reconsider how floating point values are printed

[williamstein]

some f-p values are printed like integers, which may confuse the user
 (especially if one copies them with the mouse):
 sage: 2.0^46
 70368744177664.0
 sage: 2.0^47
 140737488355328
 I would expect '140737488355328.' or '1.40737488355328e14' in the 2nd case.
 By the way, typing 140737488355328.0 outputs itself, which is inconsistent,
 since 140737488355328.0-2.0^47 gives 0.0000000000000000.

 Compare also:
 sage: 2.0^99
 633825300114115000000000000000
 sage: 2.0^100
 1.26765060022823e30

My 2 cents,
Paul Z.

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/960

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

Description changed:

--- 
+++ 
@@ -1,4 +1,6 @@
-{{{ some f-p values are printed like integers, which may confuse the user
+
+```
+some f-p values are printed like integers, which may confuse the user
  (especially if one copies them with the mouse):
  sage: 2.0^46
  70368744177664.0
@@ -16,4 +18,4 @@

 My 2 cents,
 Paul Z.
-}}}
+```

[ba94b9bb-195b-4422-a5e2-176920eaa163]

comment:3

The inconsistency mentioned is because of the automagic behavior of decimal literals, where longer literals get more bits:

sage: (2.0^47).prec()
53
sage: (140737488355328.0).prec()
56

Maybe this magic behavior should be removed, or somehow modified to be less confusing? (Although I have no idea how to make it less confusing.)

See also #962, for problems with the current implementation of the precision extension.

[mwhansen]

comment:5

Attachment: mpfr.patch.gz

I've attached a patch that makes sure that all real numbers include a "." so that they don't get confused with integers.

Here is the behavior after the patch

sage:  2.0^47
140737488355328.
sage:  2.0^46
70368744177664.0
sage:  2.0^99
633825300114115000000000000000.
sage:  2.0^100
1.26765060022823e30
sage: 140737488355328.
140737488355328.
sage: a = 2.0^47
sage: a
140737488355328.
sage: a.prec()
53
sage: b = 140737488355328.
sage: b.prec()
53