %.16e + %.16ej): expected: %.16e + %.16ej: received: " \ "%.16e + %.16ej\n", __LINE__, ADDSUFFIX(creal)(x), \ ADDSUFFIX(cimag)(x), ADDSUFFIX(creal)(y), \ ADDSUFFIX(cimag)(y), ADDSUFFIX(creal)(e), \ ADDSUFFIX(cimag)(e), ADDSUFFIX(creal)(r), \ ADDSUFFIX(cimag)(r)); \ } \ } \ while(0) #define TEST_RAISES(func, xr, xi, er, ei, fpe) \ do { \ int except; \ TYPE complex r; \ TYPE complex x = cpack(xr, xi); \ TYPE complex e = cpack(er, ei); \ feclearexcept(FE_ALL_EXCEPT); \ r = ADDSUFFIX(func)(x); \ except = fetestexcept(fpe); \ if (!(except & fpe && cisclose(r, e))) { \ ret = 0; \ TEST_PRINTF(func, x, e, r); \ } \ } \ while(0) #define TEST_RAISES_UNSPECIFIED2(func, xr, xi, er1, ei1, er2, ei2, fpe) \ do { \ int except; \ TYPE complex r; \ TYPE complex x = cpack(xr, xi); \ TYPE complex e1 = cpack(er1, ei1); \ TYPE complex e2 = cpack(er2, ei2); \ feclearexcept(FE_ALL_EXCEPT); \ r = ADDSUFFIX(func)(x); \ except = fetestexcept(fpe); \ if (!(except & fpe && (cisclose(r, e1) || cisclose(r, e2)))) { \ ret = 0; \ TEST_PRINTF(func, x, e1, r); \ printf("or"); \ TEST_PRINTF(func, x, e2, r); \ } \ } \ while(0) #define TEST_BRANCH_CUT(func, xr, xi, dxr, dxi, rsign, isign, cksignzero) \ do { \ TYPE complex x = cpack(xr, xi); \ TYPE complex dx = cpack(dxr, dxi); \ int q = check_branch_cut(ADDSUFFIX(func), x, dx, \ rsign, isign, cksignzero); \ if (!q) { \ ret = 0; \ printf(STRINGIZE(func) STRINGIZE(SUFFIX) ": branch cut failure: " \ "x = %.16g + %.16gj, dx = %.16g + %.16gj, rsign = %d, " \ "isign = %d, check_sign_zero = %d\n", creal(x), cimag(x), \ creal(dx), cimag(dx), rsign, isign, cksignzero); \ } \ } \ while(0) #define TEST_LOSS_OF_PRECISION(cfunc, rfunc, real) \ do { \ if (!check_loss_of_precision(ADDSUFFIX(cfunc), ADDSUFFIX(rfunc), real, \ STRINGIZE(cfunc) STRINGIZE(SUFFIX))) { \ ret = 0; \ } \ if (!check_near_crossover(ADDSUFFIX(cfunc), \ STRINGIZE(cfunc) STRINGIZE(SUFFIX))) { \ ret = 0; \ } \ } \ while(0) TYPE complex cpack(TYPE r, TYPE i) { union { TYPE complex z; TYPE a[2]; } z1; z1.a[0] = r; z1.a[1] = i; return z1.z; } int isclose(TYPE a, TYPE b) { const TYPE atol = CLOSE_ATOL; const TYPE rtol = CLOSE_RTOL; TYPE signa = ADDSUFFIX(copysign)(1.0, a); TYPE signb = ADDSUFFIX(copysign)(1.0, b); if (isfinite(a) && isfinite(b)) { if (ADDSUFFIX(fabs)(a - b) <= (atol + rtol*ADDSUFFIX(fabs)(b))) { if (b == 0 && signb < 0) { return (signa == signb); } } } else if (isinf(a) && isinf(b)) { return (signa == signb); @@ -153,96 +211,76 @@ int isclose(double a, double b) } } int cisclose(TYPE complex a, TYPE complex b) { TYPE ar = ADDSUFFIX(creal)(a); TYPE ai = ADDSUFFIX(cimag)(a); TYPE br = ADDSUFFIX(creal)(b); TYPE bi = ADDSUFFIX(cimag)(b); return isclose(ar, br) && isclose(ai, bi); } typedef TYPE complex (*complexfunc)(TYPE complex); typedef TYPE (*realfunc)(TYPE); int check_branch_cut(complexfunc cfunc, TYPE complex x0, TYPE complex dx, int re_sign, int im_sign, int sig_zero_ok) { const TYPE scale = EPS * 1e3; const TYPE atol = 1e-4; TYPE complex shift = dx*scale*ADDSUFFIX(cabs)(x0)/ADDSUFFIX(cabs)(dx); TYPE complex y0 = cfunc(x0); TYPE complex yp = cfunc(x0 + shift); TYPE complex ym = cfunc(x0 - shift); TYPE y0r, y0i, ypr, ypi, ymr, ymi; y0r = ADDSUFFIX(creal)(y0); y0i = ADDSUFFIX(cimag)(y0); ypr = ADDSUFFIX(creal)(yp); ypi = ADDSUFFIX(cimag)(yp); ymr = ADDSUFFIX(creal)(ym); ymi = ADDSUFFIX(cimag)(ym); if (ADDSUFFIX(fabs)(y0r - ypr) >= atol) return 0; if (ADDSUFFIX(fabs)(y0i - ypi) >= atol) return 0; if (ADDSUFFIX(fabs)(y0r - re_sign*ymr) >= atol) return 0; if (ADDSUFFIX(fabs)(y0i - im_sign*ymi) >= atol) return 0; if (sig_zero_ok) { if (ADDSUFFIX(creal)(x0) == 0 && ADDSUFFIX(creal)(dx) != 0) { x0 = cpack(NZERO, ADDSUFFIX(cimag)(x0)); ym = cfunc(x0); ymr = ADDSUFFIX(creal)(ym); ymi = ADDSUFFIX(cimag)(ym); if (ADDSUFFIX(fabs)(y0r - re_sign*ymr) >= atol) return 0; if (ADDSUFFIX(fabs)(y0i - im_sign*ymi) >= atol) return 0; } else if (ADDSUFFIX(cimag)(x0) == 0 && ADDSUFFIX(cimag)(dx) != 0) { x0 = cpack(ADDSUFFIX(creal)(x0), NZERO); ym = cfunc(x0); ymr = ADDSUFFIX(creal)(ym); ymi = ADDSUFFIX(cimag)(ym); if (ADDSUFFIX(fabs)(y0r - re_sign*ymr) >= atol) return 0; if (ADDSUFFIX(fabs)(y0i - im_sign*ymi) >= atol) return 0; } } return 1; } int check_near_crossover(complexfunc cfunc, const char* fname) { const TYPE x = 1e-3; const int rpnt[] = {-1, -1, -1, 0, 0, 1, 1, 1}; @@ -260,17 +298,22 @@ int check_near_crossover(complexfunc cfunc) drj = 2 * x * dr[j] * EPS; dij = 2 * x * di[j] * EPS; for (k = 0; k < npnt; k++) { zp = cpack(x*rpnt[k] + drj, x*ipnt[k] + dij); zm = cpack(x*rpnt[k] - drj, x*ipnt[k] - dij); czp = cfunc(zp); czm = cfunc(zm); diff = ADDSUFFIX(cabs)(czp - czm); if ( diff > 2*EPS || czp == czm) { printf(fname); printf(": Loss of precision: j = %d, k = %d\n", j, k); printf("zp = (%.16e + %.16ej) -> (%.16e + %.16ej)\n", \ ADDSUFFIX(creal)(zp), ADDSUFFIX(cimag)(zp), \ ADDSUFFIX(creal)(czp), ADDSUFFIX(cimag)(czp)); printf("zm = (%.16e + %.16ej) -> (%.16e + %.16ej)\n", \ ADDSUFFIX(creal)(zm), ADDSUFFIX(cimag)(zm), \ ADDSUFFIX(creal)(czm), ADDSUFFIX(cimag)(czm)); printf("diff = %.16e, exact match = %d\n", diff, czp == czm); ret = 0; } @@ -279,26 +322,27 @@ int check_near_crossover(complexfunc cfunc) return 1; } int clp_internal(complexfunc cfunc, realfunc rfunc, int real, TYPE x) { TYPE num = rfunc(x); TYPE den; TYPE complex z; if (real == 1) { z = cpack(x, 0); z = cfunc(z); den = ADDSUFFIX(creal)(z); } else { z = cpack(0, x); z = cfunc(z); den = ADDSUFFIX(cimag)(z); } return ADDSUFFIX(fabs)(num/den - 1); } int check_loss_of_precision(complexfunc cfunc, realfunc rfunc, int real, const char* fname) { const int n_series = 200; const int n_basic = 10; @@ -318,9 +362,10 @@ int check_loss_of_precision(complexfunc cfunc, realfunc rfunc, int real) for(k = 0; k < n_series; k++) { x = ADDSUFFIX(pow)(10.0, xsb + k*dxs); ratio = clp_internal(cfunc, rfunc, real, x); if (ratio > rtol) { printf(fname); printf(": Loss of precision vs real:\n"); printf("x = %.16e\n", x); printf("ratio = %.16e\n", ratio); ret = 0; @@ -329,18 +374,19 @@ int check_loss_of_precision(complexfunc cfunc, realfunc rfunc, int real) for(k = 0; k < n_basic; k++) { x = ADDSUFFIX(pow)(10.0, xbb + k*dxb); ratio = clp_internal(cfunc, rfunc, real, x); if (ratio > rtol) { printf(fname); printf(": Loss of precision vs. real:\n"); printf("x = %.16e\n", x); printf("ratio = %.16e\n", ratio); ret = 0; } } return ret; } #ifdef CACOS int test_cacos() { int ret = 1; @@ -385,9 +431,18 @@ int test_cacos() TEST(cacos, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(cacos, -2, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(cacos, 2, 0, 0, -1, 1, -1, 1); TEST_BRANCH_CUT(cacos, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(cacos, 0, 2, 1, 0, 1, 1, 1); TEST(cacos, .5, 0, ADDSUFFIX(acos)(0.5), 0); return ret; } #endif #ifdef CASIN int test_casin() { int ret = 1; @@ -433,23 +488,22 @@ int test_casin() TEST(casin, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(casin, asin, 0); TEST(casin, 1e-5, 1e-5, 9.999999999666666667e-6, 1.0000000000333333333e-5); TEST_BRANCH_CUT(casin, -2, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(casin, 2, 0, 0, -1, 1, -1, 1); TEST_BRANCH_CUT(casin, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(casin, 0, 2, 1, 0, 1, 1, 1); TEST(casin, 0.5, 0, ADDSUFFIX(asin)(0.5), 0); return ret; } #endif #ifdef CATAN int test_catan() { int ret = 1; @@ -499,23 +553,22 @@ int test_catan() TEST(catan, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(catan, atan, 0); TEST(catan, 1e-5, 1e-5, 1.000000000066666666e-5, 9.999999999333333333e-6); TEST_BRANCH_CUT(catan, 0, -2, 1, 0, -1, 1, 1); TEST_BRANCH_CUT(catan, 