/*************************************************************************** * __________ __ ___. * Open \______ \ ____ ____ | | _\_ |__ _______ ___ * Source | _// _ \_/ ___\| |/ /| __ \ / _ \ \/ / * Jukebox | | ( <_> ) \___| < | \_\ ( <_> > < < * Firmware |____|_ /\____/ \___ >__|_ \|___ /\____/__/\_ \ * \/ \/ \/ \/ \/ * $Id$ * * Copyright (C) 2006 Jens Arnold * * Fixed point library for plugins * * All files in this archive are subject to the GNU General Public License. * See the file COPYING in the source tree root for full license agreement. * * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY * KIND, either express or implied. * ****************************************************************************/ #include /* Inverse gain of circular cordic rotation in s0.31 format. */ static const long cordic_circular_gain = 0xb2458939; /* 0.607252929 */ /* Table of values of atan(2^-i) in 0.32 format fractions of pi where pi = 0xffffffff / 2 */ static const unsigned long atan_table[] = { 0x1fffffff, /* +0.785398163 (or pi/4) */ 0x12e4051d, /* +0.463647609 */ 0x09fb385b, /* +0.244978663 */ 0x051111d4, /* +0.124354995 */ 0x028b0d43, /* +0.062418810 */ 0x0145d7e1, /* +0.031239833 */ 0x00a2f61e, /* +0.015623729 */ 0x00517c55, /* +0.007812341 */ 0x0028be53, /* +0.003906230 */ 0x00145f2e, /* +0.001953123 */ 0x000a2f98, /* +0.000976562 */ 0x000517cc, /* +0.000488281 */ 0x00028be6, /* +0.000244141 */ 0x000145f3, /* +0.000122070 */ 0x0000a2f9, /* +0.000061035 */ 0x0000517c, /* +0.000030518 */ 0x000028be, /* +0.000015259 */ 0x0000145f, /* +0.000007629 */ 0x00000a2f, /* +0.000003815 */ 0x00000517, /* +0.000001907 */ 0x0000028b, /* +0.000000954 */ 0x00000145, /* +0.000000477 */ 0x000000a2, /* +0.000000238 */ 0x00000051, /* +0.000000119 */ 0x00000028, /* +0.000000060 */ 0x00000014, /* +0.000000030 */ 0x0000000a, /* +0.000000015 */ 0x00000005, /* +0.000000007 */ 0x00000002, /* +0.000000004 */ 0x00000001, /* +0.000000002 */ 0x00000000, /* +0.000000001 */ 0x00000000, /* +0.000000000 */ }; /* Precalculated sine and cosine * 16384 (2^14) (fixed point 18.14) */ static const short sin_table[91] = { 0, 285, 571, 857, 1142, 1427, 1712, 1996, 2280, 2563, 2845, 3126, 3406, 3685, 3963, 4240, 4516, 4790, 5062, 5334, 5603, 5871, 6137, 6401, 6663, 6924, 7182, 7438, 7691, 7943, 8191, 8438, 8682, 8923, 9161, 9397, 9630, 9860, 10086, 10310, 10531, 10748, 10963, 11173, 11381, 11585, 11785, 11982, 12175, 12365, 12550, 12732, 12910, 13084, 13254, 13420, 13582, 13740, 13894, 14043, 14188, 14329, 14466, 14598, 14725, 14848, 14967, 15081, 15190, 15295, 15395, 15491, 15582, 15668, 15749, 15825, 15897, 15964, 16025, 16082, 16135, 16182, 16224, 16261, 16294, 16321, 16344, 16361, 16374, 16381, 16384 }; /** * Implements sin and cos using CORDIC rotation. * * @param phase has range from 0 to 0xffffffff, representing 0 and * 2*pi respectively. * @param cos return address for cos * @return sin of phase, value is a signed value from LONG_MIN to LONG_MAX, * representing -1 and 1 respectively. */ long fsincos(unsigned long phase, long *cos) { int32_t x, x1, y, y1; unsigned long z, z1; int i; /* Setup initial vector */ x = cordic_circular_gain; y = 0; z = phase; /* The phase has to be somewhere