fix aversin() and acoversin()

In cases where the real value to the inverse versed sine and the
inverse coversed sine function produces a complex value, the
conversion from real to complex was incorrect.

Added c_to_q(COMPLEX *c, bool cfree) to make is easier to convert
a COMPLEX value that is real (imag part is 0) into a NUMBER and
optionally free the COMPLEX value.

The func.c code now uses c_to_q().

NOTE: There is a XXX bug marked in the f_aversin() and f_acoversin()
that still needs to be fixed.

CHANGES

@@ -126,6 +126,10 @@ The following are the changes from calc version 2.14.3.5 to date:
     builtin functions are listed by "show builtin" and the help/builtin
     to match the sorting of "LANG=C LC_ALL=C sort -d -u".
 
+    Added c_to_q(COMPLEX *c, bool cfree) to make is easier to convert
+    a COMPLEX value that is real (imag part is 0) into a NUMBER and
+    optionally free the COMPLEX value.
+
 
 The following are the changes from calc version 2.14.3.4 to 2.14.3.5:
 

LIBRARY

@@ -636,6 +636,23 @@ only used for complex numbers.	Examples of macros are:
 There is only one comparison you can make for COMPLEX values, and that is
 for equality.  The ccmp function returns true if two complex numbers differ.
 
+Sometimes to results of a COMPLEX based calculation is a real number.
+That is, the imaginary part of the COMPLEX is 0.  You may convert the
+COMPLEX into a new allocated NUMBER that is real part of the COMPLEX value.
+For example:
+
+	COMPLEX *c;
+	NUMBER *q;
+	bool ok_to_free;	/* true ==> free COMPLEX value, false ==> do not */
+
+	if (cisreal(c)) {
+		q = c_to_q(c, ok_to_free);
+	}
+
+The 2nd argument to c_to_q() determines if the complex argument should be freed
+or not.  Pass a false value as the 2nd arg if you wish to continue to use the
+COMPLEX value.
+
 There are three predefined values for complex numbers.	You should clink
 them when you want to use them.	 They are _czero_, _cone_, and _conei_.
 These have the values 0, 1, and i.

cal/regress.cal

@@ -3565,9 +3565,9 @@ define test_trig()
 		   ': round(aversin(0.5, 1e-10), 10) == 1.0471975512'));
 	vrfy(aversin(0) == 0,
 		    strcat(str(tnum++), ': aversin(0) == 0'));
-	vrfy(round(aversin(-5, 1e-10), 10) == 0.1673829554+2.4921599676i,
+	vrfy(round(aversin(-5, 1e-10), 10) == 2.4778887303i,
 	    strcat(str(tnum++),
-		   ': round(aversin(0.5, 1e-10), 10) == 0.1673829554+2.4921599676i'));
+		   ': round(aversin(-5, 1e-10), 10) == 2.4778887303i'));
 	vrfy(round(aversin(2 + 3i, 1e-10), 10) == 1.8783999763+1.8641615439i,
 	    strcat(str(tnum++),
 		   ': round(aversin(2 + 3i, 1e-10), 10) == 1.8783999763+1.8641615439i'));
@@ -3578,9 +3578,9 @@ define test_trig()
 		   ': round(acoversin(0.5, 1e-10), 10) == 0.5235987756'));
 	vrfy(acoversin(1) == 0,
 		    strcat(str(tnum++), ': acoversin(1) == 0'));
-	vrfy(round(acoversin(-5, 1e-10), 10) == 1.4034133718-2.4921599681i,
+	vrfy(round(acoversin(-5, 1e-10), 10) == 1.5707963268-2.4778887303i,
 	    strcat(str(tnum++),
-		   ': round(acoversin(0.5, 1e-10), 10) == 1.4034133718-2.4921599681i'));
+		   ': round(acoversin(-5, 1e-10), 10) == 1.5707963268-2.4778887303i'));
 	vrfy(round(acoversin(2 + 3i, 1e-10), 10) == -0.3076036495-1.8641615442i,
 	    strcat(str(tnum++),
 		   ': round(acoversin(2 + 3i, 1e-10), 10) == -0.3076036495-1.8641615442i'));

