testautomation_math: do relative comparison + more precise correct trigonometric values

test/testautomation_math.c

@@ -102,8 +102,15 @@ helper_dtod_inexact(const char *func_name, d_to_d_func func,
     Uint32 i;
     for (i = 0; i < cases_size; i++) {
         const double result = func(cases[i].input);
-        SDLTest_AssertCheck(result >= cases[i].expected - EPSILON &&
-                                result <= cases[i].expected + EPSILON,
+        double diff = result - cases[i].expected;
+        double max_err = (cases[i].expected + 1.) * EPSILON;
+        if (diff < 0) {
+            diff = -diff;
+        }
+        if (max_err < 0) {
+            max_err = -max_err;
+        }
+        SDLTest_AssertCheck(diff <= max_err,
                             "%s(%f), expected [%f,%f], got %f",
                             func_name,
                             cases[i].input,
@@ -157,8 +164,16 @@ helper_ddtod_inexact(const char *func_name, dd_to_d_func func,
     Uint32 i;
     for (i = 0; i < cases_size; i++) {
         const double result = func(cases[i].x_input, cases[i].y_input);
-        SDLTest_AssertCheck(result >= cases[i].expected - EPSILON &&
-                                result <= cases[i].expected + EPSILON,
+        double diff = result - cases[i].expected;
+        double max_err = (cases[i].expected + 1.) * EPSILON;
+        if (diff < 0) {
+            diff = -diff;
+        }
+        if (max_err < 0) {
+            max_err = -max_err;
+        }
+
+        SDLTest_AssertCheck(diff <= max_err,
                             "%s(%f,%f), expected [%f,%f], got %f",
                             func_name,
                             cases[i].x_input, cases[i].y_input,
@@ -1655,7 +1670,7 @@ pow_regularCases(void *args)
         { 39.23, -1.5, 0.0040697950366865498147972424192175822099670767784118652343750 },
         { 478.972, 12.125, 315326359630449587856007411793920.0 }
     };
-    return helper_ddtod("Pow", SDL_pow, regular_cases, SDL_arraysize(regular_cases));
+    return helper_ddtod_inexact("Pow", SDL_pow, regular_cases, SDL_arraysize(regular_cases));
 }
 
 /**
@@ -1983,24 +1998,24 @@ static int
 cos_precisionTest(void *args)
 {
     const d_to_d precision_cases[] = {
-        { M_PI * 1.0 / 10.0, 0.9510565162 },
-        { M_PI * 2.0 / 10.0, 0.8090169943 },
-        { M_PI * 3.0 / 10.0, 0.5877852522 },
-        { M_PI * 4.0 / 10.0, 0.3090169943 },
+        { M_PI * 1.0 / 10.0, 0.9510565162951535 },
+        { M_PI * 2.0 / 10.0, 0.8090169943749475 },
+        { M_PI * 3.0 / 10.0, 0.5877852522924731 },
+        { M_PI * 4.0 / 10.0, 0.30901699437494745 },
         { M_PI * 5.0 / 10.0, 0.0 },
-        { M_PI * 6.0 / 10.0, -0.3090169943 },
-        { M_PI * 7.0 / 10.0, -0.5877852522 },
-        { M_PI * 8.0 / 10.0, -0.8090169943 },
-        { M_PI * 9.0 / 10.0, -0.9510565162 },
-        { M_PI * -1.0 / 10.0, 0.9510565162 },
