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79acb088e7
Since using addresses that might change is something that finally the FSF acknowledge as a plausible scenario (after changing address twice), the license blurb in the source files should use the URI for getting the license in case the library did not come with it. Not that URIs cannot possibly change, but at least it's easier to set up a redirection at the same place. As a side note: this commit closes the oldes bug in Clutter's bug report tool. http://bugzilla.openedhand.com/show_bug.cgi?id=521
951 lines
28 KiB
C
951 lines
28 KiB
C
/*
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* Cogl
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*
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* An object oriented GL/GLES Abstraction/Utility Layer
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*
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* Copyright (C) 2007,2008,2009 Intel Corporation.
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library. If not, see <http://www.gnu.org/licenses/>.
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*
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*
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*/
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#define G_IMPLEMENT_INLINES
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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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#include "cogl-fixed.h"
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/* pre-computed sin table for 1st quadrant
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*
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* Currently contains 257 entries.
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*
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* The current maximum absolute error is about 1.9e-0.5
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* and is greatest around pi/2 where the second derivative
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* of sin(x) is greatest. If greater accuracy is needed,
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* modestly increasing the table size, or maybe using
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* quadratic interpolation would drop the interpolation
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* error below the precision limits of CoglFixed.
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*/
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static const CoglFixed sin_tbl[] =
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{
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0x00000000L, 0x00000192L, 0x00000324L, 0x000004B6L,
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0x00000648L, 0x000007DAL, 0x0000096CL, 0x00000AFEL,
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0x00000C90L, 0x00000E21L, 0x00000FB3L, 0x00001144L,
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0x000012D5L, 0x00001466L, 0x000015F7L, 0x00001787L,
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0x00001918L, 0x00001AA8L, 0x00001C38L, 0x00001DC7L,
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0x00001F56L, 0x000020E5L, 0x00002274L, 0x00002402L,
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0x00002590L, 0x0000271EL, 0x000028ABL, 0x00002A38L,
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0x00002BC4L, 0x00002D50L, 0x00002EDCL, 0x00003067L,
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0x000031F1L, 0x0000337CL, 0x00003505L, 0x0000368EL,
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0x00003817L, 0x0000399FL, 0x00003B27L, 0x00003CAEL,
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0x00003E34L, 0x00003FBAL, 0x0000413FL, 0x000042C3L,
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0x00004447L, 0x000045CBL, 0x0000474DL, 0x000048CFL,
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0x00004A50L, 0x00004BD1L, 0x00004D50L, 0x00004ECFL,
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0x0000504DL, 0x000051CBL, 0x00005348L, 0x000054C3L,
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0x0000563EL, 0x000057B9L, 0x00005932L, 0x00005AAAL,
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0x00005C22L, 0x00005D99L, 0x00005F0FL, 0x00006084L,
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0x000061F8L, 0x0000636BL, 0x000064DDL, 0x0000664EL,
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0x000067BEL, 0x0000692DL, 0x00006A9BL, 0x00006C08L,
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0x00006D74L, 0x00006EDFL, 0x00007049L, 0x000071B2L,
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0x0000731AL, 0x00007480L, 0x000075E6L, 0x0000774AL,
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0x000078ADL, 0x00007A10L, 0x00007B70L, 0x00007CD0L,
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0x00007E2FL, 0x00007F8CL, 0x000080E8L, 0x00008243L,
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0x0000839CL, 0x000084F5L, 0x0000864CL, 0x000087A1L,
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0x000088F6L, 0x00008A49L, 0x00008B9AL, 0x00008CEBL,
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0x00008E3AL, 0x00008F88L, 0x000090D4L, 0x0000921FL,
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0x00009368L, 0x000094B0L, 0x000095F7L, 0x0000973CL,
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0x00009880L, 0x000099C2L, 0x00009B03L, 0x00009C42L,
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0x00009D80L, 0x00009EBCL, 0x00009FF7L, 0x0000A130L,
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0x0000A268L, 0x0000A39EL, 0x0000A4D2L, 0x0000A605L,
