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/* |
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* FixPoint.h - Provides fixed point arithmetic (for use in SID.cpp) |
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* |
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* (C) 1997 Andreas Dehmel |
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* |
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* Frodo (C) 1994-1997,2002-2005 Christian Bauer |
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* |
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* This program is free software; you can redistribute it and/or modify |
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* it under the terms of the GNU General Public License as published by |
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* the Free Software Foundation; either version 2 of the License, or |
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* (at your option) any later version. |
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* |
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* This program 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 |
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* GNU General Public License for more details. |
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* |
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* You should have received a copy of the GNU General Public License |
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* along with this program; if not, write to the Free Software |
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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*/ |
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|
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/* |
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* You need to define FIXPOINT_PREC (number of fractional bits) and |
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* ldSINTAB (ld of the size of the sinus table) as well M_PI |
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* _before_ including this file. |
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* Requires at least 32bit ints! |
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*/ |
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|
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|
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#define FIXPOINT_BITS 32 |
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// Sign-bit |
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#define FIXPOINT_SIGN (1<<(FIXPOINT_BITS-1)) |
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|
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|
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/* |
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* Elementary functions for the FixPoint class |
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*/ |
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|
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// Multiplies two fixpoint numbers, result is a fixpoint number. |
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static inline int fixmult(int x, int y) |
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{ |
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register unsigned int a,b; |
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register bool sign; |
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|
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sign = (x ^ y) < 0; |
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if (x < 0) {x = -x;} |
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if (y < 0) {y = -y;} |
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// a, b : integer part; x, y : fractional part. All unsigned now (for shift right)!!! |
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a = (((unsigned int)x) >> FIXPOINT_PREC); x &= ~(a << FIXPOINT_PREC); |
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b = (((unsigned int)y) >> FIXPOINT_PREC); y &= ~(b << FIXPOINT_PREC); |
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x = ((a*b) << FIXPOINT_PREC) + (a*y + b*x) + |
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((unsigned int)((x*y) + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC); |
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#ifdef FIXPOINT_SIGN |
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if (x < 0) {x ^= FIXPOINT_SIGN;} |
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#endif |
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if (sign) {x = -x;} |
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return(x); |
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} |
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|
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|
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// Multiplies a fixpoint number with an integer, result is a 32 bit (!) integer in |
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// contrast to using the standard member-functions which can provide only (32-FIXPOINT_PREC) |
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// valid bits. |
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static inline int intmult(int x, int y) // x is fixpoint, y integer |
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{ |
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register unsigned int i,j; |
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register bool sign; |
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|
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sign = (x ^ y) < 0; |
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if (x < 0) {x = -x;} |
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if (y < 0) {y = -y;} |
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i = (((unsigned int)x) >> 16); x &= ~(i << 16); // split both into 16.16 parts |
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j = (((unsigned int)y) >> 16); y &= ~(j << 16); |
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#if FIXPOINT_PREC <= 16 |
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// This '32' is independent of the number of bits used, it's due to the 16 bit shift |
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i = ((i*j) << (32 - FIXPOINT_PREC)) + ((i*y + j*x) << (16 - FIXPOINT_PREC)) + |
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((unsigned int)(x*y + (1 << (FIXPOINT_PREC - 1))) >> FIXPOINT_PREC); |
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#else |
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{ |
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register unsigned int h; |
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|
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h = (i*y + j*x); |
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i = ((i*j) << (32 - FIXPOINT_PREC)) + (h >> (FIXPOINT_PREC - 16)); |
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h &= ((1 << (FIXPOINT_PREC - 16)) - 1); x *= y; |
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i += (x >> FIXPOINT_PREC); x &= ((1 << FIXPOINT_PREC) - 1); |
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i += (((h + (x >> 16)) + (1 << (FIXPOINT_PREC - 17))) >> (FIXPOINT_PREC - 16)); |
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} |
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#endif |
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#ifdef FIXPOINT_SIGN |
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if (i < 0) {i ^= FIXPOINT_SIGN;} |
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#endif |
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if (sign) {i = -i;} |
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return(i); |
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} |
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|
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|
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// Computes the product of a fixpoint number with itself. |
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static inline int fixsquare(int x) |
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{ |
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register unsigned int a; |
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|
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if (x < 0) {x = -x;} |
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a = (((unsigned int)x) >> FIXPOINT_PREC); x &= ~(a << FIXPOINT_PREC); |
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x = ((a*a) << FIXPOINT_PREC) + ((a*x) << 1) + |