0, 2, -1, 0, -1, 1, 1); TEST_BRANCH_CUT(catan, -2, 0, 0, 1, 1, 1, 1); TEST_BRANCH_CUT(catan, 2, 0, 0, 1, 1, 1, 1); TEST(catan, 0.5, 0, ADDSUFFIX(catan)(0.5), 0); return ret; } #endif #ifdef CACOSH int test_cacosh() { int ret = 1; @@ -556,9 +609,18 @@ int test_cacosh() TEST(cacosh, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(cacosh, -1, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(cacosh, 0.5, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(cacosh, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(cacosh, 0, 2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(cacosh, 2, 0, 0, 1, 1, 1, 1); TEST(cacosh, 0.5, 0, ADDSUFFIX(acosh)(1.5), 0); return ret; } #endif #ifdef CASINH int test_casinh() { int ret = 1; @@ -603,24 +665,23 @@ int test_casinh() TEST(casinh, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(casinh, asinh, 1); TEST(casinh, 1e-5, 1e-5, 1.0000000000333333333e-5, 9.999999999666666667e-6); TEST_BRANCH_CUT(casinh, 0, -2, -1, 0, -1, 1, 1); TEST_BRANCH_CUT(casinh, 0, 2, 1, 0, -1, 1, 1); TEST_BRANCH_CUT(casinh, -2, 0, 0, 1, 1, 1, 1); TEST_BRANCH_CUT(casinh, 2, 0, 0, 1, 1, 1, 1); TEST_BRANCH_CUT(casinh, 0, 0, 1, 0, 1, 1, 1); TEST(casinh, 0.5, 0, ADDSUFFIX(asinh)(0.5), 0); return ret; } #endif #ifdef CATANH int test_catanh() { int ret = 1; @@ -671,23 +732,23 @@ int test_catanh() /* TEST(catanh, NAN, INFINITY, 0, M_PI_2); */ TEST(catanh, NAN, NAN, NAN, NAN); TEST_LOSS_OF_PRECISION(catanh, atanh, 1); TEST(catanh, 1e-5, 1e-5, 9.999999999333333333e-6, 1.000000000066666666e-5); TEST_BRANCH_CUT(catanh, -2, 0, 0, 1, 1, -1, 1); TEST_BRANCH_CUT(catanh, 2, 0, 0, -1, 1, -1, 1); TEST_BRANCH_CUT(catanh, 0, -2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(catanh, 0, 2, 1, 0, 1, 1, 1); TEST_BRANCH_CUT(catanh, 0, 0, 0, 1, 1, 1, 1); TEST(catanh, 0.5, 0, ADDSUFFIX(atanh)(0.5), 0); return ret; } #endif #ifdef CCOS int test_ccos() { int ret = 1; @@ -698,7 +759,8 @@ int test_ccos() TEST(ccos, 0, NZERO, 1, 0); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccos, -INFINITY, 0, NAN, 0, \ NAN, NZERO, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccos, NAN, 0, NAN, 0, NAN, NZERO); @@ -736,7 +798,8 @@ int test_ccos() TEST(ccos, 5.0, -INFINITY, INFINITY, -INFINITY); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccos, -INFINITY, INFINITY, INFINITY, NAN, \ -INFINITY, NAN, FE_INVALID); TEST(ccos, NAN, INFINITY, INFINITY, NAN); TEST(ccos, NAN, -INFINITY, INFINITY, NAN); @@ -750,10 +813,14 @@ int test_ccos() TEST(ccos, 2.0, NAN, NAN, NAN); TEST(ccos, NAN, NAN, NAN, NAN); TEST(ccos, 0.5, 0, ADDSUFFIX(cos)(0.5), 0); return ret; } #endif #ifdef CSIN int test_csin() { int ret = 1; @@ -764,7 +831,8 @@ int test_csin() TEST(csin, NZERO, NZERO, NZERO, NZERO); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(csin, -INFINITY, 0, NAN, 0, \ NAN, NZERO, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(csin, NAN, 0, NAN, 0, NAN, NZERO); @@ -802,7 +870,8 @@ int test_csin() TEST(csin, 5.0, -INFINITY, -INFINITY, -INFINITY); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(csin, -INFINITY, INFINITY, NAN, INFINITY, \ NAN, -INFINITY, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(csin, NAN, INFINITY, NAN, INFINITY, NAN, -INFINITY); @@ -816,10 +885,14 @@ int test_csin() TEST(csin, 2.0, NAN, NAN, NAN); TEST(csin, NAN, NAN, NAN, NAN); TEST(csin, 0.5, 0, ADDSUFFIX(sin)(0.5), 0); return ret; } #endif #ifdef CTAN int test_ctan() { int ret = 1; @@ -864,9 +937,16 @@ int test_ctan() TEST(ctan, NAN, NAN, NAN, NAN); TEST(ctan, 0.5, 0, ADDSUFFIX(tan)(0.5), 0); TEST(ctan, 0, 1000, 0, 1); TEST(ctan, 0, -1000, 0, -1); return ret; } #endif #ifdef CCOSH int test_ccosh() { int ret = 1; @@ -877,7 +957,8 @@ int test_ccosh() TEST(ccosh, NZERO, NZERO, 1, 0); /* sign of imaginary part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccosh, 0, INFINITY, NAN, 0, \ NAN, NZERO, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccosh, 0, NAN, NAN, 0, NAN, NZERO); @@ -915,7 +996,8 @@ int test_ccosh() TEST(ccosh, -INFINITY, -5.0, INFINITY, -INFINITY); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(ccosh, INFINITY, INFINITY, INFINITY, NAN, \ -INFINITY, NAN, FE_INVALID); TEST(ccosh, INFINITY, NAN, INFINITY, NAN); TEST(ccosh, -INFINITY, NAN, INFINITY, NAN); @@ -930,9 +1012,13 @@ int test_ccosh() TEST(ccosh, NAN, NAN, NAN, NAN); TEST(ccosh, 0.5, 0, ADDSUFFIX(cosh)(0.5), 0); return ret; } #endif #ifdef CSINH int test_csinh() { int ret = 1; @@ -943,7 +1029,8 @@ int test_csinh() TEST(csinh, NZERO, NZERO, NZERO, NZERO); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(csinh, 0, INFINITY, 0, NAN, \ NZERO, NAN, FE_INVALID); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(csinh, 0, NAN, 0, NAN, NZERO, NAN); @@ -981,7 +1068,8 @@ int test_csinh() TEST(csinh, -INFINITY, -5.0, -INFINITY, INFINITY); /* sign of real part is unspecified */ TEST_RAISES_UNSPECIFIED2(csinh, INFINITY, INFINITY, INFINITY, NAN, \ -INFINITY, NAN, FE_INVALID); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(csinh, INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); @@ -995,10 +1083,14 @@ int test_csinh() TEST(csinh, NAN, -2.0, NAN, NAN); TEST(csinh, NAN, NAN, NAN, NAN); TEST(csinh, 0.5, 0, ADDSUFFIX(sinh)(0.5), 0); return ret; } #endif #ifdef CTANH int test_ctanh() { int ret = 1; @@ -1043,9 +1135,16 @@ int test_ctanh() TEST(ctanh, NAN, NAN, NAN, NAN); TEST(ctanh, 0.5, 0, ADDSUFFIX(tanh)(0.5), 0); TEST(ctanh, 1000, 0, 1, 0); TEST(ctanh, -1000, 0, -1, 0); return ret; } #endif #ifdef CEXP int test_cexp() { int ret = 1; @@ -1084,14 +1183,18 @@ int test_cexp() TEST(cexp, INFINITY, -5.0, INFINITY, INFINITY); /* signs of both parts are unspecified */ TEST_UNSPECIFIED4(cexp, -INFINITY, INFINITY, 0, 0, NZERO, 0, \ 0, NZERO, NZERO, NZERO); TEST_UNSPECIFIED4(cexp, -INFINITY, -INFINITY, 0, 0, NZERO, 0, \ 0, NZERO, NZERO, NZERO); /* sign of real part is unspecifed */ TEST_RAISES_UNSPECIFIED2(cexp, INFINITY, INFINITY, INFINITY, \ NAN, -INFINITY, NAN, FE_INVALID); /* signs of both parts are unspecified */ TEST_UNSPECIFIED4(cexp, -INFINITY, NAN, 0, 0, NZERO, 0, \ 0, NZERO, NZERO, NZERO); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(cexp, INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); @@ -1105,9 +1208,18 @@ int test_cexp() TEST(cexp, NAN, NAN, NAN, NAN); TEST(cexp, 0.5, 0, ADDSUFFIX(exp)(0.5), 0); TEST(cexp, 1, 0, M_E, 0); TEST(cexp, 0, 1, ADDSUFFIX(cos)(1), ADDSUFFIX(sin)(1)); TEST(cexp, 1, 1, M_E*ADDSUFFIX(cos)(1), M_E*ADDSUFFIX(sin)(1)); return ret; } #endif #ifdef CLOG int test_clog() { int ret = 1; @@ -1147,19 +1259,147 @@ int test_clog() TEST(clog, NAN, -INFINITY, INFINITY, NAN); TEST(clog, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(clog, -0.5, 0, 0, 1, 1, -1, 1); TEST(clog, 0.5, 0, ADDSUFFIX(log)(0.5), 0); TEST(clog, 1, 0, 0, 0); TEST(clog, 1, 2, 0.80471895621705014, 1.1071487177940904); return ret; } #endif #ifdef CPOW int test_cpow() { int ret = 1; /* there are _no_ annex G values for cpow. */ /* We can check for branch cuts in here */ /* tests from test_umath.py: TestPower: test_power_complex */ TEST_CPOW(1, 2, 0, 0, 1, 0); TEST_CPOW(2, 3, 0, 0, 1, 0); TEST_CPOW(3, 4, 0, 0, 1, 0); TEST_CPOW(1, 2, 1, 0, 1, 2); TEST_CPOW(2, 3, 1, 0, 2, 3); TEST_CPOW(3, 4, 1, 0, 3, 4); TEST_CPOW(1, 2, 2, 0, -3, 4); TEST_CPOW(2, 3, 2, 0, -5, 12); TEST_CPOW(3, 4, 2, 0, -7, 24); TEST_CPOW(1, 2, 3, 0, -11, -2); TEST_CPOW(2, 3, 3, 0, -46, 9); TEST_CPOW(3, 4, 3, 0, -117, 44); TEST_CPOW(1, 2, 4, 0, -7, 24); TEST_CPOW(2, 3, 4, 0, -119, -120); TEST_CPOW(3, 4, 4, 0, -527, -336); TEST_CPOW(1, 2, -1, 0, 1.0/5.0, -2.0/5.0); TEST_CPOW(2, 3, -1, 0, 2.0/13.0, -3.0/13.0); TEST_CPOW(3, 