*** empty log message ***

arccos.cpp

@@ -6,22 +6,27 @@ eval_arccos(void)
 {
 	push(cadr(p1));
 	eval();
-	arccos();
+	yyarccos();
 }
 
 void
 arccos(void)
+{
+	save();
+	yyarccos();
+	restore();
+}
+
+void
+yyarccos(void)
 {
 	int n;
 	double d;
 
-	save();
-
 	p1 = pop();
 
 	if (car(p1) == symbol(COS)) {
 		push(cadr(p1));
-		restore();
 		return;
 	}
 
@@ -31,7 +36,24 @@ arccos(void)
 		if (errno)
 			stop("arccos function argument is not in the interval [-1,1]");
 		push_double(d);
-		restore();
+		return;
+	}
+
+	// if p1 == 1/sqrt(2) then return 1/4*pi (45 degrees)
+
+	if (issqrttwo(p1)) {
+		push_rational(1, 4);
+		push_symbol(PI);
+		multiply();
+		return;
+	}
+
+	// if p1 == -1/sqrt(2) then return 3/4*pi (135 degrees)
+
+	if (isminussqrttwo(p1)) {
+		push_rational(3, 4);
+		push_symbol(PI);
+		multiply();
 		return;
 	}
 
@@ -39,7 +61,6 @@ arccos(void)
 		push_symbol(ARCCOS);
 		push(p1);
 		list(2);
-		restore();
 		return;
 	}
 
@@ -82,8 +103,6 @@ arccos(void)
 		list(2);
 		break;
 	}
-
-	restore();
 }
 
 static char *s[] = {
@@ -120,6 +139,18 @@ static char *s[] = {
 
 	"arccos(cos(x))",
 	"x",
+
+	"arccos(1/sqrt(2))",
+	"1/4*pi",
+
+	"arccos(-1/sqrt(2))",
+	"3/4*pi",
+
+	"arccos(cos(1/4*pi))",
+	"1/4*pi",
+
+	"arccos(cos(3/4*pi))",
+	"3/4*pi",
 };
 
 void

arcsin.cpp

@@ -6,22 +6,27 @@ eval_arcsin(void)
 {
 	push(cadr(p1));
 	eval();
-	arcsin();
+	yyarcsin();
 }
 
 void
 arcsin(void)
+{
+	save();
+	yyarcsin();
+	restore();
+}
+
+void
+yyarcsin(void)
 {
 	int n;
 	double d;
 
-	save();
-
 	p1 = pop();
 
 	if (car(p1) == symbol(SIN)) {
 		push(cadr(p1));
-		restore();
 		return;
 	}
 
@@ -31,7 +36,24 @@ arcsin(void)
 		if (errno)
 			stop("arcsin function argument is not in the interval [-1,1]");
 		push_double(d);
-		restore();
+		return;
+	}
+
+	// if p1 == 1/sqrt(2) then return 1/4*pi (45 degrees)
+
+	if (issqrttwo(p1)) {
+		push_rational(1, 4);
+		push_symbol(PI);
+		multiply();
+		return;
+	}
+
+	// if p1 == -1/sqrt(2) then return -1/4*pi (-45 degrees)
+
+	if (isminussqrttwo(p1)) {
+		push_rational(-1, 4);
+		push_symbol(PI);
+		multiply();
 		return;
 	}
 
@@ -39,7 +61,6 @@ arcsin(void)
 		push_symbol(ARCSIN);
 		push(p1);
 		list(2);
-		restore();
 		return;
 	}
 
@@ -84,8 +105,6 @@ arcsin(void)
 		list(2);
 		break;
 	}
-
-	restore();
 }
 
 static char *s[] = {
@@ -122,6 +141,18 @@ static char *s[] = {
 
 	"arcsin(sin(x))",
 	"x",
+
+	"arcsin(1/sqrt(2))",
+	"1/4*pi",
+
+	"arcsin(-1/sqrt(2))",
+	"-1/4*pi",
+
+	"arcsin(sin(1/4*pi))",
+	"1/4*pi",
+
+	"arcsin(sin(-1/4*pi))",
+	"-1/4*pi",
 };
 
 void

is.cpp

@@ -304,3 +304,30 @@ equalq(U *p, int a, int b)
 	}
 	return 0;
 }
+
+// p == 1/sqrt(2) ?
+
+int
+issqrttwo(U *p)
+{
+	if (car(p) == symbol(POWER)
+	&& equaln(cadr(p), 2)
+	&& equalq(caddr(p), -1, 2))
+		return 1;
+	else
+		return 0;
+}
+
+// p == -1/sqrt(2) ?
+
+int
+isminussqrttwo(U *p)
+{
+	if (car(p) == symbol(MULTIPLY)
+	&& equaln(cadr(p), -1)
+	&& issqrttwo(caddr(p))
+	&& length(p) == 3)
+		return 1;
+	else
+		return 0;
+}

prototypes.h

@@ -38,6 +38,7 @@ void append(void);
 // arccos.cpp
 void eval_arccos(void);
 void arccos(void);
+void yyarccos(void);
 void test_arccos(void);
 
 // arccosh.cpp
@@ -48,6 +49,7 @@ void test_arccosh(void);
 // arcsin.cpp
 void eval_arcsin(void);
 void arcsin(void);
+void yyarcsin(void);
 void test_arcsin(void);
 
 // arcsinh.cpp
@@ -516,6 +518,8 @@ int isoneover(U *p);
 int isfraction(U *p);
 int equaln(U *p, int n);
 int equalq(U *p, int a, int b);
+int issqrttwo(U *p);
+int isminussqrttwo(U *p);
 
 // isprime.cpp
 void eval_isprime(void);