# coding=utf-8 # # Copyright © 2011 Intel Corporation # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice (including the next # paragraph) shall be included in all copies or substantial portions of the # Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING # FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER # DEALINGS IN THE SOFTWARE. # This source file defines a set of test vectors that can be used to # test GLSL's built-in functions and operators. It is intended to be # used by Python code that generates Piglit tests. # # The key export is the dictionary test_suite. It contains an entry # for each possible overload of every pure built-in function and # operator. By iterating through this dictionary you can find a set # of test vectors for testing nearly every built-in GLSL function. # # The following functions are not included, since they are not pure, # so they can't be tested using simple vectors: # - dFdx() # - dFdy() # - fwidth() # - ftransform() # - Increment and decrement operators # # The following functions are not included, since they need to be # tested in specialized ways: # - modf(): not tested because it has an out parameter # - isnan() and isinf(): not tested because special effort is required # to create values that cause these functions to return true. # # Also not tested are array subscripting, field/method selection, # swizzling, the function call operator, assignment, and the sequence # operator. import collections import itertools import numpy as np # Floating point types used by Python and numpy FLOATING_TYPES = (float, np.float64, np.float32) class GlslBuiltinType(object): """Class representing a GLSL built-in type.""" def __init__(self, name, base_type, num_cols, num_rows, version_introduced): self.__name = name if base_type is not None: self.__base_type = base_type else: self.__base_type = self self.__num_cols = num_cols self.__num_rows = num_rows self.__version_introduced = version_introduced @property def name(self): """The name of the type, as a string.""" return self.__name @property def base_type(self): """For vectors and matrices, the type of data stored in each element. For scalars, equal to self. """ return self.__base_type @property def num_cols(self): """For matrices, the number of columns. For vectors and scalars, 1. """ return self.__num_cols @property def num_rows(self): """For vectors and matrices, the number of rows. For scalars, 1. """ return self.__num_rows @property def is_scalar(self): return self.__num_cols == 1 and self.__num_rows == 1 @property def is_vector(self): return self.__num_cols == 1 and self.__num_rows != 1 @property def is_matrix(self): return self.__num_cols != 1 @property def version_introduced(self): """The earliest version of GLSL that this type appears in (as a string, e.g. '1.10'). """ return self.__version_introduced def __str__(self): return self.__name def __repr__(self): return 'glsl_{0}'.format(self.__name) # Concrete declarations of GlslBuiltinType glsl_bool = GlslBuiltinType('bool', None, 1, 1, '1.10') glsl_int = GlslBuiltinType('int', None, 1, 1, '1.10') glsl_uint = GlslBuiltinType('uint', None, 1, 1, '1.30') glsl_float = GlslBuiltinType('float', None, 1, 1, '1.10') glsl_vec2 = GlslBuiltinType('vec2', glsl_float, 1, 2, '1.10') glsl_vec3 = GlslBuiltinType('vec3', glsl_float, 1, 3, '1.10') glsl_vec4 = GlslBuiltinType('vec4', glsl_float, 1, 4, '1.10') glsl_bvec2 = GlslBuiltinType('bvec2', glsl_bool, 1, 2, '1.10') glsl_bvec3 = GlslBuiltinType('bvec3', glsl_bool, 1, 3, '1.10') glsl_bvec4 = GlslBuiltinType('bvec4', glsl_bool, 1, 4, '1.10') glsl_ivec2 = GlslBuiltinType('ivec2', glsl_int, 1, 2, '1.10') glsl_ivec3 = GlslBuiltinType('ivec3', glsl_int, 1, 3, '1.10') glsl_ivec4 = GlslBuiltinType('ivec4', glsl_int, 1, 4, '1.10') glsl_uvec2 = GlslBuiltinType('uvec2', glsl_uint, 1, 2, '1.30') glsl_uvec3 = GlslBuiltinType('uvec3', glsl_uint, 1, 3, '1.30') glsl_uvec4 = GlslBuiltinType('uvec4', glsl_uint, 1, 4, '1.30') glsl_mat2 = GlslBuiltinType('mat2', glsl_float, 2, 2, '1.10') glsl_mat3 = GlslBuiltinType('mat3', glsl_float, 3, 3, '1.10') glsl_mat4 = GlslBuiltinType('mat4', glsl_float, 4, 4, '1.10') glsl_mat2x2 = glsl_mat2 glsl_mat3x2 = GlslBuiltinType('mat3x2', glsl_float, 3, 2, '1.20') glsl_mat4x2 = GlslBuiltinType('mat4x2', glsl_float, 4, 2, '1.20') glsl_mat2x3 = GlslBuiltinType('mat2x3', glsl_float, 2, 3, '1.20') glsl_mat3x3 = glsl_mat3 glsl_mat4x3 = GlslBuiltinType('mat4x3', glsl_float, 4, 3, '1.20') glsl_mat2x4 = GlslBuiltinType('mat2x4', glsl_float, 2, 4, '1.20') glsl_mat3x4 = GlslBuiltinType('mat3x4', glsl_float, 3, 4, '1.20') glsl_mat4x4 = glsl_mat4 # Named tuple representing the signature of a single overload of a # built-in GLSL function or operator: # - name is a name suitable for use in test filenames. For functions, # this is the name of the function. For operators, it is a short # description of the operator, beginning with "op", e.g. "op-plus". # - template is a Python format string that can be used to construct # GLSL code that invokes the function or operator. # - version_introduced earliest version of GLSL the test applies to # (as a string, e.g. '1.10'). # - rettype is the return type of the function or operator (as a # GlslBuiltinType). # - argtypes is a tuple containing the types of each parameter (as # GlslBuiltinTypes). # # For example, the function # # vec3 step(float edge, vec3 x) # # has a signature of # # Signature(name='step', template='step({0}, {1})', # version_introduced='1.10', rettype='vec3', # argtypes=('float', 'vec3')) Signature = collections.namedtuple( 'Signature', ('name', 'template', 'version_introduced', 'rettype', 'argtypes')) # Named tuple representing a single piece of test data for testing a # built-in GLSL function: # - arguments is a tuple containing the arguments to apply to the # function. Each argument is of a type native to numpy (e.g. # numpy.float32 or numpy.ndarray) # - result is the value the function is expected to return. It is # also of a type native to numpy. # - tolerance is a float32 representing how much deviation from the # result we expect, considering the floating point precision # requirements of GLSL and OpenGL. The value may be zero for test # vectors involving booleans and integers. If result is a vector or # matrix, tolerance should be interpreted as the maximum permissible # RMS error (as would be computed by the distance() function). TestVector = collections.namedtuple( 'TestVector', ('arguments', 'result', 'tolerance')) def glsl_type_of(value): """Return the GLSL type corresponding to the given native numpy value, as a GlslBuiltinType. """ if isinstance(value, FLOATING_TYPES): return glsl_float elif isinstance(value, (bool, np.bool_)): return glsl_bool elif isinstance(value, np.int32): return glsl_int elif isinstance(value, np.uint32): return glsl_uint else: assert isinstance(value, np.ndarray) if len(value.shape) == 1: # Vector vector_length = value.shape[0] assert 2 <= vector_length <= 4 if value.dtype in FLOATING_TYPES: return (glsl_vec2, glsl_vec3, glsl_vec4)[vector_length - 2] elif value.dtype == bool: return (glsl_bvec2, glsl_bvec3, glsl_bvec4)[vector_length - 2] elif value.dtype == np.int32: return (glsl_ivec2, glsl_ivec3, glsl_ivec4)[vector_length - 2] elif value.dtype == np.uint32: return (glsl_uvec2, glsl_uvec3, glsl_uvec4)[vector_length - 2] else: raise Exception( 'Unexpected vector base type {0}'.format(value.dtype)) else: # Matrix assert value.dtype in FLOATING_TYPES assert len(value.shape) == 2 matrix_rows = value.shape[0] assert 2 <= matrix_rows <= 4 matrix_columns = value.shape[1] assert 2 <= matrix_columns <= 4 matrix_types = ((glsl_mat2x2, glsl_mat2x3, glsl_mat2x4), (glsl_mat3x2, glsl_mat3x3, glsl_mat3x4), (glsl_mat4x2, glsl_mat4x3, glsl_mat4x4)) return matrix_types[matrix_columns - 2][matrix_rows - 2] def column_major_values(value): """Given a native numpy value, return a list of the scalar values comprising it, in column-major order.""" if isinstance(value, np.ndarray): return list(np.reshape(value, -1, 'F')) else: return [value] def glsl_constant(value): """Given a native numpy value, return GLSL code that constructs it.""" column_major = np.reshape(np.array(value), -1, 'F') if column_major.dtype == bool: values = ['true' if x else 'false' for x in column_major] elif column_major.dtype == np.uint32: values = [repr(x) + 'u' for x in column_major] else: values = [repr(x) for x in column_major] if len(column_major) == 1: return values[0] else: return '{0}({1})'.format(glsl_type_of(value), ', '.join(values)) def round_to_32_bits(value): """If value is a floating point type, round it down to 32 bits. Otherwise return it unchanged. """ if isinstance(value, float): return np.float32(value) elif isinstance(value, np.ndarray) and value.dtype == np.float64: return np.array(value, dtype=np.float32) else: return value def extend_to_64_bits(value): """If value is a floating point type, extend it to 64 bits. Otherwise return it unchanged. """ if isinstance(value, np.float32): return np.float64(value) elif isinstance(value, np.ndarray) and value.dtype == np.float32: return np.array(value, dtype=np.float64) else: return value # Dictionary containing the test vectors. Each entry in the # dictionary represents a single overload of a single built-in # function. Its key is a Signature tuple, and its value is a list of # TestVector tuples. # # Note: the dictionary is initialized to {} here, but it is filled # with test vectors by code later in this file. test_suite = {} # Implementation # ============== # # The functions below shouldn't be necessary to call from outside this # file. They exist solely to populate test_suite with test vectors. # Functions that simulate GLSL built-in functions (in the cases where # the GLSL built-in functions have no python or numpy equivalent, or # in cases where there is a behavioral difference). These functions # return None if the behavior of the GLSL built-in is undefined for # the given set of inputs. def _multiply(x, y): x_type = glsl_type_of(x) y_type = glsl_type_of(y) if x_type.is_vector and y_type.is_vector: # vector * vector is done componentwise. return x * y else: # All other cases are standard linear algebraic # multiplication, which numpy calls "dot". return np.dot(x, y) def _divide(x, y): if any(y_element == 0 for y_element in column_major_values(y)): # Division by zero is undefined. return None if glsl_type_of(x).base_type == glsl_int: # The GLSL spec does not make it clear what the rounding rules # are when performing integer division. C99 requires # round-toward-zero, so in the absence of any other # information, assume that's the correct behavior for GLSL. # # Python and numpy's rounding rules are inconsistent, so to # make sure we get round-toward-zero behavior, divide the # absolute values of x and y, and then fix the sign. return (np.abs(x) // np.abs(y)) * (np.sign(x) * np.sign(y)) elif glsl_type_of(x).base_type == glsl_uint: return x // y else: return x / y def _modulus(x, y): if any(x_element < 0 for x_element in column_major_values(x)): # Modulus operation with a negative