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0x0000A736L, 0x0000A866L, 0x0000A994L, 0x0000AAC1L,
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0x0000ABEBL, 0x0000AD14L, 0x0000AE3CL, 0x0000AF62L,
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0x0000B086L, 0x0000B1A8L, 0x0000B2C9L, 0x0000B3E8L,
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0x0000B505L, 0x0000B620L, 0x0000B73AL, 0x0000B852L,
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0x0000B968L, 0x0000BA7DL, 0x0000BB8FL, 0x0000BCA0L,
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0x0000BDAFL, 0x0000BEBCL, 0x0000BFC7L, 0x0000C0D1L,
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0x0000C1D8L, 0x0000C2DEL, 0x0000C3E2L, 0x0000C4E4L,
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0x0000C5E4L, 0x0000C6E2L, 0x0000C7DEL, 0x0000C8D9L,
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0x0000C9D1L, 0x0000CAC7L, 0x0000CBBCL, 0x0000CCAEL,
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0x0000CD9FL, 0x0000CE8EL, 0x0000CF7AL, 0x0000D065L,
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0x0000D14DL, 0x0000D234L, 0x0000D318L, 0x0000D3FBL,
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0x0000D4DBL, 0x0000D5BAL, 0x0000D696L, 0x0000D770L,
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0x0000D848L, 0x0000D91EL, 0x0000D9F2L, 0x0000DAC4L,
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0x0000DB94L, 0x0000DC62L, 0x0000DD2DL, 0x0000DDF7L,
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0x0000DEBEL, 0x0000DF83L, 0x0000E046L, 0x0000E107L,
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0x0000E1C6L, 0x0000E282L, 0x0000E33CL, 0x0000E3F4L,
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0x0000E4AAL, 0x0000E55EL, 0x0000E610L, 0x0000E6BFL,
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0x0000E76CL, 0x0000E817L, 0x0000E8BFL, 0x0000E966L,
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0x0000EA0AL, 0x0000EAABL, 0x0000EB4BL, 0x0000EBE8L,
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0x0000EC83L, 0x0000ED1CL, 0x0000EDB3L, 0x0000EE47L,
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0x0000EED9L, 0x0000EF68L, 0x0000EFF5L, 0x0000F080L,
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0x0000F109L, 0x0000F18FL, 0x0000F213L, 0x0000F295L,
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0x0000F314L, 0x0000F391L, 0x0000F40CL, 0x0000F484L,
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0x0000F4FAL, 0x0000F56EL, 0x0000F5DFL, 0x0000F64EL,
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0x0000F6BAL, 0x0000F724L, 0x0000F78CL, 0x0000F7F1L,
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0x0000F854L, 0x0000F8B4L, 0x0000F913L, 0x0000F96EL,
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0x0000F9C8L, 0x0000FA1FL, 0x0000FA73L, 0x0000FAC5L,
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0x0000FB15L, 0x0000FB62L, 0x0000FBADL, 0x0000FBF5L,
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0x0000FC3BL, 0x0000FC7FL, 0x0000FCC0L, 0x0000FCFEL,
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0x0000FD3BL, 0x0000FD74L, 0x0000FDACL, 0x0000FDE1L,
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0x0000FE13L, 0x0000FE43L, 0x0000FE71L, 0x0000FE9CL,
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0x0000FEC4L, 0x0000FEEBL, 0x0000FF0EL, 0x0000FF30L,
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0x0000FF4EL, 0x0000FF6BL, 0x0000FF85L, 0x0000FF9CL,
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0x0000FFB1L, 0x0000FFC4L, 0x0000FFD4L, 0x0000FFE1L,
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0x0000FFECL, 0x0000FFF5L, 0x0000FFFBL, 0x0000FFFFL,
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0x00010000L,
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};
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/* pre-computed tan table for 1st quadrant */
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static const CoglFixed tan_tbl[] =
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{
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0x00000000L, 0x00000192L, 0x00000324L, 0x000004b7L,
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0x00000649L, 0x000007dbL, 0x0000096eL, 0x00000b01L,
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0x00000c94L, 0x00000e27L, 0x00000fbaL, 0x0000114eL,
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0x000012e2L, 0x00001477L, 0x0000160cL, 0x000017a1L,
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0x00001937L, 0x00001acdL, 0x00001c64L, 0x00001dfbL,
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0x00001f93L, 0x0000212cL, 0x000022c5L, 0x0000245fL,
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0x000025f9L, 0x00002795L, 0x00002931L, 0x00002aceL,
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0x00002c6cL, 0x00002e0aL, 0x00002faaL, 0x0000314aL,
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0x000032ecL, 0x0000348eL, 0x00003632L, 0x000037d7L,
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0x0000397dL, 0x00003b24L, 0x00003cccL, 0x00003e75L,
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0x00004020L, 0x000041ccL, 0x00004379L, 0x00004528L,
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0x000046d8L, 0x0000488aL, 0x00004a3dL, 0x00004bf2L,
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0x00004da8L, 0x00004f60L, 0x0000511aL, 0x000052d5L,
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0x00005492L, 0x00005651L, 0x00005812L, 0x000059d5L,
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0x00005b99L, 0x00005d60L, 0x00005f28L, 0x000060f3L,
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0x000062c0L, 0x0000648fL, 0x00006660L, 0x00006834L,
