algorithm - Custom function failing to convert a decimal to single precision floating point -
here code attempting convert real number approximate single precision floating point representation, educational purposes demonstrate intermediate results:
function [ieee] = mydec2ieee (d) % accepts decimal number, d. % returns 1x32 bit array holding closest ieee representation. s = getsign(d); [e, f] = getcharacteristic(d); binarye = binstr2binarr(dec2bin(e)); % convert binary integer array. if numel(binarye) < 8 % extend exponent bits number. binarye = [zeros(1, 8 - numel(binarye)), binarye]; end binaryf = expandfractiontobinary(f); ieee = [s , binarye, binaryf]; end function [b] = binstr2binarr (s) % accepts binary character string, s. % returns binary integer array, b. len = numel(s); b = zeros(1, len); = 1 : len b(i) = s(i) - '0'; end end function [b] = expandfractiontobinary(f) % accepts has remained decimal number % after calculation of exponent, i.e fractional part. % returns 1x23 binary array approximation of % fractional part represented sum of negative powers of 2, % (up 22 - nd power). singleprecision = 22; b = zeros(1, singleprecision); % binary string store fraction of ieee754. = 1; % exponent of 2; (i+1) -index in binary array. while f != 0 && <= singleprecision ith = 1 / (2^(i)); if ith <= f f = f - ith; b(i) = 1; % include coefficient in sum. end = + 1; end end function [e, f] = getcharacteristic (d) % accepts number base10, d. % returns exponent , fraction in d's ieee754 representation, in base10. % write d in base-2 scientific notation % i.e. factor number in range [1, 2] , power of 2. bias = 127; = 1; f = 0; while ~(f >= 1 && f <= 2) f = d / (2^(-i)); % pause; % if number > 1 denominator -> 0 , (faster f -> inf) = + 1; end = - 1; % last check done after incrementation. e = bias - i; f = f - 1; end function [s] = getsign (d) % accepts number in base10, d. % returns sign bit of ieee754 representation. if d >= 0 s = 0; else s = 1; end end input:
ieee = mydec2ieee(0.085) output:
columns 1 through 21: 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 columns 22 through 31: 1 0 0 0 1 1 1 1 0 1 however, works decimal numbers in: 0 < d < 1.
questions
what doing wrong?
how should code modified correctly return ieee representations of numbers >= 1 , d <= 0?
note:
implementation based on relation d = (-1)sign * 2exponent - bias * (fraction + 1), fraction = sum (1/2^n), n = 0,...,22; bias = 127.
as confirmed here matlab uses ieee 754 single precision floats.
as such why not let matlab handle internals , this?:
s = dec2bin(typecast(single(0.085),'uint32'), 32) which gives:
00111101101011100001010001111011 this matches required output (from independent check mention) , works values > 1.
if need numeric, rather string, result convert this:
x = s-'0' 
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