first operand is # undefined. return None if any(y_element <= 0 for y_element in column_major_values(y)): # Modulus operation with a negative or zero second operand is # undefined. return None return x % y def _lshift(x, y): if not all(0 <= y_element < 32 for y_element in column_major_values(y)): # Shifts by less than 0 or more than the number of bits in the # type being shifted are undefined. return None # When the arguments to << don't have the same signedness, numpy # likes to promote them to int64. To avoid this, convert y to be # the same type as x. y_orig = y if glsl_type_of(x).base_type != glsl_type_of(y).base_type: y = _change_signedness(y) result = x << y # Shifting should always produce a result with the same base type # as the left argument. assert glsl_type_of(result).base_type == glsl_type_of(x).base_type return result def _rshift(x, y): if not all(0 <= y_element < 32 for y_element in column_major_values(y)): # Shifts by less than 0 or more than the number of bits in the # type being shifted are undefined. return None # When the arguments to >> don't have the same signedness, numpy # likes to promote them to int64. To avoid this, convert y to be # the same type as x. y_orig = y if glsl_type_of(x).base_type != glsl_type_of(y).base_type: y = _change_signedness(y) result = x >> y # Shifting should always produce a result with the same base type # as the left argument. assert glsl_type_of(result).base_type == glsl_type_of(x).base_type return result def _equal(x, y): return all(column_major_values(x == y)) def _not_equal(x, y): return not _equal(x, y) def _arctan2(y, x): if x == y == 0.0: return None return np.arctan2(y, x) def _pow(x, y): if x < 0.0: return None if x == 0.0 and y <= 0.0: return None return np.power(x, y) def _exp2(x): # exp2() is not available in versions of numpy < 1.3.0 so we # emulate it with power(). return np.power(2, x) def _trunc(x): # trunc() rounds toward zero. It is not available in version # 1.2.1 of numpy so we emulate it with floor(), sign(), and abs(). return np.sign(x) * np.floor(np.abs(x)) def _clamp(x, minVal, maxVal): if minVal > maxVal: return None return min(max(x, minVal), maxVal) def _smoothstep(edge0, edge1, x): if edge0 >= edge1: return None t = _clamp((x-edge0)/(edge1-edge0),0.0,1.0) return t*t*(3.0-2.0*t) def _normalize(x): return x/np.linalg.norm(x) def _faceforward(N, I, Nref): if np.dot(Nref, I) < 0.0: return N else: return -N def _reflect(I, N): return I-2*np.dot(N,I)*N def _refract(I, N, eta): k = 1.0-eta*eta*(1.0-np.dot(N,I)*np.dot(N,I)) if k < 0.0: return I*0.0 else: return eta*I-(eta*np.dot(N,I)+np.sqrt(k))*N def _change_signedness(x): """Change signed integer types to unsigned integer types and vice versa.""" if isinstance(x, np.int32): return np.uint32(x) elif isinstance(x, np.uint32): return np.int32(x) elif isinstance(x, np.ndarray): if (x.dtype == np.int32): return np.array(x, dtype=np.uint32) elif (x.dtype == np.uint32): return np.array(x, dtype=np.int32) raise Exception('Unexpected type passed to _change_signedness') def _argument_types_match(arguments, argument_indices_to_match): """Return True if all of the arguments indexed by argument_indices_to_match have the same GLSL type. """ types = [glsl_type_of(arguments[i]) for i in argument_indices_to_match] return all(x == types[0] for x in types) def _strict_tolerance(arguments, result): """Compute tolerance using a strict interpretation of the GLSL and OpenGL standards. From the GLSL 1.20 spec (4.1.4 "Floats"): "As an input value to one of the processing units, a floating-point variable is expected to match the IEEE single precision floating-point definition for precision and dynamic range. It is not required that the precision of internal processing match the IEEE floating-point specification for floating-point operations, but the guidelines for precision established by the OpenGL 1.4 specification must be met." From the OpenGL 1.4 spec (2.1.1 "Floating-Point Computation"): "We require simply that numbers' floating-point parts contain enough bits ... so that individual results of floating-point operations are accurate to about 1 part in 10^5." A harsh interpretation of the above is that (a) no precision is lost in moving numbers into or out of the GPU, and (b) any built-in function constitutes a single operation, so therefore the error in applying any built-in function should be off by no more than 1e-5 times its theoretically correct value. This is not the only possible interpretation, however. Certain built-in functions, such as the cross product, are computed by a formula consisting of many elementary multiplications and additions, in which a large amount of cancellation sometimes occurs. It's possible that these rules are meant to apply to those elementary multiplications and additions, and not the full built-in function. Other built-in functions, such as the trig functions, are typically implemented by a series approximation, in which 1 part in 10^5 accuracy seems like overkill. See below for the tolerance computation we use on these other functions. """ return 1e-5 * np.linalg.norm(result) def _trig_tolerance(arguments, result): """Compute a more lenient tolerance bound for trig functions. The GLSL and OpenGL specs don't provide any guidance as to the required accuracy of trig functions (other than the "1 part in 10^5" general accuracy requirement, which seems like overkill for trig functions. So the tolerance here is rather arbitrarily chosen to be either 1 part in 10^3 or 10^-4, whichever is larger. """ return