update examples

examples/integrals.c

@@ -732,11 +732,22 @@ scaled_bessel_select_N(arb_t N, ulong k, slong prec)
     arb_mul_2exp_si(N, N, e);
 }
 
+/* f(z) = Si(z) */
+int
+f_si(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
+{
+    if (order > 1)
+        flint_abort();  /* Would be needed for Taylor method. */
+
+    acb_hypgeom_si(res, z, prec);
+    return 0;
+}
+
 /* ------------------------------------------------------------------------- */
 /*  Main test program                                                        */
 /* ------------------------------------------------------------------------- */
 
-#define NUM_INTEGRALS 37
+#define NUM_INTEGRALS 38
 
 const char * descr[NUM_INTEGRALS] =
 {
@@ -777,6 +788,7 @@ const char * descr[NUM_INTEGRALS] =
     "int_0^{inf} exp(-x) I_0(x/15)^{15} dx   (using domain truncation)",
     "int_{-1-i}^{-1+i} 1/sqrt(x) dx",
     "int_0^{inf} 1/gamma(x) dx   (using domain truncation)",
+    "int_0^{1000} Si(x) dx",
 };
 
 int main(int argc, char *argv[])
@@ -1273,6 +1285,13 @@ int main(int argc, char *argv[])
                 arb_add_error_2exp_si(acb_realref(s), -goal);
                 break;
 
+            case 37:
+                acb_zero(a);
+                acb_set_ui(b, 1000);
+                acb_calc_integrate(s, f_si, NULL, a, b, goal, tol, options, prec);
+                break;
+
+
             default:
                 abort();
             }

src/acb_hypgeom/chi.c

@@ -206,6 +206,7 @@ acb_hypgeom_chi(acb_t res, const acb_t z, slong prec)
             wp = prec + FLINT_MAX(0, cancellation);
             wp = wp * 1.001 + 5;
             acb_hypgeom_chi_2f3(res, m, wp);
+            acb_set_round(res, res, prec);
         }
 
         if (pure_real)

src/acb_hypgeom/ci.c

@@ -271,6 +271,7 @@ acb_hypgeom_ci(acb_t res, const acb_t z, slong prec)
             wp = prec + FLINT_MAX(0, cancellation);
             wp = wp * 1.001 + 5;
             acb_hypgeom_ci_2f3(res, m, wp);
+            acb_set_round(res, res, prec);
         }
 
         acb_add_error_mag(res, err);

src/acb_hypgeom/ei.c

@@ -236,6 +236,7 @@ acb_hypgeom_ei(acb_t res, const acb_t z, slong prec)
             wp = prec + FLINT_MAX(0, cancellation);
             wp = wp * 1.001 + 5;
             acb_hypgeom_ei_2f2(res, m, wp);
+            acb_set_round(res, res, prec);
         }
 
         if (pure_real)

src/acb_hypgeom/si.c

@@ -215,6 +215,7 @@ acb_hypgeom_si(acb_t res, const acb_t z, slong prec)
             wp = prec + FLINT_MAX(0, cancellation);
             wp = wp * 1.001 + 5;
             acb_hypgeom_si_1f2(res, m, wp);
+            acb_set_round(res, res, prec);
         }
 
         if (pure_imag)

src/python/flint_ctypes.py

@@ -1913,14 +1913,18 @@ def exp_integral(ctx, x, y):
     def exp_integral_ei(ctx, x):
         """
             >>> RR.exp_integral_ei(1)
-            [1.89511781635594 +/- 5.11e-15]
+            [1.895117816355937 +/- 6.91e-16]
         """
         return ctx._unary_op(x, libgr.gr_exp_integral_ei, "exp_integral_ei($x)")
 
     def sin_integral(ctx, x):
         """
             >>> RR.sin_integral(1)
             [0.946083070367183 +/- 1.35e-16]
+            >>> CC.sin_integral(CC("(5 +/- 1e-10)*I"))
+            [20.09321183 +/- 5.79e-9]*I
+            >>> CC.sin_integral(CC("10 + (1 +/- 1e-10)*I"))
+            ([1.7002629761 +/- 6.33e-11] + [-0.0667638998 +/- 2.17e-11]*I)
         """
         return ctx._unary_op(x, libgr.gr_sin_integral, "sin_integral($x)")
 
@@ -1934,21 +1938,21 @@ def cos_integral(ctx, x):
     def sinh_integral(ctx, x):
         """
             >>> RR.sinh_integral(1)
-            [1.05725087537573 +/- 2.77e-15]
+            [1.057250875375728 +/- 6.29e-16]
         """
         return ctx._unary_op(x, libgr.gr_sinh_integral, "sinh_integral($x)")
 
     def cosh_integral(ctx, x):
         """
             >>> RR.cosh_integral(1)
-            [0.837866940980208 +/- 4.78e-16]
+            [0.837866940980208 +/- 3.15e-16]
         """
         return ctx._unary_op(x, libgr.gr_cosh_integral, "cosh_integral($x)")
 
     def log_integral(ctx, x, offset=False):
         """
             >>> RR.log_integral(2)
-            [1.04516378011749 +/- 4.01e-15]
+            [1.04516378011749 +/- 3.31e-15]
             >>> RR.log_integral(2, offset=True)
             0
         """