cmath.h

@@ -72,6 +72,7 @@ E_FUNC COMPLEX *c_shift(COMPLEX *c, long i);
 E_FUNC COMPLEX *c_square(COMPLEX *c);
 E_FUNC COMPLEX *c_conj(COMPLEX *c);
 E_FUNC COMPLEX *c_real(COMPLEX *c);
+E_FUNC NUMBER *c_to_q(COMPLEX *c, bool cfree);
 E_FUNC COMPLEX *c_imag(COMPLEX *c);
 E_FUNC COMPLEX *c_neg(COMPLEX *c);
 E_FUNC COMPLEX *c_inv(COMPLEX *c);

commath.c

@@ -396,6 +396,65 @@ c_real(COMPLEX *c)
 }
 
 
+/*
+ * c_to_q - convert a real part of a COMPLEX to a NUMBER
+ *
+ * given:
+ *	c	complex number for which the real part will be used
+ *	cfree	true ==> free c, false ==> do not free c
+ *
+ * returns:
+ *	allocated NUMBER that the equivalent of the real part of a complex number
+ *
+ * NOTE: Any imaginary part of the COMPLEX value is ignored.
+ *
+ * NOTE: To avoid a loss of value, test with cisreal(c) first:
+ *
+ *	COMPLEX *c;
+ *	NUMBER *q;
+ *	bool ok_to_free;
+ *
+ *	if (cisreal(c)) {
+ *		q = c_to_q(c, ok_to_free);
+ *	}
+ */
+NUMBER *
+c_to_q(COMPLEX *c, bool cfree)
+{
+	NUMBER *r;	/* allocated NUMBER equivalent to return */
+
+	/*
+	 * firewall
+	 */
+	if (c == NULL) {
+		math_error("%s: c is NULL", __func__);
+		not_reached();
+	}
+
+	/*
+	 * allocate a new NUMBER
+	 */
+	r = qalloc();
+
+	/*
+	 * link in the real part of the COMPLEX value
+	 */
+	r = qlink(c->real);
+
+	/*
+	 * free c if requested
+	 */
+	if (cfree == true) {
+		comfree(c);
+	}
+
+	/*
+	 * return the allocated equivalent NUMBER
+	 */
+	return r;
+}
+
+
 /*
  * Return the imaginary part of a complex number as a real.
  */

