fixed point sqrt
This commit is contained in:
Tomas Frydrych
parent
2f0737491b
commit
9a28ac34cd
5 changed files with 311 additions and 15 deletions
12
ChangeLog
12
ChangeLog
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@ -1,3 +1,15 @@
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2007-01-17 Tomas Frydrych <tf@openedhand.com>
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* clutter/clutter-fixed.h:
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* clutter/clutter-fixed.c:
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* clutter/clutter-alpha.c:
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Renamed clutter_fixed_sin() to clutter_sinx() and
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clutter_angle_sin() to clutter_sini(); added clutter_sqrtx()
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and clutter_sqrti(); added missing copyright.
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* clutter/clutter-behavior.c:
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replaced call to sqrt() with clutter_sqrti()
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2007-01-16 Emmanuele Bassi <ebassi@openedhand.com>
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* clutter/clutter-feature.c: Use clutter_vblank_method() to
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@ -513,7 +513,7 @@ sincx1024_func (ClutterAlpha *alpha,
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*/
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x = (x << 9) - (512 / angle);
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sine = (clutter_angle_sin (x) + offset)/2;
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sine = (clutter_sini (x) + offset)/2;
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CLUTTER_NOTE (ALPHA, "sine: %2f\n", CLUTTER_FIXED_TO_DOUBLE (sine));
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@ -196,9 +196,8 @@ node_distance (const ClutterKnot *begin,
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if (clutter_knot_equal (begin, end))
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return 0;
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/* FIXME: need fixed point here */
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return sqrt ((end->x - begin->x) * (end->x - begin->x) +
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(end->y - begin->y) * (end->y - begin->y));
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return clutter_sqrti ((end->x - begin->x) * (end->x - begin->x) +
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(end->y - begin->y) * (end->y - begin->y));
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}
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static gint
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@ -1,3 +1,28 @@
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/*
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* Clutter.
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*
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* An OpenGL based 'interactive canvas' library.
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*
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* Authored By Matthew Allum <mallum@openedhand.com>
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*
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* Copyright (C) 2006 OpenedHand
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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, write to the
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* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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* Boston, MA 02111-1307, USA.
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*/
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#include <clutter-fixed.h>
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/* pre-computed sin table for 1st quadrant
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@ -85,7 +110,7 @@ static ClutterFixed sin_tbl [] =
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/**
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* clutter_fixed_sin:
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* clutter_sinx:
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* @angle: a #ClutterFixed angle in radians
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*
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* Fixed point implementation of sine function
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@ -95,7 +120,7 @@ static ClutterFixed sin_tbl [] =
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* Since: 0.2
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*/
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ClutterFixed
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clutter_fixed_sin (ClutterFixed angle)
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clutter_sinx (ClutterFixed angle)
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{
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int sign = 1, indx1, indx2;
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ClutterFixed low, high, d1, d2;
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@ -144,8 +169,6 @@ clutter_fixed_sin (ClutterFixed angle)
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* Handle the end of the table gracefully
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*/
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indx1 = CLUTTER_FIXED_DIV (angle, CFX_SIN_STEP);
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indx2;
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indx1 = CLUTTER_FIXED_INT (indx1);
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if (indx1 == sizeof (sin_tbl)/sizeof (ClutterFixed) - 1)
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@ -173,10 +196,10 @@ clutter_fixed_sin (ClutterFixed angle)
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}
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/**
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* clutter_angle_sin:
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* clutter_sini:
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* @angle: a #ClutterAngle
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*
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* Fast fixed point implementation of sine function.
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* Very fast fixed point implementation of sine function.
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*
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* ClutterAngle is an integer such that 1024 represents
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* full circle.
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@ -186,7 +209,7 @@ clutter_fixed_sin (ClutterFixed angle)
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* Since: 0.2
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*/
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ClutterFixed
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clutter_angle_sin (ClutterAngle angle)
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clutter_sini (ClutterAngle angle)
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{
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int sign = 1;
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ClutterFixed result;
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@ -232,3 +255,261 @@ clutter_angle_sin (ClutterAngle angle)
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return result;
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}
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ClutterFixed 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,
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0x0007BEF8L, 0x0007CF6DL, 0x0007DFBFL, 0x0007EFF0L,
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0x00080000L, 0x00080FF0L, 0x00081FC1L, 0x00082F73L,
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0x00083F08L, 0x00084E7FL, 0x00085DDAL, 0x00086D18L,
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0x00087C3BL, 0x00088B44L, 0x00089A32L, 0x0008A906L,
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0x0008B7C2L, 0x0008C664L, 0x0008D4EEL, 0x0008E361L,
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0x0008F1BCL, 0x00090000L, 0x00090E2EL, 0x00091C45L,
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0x00092A47L, 0x00093834L, 0x0009460CL, 0x000953CFL,
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0x0009617EL, 0x00096F19L, 0x00097CA1L, 0x00098A16L,
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0x00099777L, 0x0009A4C6L, 0x0009B203L, 0x0009BF2EL,
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0x0009CC47L, 0x0009D94FL, 0x0009E645L, 0x0009F32BL,
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0x000A0000L, 0x000A0CC5L, 0x000A1979L, 0x000A261EL,
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0x000A32B3L, 0x000A3F38L, 0x000A4BAEL, 0x000A5816L,
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0x000A646EL, 0x000A70B8L, 0x000A7CF3L, 0x000A8921L,
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0x000A9540L, 0x000AA151L, 0x000AAD55L, 0x000AB94BL,
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0x000AC534L, 0x000AD110L, 0x000ADCDFL, 0x000AE8A1L,
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0x000AF457L, 0x000B0000L, 0x000B0B9DL, 0x000B172DL,
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0x000B22B2L, 0x000B2E2BL, 0x000B3998L, 0x000B44F9L,
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0x000B504FL, 0x000B5B9AL, 0x000B66D9L, 0x000B720EL,
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0x000B7D37L, 0x000B8856L, 0x000B936AL, 0x000B9E74L,
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0x000BA973L, 0x000BB467L, 0x000BBF52L, 0x000BCA32L,
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0x000BD508L, 0x000BDFD5L, 0x000BEA98L, 0x000BF551L,
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0x000C0000L, 0x000C0AA6L, 0x000C1543L, 0x000C1FD6L,
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0x000C2A60L, 0x000C34E1L, 0x000C3F59L, 0x000C49C8L,
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0x000C542EL, 0x000C5E8CL, 0x000C68E0L, 0x000C732DL,
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0x000C7D70L, 0x000C87ACL, 0x000C91DFL, 0x000C9C0AL,
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0x000CA62CL, 0x000CB047L, 0x000CBA59L, 0x000CC464L,
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0x000CCE66L, 0x000CD861L, 0x000CE254L, 0x000CEC40L,
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0x000CF624L, 0x000D0000L, 0x000D09D5L, 0x000D13A2L,
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0x000D1D69L, 0x000D2727L, 0x000D30DFL, 0x000D3A90L,
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0x000D4439L, 0x000D4DDCL, 0x000D5777L, 0x000D610CL,
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0x000D6A9AL, 0x000D7421L, 0x000D7DA1L, 0x000D871BL,
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0x000D908EL, 0x000D99FAL, 0x000DA360L, 0x000DACBFL,
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0x000DB618L, 0x000DBF6BL, 0x000DC8B7L, 0x000DD1FEL,
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0x000DDB3DL, 0x000DE477L, 0x000DEDABL, 0x000DF6D8L,
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0x000E0000L, 0x000E0922L, 0x000E123DL, 0x000E1B53L,
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0x000E2463L, 0x000E2D6DL, 0x000E3672L, 0x000E3F70L,
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0x000E4869L, 0x000E515DL, 0x000E5A4BL, 0x000E6333L,
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0x000E6C16L, 0x000E74F3L, 0x000E7DCBL, 0x000E869DL,
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0x000E8F6BL, 0x000E9832L, 0x000EA0F5L, 0x000EA9B2L,
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0x000EB26BL, 0x000EBB1EL, 0x000EC3CBL, 0x000ECC74L,
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0x000ED518L, 0x000EDDB7L, 0x000EE650L, 0x000EEEE5L,
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0x000EF775L, 0x000F0000L, 0x000F0886L, 0x000F1107L,
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0x000F1984L, 0x000F21FCL, 0x000F2A6FL, 0x000F32DDL,
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0x000F3B47L, 0x000F43ACL, 0x000F4C0CL, 0x000F5468L,
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0x000F5CBFL, 0x000F6512L, 0x000F6D60L, 0x000F75AAL,
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0x000F7DEFL, 0x000F8630L, 0x000F8E6DL, 0x000F96A5L,
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0x000F9ED9L, 0x000FA709L, 0x000FAF34L, 0x000FB75BL,
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0x000FBF7EL, 0x000FC79DL, 0x000FCFB7L, 0x000FD7CEL,
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0x000FDFE0L, 0x000FE7EEL, 0x000FEFF8L, 0x000FF7FEL,
