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MiniGUI/src/misc/math.c
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///////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT NOTICE
//
// The following open source license statement does not apply to any
// entity in the Exception List published by FMSoft.
//
// For more information, please visit:
//
// https://www.fmsoft.cn/exception-list
//
//////////////////////////////////////////////////////////////////////////////
/*
* This file is part of MiniGUI, a mature cross-platform windowing
* and Graphics User Interface (GUI) support system for embedded systems
* and smart IoT devices.
*
* Copyright (C) 2002~2018, Beijing FMSoft Technologies Co., Ltd.
* Copyright (C) 1998~2002, WEI Yongming
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Or,
*
* As this program is a library, any link to this program must follow
* GNU General Public License version 3 (GPLv3). If you cannot accept
* GPLv3, you need to be licensed from FMSoft.
*
* If you have got a commercial license of this program, please use it
* under the terms and conditions of the commercial license.
*
* For more information about the commercial license, please refer to
* <http://www.minigui.com/blog/minigui-licensing-policy/>.
*/
/*
** math.c: the fixed point math routines.
**
** Some routines come from Allegro by Shawn Hargreaves.
**
** Allegro is a gift-ware.
**
** Current maintainer: Wei Yongming.
*/
#include "common.h"
#ifdef _MGHAVE_FIXED_MATH
#include "fixedmath.h"
//if a data big than this data,can not be made left shift.
//other than it will be changed to a negative data.example:0x40000000,
//is positive data ,when make 0x40000000 left shift one bit, it will
//become 0x80000000,0x80000000 is a negative data ,it is not a result
//we want
//#define MAX_LEFTSHIFT_DATA 0x3FFFFFFF
#define MAX_LEFTSHIFT_DATA 0x7FFFFFFF
fixed fixmul (fixed x, fixed y)
{
int s1 = 1, s2 = 1;
long result;
unsigned long op1_hi;
unsigned long op1_lo;
unsigned long op2_hi;
unsigned long op2_lo;
unsigned long cross_prod;
unsigned long prod_hi;
unsigned long prod_lo;
if (x < 0) {
s1 = -1;
x = -x;
}
if (y < 0) {
s2 = -1;
y = -y;
}
op1_hi = (x >> 16) & 0xffff;
op1_lo = x & 0xffff;
op2_hi = (y >> 16) & 0xffff;
op2_lo = y & 0xffff;
cross_prod = op1_lo * op2_hi + op1_hi * op2_lo;
prod_hi = op1_hi * op2_hi;
if(prod_hi > 0x7FFF){
errno = ERANGE;
return 0x7FFFFFFF;
}
prod_lo = ((op1_lo * op2_lo) >>16) + cross_prod;
prod_hi = (prod_hi << 16) + prod_lo;
if(prod_hi > 0x7FFFFFFF){
errno = ERANGE;
return 0x7FFFFFFF;
}
result = s1 * s2 * prod_hi;
return (fixed)result;
}
fixed fixdiv (fixed dividend, fixed divisor)
{
int s1=1,s2=1,i;
unsigned long temp;
unsigned long x,y;
fixed result;