4, -1, 0, 3.0/25.0, -4.0/25.0); TEST_CPOW(1, 2, -2, 0, -3.0/25.0, -4.0/25.0); TEST_CPOW(2, 3, -2, 0, -5.0/169.0, -12.0/169.0); TEST_CPOW(3, 4, -2, 0, -7.0/625.0, -24.0/625.0); TEST_CPOW(1, 2, -3, 0, -11.0/125.0, 2.0/125.0); TEST_CPOW(2, 3, -3, 0, -46.0/2197.0, -9.0/2197.0); TEST_CPOW(3, 4, -3, 0, -117.0/15625.0, -44.0/15625.0); TEST_CPOW(1, 2, 0.5, 0, 1.272019649514069, 0.7861513777574233); TEST_CPOW(2, 3, 0.5, 0, 1.6741492280355401, 0.895977476129838); TEST_CPOW(3, 4, 0.5, 0, 2, 1); TEST_CPOW(1, 2, 14, 0, -76443, 16124); TEST_CPOW(2, 3, 14, 0, 23161315, 58317492); TEST_CPOW(3, 4, 14, 0, 5583548873, 2465133864); TEST_CPOW(0, INFINITY, 1, 0, 0, INFINITY); TEST_CPOW(0, INFINITY, 2, 0, -INFINITY, NAN); TEST_CPOW(0, INFINITY, 3, 0, NAN, NAN); TEST_CPOW(1, INFINITY, 1, 0, 1, INFINITY); TEST_CPOW(1, INFINITY, 2, 0, -INFINITY, INFINITY); TEST_CPOW(1, INFINITY, 3, 0, -INFINITY, NAN); /* tests from test_umath.py: TestPower: test_power_zero */ TEST_CPOW(0, 0, 0.33, 0, 0, 0); TEST_CPOW(0, 0, 0.5, 0, 0, 0); TEST_CPOW(0, 0, 1.0, 0, 0, 0); TEST_CPOW(0, 0, 1.5, 0, 0, 0); TEST_CPOW(0, 0, 2.0, 0, 0, 0); TEST_CPOW(0, 0, 3.0, 0, 0, 0); TEST_CPOW(0, 0, 4.0, 0, 0, 0); TEST_CPOW(0, 0, 5.0, 0, 0, 0); TEST_CPOW(0, 0, 6.6, 0, 0, 0); TEST_CPOW(0, 0, 0, 0, 1, 0); TEST_CPOW(0, 0, 0, 1, NAN, NAN); TEST_CPOW(0, 0, -0.33, 0, NAN, NAN); TEST_CPOW(0, 0, -0.5, 0, NAN, NAN); TEST_CPOW(0, 0, -1.0, 0, NAN, NAN); TEST_CPOW(0, 0, -1.5, 0, NAN, NAN); TEST_CPOW(0, 0, -2.0, 0, NAN, NAN); TEST_CPOW(0, 0, -3.0, 0, NAN, NAN); TEST_CPOW(0, 0, -4.0, 0, NAN, NAN); TEST_CPOW(0, 0, -5.0, 0, NAN, NAN); TEST_CPOW(0, 0, -6.6, 0, NAN, NAN); TEST_CPOW(0, 0, -1, 0.2, NAN, NAN); /* tests from test_umath_complex.py: TestCpow: test_simple * --- skip, duplicating existing tests --- */ /* tests from test_umath_complex.py: TestCpow: test_scalar, test_array * these tests are equilvent for this level. */ TEST_CPOW(1, 0, 1, 0, 1, 0); TEST_CPOW(1, 0, 0, 1, 1, 0); TEST_CPOW(1, 0, -0.5, 1.5, 1, 0); TEST_CPOW(1, 0, 2, 0, 1, 0); TEST_CPOW(1, 0, 3, 0, 1, 0); TEST_CPOW(0, 1, 1, 0, 0, 1); TEST_CPOW(0, 1, 0, 1, exp(-M_PI_2), 0); TEST_CPOW(0, 1, -0.5, 1.5, 0.067019739708273365, 0.067019739708273365); TEST_CPOW(0, 1, 2, 0, -1, 0); TEST_CPOW(0, 1, 3, 0, 0, -1); TEST_CPOW(2, 0, 1, 0, 2, 0); TEST_CPOW(2, 0, 0, 1, cos(M_LN2), sin(M_LN2)); TEST_CPOW(2, 0, 2, 0, 4, 0); TEST_CPOW(2, 0, 3, 0, 8, 0); TEST_CPOW(2.5, 0.375, 1, 0, 2.5, 0.375); TEST_CPOW(2.5, 0.375, 0, 1, 0.51691507509598866, 0.68939360813851125); TEST_CPOW(2.5, 0.375, -0.5, 1.5, 0.12646517347496394, 0.48690593271654437); TEST_CPOW(2.5, 0.375, 2, 0, 391.0/64.0, 15.0/8.0); TEST_CPOW(2.5, 0.375, 3, 0, 1865.0/128.0, 3573.0/512.0); TEST_CPOW(INFINITY, 0, 1, 0, NAN, NAN); TEST_CPOW(INFINITY, 0, 0, 1, NAN, NAN); TEST_CPOW(INFINITY, 0, -0.5, 1.5, NAN, NAN); TEST_CPOW(INFINITY, 0, 2, 0, NAN, NAN); TEST_CPOW(INFINITY, 0, 3, 0, NAN, NAN); TEST_CPOW(NAN, 0, 1, 0, NAN, NAN); TEST_CPOW(NAN, 0, 0, 1, NAN, NAN); TEST_CPOW(NAN, 0, -0.5, 1.5, NAN, NAN); TEST_CPOW(NAN, 0, 2, 0, NAN, NAN); TEST_CPOW(NAN, 0, 3, 0, NAN, NAN); return ret; } #endif #ifdef CSQRT int test_csqrt() { int ret = 1; @@ -1202,27 +1442,70 @@ int test_csqrt() TEST(csqrt, NAN, NAN, NAN, NAN); TEST_BRANCH_CUT(csqrt, -0.5, 0, 0, 1, 1, -1, 1); TEST(csqrt, 0.5, 0, ADDSUFFIX(sqrt)(0.5), 0); TEST(csqrt, 1, 0, 1, 0); TEST(csqrt, 0, 1, M_SQRT2/2.0, M_SQRT2/2.0); TEST(csqrt, -1, 0, 0, 1); TEST(csqrt, 1, 1, 1.0986841134678100, 0.4550898605622273); TEST(csqrt, 1, -1, 1.0986841134678100, -0.4550898605622273); return ret; } #endif int main(int argc, char** argv) { #ifdef CACOS printf("cacos: %d\n\n", test_cacos()); #endif #ifdef CASIN printf("casin: %d\n\n", test_casin()); #endif #ifdef CATAN printf("catan: %d\n\n", test_catan()); #endif #ifdef CACOSH printf("cacosh: %d\n\n", test_cacosh()); #endif #ifdef CASINH printf("casinh: %d\n\n", test_casinh()); #endif #ifdef CATANH printf("catanh: %d\n\n", test_catanh()); #endif #ifdef CCOS printf("ccos: %d\n\n", test_ccos()); #endif #ifdef CSIN printf("csin: %d\n\n", test_csin()); #endif #ifdef CTAN printf("ctan: %d\n\n", test_ctan()); #endif #ifdef CCOSH printf("ccosh: %d\n\n", test_ccosh()); #endif #ifdef CSINH printf("csinh: %d\n\n", test_csinh()); #endif #ifdef CTANH printf("ctanh: %d\n\n", test_ctanh()); #endif #ifdef CEXP printf("cexp: %d\n\n", test_cexp()); #endif #ifdef clog printf("clog: %d\n\n", test_clog()); #endif #ifdef CPOW printf("cpow, %d\n\n", test_cpow()); #endif #ifdef CSQRT printf("csqrt: %d\n\n", test_csqrt()); #endif return 0; } -
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Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -4,31 +4,102 @@ #include <math.h> #include <complex.h> #ifdef FLOAT #define TYPE float #define SUFFIX f #define EPS FLT_EPSILON #else #ifdef DOUBLE #define TYPE double #define SUFFIX #define EPS DBL_EPSILON #else #ifdef LONGDOUBLE #define TYPE long double #define SUFFIX l #define EPS LDBL_EPSILON #else #error "Define FLOAT or DOUBLE or LONGDOUBLE" #endif #endif #endif const double NZERO = -1.0 * 0.0; const float NZEROf = -1.0 * 0.0; #define STRINGIZE_INT(A) #A #define STRINGIZE(A) STRINGIZE_INT(A) #define CONCAT(A, B) A ## B #define ADDSUFFIX_INT(A, B) CONCAT(A, B) #define ADDSUFFIX(A) ADDSUFFIX_INT(A, SUFFIX) #define TEST_PRINTF(func, x, e, r) printf("%d: " STRINGIZE(func) STRINGIZE(SUFFIX) "(%.16e + %.16ej): expected: %.16e + %.16ej: received: %.16e + %.16ej\n", __LINE__, ADDSUFFIX(creal)(x), ADDSUFFIX(cimag)(x), ADDSUFFIX(creal)(e), ADDSUFFIX(cimag)(e), ADDSUFFIX(creal)(r), ADDSUFFIX(cimag)(r)) #define TEST(func, xr, xi, er, ei) \ do { \ TYPE complex x = ADDSUFFIX(cpack)(xr, xi); \ TYPE complex e = ADDSUFFIX(cpack)(er, ei); \ TYPE complex r = ADDSUFFIX(func)(x); \ if (!ADDSUFFIX(cisclose)(r, e)) { \ ret = 0; \ TEST_PRINTF(func, x, e, r); \ } \ } \ while(0) #define TEST_UNSPECIFIED2(func, xr, xi, er1, ei1, er2, ei2) \ do { \ TYPE complex x = ADDSUFFIX(cpack)(xr, xi); \ TYPE complex e1 = ADDSUFFIX(cpack)(er1, ei1); \ TYPE complex e2 = ADDSUFFIX(cpack)(er2, ei2); \ TYPE complex r = ADDSUFFIX(func)(x); \ if (!ADDSUFFIX(cisclose)(r, e1) && !ADDSUFFIX(cisclose)(r, e2)) { \ ret = 0; \ TEST_PRINTF(func, x, e1, r); \ printf("or"); \ TEST_PRINTF(func, x, e2, r); \ } \ } \ while(0) #define TEST_UNSPECIFIED4(func, xr, xi, er1, ei1, er2, ei2, er3, ei3, er4, ei4)\ do { \ TYPE complex x = ADDSUFFIX(cpack)(xr, xi); \ TYPE complex e1 = ADDSUFFIX(cpack)(er1, ei1); \ TYPE complex e2 = ADDSUFFIX(cpack)(er2, ei2); \ TYPE complex e3 = ADDSUFFIX(cpack)(er3, ei3); \ TYPE complex e4 = ADDSUFFIX(cpack)(er4, ei4); \ TYPE complex r = func(x); \ if (!ADDSUFFIX(cisclose)(r, e1) && !ADDSUFFIX(cisclose)(r, e2) \ && !ADDSUFFIX(cisclose)(r, e3) && !ADDSUFFIX(cisclose)(r, e4)) { \ ret = 0; \ TEST_PRINTF(func, x, e1, r); \ printf("or"); \ TEST_PRINTF(func, x, e2, r); \ printf("or"); \ TEST_PRINTF(func, x, e3, r); \ printf("or"); \ TEST_PRINTF(func, x, e4, r); \ } \ } \ while(0) #define TEST_RAISES(func, xr, xi, er, ei, fpe) \ do { \ int except; \ TYPE complex r; \ TYPE complex x = ADDSUFFIX(cpack)(xr, xi); \ TYPE complex e = ADDSUFFIX(cpack)(er, ei); \ feclearexcept(FE_ALL_EXCEPT); \ r = ADDSUFFIX(func)(x); \ except = fetestexcept(fpe); \ if (!