📄 num2ibm.m
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function b=num2ibm(x)
% num2ibm : convert IEEE 754 doubles to IBM 32 bit floating point format
% b=num2ibm(x)
% x is a matrix of doubles
% b is a corresponding matrix of uint32
%
% The representations for NaN and inf are arbitrary
%
% See also ibm2num
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
%
%
% (C) Brian Farrelly, 22 October 2001
% mailto:Brian.Farrelly@nho.hydro.com Norsk Hydro Research Centre
% phone +47 55 99 68 74 ((( Postboks 7190
% fax +47 55 99 69 70 2oooS N-5020 Bergen
% home +47 55 13 78 49 HYDRO Norway
%
b=repmat(uint32(0),size(x));
err=zeros(size(x));
%format long
x(x> 7.236998675585915e+75)= inf; % change big numbers to infinity
x(x<-7.236998675585915e+75)=-inf; % 7.236998675585915e+75 is
% ibm2num(uint32(hex2dec('7fffffff')) or
% ibm2num(num2ibm(inf))
[F E]=log2(abs(x));
e=E/4; % exponent of base 16
ec=ceil(e); % adjust upwards to integer
p=ec+64; % offset exponent
f=F.*2.^(-4*(ec-e)); % correct mantissa for fractional part of exponent
f=round(f*2^24); % convert to integer. Roundoff here can be as large as
% 0.5/2^20 when mantissa is close to 1/16 so that
% 3 bits of signifance are lost.
p(f==2^24)=p(f==2^24)+1; % Roundoff can cause f to be 2^24 for numbers just under a
f(f==2^24)=2^20; % power of 16, so correct for this
%format hex
psi=uint32(p*2^24); % put exponent in first byte of psi.
phi=uint32(f); % put mantissa into last 3 bytes of phi
% make bit representation
b=bitor(psi,phi); % exponent and mantissa
b(x<0)=bitset(b(x<0),32); % sign bit
%format long
% special cases
b(x==0) =uint32(0) ; % bias is incorrect for zero
b(isnan(x)) =uint32(hex2dec('7fffffff')); % 7.237005145973116e+75 in IBM format
b(isinf(x) & x>0)=uint32(hex2dec('7ffffff0')); % 7.236998675585915e+75 ,,
b(isinf(x) & x<0)=uint32(hex2dec('fffffff0')); % -7.236998675585915e+75 ,,
% Note that NaN > inf in IBM format
% check bit representation for normal cases
checkx=ibm2num(b); % note that use of base 16 in IBM format
z=x==0; % can lead to a loss of 3 bits of precision
err(z)=0; % compared with an IEEE single.
q=(checkx(~z)-x(~z))./x(~z);
err(~z) = abs(q) > 5e-7; % this is almost reached with numbers
% of the form 16^n + 0.5*16^(n-5) where
% the mantissa is 100001 hex. Roundoff
% error is then 0.5/16^5=0.5/2^20=4.7684e-7
if any(err)
warning('Conversion error in num2ibm for the following:')
disp(x(logical(err)))
end
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