if(divisor == 0){
errno = ERANGE;
return (dividend < 0) ? -0x7FFFFFFF : 0x7FFFFFFF;
}
if(dividend <0){
s1 =-1;
dividend =-dividend;
}
if(divisor <0){
s2 = -1;
divisor =-divisor;
}
x = dividend;
y = divisor;
/*we change the divide info subtract*/
temp = 0;
temp = x / y;
x = x % y;
if(temp > 0x7FFF){
errno = ERANGE;
return 0x7FFFFFFF;
}
result =(temp << 16);
i = 0;
while(i < 16){
while(x <= MAX_LEFTSHIFT_DATA){
x <<= 1;
i += 1;
if(i >= 16)
break;
}
temp = 0;
temp = x / y;
x = x % y;
if((0x7FFFFFFF -(temp <<(16 - i))) < result){
errno = ERANGE;
return 0x7FFFFFFF;
}
result +=(temp << (16 - i));
}
result = s1 * s2 * result;
return result;
}
const fixed __mg_cos_tbl[512] =
{
/* precalculated fixed point (16.16) cosines for a full circle (0-255) */
65536L, 65531L, 65516L, 65492L, 65457L, 65413L, 65358L, 65294L,
65220L, 65137L, 65043L, 64940L, 64827L, 64704L, 64571L, 64429L,
64277L, 64115L, 63944L, 63763L, 63572L, 63372L, 63162L, 62943L,
62714L, 62476L, 62228L, 61971L, 61705L, 61429L, 61145L, 60851L,
60547L, 60235L, 59914L, 59583L, 59244L, 58896L, 58538L, 58172L,
57798L, 57414L, 57022L, 56621L, 56212L, 55794L, 55368L, 54934L,
54491L, 54040L, 53581L, 53114L, 52639L, 52156L, 51665L, 51166L,
50660L, 50146L, 49624L, 49095L, 48559L, 48015L, 47464L, 46906L,
46341L, 45769L, 45190L, 44604L, 44011L, 43412L, 42806L, 42194L,
41576L, 40951L, 40320L, 39683L, 39040L, 38391L, 37736L, 37076L,
36410L, 35738L, 35062L, 34380L, 33692L, 33000L, 32303L, 31600L,
30893L, 30182L, 29466L, 28745L, 28020L, 27291L, 26558L, 25821L,
25080L, 24335L, 23586L, 22834L, 22078L, 21320L, 20557L, 19792L,
19024L, 18253L, 17479L, 16703L, 15924L, 15143L, 14359L, 13573L,
12785L, 11996L, 11204L, 10411L, 9616L, 8820L, 8022L, 7224L,
6424L, 5623L, 4821L, 4019L, 3216L, 2412L, 1608L, 804L,
0L, -804L, -1608L, -2412L, -3216L, -4019L, -4821L, -5623L,
-6424L, -7224L, -8022L, -8820L, -9616L, -10411L, -11204L, -11996L,
-12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
-19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
-25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
-30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
-36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
-41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
-46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
-50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
-54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
-57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
-60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
-62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
-64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
-65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
