[Python-checkins] r62418 - python/trunk/Modules/cmathmodule.c
mark.dickinson
python-checkins at python.org
Sun Apr 20 18:13:17 CEST 2008
Author: mark.dickinson
Date: Sun Apr 20 18:13:17 2008
New Revision: 62418
Log:
Issue 2662: Initialize special value tables dynamically (i.e. when
cmath module is loaded) instead of statically. This fixes compile-time
problems on platforms where HUGE_VAL is an extern variable rather than
a constant.
Thanks Hirokazu Yamamoto for the patch.
Modified:
python/trunk/Modules/cmathmodule.c
Modified: python/trunk/Modules/cmathmodule.c
==============================================================================
--- python/trunk/Modules/cmathmodule.c (original)
+++ python/trunk/Modules/cmathmodule.c Sun Apr 20 18:13:17 2008
@@ -107,16 +107,8 @@
#define P14 0.25*Py_MATH_PI
#define P12 0.5*Py_MATH_PI
#define P34 0.75*Py_MATH_PI
-#ifdef MS_WINDOWS
-/* On Windows HUGE_VAL is an extern variable and not a constant. Since the
- special value arrays need a constant we have to roll our own infinity
- and nan. */
-# define INF (DBL_MAX*DBL_MAX)
-# define N (INF*0.)
-#else
-# define INF Py_HUGE_VAL
-# define N Py_NAN
-#endif /* MS_WINDOWS */
+#define INF Py_HUGE_VAL
+#define N Py_NAN
#define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
/* First, the C functions that do the real work. Each of the c_*
@@ -128,15 +120,7 @@
raised.
*/
-static Py_complex acos_special_values[7][7] = {
- {{P34,INF},{P,INF}, {P,INF}, {P,-INF}, {P,-INF}, {P34,-INF},{N,INF}},
- {{P12,INF},{U,U}, {U,U}, {U,U}, {U,U}, {P12,-INF},{N,N}},
- {{P12,INF},{U,U}, {P12,0.},{P12,-0.},{U,U}, {P12,-INF},{P12,N}},
- {{P12,INF},{U,U}, {P12,0.},{P12,-0.},{U,U}, {P12,-INF},{P12,N}},
- {{P12,INF},{U,U}, {U,U}, {U,U}, {U,U}, {P12,-INF},{N,N}},
- {{P14,INF},{0.,INF},{0.,INF},{0.,-INF},{0.,-INF},{P14,-INF},{N,INF}},
- {{N,INF}, {N,N}, {N,N}, {N,N}, {N,N}, {N,-INF}, {N,N}}
-};
+static Py_complex acos_special_values[7][7];
static Py_complex
c_acos(Py_complex z)
@@ -177,15 +161,7 @@
"Return the arc cosine of x.");
-static Py_complex acosh_special_values[7][7] = {
- {{INF,-P34},{INF,-P}, {INF,-P}, {INF,P}, {INF,P}, {INF,P34},{INF,N}},
- {{INF,-P12},{U,U}, {U,U}, {U,U}, {U,U}, {INF,P12},{N,N}},
- {{INF,-P12},{U,U}, {0.,-P12},{0.,P12},{U,U}, {INF,P12},{N,N}},
- {{INF,-P12},{U,U}, {0.,-P12},{0.,P12},{U,U}, {INF,P12},{N,N}},
- {{INF,-P12},{U,U}, {U,U}, {U,U}, {U,U}, {INF,P12},{N,N}},
- {{INF,-P14},{INF,-0.},{INF,-0.},{INF,0.},{INF,0.},{INF,P14},{INF,N}},
- {{INF,N}, {N,N}, {N,N}, {N,N}, {N,N}, {INF,N}, {N,N}}
-};
+static Py_complex acosh_special_values[7][7];
static Py_complex
c_acosh(Py_complex z)
@@ -237,15 +213,7 @@
"Return the arc sine of x.");
-static Py_complex asinh_special_values[7][7] = {
- {{-INF,-P14},{-INF,-0.},{-INF,-0.},{-INF,0.},{-INF,0.},{-INF,P14},{-INF,N}},
- {{-INF,-P12},{U,U}, {U,U}, {U,U}, {U,U}, {-INF,P12},{N,N}},
- {{-INF,-P12},{U,U}, {-0.,-0.}, {-0.,0.}, {U,U}, {-INF,P12},{N,N}},
- {{INF,-P12}, {U,U}, {0.,-0.}, {0.,0.}, {U,U}, {INF,P12}, {N,N}},
- {{INF,-P12}, {U,U}, {U,U}, {U,U}, {U,U}, {INF,P12}, {N,N}},
- {{INF,-P14}, {INF,-0.}, {INF,-0.}, {INF,0.}, {INF,0.}, {INF,P14}, {INF,N}},
- {{INF,N}, {N,N}, {N,-0.}, {N,0.}, {N,N}, {INF,N}, {N,N}}
-};
+static Py_complex asinh_special_values[7][7];
static Py_complex