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0x00006a0aL, 0x00006be2L, 0x00006dbdL, 0x00006f9aL,
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0x0000717aL, 0x0000735dL, 0x00007542L, 0x0000772aL,
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0x00007914L, 0x00007b02L, 0x00007cf2L, 0x00007ee6L,
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0x000080dcL, 0x000082d6L, 0x000084d2L, 0x000086d2L,
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0x000088d6L, 0x00008adcL, 0x00008ce7L, 0x00008ef4L,
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0x00009106L, 0x0000931bL, 0x00009534L, 0x00009750L,
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0x00009971L, 0x00009b95L, 0x00009dbeL, 0x00009febL,
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0x0000a21cL, 0x0000a452L, 0x0000a68cL, 0x0000a8caL,
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0x0000ab0eL, 0x0000ad56L, 0x0000afa3L, 0x0000b1f5L,
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0x0000b44cL, 0x0000b6a8L, 0x0000b909L, 0x0000bb70L,
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0x0000bdddL, 0x0000c04fL, 0x0000c2c7L, 0x0000c545L,
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0x0000c7c9L, 0x0000ca53L, 0x0000cce3L, 0x0000cf7aL,
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0x0000d218L, 0x0000d4bcL, 0x0000d768L, 0x0000da1aL,
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0x0000dcd4L, 0x0000df95L, 0x0000e25eL, 0x0000e52eL,
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0x0000e806L, 0x0000eae7L, 0x0000edd0L, 0x0000f0c1L,
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0x0000f3bbL, 0x0000f6bfL, 0x0000f9cbL, 0x0000fce1L,
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0x00010000L, 0x00010329L, 0x0001065dL, 0x0001099aL,
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0x00010ce3L, 0x00011036L, 0x00011394L, 0x000116feL,
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0x00011a74L, 0x00011df6L, 0x00012184L, 0x0001251fL,
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0x000128c6L, 0x00012c7cL, 0x0001303fL, 0x00013410L,
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0x000137f0L, 0x00013bdfL, 0x00013fddL, 0x000143ebL,
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0x00014809L, 0x00014c37L, 0x00015077L, 0x000154c9L,
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0x0001592dL, 0x00015da4L, 0x0001622eL, 0x000166ccL,
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0x00016b7eL, 0x00017045L, 0x00017523L, 0x00017a17L,
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0x00017f22L, 0x00018444L, 0x00018980L, 0x00018ed5L,
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0x00019445L, 0x000199cfL, 0x00019f76L, 0x0001a53aL,
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0x0001ab1cL, 0x0001b11dL, 0x0001b73fL, 0x0001bd82L,
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0x0001c3e7L, 0x0001ca71L, 0x0001d11fL, 0x0001d7f4L,
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0x0001def1L, 0x0001e618L, 0x0001ed6aL, 0x0001f4e8L,
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0x0001fc96L, 0x00020473L, 0x00020c84L, 0x000214c9L,
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0x00021d44L, 0x000225f9L, 0x00022ee9L, 0x00023818L,
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0x00024187L, 0x00024b3aL, 0x00025534L, 0x00025f78L,
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0x00026a0aL, 0x000274edL, 0x00028026L, 0x00028bb8L,
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0x000297a8L, 0x0002a3fbL, 0x0002b0b5L, 0x0002bdddL,
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0x0002cb79L, 0x0002d98eL, 0x0002e823L, 0x0002f740L,
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0x000306ecL, 0x00031730L, 0x00032816L, 0x000339a6L,
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0x00034bebL, 0x00035ef2L, 0x000372c6L, 0x00038776L,
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0x00039d11L, 0x0003b3a6L, 0x0003cb48L, 0x0003e40aL,
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0x0003fe02L, 0x00041949L, 0x000435f7L, 0x0004542bL,
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0x00047405L, 0x000495a9L, 0x0004b940L, 0x0004def6L,
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0x00050700L, 0x00053196L, 0x00055ef9L, 0x00058f75L,
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0x0005c35dL, 0x0005fb14L, 0x00063709L, 0x000677c0L,
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0x0006bdd0L, 0x000709ecL, 0x00075ce6L, 0x0007b7bbL,
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0x00081b98L, 0x000889e9L, 0x0009046eL, 0x00098d4dL,
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0x000a2736L, 0x000ad593L, 0x000b9cc6L, 0x000c828aL,
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0x000d8e82L, 0x000ecb1bL, 0x001046eaL, 0x00121703L,
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0x00145b00L, 0x0017448dL, 0x001b2672L, 0x002095afL,
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0x0028bc49L, 0x0036519aL, 0x00517bb6L, 0x00a2f8fdL,
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0x46d3eab2L,
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};
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/* 257-value table of atan.
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*
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* atan_tbl[0] is atan(0.0) and atan_tbl[256] is atan(1).
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* The angles are radians in CoglFixed truncated to 16-bit (they're
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* all less than one)
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*/
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static const guint16 atan_tbl[] =