-65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
-65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
-64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
-62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
-60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
-57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
-54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
-50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
-46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
-41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
-36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
-30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
-25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
-19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
-12785L, -11996L, -11204L, -10411L, -9616L, -8820L, -8022L, -7224L,
-6424L, -5623L, -4821L, -4019L, -3216L, -2412L, -1608L, -804L,
0L, 804L, 1608L, 2412L, 3216L, 4019L, 4821L, 5623L,
6424L, 7224L, 8022L, 8820L, 9616L, 10411L, 11204L, 11996L,
12785L, 13573L, 14359L, 15143L, 15924L, 16703L, 17479L, 18253L,
19024L, 19792L, 20557L, 21320L, 22078L, 22834L, 23586L, 24335L,
25080L, 25821L, 26558L, 27291L, 28020L, 28745L, 29466L, 30182L,
30893L, 31600L, 32303L, 33000L, 33692L, 34380L, 35062L, 35738L,
36410L, 37076L, 37736L, 38391L, 39040L, 39683L, 40320L, 40951L,
41576L, 42194L, 42806L, 43412L, 44011L, 44604L, 45190L, 45769L,
46341L, 46906L, 47464L, 48015L, 48559L, 49095L, 49624L, 50146L,
50660L, 51166L, 51665L, 52156L, 52639L, 53114L, 53581L, 54040L,
54491L, 54934L, 55368L, 55794L, 56212L, 56621L, 57022L, 57414L,
57798L, 58172L, 58538L, 58896L, 59244L, 59583L, 59914L, 60235L,
60547L, 60851L, 61145L, 61429L, 61705L, 61971L, 62228L, 62476L,
62714L, 62943L, 63162L, 63372L, 63572L, 63763L, 63944L, 64115L,
64277L, 64429L, 64571L, 64704L, 64827L, 64940L, 65043L, 65137L,
65220L, 65294L, 65358L, 65413L, 65457L, 65492L, 65516L, 65531L
};
const fixed __mg_tan_tbl[256] =
{
/* precalculated fixed point (16.16) tangents for a half circle (0-127) */
0L, 804L, 1609L, 2414L, 3220L, 4026L, 4834L, 5644L,
6455L, 7268L, 8083L, 8901L, 9721L, 10545L, 11372L, 12202L,
13036L, 13874L, 14717L, 15564L, 16416L, 17273L, 18136L, 19005L,
19880L, 20762L, 21650L, 22546L, 23449L, 24360L, 25280L, 26208L,
27146L, 28093L, 29050L, 30018L, 30996L, 31986L, 32988L, 34002L,
35030L, 36071L, 37126L, 38196L, 39281L, 40382L, 41500L, 42636L,
43790L, 44963L, 46156L, 47369L, 48605L, 49863L, 51145L, 52451L,
53784L, 55144L, 56532L, 57950L, 59398L, 60880L, 62395L, 63947L,
65536L, 67165L, 68835L, 70548L, 72308L, 74116L, 75974L, 77887L,
79856L, 81885L, 83977L, 86135L, 88365L, 90670L, 93054L, 95523L,
98082L, 100736L, 103493L, 106358L, 109340L, 112447L, 115687L, 119071L,