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((unsigned int)((x*x) + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC); |
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#ifdef FIXPOINT_SIGN |
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if (x < 0) {x ^= FIXPOINT_SIGN;} |
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#endif |
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return(x); |
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} |
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|
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|
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// Computes the square root of a fixpoint number. |
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static inline int fixsqrt(int x) |
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{ |
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register int test, step; |
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|
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if (x < 0) return(-1); if (x == 0) return(0); |
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step = (x <= (1<<FIXPOINT_PREC)) ? (1<<FIXPOINT_PREC) : (1<<((FIXPOINT_BITS - 2 + FIXPOINT_PREC)>>1)); |
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test = 0; |
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while (step != 0) |
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{ |
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register int h; |
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|
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h = fixsquare(test + step); |
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if (h <= x) {test += step;} |
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if (h == x) break; |
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step >>= 1; |
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} |
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return(test); |
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} |
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|
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|
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// Divides a fixpoint number by another fixpoint number, yielding a fixpoint result. |
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static inline int fixdiv(int x, int y) |
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{ |
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register int res, mask; |
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register bool sign; |
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|
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sign = (x ^ y) < 0; |
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if (x < 0) {x = -x;} |
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if (y < 0) {y = -y;} |
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mask = (1<<FIXPOINT_PREC); res = 0; |
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while (x > y) {y <<= 1; mask <<= 1;} |
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while (mask != 0) |
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{ |
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if (x >= y) {res |= mask; x -= y;} |
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mask >>= 1; y >>= 1; |
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} |
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#ifdef FIXPOINT_SIGN |
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if (res < 0) {res ^= FIXPOINT_SIGN;} |
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#endif |
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if (sign) {res = -res;} |
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return(res); |
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} |
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|
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|
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|
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|
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|
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/* |
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* The C++ Fixpoint class. By no means exhaustive... |
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* Since it contains only one int data, variables of type FixPoint can be |
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* passed directly rather than as a reference. |
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*/ |
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|
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class FixPoint |
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{ |
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private: |
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int x; |
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|
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public: |
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FixPoint(void); |
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FixPoint(int y); |
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~FixPoint(void); |
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|
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// conversions |
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int Value(void); |
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int round(void); |
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operator int(void); |
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|
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// unary operators |
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FixPoint sqrt(void); |
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FixPoint sqr(void); |
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FixPoint abs(void); |
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FixPoint operator+(void); |
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FixPoint operator-(void); |
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FixPoint operator++(void); |
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FixPoint operator--(void); |
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|
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// binary operators |
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int imul(int y); |
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FixPoint operator=(FixPoint y); |
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FixPoint operator=(int y); |
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FixPoint operator+(FixPoint y); |
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FixPoint operator+(int y); |
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FixPoint operator-(FixPoint y); |
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FixPoint operator-(int y); |
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FixPoint operator/(FixPoint y); |
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FixPoint operator/(int y); |
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FixPoint operator*(FixPoint y); |
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FixPoint operator*(int y); |
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FixPoint operator+=(FixPoint y); |
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FixPoint operator+=(int y); |
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FixPoint operator-=(FixPoint y); |
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FixPoint operator-=(int y); |
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FixPoint operator*=(FixPoint y); |
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FixPoint operator*=(int y); |
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FixPoint operator/=(FixPoint y); |
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FixPoint operator/=(int y); |
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FixPoint operator<<(int y); |
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FixPoint operator>>(int y); |
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FixPoint operator<<=(int y); |
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FixPoint operator>>=(int y); |
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|
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// conditional operators |
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bool operator<(FixPoint y); |
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bool operator<(int y); |
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bool operator<=(FixPoint y); |
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bool operator<=(int y); |