max(1e-4, 1e-3 * np.linalg.norm(result)) def _cross_product_tolerance(arguments, result): """Compute a more lenient tolerance bound for cross product. Since the computation of a cross product may involve a large amount of cancellation, an error tolerance of 1 part in 10^5 (referred to the magnitude of the result vector) is overly tight. So instead we allow the error to be 1 part in 10^5 referred to the product of the magnitudes of the arguments. """ assert len(arguments) == 2 return 1e-5 * np.linalg.norm(arguments[0]) * np.linalg.norm(arguments[1]) def _simulate_function(test_inputs, python_equivalent, tolerance_function): """Construct test vectors by simulating a GLSL function on a list of possible inputs, and return a list of test vectors. test_inputs is a list of possible input sequences, each of which represents a set of arguments that should be applied to the function. python_equivalent is the function to simulate--it should return None if the GLSL function returns undefined results for the given set of inputs, otherwise it should return the expected result. Input sequences for which python_equivalent returns None are ignored. The function is simulated using 64 bit floats for maximum possible accuracy, but the output is rounded to 32 bits since that is the data type that we expect to get back form OpenGL. tolerance_function is the function to call to compute the tolerance. It should take the set of arguments and the expected result as its parameters. It is only used for functions that return floating point values. """ test_vectors = [] for inputs in test_inputs: expected_output = round_to_32_bits( python_equivalent(*[extend_to_64_bits(x) for x in inputs])) if expected_output is not None: if glsl_type_of(expected_output).base_type != glsl_float: tolerance = np.float32(0.0) else: tolerance = np.float32( tolerance_function(inputs, expected_output)) test_vectors.append(TestVector(inputs, expected_output, tolerance)) return test_vectors def _vectorize_test_vectors(test_vectors, scalar_arg_indices, vector_length): """Build a new set of test vectors by combining elements of test_vectors into vectors of length vector_length. For example, vectorizing the test vectors [TestVector((10, 20), 30, tolerance), TestVector((11, 20), 31, tolerance)] into vectors of length 2 would produce the result: [TestVector((vec2(10, 11), vec2(20, 20)), vec2(30, 31), new_tolerance)]. Tolerances are combined in root-sum-square fashion. scalar_arg_indices is a sequence of argument indices which should not be vectorized. So, if scalar_arg_indices is [1] in the above example, the result would be: [TestVector((vec2(10, 11), 20), vec2(30, 31), new_tolerance)]. """ def make_groups(test_vectors): """Group test vectors according to the values passed to the arguments that should not be vectorized. """ groups = {} for tv in test_vectors: key = tuple(tv.arguments[i] for i in scalar_arg_indices) if key not in groups: groups[key] = [] groups[key].append(tv) return groups def partition_vectors(test_vectors, partition_size): """Partition test_vectors into lists of length partition_size. If partition_size does not evenly divide the number of test vectors, wrap around as necessary to ensure that every input test vector is included. """ for i in xrange(0, len(test_vectors), partition_size): partition = [] for j in xrange(partition_size): partition.append(test_vectors[(i + j) % len(test_vectors)]) yield partition def merge_vectors(test_vectors): """Merge the given set of test vectors (whose arguments and result are scalars) into a single test vector whose arguments and result are vectors. For argument indices in scalar_arg_indices, leave the argument as a scalar. """ arity = len(test_vectors[0].arguments) arguments = [] for j in xrange(arity): if j in scalar_arg_indices: arguments.append(test_vectors[0].arguments[j]) else: arguments.append( np.array([tv.arguments[j] for tv in test_vectors])) result = np.array([tv.result for tv in test_vectors]) tolerance = np.float32( np.linalg.norm([tv.tolerance for tv in test_vectors])) return TestVector(arguments, result, tolerance) vectorized_test_vectors = [] groups = make_groups(test_vectors) for key in sorted(groups.keys()): test_vectors = groups[key] vectorized_test_vectors.extend( merge_vectors(partition) for partition in partition_vectors(test_vectors, vector_length)) return vectorized_test_vectors def _store_test_vector(test_suite_dict, name, glsl_version, test_vector, template = None): """Store a test vector in the appropriate place in test_suite_dict. The dictionary key (which is a Signature tuple) is generated by consulting the argument and return types of the test vector, and combining them with name and glsl_version. glsl_version is adjusted if necessary to reflect when the argument and return types were introduced into GLSL. If template is supplied, it is used insted as the template for the Signature objects generated. """ if template is None: arg_indices = xrange(len(test_vector.arguments)) template = '{0}({1})'.format( name, ', '.join('{{{0}}}'.format(i) for i in arg_indices)) rettype = glsl_type_of(test_vector.result) argtypes = tuple(glsl_type_of(arg) for arg in test_vector.arguments) adjusted_glsl_version = max( glsl_version, rettype.version_introduced, *[t.version_introduced for t in argtypes]) signature = Signature( name, template, adjusted_glsl_version, rettype, argtypes) if signature not in test_suite_dict: test_suite_dict[signature] = [] test_suite_dict[signature].append(test_vector) def _store_test_vectors(test_suite_dict, name, glsl_version, test_vectors, template = None): """Store multiple test vectors in the appropriate places in test_suite_dict. If template is supplied, it is used insted as the template for the Signature objects generated. """ for test_vector in test_vectors: _store_test_vector(test_suite_dict, name, glsl_version, test_vector, template = template) def make_arguments(input_generators): """Construct a list of tuples of input arguments to test. input_generators is a list, the ith element of which is a sequence of values that are suitable for use as the ith argument of the function under test. Output is a list, each element of which is a tuple of arguments to be passed to the function under test. These values are produced by taking the cartesian product of the input sequences. In addition, this function rounds floating point inputs to 32 bits, so that there will be no rounding errors when the input values are passed into OpenGL. """ input_generators = [ [round_to_32_bits(x) for x in seq] for seq in input_generators] return list(itertools.product(*input_generators)) def _make_componentwise_test_vectors(test_suite_dict): """Add test vectors to test_suite_dict for GLSL built-in functions that operate on vectors in componentwise fashion. Examples include sin(), cos(), min(), max(), and clamp(). """ # Make sure atan(x) and atan(x,y) don't misbehave for very large # or very small input values. atan_inputs = [0.0] for exponent in (-10, -1, 0, 1, 10): atan_inputs.append(pow(10.0, exponent)) atan_inputs.append(-pow(10.0, exponent)) # Make a similar set of inputs for acosh(), except don't use any # values < 1, since acosh() is only defined for x >= 1. acosh_inputs = [1.0 + x for x in atan_inputs if x >= 0] ints = [np.int32(x) for x in [-5, -2, -1, 0, 1, 2, 5]] uints = [np.uint32(x) for x in [0, 1, 2, 5, 34]] def f(name, arity, glsl_version, python_equivalent, alternate_scalar_arg_indices, test_inputs, tolerance_function = _strict_tolerance): """Create test vectors for the function with the given name and arity, which was introduced in the given glsl_version. python_equivalent is a Python function which operates on scalars, and simulates the GLSL function. This function should return None in any case where the output of the GLSL function is undefined. If alternate_scalar_arg_indices is not None, also create test vectors for an alternate vectorized version of the function, in which some arguments are scalars. alternate_scalar_arg_indices is a sequence of the indices of the arguments which are scalars. test_inputs is a list, the ith element of which is a list of values that are suitable for use as the ith argument of the function. If tolerance_function is supplied, it is a function which should be used to compute the tolerance for the test vectors. Otherwise, _strict_tolerance is used. """ scalar_test_vectors = _simulate_function( make_arguments(test_inputs), python_equivalent, tolerance_function) _store_test_vectors( test_suite_dict, name, glsl_version, scalar_test_vectors) if alternate_scalar_arg_indices is None: scalar_arg_indices_list = [()] else: scalar_arg_indices_list = [(), alternate_scalar_arg_indices] for scalar_arg_indices in scalar_arg_indices_list: for vector_length in (2, 3, 4): _store_test_vectors( test_suite_dict, name, glsl_version, _vectorize_test_vectors( scalar_test_vectors, scalar_arg_indices, vector_length)) f('radians', 1, '1.10', np.radians, None, [np.linspace(-180.0, 180.0, 4)]) f('degrees', 1, '1.10', np.degrees, None, [np.linspace(-np.pi, np.pi, 4)]) f('sin', 1, '1.10', np.sin, None, [np.linspace(-np.pi, np.pi, 4)], _trig_tolerance) f('cos', 1, '1.10', np.cos, None, [np.linspace(-np.pi, np.pi, 4)], _trig_tolerance) f('tan', 1, '1.10', np.tan, None, [np.linspace(-np.pi, np.pi, 4)], _trig_tolerance) f('asin', 1, '1.10', np.arcsin, None, [np.linspace(-1.0, 1.0, 4)], _trig_tolerance) f('acos', 1, '1.10', np.arccos, None, [np.linspace(-1.0, 1.0, 4)], _trig_tolerance) f('atan', 1, '1.10', np.arctan, None, [atan_inputs], _trig_tolerance) f('atan', 2, '1.10', _arctan2, None, [atan_inputs, atan_inputs], _trig_tolerance) f('sinh', 1, '1.30', np.sinh, None, [np.linspace(-2.0, 2.0, 4)], _trig_tolerance) f('cosh', 1, '1.30', np.cosh, None, [np.linspace(-2.0, 2.0, 4)], _trig_tolerance) f('tanh', 1, '1.30', np.tanh, None, [np.linspace(-2.0, 2.0, 4)], _trig_tolerance) f('asinh', 1, '1.30', np.arcsinh, None, [atan_inputs], _trig_tolerance) f('acosh', 1, '1.30', np.arccosh, None, [acosh_inputs], _trig_tolerance) f('atanh', 1, '1.30', np.arctanh, None, [np.linspace(-0.99, 0.99, 4)], _trig_tolerance) f('pow', 2, '1.10', _pow, None, [np.linspace(0.0, 2.0, 4), np.linspace(-2.0, 2.0, 4)]) f('exp', 1, '1.10', np.exp, None, [np.linspace(-2.0, 2.0, 4)]) f('log', 1, '1.10', np.log, None, [np.linspace(0.01, 2.0, 4)]) f('exp2', 1, '1.10', _exp2, None, [np.linspace(-2.0, 2.0, 4)]) f('log2', 1, '1.10', np.log2, None, [np.linspace(0.01, 2.0, 4)]) f('sqrt', 1, '1.10', np.sqrt, None, [np.linspace(0.0, 2.0, 4)]) f('inversesqrt', 1, '1.10', lambda x: 1.0/np.sqrt(x), None, [np.linspace(0.1, 2.0, 4)]) f('abs', 1, '1.10', np.abs, None, [np.linspace(-1.5, 1.5, 5)]) f('abs', 1, '1.30', np.abs, None, [ints]) f('sign', 1, '1.10', np.sign, None, [np.linspace(-1.5, 1.5, 5)]) f('sign', 1, '1.30', np.sign, None, [ints]) f('floor', 1, '1.10', np.floor, None, [np.linspace(-2.0, 2.0, 4)]) f('trunc', 1, '1.30', _trunc, None, [np.linspace(-2.0, 2.0, 8)]) # Note: the direction of rounding used by round() is not specified # for half-integer values, so we test it over a range