122609L, 126314L, 130198L, 134276L, 138564L, 143081L, 147847L, 152884L,
158218L, 163878L, 169896L, 176309L, 183161L, 190499L, 198380L, 206870L,
216043L, 225990L, 236817L, 248648L, 261634L, 275959L, 291845L, 309568L,
329472L, 351993L, 377693L, 407305L, 441808L, 482534L, 531352L, 590958L,
665398L, 761030L, 888450L, 1066730L,1334016L,1779314L,2669641L,5340086L,
-2147483647L,-5340086L,-2669641L,-1779314L,-1334016L,-1066730L,-888450L,-761030L,
-665398L,-590958L,-531352L,-482534L,-441808L,-407305L,-377693L,-351993L,
-329472L,-309568L,-291845L,-275959L,-261634L,-248648L,-236817L,-225990L,
-216043L,-206870L,-198380L,-190499L,-183161L,-176309L,-169896L,-163878L,
-158218L,-152884L,-147847L,-143081L,-138564L,-134276L,-130198L,-126314L,
-122609L,-119071L,-115687L,-112447L,-109340L,-106358L,-103493L,-100736L,
-98082L, -95523L, -93054L, -90670L, -88365L, -86135L, -83977L, -81885L,
-79856L, -77887L, -75974L, -74116L, -72308L, -70548L, -68835L, -67165L,
-65536L, -63947L, -62395L, -60880L, -59398L, -57950L, -56532L, -55144L,
-53784L, -52451L, -51145L, -49863L, -48605L, -47369L, -46156L, -44963L,
-43790L, -42636L, -41500L, -40382L, -39281L, -38196L, -37126L, -36071L,
-35030L, -34002L, -32988L, -31986L, -30996L, -30018L, -29050L, -28093L,
-27146L, -26208L, -25280L, -24360L, -23449L, -22546L, -21650L, -20762L,
-19880L, -19005L, -18136L, -17273L, -16416L, -15564L, -14717L, -13874L,
-13036L, -12202L, -11372L, -10545L, -9721L, -8901L, -8083L, -7268L,
-6455L, -5644L, -4834L, -4026L, -3220L, -2414L, -1609L, -804L
};
const fixed __mg_acos_tbl[513] =
{
/* precalculated fixed point (16.16) inverse cosines (-1 to 1) */
0x800000L, 0x7C65C7L, 0x7AE75AL, 0x79C19EL, 0x78C9BEL, 0x77EF25L, 0x772953L, 0x76733AL,
0x75C991L, 0x752A10L, 0x74930CL, 0x740345L, 0x7379C1L, 0x72F5BAL, 0x72768FL, 0x71FBBCL,
0x7184D3L, 0x711174L, 0x70A152L, 0x703426L, 0x6FC9B5L, 0x6F61C9L, 0x6EFC36L, 0x6E98D1L,
0x6E3777L, 0x6DD805L, 0x6D7A5EL, 0x6D1E68L, 0x6CC40BL, 0x6C6B2FL, 0x6C13C1L, 0x6BBDAFL,
0x6B68E6L, 0x6B1558L, 0x6AC2F5L, 0x6A71B1L, 0x6A217EL, 0x69D251L, 0x698420L, 0x6936DFL,
0x68EA85L, 0x689F0AL, 0x685465L, 0x680A8DL, 0x67C17DL, 0x67792CL, 0x673194L, 0x66EAAFL,
0x66A476L, 0x665EE5L, 0x6619F5L, 0x65D5A2L, 0x6591E7L, 0x654EBFL, 0x650C26L, 0x64CA18L,
0x648890L, 0x64478CL, 0x640706L, 0x63C6FCL, 0x63876BL, 0x63484FL, 0x6309A5L, 0x62CB6AL,
0x628D9CL, 0x625037L, 0x621339L, 0x61D69FL, 0x619A68L, 0x615E90L, 0x612316L, 0x60E7F7L,
0x60AD31L, 0x6072C3L, 0x6038A9L, 0x5FFEE3L, 0x5FC56EL, 0x5F8C49L, 0x5F5372L, 0x5F1AE7L,
0x5EE2A7L, 0x5EAAB0L, 0x5E7301L, 0x5E3B98L, 0x5E0473L, 0x5DCD92L, 0x5D96F3L, 0x5D6095L,
0x5D2A76L, 0x5CF496L, 0x5CBEF2L, 0x5C898BL, 0x5C545EL, 0x5C1F6BL, 0x5BEAB0L, 0x5BB62DL,