(except & fpe && ADDSUFFIX(cisclose)(r, e))) { \ ret = 0; \ TEST_PRINTF(func, x, e, r); \ } \ } \ while(0) double complex cpack(double r, double i) { @@ -41,13 +112,70 @@ double complex cpack(double r, double i) return z1.z; } float complex cpackf(float r, float i) { union { float complex z; float a[2]; } z1; z1.a[0] = r; z1.a[1] = i; return z1.z; } long double complex cpackl(long double r, long double i) { union { long double complex z; long double a[2]; } z1; z1.a[0] = r; z1.a[1] = i; return z1.z; } int isclose(double a, double b) { double atol = 0.0; double rtol = 1e-12; double signa = copysign(1.0, a); double signb = copysign(1.0, b); if (isfinite(a) && isfinite(b)) { return (fabs(a - b) <= (atol + rtol*fabs(b))) && (signa == signb); } else if (isinf(a) && isinf(b)) { return (signa == signb); } else { return (isnan(a) && isnan(b)); } } int isclosef(float a, float b) { float atol = 0.0; float rtol = 1e-5; if (isfinite(a) && isfinite(b)) { return (fabsf(a - b) <= (atol + rtol*fabsf(b))) && (copysignf(1.0, a) == copysignf(1.0, b)); } else if (isinf(a) && isinf(b)) { return (signbit(a) == signbit(b)); } else { return (isnan(a) && isnan(b)); } } int isclosel(long double a, long double b) { long double atol = 0.0; long double rtol = 1e-12; if (isfinite(a) && isfinite(b)) { return (fabsl(a - b) <= (atol + rtol*fabsl(b))) && (copysignl(1.0, a) == copysignl(1.0, b)); } else if (isinf(a) && isinf(b)) { return (signbit(a) == signbit(b)); @@ -57,7 +185,7 @@ int isclose(double a, double b) } } int cisclose(double complex a, double complex b) { double ar = creal(a); double ai = cimag(a); @@ -67,16 +195,26 @@ int cd_isclose(double complex a, double complex b) return isclose(ar, br) && isclose(ai, bi); } int cisclosef(float complex a, float complex b) { float ar = crealf(a); float ai = cimagf(a); float br = crealf(b); float bi = cimagf(b); return isclosef(ar, br) && isclose(ai, bi); } int cisclosel(long double complex a, long double complex b) { long double ar = creall(a); long double ai = cimagl(a); long double br = creall(b); long double bi = cimagl(b); return isclosel(ar, br) && isclosel(ai, bi); } /* int check_branch_cut(double complex (*func)(double complex), double complex x0, double complex dx, double re_sign, double im_sign, int sig_zero_ok) { double scale = DBL_EPSILON * 1e3; @@ -95,152 +233,996 @@ int check_branch_cut(double complex (*func)(double complex), double complex x0, if (fabs(cimag(y0) - im_sign*cimag(ym)) >= atol) return 0; if (sig_zero_ok) { return 0; } return 1; } */ typedef TYPE complex (*complexfunc)(TYPE complex); typedef TYPE (*realfunc)(TYPE); int check_near_crossover(complexfunc cfunc) { const TYPE x = 1e-3; const int rpnt[] = {-1, -1, -1, 0, 0, 1, 1, 1}; const int ipnt[] = {-1, 0, 1, -1, 1, -1, 0, -1}; const int npnt = sizeof(rpnt) / sizeof(int); const int dr[] = {1, 0, 1}; const int di[] = {0, 1, 1}; const int ndr = sizeof(dr) / sizeof(int); int k, j; int ret = 1; TYPE drj, dij, diff; TYPE complex zp, zm, czp, czm; for (j = 0; j < ndr; j++) { drj = 2 * x * dr[j] * EPS; dij = 2 * x * di[j] * EPS; for (k = 0; k < npnt; k++) { zp = ADDSUFFIX(cpack)(x*rpnt[k] + drj, x*ipnt[k] + dij); zm = ADDSUFFIX(cpack)(x*rpnt[k] - drj, x*ipnt[k] - dij); czp = cfunc(zp); czm = cfunc(zm); diff = ADDSUFFIX(cabs)(czp - czm); if ( diff > 2*EPS || czp == czm) { printf("Loss of precision near crossover: j = %d, k = %d\n", j, k); printf("zp = (%.16e + %.16ej) -> (%.16e + %.16ej)\n", ADDSUFFIX(creal)(zp), ADDSUFFIX(cimag)(zp), ADDSUFFIX(creal)(czp), ADDSUFFIX(cimag)(czp)); printf("zm = (%.16e + %.16ej) -> (%.16e + %.16ej)\n", ADDSUFFIX(creal)(zm), ADDSUFFIX(cimag)(zm), ADDSUFFIX(creal)(czm), ADDSUFFIX(cimag)(czm)); printf("diff = %.16e, exact match = %d\n", diff, czp == czm); ret = 0; } } } return 1; } int foo(complexfunc cfunc, realfunc rfunc, int real, TYPE x) { TYPE num = rfunc(x); TYPE den; TYPE complex z; if (real == 1) { z = ADDSUFFIX(cpack)(x, 0); z = cfunc(z); den = ADDSUFFIX(creal)(z); } else { z = ADDSUFFIX(cpack)(0, x); z = cfunc(z); den = ADDSUFFIX(cimag)(z); } return ADDSUFFIX(fabs)(num/den - 1); } int check_loss_of_precision(complexfunc cfunc, realfunc rfunc, int real) { const int n_series = 200; const int n_basic = 10; const TYPE rtol = 2*EPS; const TYPE xsb = -20; const TYPE xse = -3.001; const TYPE dxs = (xse - xsb) / n_series; const TYPE xbb = -2.999; const TYPE xbe = 0; const TYPE dxb = (xbe - xbb) / n_basic; TYPE x, ratio; int k; int ret = 1; for(k = 0; k < n_series; k++) { x = ADDSUFFIX(pow)(10.0, xsb + k*dxs); ratio = foo(cfunc, rfunc, real, x); if (ratio > rtol) { printf("Loss of precision:\n"); printf("x = %.16e\n", x); printf("ratio = %.16e\n", ratio); ret = 0; } } for(k = 0; k < n_basic; k++) { x = ADDSUFFIX(pow)(10.0, xbb + k*dxb); ratio = foo(cfunc, rfunc, real, x); if (ratio > rtol) { printf("Loss of precision:\n"); printf("x = %.16e\n", x); printf("ratio = %.16e\n", ratio); ret = 0; return 0; } } return 1; } int test_cacos() { int ret = 1; /* cacos(conj(z)) = conj(cacos(z)) */ TEST(cacos, 0, 0, M_PI_2, NZERO); TEST(cacos, 0, NZERO, M_PI_2, 0); TEST(cacos, NZERO, 0, M_PI_2, NZERO); TEST(cacos, NZERO, NZERO, M_PI_2, 0); TEST(cacos, 0, NAN, M_PI_2, NAN); TEST(cacos, NZERO, NAN, M_PI_2, NAN); TEST(cacos, 2.0, INFINITY, M_PI_2, -INFINITY); TEST(cacos, 2.0, -INFINITY, M_PI_2, INFINITY); /* can raise FE_INVALID or not */ TEST(cacos, 2.0, NAN, NAN, NAN); TEST(cacos, -INFINITY, 2.0, M_PI, -INFINITY); TEST(cacos, -INFINITY, -2.0, M_PI, INFINITY); TEST(cacos, INFINITY, 2.0, 0, -INFINITY); TEST(cacos, INFINITY, -2.0, 0, INFINITY); TEST(cacos, -INFINITY, INFINITY, 0.75 * M_PI, -INFINITY); TEST(cacos, -INFINITY, -INFINITY, 0.75 * M_PI, INFINITY); TEST(cacos, INFINITY, INFINITY, 0.25 * M_PI, -INFINITY); TEST(cacos, INFINITY, -INFINITY, 0.25 * M_PI, -INFINITY); /* sign of imaginary part is unspecified. */ TEST_UNSPECIFIED2(cacos, INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST_UNSPECIFIED2(cacos, -INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); /* can raise FE_INVALID or not */ TEST(cacos, NAN, 2.0, NAN, NAN); TEST(cacos, NAN, -2.0, NAN, NAN); TEST(cacos, NAN, INFINITY, NAN, -INFINITY); TEST(cacos, NAN, -INFINITY, NAN, INFINITY); TEST(cacos, NAN, NAN, NAN, NAN); return ret; } int test_casin() { int ret = 1; /* casin(conj(z)) = conj(casin(z)) and casin is odd */ TEST(casin, 0, 0, 0, 0); TEST(casin, 0, NZERO, 0, NZERO); TEST(casin, NZERO, 0, NZERO, 0); TEST(casin, NZERO, NZERO, NZERO, NZERO); TEST(casin, -INFINITY, 2.0, -M_PI_2, INFINITY); TEST(casin, INFINITY, 2.0, M_PI_2, INFINITY); TEST(casin, -INFINITY, -2.0, -M_PI_2, -INFINITY); TEST(casin, INFINITY, -2.0, M_PI_2, -INFINITY); /* can raise FE_INVALID or not */ TEST(casin, NAN, -2.0, NAN, NAN); TEST(casin, NAN, 2.0, NAN, NAN); TEST(casin, -2.0, INFINITY, NZERO, INFINITY); TEST(casin, 2.0, INFINITY, 0, INFINITY); TEST(casin, -2.0, -INFINITY, NZERO, -INFINITY); TEST(casin, 2.0, -INFINITY, 0, -INFINITY); TEST(casin, -INFINITY, INFINITY, -0.25*M_PI, INFINITY); TEST(casin, INFINITY, INFINITY, 0.25*M_PI, INFINITY); TEST(casin, -INFINITY, -INFINITY, -0.25*M_PI, -INFINITY); TEST(casin, INFINITY, -INFINITY, 0.25*M_PI, -INFINITY); TEST(casin, NAN, INFINITY, NAN, INFINITY); TEST(casin, NAN, -INFINITY, NAN, -INFINITY); TEST(casin, 0, NAN, 0, NAN); TEST(casin, NZERO, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST(casin, -2.0, NAN, NAN, NAN); TEST(casin, 2.0, NAN, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(casin, -INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST_UNSPECIFIED2(casin, INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST(casin, NAN, NAN, NAN, NAN); /* * loss of precision */ if (!check_loss_of_precision(ADDSUFFIX(casin), ADDSUFFIX(asinh), 0)) { printf("loss of precision: casin\n"); ret = 0; } TEST(casin, 1e-5, 1e-5, 9.999999999666666667e-6, 1.0000000000333333333e-5); if (!check_near_crossover(ADDSUFFIX(casin))) { printf("loss of precision near crossover: casin\n"); ret = 0; } return ret; } int test_catan() { int ret = 1; /* catan(conj(z)) = conj(catan(z)) and catan is odd */ TEST(catan, 0, 0, 0, 0); TEST(catan, 0, NZERO, 0, NZERO); TEST(catan, NZERO, 0, NZERO, 0); TEST(catan, NZERO, NZERO, NZERO, NZERO); TEST(catan, NAN, 0, NAN, 0); TEST(catan, NAN, NZERO, NAN, NZERO); TEST_RAISES(catan, NZERO, 1, NZERO, INFINITY, FE_DIVBYZERO); TEST_RAISES(catan, 0, 1, 0, INFINITY, FE_DIVBYZERO); TEST_RAISES(catan, NZERO, -1, NZERO, -INFINITY, FE_DIVBYZERO); TEST_RAISES(catan, 0, -1, 0, -INFINITY, FE_DIVBYZERO); TEST(catan, -INFINITY, 2.0, -M_PI_2, 0); TEST(catan, INFINITY, 2.0, M_PI_2, 0); TEST(catan, -INFINITY, -2.0, -M_PI_2, NZERO); TEST(catan, INFINITY, -2.0, M_PI_2, NZERO); /* can raise FE_INVALID or not */ TEST(catan, NAN, -2.0, NAN, NAN); TEST(catan, NAN, 2.0, NAN, NAN); TEST(catan, -2.0, INFINITY, -M_PI_2, 0); TEST(catan, 2.0, INFINITY, M_PI_2, 0); TEST(catan, -2.0, -INFINITY, -M_PI_2, NZERO); TEST(catan, 2.0, -INFINITY, M_PI_2, NZERO); TEST(catan, -INFINITY, INFINITY, -M_PI_2, 0); TEST(catan, INFINITY, INFINITY, M_PI_2, 0); TEST(catan, -INFINITY, -INFINITY, -M_PI_2, NZERO); TEST(catan, INFINITY, -INFINITY, M_PI_2, NZERO); TEST(catan, NAN, INFINITY, NAN, 0); TEST(catan, NAN, -INFINITY, NAN, NZERO); /* can raise FE_INVALID or not */ TEST(catan, -2.0, NAN, NAN, NAN); TEST(catan, 2.0, NAN, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(catan, -INFINITY, NAN, -M_PI_2, 0, -M_PI_2, NZERO); TEST_UNSPECIFIED2(catan, INFINITY, NAN, M_PI_2, 0, M_PI_2, NZERO); TEST(catan, NAN, NAN, NAN, NAN); /* * loss of precision */ if(!check_loss_of_precision(ADDSUFFIX(catan), ADDSUFFIX(atanh), 0)) { printf("loss of precision: catan\n"); ret = 0; } TEST(catan, 1e-5, 1e-5, 1.000000000066666666e-5, 9.999999999333333333e-6); if (!check_near_crossover(ADDSUFFIX(catan))) { printf("loss of precision near crossover: catan\n"); ret = 0; } return ret; } int test_cacosh() { int ret = 1; /* cacosh(conj(z)) = conj(cacosh(z)) */ TEST(cacosh, 0, 0, 0, M_PI_2); TEST(cacosh, 0, NZERO, 0, -M_PI_2); TEST(cacosh, NZERO, 0, 0, M_PI_2); TEST(cacosh, NZERO, NZERO, 0, -M_PI_2); TEST(cacosh, 2.0, INFINITY, INFINITY, M_PI_2); TEST(cacosh, 2.0, -INFINITY, INFINITY, -M_PI_2); /* can raise FE_INVALID or not */ TEST(cacosh, 2.0, NAN, NAN, NAN); TEST(cacosh, -INFINITY, 2.0, INFINITY, M_PI); TEST(cacosh, -INFINITY, -2.0, INFINITY, -M_PI); TEST(cacosh, INFINITY, 2.0, INFINITY, 0); TEST(cacosh, INFINITY, -2.0, INFINITY, NZERO); TEST(cacosh, -INFINITY, INFINITY, INFINITY, 0.75*M_PI); TEST(cacosh, -INFINITY, -INFINITY, INFINITY, -0.75*M_PI); TEST(cacosh, INFINITY, INFINITY, INFINITY, 0.25*M_PI); TEST(cacosh, INFINITY, -INFINITY, INFINITY, -0.25*M_PI); TEST(cacosh, INFINITY, NAN, INFINITY, NAN); TEST(cacosh, -INFINITY, NAN, INFINITY, NAN); /* can raise FE_INVALID or not */ TEST(cacosh, NAN, 2.0, NAN, NAN); TEST(cacosh, NAN, -2.0, NAN, NAN); TEST(cacosh, NAN, INFINITY, INFINITY, NAN); TEST(cacosh, NAN, -INFINITY, INFINITY, NAN); TEST(cacosh, NAN, NAN, NAN, NAN); return ret; } int test_casinh() { int ret = 1; /* casinh(conj(z)) = conj(casinh(z)) and casinh is odd */ TEST(casinh, 0, 0, 0, 0); TEST(casinh, 0, NZERO, 0, NZERO); TEST(casinh, NZERO, 0, NZERO, 0); TEST(casinh, NZERO, NZERO, NZERO, NZERO); TEST(casinh, 2.0, INFINITY, INFINITY, M_PI_2); TEST(casinh, 2.0, -INFINITY, INFINITY, -M_PI_2); TEST(casinh, -2.0, INFINITY, -INFINITY, M_PI_2); TEST(casinh, -2.0, -INFINITY, -INFINITY, -M_PI_2); /* can raise FE_INVALID or not */ TEST(casinh, 2.0, NAN, NAN, NAN); TEST(casinh, -2.0, NAN, NAN, NAN); TEST(casinh, INFINITY, 2.0, INFINITY, 0); TEST(casinh, INFINITY, -2.0, INFINITY, NZERO); TEST(casinh, -INFINITY, 2.0, -INFINITY, 0); TEST(casinh, -INFINITY, -2.0, -INFINITY, NZERO); TEST(casinh, INFINITY, INFINITY, INFINITY, 0.25*M_PI); TEST(casinh, INFINITY, -INFINITY, INFINITY, -0.25*M_PI); TEST(casinh, -INFINITY, INFINITY, -INFINITY, 0.25*M_PI); TEST(casinh, -INFINITY, -INFINITY, -INFINITY, -0.25*M_PI); TEST(casinh, INFINITY, NAN, INFINITY, NAN); TEST(casinh, -INFINITY, NAN, -INFINITY, NAN); TEST(casinh, NAN, 0, NAN, 0); TEST(casinh, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST(casinh, NAN, 2.0, NAN, NAN); TEST(casinh, NAN, -2.0, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(casinh, NAN, INFINITY, INFINITY, NAN, -INFINITY, NAN); TEST_UNSPECIFIED2(casinh, NAN, -INFINITY, INFINITY, NAN, -INFINITY, NAN); TEST(casinh, NAN, NAN, NAN, NAN); /* * loss of precision */ if(check_loss_of_precision(ADDSUFFIX(casinh), ADDSUFFIX(asinh), 1)) { printf("loss of precision: casinh\n"); ret = 0; } TEST(casinh, 1e-5, 1e-5, 1.0000000000333333333e-5, 9.999999999666666667e-6); if (!check_near_crossover(ADDSUFFIX(casinh))) { printf("loss of precision near crossover: casinh\n"); ret = 0; } return ret; } int test_catanh() { int ret = 1; /* catanh(conj(z)) = conj(catanh(z)) and catanh is odd */ TEST(catanh, 0, 0, 0, 0); TEST(catanh, 0, NZERO, 0, NZERO); TEST(catanh, NZERO, 0, NZERO, 0); TEST(catanh, NZERO, NZERO, NZERO, NZERO); TEST(catanh, 0, NAN, 0, NAN); TEST(catanh, NZERO, NAN, NZERO, NAN); TEST_RAISES(catanh, 1, 0, INFINITY, 0, FE_DIVBYZERO); TEST_RAISES(catanh, 1, NZERO, INFINITY, NZERO, FE_DIVBYZERO); TEST_RAISES(catanh, -1, 0, -INFINITY, 0, FE_DIVBYZERO); TEST_RAISES(catanh, -1, NZERO, -INFINITY, NZERO, FE_DIVBYZERO); TEST(catanh, 2.0, INFINITY, 0, M_PI_2); TEST(catanh, 2.0, -INFINITY, 0, -M_PI_2); TEST(catanh, -2.0, INFINITY, NZERO, M_PI_2); TEST(catanh, -2.0, -INFINITY, NZERO, -M_PI_2); /* can raise FE_INVALID or not */ TEST(catanh, 2.0, NAN, NAN, NAN); TEST(catanh, -2.0, NAN, NAN, NAN); TEST(catanh, INFINITY, 2.0, 0, M_PI_2); TEST(catanh, INFINITY, -2.0, 0, -M_PI_2); TEST(catanh, -INFINITY, 2.0, NZERO, M_PI_2); TEST(catanh, -INFINITY, -2.0, NZERO, -M_PI_2); TEST(catanh, INFINITY, INFINITY, 0, M_PI_2); TEST(catanh, INFINITY, -INFINITY, 0, -M_PI_2); TEST(catanh, -INFINITY, INFINITY, NZERO, M_PI_2); TEST(catanh, -INFINITY, -INFINITY, NZERO, -M_PI_2); TEST(catanh, INFINITY, NAN, 0, NAN); TEST(catanh, -INFINITY, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST(catanh, NAN, 2.0, NAN, NAN); TEST(catanh, NAN, -2.0, NAN, NAN); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(catanh, NAN, INFINITY, 0, M_PI_2, NZERO, M_PI_2); TEST_UNSPECIFIED2(catanh, NAN, -INFINITY, 0, -M_PI_2, NZERO, -M_PI_2); /* TEST(catanh, NAN, INFINITY, 0, M_PI_2); */ TEST(catanh, NAN, NAN, NAN, NAN); /* * loss of precision */ if(check_loss_of_precision(ADDSUFFIX(catanh), ADDSUFFIX(atanh), 1)) { printf("loss of precision: catanh\n"); ret = 0; } TEST(catanh, 1e-5, 1e-5, 9.999999999333333333e-6, 1.000000000066666666e-5); if (!check_near_crossover(ADDSUFFIX(catanh))) { printf("loss of precision near crossover: casinh\n"); ret = 0; } return ret; } int test_ccos() { int ret = 1; /* ccos(conj(z)) = conj(ccos(z)) and ccos is even */ TEST(ccos, NZERO, 0, 1, 0); TEST(ccos, 0, 0, 1, NZERO); TEST(ccos, NZERO, NZERO, 1, NZERO); TEST(ccos, 0, NZERO, 1, 0); /* sign of imaginary part is unspecified */ TEST_RAISES(ccos, -INFINITY, 0, NAN, 0, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccos, NAN, 0, NAN, 0, NAN, NZERO); TEST_UNSPECIFIED2(ccos, NAN, NZERO, NAN, 0, NAN, NZERO); TEST_RAISES(ccos, -INFINITY, 2.0, NAN, NAN, FE_INVALID); TEST_RAISES(ccos, INFINITY, 2.0, NAN, NAN, FE_INVALID); TEST_RAISES(ccos, -INFINITY, -2.0, NAN, NAN, FE_INVALID); TEST_RAISES(ccos, INFINITY, -2.0, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST(ccos, NAN, 2.0, NAN, NAN); TEST(ccos, NAN, -2.0, NAN, NAN); TEST(ccos, NZERO, INFINITY, INFINITY, 0); TEST(ccos, 0, INFINITY, INFINITY, NZERO); TEST(ccos, NZERO, -INFINITY, INFINITY, NZERO); TEST(ccos, 0, -INFINITY, INFINITY, 0); TEST(ccos, -1.0, INFINITY, INFINITY, INFINITY); TEST(ccos, 