-        { M_PI * -2.0 / 10.0, 0.8090169943 },
-        { M_PI * -3.0 / 10.0, 0.5877852522 },
-        { M_PI * -4.0 / 10.0, 0.3090169943 },
+        { M_PI * 6.0 / 10.0, -0.30901699437494734 },
+        { M_PI * 7.0 / 10.0, -0.587785252292473 },
+        { M_PI * 8.0 / 10.0, -0.8090169943749473 },
+        { M_PI * 9.0 / 10.0, -0.9510565162951535 },
+        { M_PI * -1.0 / 10.0, 0.9510565162951535 },
+        { M_PI * -2.0 / 10.0, 0.8090169943749475 },
+        { M_PI * -3.0 / 10.0, 0.5877852522924731 },
+        { M_PI * -4.0 / 10.0, 0.30901699437494745 },
         { M_PI * -5.0 / 10.0, 0.0 },
-        { M_PI * -6.0 / 10.0, -0.3090169943 },
-        { M_PI * -7.0 / 10.0, -0.5877852522 },
-        { M_PI * -8.0 / 10.0, -0.8090169943 },
-        { M_PI * -9.0 / 10.0, -0.9510565162 }
+        { M_PI * -6.0 / 10.0, -0.30901699437494734 },
+        { M_PI * -7.0 / 10.0, -0.587785252292473 },
+        { M_PI * -8.0 / 10.0, -0.8090169943749473 },
+        { M_PI * -9.0 / 10.0, -0.9510565162951535 }
     };
     return helper_dtod_inexact("Cos", SDL_cos, precision_cases, SDL_arraysize(precision_cases));
 }
@@ -2101,23 +2116,23 @@ static int
 sin_precisionTest(void *args)
 {
     const d_to_d precision_cases[] = {
-        { M_PI * 1.0 / 10.0, 0.3090169943 },
-        { M_PI * 2.0 / 10.0, 0.5877852522 },
-        { M_PI * 3.0 / 10.0, 0.8090169943 },
-        { M_PI * 4.0 / 10.0, 0.9510565162 },
-        { M_PI * 6.0 / 10.0, 0.9510565162 },
-        { M_PI * 7.0 / 10.0, 0.8090169943 },
-        { M_PI * 8.0 / 10.0, 0.5877852522 },
-        { M_PI * 9.0 / 10.0, 0.3090169943 },
+        { M_PI * 1.0 / 10.0, 0.3090169943749474 },
+        { M_PI * 2.0 / 10.0, 0.5877852522924731 },
+        { M_PI * 3.0 / 10.0, 0.8090169943749475 },
+        { M_PI * 4.0 / 10.0, 0.9510565162951535 },
+        { M_PI * 6.0 / 10.0, 0.9510565162951536 },
+        { M_PI * 7.0 / 10.0, 0.8090169943749475 },
+        { M_PI * 8.0 / 10.0, 0.5877852522924732 },
+        { M_PI * 9.0 / 10.0, 0.3090169943749475 },
         { M_PI, 0.0 },
-        { M_PI * -1.0 / 10.0, -0.3090169943 },
-        { M_PI * -2.0 / 10.0, -0.5877852522 },
-        { M_PI * -3.0 / 10.0, -0.8090169943 },
-        { M_PI * -4.0 / 10.0, -0.9510565162 },
-        { M_PI * -6.0 / 10.0, -0.9510565162 },
-        { M_PI * -7.0 / 10.0, -0.8090169943 },
-        { M_PI * -8.0 / 10.0, -0.5877852522 },
-        { M_PI * -9.0 / 10.0, -0.3090169943 },
+        { M_PI * -1.0 / 10.0, -0.3090169943749474 },
+        { M_PI * -2.0 / 10.0, -0.5877852522924731 },
+        { M_PI * -3.0 / 10.0, -0.8090169943749475 },
+        { M_PI * -4.0 / 10.0, -0.9510565162951535 },
+        { M_PI * -6.0 / 10.0, -0.9510565162951536 },
+        { M_PI * -7.0 / 10.0, -0.8090169943749475 },
+        { M_PI * -8.0 / 10.0, -0.5877852522924732 },
+        { M_PI * -9.0 / 10.0, -0.3090169943749475 },
         { -M_PI, 0.0 },
     };
