add rel_one_accuracy_bits methods; improvement to precision handling for hypgeom_m

acb.h

@@ -1012,6 +1012,8 @@ acb_rel_accuracy_bits(const acb_t x)
     return -acb_rel_error_bits(x);
 }
 
+slong acb_rel_one_accuracy_bits(const acb_t x);
+
 ACB_INLINE slong
 acb_bits(const acb_t x)
 {

acb/rel_error_bits.c

@@ -64,3 +64,22 @@ acb_rel_error_bits(const acb_t x)
     return result;
 }
 
+slong acb_rel_one_accuracy_bits(const acb_t z)
+{
+    if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -1) < 0 &&
+        arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -1) < 0)
+    {
+        acb_t t;
+        arf_init(arb_midref(acb_realref(t)));
+        arf_one(arb_midref(acb_realref(t)));
+        arf_init(arb_midref(acb_imagref(t)));
+        *arb_radref(acb_realref(t)) = *arb_radref(acb_realref(z));
+        *arb_radref(acb_imagref(t)) = *arb_radref(acb_imagref(z));
+        return acb_rel_accuracy_bits(t);
+    }
+    else
+    {
+        return acb_rel_accuracy_bits(z);
+    }
+}
+

acb_hypgeom/m.c

@@ -228,10 +228,10 @@ acb_hypgeom_m_choose(int * asymp, int * kummer, slong * wp,
         return;
     }
 
-    input_accuracy = acb_rel_accuracy_bits(z);
-    t = acb_rel_accuracy_bits(a);
+    input_accuracy = acb_rel_one_accuracy_bits(z);
+    t = acb_rel_one_accuracy_bits(a);
     input_accuracy = FLINT_MIN(input_accuracy, t);
-    t = acb_rel_accuracy_bits(b);
+    t = acb_rel_one_accuracy_bits(b);
     input_accuracy = FLINT_MIN(input_accuracy, t);
     input_accuracy = FLINT_MAX(input_accuracy, 0.0);
 

arb.h

@@ -307,6 +307,8 @@ arb_rel_accuracy_bits(const arb_t x)
     return -arb_rel_error_bits(x);
 }
 
+slong arb_rel_one_accuracy_bits(const arb_t x);
+
 ARB_INLINE slong
 arb_bits(const arb_t x)
 {

arb/rel_error_bits.c

@@ -47,3 +47,19 @@ arb_rel_error_bits(const arb_t x)
     return result;
 }
 
+slong arb_rel_one_accuracy_bits(const arb_t x)
+{
+    if (arf_cmpabs_2exp_si(arb_midref(x), -1) < 0)
+    {
+        arb_t t;
+        arf_init(arb_midref(t));
+        arf_one(arb_midref(t));
+        *arb_radref(t) = *arb_radref(x);
+        return arb_rel_accuracy_bits(t);
+    }
+    else
+    {
+        return arb_rel_accuracy_bits(x);
+    }
+}
+

doc/source/acb.rst

@@ -321,6 +321,11 @@ Precision and comparisons
     Returns the effective relative accuracy of *x* measured in bits,
     equal to the negative of the return value from :func:`acb_rel_error_bits`.
 
+.. function:: slong acb_rel_one_accuracy_bits(const acb_t x)
+
+    Given a ball with midpoint *m* and radius *r*, returns an approximation of
+    the relative accuracy of `[\max(1,|m|) \pm r]` measured in bits.
+
 .. function:: slong acb_bits(const acb_t x)
 
     Returns the maximum of *arb_bits* applied to the real

doc/source/arb.rst

@@ -444,6 +444,11 @@ Radius and interval operations
     Returns the effective relative accuracy of *x* measured in bits,
     equal to the negative of the return value from :func:`arb_rel_error_bits`.
 
+.. function:: slong arb_rel_one_accuracy_bits(const arb_t x)
+
+    Given a ball with midpoint *m* and radius *r*, returns an approximation of
+    the relative accuracy of `[\max(1,|m|) \pm r]` measured in bits.
+
 .. function:: slong arb_bits(const arb_t x)
 
     Returns the number of bits needed to represent the absolute value