-- C490001.A -- -- Grant of Unlimited Rights -- -- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687, -- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained -- unlimited rights in the software and documentation contained herein. -- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making -- this public release, the Government intends to confer upon all -- recipients unlimited rights equal to those held by the Government. -- These rights include rights to use, duplicate, release or disclose the -- released technical data and computer software in whole or in part, in -- any manner and for any purpose whatsoever, and to have or permit others -- to do so. -- -- DISCLAIMER -- -- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR -- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED -- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE -- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE -- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A -- PARTICULAR PURPOSE OF SAID MATERIAL. --* -- -- OBJECTIVE: -- Check that, for a real static expression that is not part of a larger -- static expression, and whose expected type T is a floating point type -- that is not a descendant of a formal scalar type, the value is rounded -- to the nearest machine number of T if T'Machine_Rounds is true, and is -- truncated otherwise. Check that if rounding is performed, and the value -- is exactly halfway between two machine numbers, one of the two machine -- numbers is used. -- -- TEST DESCRIPTION: -- The test obtains a machine number M1 for a floating point subtype S by -- passing a real literal to S'Machine. It then obtains an adjacent -- machine number M2 by using S'Succ (or S'Pred). It then constructs -- values which lie between these two machine numbers: one (A) which is -- closer to M1, one (B) which is exactly halfway between M1 and M2, and -- one (C) which is closer to M2. This is done for both positive and -- negative machine numbers. -- -- Let M1 be closer to zero than M2. Then if S'Machine_Rounds is true, -- C must be rounded to M2, A must be rounded to M1, and B must be rounded -- to either M1 or M2. If S'Machine_Rounds is false, all the values must -- be truncated to M1. -- -- A, B, and C are constructed using the following static expressions: -- -- A: constant S := M1 + (M2 - M1)*Z; -- Z slightly less than 0.5. -- B: constant S := M1 + (M2 - M1)*Z; -- Z equals 0.5. -- C: constant S := M1 + (M2 - M1)*Z; -- Z slightly more than 0.5. -- -- Since these are static expressions, they must be evaluated exactly, -- and no rounding may occur until the final result is calculated. -- -- The checks for equality between the members of (A, B, C) and (M1, M2) -- are performed at run-time within the body of a subprogram. -- -- The test performs additional checks that the rounding performed on -- real literals is consistent for a floating point subtype. A literal is -- assigned to a constant of a floating point subtype S. The same literal -- is then passed to a subprogram, along with the constant, and an -- equality check is performed within the body of the subprogram. -- -- -- CHANGE HISTORY: -- 25 Sep 95 SAIC Initial prerelease version. -- 25 May 01 RLB Repaired to work with the repeal of the round away -- rule by AI-268. -- --! with System; package C490001_0 is type My_Flt is digits System.Max_Digits; procedure Float_Subtest (A, B: in My_Flt; Msg: in String); procedure Float_Subtest (A, B, C: in My_Flt; Msg: in String); -- -- Positive cases: -- -- |----|-------------|-----------------|-------------------|-----------| -- | | | | | | -- 0 P_M1 Less_Pos_Than_Half Pos_Exactly_Half More_Pos_Than_Half P_M2 Positive_Float : constant My_Flt := 12.440193950021943; -- The literal value 12.440193950021943 is rounded up or down to the -- nearest machine number of My_Flt when Positive_Float is initialized. -- The value of Positive_Float should therefore be a machine number, and -- the use of 'Machine in the initialization of P_M1 will be redundant for -- a correct implementation. It's done anyway to make certain that P_M1 is -- a machine number, independent of whether an implementation correctly -- performs rounding. P_M1 : constant My_Flt := My_Flt'Machine(Positive_Float); P_M2 : constant My_Flt := My_Flt'Succ(P_M1); -- P_M1 and P_M2 are adjacent machine numbers. Note that because it is not -- certain whether 12.440193950021943 is a machine number, nor whether -- 'Machine rounds it up or down, 12.440193950021943 may not lie between -- P_M1 and P_M2. The test does not depend on this information, however; -- the literal is only used as a "seed" to obtain the machine numbers. -- The following entities are used to verify that rounding is performed -- according to the value of 'Machine_Rounds. If language rules are -- obeyed, the intermediate expressions in the following static -- initialization expressions will not be rounded; all calculations will -- be performed exactly. The final result, however, will be rounded to -- a machine number (either P_M1 or P_M2, depending on the value of -- My_Flt'Machine_Rounds). Thus, the value of each constant below will -- equal that of P_M1 or P_M2. Less_Pos_Than_Half : constant My_Flt := P_M1 + ((P_M2 - P_M1)*2.9/6.0); Pos_Exactly_Half : constant My_Flt := P_M1 + ((P_M2 - P_M1)/2.0); More_Pos_Than_Half : constant My_Flt := P_M1 + ((P_M2 - P_M1)*4.6/9.0); -- -- Negative cases: -- -- -|-------------|-----------------|-------------------|-----------|----| -- | | | | | | -- N_M2 More_Neg_Than_Half Neg_Exactly_Half Less_Neg_Than_Half N_M1 0 -- The descriptions for the positive cases above apply to the negative -- cases below as well. Note that, for N_M2, 'Pred is used rather than -- 'Succ. Thus, N_M2 is further from 0.0 (i.e. more negative) than N_M1. Negative_Float : constant My_Flt := -0.692074550952117; N_M1 : constant My_Flt := My_Flt'Machine(Negative_Float); N_M2 : constant My_Flt := My_Flt'Pred(N_M1); More_Neg_Than_Half : constant My_Flt := N_M1 + ((N_M2 - N_M1)*4.1/8.0); Neg_Exactly_Half : constant My_Flt := N_M1 + ((N_M2 - N_M1)/2.0); Less_Neg_Than_Half : constant My_Flt := N_M1 + ((N_M2 - N_M1)*2.4/5.0); end C490001_0; --==================================================================-- with TCTouch; package body C490001_0 is procedure Float_Subtest (A, B: in My_Flt; Msg: in String) is begin TCTouch.Assert (A = B, Msg); end Float_Subtest; procedure Float_Subtest (A, B, C: in My_Flt; Msg: in String) is begin TCTouch.Assert (A = B or A = C, Msg); end Float_Subtest; end C490001_0; --==================================================================-- with C490001_0; -- Floating point support. use C490001_0; with Report; procedure C490001 is begin Report.Test ("C490001", "Rounding of real static expressions: " & "floating point subtypes"); -- Check that rounding direction is consistent for literals: Float_Subtest (12.440193950021943, P_M1, "Positive Float: literal"); Float_Subtest (-0.692074550952117, N_M1, "Negative Float: literal"); -- Now check that rounding is performed correctly for values between -- machine numbers, according to the value of 'Machine_Rounds: if My_Flt'Machine_Rounds then Float_Subtest (Pos_Exactly_Half, P_M1, P_M2, "Positive Float: = half"); Float_Subtest (More_Pos_Than_Half, P_M2, "Positive Float: > half"); Float_Subtest (Less_Pos_Than_Half, P_M1, "Positive Float: < half"); Float_Subtest (Neg_Exactly_Half, N_M1, N_M2, "Negative Float: = half"); Float_Subtest (More_Neg_Than_Half, N_M2, "Negative Float: > half"); Float_Subtest (Less_Neg_Than_Half, N_M1, "Negative Float: < half"); else Float_Subtest (Pos_Exactly_Half, P_M1, "Positive Float: = half"); Float_Subtest (More_Pos_Than_Half, P_M1, "Positive Float: > half"); Float_Subtest (Less_Pos_Than_Half, P_M1, "Positive Float: < half"); Float_Subtest (Neg_Exactly_Half, N_M1, "Negative Float: = half"); Float_Subtest (More_Neg_Than_Half, N_M1, "Negative Float: > half"); Float_Subtest (Less_Neg_Than_Half, N_M1, "Negative Float: < half"); end if; Report.Result; end C490001;