Generated by Cython 0.12.1 on Fri May 7 13:40:01 2010
Raw output: _Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0.c
1:
2: include "interrupt.pxi" # ctrl-c interrupt block support
3: include "stdsage.pxi" # ctrl-c interrupt block support
4:
5: include "cdefs.pxi"
6: from math import sin
__pyx_t_1 = PyList_New(1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(((PyObject *)__pyx_t_1)); __Pyx_INCREF(((PyObject *)__pyx_n_s__sin)); PyList_SET_ITEM(__pyx_t_1, 0, ((PyObject *)__pyx_n_s__sin)); __Pyx_GIVEREF(((PyObject *)__pyx_n_s__sin)); __pyx_t_2 = __Pyx_Import(((PyObject *)__pyx_n_s__math), ((PyObject *)__pyx_t_1)); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __Pyx_DECREF(((PyObject *)__pyx_t_1)); __pyx_t_1 = 0; __pyx_t_1 = PyObject_GetAttr(__pyx_t_2, __pyx_n_s__sin); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); if (PyObject_SetAttr(__pyx_m, __pyx_n_s__sin, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
7:
8: def f(x):
static PyObject *__pyx_pf_75_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0_f(PyObject *__pyx_self, PyObject *__pyx_v_x); /*proto*/
static char __pyx_doc_75_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0_f[] = "File: _Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0.pyx (starting at line 8)";
static PyObject *__pyx_pf_75_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0_f(PyObject *__pyx_self, PyObject *__pyx_v_x) {
PyObject *__pyx_r = NULL;
__Pyx_RefNannySetupContext("f");
__pyx_self = __pyx_self;
9: return sin(x**2)
__Pyx_XDECREF(__pyx_r); __pyx_t_1 = __Pyx_GetName(__pyx_m, __pyx_n_s__sin); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 9; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __pyx_t_2 = PyNumber_Power(__pyx_v_x, __pyx_int_2, Py_None); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 9; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __pyx_t_3 = PyTuple_New(1); if (unlikely(!__pyx_t_3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 9; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_3); PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_2); __Pyx_GIVEREF(__pyx_t_2); __pyx_t_2 = 0; __pyx_t_2 = PyObject_Call(__pyx_t_1, __pyx_t_3, NULL); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 9; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0; __pyx_r = __pyx_t_2; __pyx_t_2 = 0; goto __pyx_L0; __pyx_r = Py_None; __Pyx_INCREF(Py_None); goto __pyx_L0; __pyx_L1_error:; __Pyx_XDECREF(__pyx_t_1); __Pyx_XDECREF(__pyx_t_2); __Pyx_XDECREF(__pyx_t_3); __Pyx_AddTraceback("_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0.f"); __pyx_r = NULL; __pyx_L0:; __Pyx_XGIVEREF(__pyx_r); __Pyx_RefNannyFinishContext(); return __pyx_r; }
10:
11: def integral(a, b, N):
static PyObject *__pyx_pf_75_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0_integral(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/ static char __pyx_doc_75_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0_integral[] = "File: _Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0.pyx (starting at line 11)"; static PyObject *__pyx_pf_75_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0_integral(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) { PyObject *__pyx_v_a = 0; PyObject *__pyx_v_b = 0; PyObject *__pyx_v_N = 0; PyObject *__pyx_v_dx; PyObject *__pyx_v_s; PyObject *__pyx_v_i; PyObject *__pyx_r = NULL; static PyObject **__pyx_pyargnames[] = {&__pyx_n_s__a,&__pyx_n_s__b,&__pyx_n_s__N,0}; __Pyx_RefNannySetupContext("integral"); __pyx_self = __pyx_self; if (unlikely(__pyx_kwds)) { Py_ssize_t kw_args = PyDict_Size(__pyx_kwds); PyObject* values[3] = {0,0,0}; switch (PyTuple_GET_SIZE(__pyx_args)) { case 3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2); case 2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1); case 1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0); case 0: break; default: goto __pyx_L5_argtuple_error; } switch (PyTuple_GET_SIZE(__pyx_args)) { case 0: values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__a); if (likely(values[0])) kw_args--; else goto __pyx_L5_argtuple_error; case 1: values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__b); if (likely(values[1])) kw_args--; else { __Pyx_RaiseArgtupleInvalid("integral", 1, 3, 3, 1); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 11; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } case 2: values[2] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__N); if (likely(values[2])) kw_args--; else { __Pyx_RaiseArgtupleInvalid("integral", 1, 3, 3, 2); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 11; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } } if (unlikely(kw_args > 0)) { if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, PyTuple_GET_SIZE(__pyx_args), "integral") < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 11; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } __pyx_v_a = values[0]; __pyx_v_b = values[1]; __pyx_v_N = values[2]; } else if (PyTuple_GET_SIZE(__pyx_args) != 3) { goto __pyx_L5_argtuple_error; } else { __pyx_v_a = PyTuple_GET_ITEM(__pyx_args, 0); __pyx_v_b = PyTuple_GET_ITEM(__pyx_args, 1); __pyx_v_N = PyTuple_GET_ITEM(__pyx_args, 2); } goto __pyx_L4_argument_unpacking_done; __pyx_L5_argtuple_error:; __Pyx_RaiseArgtupleInvalid("integral", 1, 3, 3, PyTuple_GET_SIZE(__pyx_args)); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 11; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_L3_error:; __Pyx_AddTraceback("_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0.integral"); return NULL; __pyx_L4_argument_unpacking_done:; __Pyx_INCREF(__pyx_v_a); __Pyx_INCREF(__pyx_v_b); __Pyx_INCREF(__pyx_v_N); __pyx_v_dx = Py_None; __Pyx_INCREF(Py_None); __pyx_v_s = Py_None; __Pyx_INCREF(Py_None); __pyx_v_i = Py_None; __Pyx_INCREF(Py_None);
12: dx = (b-a)/N
__pyx_t_1 = PyNumber_Subtract(__pyx_v_b, __pyx_v_a); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 12; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __pyx_t_2 = __Pyx_PyNumber_Divide(__pyx_t_1, __pyx_v_N); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 12; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __Pyx_DECREF(__pyx_v_dx); __pyx_v_dx = __pyx_t_2; __pyx_t_2 = 0;
13: s = 0
__Pyx_INCREF(__pyx_int_0); __Pyx_DECREF(__pyx_v_s); __pyx_v_s = __pyx_int_0;
14: for i in range(N):
__pyx_t_2 = PyTuple_New(1); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 14; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __Pyx_INCREF(__pyx_v_N); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_v_N); __Pyx_GIVEREF(__pyx_v_N); __pyx_t_1 = PyObject_Call(__pyx_builtin_range, __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 14; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; if (PyList_CheckExact(__pyx_t_1) || PyTuple_CheckExact(__pyx_t_1)) { __pyx_t_3 = 0; __pyx_t_2 = __pyx_t_1; __Pyx_INCREF(__pyx_t_2); } else { __pyx_t_3 = -1; __pyx_t_2 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 14; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); } __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; for (;;) { if (likely(PyList_CheckExact(__pyx_t_2))) { if (__pyx_t_3 >= PyList_GET_SIZE(__pyx_t_2)) break; __pyx_t_1 = PyList_GET_ITEM(__pyx_t_2, __pyx_t_3); __Pyx_INCREF(__pyx_t_1); __pyx_t_3++; } else if (likely(PyTuple_CheckExact(__pyx_t_2))) { if (__pyx_t_3 >= PyTuple_GET_SIZE(__pyx_t_2)) break; __pyx_t_1 = PyTuple_GET_ITEM(__pyx_t_2, __pyx_t_3); __Pyx_INCREF(__pyx_t_1); __pyx_t_3++; } else { __pyx_t_1 = PyIter_Next(__pyx_t_2); if (!__pyx_t_1) { if (unlikely(PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 14; __pyx_clineno = __LINE__; goto __pyx_L1_error;} break; } __Pyx_GOTREF(__pyx_t_1); } __Pyx_DECREF(__pyx_v_i); __pyx_v_i = __pyx_t_1; __pyx_t_1 = 0;
15: s += f(a+dx*i)
__pyx_t_1 = __Pyx_GetName(__pyx_m, __pyx_n_s__f); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __pyx_t_4 = PyNumber_Multiply(__pyx_v_dx, __pyx_v_i); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_5 = PyNumber_Add(__pyx_v_a, __pyx_t_4); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_4 = PyTuple_New(1); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_5); __Pyx_GIVEREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_5 = PyObject_Call(__pyx_t_1, __pyx_t_4, NULL); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_4 = PyNumber_InPlaceAdd(__pyx_v_s, __pyx_t_5); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_DECREF(__pyx_v_s); __pyx_v_s = __pyx_t_4; __pyx_t_4 = 0; } __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
16: return s * dx
__Pyx_XDECREF(__pyx_r); __pyx_t_2 = PyNumber_Multiply(__pyx_v_s, __pyx_v_dx); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 16; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __pyx_r = __pyx_t_2; __pyx_t_2 = 0; goto __pyx_L0; __pyx_r = Py_None; __Pyx_INCREF(Py_None); goto __pyx_L0; __pyx_L1_error:; __Pyx_XDECREF(__pyx_t_1); __Pyx_XDECREF(__pyx_t_2); __Pyx_XDECREF(__pyx_t_4); __Pyx_XDECREF(__pyx_t_5); __Pyx_AddTraceback("_Users_robertwb__sage_sage_notebook_sagenb_home_admin_91_code_sage19_spyx_0.integral"); __pyx_r = NULL; __pyx_L0:; __Pyx_DECREF(__pyx_v_dx); __Pyx_DECREF(__pyx_v_s); __Pyx_DECREF(__pyx_v_i); __Pyx_DECREF(__pyx_v_a); __Pyx_DECREF(__pyx_v_b); __Pyx_DECREF(__pyx_v_N); __Pyx_XGIVEREF(__pyx_r); __Pyx_RefNannyFinishContext(); return __pyx_r; }