0x5B81E1L, 0x5B4DCAL, 0x5B19E7L, 0x5AE638L, 0x5AB2BCL, 0x5A7F72L, 0x5A4C59L, 0x5A1970L,
0x59E6B6L, 0x59B42AL, 0x5981CCL, 0x594F9BL, 0x591D96L, 0x58EBBDL, 0x58BA0EL, 0x588889L,
0x58572DL, 0x5825FAL, 0x57F4EEL, 0x57C40AL, 0x57934DL, 0x5762B5L, 0x573243L, 0x5701F5L,
0x56D1CCL, 0x56A1C6L, 0x5671E4L, 0x564224L, 0x561285L, 0x55E309L, 0x55B3ADL, 0x558471L,
0x555555L, 0x552659L, 0x54F77BL, 0x54C8BCL, 0x549A1BL, 0x546B98L, 0x543D31L, 0x540EE7L,
0x53E0B9L, 0x53B2A7L, 0x5384B0L, 0x5356D4L, 0x532912L, 0x52FB6BL, 0x52CDDDL, 0x52A068L,
0x52730CL, 0x5245C9L, 0x52189EL, 0x51EB8BL, 0x51BE8FL, 0x5191AAL, 0x5164DCL, 0x513825L,
0x510B83L, 0x50DEF7L, 0x50B280L, 0x50861FL, 0x5059D2L, 0x502D99L, 0x500175L, 0x4FD564L,
0x4FA967L, 0x4F7D7DL, 0x4F51A6L, 0x4F25E2L, 0x4EFA30L, 0x4ECE90L, 0x4EA301L, 0x4E7784L,
0x4E4C19L, 0x4E20BEL, 0x4DF574L, 0x4DCA3AL, 0x4D9F10L, 0x4D73F6L, 0x4D48ECL, 0x4D1DF1L,
0x4CF305L, 0x4CC829L, 0x4C9D5AL, 0x4C729AL, 0x4C47E9L, 0x4C1D45L, 0x4BF2AEL, 0x4BC826L,
0x4B9DAAL, 0x4B733BL, 0x4B48D9L, 0x4B1E84L, 0x4AF43BL, 0x4AC9FEL, 0x4A9FCDL, 0x4A75A7L,
0x4A4B8DL, 0x4A217EL, 0x49F77AL, 0x49CD81L, 0x49A393L, 0x4979AFL, 0x494FD5L, 0x492605L,
0x48FC3FL, 0x48D282L, 0x48A8CFL, 0x487F25L, 0x485584L, 0x482BECL, 0x48025DL, 0x47D8D6L,
0x47AF57L, 0x4785E0L, 0x475C72L, 0x47330AL, 0x4709ABL, 0x46E052L, 0x46B701L, 0x468DB7L,
0x466474L, 0x463B37L, 0x461201L, 0x45E8D0L, 0x45BFA6L, 0x459682L, 0x456D64L, 0x45444BL,
0x451B37L, 0x44F229L, 0x44C920L, 0x44A01CL, 0x44771CL, 0x444E21L, 0x44252AL, 0x43FC38L,
0x43D349L, 0x43AA5FL, 0x438178L, 0x435894L, 0x432FB4L, 0x4306D8L, 0x42DDFEL, 0x42B527L,
0x428C53L, 0x426381L, 0x423AB2L, 0x4211E5L, 0x41E91AL, 0x41C051L, 0x41978AL, 0x416EC5L,
0x414601L, 0x411D3EL, 0x40F47CL, 0x40CBBBL, 0x40A2FBL, 0x407A3CL, 0x40517DL, 0x4028BEL,
0x400000L, 0x3FD742L, 0x3FAE83L, 0x3F85C4L, 0x3F5D05L, 0x3F3445L, 0x3F0B84L, 0x3EE2C2L,
0x3EB9FFL, 0x3E913BL, 0x3E6876L, 0x3E3FAFL, 0x3E16E6L, 0x3DEE1BL, 0x3DC54EL, 0x3D9C7FL,
0x3D73ADL, 0x3D4AD9L, 0x3D2202L, 0x3CF928L, 0x3CD04CL, 0x3CA76CL, 0x3C7E88L, 0x3C55A1L,
0x3C2CB7L, 0x3C03C8L, 0x3BDAD6L, 0x3BB1DFL, 0x3B88E4L, 0x3B5FE4L, 0x3B36E0L, 0x3B0DD7L,
0x3AE4C9L, 0x3ABBB5L, 0x3A929CL, 0x3A697EL, 0x3A405AL, 0x3A1730L, 0x39EDFFL, 0x39C4C9L,
0x399B8CL, 0x397249L, 0x3948FFL, 0x391FAEL, 0x38F655L, 0x38CCF6L, 0x38A38EL, 0x387A20L,
0x3850A9L, 0x38272AL, 0x37FDA3L, 0x37D414L, 0x37AA7CL, 0x3780DBL, 0x375731L, 0x372D7EL,
0x3703C1L, 0x36D9FBL, 0x36B02BL, 0x368651L, 0x365C6DL, 0x36327FL, 0x360886L, 0x35DE82L,
0x35B473L, 0x358A59L, 0x356033L, 0x353602L, 0x350BC5L, 0x34E17CL, 0x34B727L, 0x348CC5L,
0x346256L, 0x3437DAL, 0x340D52L, 0x33E2BBL, 0x33B817L, 0x338D66L, 0x3362A6L, 0x3337D7L,
0x330CFBL, 0x32E20FL, 0x32B714L, 0x328C0AL, 0x3260F0L, 0x3235C6L, 0x320A8CL, 0x31DF42L,
