Thank you for creating and sharing this example. I think the fact of merely loading a shared library as modifying the FP behavior is the real shocker, more than any particular FP computation that hinges on denormals.
Still, I think one of the great wins with denormals is that they make "x == y iff x-y == 0" true; absent denormals you can have two normalized x and y, x != y, such y-x evaluates to 0. So for an example, maybe something that involves y > x and yet ceil(y-x) == 0, which is surprising. The only setting I can think of is something like making a histogram (with flipped indices, like your pixel row) of differences of values, so that ceil(y-x) == 0 leads to an invalid histogram index.
Some values are x=1e-32 and y=1.0000011e-32, which parse (via sscanf) to:
x = 0:00010100:10011111011000100011111 = (-1)^0 * 2^( 20-127) * (1+5222687/2^23)
y = 0:00010100:10011111011000100101110 = (-1)^0 * 2^( 20-127) * (1+5222702/2^23)
and then the denormalized difference d = x-y should be:
d = 0:00000000:11110000000000000000000 = (-1)^0 * 2^(1-127) * (0+7864320/2^23)
Having some specific values sidesteps concerns about nextafterf(). In this case I think y is many ulps above x, not just 1.
Still, I think one of the great wins with denormals is that they make "x == y iff x-y == 0" true; absent denormals you can have two normalized x and y, x != y, such y-x evaluates to 0. So for an example, maybe something that involves y > x and yet ceil(y-x) == 0, which is surprising. The only setting I can think of is something like making a histogram (with flipped indices, like your pixel row) of differences of values, so that ceil(y-x) == 0 leads to an invalid histogram index.
Some values are x=1e-32 and y=1.0000011e-32, which parse (via sscanf) to:
and then the denormalized difference d = x-y should be: Having some specific values sidesteps concerns about nextafterf(). In this case I think y is many ulps above x, not just 1.