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bool operator>(FixPoint y); |
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bool operator>(int y); |
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bool operator>=(FixPoint y); |
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bool operator>=(int y); |
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bool operator==(FixPoint y); |
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bool operator==(int y); |
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bool operator!=(FixPoint y); |
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bool operator!=(int y); |
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}; |
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|
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|
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/* |
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* int gets treated differently according to the case: |
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* |
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* a) Equations (=) or condition checks (==, <, <= ...): raw int (i.e. no conversion) |
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* b) As an argument for an arithmetic operation: conversion to fixpoint by shifting |
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* |
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* Otherwise loading meaningful values into FixPoint variables would be very awkward. |
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*/ |
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|
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FixPoint::FixPoint(void) {x = 0;} |
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|
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FixPoint::FixPoint(int y) {x = y;} |
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|
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FixPoint::~FixPoint(void) {;} |
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|
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inline int FixPoint::Value(void) {return(x);} |
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|
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inline int FixPoint::round(void) {return((x + (1 << (FIXPOINT_PREC-1))) >> FIXPOINT_PREC);} |
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|
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inline FixPoint::operator int(void) {return(x);} |
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|
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|
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// unary operators |
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inline FixPoint FixPoint::sqrt(void) {return(fixsqrt(x));} |
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|
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inline FixPoint FixPoint::sqr(void) {return(fixsquare(x));} |
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|
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inline FixPoint FixPoint::abs(void) {return((x < 0) ? -x : x);} |
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|
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inline FixPoint FixPoint::operator+(void) {return(x);} |
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|
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inline FixPoint FixPoint::operator-(void) {return(-x);} |
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|
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inline FixPoint FixPoint::operator++(void) {x += (1 << FIXPOINT_PREC); return x;} |
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|
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inline FixPoint FixPoint::operator--(void) {x -= (1 << FIXPOINT_PREC); return x;} |
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|
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|
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// binary operators |
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inline int FixPoint::imul(int y) {return(intmult(x,y));} |
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|
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inline FixPoint FixPoint::operator=(FixPoint y) {x = y.Value(); return x;} |
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|
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inline FixPoint FixPoint::operator=(int y) {x = y; return x;} |
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|
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inline FixPoint FixPoint::operator+(FixPoint y) {return(x + y.Value());} |
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|
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inline FixPoint FixPoint::operator+(int y) {return(x + (y << FIXPOINT_PREC));} |
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|
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inline FixPoint FixPoint::operator-(FixPoint y) {return(x - y.Value());} |
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|
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inline FixPoint FixPoint::operator-(int y) {return(x - (y << FIXPOINT_PREC));} |
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|
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inline FixPoint FixPoint::operator/(FixPoint y) {return(fixdiv(x,y.Value()));} |
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|
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inline FixPoint FixPoint::operator/(int y) {return(x/y);} |
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|
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inline FixPoint FixPoint::operator*(FixPoint y) {return(fixmult(x,y.Value()));} |
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|
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inline FixPoint FixPoint::operator*(int y) {return(x*y);} |
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|
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inline FixPoint FixPoint::operator+=(FixPoint y) {x += y.Value(); return x;} |
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|
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inline FixPoint FixPoint::operator+=(int y) {x += (y << FIXPOINT_PREC); return x;} |
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|
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inline FixPoint FixPoint::operator-=(FixPoint y) {x -= y.Value(); return x;} |
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|
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inline FixPoint FixPoint::operator-=(int y) {x -= (y << FIXPOINT_PREC); return x;} |
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|
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inline FixPoint FixPoint::operator*=(FixPoint y) {x = fixmult(x,y.Value()); return x;} |
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|
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inline FixPoint FixPoint::operator*=(int y) {x *= y; return x;} |
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|
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inline FixPoint FixPoint::operator/=(FixPoint y) {x = fixdiv(x,y.Value()); return x;} |
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|
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inline FixPoint FixPoint::operator/=(int y) {x /= y; return x;} |
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|
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inline FixPoint FixPoint::operator<<(int y) {return(x << y);} |
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|
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inline FixPoint FixPoint::operator>>(int y) {return(x >> y);} |
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|
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inline FixPoint FixPoint::operator<<=(int y) {x <<= y; return x;} |
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|
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inline FixPoint FixPoint::operator>>=(int y) {x >>= y; return x;} |
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|
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|
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// conditional operators |
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inline bool FixPoint::operator<(FixPoint y) {return(x < y.Value());} |
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|
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inline bool FixPoint::operator<(int y) {return(x < y);} |
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|