func.c

@@ -2140,9 +2140,8 @@ f_exp(int count, VALUE **vals)
 			result.v_com = c;
 			result.v_type = V_COM;
 			if (cisreal(c)) {
-				result.v_num = qlink(c->real);
+				result.v_num = c_to_q(c, true);
 				result.v_type = V_NUM;
-				comfree(c);
 			}
 			break;
 		default:
@@ -2202,9 +2201,8 @@ f_ln(int count, VALUE **vals)
 	result.v_type = V_COM;
 	result.v_com = c;
 	if (cisreal(c)) {
-		result.v_num = qlink(c->real);
+		result.v_num = c_to_q(c, true);
 		result.v_type = V_NUM;
-		comfree(c);
 	}
 	return result;
 }
@@ -2263,9 +2261,8 @@ f_log(int count, VALUE **vals)
 	result.v_type = V_COM;
 	result.v_com = c;
 	if (cisreal(c)) {
-		result.v_num = qlink(c->real);
+		result.v_num = c_to_q(c, true);
 		result.v_type = V_NUM;
-		comfree(c);
 	}
 	return result;
 }
@@ -2324,9 +2321,8 @@ f_log2(int count, VALUE **vals)
 	result.v_type = V_COM;
 	result.v_com = c;
 	if (cisreal(c)) {
-		result.v_num = qlink(c->real);
+		result.v_num = c_to_q(c, true);
 		result.v_type = V_NUM;
-		comfree(c);
 	}
 	return result;
 }
@@ -2409,8 +2405,7 @@ f_logn(int count, VALUE **vals)
 				return error_value(E_LOGN_3);
 			}
 			if (cisreal(ln_x_c)) {
-				ln_x_r = qcopy(ln_x_c->real);
+				ln_x_r = c_to_q(ln_x_c, true);
-				comfree(ln_x_c);
 			} else {
 				ln_of_x_is_complex = true;
 			}
@@ -2430,8 +2425,7 @@ f_logn(int count, VALUE **vals)
 			return error_value(E_LOGN_3);
 		}
 		if (cisreal(ln_x_c)) {
-			ln_x_r = qcopy(ln_x_c->real);
+			ln_x_r = c_to_q(ln_x_c, true);
-			comfree(ln_x_c);
 		} else {
 			ln_of_x_is_complex = true;
 		}
@@ -2464,8 +2458,7 @@ f_logn(int count, VALUE **vals)
 				return error_value(E_LOGN_4);
 			}
 			if (cisreal(ln_n_c)) {
-				ln_n_r = qcopy(ln_n_c->real);
+				ln_n_r = c_to_q(ln_n_c, true);
-				comfree(ln_n_c);
 			} else {
 				ln_of_n_is_complex = true;
 			}
@@ -2493,8 +2486,7 @@ f_logn(int count, VALUE **vals)
 			return error_value(E_LOGN_4);
 		}
 		if (cisreal(ln_n_c)) {
-			ln_n_r = qcopy(ln_n_c->real);
+			ln_n_r = c_to_q(ln_n_c, true);
-			comfree(ln_n_c);
 		} else {
 			ln_of_n_is_complex = true;
 		}
@@ -2519,9 +2511,8 @@ f_logn(int count, VALUE **vals)
 			/* check if division is COMPLEX or NUMBER */
 			if (cisreal(p_cval)) {
 				/* ln(x) / ln(n) was NUMBER, not COMPLEX */
-				result.v_num = qlink(p_cval->real);
+				result.v_num = c_to_q(p_cval, true);
 				result.v_type = V_NUM;
-				comfree(p_cval);
 			} else {
 				/* ln(x) / ln(n) is COMPLEX */
 				result.v_type = V_COM;
@@ -2540,9 +2531,8 @@ f_logn(int count, VALUE **vals)
 			/* check if division is COMPLEX or NUMBER */
 			if (cisreal(p_cval)) {
 				/* ln(x) / ln(n) was NUMBER, not COMPLEX */
-				result.v_num = qlink(p_cval->real);
+				result.v_num = c_to_q(p_cval, true);
 				result.v_type = V_NUM;
-				comfree(p_cval);
 			} else {
 				/* ln(x) / ln(n) is COMPLEX */
 				result.v_type = V_COM;
@@ -2567,9 +2557,8 @@ f_logn(int count, VALUE **vals)
 			/* check if division is COMPLEX or NUMBER */
 			if (cisreal(p_cval)) {
 				/* ln(x) / ln(n) was NUMBER, not COMPLEX */
-				result.v_num = qlink(p_cval->real);
+				result.v_num = c_to_q(p_cval, true);
 				result.v_type = V_NUM;
-				comfree(p_cval);
 			} else {
 				/* ln(x) / ln(n) is COMPLEX */
 				result.v_type = V_COM;
@@ -2633,9 +2622,8 @@ f_cos(int count, VALUE **vals)
 			result.v_com = c;
 			result.v_type = V_COM;
 			if (cisreal(c)) {
-				result.v_num = qlink(c->real);
+				result.v_num = c_to_q(c, true);
 				result.v_type = V_NUM;
-				comfree(c);
 			}
 			break;
 		default:
@@ -2945,9 +2933,8 @@ f_sin(int count, VALUE **vals)
 			result.v_com = c;
 			result.v_type = V_COM;
 			if (cisreal(c)) {
-				result.v_num = qlink(c->real);
+				result.v_num = c_to_q(c, true);
 				result.v_type = V_NUM;
-				comfree(c);
 			}
 			break;
 		default:
@@ -3208,8 +3195,7 @@ f_sinh(int count, VALUE **vals)
 			result.v_com = c;
 			result.v_type = V_COM;
 			if (cisreal(c)) {
-				result.v_num = qlink(c->real);
+				result.v_num = c_to_q(c, true);
-				comfree(c);
 				result.v_type = V_NUM;
 			}
 			break;
@@ -3262,8 +3248,7 @@ f_cosh(int count, VALUE **vals)
 			result.v_com = c;
 			result.v_type = V_COM;
 			if (cisreal(c)) {
-				result.v_num = qlink(c->real);
