[Piglit] [PATCH 2/4] arb_shader_precision: add framework for calculating tolerances for complex functions

Dylan Baker baker.dylan.c at gmail.com
Thu Feb 19 09:59:00 PST 2015


On Thu, Feb 19, 2015 at 12:06:32AM -0600, Micah Fedke wrote:
> ---
>   generated_tests/gen_shader_precision_tests.py | 148 
> ++++++++++++++++++++++++--
>   1 file changed, 137 insertions(+), 11 deletions(-)
> 
> diff --git a/generated_tests/gen_shader_precision_tests.py 
> b/generated_tests/gen_shader_precision_tests.py
> index cfa5065..0bda05a 100644
> --- a/generated_tests/gen_shader_precision_tests.py
> +++ b/generated_tests/gen_shader_precision_tests.py
> @@ -49,29 +49,155 @@
>   from builtin_function import *  import mako.template  import os 
> +import struct
> +import bigfloat

What does bigfloat buy us that numpy doesn't? That should be part of
yoru commit message.

You'll also need to add a cmake check for bigfloat in this patch. Also,
looking at bigfloat it seems to be a wrapper around GNU MPFR, can it be
used on windows?

>    from templates import template_file
>   -tolerances = {'pow': 16.0, -              'exp': 3.0,
> -              'exp2': 3.0,
> -              'log': 3.0,
> -              'log2': 3.0,
> -              'sqrt': 3.0,
> -              'inversesqrt': 2.0,
> -              'op-div': 2.5,
> -              'op-assign-div': 2.5,
> -              }
> +
> +allowed_error_scale = 4.0
>    trig_builtins = ('sin', 'cos', 'tan',                   'asin', 
> 'acos', 'atan',                   'sinh', 'cosh', 'tanh', 
>      'asinh', 'acosh', 'atanh')
>   +high_precision = bigfloat.precision(113)
> +low_precision = bigfloat.precision(23)
> +
>   def _is_sequence(arg):
>       return (not hasattr(arg, "strip") and
>               hasattr(arg, "__iter__"))
>   +def _len_any(a):
> +    """ a version of len that returns 1 if passed a non-sequence type
> +    """
> +    return len(a) if _is_sequence(a) else 1

I'm not sure how I feel about this. I have a feeling that passing
different data types around for long periods is going to result in lots
of hard to find bugs. Is it possible to just put non-sequence items into
a list of one elements?

> +
> +def _floatToBits(f):
> +    s = struct.pack('>f', f)
> +    return struct.unpack('>l', s)[0]
> +
> +def _bitsToFloat(b):
> +    s = struct.pack('>l', b)
> +    return struct.unpack('>f', s)[0]
> +
> +def _ulpsize(f):
> +    """ determine _ulpsize in the direction of nearest infinity
> +        which gives the worst case scenario for edge cases
> +    """
> +    return bigfloat.next_up(f)-f if f >= 0.0 \
> +            else f-bigfloat.next_down(f)
> +
> +def _capture_error(precise, imprecise):
> +    """Perform the legwork of calculating the difference in error of 
> the high
> +    precision and low precision runs.  Decide whether this difference 
> in error
> +    is within allowable tolerances.  The range of allowable tolerances is
> +    subjective, as ARB_shader_precision (and GLSL spec as of v4.5) gives no
> +    direct guidance for complex functions.  Toronto, et.  al. use 
> quadrupled
> +    error as a limit in "Practically Accurate Floating-Point Math," 
> Computing
> +    Now, Oct. 2014.  Also use the difference in error and the value of 
> one ulp
> +    at the output to calculate the tolerance range in ulps for use by the
> +    shader test, should this vector pass the badlands check.
> +    """
> +
> +    ers = []
> +    bls = []
> +    cts = []
> +    with high_precision:
> +        error = bigfloat.abs(precise - imprecise)
> +    ers.append(error)
> +    with low_precision:
> +        ulpsz = _ulpsize(imprecise)
> +    with high_precision:
> +        bls.append(error > ulpsz*allowed_error_scale)
> +        cts.append(bigfloat.round(error/ulpsz))
> +    return {'errors':ers, 'badlands':bls, 'component_tolerances':cts}
> +
> +def _analyze_ref_fn(fn, args):
> +    """Many functions contain ill-conditioned regions referred to as 
> "badlands"
> +    (see Toronto, et. al., "Practically Accurate Floating-Point Math,"
> +    Computing Now, Oct. 2014).  Within these regions errors in the 
> inputs are
> +    magnified significantly, making the function impossible to test 
> with any
> +    reasonable accuracy.  A complex function that operates on floating 
> point
> +    numbers has the potential to generate such error propagation even 
> if the
> +    inputs are exact floating point numbers, since intermediate results 
> can be
> +    generated with error.  In order to identify and avoid these areas, 
> we run
> +    the function once at a lower precision and once at a higher 
> precision, and
> +    compare the outputs.  Propagating errors will be greater at lower 
> precision
> +    and less at higher precision for a given set of function inputs, 
> allowing
> +    us to identify the badlands of the function.
> +    """
> +
> +    ret = {'errors':[], 'badlands':[], 'component_tolerances':[]}
> +    with high_precision:
> +        precise = fn(args)
> +    with low_precision:
> +        imprecise = fn(args)
> +    if _len_any(imprecise) == 1:
> +        ret = _capture_error(precise, imprecise)
> +    else:
> +        for i, arg in enumerate(imprecise):
> +            rettmp = _capture_error(precise[i], arg)
> +            ret['errors'].extend(rettmp['errors'])
> +            ret['badlands'].extend(rettmp['badlands'])
> + 
> ret['component_tolerances'].extend(rettmp['component_tolerances'])
> +    return ret
> +
> +simple_fns = {'op-mult': 0.0,
> +              'op-assign-mult': 0.0,
> +              'op-div': 2.5,
> +              'op-assign-div': 2.5,
> +              'pow': 16.0, +              'exp': 3.0,
> +              'exp2': 3.0,
> +              'log': 3.0,
> +              'log2': 3.0,
> +              'sqrt': 3.0,
> +              'inversesqrt': 2.0}
> + +complex_fns = {}
> +
> +componentwise_fns = ('mod', 'mix', 'smoothstep' )
> +
> +def _gen_tolerance(name, rettype, args):
> +    """Return the tolerance that should be allowed for a function for the
> +    test vector passed in.  Return -1 for any vectors that would push the
> +    tolerance outside of acceptable bounds +    """
> +    if name in simple_fns:
> +        if name == 'op-mult' or name == 'op-assign-mult':