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0x00100000L,
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};
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/**
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* clutter_sqrtx:
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* @x: a #ClutterFixed
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*
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* A fixed point implementation of squre root
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*
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* Return value: square root (as fixed point).
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*
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* Since: 0.2
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*/
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ClutterFixed
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clutter_sqrtx (ClutterFixed x)
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{
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/* The idea for this comes from the Alegro library, exploiting the
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* fact that,
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* sqrt (x) = sqrt (x/d) * sqrt (d);
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*
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* For d == 2^(n):
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*
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* sqrt (x) = sqrt (x/2^(2n)) * 2^n
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*
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* By locating suitable n for given x such that x >> 2n is in <0,255>
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* we can use a LUT of precomputed values.
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*
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* This algorithm provides both good performance and precission;
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* on ARM this function is about 5 times faster than c-lib sqrt, whilst
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* producing errors < 1%.
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*
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* (There are faster algorithm's available; the Carmack 'magic'
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* algorithm, http://www.codemaestro.com/reviews/review00000105.html,
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* is about five times faster than this one when implemented
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* as fixed point, but it's error is much greater and grows with the
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* size of the argument (reaches about 10% around x == 800).
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*
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* Note: on systems with FPU, the clib sqrt can be noticeably faster
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* than this function.
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*/
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int t = 0;
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int sh = 0;
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unsigned int mask = 0x40000000;
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unsigned fract = x & 0x0000ffff;
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unsigned int d1, d2;
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if (x <= 0)
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return 0;
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if (x > CFX_255 || x < CFX_ONE)
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{
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/*
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* Find the highest bit set
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*/
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#if __arm__
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/* This actually requires at least arm v5, but gcc does not seem
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* to set the architecture defines correctly, and it is I think
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* very unlikely that anyone will want to use clutter on anything
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* less than v5.
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*/
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int bit;
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__asm__ ("clz %0, %1\n"
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"rsb %0, %0, #31\n"
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:"=r"(bit)
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:"r" (x));
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/* make even (2n) */
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bit &= 0xfffffffe;
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#else
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/* TODO -- add i386 branch using bshr */
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int bit = 30;
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while (bit >= 0)
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{
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if (x & mask)
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break;
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mask = (mask >> 1 | mask >> 2);
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bit -= 2;
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}
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#endif
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/* now bit indicates the highest bit set; there are two scenarios
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*
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* 1) bit < 23: Our number is smaller so we shift it left to maximase
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* precision (< 16 really, since <16,23> never goes
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* through here.