1.0, INFINITY, INFINITY, -INFINITY); TEST(ccos, -1.0, -INFINITY, INFINITY, -INFINITY); TEST(ccos, 1.0, -INFINITY, INFINITY, INFINITY); TEST(ccos, -2.0, INFINITY, -INFINITY, INFINITY); TEST(ccos, 2.0, INFINITY, -INFINITY, -INFINITY); TEST(ccos, -2.0, -INFINITY, -INFINITY, -INFINITY); TEST(ccos, 2.0, -INFINITY, -INFINITY, INFINITY); TEST(ccos, -4.0, INFINITY, -INFINITY, -INFINITY); TEST(ccos, 4.0, INFINITY, -INFINITY, INFINITY); TEST(ccos, -4.0, -INFINITY, -INFINITY, INFINITY); TEST(ccos, 4.0, -INFINITY, -INFINITY, -INFINITY); TEST(ccos, -5.0, INFINITY, INFINITY, -INFINITY); TEST(ccos, 5.0, INFINITY, INFINITY, INFINITY); TEST(ccos, -5.0, -INFINITY, INFINITY, INFINITY); TEST(ccos, 5.0, -INFINITY, INFINITY, -INFINITY); /* sign of real part is unspecified */ TEST_RAISES(ccos, -INFINITY, INFINITY, INFINITY, NAN, FE_INVALID); TEST(ccos, NAN, INFINITY, INFINITY, NAN); TEST(ccos, NAN, -INFINITY, INFINITY, NAN); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccos, 0, NAN, NAN, 0, NAN, NZERO); TEST_UNSPECIFIED2(ccos, NZERO, NAN, NAN, 0, NAN, NZERO); /* can raise FE_INVALID or not */ TEST(ccos, -2.0, NAN, NAN, NAN); TEST(ccos, 2.0, NAN, NAN, NAN); TEST(ccos, NAN, NAN, NAN, NAN); return ret; } int test_csin() { int ret = 1; /* csin(conj(z)) = conj(csin(z)) and csin is odd */ TEST(csin, 0, 0, 0, 0); TEST(csin, 0, NZERO, 0, NZERO); TEST(csin, NZERO, 0, NZERO, 0); TEST(csin, NZERO, NZERO, NZERO, NZERO); /* sign of imaginary part is unspecified */ TEST_RAISES(csin, -INFINITY, 0, NAN, 0, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(csin, NAN, 0, NAN, 0, NAN, NZERO); TEST_UNSPECIFIED2(csin, NAN, NZERO, NAN, 0, NAN, NZERO); TEST_RAISES(csin, -INFINITY, 2.0, NAN, NAN, FE_INVALID); TEST_RAISES(csin, INFINITY, 2.0, NAN, NAN, FE_INVALID); TEST_RAISES(csin, -INFINITY, -2.0, NAN, NAN, FE_INVALID); TEST_RAISES(csin, INFINITY, -2.0, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST(csin, NAN, 2.0, NAN, NAN); TEST(csin, NAN, -2.0, NAN, NAN); TEST(csin, NZERO, INFINITY, NZERO, INFINITY); TEST(csin, 0, INFINITY, 0, INFINITY); TEST(csin, NZERO, -INFINITY, NZERO, -INFINITY); TEST(csin, 0, -INFINITY, 0, -INFINITY); TEST(csin, -1.0, INFINITY, -INFINITY, INFINITY); TEST(csin, 1.0, INFINITY, INFINITY, INFINITY); TEST(csin, -1.0, -INFINITY, -INFINITY, -INFINITY); TEST(csin, 1.0, -INFINITY, INFINITY, -INFINITY); TEST(csin, -2.0, INFINITY, -INFINITY, -INFINITY); TEST(csin, 2.0, INFINITY, INFINITY, -INFINITY); TEST(csin, -2.0, -INFINITY, -INFINITY, INFINITY); TEST(csin, 2.0, -INFINITY, INFINITY, INFINITY); TEST(csin, -4.0, INFINITY, INFINITY, -INFINITY); TEST(csin, 4.0, INFINITY, -INFINITY, -INFINITY); TEST(csin, -4.0, -INFINITY, INFINITY, INFINITY); TEST(csin, 4.0, -INFINITY, -INFINITY, INFINITY); TEST(csin, -5.0, INFINITY, INFINITY, INFINITY); TEST(csin, 5.0, INFINITY, -INFINITY, INFINITY); TEST(csin, -5.0, -INFINITY, INFINITY, -INFINITY); TEST(csin, 5.0, -INFINITY, -INFINITY, -INFINITY); /* sign of imaginary part is unspecified */ TEST_RAISES(csin, -INFINITY, INFINITY, NAN, INFINITY, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(csin, NAN, INFINITY, NAN, INFINITY, NAN, -INFINITY); TEST_UNSPECIFIED2(csin, NAN, -INFINITY, NAN, INFINITY, NAN, -INFINITY); TEST(csin, 0, NAN, 0, NAN); TEST(csin, NZERO, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST(csin, -2.0, NAN, NAN, NAN); TEST(csin, 2.0, NAN, NAN, NAN); TEST(csin, NAN, NAN, NAN, NAN); return ret; } int test_ctan() { int ret = 1; /* ctan(conj(z)) = conj(ctan(z)) and ctan is odd */ TEST(ctan, 0, 0, 0, 0); TEST(ctan, 0, NZERO, 0, NZERO); TEST(ctan, NZERO, 0, NZERO, 0); TEST(ctan, NZERO, NZERO, NZERO, NZERO); TEST_RAISES(ctan, -INFINITY, 2.0, NAN, NAN, FE_INVALID); TEST_RAISES(ctan, -INFINITY, -2.0, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST(ctan, NAN, 2.0, NAN, NAN); TEST(ctan, NAN, -2.0, NAN, NAN); TEST(ctan, -1.0, INFINITY, NZERO, 1.0); TEST(ctan, 1.0, INFINITY, 0, 1.0); TEST(ctan, -1.0, -INFINITY, NZERO, -1.0); TEST(ctan, 1.0, -INFINITY, 0, -1.0); TEST(ctan, -2.0, INFINITY, 0, 1); TEST(ctan, 2.0, INFINITY, NZERO, 1); TEST(ctan, -2.0, -INFINITY, 0, -1); TEST(ctan, 2.0, -INFINITY, NZERO, -1); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(ctan, INFINITY, INFINITY, 0, 1, NZERO, 1); TEST_UNSPECIFIED2(ctan, -INFINITY, INFINITY, 0, 1, NZERO, 1); TEST_UNSPECIFIED2(ctan, INFINITY, -INFINITY, 0, -1, NZERO, -1); TEST_UNSPECIFIED2(ctan, -INFINITY, -INFINITY, 0, -1, NZERO, -1); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(ctan, NAN, INFINITY, 0, 1, NZERO, 1); TEST_UNSPECIFIED2(ctan, NAN, -INFINITY, 0, -1, NZERO, -1); TEST(ctan, 0, NAN, 0, NAN); TEST(ctan, NZERO, NAN, NZERO, NAN); /* can raise FE_INVALID or not */ TEST(ctan, 2.0, NAN, NAN, NAN); TEST(ctan, -2.0, NAN, NAN, NAN); TEST(ctan, NAN, NAN, NAN, NAN); return ret; } int test_ccosh() { int ret = 1; /* ccosh(conj(z)) = conj(ccosh(z)) and ccosh is even */ TEST(ccosh, 0, 0, 1, 0); TEST(ccosh, 0, NZERO, 1, NZERO); TEST(ccosh, NZERO, 0, 1, NZERO); TEST(ccosh, NZERO, NZERO, 1, 0); /* sign of imaginary part is unspecified */ TEST_RAISES(ccosh, 0, INFINITY, NAN, 0, FE_INVALID); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccosh, 0, NAN, NAN, 0, NAN, NZERO); TEST_UNSPECIFIED2(ccosh, NZERO, NAN, NAN, 0, NAN, NZERO); TEST_RAISES(ccosh, 2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(ccosh, 2.0, -INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(ccosh, -2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(ccosh, -2.0, -INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST(ccosh, 2.0, NAN, NAN, NAN); TEST(ccosh, -2.0, NAN, NAN, NAN); TEST(ccosh, INFINITY, 0, INFINITY, 0); TEST(ccosh, INFINITY, NZERO, INFINITY, NZERO); TEST(ccosh, -INFINITY, 0, INFINITY, NZERO); TEST(ccosh, -INFINITY, NZERO, INFINITY, 0); TEST(ccosh, INFINITY, 1.0, INFINITY, INFINITY); TEST(ccosh, INFINITY, -1.0, INFINITY, -INFINITY); TEST(ccosh, -INFINITY, 1.0, INFINITY, -INFINITY); TEST(ccosh, -INFINITY, -1.0, INFINITY, INFINITY); TEST(ccosh, INFINITY, 2.0, -INFINITY, INFINITY); TEST(ccosh, INFINITY, -2.0, -INFINITY, -INFINITY); TEST(ccosh, -INFINITY, 2.0, -INFINITY, -INFINITY); TEST(ccosh, -INFINITY, -2.0, -INFINITY, INFINITY); TEST(ccosh, INFINITY, 4.0, -INFINITY, -INFINITY); TEST(ccosh, INFINITY, -4.0, -INFINITY, INFINITY); TEST(ccosh, -INFINITY, 4.0, -INFINITY, INFINITY); TEST(ccosh, -INFINITY, -4.0, -INFINITY, -INFINITY); TEST(ccosh, INFINITY, 5.0, INFINITY, -INFINITY); TEST(ccosh, INFINITY, -5.0, INFINITY, INFINITY); TEST(ccosh, -INFINITY, 5.0, INFINITY, INFINITY); TEST(ccosh, -INFINITY, -5.0, INFINITY, -INFINITY); /* sign of real part is unspecified */ TEST_RAISES(ccosh, INFINITY, INFINITY, INFINITY, NAN, FE_INVALID); TEST(ccosh, INFINITY, NAN, INFINITY, NAN); TEST(ccosh, -INFINITY, NAN, INFINITY, NAN); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ccosh, NAN, 0, NAN, 0, NAN, NZERO); TEST_UNSPECIFIED2(ccosh, NAN, NZERO, NAN, 0, NAN, NZERO); /* can raise FE_INVALID or not */ TEST(ccosh, NAN, 2.0, NAN, NAN); TEST(ccosh, NAN, -2.0, NAN, NAN); TEST(ccosh, NAN, NAN, NAN, NAN); return ret; } int test_csinh() { int ret = 1; /* csinh(conj(z)) = conj(csinh(z)) and csinh is odd */ TEST(csinh, 0, 0, 0, 0); TEST(csinh, 0, NZERO, 0, NZERO); TEST(csinh, NZERO, 0, NZERO, 0); TEST(csinh, NZERO, NZERO, NZERO, NZERO); /* sign of real part is unspecified */ TEST_RAISES(csinh, 0, INFINITY, 0, NAN, FE_INVALID); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(csinh, 0, NAN, 0, NAN, NZERO, NAN); TEST_UNSPECIFIED2(csinh, NZERO, NAN, 0, NAN, NZERO, NAN); TEST_RAISES(csinh, 2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(csinh, 