Merge pull request #160 from roos-j/master

add arb_log_base, arb_bits, acb_bits

Author: oscarbenjamin

README.md

@@ -132,7 +132,8 @@ CHANGELOG
 -------------
 
 Next release:
-
+- [gh-160](https://github.com/flintlib/python-flint/pull/160)
+  Add `bits` to `arb` and `acb`, add `log_base` to `arb`.
 - [gh-148](https://github.com/flintlib/python-flint/pull/148)
   Remove debug symbols to make smaller Linux binaries.
 - [gh-144](https://github.com/flintlib/python-flint/pull/144)

src/flint/flintlib/arb.pxd

@@ -183,6 +183,7 @@ cdef extern from "flint/arb.h":
     void arb_log_ui(arb_t z, ulong x, long prec)
     void arb_log_fmpz(arb_t z, const fmpz_t x, long prec)
     void arb_log1p(arb_t z, const arb_t x, long prec)
+    void arb_log_base_ui(arb_t z, const arb_t x, ulong b, long prec)
     void arb_exp(arb_t z, const arb_t x, long prec)
     void arb_expm1(arb_t z, const arb_t x, long prec)
     void arb_sin(arb_t s, const arb_t x, long prec)

src/flint/types/acb.pyx

@@ -1403,6 +1403,14 @@ cdef class acb(flint_scalar):
     def rel_one_accuracy_bits(self):
         return acb_rel_one_accuracy_bits(self.val)
 
+    def bits(self):
+        r"""Returns maximum of :meth:`.arb.bits` called on real and imaginary part.
+        
+            >>> acb("2047/2048").bits()
+            11
+        """
+        return acb_bits(self.val)
+
     def ei(s):
         r"""
         Exponential integral `\operatorname{Ei}(s)`.

src/flint/types/arb.pyx

@@ -809,6 +809,16 @@ cdef class arb(flint_scalar):
         arb_log1p((<arb>u).val, (<arb>s).val, getprec())
         return u
 
+    def log_base(s, ulong b):
+        r"""Returns `\log_b(s)`, computed exactly when possible.
+        
+            >>> arb(2048).log_base(2)
+            11.0000000000000
+        """
+        u = arb.__new__(arb)
+        arb_log_base_ui((<arb>u).val, (<arb>s).val, b, getprec())
+        return u
+
     def sin(s):
         r"""
         Sine function `\sin(s)`.
@@ -2416,6 +2426,14 @@ cdef class arb(flint_scalar):
     def rel_one_accuracy_bits(self):
         return arb_rel_one_accuracy_bits(self.val)
 
+    def bits(self):
+        r"""Returns number of bits needed to represent absolute value of mantissa of the midpoint; returns 0 if midpoint is special value.
+        
+            >>> arb("2047/2048").bits()
+            11
+        """
+        return arb_bits(self.val)
+
     def lambertw(s, int branch=0):
         r"""
         Lambert *W* function, `W_k(s)`. Either the principal