+				result.v_num = c_to_q(c, true);
-				comfree(c);
 				result.v_type = V_NUM;
 			}
 			break;
@@ -3524,9 +3509,8 @@ f_atan(int count, VALUE **vals)
 			result.v_type = V_COM;
 			result.v_com = tmp;
 			if (cisreal(tmp)) {
-				result.v_num = qlink(tmp->real);
+				result.v_num = c_to_q(tmp, true);
 				result.v_type = V_NUM;
-				comfree(tmp);
 			}
 			break;
 		default:
@@ -3574,9 +3558,8 @@ f_acot(int count, VALUE **vals)
 			result.v_type = V_COM;
 			result.v_com = tmp;
 			if (cisreal(tmp)) {
-				result.v_num = qlink(tmp->real);
+				result.v_num = c_to_q(tmp, true);
 				result.v_type = V_NUM;
-				comfree(tmp);
 			}
 			break;
 		default:
@@ -3591,7 +3574,6 @@ f_asin(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -3636,10 +3618,8 @@ f_asin(int count, VALUE **vals)
 		return error_value(E_ASIN3);
 	}
 	if (result.v_type == V_COM && cisreal(result.v_com)) {
-		q = qlink(result.v_com->real);
+		result.v_num = c_to_q(result.v_com, true);
-		comfree(result.v_com);
 		result.v_type = V_NUM;
-		result.v_num = q;
 	}
 	return result;
 }
@@ -3650,7 +3630,6 @@ f_acos(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -3695,10 +3674,8 @@ f_acos(int count, VALUE **vals)
 		return error_value(E_ACOS3);
 	}
 	if (result.v_type == V_COM && cisreal(result.v_com)) {
-		q = qlink(result.v_com->real);
+		result.v_num = c_to_q(result.v_com, true);
-		comfree(result.v_com);
 		result.v_type = V_NUM;
-		result.v_num = q;
 	}
 	return result;
 }
@@ -3710,7 +3687,6 @@ f_asec(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -3758,10 +3734,8 @@ f_asec(int count, VALUE **vals)
 	}
 	if (result.v_type == V_COM) {
 		if (cisreal(result.v_com)) {
-			q = qlink(result.v_com->real);
+			result.v_num = c_to_q(result.v_com, true);
-			comfree(result.v_com);
 			result.v_type = V_NUM;
-			result.v_num = q;
 		}
 	}
 	return result;
@@ -3774,7 +3748,6 @@ f_acsc(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -3822,10 +3795,8 @@ f_acsc(int count, VALUE **vals)
 	}
 	if (result.v_type == V_COM) {
 		if (cisreal(result.v_com)) {
-			q = qlink(result.v_com->real);
+			result.v_num = c_to_q(result.v_com, true);
-			comfree(result.v_com);
 			result.v_type = V_NUM;
-			result.v_num = q;
 		}
 	}
 	return result;
@@ -3871,9 +3842,8 @@ f_asinh(int count, VALUE **vals)
 			result.v_type = V_COM;
 			result.v_com = tmp;
 			if (cisreal(tmp)) {
-				result.v_num = qlink(tmp->real);
+				result.v_num = c_to_q(tmp, true);
 				result.v_type = V_NUM;
-				comfree(tmp);
 			}
 			break;
 		default:
@@ -3889,7 +3859,6 @@ f_acosh(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -3934,10 +3903,8 @@ f_acosh(int count, VALUE **vals)
 		return error_value(E_ACOSH3);
 	}
 	if (result.v_type == V_COM && cisreal(result.v_com)) {
-		q = qlink(result.v_com->real);
+		result.v_num = c_to_q(result.v_com, true);
-		comfree(result.v_com);
 		result.v_type = V_NUM;
-		result.v_num = q;
 	}
 	return result;
 }
@@ -3949,7 +3916,6 @@ f_atanh(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -3995,10 +3961,8 @@ f_atanh(int count, VALUE **vals)
 	}
 	if (result.v_type == V_COM) {
 		if (cisreal(result.v_com)) {
-			q = qlink(result.v_com->real);
+			result.v_num = c_to_q(result.v_com, true);
-			comfree(result.v_com);
 			result.v_type = V_NUM;
-			result.v_num = q;
 		}
 	}
 	return result;
@@ -4011,7 +3975,6 @@ f_acoth(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -4057,10 +4020,8 @@ f_acoth(int count, VALUE **vals)
 	}
 	if (result.v_type == V_COM) {
 		if (cisreal(result.v_com)) {
-			q = qlink(result.v_com->real);
+			result.v_num = c_to_q(result.v_com, true);
-			comfree(result.v_com);
 			result.v_type = V_NUM;
-			result.v_num = q;
 		}
 	}
 	return result;
@@ -4073,7 +4034,6 @@ f_asech(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -4121,10 +4081,8 @@ f_asech(int count, VALUE **vals)
 	}
 	if (result.v_type == V_COM) {
 		if (cisreal(result.v_com)) {
-			q = qlink(result.v_com->real);
+			result.v_num = c_to_q(result.v_com, true);
-			comfree(result.v_com);
 			result.v_type = V_NUM;
-			result.v_num = q;
 		}
 	}
 	return result;
@@ -4137,7 +4095,6 @@ f_acsch(int count, VALUE **vals)
 	VALUE result;
 	COMPLEX *tmp;
 	NUMBER *err;
-	NUMBER *q;
 