c_asinh(Py_complex z)
@@ -323,15 +291,7 @@
"Return the arc tangent of x.");
-static Py_complex atanh_special_values[7][7] = {
- {{-0.,-P12},{-0.,-P12},{-0.,-P12},{-0.,P12},{-0.,P12},{-0.,P12},{-0.,N}},
- {{-0.,-P12},{U,U}, {U,U}, {U,U}, {U,U}, {-0.,P12},{N,N}},
- {{-0.,-P12},{U,U}, {-0.,-0.}, {-0.,0.}, {U,U}, {-0.,P12},{-0.,N}},
- {{0.,-P12}, {U,U}, {0.,-0.}, {0.,0.}, {U,U}, {0.,P12}, {0.,N}},
- {{0.,-P12}, {U,U}, {U,U}, {U,U}, {U,U}, {0.,P12}, {N,N}},
- {{0.,-P12}, {0.,-P12}, {0.,-P12}, {0.,P12}, {0.,P12}, {0.,P12}, {0.,N}},
- {{0.,-P12}, {N,N}, {N,N}, {N,N}, {N,N}, {0.,P12}, {N,N}}
-};
+static Py_complex atanh_special_values[7][7];
static Py_complex
c_atanh(Py_complex z)
@@ -404,15 +364,7 @@
/* cosh(infinity + i*y) needs to be dealt with specially */
-static Py_complex cosh_special_values[7][7] = {
- {{INF,N},{U,U},{INF,0.}, {INF,-0.},{U,U},{INF,N},{INF,N}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{N,0.}, {U,U},{1.,0.}, {1.,-0.}, {U,U},{N,0.}, {N,0.}},
- {{N,0.}, {U,U},{1.,-0.}, {1.,0.}, {U,U},{N,0.}, {N,0.}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{INF,N},{U,U},{INF,-0.},{INF,0.}, {U,U},{INF,N},{INF,N}},
- {{N,N}, {N,N},{N,0.}, {N,0.}, {N,N},{N,N}, {N,N}}
-};
+static Py_complex cosh_special_values[7][7];
static Py_complex
c_cosh(Py_complex z)
@@ -472,15 +424,7 @@
/* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for
finite y */
-static Py_complex exp_special_values[7][7] = {
- {{0.,0.},{U,U},{0.,-0.}, {0.,0.}, {U,U},{0.,0.},{0.,0.}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{N,N}, {U,U},{1.,-0.}, {1.,0.}, {U,U},{N,N}, {N,N}},
- {{N,N}, {U,U},{1.,-0.}, {1.,0.}, {U,U},{N,N}, {N,N}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{INF,N},{U,U},{INF,-0.},{INF,0.},{U,U},{INF,N},{INF,N}},
- {{N,N}, {N,N},{N,-0.}, {N,0.}, {N,N},{N,N}, {N,N}}
-};
+static Py_complex exp_special_values[7][7];
static Py_complex
c_exp(Py_complex z)
@@ -538,15 +482,7 @@
"Return the exponential value e**x.");
-static Py_complex log_special_values[7][7] = {
- {{INF,-P34},{INF,-P}, {INF,-P}, {INF,P}, {INF,P}, {INF,P34}, {INF,N}},
- {{INF,-P12},{U,U}, {U,U}, {U,U}, {U,U}, {INF,P12}, {N,N}},
- {{INF,-P12},{U,U}, {-INF,-P}, {-INF,P}, {U,U}, {INF,P12}, {N,N}},
- {{INF,-P12},{U,U}, {-INF,-0.},{-INF,0.},{U,U}, {INF,P12}, {N,N}},
- {{INF,-P12},{U,U}, {U,U}, {U,U}, {U,U}, {INF,P12}, {N,N}},
- {{INF,-P14},{INF,-0.},{INF,-0.}, {INF,0.}, {INF,0.},{INF,P14}, {INF,N}},
- {{INF,N}, {N,N}, {N,N}, {N,N}, {N,N}, {INF,N}, {N,N}}
-};
+static Py_complex log_special_values[7][7];
static Py_complex
c_log(Py_complex z)
@@ -658,15 +594,7 @@
/* sinh(infinity + i*y) needs to be dealt with specially */
-static Py_complex sinh_special_values[7][7] = {
- {{INF,N},{U,U},{-INF,-0.},{-INF,0.},{U,U},{INF,N},{INF,N}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{0.,N}, {U,U},{-0.,-0.}, {-0.,0.}, {U,U},{0.,N}, {0.,N}},
- {{0.,N}, {U,U},{0.,-0.}, {0.,0.}, {U,U},{0.,N}, {0.,N}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{INF,N},{U,U},{INF,-0.}, {INF,0.}, {U,U},{INF,N},{INF,N}},
- {{N,N}, {N,N},{N,-0.}, {N,0.}, {N,N},{N,N}, {N,N}}
-};
+static Py_complex sinh_special_values[7][7];
static Py_complex
c_sinh(Py_complex z)
@@ -723,15 +651,7 @@
"Return the hyperbolic sine of x.");
-static Py_complex sqrt_special_values[7][7] = {