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inline bool FixPoint::operator<=(FixPoint y) {return(x <= y.Value());} |
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|
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inline bool FixPoint::operator<=(int y) {return(x <= y);} |
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|
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inline bool FixPoint::operator>(FixPoint y) {return(x > y.Value());} |
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|
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inline bool FixPoint::operator>(int y) {return(x > y);} |
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|
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inline bool FixPoint::operator>=(FixPoint y) {return(x >= y.Value());} |
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|
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inline bool FixPoint::operator>=(int y) {return(x >= y);} |
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|
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inline bool FixPoint::operator==(FixPoint y) {return(x == y.Value());} |
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|
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inline bool FixPoint::operator==(int y) {return(x == y);} |
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|
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inline bool FixPoint::operator!=(FixPoint y) {return(x != y.Value());} |
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|
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inline bool FixPoint::operator!=(int y) {return(x != y);} |
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|
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|
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|
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/* |
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* In case the first argument is an int (i.e. member-operators not applicable): |
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* Not supported: things like int/FixPoint. The same difference in conversions |
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* applies as mentioned above. |
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*/ |
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|
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|
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// binary operators |
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inline FixPoint operator+(int x, FixPoint y) {return((x << FIXPOINT_PREC) + y.Value());} |
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|
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inline FixPoint operator-(int x, FixPoint y) {return((x << FIXPOINT_PREC) - y.Value());} |
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|
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inline FixPoint operator*(int x, FixPoint y) {return(x*y.Value());} |
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|
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|
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// conditional operators |
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inline bool operator==(int x, FixPoint y) {return(x == y.Value());} |
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|
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inline bool operator!=(int x, FixPoint y) {return(x != y.Value());} |
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|
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inline bool operator<(int x, FixPoint y) {return(x < y.Value());} |
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|
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inline bool operator<=(int x, FixPoint y) {return(x <= y.Value());} |
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|
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inline bool operator>(int x, FixPoint y) {return(x > y.Value());} |
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|
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inline bool operator>=(int x, FixPoint y) {return(x >= y.Value());} |
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|
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|
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|
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/* |
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* For more convenient creation of constant fixpoint numbers from constant floats. |
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*/ |
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|
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#define FixNo(n) (FixPoint)((int)(n*(1<<FIXPOINT_PREC))) |
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|
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|
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|
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|
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|
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|
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/* |
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* Stuff re. the sinus table used with fixpoint arithmetic |
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*/ |
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|
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|
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// define as global variable |
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FixPoint SinTable[(1<<ldSINTAB)]; |
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|
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|
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#define FIXPOINT_SIN_COS_GENERIC \ |
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if (angle >= 3*(1<<ldSINTAB)) {return(-SinTable[(1<<(ldSINTAB+2)) - angle]);}\ |
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if (angle >= 2*(1<<ldSINTAB)) {return(-SinTable[angle - 2*(1<<ldSINTAB)]);}\ |
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if (angle >= (1<<ldSINTAB)) {return(SinTable[2*(1<<ldSINTAB) - angle]);}\ |
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return(SinTable[angle]); |
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|
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|
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// sin and cos: angle is fixpoint number 0 <= angle <= 2 (*PI) |
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static inline FixPoint fixsin(FixPoint x) |
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{ |
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int angle = x; |
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|
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angle = (angle >> (FIXPOINT_PREC - ldSINTAB - 1)) & ((1<<(ldSINTAB+2))-1); |
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FIXPOINT_SIN_COS_GENERIC |
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} |
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|
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|
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static inline FixPoint fixcos(FixPoint x) |
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{ |
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int angle = x; |
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|
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// cos(x) = sin(x+PI/2) |
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angle = (angle + (1<<(FIXPOINT_PREC-1)) >> (FIXPOINT_PREC - ldSINTAB - 1)) & ((1<<(ldSINTAB+2))-1); |
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FIXPOINT_SIN_COS_GENERIC |
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} |
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|
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|
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|
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static inline void InitFixSinTab(void) |
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{ |
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int i; |
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float step; |
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|
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for (i=0, step=0; i<(1<<ldSINTAB); i++, step+=0.5/(1<<ldSINTAB)) |
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{ |
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SinTable[i] = FixNo(sin(M_PI * step)); |
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} |
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} |