0x31B3E7L, 0x31887CL, 0x315CFFL, 0x313170L, 0x3105D0L, 0x30DA1EL, 0x30AE5AL, 0x308283L,
0x305699L, 0x302A9CL, 0x2FFE8BL, 0x2FD267L, 0x2FA62EL, 0x2F79E1L, 0x2F4D80L, 0x2F2109L,
0x2EF47DL, 0x2EC7DBL, 0x2E9B24L, 0x2E6E56L, 0x2E4171L, 0x2E1475L, 0x2DE762L, 0x2DBA37L,
0x2D8CF4L, 0x2D5F98L, 0x2D3223L, 0x2D0495L, 0x2CD6EEL, 0x2CA92CL, 0x2C7B50L, 0x2C4D59L,
0x2C1F47L, 0x2BF119L, 0x2BC2CFL, 0x2B9468L, 0x2B65E5L, 0x2B3744L, 0x2B0885L, 0x2AD9A7L,
0x2AAAABL, 0x2A7B8FL, 0x2A4C53L, 0x2A1CF7L, 0x29ED7BL, 0x29BDDCL, 0x298E1CL, 0x295E3AL,
0x292E34L, 0x28FE0BL, 0x28CDBDL, 0x289D4BL, 0x286CB3L, 0x283BF6L, 0x280B12L, 0x27DA06L,
0x27A8D3L, 0x277777L, 0x2745F2L, 0x271443L, 0x26E26AL, 0x26B065L, 0x267E34L, 0x264BD6L,
0x26194AL, 0x25E690L, 0x25B3A7L, 0x25808EL, 0x254D44L, 0x2519C8L, 0x24E619L, 0x24B236L,
0x247E1FL, 0x2449D3L, 0x241550L, 0x23E095L, 0x23ABA2L, 0x237675L, 0x23410EL, 0x230B6AL,
0x22D58AL, 0x229F6BL, 0x22690DL, 0x22326EL, 0x21FB8DL, 0x21C468L, 0x218CFFL, 0x215550L,
0x211D59L, 0x20E519L, 0x20AC8EL, 0x2073B7L, 0x203A92L, 0x20011DL, 0x1FC757L, 0x1F8D3DL,
0x1F52CFL, 0x1F1809L, 0x1EDCEAL, 0x1EA170L, 0x1E6598L, 0x1E2961L, 0x1DECC7L, 0x1DAFC9L,
0x1D7264L, 0x1D3496L, 0x1CF65BL, 0x1CB7B1L, 0x1C7895L, 0x1C3904L, 0x1BF8FAL, 0x1BB874L,
0x1B7770L, 0x1B35E8L, 0x1AF3DAL, 0x1AB141L, 0x1A6E19L, 0x1A2A5EL, 0x19E60BL, 0x19A11BL,
0x195B8AL, 0x191551L, 0x18CE6CL, 0x1886D4L, 0x183E83L, 0x17F573L, 0x17AB9BL, 0x1760F6L,
0x17157BL, 0x16C921L, 0x167BE0L, 0x162DAFL, 0x15DE82L, 0x158E4FL, 0x153D0BL, 0x14EAA8L,
0x14971AL, 0x144251L, 0x13EC3FL, 0x1394D1L, 0x133BF5L, 0x12E198L, 0x1285A2L, 0x1227FBL,
0x11C889L, 0x11672FL, 0x1103CAL, 0x109E37L, 0x10364BL, 0xFCBDAL, 0xF5EAEL, 0xEEE8CL,
0xE7B2DL, 0xE0444L, 0xD8971L, 0xD0A46L, 0xC863FL, 0xBFCBBL, 0xB6CF4L, 0xAD5F0L,
0xA366FL, 0x98CC6L, 0x8D6ADL, 0x810DBL, 0x73642L, 0x63E62L, 0x518A6L, 0x39A39L,
0x0L
};
/* fixatan:
* Fixed point inverse tangent. Does a binary search on the tan table.
*/
fixed fixatan(fixed x)
{
int a, b, c; /* for binary search */
fixed d; /* difference value for search */
if (x >= 0) { /* search the first part of tan table */
a = 0;
b = 127;
}
else { /* search the second half instead */
a = 128;
b = 255;
}
do {
c = (a + b) >> 1;
d = x - __mg_tan_tbl[c];
if (d > 0)
a = c + 1;
else
if (d < 0)
b = c - 1;
} while ((a <= b) && (d));
if (x >= 0)
return ((long)c) << 15;
return (-0x00800000L + (((long)c) << 15));
}
/* fixatan2:
* Like the libc atan2, but for fixed point numbers.
*/
fixed fixatan2(fixed y, fixed x)
{
fixed r;
if (x==0) {
if (y==0) {
errno = EDOM;
return 0L;
}
else
return ((y < 0) ? -0x00400000L : 0x00400000L);
}
errno = 0;
r = fixdiv(y, x);
if (errno) {
errno = 0;
return ((y < 0) ? -0x00400000L : 0x00400000L);
}
r = fixatan(r);
if (x >= 0)
return r;