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*
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* 2) bit > 23: our number is above the table, so we shift right
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*/
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sh = ((bit - 22) >> 1);
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if (bit >= 8)
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t = (x >> (16 - 22 + bit));
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else
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t = (x << (22 - 16 - bit));
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}
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else
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{
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t = CLUTTER_FIXED_INT (x);
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}
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/* Do a weighted average of the two nearest values */
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ClutterFixed v1 = sqrt_tbl[t];
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ClutterFixed v2 = sqrt_tbl[t+1];
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/*
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* 12 is fairly arbitrary -- we want integer that is not too big to cost
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* us precission
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*/
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d1 = (unsigned)(fract) >> 12;
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d2 = ((unsigned)CFX_ONE >> 12) - d1;
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x = ((v1*d2) + (v2*d1))/(CFX_ONE >> 12);
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if (sh > 0)
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x = x << sh;
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else if (sh < 0)
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x = (x >> (1 + ~sh));
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return x;
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}
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/**
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* clutter_sqrti:
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* @x: integer value
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*
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* A fixed point implementation of square root for integers
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*
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* Return value: square root (as truncated integer).
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*
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*
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* Since: 0.2
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*/
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int
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clutter_sqrti (int x)
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{
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int t = 0;
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int sh = 0;
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unsigned int mask = 0x40000000;
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if (x <= 0)
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return 0;
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if (x > (sizeof (sqrt_tbl)/sizeof(ClutterFixed) - 1))
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{
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/*
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* Find the highest bit set
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*/
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#if __arm__
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/* This actually requires at least arm v5, but gcc does not seem
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* to set the architecture defines correctly, and it is probably
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* very unlikely that anyone will want to use clutter on anything
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* less than v5.
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*/
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int bit;
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__asm__ ("clz %0, %1\n"
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"rsb %0, %0, #31\n"
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:"=r"(bit)
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:"r" (x));
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/* make even (2n) */
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bit &= 0xfffffffe;
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#else
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/* TODO -- add i386 branch using bshr */
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int bit = 30;
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while (bit >= 0)
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{
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if (x & mask)
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break;
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mask = (mask >> 1 | mask >> 2);
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bit -= 2;
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}
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#endif
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sh = ((bit - 6) >> 1);
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t = (x >> (bit - 6));
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}
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else
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{
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return (sqrt_tbl[x] >> CFX_Q);
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}
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x = sqrt_tbl[t];
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if (sh > 0)
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x = x << sh;
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else if (sh < 0)
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x = (x >> (1 + ~sh));
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return (x >> CFX_Q);
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}
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@ -52,6 +52,7 @@ typedef gint32 ClutterAngle; /* angle such that 1024 == 2*PI */
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#define CFX_180 CLUTTER_INT_TO_FIXED (180)
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#define CFX_120 CLUTTER_INT_TO_FIXED (120)
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#define CFX_60 CLUTTER_INT_TO_FIXED (60)
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#define CFX_255 CLUTTER_INT_TO_FIXED (255)
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#define CLUTTER_FIXED_TO_FLOAT(x) ((float)((int)(x)/65536.0))
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@ -84,12 +85,15 @@ typedef gint32 ClutterAngle; /* angle such that 1024 == 2*PI */
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#define CFX_DIV CLUTTER_FIXED_DIV
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/* Fixed point math routines */
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ClutterFixed clutter_fixed_sin (ClutterFixed angle);
|
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ClutterFixed clutter_angle_sin (ClutterAngle angle);
|
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ClutterFixed clutter_sinx (ClutterFixed anx);
|
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ClutterFixed clutter_sini (ClutterAngle angle);
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/* convenience macros for the cos functions */
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#define clutter_fixed_cos(x) clutter_fixed_sin((x) - CFX_PI_2)
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#define clutter_angle_cos(x) clutter_fixed_sin((x) - 256)
|
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#define clutter_cosx(x) clutter_fixed_sin((x) - CFX_PI_2)
|
||||
#define clutter_cosi(x) clutter_sini((x) - 256)
|
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|
||||
ClutterFixed clutter_sqrtx (ClutterFixed x);
|
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int clutter_sqrti (int x);
|
||||
|
||||
G_END_DECLS
|
||||
|
||||
|
|
|
|||
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Reference in a new issue