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-/* 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 NEG16(_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
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