 	/* initialize VALUE */
 	result.v_subtype = V_NOSUBTYPE;
@@ -4185,10 +4142,8 @@ f_acsch(int count, VALUE **vals)
 	}
 	if (result.v_type == V_COM) {
 		if (cisreal(result.v_com)) {
-			q = qlink(result.v_com->real);
+			result.v_num = c_to_q(result.v_com, true);
-			comfree(result.v_com);
 			result.v_type = V_NUM;
-			result.v_num = q;
 		}
 	}
 	return result;
@@ -4200,7 +4155,6 @@ f_gd(int count, VALUE **vals)
 {
 	VALUE result;
 	NUMBER *eps;
-	NUMBER *q;
 	COMPLEX *tmp;
 
 	/* initialize VALUE */
@@ -4245,9 +4199,7 @@ f_gd(int count, VALUE **vals)
 	if (result.v_com == NULL)
 		return error_value(E_GD3);
 	if (cisreal(result.v_com)) {
-		q = qlink(result.v_com->real);
+		result.v_num = c_to_q(result.v_com, true);
-		comfree(result.v_com);
-		result.v_num = q;
 		result.v_type = V_NUM;
 	}
 	return result;
@@ -4259,7 +4211,6 @@ f_agd(int count, VALUE **vals)
 {
 	VALUE result;
 	NUMBER *eps;
-	NUMBER *q;
 	COMPLEX *tmp;
 