- {{INF,-INF},{0.,-INF},{0.,-INF},{0.,INF},{0.,INF},{INF,INF},{N,INF}},
- {{INF,-INF},{U,U}, {U,U}, {U,U}, {U,U}, {INF,INF},{N,N}},
- {{INF,-INF},{U,U}, {0.,-0.}, {0.,0.}, {U,U}, {INF,INF},{N,N}},
- {{INF,-INF},{U,U}, {0.,-0.}, {0.,0.}, {U,U}, {INF,INF},{N,N}},
- {{INF,-INF},{U,U}, {U,U}, {U,U}, {U,U}, {INF,INF},{N,N}},
- {{INF,-INF},{INF,-0.},{INF,-0.},{INF,0.},{INF,0.},{INF,INF},{INF,N}},
- {{INF,-INF},{N,N}, {N,N}, {N,N}, {N,N}, {INF,INF},{N,N}}
-};
+static Py_complex sqrt_special_values[7][7];
static Py_complex
c_sqrt(Py_complex z)
@@ -826,15 +746,7 @@
/* tanh(infinity + i*y) needs to be dealt with specially */
-static Py_complex tanh_special_values[7][7] = {
- {{-1.,0.},{U,U},{-1.,-0.},{-1.,0.},{U,U},{-1.,0.},{-1.,0.}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{N,N}, {U,U},{-0.,-0.},{-0.,0.},{U,U},{N,N}, {N,N}},
- {{N,N}, {U,U},{0.,-0.}, {0.,0.}, {U,U},{N,N}, {N,N}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{1.,0.}, {U,U},{1.,-0.}, {1.,0.}, {U,U},{1.,0.}, {1.,0.}},
- {{N,N}, {N,N},{N,-0.}, {N,0.}, {N,N},{N,N}, {N,N}}
-};
+static Py_complex tanh_special_values[7][7];
static Py_complex
c_tanh(Py_complex z)
@@ -1043,15 +955,7 @@
*/
-static Py_complex rect_special_values[7][7] = {
- {{INF,N},{U,U},{-INF,0.},{-INF,-0.},{U,U},{INF,N},{INF,N}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{0.,0.},{U,U},{-0.,0.}, {-0.,-0.}, {U,U},{0.,0.},{0.,0.}},
- {{0.,0.},{U,U},{0.,-0.}, {0.,0.}, {U,U},{0.,0.},{0.,0.}},
- {{N,N}, {U,U},{U,U}, {U,U}, {U,U},{N,N}, {N,N}},
- {{INF,N},{U,U},{INF,-0.},{INF,0.}, {U,U},{INF,N},{INF,N}},
- {{N,N}, {N,N},{N,0.}, {N,0.}, {N,N},{N,N}, {N,N}}
-};
+static Py_complex rect_special_values[7][7];
static PyObject *
cmath_rect(PyObject *self, PyObject *args)
@@ -1176,4 +1080,119 @@
PyModule_AddObject(m, "pi",
PyFloat_FromDouble(Py_MATH_PI));
PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
+
+ /* initialize special value tables */
+
+#define INIT_SPECIAL_VALUES(NAME, BODY) { Py_complex* p = (Py_complex*)NAME; BODY }
+#define C(REAL, IMAG) p->real = REAL; p->imag = IMAG; ++p;
+
+ INIT_SPECIAL_VALUES(acos_special_values, {
+ C(P34,INF) C(P,INF) C(P,INF) C(P,-INF) C(P,-INF) C(P34,-INF) C(N,INF)
+ C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
+ C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
+ C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
+ C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
+ C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
+ C(N,INF) C(N,N) C(N,N) C(N,N) C(N,N) C(N,-INF) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(acosh_special_values, {
+ C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
+ C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
+ C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(asinh_special_values, {
+ C(-INF,-P14) C(-INF,-0.) C(-INF,-0.) C(-INF,0.) C(-INF,0.) C(-INF,P14) C(-INF,N)
+ C(-INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-INF,P12) C(N,N)
+ C(-INF,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
+ C(INF,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(INF,N) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(atanh_special_values, {
+ C(-0.,-P12) C(-0.,-P12) C(-0.,-P12) C(-0.,P12) C(-0.,P12) C(-0.,P12) C(-0.,N)