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{
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0x0000, 0x00FF, 0x01FF, 0x02FF, 0x03FF, 0x04FF, 0x05FF, 0x06FF,
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0x07FF, 0x08FF, 0x09FE, 0x0AFE, 0x0BFD, 0x0CFD, 0x0DFC, 0x0EFB,
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0x0FFA, 0x10F9, 0x11F8, 0x12F7, 0x13F5, 0x14F3, 0x15F2, 0x16F0,
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0x17EE, 0x18EB, 0x19E9, 0x1AE6, 0x1BE3, 0x1CE0, 0x1DDD, 0x1ED9,
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0x1FD5, 0x20D1, 0x21CD, 0x22C8, 0x23C3, 0x24BE, 0x25B9, 0x26B3,
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0x27AD, 0x28A7, 0x29A1, 0x2A9A, 0x2B93, 0x2C8B, 0x2D83, 0x2E7B,
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0x2F72, 0x306A, 0x3160, 0x3257, 0x334D, 0x3442, 0x3538, 0x362D,
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0x3721, 0x3815, 0x3909, 0x39FC, 0x3AEF, 0x3BE2, 0x3CD4, 0x3DC5,
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0x3EB6, 0x3FA7, 0x4097, 0x4187, 0x4277, 0x4365, 0x4454, 0x4542,
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0x462F, 0x471C, 0x4809, 0x48F5, 0x49E0, 0x4ACB, 0x4BB6, 0x4CA0,
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0x4D89, 0x4E72, 0x4F5B, 0x5043, 0x512A, 0x5211, 0x52F7, 0x53DD,
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0x54C2, 0x55A7, 0x568B, 0x576F, 0x5852, 0x5934, 0x5A16, 0x5AF7,
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0x5BD8, 0x5CB8, 0x5D98, 0x5E77, 0x5F55, 0x6033, 0x6110, 0x61ED,
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0x62C9, 0x63A4, 0x647F, 0x6559, 0x6633, 0x670C, 0x67E4, 0x68BC,
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0x6993, 0x6A6A, 0x6B40, 0x6C15, 0x6CEA, 0x6DBE, 0x6E91, 0x6F64,
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0x7036, 0x7108, 0x71D9, 0x72A9, 0x7379, 0x7448, 0x7516, 0x75E4,
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0x76B1, 0x777E, 0x7849, 0x7915, 0x79DF, 0x7AA9, 0x7B72, 0x7C3B,
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0x7D03, 0x7DCA, 0x7E91, 0x7F57, 0x801C, 0x80E1, 0x81A5, 0x8269,
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0x832B, 0x83EE, 0x84AF, 0x8570, 0x8630, 0x86F0, 0x87AF, 0x886D,
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0x892A, 0x89E7, 0x8AA4, 0x8B5F, 0x8C1A, 0x8CD5, 0x8D8E, 0x8E47,
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0x8F00, 0x8FB8, 0x906F, 0x9125, 0x91DB, 0x9290, 0x9345, 0x93F9,
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0x94AC, 0x955F, 0x9611, 0x96C2, 0x9773, 0x9823, 0x98D2, 0x9981,
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0x9A2F, 0x9ADD, 0x9B89, 0x9C36, 0x9CE1, 0x9D8C, 0x9E37, 0x9EE0,
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0x9F89, 0xA032, 0xA0DA, 0xA181, 0xA228, 0xA2CE, 0xA373, 0xA418,
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0xA4BC, 0xA560, 0xA602, 0xA6A5, 0xA746, 0xA7E8, 0xA888, 0xA928,
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0xA9C7, 0xAA66, 0xAB04, 0xABA1, 0xAC3E, 0xACDB, 0xAD76, 0xAE11,
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0xAEAC, 0xAF46, 0xAFDF, 0xB078, 0xB110, 0xB1A7, 0xB23E, 0xB2D5,
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0xB36B, 0xB400, 0xB495, 0xB529, 0xB5BC, 0xB64F, 0xB6E2, 0xB773,
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0xB805, 0xB895, 0xB926, 0xB9B5, 0xBA44, 0xBAD3, 0xBB61, 0xBBEE,
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0xBC7B, 0xBD07, 0xBD93, 0xBE1E, 0xBEA9, 0xBF33, 0xBFBC, 0xC046,
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0xC0CE, 0xC156, 0xC1DD, 0xC264, 0xC2EB, 0xC371, 0xC3F6, 0xC47B,
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0xC4FF, 0xC583, 0xC606, 0xC689, 0xC70B, 0xC78D, 0xC80E, 0xC88F,
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0xC90F
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};
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/* look up table for square root */
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static const CoglFixed sqrt_tbl[] =
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{
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0x00000000L, 0x00010000L, 0x00016A0AL, 0x0001BB68L,
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0x00020000L, 0x00023C6FL, 0x00027312L, 0x0002A550L,
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0x0002D414L, 0x00030000L, 0x0003298BL, 0x0003510EL,
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0x000376CFL, 0x00039B05L, 0x0003BDDDL, 0x0003DF7CL,
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0x00040000L, 0x00041F84L, 0x00043E1EL, 0x00045BE1L,
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0x000478DEL, 0x00049524L, 0x0004B0BFL, 0x0004CBBCL,
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0x0004E624L, 0x00050000L, 0x00051959L, 0x00053237L,
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0x00054AA0L, 0x0005629AL, 0x00057A2BL, 0x00059159L,
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0x0005A828L, 0x0005BE9CL, 0x0005D4B9L, 0x0005EA84L,
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0x00060000L, 0x00061530L, 0x00062A17L, 0x00063EB8L,
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0x00065316L, 0x00066733L, 0x00067B12L, 0x00068EB4L,
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0x0006A21DL, 0x0006B54DL, 0x0006C847L, 0x0006DB0CL,
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0x0006ED9FL, 0x00070000L, 0x00071232L, 0x00072435L,
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0x0007360BL, 0x000747B5L, 0x00075935L, 0x00076A8CL,
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0x00077BBBL, 0x00078CC2L, 0x00079DA3L, 0x0007AE60L,
