From 4fedad85efa84f25cad199eb325d3a300778a046 Mon Sep 17 00:00:00 2001
From: nobu <nobu@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>
Date: Sun, 17 Jun 2018 02:37:32 +0000
Subject: [PATCH] refine Integer#** and Float#**

* complex.c (rb_dbl_complex_polar): utility function, which
  returns more precise value in right angle cases.

* bignum.c (rb_big_pow): use rb_dbl_complex_polar().

* numeric.c (rb_float_pow, fix_pow): create a Complex by polar
  form.

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@63678 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
---
 bignum.c   |  5 ++---
 complex.c  | 22 ++++++++++++++++++++++
 internal.h |  1 +
 numeric.c  |  4 ++--
 4 files changed, 27 insertions(+), 5 deletions(-)

diff --git a/bignum.c b/bignum.c
index 00d46ee662..7e5ce4d585 100644
--- a/bignum.c
+++ b/bignum.c
@@ -6209,9 +6209,8 @@ rb_big_pow(VALUE x, VALUE y)
     if (y == INT2FIX(0)) return INT2FIX(1);
     if (RB_FLOAT_TYPE_P(y)) {
 	d = RFLOAT_VALUE(y);
-	if ((BIGNUM_NEGATIVE_P(x) && !BIGZEROP(x)) && d != round(d)) {
-	    x = DBL2NUM(pow(-rb_big2dbl(x),  d));
-	    return rb_complex_polar(x, DBL2NUM(d * M_PI));
+	if ((BIGNUM_NEGATIVE_P(x) && !BIGZEROP(x))) {
+	    return rb_dbl_complex_polar(pow(-rb_big2dbl(x), d), d);
 	}
     }
     else if (RB_BIGNUM_TYPE_P(y)) {
diff --git a/complex.c b/complex.c
index e9bfc02f7a..2b452e23c0 100644
--- a/complex.c
+++ b/complex.c
@@ -540,6 +540,28 @@ f_complex_polar(VALUE klass, VALUE x, VALUE y)
 					  f_mul(x, m_sin(y)));
 }
 
+/* returns a Complex or Float of ang*PI-rotated abs */
+VALUE
+rb_dbl_complex_polar(double abs, double ang)
+{
+    double fi;
+    const double fr = modf(ang, &fi);
+    int pos = fr == +0.5;
+
+    if (pos || fr == -0.5) {
+	if ((modf(fi / 2.0, &fi) != fr) ^ pos) abs = -abs;
+	return rb_complex_new(RFLOAT_0, DBL2NUM(abs));
+    }
+    else if (fr == 0.0) {
+	if (modf(fi / 2.0, &fi) != 0.0) abs = -abs;
+	return DBL2NUM(abs);
+    }
+    else {
+	ang *= M_PI;
+	return rb_complex_new(DBL2NUM(abs * cos(ang)), DBL2NUM(abs * sin(ang)));
+    }
+}
+
 /*
  * call-seq:
  *    Complex.polar(abs[, arg])  ->  complex
diff --git a/internal.h b/internal.h
index 7944f87043..c486a46d99 100644
--- a/internal.h
+++ b/internal.h
@@ -1171,6 +1171,7 @@ VALUE rb_complex_plus(VALUE, VALUE);
 VALUE rb_complex_mul(VALUE, VALUE);
 VALUE rb_complex_abs(VALUE x);
 VALUE rb_complex_sqrt(VALUE x);
+VALUE rb_dbl_complex_polar(double abs, double ang);
 
 /* cont.c */
 VALUE rb_obj_is_fiber(VALUE);
diff --git a/numeric.c b/numeric.c
index 30afc581fe..fe867f9fd3 100644
--- a/numeric.c
+++ b/numeric.c
@@ -1276,7 +1276,7 @@ rb_float_pow(VALUE x, VALUE y)
 	dx = RFLOAT_VALUE(x);
 	dy = RFLOAT_VALUE(y);
 	if (dx < 0 && dy != round(dy))
-	    return num_funcall1(rb_complex_raw1(x), idPow, y);
+	    return rb_dbl_complex_polar(pow(-dx, dy), dy);
     }
     else {
 	return rb_num_coerce_bin(x, y, idPow);
@@ -4010,7 +4010,7 @@ fix_pow(VALUE x, VALUE y)
 	if (a == 1) return DBL2NUM(1.0);
 	{
 	    if (a < 0 && dy != round(dy))
-		return num_funcall1(rb_complex_raw1(x), idPow, y);
+		return rb_dbl_complex_polar(pow(-(double)a, dy), dy);
 	    return DBL2NUM(pow((double)a, dy));
 	}
     }