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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.
-*/
-
-#ifndef MATHOPS_H
-#define MATHOPS_H
-
-#include "arch.h"
-#include "entcode.h"
-#include "os_support.h"
-
-/* Multiplies two 16-bit fractional values. Bit-exactness of this macro is important */
-#define FRAC_MUL16(a,b) ((16384+((opus_int32)(opus_int16)(a)*(opus_int16)(b)))>>15)
-
-unsigned isqrt32(opus_uint32 _val);
-
-#ifndef OVERRIDE_CELT_MAXABS16
-static OPUS_INLINE opus_val32 celt_maxabs16(const opus_val16 *x, int len)
-{
- int i;
- opus_val16 maxval = 0;
- opus_val16 minval = 0;
- for (i=0;i<len;i++)
- {
- maxval = MAX16(maxval, x[i]);
- minval = MIN16(minval, x[i]);
- }
- return MAX32(EXTEND32(maxval),-EXTEND32(minval));
-}
-#endif
-
-#ifndef OVERRIDE_CELT_MAXABS32
-#ifdef FIXED_POINT
-static OPUS_INLINE opus_val32 celt_maxabs32(const opus_val32 *x, int len)
-{
- int i;
- opus_val32 maxval = 0;
- opus_val32 minval = 0;
- for (i=0;i<len;i++)
- {
- maxval = MAX32(maxval, x[i]);
- minval = MIN32(minval, x[i]);
- }
- return MAX32(maxval, -minval);
-}
-#else
-#define celt_maxabs32(x,len) celt_maxabs16(x,len)
-#endif
-#endif
-
-
-#ifndef FIXED_POINT
-
-#define PI 3.141592653f
-#define celt_sqrt(x) ((float)sqrt(x))
-#define celt_rsqrt(x) (1.f/celt_sqrt(x))
-#define celt_rsqrt_norm(x) (celt_rsqrt(x))
-#define celt_cos_norm(x) ((float)cos((.5f*PI)*(x)))
-#define celt_rcp(x) (1.f/(x))
-#define celt_div(a,b) ((a)/(b))
-#define frac_div32(a,b) ((float)(a)/(b))
-
-#ifdef FLOAT_APPROX
-
-/* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127
- denorm, +/- inf and NaN are *not* handled */
-
-/** Base-2 log approximation (log2(x)). */
-static OPUS_INLINE float celt_log2(float x)
-{
- int integer;
- float frac;
- union {
- float f;
- opus_uint32 i;
- } in;
- in.f = x;
- integer = (in.i>>23)-127;
- in.i -= integer<<23;
- frac = in.f - 1.5f;
- frac = -0.41445418f + frac*(0.95909232f
- + frac*(-0.33951290f + frac*0.16541097f));
- return 1+integer+frac;
-}
-
-/** Base-2 exponential approximation (2^x). */
-static OPUS_INLINE float celt_exp2(float x)
-{
- int integer;
- float frac;
- union {
- float f;
- opus_uint32 i;
- } res;
- integer = floor(x);
- if (integer < -50)
- return 0;
- frac = x-integer;
- /* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
- res.f = 0.99992522f + frac * (0.69583354f
- + frac * (0.22606716f + 0.078024523f*frac));
- res.i = (res.i + (integer<<23)) & 0x7fffffff;
- return res.f;
-}
-
-#else
-#define celt_log2(x) ((float)(1.442695040888963387*log(x)))
-#define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
-#endif
-
-#endif
-
-#ifdef FIXED_POINT
-
-#include "os_support.h"
-
-#ifndef OVERRIDE_CELT_ILOG2
-/** Integer log in base2. Undefined for zero and negative numbers */
-static OPUS_INLINE opus_int16 celt_ilog2(opus_int32 x)
-{
- celt_assert2(x>0, "celt_ilog2() only defined for strictly positive numbers");
- return EC_ILOG(x)-1;
-}
-#endif
-
-
-/** Integer log in base2. Defined for zero, but not for negative numbers */
-static OPUS_INLINE opus_int16 celt_zlog2(opus_val32 x)
-{
- return x <= 0 ? 0 : celt_ilog2(x);
-}
-
-opus_val16 celt_rsqrt_norm(opus_val32 x);
-
-opus_val32 celt_sqrt(opus_val32 x);
-
-opus_val16 celt_cos_norm(opus_val32 x);
-
-/** Base-2 logarithm approximation (log2(x)). (Q14 input, Q10 output) */
-static OPUS_INLINE opus_val16 celt_log2(opus_val32 x)
-{
- int i;
- opus_val16 n, frac;
- /* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
- 0.15530808010959576, -0.08556153059057618 */
- static const opus_val16 C[5] = {-6801+(1<<(13-DB_SHIFT)), 15746, -5217, 2545, -1401};
- if (x==0)
- return -32767;
- i = celt_ilog2(x);
- n = VSHR32(x,i-15)-32768-16384;
- frac = 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]))))))));
- return SHL16(i-13,DB_SHIFT)+SHR16(frac,14-DB_SHIFT);
-}
-
-/*
- K0 = 1
- K1 = log(2)
- K2 = 3-4*log(2)
- K3 = 3*log(2) - 2
-*/
-#define D0 16383
-#define D1 22804
-#define D2 14819
-#define D3 10204
-
-static OPUS_INLINE opus_val32 celt_exp2_frac(opus_val16 x)
-{
- opus_val16 frac;
- frac = SHL16(x, 4);
- return ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac))))));
-}
-/** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
-static OPUS_INLINE opus_val32 celt_exp2(opus_val16 x)
-{
- int integer;
- opus_val16 frac;
- integer = SHR16(x,10);
- if (integer>14)
- return 0x7f000000;
- else if (integer < -15)
- return 0;
- frac = celt_exp2_frac(x-SHL16(integer,10));
- return VSHR32(EXTEND32(frac), -integer-2);
-}
-
-opus_val32 celt_rcp(opus_val32 x);
-
-#define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
-
-opus_val32 frac_div32(opus_val32 a, opus_val32 b);
-
-#define M1 32767
-#define M2 -21
-#define M3 -11943
-#define M4 4936
-
-/* Atan approximation using a 4th order polynomial. Input is in Q15 format
- and normalized by pi/4. Output is in Q15 format */
-static OPUS_INLINE opus_val16 celt_atan01(opus_val16 x)
-{
- return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x)))))));
-}
-
-#undef M1
-#undef M2
-#undef M3
-#undef M4
-
-/* atan2() approximation valid for positive input values */
-static OPUS_INLINE opus_val16 celt_atan2p(opus_val16 y, opus_val16 x)
-{
- if (y < x)
- {
- opus_val32 arg;
- arg = celt_div(SHL32(EXTEND32(y),15),x);
- if (arg >= 32767)
- arg = 32767;
- return SHR16(celt_atan01(EXTRACT16(arg)),1);
- } else {
- opus_val32 arg;
- arg = celt_div(SHL32(EXTEND32(x),15),y);
- if (arg >= 32767)
- arg = 32767;
- return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1);
- }
-}
-
-#endif /* FIXED_POINT */
-#endif /* MATHOPS_H */
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