|
|
0x0007BEF8L, 0x0007CF6DL, 0x0007DFBFL, 0x0007EFF0L,
|
|
0x00080000L, 0x00080FF0L, 0x00081FC1L, 0x00082F73L,
|
|
0x00083F08L, 0x00084E7FL, 0x00085DDAL, 0x00086D18L,
|
|
0x00087C3BL, 0x00088B44L, 0x00089A32L, 0x0008A906L,
|
|
0x0008B7C2L, 0x0008C664L, 0x0008D4EEL, 0x0008E361L,
|
|
0x0008F1BCL, 0x00090000L, 0x00090E2EL, 0x00091C45L,
|
|
0x00092A47L, 0x00093834L, 0x0009460CL, 0x000953CFL,
|
|
0x0009617EL, 0x00096F19L, 0x00097CA1L, 0x00098A16L,
|
|
0x00099777L, 0x0009A4C6L, 0x0009B203L, 0x0009BF2EL,
|
|
0x0009CC47L, 0x0009D94FL, 0x0009E645L, 0x0009F32BL,
|
|
0x000A0000L, 0x000A0CC5L, 0x000A1979L, 0x000A261EL,
|
|
0x000A32B3L, 0x000A3F38L, 0x000A4BAEL, 0x000A5816L,
|
|
0x000A646EL, 0x000A70B8L, 0x000A7CF3L, 0x000A8921L,
|
|
0x000A9540L, 0x000AA151L, 0x000AAD55L, 0x000AB94BL,
|
|
0x000AC534L, 0x000AD110L, 0x000ADCDFL, 0x000AE8A1L,
|
|
0x000AF457L, 0x000B0000L, 0x000B0B9DL, 0x000B172DL,
|
|
0x000B22B2L, 0x000B2E2BL, 0x000B3998L, 0x000B44F9L,
|
|
0x000B504FL, 0x000B5B9AL, 0x000B66D9L, 0x000B720EL,
|
|
0x000B7D37L, 0x000B8856L, 0x000B936AL, 0x000B9E74L,
|
|
0x000BA973L, 0x000BB467L, 0x000BBF52L, 0x000BCA32L,
|
|
0x000BD508L, 0x000BDFD5L, 0x000BEA98L, 0x000BF551L,
|
|
0x000C0000L, 0x000C0AA6L, 0x000C1543L, 0x000C1FD6L,
|
|
0x000C2A60L, 0x000C34E1L, 0x000C3F59L, 0x000C49C8L,
|
|
0x000C542EL, 0x000C5E8CL, 0x000C68E0L, 0x000C732DL,
|
|
0x000C7D70L, 0x000C87ACL, 0x000C91DFL, 0x000C9C0AL,
|
|
0x000CA62CL, 0x000CB047L, 0x000CBA59L, 0x000CC464L,
|
|
0x000CCE66L, 0x000CD861L, 0x000CE254L, 0x000CEC40L,
|
|
0x000CF624L, 0x000D0000L, 0x000D09D5L, 0x000D13A2L,
|
|
0x000D1D69L, 0x000D2727L, 0x000D30DFL, 0x000D3A90L,
|
|
0x000D4439L, 0x000D4DDCL, 0x000D5777L, 0x000D610CL,
|
|
0x000D6A9AL, 0x000D7421L, 0x000D7DA1L, 0x000D871BL,
|
|
0x000D908EL, 0x000D99FAL, 0x000DA360L, 0x000DACBFL,
|
|
0x000DB618L, 0x000DBF6BL, 0x000DC8B7L, 0x000DD1FEL,
|
|
0x000DDB3DL, 0x000DE477L, 0x000DEDABL, 0x000DF6D8L,
|
|
0x000E0000L, 0x000E0922L, 0x000E123DL, 0x000E1B53L,
|
|
0x000E2463L, 0x000E2D6DL, 0x000E3672L, 0x000E3F70L,
|
|
0x000E4869L, 0x000E515DL, 0x000E5A4BL, 0x000E6333L,
|
|
0x000E6C16L, 0x000E74F3L, 0x000E7DCBL, 0x000E869DL,
|
|
0x000E8F6BL, 0x000E9832L, 0x000EA0F5L, 0x000EA9B2L,
|
|
0x000EB26BL, 0x000EBB1EL, 0x000EC3CBL, 0x000ECC74L,
|
|
0x000ED518L, 0x000EDDB7L, 0x000EE650L, 0x000EEEE5L,
|
|
0x000EF775L, 0x000F0000L, 0x000F0886L, 0x000F1107L,
|
|
0x000F1984L, 0x000F21FCL, 0x000F2A6FL, 0x000F32DDL,
|
|
0x000F3B47L, 0x000F43ACL, 0x000F4C0CL, 0x000F5468L,
|
|
0x000F5CBFL, 0x000F6512L, 0x000F6D60L, 0x000F75AAL,
|
|
0x000F7DEFL, 0x000F8630L, 0x000F8E6DL, 0x000F96A5L,
|
|
0x000F9ED9L, 0x000FA709L, 0x000FAF34L, 0x000FB75BL,
|
|
0x000FBF7EL, 0x000FC79DL, 0x000FCFB7L, 0x000FD7CEL,
|
|
0x000FDFE0L, 0x000FE7EEL, 0x000FEFF8L, 0x000FF7FEL,
|
|
0x00100000L,
|
|
};
|
|
|
|
/* the difference of the angle for two adjacent values in the
|
|
* sin_tbl table, expressed as CoglFixed number
|
|
*/
|
|
static const int sin_tbl_size = G_N_ELEMENTS (sin_tbl) - 1;
|
|
|
|
static const double _magic = 68719476736.0 * 1.5;
|
|
|
|
/* Where in the 64 bits of double is the mantissa.
|
|
*
|
|
* FIXME - this should go inside the configure.ac
|
|
*/
|
|
#if (__FLOAT_WORD_ORDER == 1234)
|
|
#define _COGL_MAN 0
|
|
#elif (__FLOAT_WORD_ORDER == 4321)
|
|
#define _COGL_MAN 1
|
|
#else
|
|
#define COGL_NO_FAST_CONVERSIONS
|
|
#endif
|
|
|
|
/*
|
|
* cogl_double_to_fixed :
|
|
* @value: value to be converted
|
|
*
|
|
* A fast conversion from double precision floating to fixed point
|
|
*
|
|
* Return value: Fixed point representation of the value
|
|
*/
|
|
CoglFixed
|
|
cogl_double_to_fixed (double val)
|
|
{
|
|
#ifdef COGL_NO_FAST_CONVERSIONS
|
|
return (CoglFixed) (val * (double) COGL_FIXED_1);
|
|
#else
|
|
union {
|
|
double d;
|
|
unsigned int i[2];
|
|
} dbl;
|
|
|
|
dbl.d = val;
|
|
dbl.d = dbl.d + _magic;
|
|
|
|
return dbl.i[_COGL_MAN];
|
|
#endif
|
|
}
|
|
|
|
/*
|
|
* cogl_double_to_int :
|
|
* @value: value to be converted
|
|
*
|
|
* A fast conversion from doulbe precision floatint point to int;
|
|
* used this instead of casting double/float to int.
|
|
*
|
|
* Return value: Integer part of the double
|
|
*/
|
|
int
|
|
cogl_double_to_int (double val)
|
|
{
|
|
#ifdef COGL_NO_FAST_CONVERSIONS
|
|
return (int) (val);
|
|
#else
|
|
union {
|
|
double d;
|
|
unsigned int i[2];
|
|
} dbl;
|
|
|
|
dbl.d = val;
|
|
dbl.d = dbl.d + _magic;
|
|
|
|
return ((int) dbl.i[_COGL_MAN]) >> 16;
|
|
#endif
|
|
}
|
|
|
|
unsigned int
|
|
cogl_double_to_uint (double val)
|
|
{
|
|
#ifdef COGL_NO_FAST_CONVERSIONS
|
|
return (unsigned int)(val);
|
|
#else
|
|
union {
|
|
double d;
|
|
unsigned int i[2];
|
|
} dbl;
|
|
|
|
dbl.d = val;
|
|
dbl.d = dbl.d + _magic;
|
|
|
|
return (dbl.i[_COGL_MAN]) >> 16;
|
|
#endif
|
|
}
|
|
|
|
#undef _COGL_MAN
|
|
|
|
CoglFixed
|
|
cogl_fixed_sin (CoglFixed angle)
|
|
{
|
|
int sign = 1, indx1, indx2;
|
|
CoglFixed low, high;
|
|
CoglFixed p1, p2;
|
|
CoglFixed d1, d2;
|
|
|
|
/* convert negative angle to positive + sign */
|
|
if ((int) angle < 0)
|
|
{
|
|
sign = -sign;
|
|
angle = -angle;
|
|
}
|
|
|
|
/* reduce to <0, 2*pi) */
|
|
angle = angle % COGL_FIXED_2_PI;
|
|
|
|
/* reduce to first quadrant and sign */
|
|
if (angle > COGL_FIXED_PI)
|
|
{
|
|
sign = -sign;
|
|
|
|
if (angle > COGL_FIXED_PI + COGL_FIXED_PI_2)
|
|
{
|
|
/* fourth qudrant */
|
|
angle = COGL_FIXED_2_PI - angle;
|
|
}
|
|
else
|
|
{
|
|
/* third quadrant */
|
|
angle -= COGL_FIXED_PI;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if (angle > COGL_FIXED_PI_2)
|
|
{
|
|
/* second quadrant */
|
|
angle = COGL_FIXED_PI - angle;
|
|
}
|
|
}
|
|
|
|
/* Calculate indices of the two nearest values in our table
|
|
* and return weighted average.