if name in ['op-mult', 'op-assign-mult']:

> +            x_type = glsl_type_of(args[0])
> +            y_type = glsl_type_of(args[1])
> +            if x_type.is_vector and y_type.is_matrix:
> +                mult_func = _vec_times_mat_ref
> +            elif x_type.is_matrix and y_type.is_vector:
> +                mult_func = _mat_times_vec_ref
> +            elif x_type.is_matrix and y_type.is_matrix:
> +                mult_func = _mat_times_mat_ref
> +            else:
> +                return simple_fns[name] +            ret = 
> _analyze_ref_fn(mult_func, args)
> +            return -1.0 if any(ret['badlands']) else map(float, 
> ret['component_tolerances'])

Generally at this point python (both upstream and community) discourage
the use of map and filter, with a preference for comprehensions.
[float(x) for x in ret['component_tolerances']] should be what you want.

I'm also assuming that you are aware that any() will find any truthy
value: so any number that isn't 0, any non-empty string, any non-empty
container, etc.

> +        else:
> +            return simple_fns[name] +    elif name in complex_fns:
> +        if name in componentwise_fns:
> +            ret = {'errors':[], 'badlands':[], 'component_tolerances':[]}
> +            for component in range(rettype.num_cols*rettype.num_rows):
> +                current_args = []
> +                for i, arg in enumerate(args):
> +                    current_args.append(arg[component%len(arg)] if 
> _len_any(arg) > 1 else arg)
> +                rettmp = _analyze_ref_fn(complex_fns[name], current_args)
> +                ret['errors'].extend(rettmp['errors'])
> +                ret['badlands'].extend(rettmp['badlands'])
> + 
> ret['component_tolerances'].extend(rettmp['component_tolerances'])
> +        else:
> +            ret = _analyze_ref_fn(complex_fns[name], args)
> +        return -1.0 if any(ret['badlands']) else map(float, 
> ret['component_tolerances'])
> +    else:
> +        return 0.0
> +
>   def make_indexers(signature):
>      """Build a list of strings which index into every possible
>      value of the result.  For example, if the result is a vec2,
> @@ -160,7 +286,7 @@ def main():
>                   with open(output_filename, 'w') as f:
>                       f.write(template.render_unicode( 
> signature=signature, 
>     test_vectors=test_vectors,
> -                                                     tolerances=tolerances,
> +                                                     tolerances=simple_fns,
>  
> invocation=invocation,
>  
> num_elements=num_elements,
>                                                        indexers=indexers,
> -- 
> 2.2.2
> 
> _______________________________________________
> Piglit mailing list
> Piglit at lists.freedesktop.org
> http://lists.freedesktop.org/mailman/listinfo/piglit
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