+ C(-0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-0.,P12) C(N,N)
+ C(-0.,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-0.,P12) C(-0.,N)
+ C(0.,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,P12) C(0.,N)
+ C(0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(0.,P12) C(N,N)
+ C(0.,-P12) C(0.,-P12) C(0.,-P12) C(0.,P12) C(0.,P12) C(0.,P12) C(0.,N)
+ C(0.,-P12) C(N,N) C(N,N) C(N,N) C(N,N) C(0.,P12) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(cosh_special_values, {
+ C(INF,N) C(U,U) C(INF,0.) C(INF,-0.) C(U,U) C(INF,N) C(INF,N)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(N,0.) C(U,U) C(1.,0.) C(1.,-0.) C(U,U) C(N,0.) C(N,0.)
+ C(N,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,0.) C(N,0.)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
+ C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(exp_special_values, {
+ C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
+ C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
+ C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(log_special_values, {
+ C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
+ C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(-INF,-P) C(-INF,P) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
+ C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
+ C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(sinh_special_values, {
+ C(INF,N) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,N) C(INF,N)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(0.,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(0.,N) C(0.,N)
+ C(0.,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,N) C(0.,N)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
+ C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(sqrt_special_values, {
+ C(INF,-INF) C(0.,-INF) C(0.,-INF) C(0.,INF) C(0.,INF) C(INF,INF) C(N,INF)
+ C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
+ C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
+ C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
+ C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
+ C(INF,-INF) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,INF) C(INF,N)
+ C(INF,-INF) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,INF) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(tanh_special_values, {
+ C(-1.,0.) C(U,U) C(-1.,-0.) C(-1.,0.) C(U,U) C(-1.,0.) C(-1.,0.)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(N,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(N,N) C(N,N)
+ C(N,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(N,N) C(N,N)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(1.,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(1.,0.) C(1.,0.)
+ C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
+ })
+
+ INIT_SPECIAL_VALUES(rect_special_values, {
+ C(INF,N) C(U,U) C(-INF,0.) C(-INF,-0.) C(U,U) C(INF,N) C(INF,N)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(0.,0.) C(U,U) C(-0.,0.) C(-0.,-0.) C(U,U) C(0.,0.) C(0.,0.)
+ C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
+ C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
+ C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
+ C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
+ })
}
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