if (y >= 0)
return 0x00800000L + r;
return r - 0x00800000L;
}
static unsigned short _sqrt_tabl[256] =
{
/* this table is used by the fixsqrt() and fixhypot() routines */
0x2D4, 0x103F, 0x16CD, 0x1BDB, 0x201F, 0x23E3, 0x274B, 0x2A6D,
0x2D57, 0x3015, 0x32AC, 0x3524, 0x377F, 0x39C2, 0x3BEE, 0x3E08,
0x400F, 0x4207, 0x43F0, 0x45CC, 0x479C, 0x4960, 0x4B19, 0x4CC9,
0x4E6F, 0x500C, 0x51A2, 0x532F, 0x54B6, 0x5635, 0x57AE, 0x5921,
0x5A8D, 0x5BF4, 0x5D56, 0x5EB3, 0x600A, 0x615D, 0x62AB, 0x63F5,
0x653B, 0x667D, 0x67BA, 0x68F5, 0x6A2B, 0x6B5E, 0x6C8D, 0x6DBA,
0x6EE3, 0x7009, 0x712C, 0x724C, 0x7369, 0x7484, 0x759C, 0x76B1,
0x77C4, 0x78D4, 0x79E2, 0x7AEE, 0x7BF7, 0x7CFE, 0x7E04, 0x7F07,
0x8007, 0x8106, 0x8203, 0x82FF, 0x83F8, 0x84EF, 0x85E5, 0x86D9,
0x87CB, 0x88BB, 0x89AA, 0x8A97, 0x8B83, 0x8C6D, 0x8D56, 0x8E3D,
0x8F22, 0x9007, 0x90E9, 0x91CB, 0x92AB, 0x938A, 0x9467, 0x9543,
0x961E, 0x96F8, 0x97D0, 0x98A8, 0x997E, 0x9A53, 0x9B26, 0x9BF9,
0x9CCA, 0x9D9B, 0x9E6A, 0x9F39, 0xA006, 0xA0D2, 0xA19D, 0xA268,
0xA331, 0xA3F9, 0xA4C1, 0xA587, 0xA64D, 0xA711, 0xA7D5, 0xA898,
0xA95A, 0xAA1B, 0xAADB, 0xAB9A, 0xAC59, 0xAD16, 0xADD3, 0xAE8F,
0xAF4B, 0xB005, 0xB0BF, 0xB178, 0xB230, 0xB2E8, 0xB39F, 0xB455,
0xB50A, 0xB5BF, 0xB673, 0xB726, 0xB7D9, 0xB88A, 0xB93C, 0xB9EC,
0xBA9C, 0xBB4B, 0xBBFA, 0xBCA8, 0xBD55, 0xBE02, 0xBEAE, 0xBF5A,
0xC005, 0xC0AF, 0xC159, 0xC202, 0xC2AB, 0xC353, 0xC3FA, 0xC4A1,
0xC548, 0xC5ED, 0xC693, 0xC737, 0xC7DC, 0xC87F, 0xC923, 0xC9C5,
0xCA67, 0xCB09, 0xCBAA, 0xCC4B, 0xCCEB, 0xCD8B, 0xCE2A, 0xCEC8,
0xCF67, 0xD004, 0xD0A2, 0xD13F, 0xD1DB, 0xD277, 0xD312, 0xD3AD,
0xD448, 0xD4E2, 0xD57C, 0xD615, 0xD6AE, 0xD746, 0xD7DE, 0xD876,
0xD90D, 0xD9A4, 0xDA3A, 0xDAD0, 0xDB66, 0xDBFB, 0xDC90, 0xDD24,
0xDDB8, 0xDE4C, 0xDEDF, 0xDF72, 0xE004, 0xE096, 0xE128, 0xE1B9,
0xE24A, 0xE2DB, 0xE36B, 0xE3FB, 0xE48B, 0xE51A, 0xE5A9, 0xE637,
0xE6C5, 0xE753, 0xE7E1, 0xE86E, 0xE8FB, 0xE987, 0xEA13, 0xEA9F,
0xEB2B, 0xEBB6, 0xEC41, 0xECCB, 0xED55, 0xEDDF, 0xEE69, 0xEEF2,
0xEF7B, 0xF004, 0xF08C, 0xF114, 0xF19C, 0xF223, 0xF2AB, 0xF332,
0xF3B8, 0xF43E, 0xF4C4, 0xF54A, 0xF5D0, 0xF655, 0xF6DA, 0xF75E,
0xF7E3, 0xF867, 0xF8EA, 0xF96E, 0xF9F1, 0xFA74, 0xFAF7, 0xFB79,
0xFBFB, 0xFC7D, 0xFCFF, 0xFD80, 0xFE02, 0xFE82, 0xFF03, 0xFF83
};
/* fixsqrt:
* Fixed point square root routine.
*
* This routine is based upon the following idea:
* sqrt (x) = sqrt (x/d) * sqrt(d)
* d = 2^(2n)
* sqrt (x) = sqrt (x / 2^(2n)) * 2^n
* `x/2^(2n)' has to fall into the range 0..255 so that we can use the
* square root lookup table. So `2n' is the number of bits `x' has to be
* shifted to the left to become smaller than 256. The best way to find `2n'
* is to do a reverse bit scan on `x'. This is achieved by the i386 ASM
* instruction `bsr'.