that doesn't # include exact half-integer values. roundEven() is required to # round half-integer values to the nearest even integer, so we # test it over a range that does include exact half-integer # values. In both cases, we can use numpy's round() function, # because it rounds half-integer values to even, and all other # values to nearest. f('round', 1, '1.30', np.round, None, [np.linspace(-2.0, 2.0, 8)]) f('roundEven', 1, '1.30', np.round, None, [np.linspace(-2.0, 2.0, 25)]) f('ceil', 1, '1.10', np.ceil, None, [np.linspace(-2.0, 2.0, 4)]) f('fract', 1, '1.10', lambda x: x-np.floor(x), None, [np.linspace(-2.0, 2.0, 4)]) f('mod', 2, '1.10', lambda x, y: x-y*np.floor(x/y), [1], [np.linspace(-1.9, 1.9, 4), np.linspace(-2.0, 2.0, 4)]) f('min', 2, '1.10', min, [1], [np.linspace(-2.0, 2.0, 4), np.linspace(-2.0, 2.0, 4)]) f('min', 2, '1.30', min, [1], [ints, ints]) f('min', 2, '1.30', min, [1], [uints, uints]) f('max', 2, '1.10', max, [1], [np.linspace(-2.0, 2.0, 4), np.linspace(-2.0, 2.0, 4)]) f('max', 2, '1.30', max, [1], [ints, ints]) f('max', 2, '1.30', max, [1], [uints, uints]) f('clamp', 3, '1.10', _clamp, [1, 2], [np.linspace(-2.0, 2.0, 4), np.linspace(-1.5, 1.5, 3), np.linspace(-1.5, 1.5, 3)]) f('clamp', 3, '1.30', _clamp, [1, 2], [ints, ints, ints]) f('clamp', 3, '1.30', _clamp, [1, 2], [uints, uints, uints]) f('mix', 3, '1.10', lambda x, y, a: x*(1-a)+y*a, [2], [np.linspace(-2.0, 2.0, 2), np.linspace(-3.0, 3.0, 2), np.linspace(0.0, 1.0, 4)]) f('step', 2, '1.10', lambda edge, x: 0.0 if x < edge else 1.0, [0], [np.linspace(-2.0, 2.0, 4), np.linspace(-2.0, 2.0, 4)]) f('smoothstep', 3, '1.10', _smoothstep, [0, 1], [np.linspace(-1.9, 1.9, 4), np.linspace(-1.9, 1.9, 4), np.linspace(-2.0, 2.0, 4)]) _make_componentwise_test_vectors(test_suite) def _make_vector_relational_test_vectors(test_suite_dict): """Add test vectors to test_suite_dict for GLSL built-in functions that operate on vectors of floats, ints, or bools, but not on single floats, ints, or bools. Examples include lessThan(), equal(), and not(). """ _default_inputs = { 'v': np.linspace(-1.5, 1.5, 4), 'i': np.array([-5, -2, -1, 0, 1, 2, 5], dtype=np.int32), 'u': np.array([0, 1, 2, 5, 34], dtype=np.uint32), 'b': np.array([False, True]) } def f(name, arity, glsl_version, python_equivalent, arg_types, tolerance_function = _strict_tolerance): """Make test vectors for the function with the given name and arity, which was introduced in the given glsl_version. python_equivalent is a Python function which operates on scalars, and simulates the GLSL function. arg_types is a string containing 'v' if the function supports standard "vec" inputs, 'i' if it supports "ivec" inputs, and 'b' if it supports "bvec" inputs. The output type of the function is assumed to be the same as its input type. If tolerance_function is supplied, it is a function which should be used to compute the tolerance for the test vectors. Otherwise, _strict_tolerance is used. """ for arg_type in arg_types: test_inputs = [_default_inputs[arg_type]]*arity scalar_test_vectors = _simulate_function( make_arguments(test_inputs), python_equivalent, tolerance_function) for vector_length in (2, 3, 4): _store_test_vectors( test_suite_dict, name, glsl_version, _vectorize_test_vectors( scalar_test_vectors, (), vector_length)) f('lessThan', 2, '1.10', lambda x, y: x < y, 'viu') f('lessThanEqual', 2, '1.10', lambda x, y: x <= y, 'viu') f('greaterThan', 2, '1.10', lambda x, y: x > y, 'viu') f('greaterThanEqual', 2, '1.10', lambda x, y: x >= y, 'viu') f('equal', 2, '1.10', lambda x, y: x == y, 'viub') f('notEqual', 2, '1.10', lambda x, y: x != y, 'viub') f('not', 1, '1.10', lambda x: not x, 'b') _make_vector_relational_test_vectors(test_suite) def _make_vector_or_matrix_test_vectors(test_suite_dict): """Add test vectors to test_suite_dict for GLSL built-in functions that operate on vectors/matrices as a whole. Examples include length(), dot(), cross(), normalize(), and refract(). """ def match_args(*indices): """Return a function that determines whether the type of the arguments at the given indices match. For example: match(1, 3) is equivalent to: lambda a, b, c, d: glsl_type_of(b) == glsl_type_of(d) """ return lambda *args: _argument_types_match(args, indices) def match_simple_binop(x, y): """Detemine whether the type of the arguments is compatible for a simple binary operator (such as '+'). Arguments are compatible if one is a scalar and the other is a vector/matrix with the same base type, or if they are the same type. """ x_type = glsl_type_of(x) y_type = glsl_type_of(y) if x_type.base_type != y_type.base_type: return False if x_type.is_scalar or y_type.is_scalar: return True return x_type == y_type def match_multiply(x, y): """Determine whether the type of the arguments is compatible for multiply. Arguments are compatible if they are scalars, vectors, or matrices with the same base type, and the vector/matrix sizes are properly matched. """ x_type = glsl_type_of(x) y_type = glsl_type_of(y) if x_type.base_type != y_type.base_type: return False if x_type.is_scalar or y_type.is_scalar: return True if x_type.is_vector and y_type.is_matrix: # When multiplying vector * matrix, the vector is # transposed to a row vector. So its row count must match # the row count of the matrix. return x_type.num_rows == y_type.num_rows elif x_type.is_vector: assert y_type.is_vector # When multiplying vector * vector, the multiplication is # done componentwise, so the types must match exactly. return x_type == y_type else: assert x_type.is_matrix # When