|
|
*
|
|
* We multiple first than divide to preserve precision. Since
|
|
* angle is in the first quadrant, angle * SIN_TBL_SIZE (=256)
|
|
* can't overflow.
|
|
*
|
|
* Handle the end of the table gracefully
|
|
*/
|
|
indx1 = (angle * sin_tbl_size) / COGL_FIXED_PI_2;
|
|
|
|
if (indx1 == sin_tbl_size)
|
|
{
|
|
indx2 = indx1;
|
|
indx1 = indx2 - 1;
|
|
}
|
|
else
|
|
{
|
|
indx2 = indx1 + 1;
|
|
}
|
|
|
|
low = sin_tbl[indx1];
|
|
high = sin_tbl[indx2];
|
|
|
|
/* Again multiply the divide; no danger of overflow */
|
|
p1 = (indx1 * COGL_FIXED_PI_2) / sin_tbl_size;
|
|
p2 = (indx2 * COGL_FIXED_PI_2) / sin_tbl_size;
|
|
d1 = angle - p1;
|
|
d2 = p2 - angle;
|
|
|
|
angle = ((low * d2 + high * d1) / (p2 - p1));
|
|
|
|
if (sign < 0)
|
|
angle = -angle;
|
|
|
|
return angle;
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_angle_sin (CoglAngle angle)
|
|
{
|
|
int sign = 1;
|
|
CoglFixed result;
|
|
|
|
/* reduce negative angle to positive + sign */
|
|
if (angle < 0)
|
|
{
|
|
sign = -sign;
|
|
angle = -angle;
|
|
}
|
|
|
|
/* reduce to <0, 2*pi) */
|
|
angle &= 0x3ff;
|
|
|
|
/* reduce to first quadrant and sign */
|
|
if (angle > 512)
|
|
{
|
|
sign = -sign;
|
|
|
|
if (angle > 768)
|
|
{
|
|
/* fourth qudrant */
|
|
angle = 1024 - angle;
|
|
}
|
|
else
|
|
{
|
|
/* third quadrant */
|
|
angle -= 512;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if (angle > 256)
|
|
{
|
|
/* second quadrant */
|
|
angle = 512 - angle;
|
|
}
|
|
}
|
|
|
|
result = sin_tbl[angle];
|
|
|
|
if (sign < 0)
|
|
result = -result;
|
|
|
|
return result;
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_tan (CoglFixed angle)
|
|
{
|
|
return cogl_angle_tan (COGL_ANGLE_FROM_DEGX (angle));
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_angle_tan (CoglAngle angle)
|
|
{
|
|
int sign = 1;
|
|
CoglFixed result;
|
|
|
|
/* reduce negative angle to positive + sign */
|
|
if (angle < 0)
|
|
{
|
|
sign = -sign;
|
|
angle = -angle;
|
|
}
|
|
|
|
/* reduce to <0, pi) */
|
|
angle &= 0x1ff;
|
|
|
|
/* reduce to first quadrant and sign */
|
|
if (angle > 256)
|
|
{
|
|
sign = -sign;
|
|
angle = 512 - angle;
|
|
}
|
|
|
|
result = tan_tbl[angle];
|
|
|
|
if (sign < 0)
|
|
result = -result;
|
|
|
|
return result;
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_atan (CoglFixed x)
|
|
{
|
|
gboolean negative = FALSE;
|
|
CoglFixed angle;
|
|
|
|
if (x < 0)
|
|
{
|
|
negative = TRUE;
|
|
x = -x;
|
|
}
|
|
|
|
if (x > COGL_FIXED_1)
|
|
{
|
|
/* if x > 1 then atan(x) = pi/2 - atan(1/x) */
|
|
angle = COGL_FIXED_PI / 2
|
|
- atan_tbl[COGL_FIXED_DIV (COGL_FIXED_1, x) >> 8];
|
|
}
|
|
else
|
|
angle = atan_tbl[x >> 8];
|
|
|
|
return negative ? -angle : angle;
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_atan2 (CoglFixed y, CoglFixed x)
|
|
{
|
|
CoglFixed angle;
|
|
|
|
if (x == 0)
|
|
angle = y >= 0 ? COGL_FIXED_PI_2 : -COGL_FIXED_PI_2;
|
|
else
|
|
{
|
|
angle = cogl_fixed_atan (COGL_FIXED_DIV (y, x));
|
|
|
|
if (x < 0)
|
|
angle += y >= 0 ? COGL_FIXED_PI : -COGL_FIXED_PI;
|
|
}
|
|
|
|
return angle;
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_sqrt (CoglFixed x)
|
|
{
|
|
/* The idea for this comes from the Alegro library, exploiting the
|
|
* fact that,
|
|
* sqrt (x) = sqrt (x/d) * sqrt (d);
|
|
*
|
|
* For d == 2^(n):
|
|
*
|
|
* sqrt (x) = sqrt (x/2^(2n)) * 2^n
|
|
*
|
|
* By locating suitable n for given x such that x >> 2n is in <0,255>
|
|
* we can use a LUT of precomputed values.
|
|
*
|
|
* This algorithm provides both good performance and precision;
|
|
* on ARM this function is about 5 times faster than c-lib sqrt,
|
|
* whilst producing errors < 1%.
|
|
*/
|
|
int t = 0;
|
|
int sh = 0;
|
|
unsigned int mask = 0x40000000;
|
|
unsigned fract = x & 0x0000ffff;
|
|
unsigned int d1, d2;
|
|
CoglFixed v1, v2;
|
|
|
|
if (x <= 0)
|
|
return 0;
|
|
|
|
if (x > COGL_FIXED_255 || x < COGL_FIXED_1)
|
|
{
|
|
/*
|
|
* Find the highest bit set
|
|
*/
|
|
#if __arm__
|
|
/* This actually requires at least arm v5, but gcc does not seem
|
|
* to set the architecture defines correctly, and it is I think
|
|
* very unlikely that anyone will want to use clutter on anything
|
|
* less than v5.
