New zero coefficient stripping and solve_quadratic implementation.

General effort to implement better 'effective zero' coefficient handling.
Created new POV_DBL_EPSILON macro value which is 2x the C++ standards <float
type>_EPSILON value and updated PRECISE_EPSILON to be 2x the single bit
epsilon as well.

Zero filtering in polysolve now looks at all polynomial coefficients and
either sets 'effective zeros' to exactly 0.0 or strips them if they are leading
coefficients.

The much more accurate near zero coefficients drove the need for a better
solve_quadratic implementation included with this commit. Note it supports
the PRECISE_FLOAT options like polysolve.

Zero filtering in solve_quadratic, solve_cubic and solve_quartic now standardized
both in implementation and use of POV_DBL_EPSILON.

Author: wfpokorny

source/base/configbase.h

@@ -399,15 +399,22 @@ constexpr int CX_STRCMP(char const* lhs, char const* rhs)
 /// Where @ref PRECISE_FLOAT a C++11 standard floating point type this should be
 /// the default fabs. When using, for example, __float128 with GNU g++ in a supported 64 bit
 /// environment the value would defined to be __builtin_fabsq - as that function is a built-in
-/// for 64 bit compiles. It might be set to fabsq if using GNU g++'s quadmath library.
-///
-/// @note
-///    At present PRECISE_FABS, like @ref PRECISE_FLOAT, applies only within polysolve().
+/// for 64 bit compiles. It would be set to fabsq if using GNU g++'s quadmath library.
 ///
 #ifndef PRECISE_FABS
     #define PRECISE_FABS fabs
 #endif
 
+/// @def PRECISE_SQRT
+/// The floating point square root function name to use with @ref PRECISE_FLOAT.
+///
+/// Where @ref PRECISE_FLOAT a C++11 standard floating point type this should be
+/// the default sqrt. It would be set to sqrtq if using GNU g++'s quadmath library.
+///
+#ifndef PRECISE_SQRT
+    #define PRECISE_SQRT sqrt
+#endif
+
 /// @def PRECISE_DIGITS
 /// Base 10 digits where @ref PRECISE_FLOAT type not a C++11 floating point standard.
 ///
@@ -445,17 +452,45 @@ constexpr int PRECISE_DIG  = PRECISE_FLT  ?
                              : FLT_DIG;
 
 /// @def PRECISE_EPSILON
-/// Internal 'constexpr DBL' value for minimum epsilon step for given @ref PRECISE_FLOAT.
+/// Internal 'constexpr DBL' value*2.0 for minimum epsilon step for given @ref PRECISE_FLOAT.
 ///
 /// Set to C+11 standard value where defined and to @ref PRECISE_EPSLN otherwise.
 ///
+/// @note
+///     Using 2.0 multiplier due maths calculating coefficients for higher order polynomials
+///     introducing more than single bit/step error in practice.
+///
 
 constexpr DBL PRECISE_EPSILON = PRECISE_FLT  ?
                                 PRECISE_DBL  ?
-                                PRECISE_LDBL ? PRECISE_EPSLN
-                                : LDBL_EPSILON
-                                : DBL_EPSILON
-                                : FLT_EPSILON;
+                                PRECISE_LDBL ? PRECISE_EPSLN*2.0
+                                : LDBL_EPSILON*2.0
+                                : DBL_EPSILON*2.0
+                                : FLT_EPSILON*2.0;
+
+/// @def POV_DBL_EPSILON
+/// Internal 'constexpr DBL' value for minimum epsilon step for given POV-Ray's @ref DBL.
+///
+/// Set to C+11 standard value*2.0 where defined and to @ref PRECISE_EPSLN*2.0 otherwise.
+///
+/// Using this value where we want a more accurate 'meaningful value not zero' tests than
+/// the EPSILON, SMALL_ENOUGH, etc. values which tend to be around 1e-10 which is much larger
+/// than, for example, the double DBL_EPSILON value of 2.2204460492503131e-16.
+///
+/// @note
+///     Using 2.0 multiplier due maths calculating coefficients for higher order polynomials
+///     introducing more than single bit/step error in practice.
+///
+constexpr int POV_DBL_IS_FLT  = CX_STRCMP(CX_XSTR(DBL), "float");
+constexpr int POV_DBL_IS_DBL  = CX_STRCMP(CX_XSTR(DBL), "double");
+constexpr int POV_DBL_IS_LDBL = CX_STRCMP(CX_XSTR(DBL), "long double");
+
+constexpr DBL POV_DBL_EPSILON = POV_DBL_IS_FLT  ?
+                                POV_DBL_IS_DBL  ?
+                                POV_DBL_IS_LDBL ? PRECISE_EPSLN*2.0
+                                : LDBL_EPSILON*2.0
+                                : DBL_EPSILON*2.0
+                                : FLT_EPSILON*2.0;
 
 /// @}
 ///