feat: implemented the numerical evaluation of the atan2_ function.

Author: cbmarini

check/features.frm

@@ -1225,6 +1225,27 @@ assert result("ATAN") =~ expr("
        + 7.85398163397448309615661e-01*atan(1)
 ")
 *--#] evaluate_atan : 
+*--#[ evaluate_atan2 :
+#Startfloat 21d
+CFunction atan2;
+Local ATAN2 = atan2(0,0)*atan2_(0,0)
+			+atan2(0,24)*atan2_(0,24)
+			+atan2(24/13,0)*atan2_(24/13,0)
+			+atan2(3,-1.45)*atan2_(3,-1.45)
+			+atan2(0.54321,-1.2345)*atan2_(0.54321,-1.2345)
+			+atan2(5.4321,-45/11)*atan2_(5.4321,-45/11);
+Evaluate;
+Print +s;
+.end
+#pend_if wordsize == 2
+assert succeeded?
+assert result("ATAN2") =~ expr("
+         + 1.57079632679489661923e+00*atan2(24/13,0)
+       + 2.72706541948852419832e+00*atan2(5.4321e-01, - 1.2345e+00)
+       + 2.21627784862167698618e+00*atan2(5.4321e+00, - 45/11)
+       + 2.02102192305561165724e+00*atan2(3, - 1.45e+00)
+")
+*--#] evaluate_atan2 : 
 *--#[ evaluate_sqrt :
 #Startfloat 21d
 CFunction sqrt;

sources/evaluate.c

@@ -373,7 +373,7 @@ int EvaluateFun(PHEAD WORD *term, WORD level, WORD *pars)
 		if ( pars[2] == *t ) {	/* have to do this one if possible */
 TestArgument:
 /*
-			There must be a single argument, except for the AGM function
+			There must be a single argument, except for the AGM or atan2 functions
 */
 			tnext = t+t[1]; tt = t+FUNHEAD; NEXTARG(tt);
 			if( *t == SYMBOL) {
@@ -397,7 +397,7 @@ int EvaluateFun(PHEAD WORD *term, WORD level, WORD *pars)
 				first = 0;
 				goto nextfun;
 			}
-			if ( tt != tnext && *t != AGMFUNCTION ) goto nextfun;
+			if ( tt != tnext && *t != AGMFUNCTION && *t != ATAN2FUNCTION) goto nextfun;
 			if ( *t == SINFUNCTION ) {
 				pimul = GetPiArgument(BHEAD t+FUNHEAD);
 				if ( pimul >= 0 && pimul < 24 ) {
@@ -511,7 +511,7 @@ int EvaluateFun(PHEAD WORD *term, WORD level, WORD *pars)
 				}
 			}
 
-			if ( *t == AGMFUNCTION ) {
+			if ( *t == AGMFUNCTION || *t == ATAN2FUNCTION ) {
 				if ( GetFloatArgument(BHEAD auxr1,t,1) < 0 ) goto nextfun;
 				if ( GetFloatArgument(BHEAD auxr3,t,-2) < 0 ) goto nextfun;
 			}
@@ -619,6 +619,14 @@ int EvaluateFun(PHEAD WORD *term, WORD level, WORD *pars)
 					mpfr_atan(auxr3,auxr1,RND);
 					mpfr_mul(auxr2,auxr2,auxr3,RND);
 				break;
+				case ATAN2FUNCTION:
+					nsgn = mpfr_sgn(auxr1);
+					nsgn2 = mpfr_sgn(auxr3);
+					// We follow the conventions of mpfr here:
+					if ( nsgn == 0 && nsgn2 >= 0) goto getout;
+					mpfr_atan2(auxr3,auxr1,auxr3,RND);
+					mpfr_mul(auxr2,auxr2,auxr3,RND);
+				break;
 				case SINFUNCTION:
 					mpfr_sin(auxr3,auxr1,RND);
 					mpfr_mul(auxr2,auxr2,auxr3,RND);
@@ -653,6 +661,7 @@ int EvaluateFun(PHEAD WORD *term, WORD level, WORD *pars)
 				case ASINFUNCTION:
 				case ACOSFUNCTION:
 				case ATANFUNCTION:
+				case ATAN2FUNCTION:
 				case SINHFUNCTION:
 				case COSHFUNCTION:
 				case TANHFUNCTION: