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arithmetic_ops
[b,p:above(1),
alpha,E_max:integer,
E_min:{i:integer|E_max>i}]: THEORY
BEGIN
IMPORTING IEEE_854_values[b,p,E_max,E_min],
real_to_fp[b,p,alpha,E_max,E_min],
enumerated_type_defs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fp_op provides a template for defining a floating point operation
% for the case when both arguments are finites.
fin,fin1,fin2: var (finite?)
op: var fp_ops
mode: var rounding_mode
apply(op,fin1,(fin2:{fin| div?(op) => not zero?(fin)})): real =
cases op of
add: value(fin1) + value(fin2),
sub: value(fin1) - value(fin2),
mult: value(fin1) * value(fin2),
div: value(fin1) / value(fin2)
endcases
signed_zero(op, fin1, fin2, mode): {fin | zero?(fin)} =
CASES op OF
add:
IF zero?(fin1)
& zero?(fin2) & sign(fin1) = sign(fin2) THEN fin1
ELSIF to_neg?(mode) THEN neg_zero
ELSE pos_zero
ENDIF,
sub:
IF zero?(fin1)
& zero?(fin2) & sign(fin1) /= sign(fin2) THEN fin1
ELSIF to_neg?(mode) THEN neg_zero
ELSE pos_zero
ENDIF,
mult:
IF sign(fin1) = sign(fin2) THEN pos_zero
ELSE neg_zero
ENDIF,
div:
IF sign(fin1) = sign(fin2) THEN pos_zero
ELSE neg_zero
ENDIF
ENDCASES
fp_op(op, fin1, (fin2: {fin | div?(op) => NOT zero?(fin)}), mode): fp_num =
LET r = fp_round(apply(op, fin1, fin2), mode)
IN IF r = 0 THEN signed_zero(op, fin1, fin2, mode)
ELSE real_to_fp(r)
ENDIF
fp_op_x(op,fin1,(fin2:{fin| div?(op) => not zero?(fin)}),mode):
[fp_num, exception]
=
LET rp = fp_round_x(apply(op, fin1, fin2), mode)
IN IF proj_1(rp) = 0 THEN (signed_zero(op, fin1, fin2, mode),proj_2(rp))
ELSE real_to_fp_x(rp)
ENDIF
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
END arithmetic_ops
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