multiplying matrix * matrix or matrix * vector, a # standard linear algebraic multiply is used, so x's # column count must match y's row count. return x_type.num_cols == y_type.num_rows def match_shift(x, y): """Determine whether the type of the arguments is compatible for shift operations. Arguments are compatible if they are the same length or the first one is a vector and the second is a scalar. Their base types need not be the same, but they both must be integral. """ x_type = glsl_type_of(x) y_type = glsl_type_of(y) if x_type.base_type not in (glsl_int, glsl_uint): return False if y_type.base_type not in (glsl_int, glsl_uint): return False if y_type.is_scalar: return True assert not x_type.is_matrix assert not y_type.is_matrix return x_type.num_rows == y_type.num_rows bools = [False, True] bvecs = [np.array(bs) for bs in itertools.product(bools, bools)] + \ [np.array(bs) for bs in itertools.product(bools, bools, bools)] + \ [np.array(bs) for bs in itertools.product(bools, bools, bools, bools)] ints = [np.int32(x) for x in [12, -6, 74, -32, 0]] small_ints = [np.int32(x) for x in [-31, -25, -5, -2, -1, 0, 1, 2, 5, 25, 31]] ivecs = [ np.array([38, 35], dtype=np.int32), np.array([64, -9], dtype=np.int32), np.array([64, 9], dtype=np.int32), np.array([-36, 32, -88], dtype=np.int32), np.array([36, 32, 88], dtype=np.int32), np.array([59, 77, 68], dtype=np.int32), np.array([-66, 72, 87, -75], dtype=np.int32), np.array([66, 72, 87, 75], dtype=np.int32), np.array([-24, 40, -23, 74], dtype=np.int32), np.array([24, 40, 23, 74], dtype=np.int32), ] small_ivecs = [ np.array([13, 26], dtype=np.int32), np.array([-2, 26], dtype=np.int32), np.array([2, 26], dtype=np.int32), np.array([22, -23, 4], dtype=np.int32), np.array([22, 23, 4], dtype=np.int32), np.array([-19, 1, -13], dtype=np.int32), np.array([19, 1, 13], dtype=np.int32), np.array([16, 24, -23, -25], dtype=np.int32), np.array([16, 24, 23, 25], dtype=np.int32), np.array([-23, -12, 14, 19], dtype=np.int32), np.array([23, 12, 14, 19], dtype=np.int32), ] uints = [np.uint32(x) for x in [0, 6, 12, 32, 74]] small_uints = [np.uint32(x) for x in [0, 1, 2, 5, 25, 31]] uvecs = [ np.array([38, 35], dtype=np.uint32), np.array([64, 9], dtype=np.uint32), np.array([36, 32, 88], dtype=np.uint32), np.array([59, 77, 68], dtype=np.uint32), np.array([66, 72, 87, 75], dtype=np.uint32), np.array([24, 40, 23, 74], dtype=np.uint32) ] small_uvecs = [ np.array([13, 26], dtype=np.uint32), np.array([2, 26], dtype=np.uint32), np.array([22, 23, 4], dtype=np.uint32), np.array([19, 1, 13], dtype=np.uint32), np.array([16, 24, 23, 25], dtype=np.uint32), np.array([23, 12, 14, 19], dtype=np.uint32), ] nz_floats = [-1.33, 0.85] floats = [0.0] + nz_floats vecs = [ np.array([-0.10, -1.20]), np.array([-0.42, 0.48]), np.array([-0.03, -0.85, -0.94]), np.array([1.67, 0.66, 1.87]), np.array([-1.65, 1.33, 1.93, 0.76]), np.array([0.80, -0.15, -0.51, 0.0]) ] nz_floats_vecs = nz_floats + vecs vec3s = [ np.array([-0.03, -0.85, -0.94]), np.array([1.67, 0.66, 1.87]), ] norm_floats_vecs = [_normalize(x) for x in nz_floats_vecs] mats = [ np.array([[ 1.60, 0.76], [ 1.53, -1.00]]), # mat2 np.array([[-0.13, -0.87], [-1.40, 1.40]]), # mat2 np.array([[-1.11, 1.67, -0.41], [ 0.13, 1.09, -0.02], [ 0.56, 0.95, 0.24]]), # mat3 np.array([[-1.69, -0.46, -0.18], [-1.09, 1.75, 2.00], [-1.53, -0.70, -1.47]]), # mat3 np.array([[-1.00, -0.55, -1.08, 1.79], [ 1.77, 0.62, 0.48, -1.35], [ 0.09, -0.71, -1.39, -1.21], [-0.91, -1.82, -1.43, 0.72]]), # mat4 np.array([[ 0.06, 1.31, 1.52, -1.96], [ 1.60, -0.32, 0.51, -1.84], [ 1.25, 0.45, 1.90, -0.72], [-0.16, 0.45, -0.88, 0.39]]), # mat4 np.array([[ 0.09, 1.30, 1.25], [-1.19, 0.08, 1.08]]), # mat3x2 np.array([[-0.36, -1.08, -0.60], [-0.53, 0.88, -1.79]]), # mat3x2 np.array([[-0.46, 1.94], [-0.45, -0.75], [ 1.03, -0.50]]), # mat2x3 np.array([[ 1.38, -1.08], [-1.27, 1.83], [ 1.00, -0.74]]), # mat2x3 np.array([[ 1.81, -0.87, 0.81, 0.65], [-1.16, -1.52, 0.25, -1.51]]), # mat4x2 np.array([[ 1.93, -1.63, 0.29, 1.60], [ 0.49, 0.27, 0.14, 0.94]]), # mat4x2 np.array([[ 0.16, -1.69], [-0.80, 0.59], [-1.74, -1.43], [-0.02, -1.21]]), # mat2x4 np.array([[-1.02, 0.74], [-1.64, -0.13], [-1.59, 0.47], [ 0.30, 1.13]]), # mat2x4 np.array([[-0.27, -1.38, -1.41, -0.12], [-0.17, -0.56, 1.47, 1.86], [-1.85, -1.29, 1.77, 0.01]]), # mat4x3 np.array([[-0.47, -0.15, 1.97, -1.05], [-0.20, 0.53, -1.82, -1.41], [-1.39, -0.19, 1.62, 1.58]]), # mat4x3 np.array([[ 1.42, -0.86, 0.27], [ 1.80, -1.74, 0.04], [-1.88, -0.37, 0.43], [ 1.37, 1.90, 0.71]]), # mat3x4 np.array([[-1.72, 0.09, 0.45], [-0.31, -1.58, 1.92], [ 0.14, 0.18, -0.56], [ 0.40, -0.77, 1.76]]), # mat3x4 ] def f(name, arity, glsl_version, python_equivalent, filter, test_inputs, tolerance_function = _strict_tolerance, template = None): """Make test vectors for the function with the given name and arity, which was introduced in the given glsl_version. python_equivalent is a Python function which simulates the GLSL function. This function should return None in any case where the output of the GLSL function is undefined. However, it need not check that the lengths of the input vectors are all the same. If filter is not None, it will be called with each set of arguments, and test cases will only be generated if the filter returns True. test_inputs is a list, the ith element of which is a list of vectors and/or scalars that are suitable for use as the ith argument of the function. If tolerance_function is supplied, it is a function which should be used to compute the tolerance for the test