1------------------------------------------------------------------------- 2drawElements Quality Program Test Specification 3----------------------------------------------- 4 5Copyright 2014 The Android Open Source Project 6 7Licensed under the Apache License, Version 2.0 (the "License"); 8you may not use this file except in compliance with the License. 9You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13Unless required by applicable law or agreed to in writing, software 14distributed under the License is distributed on an "AS IS" BASIS, 15WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16See the License for the specific language governing permissions and 17limitations under the License. 18------------------------------------------------------------------------- 19 Precision tests for built-in functions 20 21Tests: 22 + dEQP-GLES3.functional.shaders.builtin_functions.precision.* 23 24 25These tests check that the GLSL built-in numerical functions produce 26results that are compliant with the range and precision requirements in 27the GLSL ES specification. 28 29The tests operate by calling the functions with predefined (mostly 30random) input values in either the vertex or the fragment shader. The 31result is stored in a transform feedback buffer or in a framebuffer 32pixel, and then read and compared to a reference interval of acceptable 33values. Functions are tested with all possible vector and matrix sizes. 34In the test log floating point numbers are printed out as hexadecimal 35constants of the form used in e.g. C99. 36 37Where the GLSL specification does not specify a particular precision, 38the tests try to make reasonable requirements. When behavior at 39infinities hasn't been otherwise specified, C99 Appendix F is used as a 40reference. Moreover, the highp precision requirements have been adapted 41to lowp and mediump precisions even though the GLSL specification 42doesn't provide any guarantees about them. For instance, mediump and 43lowp operations are expected to produce either an infinity or the 44maximum/minimum value on overflow. 45 46The acceptable results are constrained further by only allowing values 47from within the codomain of the function. Thus, for instance, sin(x) is 48not allowed to return a number greater than 1 even when when the nominal 49error bound would be greater. 50 51A number of functions have been defined as derived forms. This means 52that they are required to produce only results that their expansions 53could produce, given the precision requirements for the constituent 54 55operations. 56 57* Arithmetic operations 58 59These 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 71The precisions for trigonometric functions have been adapted from OpenCL 72fast relaxed math and half-float specifications. Hyperbolic functions 73take their precisions from standard formulae as derived forms. 74 75Primitives: 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 94Derived 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 111The precisions for exponential functions for mediump and lowp have been 112adapted from the OpenCL half-float specification. 113 114Primitives: 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 136Derived 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 146The operations that don't do any arithmetic are required to produce 147exact results. The round() function is allowed to round in either 148direction on a tie. 149 150Primitives: 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 167Derived 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 180These are generally defined as derived forms with reference algorithms. 181For determinant and inverse operations only 2x2 matrices are tested: 182there are a number of possible algorithms for larger matrices, and the 183specification does not provide precision requirements for these operations. 184