     return helper_dtod_inexact("Sin", SDL_sin, precision_cases, SDL_arraysize(precision_cases));
@@ -2217,26 +2232,26 @@ static int
 tan_precisionTest(void *args)
 {
     const d_to_d precision_cases[] = {
-        { M_PI * 1.0 / 11.0, 0.2936264929 },
-        { M_PI * 2.0 / 11.0, 0.6426609771 },
-        { M_PI * 3.0 / 11.0, 1.1540615205 },
-        { M_PI * 4.0 / 11.0, 2.1896945629 },
-        { M_PI * 5.0 / 11.0, 6.9551527717 },
-        { M_PI * 6.0 / 11.0, -6.9551527717 },
-        { M_PI * 7.0 / 11.0, -2.1896945629 },
-        { M_PI * 8.0 / 11.0, -1.1540615205 },
-        { M_PI * 9.0 / 11.0, -0.6426609771 },
-        { M_PI * 10.0 / 11.0, -0.2936264929 },
-        { M_PI * -1.0 / 11.0, -0.2936264929 },
-        { M_PI * -2.0 / 11.0, -0.6426609771 },
-        { M_PI * -3.0 / 11.0, -1.1540615205 },
-        { M_PI * -4.0 / 11.0, -2.1896945629 },
-        { M_PI * -5.0 / 11.0, -6.9551527717 },
-        { M_PI * -6.0 / 11.0, 6.9551527717 },
-        { M_PI * -7.0 / 11.0, 2.1896945629 },
-        { M_PI * -8.0 / 11.0, 1.1540615205 },
-        { M_PI * -9.0 / 11.0, 0.6426609771 },
-        { M_PI * -10.0 / 11.0, 0.2936264929 }
+        { M_PI * 1.0 / 11.0, 0.29362649293836673 },
+        { M_PI * 2.0 / 11.0, 0.642660977168331 },
+        { M_PI * 3.0 / 11.0, 1.1540615205330094 },
+        { M_PI * 4.0 / 11.0, 2.189694562989681 },
+        { M_PI * 5.0 / 11.0, 6.9551527717734745 },
+        { M_PI * 6.0 / 11.0, -6.955152771773481 },
+        { M_PI * 7.0 / 11.0, -2.189694562989682 },
+        { M_PI * 8.0 / 11.0, -1.1540615205330096 },
+        { M_PI * 9.0 / 11.0, -0.6426609771683314 },
+        { M_PI * 10.0 / 11.0, -0.2936264929383667 },
+        { M_PI * -1.0 / 11.0, -0.29362649293836673 },
+        { M_PI * -2.0 / 11.0, -0.642660977168331 },
+        { M_PI * -3.0 / 11.0, -1.1540615205330094 },
+        { M_PI * -4.0 / 11.0, -2.189694562989681 },
+        { M_PI * -5.0 / 11.0, -6.9551527717734745 },
+        { M_PI * -6.0 / 11.0, 6.955152771773481 },
+        { M_PI * -7.0 / 11.0, 2.189694562989682 },
+        { M_PI * -8.0 / 11.0, 1.1540615205330096 },
+        { M_PI * -9.0 / 11.0, 0.6426609771683314 },
+        { M_PI * -10.0 / 11.0, 0.2936264929383667 }
     };
     return helper_dtod_inexact("Tan", SDL_tan, precision_cases, SDL_arraysize(precision_cases));
 }
@@ -2401,26 +2416,26 @@ static int
 asin_precisionTest(void *args)
 {
     const d_to_d precision_cases[] = {
-        { 0.9, 1.1197695149 },
-        { 0.8, 0.9272952180 },
-        { 0.7, 0.7753974966 },
-        { 0.6, 0.6435011087 },
-        { 0.5, 0.5235987755 },
-        { 0.4, 0.4115168460 },
-        { 0.3, 0.3046926540 },
-        { 0.2, 0.2013579207 },
-        { 0.1, 0.1001674211 },
+        { 0.9, 1.1197695149986342 },
+        { 0.8, 0.9272952180016123 },
+        { 0.7, 0.775397496610753 },
+        { 0.6, 0.6435011087932844 },
+        { 0.5, 0.5235987755982989 },
+        { 0.4, 0.41151684606748806 },
+        { 0.3, 0.3046926540153976 },