2.0, -INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(csinh, -2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(csinh, -2.0, -INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST(csinh, 2.0, NAN, NAN, NAN); TEST(csinh, -2.0, NAN, NAN, NAN); TEST(csinh, INFINITY, 0, INFINITY, 0); TEST(csinh, INFINITY, NZERO, INFINITY, NZERO); TEST(csinh, -INFINITY, 0, -INFINITY, 0); TEST(csinh, -INFINITY, NZERO, -INFINITY, NZERO); TEST(csinh, INFINITY, 1.0, INFINITY, INFINITY); TEST(csinh, INFINITY, -1.0, INFINITY, -INFINITY); TEST(csinh, -INFINITY, 1.0, -INFINITY, INFINITY); TEST(csinh, -INFINITY, -1.0, -INFINITY, -INFINITY); TEST(csinh, INFINITY, 2.0, -INFINITY, INFINITY); TEST(csinh, INFINITY, -2.0, -INFINITY, -INFINITY); TEST(csinh, -INFINITY, 2.0, INFINITY, INFINITY); TEST(csinh, -INFINITY, -2.0, INFINITY, -INFINITY); TEST(csinh, INFINITY, 4.0, -INFINITY, -INFINITY); TEST(csinh, INFINITY, -4.0, -INFINITY, INFINITY); TEST(csinh, -INFINITY, 4.0, INFINITY, -INFINITY); TEST(csinh, -INFINITY, -4.0, INFINITY, INFINITY); TEST(csinh, INFINITY, 5.0, INFINITY, -INFINITY); TEST(csinh, INFINITY, -5.0, INFINITY, INFINITY); TEST(csinh, -INFINITY, 5.0, -INFINITY, -INFINITY); TEST(csinh, -INFINITY, -5.0, -INFINITY, INFINITY); /* sign of real part is unspecified */ TEST_RAISES(csinh, INFINITY, INFINITY, INFINITY, NAN, FE_INVALID); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(csinh, INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); TEST_UNSPECIFIED2(csinh, -INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); TEST(csinh, NAN, 0, NAN, 0); TEST(csinh, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST(csinh, NAN, 2.0, NAN, NAN); TEST(csinh, NAN, -2.0, NAN, NAN); TEST(csinh, NAN, NAN, NAN, NAN); return ret; } int test_ctanh() { int ret = 1; /* ctanh(conj(z)) = conj(ctanh(z)) and ctanh is odd */ TEST(ctanh, 0, 0, 0, 0); TEST(ctanh, 0, NZERO, 0, NZERO); TEST(ctanh, NZERO, 0, NZERO, 0); TEST(ctanh, NZERO, NZERO, NZERO, NZERO); TEST_RAISES(ctanh, 2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(ctanh, -2.0, INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST(ctanh, 2.0, NAN, NAN, NAN); TEST(ctanh, -2.0, NAN, NAN, NAN); TEST(ctanh, INFINITY, 1.0, 1.0, 0); TEST(ctanh, INFINITY, -1.0, 1.0, NZERO); TEST(ctanh, -INFINITY, 1.0, -1.0, 0); TEST(ctanh, -INFINITY, -1.0, -1.0, NZERO); TEST(ctanh, INFINITY, 2.0, 1.0, NZERO); TEST(ctanh, INFINITY, -2.0, 1.0, 0); TEST(ctanh, -INFINITY, 2.0, -1.0, NZERO); TEST(ctanh, -INFINITY, -2.0, -1.0, 0); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ctanh, INFINITY, INFINITY, 1, 0, 1, NZERO); TEST_UNSPECIFIED2(ctanh, INFINITY, -INFINITY, 1, 0, 1, NZERO); TEST_UNSPECIFIED2(ctanh, -INFINITY, INFINITY, -1, 0, -1, NZERO); TEST_UNSPECIFIED2(ctanh, -INFINITY, -INFINITY, -1, 0, -1, NZERO); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(ctanh, INFINITY, NAN, 1, 0, 1, NZERO); TEST_UNSPECIFIED2(ctanh, -INFINITY, NAN, -1, 0, -1, NZERO); TEST(ctanh, NAN, 0, NAN, 0); TEST(ctanh, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST(ctanh, NAN, 2.0, NAN, NAN); TEST(ctanh, NAN, -2.0, NAN, NAN); TEST(ctanh, NAN, NAN, NAN, NAN); return ret; } int test_cexp() { int ret = 1; /* cexp(conj(z)) = conj(cexp(z)) */ TEST(cexp, 0, 0, 1, 0); TEST(cexp, 0, NZERO, 1, NZERO); TEST(cexp, NZERO, 0, 1, 0); TEST(cexp, NZERO, NZERO, 1, NZERO); TEST_RAISES(cexp, 2.0, INFINITY, NAN, NAN, FE_INVALID); TEST_RAISES(cexp, 2.0, -INFINITY, NAN, NAN, FE_INVALID); /* can raise FE_INVALID or not */ TEST(cexp, 42.0, NAN, NAN, NAN); TEST(cexp, INFINITY, 0, INFINITY, 0); TEST(cexp, INFINITY, NZERO, INFINITY, NZERO); TEST(cexp, -INFINITY, 1.0, 0, 0); TEST(cexp, -INFINITY, -1.0, 0, NZERO); TEST(cexp, -INFINITY, 2.0, NZERO, 0); TEST(cexp, -INFINITY, -2.0, NZERO, NZERO); TEST(cexp, -INFINITY, 4.0, NZERO, NZERO); TEST(cexp, -INFINITY, -4.0, NZERO, 0); TEST(cexp, -INFINITY, 5.0, 0, NZERO); TEST(cexp, -INFINITY, -5.0, 0, 0); TEST(cexp, INFINITY, 1.0, INFINITY, INFINITY); TEST(cexp, INFINITY, -1.0, INFINITY, -INFINITY); TEST(cexp, INFINITY, 2.0, -INFINITY, INFINITY); TEST(cexp, INFINITY, -2.0, -INFINITY, -INFINITY); TEST(cexp, INFINITY, 4.0, -INFINITY, -INFINITY); TEST(cexp, INFINITY, -4.0, -INFINITY, INFINITY); TEST(cexp, INFINITY, 5.0, INFINITY, -INFINITY); TEST(cexp, INFINITY, -5.0, INFINITY, INFINITY); /* signs of both parts are unspecified */ TEST_UNSPECIFIED4(cexp, -INFINITY, INFINITY, 0, 0, NZERO, 0, 0, NZERO, NZERO, NZERO); TEST_UNSPECIFIED4(cexp, -INFINITY, -INFINITY, 0, 0, NZERO, 0, 0, NZERO, NZERO, NZERO); /* sign of real part is unspecifed */ TEST_RAISES(cexp, INFINITY, INFINITY, INFINITY, NAN, FE_INVALID); /* signs of both parts are unspecified */ TEST_UNSPECIFIED4(cexp, -INFINITY, NAN, 0, 0, NZERO, 0, 0, NZERO, NZERO, NZERO); /* sign of real part is unspecified */ TEST_UNSPECIFIED2(cexp, INFINITY, NAN, INFINITY, NAN, -INFINITY, NAN); TEST(cexp, NAN, 0, NAN, 0); TEST(cexp, NAN, NZERO, NAN, NZERO); /* can raise FE_INVALID or not */ TEST(cexp, NAN, 2.0, NAN, NAN); TEST(cexp, NAN, -2.0, NAN, NAN); TEST(cexp, NAN, NAN, NAN, NAN); return ret; } int test_clog() { int ret = 1; /* clog(conj(z)) = conj(clog(z)) */ TEST_RAISES(clog, NZERO, 0, -INFINITY, M_PI, FE_DIVBYZERO); TEST_RAISES(clog, NZERO, NZERO, -INFINITY, -M_PI, FE_DIVBYZERO); TEST_RAISES(clog, 0, 0, -INFINITY, 0, FE_DIVBYZERO); TEST_RAISES(clog, 0, NZERO, -INFINITY, NZERO, FE_DIVBYZERO); TEST(clog, 2.0, INFINITY, INFINITY, M_PI_2); TEST(clog, 2.0, -INFINITY, INFINITY, -M_PI_2); /* can raise FE_INVALID or not */ TEST(clog, 2.0, NAN, NAN, NAN); TEST(clog, -INFINITY, 2.0, INFINITY, M_PI); TEST(clog, -INFINITY, -2.0, INFINITY, -M_PI); TEST(clog, INFINITY, 2.0, INFINITY, 0); TEST(clog, INFINITY, -2.0, INFINITY, NZERO); TEST(clog, -INFINITY, INFINITY, INFINITY, 0.75 * M_PI); TEST(clog, -INFINITY, -INFINITY, INFINITY, -0.75 * M_PI); TEST(clog, INFINITY, INFINITY, INFINITY, 0.25 * M_PI); TEST(clog, INFINITY, -INFINITY, INFINITY, -0.25 * M_PI); TEST(clog, INFINITY, NAN, INFINITY, NAN); TEST(clog, -INFINITY, NAN, INFINITY, NAN); /* can raise FE_INVALID or not */ TEST(clog, NAN, 2.0, NAN, NAN); TEST(clog, NAN, -2.0, NAN, NAN); TEST(clog, NAN, INFINITY, INFINITY, NAN); TEST(clog, NAN, -INFINITY, INFINITY, NAN); TEST(clog, NAN, NAN, NAN, NAN); return ret; } int test_cpow() { int ret = 1; /* there are _no_ annex G values for cpow. */ return ret; } int test_csqrt() { int ret = 1; /* csqrt(conj(z)) = conj(csqrt(z)) */ TEST(csqrt, 0, 0, 0, 0); TEST(csqrt, 0, NZERO, 0, NZERO); TEST(csqrt, NZERO, 0, 0, 0); TEST(csqrt, NZERO, NZERO, 0, NZERO); TEST(csqrt, 2.0, INFINITY, INFINITY, INFINITY); TEST(csqrt, 2.0, -INFINITY, INFINITY, -INFINITY); TEST(csqrt, NAN, INFINITY, INFINITY, INFINITY); TEST(csqrt, NAN, -INFINITY, INFINITY, -INFINITY); TEST(csqrt, INFINITY, INFINITY, INFINITY, INFINITY); TEST(csqrt, INFINITY, -INFINITY, INFINITY, -INFINITY); TEST(csqrt, -INFINITY, INFINITY, INFINITY, INFINITY); TEST(csqrt, -INFINITY, -INFINITY, INFINITY, -INFINITY); /* can raise FE_INVALID or not */ TEST(csqrt, 2.0, NAN, NAN, NAN); TEST(csqrt, -INFINITY, 2.0, 0, INFINITY); TEST(csqrt, -INFINITY, -2.0, 0, -INFINITY); TEST(csqrt, INFINITY, 2.0, INFINITY, 0); TEST(csqrt, INFINITY, -2.0, INFINITY, NZERO); /* sign of imaginary part is unspecified */ TEST_UNSPECIFIED2(csqrt, -INFINITY, NAN, NAN, INFINITY, NAN, -INFINITY); TEST(csqrt, INFINITY, NAN, INFINITY, NAN); /* can raise FE_INVALID or not */ TEST(csqrt, NAN, 2.0, NAN, NAN); TEST(csqrt, NAN, -2.0, NAN, NAN); TEST(csqrt, NAN, NAN, NAN, NAN); return ret; } int main(int argc, char** argv) { printf("cacos: %d\n\n", test_cacos()); printf("casin: %d\n\n", test_casin()); printf("catan: %d\n\n", test_catan()); printf("cacosh: %d\n\n", test_cacosh()); printf("casinh: %d\n\n", test_casinh()); printf("catanh: %d\n\n", test_catanh()); printf("ccos: %d\n\n", test_ccos()); printf("csin: %d\n\n", test_csin()); printf("ctan: %d\n\n", test_ctan()); printf("ccosh: %d\n\n", test_ccosh()); printf("csinh: %d\n\n", test_csinh()); printf("ctanh: %d\n\n", test_ctanh()); printf("cexp: %d\n\n", test_cexp()); printf("clog: %d\n\n", test_clog()); printf("cpow, %d\n\n", test_cpow()); printf("csqrt: %d\n\n", test_csqrt()); return 0; } -