|
|
*/
|
|
int bit;
|
|
__asm__ ("clz %0, %1\n"
|
|
"rsb %0, %0, #31\n"
|
|
:"=r"(bit)
|
|
:"r" (x));
|
|
|
|
/* make even (2n) */
|
|
bit &= 0xfffffffe;
|
|
#else
|
|
/* TODO -- add i386 branch using bshr
|
|
*
|
|
* NB: it's been said that the bshr instruction is poorly implemented
|
|
* and that it is possible to write a faster code in C using binary
|
|
* search -- at some point we should explore this
|
|
*/
|
|
int bit = 30;
|
|
while (bit >= 0)
|
|
{
|
|
if (x & mask)
|
|
break;
|
|
|
|
mask = (mask >> 1 | mask >> 2);
|
|
bit -= 2;
|
|
}
|
|
#endif
|
|
|
|
/* now bit indicates the highest bit set; there are two scenarios
|
|
*
|
|
* 1) bit < 23: Our number is smaller so we shift it left to maximase
|
|
* precision (< 16 really, since <16,23> never goes
|
|
* through here.
|
|
*
|
|
* 2) bit > 23: our number is above the table, so we shift right
|
|
*/
|
|
|
|
sh = ((bit - 22) >> 1);
|
|
if (bit >= 8)
|
|
t = (x >> (16 - 22 + bit));
|
|
else
|
|
t = (x << (22 - 16 - bit));
|
|
}
|
|
else
|
|
{
|
|
t = COGL_FIXED_TO_INT (x);
|
|
}
|
|
|
|
/* Do a weighted average of the two nearest values */
|
|
v1 = sqrt_tbl[t];
|
|
v2 = sqrt_tbl[t+1];
|
|
|
|
/*
|
|
* 12 is fairly arbitrary -- we want integer that is not too big to cost
|
|
* us precision
|
|
*/
|
|
d1 = (unsigned)(fract) >> 12;
|
|
d2 = ((unsigned)COGL_FIXED_1 >> 12) - d1;
|
|
|
|
x = ((v1*d2) + (v2*d1))/(COGL_FIXED_1 >> 12);
|
|
|
|
if (sh > 0)
|
|
x = x << sh;
|
|
else if (sh < 0)
|
|
x = x >> -sh;
|
|
|
|
return x;
|
|
}
|
|
|
|
/**
|
|
* cogl_sqrti:
|
|
* @x: integer value
|
|
*
|
|
* Very fast fixed point implementation of square root for integers.
|
|
*
|
|
* This function is at least 6x faster than clib sqrt() on x86, and (this is
|
|
* not a typo!) about 500x faster on ARM without FPU. It's error is < 5%
|
|
* for arguments < %COGL_SQRTI_ARG_5_PERCENT and < 10% for arguments <
|
|
* %COGL_SQRTI_ARG_10_PERCENT. The maximum argument that can be passed to
|
|
* this function is COGL_SQRTI_ARG_MAX.
|
|
*
|
|
* Return value: integer square root.
|
|
*
|
|
*
|
|
* Since: 0.2
|
|
*/
|
|
int
|
|
cogl_sqrti (int number)
|
|
{
|
|
#if defined __SSE2__
|
|
/* The GCC built-in with SSE2 (sqrtsd) is up to twice as fast as
|
|
* the pure integer code below. It is also more accurate.
|
|
*/
|
|
return __builtin_sqrt (number);
|
|
#else
|
|
/* This is a fixed point implementation of the Quake III sqrt algorithm,
|
|
* described, for example, at
|
|
* http://www.codemaestro.com/reviews/review00000105.html
|
|
*
|
|
* While the original QIII is extremely fast, the use of floating division
|
|
* and multiplication makes it perform very on arm processors without FPU.
|
|
*
|
|
* The key to successfully replacing the floating point operations with
|
|
* fixed point is in the choice of the fixed point format. The QIII
|
|
* algorithm does not calculate the square root, but its reciprocal ('y'
|
|
* below), which is only at the end turned to the inverse value. In order
|
|
* for the algorithm to produce satisfactory results, the reciprocal value
|
|
* must be represented with sufficient precission; the 16.16 we use
|
|
* elsewhere in clutter is not good enough, and 10.22 is used instead.
|
|
*/
|
|
CoglFixed x;
|
|
guint32 y_1; /* 10.22 fixed point */
|
|
guint32 f = 0x600000; /* '1.5' as 10.22 fixed */
|
|
|
|
union
|
|
{
|
|
float f;
|
|
guint32 i;
|
|
} flt, flt2;
|
|
|
|
flt.f = number;
|
|
|
|
x = COGL_FIXED_FROM_INT (number) / 2;
|
|
|
|
/* The QIII initial estimate */
|
|
flt.i = 0x5f3759df - ( flt.i >> 1 );
|
|
|
|
/* Now, we convert the float to 10.22 fixed. We exploit the mechanism
|
|
* described at http://www.d6.com/users/checker/pdfs/gdmfp.pdf.
|
|
*
|
|
* We want 22 bit fraction; a single precission float uses 23 bit
|
|
* mantisa, so we only need to add 2^(23-22) (no need for the 1.5
|
|
* multiplier as we are only dealing with positive numbers).
|
|
*
|
|
* Note: we have to use two separate variables here -- for some reason,
|
|
* if we try to use just the flt variable, gcc on ARM optimises the whole
|
|
* addition out, and it all goes pear shape, since without it, the bits
|
|
* in the float will not be correctly aligned.
|
|
*/
|
|
flt2.f = flt.f + 2.0;
|
|
flt2.i &= 0x7FFFFF;
|
|
|
|
/* Now we correct the estimate */
|
|
y_1 = (flt2.i >> 11) * (flt2.i >> 11);
|
|
y_1 = (y_1 >> 8) * (x >> 8);
|
|
|
|
y_1 = f - y_1;
|
|
flt2.i = (flt2.i >> 11) * (y_1 >> 11);
|
|
|
|
/* If the original argument is less than 342, we do another
|
|
* iteration to improve precission (for arguments >= 342, the single
|
|
* iteration produces generally better results).
