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From: "Martin Dowie" <martin.dowie@gecm.com>
Newsgroups: comp.lang.ada
Subject: Floating point accuracy
Date: Thu, 15 Feb 2001 11:27:43 -0000
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Date: 2001-02-15T11:27:43+00:00
List-Id: <comp.lang.ada>

I'm trying to mimic 64-bit unsigned integers (that will represent
nanoseconds) on a
PowerPC (Green Hills target compiler for the PowerPC doesn't support 64 bit
unsigned directly - unless you know differently!).

I'm doing this by having a most sigificant and least significant 32bit
unsigned in what will
eventually be a private record and providing my own operators. However my
routine to
convert from microseconds to nanoseconds is puzzling me. I had always
thought that a
float declared a 'digits 15' would give me 15 significant digits of
accuracy - I'm sure I'm
only using up to 13 in these test, yet the last two results return the same
values.

clearly, I'm missing something...
(on both WinNT/Gnat 3.13p & PPC/GreenHills/VxWorks5.4)


Program =
with Ada.Text_IO; use Ada.Text_IO;
with Interfaces;

procedure ns_test is

   type ns_type is record
      MS, LS : Interfaces.Unsigned_32;
   end record;

   type Real_15_Type is digits 15;

   function us_to_ns (Microseconds : Interfaces.Unsigned_32) return ns_Type
is
      -- 16#FFFF_FFFF# = (2^32)-1 = 10#4_294_967_295#, which has 10
significant digits
      -- multiply by 1,000 (to convert to nanoseconds) =>
      -- 10#4_294_967_295_000#, which has 13 significant digits =>
      -- Real_15_Type has enough significant digits to represent the value
in ns.
      --
      Two_To_The_Thirty_Two : constant Real_15_Type := 2.0 ** 32;
      Float_ns : constant Real_15_Type := Real_15_Type (Microseconds) *
1_000.0;
      Float_MS : constant Real_15_Type := Real_15_Type'Floor (Float_ns /
Two_To_The_Thirty_Two);
      MS : constant Real_15_Type := (Float_MS * Two_To_The_Thirty_Two);
      Float_LS : constant Real_15_Type := Float_ns - MS;
   begin
      Put_line ("ns = " & Real_15_Type'Image (Float_ns));
      Put_line ("ms = " & Real_15_Type'Image (Float_MS));
      Put_line ("MS = " & Real_15_Type'Image (MS));
      Put_line ("ls = " & Real_15_Type'Image (Float_LS));
      New_Line;
      return (MS => Interfaces.Unsigned_32 (Float_MS), LS =>
Interfaces.Unsigned_32 (Float_LS));
   end us_to_ns;

   procedure display (value : ns_type) is
   begin
     put_line ("ms =>" & Interfaces.Unsigned_32'Image (Value.MS) & " ls =>"
& Interfaces.Unsigned_32'Image (Value.LS));
   end display;

begin
   new_line;
   put_line ("test 0");
   display (value => us_to_ns (microseconds => 0));
   put_line ("test 1");
   display (value => us_to_ns (microseconds => 1));
   put_line ("test 1,000");
   display (value => us_to_ns (microseconds => 1_000));
   put_line ("test 16#0FFF_FFFF#");
   display (value => us_to_ns (microseconds => 16#0FFF_FFFF#));  -- random
mid-value
   put_line ("test 'Last - 1");
   display (value => us_to_ns (microseconds => Interfaces.Unsigned_32'Pred
(Interfaces.Unsigned_32'Last)));
   put_line ("test 'Last");
   display (value => us_to_ns (microseconds =>
Interfaces.Unsigned_32'Last));
end ns_test;


Results =
->
test 0
ns =  0.00000000000000E+00
ms =  0.00000000000000E+00
MS =  0.00000000000000E+00
ls =  0.00000000000000E+00

ms => 0 ls => 0
test 1
ns =  1.00000000000000E+03
ms =  0.00000000000000E+00
MS =  0.00000000000000E+00
ls =  1.00000000000000E+03

ms => 0 ls => 1000
test 1,000
ns =  1.00000000000000E+06
ms =  0.00000000000000E+00
MS =  0.00000000000000E+00
ls =  1.00000000000000E+06

ms => 0 ls => 1000000
test 16#0FFF_FFFF#
ns =  2.68435455000000E+11
ms =  6.20000000000000E+01
MS =  2.66287972352000E+11
ls =  2.14748264800000E+09

ms => 62 ls => 2147482648
test 'Last - 1
ns =  4.29496729400000E+12
ms =  9.99000000000000E+02
MS =  4.29067232870400E+12
ls =  4.29496529600000E+09

ms => 999 ls => 4294965296
test 'Last
ns =  4.29496729500000E+12
ms =  9.99000000000000E+02
MS =  4.29067232870400E+12
ls =  4.29496629600000E+09

ms => 999 ls => 4294966296