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Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,246 @@ #include <fenv.h> #include <float.h> #include <stdio.h> #include <math.h> #include <complex.h> const double NZERO = 1.0 * 0.0; #define STRINGIZE_INT(A) #A #define STRINGIZE(A) STRINGIZE_INT(A) #define TEST_PRINTF(func, x, e, r) printf("%d: " STRINGIZE(func) "(%g + %gj): expected: %g + %gj: received: %g + %gj\n", __LINE__, creal(x), cimag(x), creal(e), cimag(e), creal(r), cimag(r)) #define TEST(func, x, e) do { \ double complex r = func(x); \ if (!cd_isclose(r, e)) { \ ret = 0; \ TEST_PRINTF(func, x, e, r); \ } \ } \ while(0) #define TEST_RAISES(func, x, e, fpe) do { \ int except; \ double complex r; \ feclearexcept(FE_ALL_EXCEPT); \ r = func(x); \ except = fetestexcept(fpe); \ if (!(except & fpe && cd_isclose(r, e))) { \ ret = 0; \ TEST_PRINTF(func, x, e, r); \ } \ } \ while(0) double complex cpack(double r, double i) { union { double complex z; double a[2]; } z1; z1.a[0] = r; z1.a[1] = i; return z1.z; } int isclose(double a, double b) { double atol = 0.0; double rtol = 1e-7; if (isfinite(a) && isfinite(b)) { return fabs(a - b) <= (atol + rtol*fabs(b)); } else if (isinf(a) && isinf(b)) { return (signbit(a) == signbit(b)); } else { return (isnan(a) && isnan(b)); } } int cd_isclose(double complex a, double complex b) { double ar = creal(a); double ai = cimag(a); double br = creal(b); double bi = cimag(b); return isclose(ar, br) && isclose(ai, bi); } int cd_isnan(double complex x) { return isnan(creal(x)) && isnan(cimag(x)); } int cd_isinf(double complex x) { return isinf(creal(x)) && isinf(cimag(x)); } int check_branch_cut(double complex (*func)(double complex), double complex x0, double complex dx, double re_sign, double im_sign, int sig_zero_ok) { double scale = DBL_EPSILON * 1e3; double atol = 1e-4; double complex y0 = func(x0); double complex yp = func(x0 + dx*scale*cabs(x0)/cabs(dx)); double complex ym = func(x0 - dx*scale*cabs(x0)/cabs(dx)); if (fabs(creal(y0) - creal(yp)) >= atol) return 0; if (fabs(cimag(y0) - cimag(yp)) >= atol) return 0; if (fabs(creal(y0) - re_sign*creal(ym)) >= atol) return 0; if (fabs(cimag(y0) - im_sign*cimag(ym)) >= atol) return 0; if (sig_zero_ok) { /* check that signed zeros also work as a displacement. */ return 0; } return 1; } /* * We assume that if we make it here at all, we have c99 complex support in * the compiler that we are using. * * We define a single test_fname function for each function that will be * tested. These function return 1 if the tests pass and 0 if the tests * fail. These are go/no go tests and which test failed is not reported. */ /*========================================================== * clog *=========================================================*/ #define TEST_CLOG(x, e) TEST(clog, x, e) #define TEST_RAISES_CLOG(x, e, fpe) TEST_RAISES(clog, x, e, fpe) int test_clog() { int ret = 1; const double NZERO = -1.0 * 0.0; /* tests from test_umath.py: TestComplexFunctions: test_it */ TEST_CLOG(0.5, log(0.5)); /* tests from test_umath_complex.py: TestCLog: test_simple */ TEST_CLOG(1, 0); TEST_CLOG(1 + 2*I, 0.80471895621705014 + 1.1071487177940904*I); /* tests from test_umath_complex.py: TestCLog: test_special_values * These are testing the the value in Appendix G. */ TEST_RAISES_CLOG(cpack(NZERO, 0), cpack(-INFINITY, M_PI), FE_DIVBYZERO); TEST_RAISES_CLOG(cpack(0, 0), cpack(-INFINITY, 0), FE_DIVBYZERO); TEST_CLOG(cpack(1, INFINITY), cpack(INFINITY, M_PI_2)); TEST_CLOG(cpack(1, NAN), cpack(NAN, NAN)); /* can raise FE_INVALID or not. */ TEST_CLOG(cpack(-INFINITY, 1), cpack(+INFINITY, M_PI)); TEST_CLOG(cpack(+INFINITY, 1), cpack(+INFINITY, 0)); TEST_CLOG(cpack(-INFINITY, +INFINITY), cpack(INFINITY, 0.75 * M_PI)); TEST_CLOG(cpack(+INFINITY, +INFINITY), cpack(INFINITY, 0.25 * M_PI)); TEST_CLOG(cpack(-INFINITY, NAN), cpack(INFINITY, NAN)); TEST_CLOG(cpack(+INFINITY, NAN), cpack(INFINITY, NAN)); TEST_CLOG(cpack(NAN, 1), cpack(NAN, NAN)); /* can raise FE_INVALID or not */ TEST_CLOG(cpack(NAN, INFINITY), cpack(INFINITY, NAN)); TEST_CLOG(cpack(NAN, NAN), cpack(NAN, NAN)); /* clog(conj(z)) = conj(clog(z)) */ /* tests concerning the sign of nan are not included. */ TEST_RAISES_CLOG(cpack(NZERO, NZERO), cpack(-INFINITY, -M_PI), FE_DIVBYZERO); TEST_RAISES_CLOG(cpack(0, NZERO), cpack(-INFINITY, NZERO), FE_DIVBYZERO); TEST_CLOG(cpack(1, -INFINITY), cpack(INFINITY, -M_PI_2)); TEST_CLOG(cpack(-INFINITY, -1), cpack(+INFINITY, -M_PI)); TEST_CLOG(cpack(+INFINITY, -1), cpack(+INFINITY, NZERO)); TEST_CLOG(cpack(-INFINITY, -INFINITY), cpack(INFINITY, -0.75 * M_PI)); TEST_CLOG(cpack(+INFINITY, -INFINITY), cpack(INFINITY, -0.25 * M_PI)); TEST_CLOG(cpack(NAN, -INFINITY), cpack(INFINITY, NAN)); if(!check_branch_cut(clog, -0.5, 1*I, 1, -1, 0)) { ret = 0; printf("clog branch cut bad!\n"); } if(!check_branch_cut(clog, -0.5, 1*I, 1, -1, 1)) { ret = 0; printf("clog branch cut bad! 2\n"); } return ret; } #undef TEST_CLOG #undef TEST_RAISES_CLOG /*========================================================== * ctanh *=========================================================*/ #define TEST_CTANH(x, e) TEST(ctanh, x, e) #define TEST_RAISES_CTANH(x, e, fpe) TEST_RAISES(ctanh, x, e, fpe) int test_ctanh() { int ret = 1; /**** Test Appendix G special values ****/ TEST_CTANH(cpack(0.0, 0.0), cpack(0.0, 0.0)); TEST_RAISES_CTANH(cpack(1.0, INFINITY), cpack(NAN, NAN), FE_INVALID); /* can raise FE_INVALID or not */ TEST_CTANH(cpack(1.0, NAN), cpack(NAN, NAN)); /* only for positive, nonzero imag part */ TEST_CTANH(cpack(INFINITY, 1.0), cpack(1.0, 0.0)); /* only for positive nonzero imag part */ TEST_CTANH(cpack(INFINITY, 2.0), cpack(1.0, NZERO)); /* signbit(cimag(r)) is unspecified. */ TEST_CTANH(cpack(INFINITY, INFINITY), cpack(1.0, 0.0)); /* signbit(cimag(r)) is unspecified */ TEST_CTANH(cpack(INFINITY, NAN), cpack(1.0, 0.0)); TEST_CTANH(cpack(NAN, 0.0), cpack(NAN, 0.0)); /* can raise FE_INVALID or not */ TEST_CTANH(cpack(NAN, 1.0), cpack(NAN, NAN)); TEST_CTANH(cpack(NAN, NAN), cpack(NAN, NAN)); /* ctanh(conj(z)) = conj(ctanh(z)) */ TEST_CTANH(cpack(0.0, NZERO), cpack(0.0, NZERO)); TEST_RAISES_CTANH(cpack(1.0, -INFINITY), cpack(NAN, NAN), FE_INVALID); TEST_CTANH(cpack(NAN, NZERO), cpack(NAN, NZERO)); /* ctanh is odd */ TEST_CTANH(cpack(NZERO, NZERO), cpack(NZERO, NZERO)); TEST_RAISES_CTANH(cpack(-1.0, INFINITY), cpack(NAN, NAN), FE_INVALID); /* can raise FE_INVALID or not */ TEST_CTANH(cpack(-1.0, NAN), cpack(NAN, NAN)); /* signbit(cimag(r)) is unspecified. */ TEST_CTANH(cpack(-INFINITY, -INFINITY), cpack(-1.0, 0.0)); /* signbit(cimag(r)) is unspecified */ TEST_CTANH(cpack(-INFINITY, NAN), cpack(-1.0, 0.0)); TEST_CTANH(cpack(NAN, NZERO), cpack(NAN, NZERO)); /* can raise FE_INVALID or not */ TEST_CTANH(cpack(NAN, -1.0), cpack(NAN, NAN)); /**** Github Issue 2321: nans for large arguments ****/ TEST_CTANH(cpack(1000.0, 0.0), cpack(1.0, 0.0)); return ret; } #undef TEST_CTANH #undef TEST_RAISES_CTANH int main(int argc, char** argv) { int tclog, tctanh; tclog = test_clog(); printf("clog: %d\n\n", tclog); tctanh = test_ctanh(); printf("ctanh: %d\n\n", tctanh); return 0; }