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Diffstat (limited to 'thirdparty/opus/celt/mathops.c')
| -rw-r--r-- | thirdparty/opus/celt/mathops.c | 208 |
1 files changed, 208 insertions, 0 deletions
diff --git a/thirdparty/opus/celt/mathops.c b/thirdparty/opus/celt/mathops.c new file mode 100644 index 0000000000..3f8c5dcc0e --- /dev/null +++ b/thirdparty/opus/celt/mathops.c @@ -0,0 +1,208 @@ +/* Copyright (c) 2002-2008 Jean-Marc Valin + Copyright (c) 2007-2008 CSIRO + Copyright (c) 2007-2009 Xiph.Org Foundation + Written by Jean-Marc Valin */ +/** + @file mathops.h + @brief Various math functions +*/ +/* + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions + are met: + + - Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + + - Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + + THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR + A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER + OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF + LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING + NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +*/ + +#ifdef HAVE_CONFIG_H +#include "config.h" +#endif + +#include "mathops.h" + +/*Compute floor(sqrt(_val)) with exact arithmetic. + This has been tested on all possible 32-bit inputs.*/ +unsigned isqrt32(opus_uint32 _val){ + unsigned b; + unsigned g; + int bshift; + /*Uses the second method from + http://www.azillionmonkeys.com/qed/sqroot.html + The main idea is to search for the largest binary digit b such that + (g+b)*(g+b) <= _val, and add it to the solution g.*/ + g=0; + bshift=(EC_ILOG(_val)-1)>>1; + b=1U<<bshift; + do{ + opus_uint32 t; + t=(((opus_uint32)g<<1)+b)<<bshift; + if(t<=_val){ + g+=b; + _val-=t; + } + b>>=1; + bshift--; + } + while(bshift>=0); + return g; +} + +#ifdef FIXED_POINT + +opus_val32 frac_div32(opus_val32 a, opus_val32 b) +{ + opus_val16 rcp; + opus_val32 result, rem; + int shift = celt_ilog2(b)-29; + a = VSHR32(a,shift); + b = VSHR32(b,shift); + /* 16-bit reciprocal */ + rcp = ROUND16(celt_rcp(ROUND16(b,16)),3); + result = MULT16_32_Q15(rcp, a); + rem = PSHR32(a,2)-MULT32_32_Q31(result, b); + result = ADD32(result, SHL32(MULT16_32_Q15(rcp, rem),2)); + if (result >= 536870912) /* 2^29 */ + return 2147483647; /* 2^31 - 1 */ + else if (result <= -536870912) /* -2^29 */ + return -2147483647; /* -2^31 */ + else + return SHL32(result, 2); +} + +/** Reciprocal sqrt approximation in the range [0.25,1) (Q16 in, Q14 out) */ +opus_val16 celt_rsqrt_norm(opus_val32 x) +{ + opus_val16 n; + opus_val16 r; + opus_val16 r2; + opus_val16 y; + /* Range of n is [-16384,32767] ([-0.5,1) in Q15). */ + n = x-32768; + /* Get a rough initial guess for the root. + The optimal minimax quadratic approximation (using relative error) is + r = 1.437799046117536+n*(-0.823394375837328+n*0.4096419668459485). + Coefficients here, and the final result r, are Q14.