*
*/
fixed fixsqrt(fixed x)
{
int i, dx;
int cx = 0; /* if no bit set: default %cl = 2n = 0 */
/* check whether `x' is negative... */
if (x <= 0) {
if (x < 0)
errno = EDOM;
return 0;
}
/* bit-scan is done on dx */
dx = x >> 6;
for (i = 0; i < 32; i++) {
if (dx << i & 0x80000000) {
cx = 32 - i;
break;
}
}
cx &= 0xFE; /* make result even --> %cl = 2n */
x >>= cx; /* shift x to fall into range 0..255 */
x = _sqrt_tabl [x]; /* table lookup... */
cx >>= 1; /* %cl = n */
x <<= cx; /* multiply `sqrt(x/2^(2n))' by `2^n' */
return x >> 4; /* adjust the result */
}
/* fixhypot:
* Fixed point sqrt (x*x+y*y).
*
* Return fixed point sqrt (x*x+y*y), which is the length of the
* hypotenuse of a right triangle with sides of length x and y, or the
* distance of point (x|y) from the origin. This routine is faster and more
* accurate than using the direct formula fixsqrt (fixmul (x,x), fixmul(y,y)).
* It will also return correct results for x>=256 or y>=256 where fixmul(x)
* or fixmul(y) would overflow.
*
* The idea of this routine is:
* sqrt (x^2+y^2) = sqrt ((x/d)^2+(y/d)^2) * d
* d = 2^n
* Since `x' and `y' are fixed point numbers, they are multiplied in the
* following way:
* x^2 = (x*x)/2^16
* so we come to the formula:
* sqrt(x^2+y^2) = sqrt((x*x + y*y)/2^(16+2n)) * 2^n
* and this is almost the same problem as calculating the square root in
* `fixsqrt': find `2n' so that `(x*x+y*y)/2^(16+2n)' is in the range 0..255
* so that we can use the square root lookup table.
*
*/
#ifdef MGUI_HAS_64BIT_TYPE
fixed fixhypot (fixed x, fixed y)
{
int i, cx = 0;
Uint64 sum, _x, _y;
fixed hi_sum, lo_sum;
_x = x; _y = y;
/* check for overflow */
sum = _x*_x + _y*_y;
if ((sum >> 32) > 0x3FFFFFFF) {
errno = ERANGE;
return 0x7FFFFFFF;
}
/* And now we're doing a bit-scan on `x*x+y*y' to find out by how
* many bits it needs to be shifted to fall into the range 0..255.
* Since the intermediate result is 64 bit we may need two bitscans
* in case that no bit is set in the upper 32 bit.
*/
hi_sum = (sum >> 32) & 0xFFFFFFFF;
lo_sum = sum & 0xFFFFFFFF;
for (i = 0; i < 32; i++) {
if (hi_sum << i & 0x80000000) {
cx = 32 - i;
break;
}
}
if (cx) {
cx += 2; /* make cl even */
cx &= 0xFE;
sum >>= cx;
lo_sum = sum & 0xFFFFFFFF; /* make lo_sum fall into range 0..255 */
lo_sum >>= 24;
x = _sqrt_tabl [lo_sum]; /* table lookup... */
cx >>= 1; /* adjust the result */
x <<= cx;
}
else {
fixed dx;
/* bit-scan is done on dx */
lo_sum = lo_sum >> 16;
dx = lo_sum >> 6;
for (i = 0; i < 32; i++) {
if (dx << i & 0x80000000) {
cx = 32 - i;
break;
}
}
cx &= 0xFE; /* make result even --> %cl = 2n */
lo_sum >>= cx; /* shift lo_sum to fall into range 0..255 */
x = _sqrt_tabl [lo_sum]; /* table lookup... */
cx >>= 1; /* adjust the result */
x <<= cx;
x >>= 4;
}
return x;
}
#elif defined (_HAVE_MATH_H) /* MGUI_HAS_64BIT_TYPE */
#include <math.h>
/* fixhypot:
* Fixed point sqrt (x*x+y*y) for non-64bit int type.
*/
fixed fixhypot (fixed x, fixed y)
{
return ftofix (hypot (fixtof(x), fixtof (y)));
}
#else
/* fixhypot:
* Not supported routine, always return zero.
*/
fixed fixhypot (fixed x, fixed y)
{
errno = ENOTSUP;
return 0;
}
#endif /* !MGUI_HAS_64BIT_TYPE */
#endif /* _MGHAVE_FIXED_MATH */
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