+        { 0.2, 0.20135792079033074 },
+        { 0.1, 0.10016742116155977 },
         { 0.0, 0.0 },
         { -0.0, -0.0 },
-        { -0.1, -0.1001674211 },
-        { -0.2, -0.2013579207 },
-        { -0.3, -0.3046926540 },
-        { -0.4, -0.4115168460 },
-        { -0.5, -0.5235987755 },
-        { -0.6, -0.6435011087 },
-        { -0.7, -0.7753974966 },
-        { -0.8, -0.9272952180 },
-        { -0.9, -1.1197695149 }
+        { -0.1, -0.10016742116155977 },
+        { -0.2, -0.20135792079033074 },
+        { -0.3, -0.3046926540153976 },
+        { -0.4, -0.41151684606748806 },
+        { -0.5, -0.5235987755982989 },
+        { -0.6, -0.6435011087932844 },
+        { -0.7, -0.775397496610753 },
+        { -0.8, -0.9272952180016123 },
+        { -0.9, -1.1197695149986342 }
     };
     return helper_dtod_inexact("Asin", SDL_asin, precision_cases, SDL_arraysize(precision_cases));
 }
@@ -2495,24 +2510,24 @@ static int
 atan_precisionTest(void *args)
 {
     const d_to_d precision_cases[] = {
-        { 6.313751514675041, 1.4137166941 },
-        { 3.0776835371752527, 1.2566370614 },
-        { 1.9626105055051504, 1.0995574287 },
-        { 1.3763819204711734, 0.9424777960 },
-        { 1.0, 0.7853981633 },
-        { 0.7265425280053609, 0.6283185307 },
-        { 0.5095254494944288, 0.4712388980 },
-        { 0.3249196962329063, 0.3141592653 },
-        { 0.15838444032453627, 0.1570796326 },
-        { -0.15838444032453627, -0.1570796326 },
-        { -0.3249196962329063, -0.3141592653 },
-        { -0.5095254494944288, -0.4712388980 },
-        { -0.7265425280053609, -0.6283185307 },
-        { -1.0, -0.7853981633 },
-        { -1.3763819204711734, -0.9424777960 },
-        { -1.9626105055051504, -1.0995574287 },
-        { -3.0776835371752527, -1.2566370614 },
-        { -6.313751514675041, -1.4137166941 },
+        { 6.313751514675041, 1.413716694115407 },
+        { 3.0776835371752527, 1.2566370614359172 },
+        { 1.9626105055051504, 1.0995574287564276 },
+        { 1.3763819204711734, 0.9424777960769379 },
+        { 1.0, 0.7853981633974483 },
+        { 0.7265425280053609, 0.6283185307179586 },
+        { 0.5095254494944288, 0.47123889803846897 },
+        { 0.3249196962329063, 0.3141592653589793 },
+        { 0.15838444032453627, 0.15707963267948966 },
+        { -0.15838444032453627, -0.15707963267948966 },
+        { -0.3249196962329063, -0.3141592653589793 },
+        { -0.5095254494944288, -0.47123889803846897 },
+        { -0.7265425280053609, -0.6283185307179586 },
+        { -1.0, -0.7853981633974483 },
+        { -1.3763819204711734, -0.9424777960769379 },
+        { -1.9626105055051504, -1.0995574287564276 },
+        { -3.0776835371752527, -1.2566370614359172 },
+        { -6.313751514675041, -1.413716694115407 },
     };
     return helper_dtod_inexact("Atan", SDL_atan, precision_cases, SDL_arraysize(precision_cases));
 }