|
|
*/
|
|
if (x < 171)
|
|
{
|
|
y_1 = (flt2.i >> 11) * (flt2.i >> 11);
|
|
y_1 = (y_1 >> 8) * (x >> 8);
|
|
|
|
y_1 = f - y_1;
|
|
flt2.i = (flt2.i >> 11) * (y_1 >> 11);
|
|
}
|
|
|
|
/* Invert, round and convert from 10.22 to an integer
|
|
* 0x1e3c68 is a magical rounding constant that produces slightly
|
|
* better results than 0x200000.
|
|
*/
|
|
return (number * flt2.i + 0x1e3c68) >> 22;
|
|
#endif
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_mul (CoglFixed a,
|
|
CoglFixed b)
|
|
{
|
|
#ifdef __arm__
|
|
/* This provides about 12% speedeup on the gcc -O2 optimised
|
|
* C version
|
|
*
|
|
* Based on code found in the following thread:
|
|
* http://lists.mplayerhq.hu/pipermail/ffmpeg-devel/2006-August/014405.html
|
|
*/
|
|
int res_low, res_hi;
|
|
|
|
__asm__ ("smull %0, %1, %2, %3 \n"
|
|
"mov %0, %0, lsr %4 \n"
|
|
"add %1, %0, %1, lsl %5 \n"
|
|
: "=r"(res_hi), "=r"(res_low) \
|
|
: "r"(a), "r"(b), "i"(COGL_FIXED_Q), "i"(32 - COGL_FIXED_Q));
|
|
|
|
return (CoglFixed) res_low;
|
|
#else
|
|
gint64 r = (gint64) a * (gint64) b;
|
|
|
|
return (CoglFixed) (r >> COGL_FIXED_Q);
|
|
#endif
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_div (CoglFixed a,
|
|
CoglFixed b)
|
|
{
|
|
return (CoglFixed) ((((gint64) a) << COGL_FIXED_Q) / b);
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_mul_div (CoglFixed a,
|
|
CoglFixed b,
|
|
CoglFixed c)
|
|
{
|
|
CoglFixed ab = cogl_fixed_mul (a, b);
|
|
CoglFixed quo = cogl_fixed_div (ab, c);
|
|
|
|
return quo;
|
|
}
|
|
|
|
/*
|
|
* The log2x() and pow2x() functions
|
|
*
|
|
* The implementation of the log2x() and pow2x() exploits the
|
|
* well-documented fact that the exponent part of IEEE floating
|
|
* number provides a good estimate of log2 of that number, while
|
|
* the mantissa serves as a good error-correction.
|
|
*
|
|
* The implementation here uses a quadratic error correction as
|
|
* described by Ian Stephenson at:
|
|
* http://www.dctsystems.co.uk/Software/power.html.
|
|
*/
|
|
|
|
CoglFixed
|
|
cogl_fixed_log2 (unsigned int x)
|
|
{
|
|
/* Note: we could easily have a version for CoglFixed x, but the int
|
|
* precision is enough for the current purposes.
|
|
*/
|
|
union
|
|
{
|
|
float f;
|
|
CoglFixed i;
|
|
} flt;
|
|
|
|
CoglFixed magic = 0x58bb;
|
|
CoglFixed y;
|
|
|
|
/*
|
|
* Convert x to float, then extract exponent.
|
|
*
|
|
* We want the result to be 16.16 fixed, so we shift (23-16) bits only
|
|
*/
|
|
flt.f = x;
|
|
flt.i >>= 7;
|
|
flt.i -= COGL_FIXED_FROM_INT (127);
|
|
|
|
y = COGL_FIXED_FRACTION (flt.i);
|
|
|
|
y = COGL_FIXED_MUL ((y - COGL_FIXED_MUL (y, y)), magic);
|
|
|
|
return flt.i + y;
|
|
}
|
|
|
|
unsigned int
|
|
cogl_fixed_pow2 (CoglFixed x)
|
|
{
|
|
/* Note: we could easily have a version that produces CoglFixed result,
|
|
* but the the range would be limited to x < 15, and the int precision
|
|
* is enough for the current purposes.
|
|
*/
|
|
|
|
union
|
|
{
|
|
float f;
|
|
guint32 i;
|
|
} flt;
|
|
|
|
CoglFixed magic = 0x56f7;
|
|
CoglFixed y;
|
|
|
|
flt.i = x;
|
|
|
|
/*
|
|
* Reverse of the log2x function -- convert the fixed value to a suitable
|
|
* floating point exponent, and mantisa adjusted with quadratic error
|
|
* correction y.
|
|
*/
|
|
y = COGL_FIXED_FRACTION (x);
|
|
y = COGL_FIXED_MUL ((y - COGL_FIXED_MUL (y, y)), magic);
|
|
|
|
/* Shift the exponent into it's position in the floating point
|
|
* representation; as our number is not int but 16.16 fixed, shift only
|
|
* by (23 - 16)
|
|
*/
|
|
flt.i += (COGL_FIXED_FROM_INT (127) - y);
|
|
flt.i <<= 7;
|
|
|
|
return COGL_FLOAT_TO_UINT (flt.f);
|
|
}
|
|
|
|
unsigned int
|
|
cogl_fixed_pow (unsigned int x,
|
|
CoglFixed y)
|
|
{
|
|
return cogl_fixed_pow2 (COGL_FIXED_MUL (y, cogl_fixed_log2 (x)));
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_angle_cos (CoglAngle angle)
|
|
{
|
|
CoglAngle a = angle + 256;
|
|
|
|
return cogl_angle_sin (a);
|
|
}
|
|
|
|
CoglFixed
|
|
cogl_fixed_cos (CoglFixed angle)
|
|
{
|
|
CoglFixed a = angle + COGL_FIXED_PI_2;
|
|
|
|
return cogl_fixed_sin (a);
|
|
}
|