1 ------------------------------------------------------------------------- 2 drawElements Quality Program Test Specification 3 ----------------------------------------------- 4 5 Copyright 2014 The Android Open Source Project 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 ------------------------------------------------------------------------- 19 Precision tests for built-in functions 20 21 Tests: 22 + dEQP-GLES3.functional.shaders.builtin_functions.precision.* 23 24 25 These tests check that the GLSL built-in numerical functions produce 26 results that are compliant with the range and precision requirements in 27 the GLSL ES specification. 28 29 The tests operate by calling the functions with predefined (mostly 30 random) input values in either the vertex or the fragment shader. The 31 result is stored in a transform feedback buffer or in a framebuffer 32 pixel, and then read and compared to a reference interval of acceptable 33 values. Functions are tested with all possible vector and matrix sizes. 34 In the test log floating point numbers are printed out as hexadecimal 35 constants of the form used in e.g. C99. 36 37 Where the GLSL specification does not specify a particular precision, 38 the tests try to make reasonable requirements. When behavior at 39 infinities hasn't been otherwise specified, C99 Appendix F is used as a 40 reference. Moreover, the highp precision requirements have been adapted 41 to lowp and mediump precisions even though the GLSL specification 42 doesn't provide any guarantees about them. For instance, mediump and 43 lowp operations are expected to produce either an infinity or the 44 maximum/minimum value on overflow. 45 46 The acceptable results are constrained further by only allowing values 47 from within the codomain of the function. Thus, for instance, sin(x) is 48 not allowed to return a number greater than 1 even when when the nominal 49 error bound would be greater. 50 51 A number of functions have been defined as derived forms. This means 52 that they are required to produce only results that their expansions 53 could produce, given the precision requirements for the constituent 54 55 operations. 56 57 * Arithmetic operations 58 59 These are as defined in the GLSL ES specification. 60 61 | operation | precision | domain | 62 |-----------+-----------+-----------------------------| 63 | x + y | < 1 ULP | | 64 | x / y | 2.5 ULP | 2^-126 <= abs(y) <= 2^127-1 | 65 | x - y | < 1 ULP | | 66 | x * y | < 1 ULP | | 67 68 69 * Trigonometric functions 70 71 The precisions for trigonometric functions have been adapted from OpenCL 72 fast relaxed math and half-float specifications. Hyperbolic functions 73 take their precisions from standard formulae as derived forms. 74 75 Primitives: 76 77 | function | precision | domain | prec qual | 78 |------------+----------------+---------------------+---------------| 79 | sin(x) | 2^-11 | -pi <= x <= pi | highp | 80 | | 2^-12 * abs(x) | elsewhere | highp | 81 | | 2 ULP | | mediump, lowp | 82 | cos(x) | 2^-11 | -pi <= x <= pi | highp | 83 | | 2^-12 * abs(x) | elsewhere | highp | 84 | | 2 ULP | | mediump, lowp | 85 | asin(x) | 4 ULP | -1 <= x <= 1 | highp | 86 | | 2 ULP | -1 <= x <= 1 | mediump, lowp | 87 | acos(x) | 4 ULP | -1 <= x <= 1 | highp | 88 | | 2 ULP | -1 <= x <= 1 | mediump, lowp | 89 | atan(x, y) | 6 ULP | !(x == 0 && y == 0) | highp | 90 | | 2 ULP | !(x == 0 && y == 0) | mediump, lowp | 91 | atan(x) | 5 ULP | | highp | 92 | | 2 ULP | | mediump, lowp | 93 94 Derived functions: 95 96 | function | defined as | 97 |------------+----------------------------------| 98 | radians(x) | (pi / 180.0) * x | 99 | degrees(x) | (180.0 / pi) * x | 100 | tan(x) | sin(x) * (1.0 / cos(x)) | 101 | sinh(x) | (exp(x) - exp(-x)) / 2.0 | 102 | cosh(x) | (exp(x) + exp(-x)) / 2.0 | 103 | tanh(x) | sinh(x) / cosh(x) | 104 | asinh(x) | log(x + sqrt(x * x + 1.0)) | 105 | acosh(x) | log(x + sqrt((x+1.0) * (x-1.0))) | 106 | atanh(x) | 0.5 * log(1.0 + x / (1.0 - x)) | 107 108 109 * Exponential functions 110 111 The precisions for exponential functions for mediump and lowp have been 112 adapted from the OpenCL half-float specification. 113 114 Primitives: 115 116 | function | precision | domain | prec qual | 117 |----------------+----------------------+----------------------+-----------| 118 | exp(x) | (3 + 2 * abs(x)) ULP | | highp | 119 | | (2 + 2 * abs(x)) ULP | | mediump | 120 | | 2 ULP | | lowp | 121 | log(x) | 2^-21 | 0.5 <= x && x <= 0.5 | highp | 122 | | 3 ULP | elsewhere | highp | 123 | | 2^-7 | 0.5 <= x && x <= 0.5 | mediump | 124 | | 2 ULP | elsewhere | mediump | 125 | | 2 ULP | | lowp | 126 | exp(x) | (3 + 2 * abs(x)) ULP | | highp | 127 | | (2 + 2 * abs(x)) ULP | | mediump | 128 | | 2 ULP | | lowp | 129 | log2(x) | 2^-21 | 0.5 <= x && x <= 0.5 | highp | 130 | | 3 ULP | elsewhere | highp | 131 | | 2^-7 | 0.5 <= x && x <= 0.5 | mediump | 132 | | 2 ULP | elsewhere | mediump | 133 | | 2 ULP | | lowp | 134 | inversesqrt(x) | 2 ULP | | | 135 136 Derived functions: 137 138 | function | defined as | 139 |----------+----------------------| 140 | pow(x) | exp2(y * log2(x)) | 141 | sqrt(x) | 1.0 / inversesqrt(x) | 142 143 144 * Common functions 145 146 The operations that don't do any arithmetic are required to produce 147 exact results. The round() function is allowed to round in either 148 direction on a tie. 149 150 Primitives: 151 152 | function | precision | 153 |------------------+-----------| 154 | abs(x) | 0 | 155 | sign(x) | 0 | 156 | floor(x) | 0 | 157 | trunc(x) | 0 | 158 | round(x) | special | 159 | roundEven(x) | 0 | 160 | ceil(x) | 0 | 161 | modf(x, i) | 0 | 162 | min(x, y) | 0 | 163 | max(x, y) | 0 | 164 | clamp(x, lo, hi) | 0 | 165 | step(edge, x) | 0 | 166 167 Derived functions: 168 169 | function | defined as | 170 |-----------------------+------------------------------------------------| 171 | fract(x) | x - floor(x) | 172 | mod(x, y) | x - y * floor(x / y) | 173 | mix(x, y, a) | x * (1 - a) + y * a | 174 | smoothstep(e0, e1, x) | { float t = clamp((x - e0) / (e1 - e0),0,1); | 175 | | return t * t * (3 - 2*t); } | 176 177 178 * Geometric and matrix functions 179 180 These are generally defined as derived forms with reference algorithms. 181 For determinant and inverse operations only 2x2 matrices are tested: 182 there are a number of possible algorithms for larger matrices, and the 183 specification does not provide precision requirements for these operations. 184