*/ + r = ADD16(23557, MULT16_16_Q15(n, ADD16(-13490, MULT16_16_Q15(n, 6713)))); + /* We want y = x*r*r-1 in Q15, but x is 32-bit Q16 and r is Q14. + We can compute the result from n and r using Q15 multiplies with some + adjustment, carefully done to avoid overflow. + Range of y is [-1564,1594]. */ + r2 = MULT16_16_Q15(r, r); + y = SHL16(SUB16(ADD16(MULT16_16_Q15(r2, n), r2), 16384), 1); + /* Apply a 2nd-order Householder iteration: r += r*y*(y*0.375-0.5). + This yields the Q14 reciprocal square root of the Q16 x, with a maximum + relative error of 1.04956E-4, a (relative) RMSE of 2.80979E-5, and a + peak absolute error of 2.26591/16384. */ + return ADD16(r, MULT16_16_Q15(r, MULT16_16_Q15(y, + SUB16(MULT16_16_Q15(y, 12288), 16384)))); +} + +/** Sqrt approximation (QX input, QX/2 output) */ +opus_val32 celt_sqrt(opus_val32 x) +{ + int k; + opus_val16 n; + opus_val32 rt; + static const opus_val16 C[5] = {23175, 11561, -3011, 1699, -664}; + if (x==0) + return 0; + else if (x>=1073741824) + return 32767; + k = (celt_ilog2(x)>>1)-7; + x = VSHR32(x, 2*k); + n = x-32768; + rt = ADD16(C[0], MULT16_16_Q15(n, ADD16(C[1], MULT16_16_Q15(n, ADD16(C[2], + MULT16_16_Q15(n, ADD16(C[3], MULT16_16_Q15(n, (C[4]))))))))); + rt = VSHR32(rt,7-k); + return rt; +} + +#define L1 32767 +#define L2 -7651 +#define L3 8277 +#define L4 -626 + +static OPUS_INLINE opus_val16 _celt_cos_pi_2(opus_val16 x) +{ + opus_val16 x2; + + x2 = MULT16_16_P15(x,x); + return ADD16(1,MIN16(32766,ADD32(SUB16(L1,x2), MULT16_16_P15(x2, ADD32(L2, MULT16_16_P15(x2, ADD32(L3, MULT16_16_P15(L4, x2 + )))))))); +} + +#undef L1 +#undef L2 +#undef L3 +#undef L4 + +opus_val16 celt_cos_norm(opus_val32 x) +{ + x = x&0x0001ffff; + if (x>SHL32(EXTEND32(1), 16)) + x = SUB32(SHL32(EXTEND32(1), 17),x); + if (x&0x00007fff) + { + if (x<SHL32(EXTEND32(1), 15)) + { + return _celt_cos_pi_2(EXTRACT16(x)); + } else { + return NEG32(_celt_cos_pi_2(EXTRACT16(65536-x))); + } + } else { + if (x&0x0000ffff) + return 0; + else if (x&0x0001ffff) + return -32767; + else + return 32767; + } +} + +/** Reciprocal approximation (Q15 input, Q16 output) */ +opus_val32 celt_rcp(opus_val32 x) +{ + int i; + opus_val16 n; + opus_val16 r; + celt_assert2(x>0, "celt_rcp() only defined for positive values"); + i = celt_ilog2(x); + /* n is Q15 with range [0,1). */ + n = VSHR32(x,i-15)-32768; + /* Start with a linear approximation: + r = 1.8823529411764706-0.9411764705882353*n. + The coefficients and the result are Q14 in the range [15420,30840].*/ + r = ADD16(30840, MULT16_16_Q15(-15420, n)); + /* Perform two Newton iterations: + r -= r*((r*n)-1.Q15) + = r*((r*n)+(r-1.Q15)). */ + r = SUB16(r, MULT16_16_Q15(r, + ADD16(MULT16_16_Q15(r, n), ADD16(r, -32768)))); + /* We subtract an extra 1 in the second iteration to avoid overflow; it also + neatly compensates for truncation error in the rest of the process. */ + r = SUB16(r, ADD16(1, MULT16_16_Q15(r, + ADD16(MULT16_16_Q15(r, n), ADD16(r, -32768))))); + /* r is now the Q15 solution to 2/(n+1), with a maximum relative error + of 7.05346E-5, a (relative) RMSE of 2.14418E-5, and a peak absolute + error of 1.24665/32768. */ + return VSHR32(EXTEND32(r),i-16); +} + +#endif |