between 0..pi for this to work right */ if (z < 0xffffffff / 4) { /* z in first quadrant, z += pi/2 to correct */ x = -x; z += 0xffffffff / 4; } else if (z < 3 * (0xffffffff / 4)) { /* z in third quadrant, z -= pi/2 to correct */ z -= 0xffffffff / 4; } else { /* z in fourth quadrant, z -= 3pi/2 to correct */ x = -x; z -= 3 * (0xffffffff / 4); } /* Each iteration adds roughly 1-bit of extra precision */ for (i = 0; i < 31; i++) { x1 = x >> i; y1 = y >> i; z1 = atan_table[i]; /* Decided which direction to rotate vector. Pivot point is pi/2 */ if (z >= 0xffffffff / 4) { x -= y1; y += x1; z -= z1; } else { x += y1; y -= x1; z += z1; } } if (cos) *cos = x; return y; } /** * Fixed point square root via Newton-Raphson. * @param a square root argument. * @param fracbits specifies number of fractional bits in argument. * @return Square root of argument in same fixed point format as input. */ long fsqrt(long a, unsigned int fracbits) { long b = a/2 + (1 << fracbits); /* initial approximation */ unsigned n; const unsigned iterations = 4; for (n = 0; n < iterations; ++n) b = (b + (long)(((long long)(a) << fracbits)/b))/2; return b; } /** * Fixed point sinus using a lookup table * don't forget to divide the result by 16384 to get the actual sinus value * @param val sinus argument in degree * @return sin(val)*16384 */ long sin_int(int val) { val = (val+360)%360; if (val < 181) { if (val < 91)/* phase 0-90 degree */ return (long)sin_table[val]; else/* phase 91-180 degree */ return (long)sin_table[180-val]; } else { if (val < 271)/* phase 181-270 degree */ return -(long)sin_table[val-180]; else/* phase 270-359 degree */ return -(long)sin_table[360-val]; } return 0; } /** * Fixed point cosinus using a lookup table * don't forget to divide the result by 16384 to get the actual cosinus value * @param val sinus argument in degree * @return cos(val)*16384 */ long cos_int(int val) { val = (val+360)%360; if (val < 181) { if (val < 91)/* phase 0-90 degree */ return (long)sin_table[90-val]; else/* phase 91-180 degree */ return -(long)sin_table[val-90]; } else { if (val < 271)/* phase 181-270 degree */ return -(long)sin_table[270-val]; else/* phase 270-359 degree */ return (long)sin_table[val-270]; } return 0; } /** * Fixed-point natural log * taken from http://www.quinapalus.com/efunc.html * "The code assumes integers are at least 32 bits long. The (positive) * argument and the result of the function are both expressed as fixed-point * values with 16 fractional bits, although intermediates are kept with 28 * bits of precision to avoid loss of accuracy during shifts." */ long flog(int x) { long t,y; y=0xa65af; if(x<0x00008000) x<<=16, y-=0xb1721; if(x<0x00800000) x<<= 8, y-=0x58b91; if(x<0x08000000) x<<= 4, y-=0x2c5c8; if(x<0x20000000) x<<= 2, y-=0x162e4; if(x<0x40000000) x<<= 1, y-=0x0b172; t=x+(x>>1); if((t&0x80000000)==0) x=t,y-=0x067cd; t=x+(x>>2); if((t&0x80000000)==0) x=t,y-=0x03920; t=x+(x>>3); if((t&0x80000000)==0) x=t,y-=0x01e27; t=x+(x>>4); if((t&0x80000000)==0) x=t,y-=0x00f85; t=x+(x>>5); if((t&0x80000000)==0) x=t,y-=0x007e1; t=x+(x>>6); if((t&0x80000000)==0) x=t,y-=0x003f8; t=x+(x>>7); if((t&0x80000000)==0) x=t,y-=0x001fe; x=0x80000000-x; y-=x>>15; return y; }