vectors. Otherwise, _strict_tolerance is used. If template is supplied, it is used insted as the template for the Signature objects generated. """ test_inputs = make_arguments(test_inputs) if filter is not None: test_inputs = [ arguments for arguments in test_inputs if filter(*arguments)] _store_test_vectors( test_suite_dict, name, glsl_version, _simulate_function( test_inputs, python_equivalent, tolerance_function), template = template) f('op-add', 2, '1.10', lambda x, y: x + y, match_simple_binop, [floats+vecs+mats+ints+ivecs+uints+uvecs, floats+vecs+mats+ints+ivecs+uints+uvecs], template = '({0} + {1})') f('op-sub', 2, '1.10', lambda x, y: x - y, match_simple_binop, [floats+vecs+mats+ints+ivecs+uints+uvecs, floats+vecs+mats+ints+ivecs+uints+uvecs], template = '({0} - {1})') f('op-mult', 2, '1.10', _multiply, match_multiply, [floats+vecs+mats+ints+ivecs+uints+uvecs, floats+vecs+mats+ints+ivecs+uints+uvecs], template = '({0} * {1})') f('op-div', 2, '1.10', _divide, match_simple_binop, [floats+vecs+mats+ints+ivecs+uints+uvecs, floats+vecs+mats+ints+ivecs+uints+uvecs], template = '({0} / {1})') f('op-mod', 2, '1.30', _divide, match_simple_binop, [ints+ivecs+uints+uvecs, ints+ivecs+uints+uvecs], template = '({0} / {1})') f('op-uplus', 1, '1.10', lambda x: +x, None, [floats+vecs+mats+ints+ivecs+uints+uvecs], template = '(+ {0})') f('op-neg', 1, '1.10', lambda x: -x, None, [floats+vecs+mats+ints+ivecs+uints+uvecs], template = '(- {0})') f('op-gt', 2, '1.10', lambda x, y: x > y, match_args(0, 1), [ints+uints+floats, ints+uints+floats], template = '({0} > {1})') f('op-lt', 2, '1.10', lambda x, y: x < y, match_args(0, 1), [ints+uints+floats, ints+uints+floats], template = '({0} < {1})') f('op-ge', 2, '1.10', lambda x, y: x >= y, match_args(0, 1), [ints+uints+floats, ints+uints+floats], template = '({0} >= {1})') f('op-le', 2, '1.10', lambda x, y: x <= y, match_args(0, 1), [ints+uints+floats, ints+uints+floats], template = '({0} <= {1})') f('op-eq', 2, '1.10', _equal, match_args(0, 1), [floats+vecs+mats+ints+ivecs+uints+uvecs+bools+bvecs, floats+vecs+mats+ints+ivecs+uints+uvecs+bools+bvecs], template = '({0} == {1})') f('op-ne', 2, '1.10', _not_equal, match_args(0, 1), [floats+vecs+mats+ints+ivecs+uints+uvecs+bools+bvecs, floats+vecs+mats+ints+ivecs+uints+uvecs+bools+bvecs], template = '({0} != {1})') f('op-and', 2, '1.10', lambda x, y: x and y, None, [bools, bools], template = '({0} && {1})') f('op-or', 2, '1.10', lambda x, y: x or y, None, [bools, bools], template = '({0} || {1})') f('op-xor', 2, '1.10', lambda x, y: x != y, None, [bools, bools], template = '({0} ^^ {1})') f('op-not', 1, '1.10', lambda x: not x, None, [bools], template = '(! {0})') f('op-selection', 3, '1.10', lambda x, y, z: y if x else z, match_args(1, 2), [bools, floats+vecs+mats+ints+ivecs+uints+uvecs+bools+bvecs, floats+vecs+mats+ints+ivecs+uints+uvecs+bools+bvecs], template = '({0} ? {1} : {2})') f('op-complement', 1, '1.30', lambda x: ~x, None, [ints+ivecs+uints+uvecs], template = '(~ {0})') f('op-lshift', 2, '1.30', _lshift, match_shift, [small_ints+small_ivecs+small_uints+small_uvecs, small_ints+small_ivecs+small_uints+small_uvecs], template = '({0} << {1})') f('op-rshift', 2, '1.30', _rshift, match_shift, [small_ints+small_ivecs+small_uints+small_uvecs, small_ints+small_ivecs+small_uints+small_uvecs], template = '({0} >> {1})') f('op-bitand', 2, '1.30', lambda x, y: x & y, match_simple_binop, [ints+ivecs+uints+uvecs, ints+ivecs+uints+uvecs], template = '({0} & {1})') f('op-bitor', 2, '1.30', lambda x, y: x | y, match_simple_binop, [ints+ivecs+uints+uvecs, ints+ivecs+uints+uvecs], template = '({0} | {1})') f('op-bitxor', 2, '1.30', lambda x, y: x ^ y, match_simple_binop, [ints+ivecs+uints+uvecs, ints+ivecs+uints+uvecs], template = '({0} ^ {1})') f('length', 1, '1.10', np.linalg.norm, None, [floats+vecs]) f('distance', 2, '1.10', lambda x, y: np.linalg.norm(x-y), match_args(0, 1), [floats+vecs, floats+vecs]) f('dot', 2, '1.10', np.dot, match_args(0, 1), [floats+vecs, floats+vecs]) f('cross', 2, '1.10', np.cross, match_args(0, 1), [vec3s, vec3s], _cross_product_tolerance) f('normalize', 1, '1.10', _normalize, None, [nz_floats_vecs]) f('faceforward', 3, '1.10', _faceforward, match_args(0, 1, 2), [floats+vecs, floats+vecs, floats+vecs]) f('reflect', 2, '1.10', _reflect, match_args(0, 1), [floats+vecs, norm_floats_vecs]) f('refract', 3, '1.10', _refract, match_args(0, 1), [norm_floats_vecs, norm_floats_vecs, [0.5, 2.0]]) # Note: technically matrixCompMult operates componentwise. # However, since it is the only componentwise function to operate # on matrices, it is easier to generate test cases for it here # than to add matrix support to _make_componentwise_test_vectors. f('matrixCompMult', 2, '1.10', lambda x, y: x*y, match_args(0, 1), [mats, mats]) f('outerProduct', 2, '1.20', np.outer, None, [vecs, vecs]) f('transpose', 1, '1.20', np.transpose, None, [mats]) f('any', 1, '1.10', any, None, [bvecs]) f('all', 1, '1.10', all, None, [bvecs]) _make_vector_or_matrix_test_vectors(test_suite) def _check_signature_safety(test_suite_dict): """As a final safety check, verify that for each possible combination of name and argtypes, there is exactly one signature. """ name_argtype_combos = set() for signature in test_suite_dict: name_argtype_combo = (signature.name, signature.argtypes) if name_argtype_combo in name_argtype_combos: raise Exception( 'Duplicate signature found for {0}'.format(name_argtype_combo)) name_argtype_combos.add(name_argtype_combo) _check_signature_safety(test_suite)