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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"
+
+#define PI 3.141592653f
+
+/* 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);
+
+/* CELT doesn't need it for fixed-point, by analysis.c does. */
+#if !defined(FIXED_POINT) || defined(ANALYSIS_C)
+#define cA 0.43157974f
+#define cB 0.67848403f
+#define cC 0.08595542f
+#define cE ((float)PI/2)
+static OPUS_INLINE float fast_atan2f(float y, float x) {
+ float x2, y2;
+ x2 = x*x;
+ y2 = y*y;
+ /* For very small values, we don't care about the answer, so
+ we can just return 0. */
+ if (x2 + y2 < 1e-18f)
+ {
+ return 0;
+ }
+ if(x2<y2){
+ float den = (y2 + cB*x2) * (y2 + cC*x2);
+ return -x*y*(y2 + cA*x2) / den + (y<0 ? -cE : cE);
+ }else{
+ float den = (x2 + cB*y2) * (x2 + cC*y2);
+ return x*y*(x2 + cA*y2) / den + (y<0 ? -cE : cE) - (x*y<0 ? -cE : cE);
+ }
+}
+#undef cA
+#undef cB
+#undef cC
+#undef cE
+#endif
+
+
+#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 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 -= (opus_uint32)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 = (int)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 + ((opus_uint32)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_sig_assert(x>0);
+ 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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