 	/* initialize VALUE */
@@ -4304,9 +4255,7 @@ f_agd(int count, VALUE **vals)
 	if (result.v_com == NULL)
 		return error_value(E_AGD3);
 	if (cisreal(result.v_com)) {
-		q = qlink(result.v_com->real);
+		result.v_num = c_to_q(result.v_com, true);
-		comfree(result.v_com);
-		result.v_num = q;
 		result.v_type = V_NUM;
 	}
 	return result;
@@ -5974,9 +5923,8 @@ f_polar(int count, VALUE **vals)
 	result.v_com = c;
 	result.v_type = V_COM;
 	if (cisreal(c)) {
-		result.v_num = qlink(c->real);
+		result.v_num = c_to_q(c, true);
 		result.v_type = V_NUM;
-		comfree(c);
 	}
 	return result;
 }
@@ -10660,9 +10608,8 @@ f_versin(int count, VALUE **vals)
 			 * case: complex trig function returned real, convert result to NUMBER
 			 */
 			if (cisreal(c)) {
-				result.v_num = qlink(c->real);
+				result.v_num = c_to_q(c, true);
 				result.v_type = V_NUM;
-				comfree(c);
 			}
 			break;
 		default:
@@ -10717,7 +10664,8 @@ f_aversin(int count, VALUE **vals)
 		 */
 		} else {
 			/* convert NUMBER argument from NUMBER to COMPLEX */
-			vals[0]->v_com = qqtoc(vals[0]->v_num, &_qone_);
+			/* XXX - WRONG - do not change the arg! */
+			vals[0]->v_com = qqtoc(vals[0]->v_num, &_qzero_);
 			vals[0]->v_type = V_COM;
 		}
 	}
@@ -10738,9 +10686,8 @@ f_aversin(int count, VALUE **vals)
 		 * case: complex trig function returned real, convert result to NUMBER
 		 */
 		if (cisreal(c)) {
-			result.v_num = qlink(c->real);
+			result.v_num = c_to_q(c, true);
 			result.v_type = V_NUM;
-			comfree(c);
 		}
 	}
 	if (vals[0]->v_type != V_NUM && vals[0]->v_type != V_COM) {
@@ -10800,9 +10747,8 @@ f_coversin(int count, VALUE **vals)
 			 * case: complex trig function returned real, convert result to NUMBER
 			 */
 			if (cisreal(c)) {
-				result.v_num = qlink(c->real);
+				result.v_num = c_to_q(c, true);
 				result.v_type = V_NUM;
-				comfree(c);
 			}
 			break;
 		default:
@@ -10857,7 +10803,8 @@ f_acoversin(int count, VALUE **vals)
 		 */
 		} else {
 			/* convert NUMBER argument from NUMBER to COMPLEX */
-			vals[0]->v_com = qqtoc(vals[0]->v_num, &_qone_);
+			/* XXX - WRONG - do not change the arg! */
+			vals[0]->v_com = qqtoc(vals[0]->v_num, &_qzero_);
 			vals[0]->v_type = V_COM;
 		}
 	}
@@ -10878,9 +10825,8 @@ f_acoversin(int count, VALUE **vals)
 		 * case: complex trig function returned real, convert result to NUMBER
 		 */
 		if (cisreal(c)) {
-			result.v_num = qlink(c->real);
+			result.v_num = c_to_q(c, true);
 			result.v_type = V_NUM;
-			comfree(c);
 		}
 	}
 	if (vals[0]->v_type != V_NUM && vals[0]->v_type != V_COM) {

help/acoversin

@@ -24,7 +24,7 @@ EXAMPLE
     0.5236 0.5235987756 0.523598775598299 0.52359877559829887308
 
     ; print acoversin(1), acoversin(-5), acoversin(2 + 3i)
-    0 1.40341337183925787843-2.49215996813383545614i -0.30760364953071124992-1.86416154415788242834i
+    0 1.57079632679489661923-2.47788873028847500481i -0.30760364953071124992-1.86416154415788242834i
 
 LIMITS
     0 < eps < 1

help/aversin

@@ -24,7 +24,7 @@ EXAMPLE
     1.0472 1.0471975512 1.047197551196598 1.04719755119659774615
 
     ; print aversin(0), aversin(-5), aversin(2 + 3i)
-    0 0.16738295495563874081+2.49215996813383545614i 1.87839997632560786916+1.86416154415788242831i
+    0 2.47788873028847500485i 1.87839997632560786916+1.86416154415788242831i
 
 LIMITS
     0 < eps < 1