| /* Copyright (C) 2002 Jean-Marc Valin */ |
| /** |
| @file math_approx.h |
| @brief Various math approximation functions for Speex |
| */ |
| /* |
| 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. |
| |
| - Neither the name of the Xiph.org Foundation nor the names of its |
| contributors may be used to endorse or promote products derived from |
| this software without specific prior written permission. |
| |
| 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 FOUNDATION 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 MATH_APPROX_H |
| #define MATH_APPROX_H |
| |
| #include "arch.h" |
| |
| #ifndef FIXED_POINT |
| |
| #define spx_sqrt sqrt |
| #define spx_acos acos |
| #define spx_exp exp |
| #define spx_cos_norm(x) (cos((.5f*M_PI)*(x))) |
| #define spx_atan atan |
| |
| /** Generate a pseudo-random number */ |
| static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed) |
| { |
| const unsigned int jflone = 0x3f800000; |
| const unsigned int jflmsk = 0x007fffff; |
| union {int i; float f;} ran; |
| *seed = 1664525 * *seed + 1013904223; |
| ran.i = jflone | (jflmsk & *seed); |
| ran.f -= 1.5; |
| return 3.4642*std*ran.f; |
| } |
| |
| |
| #endif |
| |
| |
| static inline spx_int16_t spx_ilog2(spx_uint32_t x) |
| { |
| int r=0; |
| if (x>=(spx_int32_t)65536) |
| { |
| x >>= 16; |
| r += 16; |
| } |
| if (x>=256) |
| { |
| x >>= 8; |
| r += 8; |
| } |
| if (x>=16) |
| { |
| x >>= 4; |
| r += 4; |
| } |
| if (x>=4) |
| { |
| x >>= 2; |
| r += 2; |
| } |
| if (x>=2) |
| { |
| r += 1; |
| } |
| return r; |
| } |
| |
| static inline spx_int16_t spx_ilog4(spx_uint32_t x) |
| { |
| int r=0; |
| if (x>=(spx_int32_t)65536) |
| { |
| x >>= 16; |
| r += 8; |
| } |
| if (x>=256) |
| { |
| x >>= 8; |
| r += 4; |
| } |
| if (x>=16) |
| { |
| x >>= 4; |
| r += 2; |
| } |
| if (x>=4) |
| { |
| r += 1; |
| } |
| return r; |
| } |
| |
| #ifdef FIXED_POINT |
| |
| /** Generate a pseudo-random number */ |
| static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed) |
| { |
| spx_word32_t res; |
| *seed = 1664525 * *seed + 1013904223; |
| res = MULT16_16(EXTRACT16(SHR32(*seed,16)),std); |
| return EXTRACT16(PSHR32(SUB32(res, SHR32(res, 3)),14)); |
| } |
| |
| /* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25723*x^3 (for .25 < x < 1) */ |
| /*#define C0 3634 |
| #define C1 21173 |
| #define C2 -12627 |
| #define C3 4215*/ |
| |
| /* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25659*x^3 (for .25 < x < 1) */ |
| #define C0 3634 |
| #define C1 21173 |
| #define C2 -12627 |
| #define C3 4204 |
| |
| static inline spx_word16_t spx_sqrt(spx_word32_t x) |
| { |
| int k; |
| spx_word32_t rt; |
| k = spx_ilog4(x)-6; |
| x = VSHR32(x, (k<<1)); |
| rt = ADD16(C0, MULT16_16_Q14(x, ADD16(C1, MULT16_16_Q14(x, ADD16(C2, MULT16_16_Q14(x, (C3))))))); |
| rt = VSHR32(rt,7-k); |
| return rt; |
| } |
| |
| /* log(x) ~= -2.18151 + 4.20592*x - 2.88938*x^2 + 0.86535*x^3 (for .5 < x < 1) */ |
| |
| |
| #define A1 16469 |
| #define A2 2242 |
| #define A3 1486 |
| |
| static inline spx_word16_t spx_acos(spx_word16_t x) |
| { |
| int s=0; |
| spx_word16_t ret; |
| spx_word16_t sq; |
| if (x<0) |
| { |
| s=1; |
| x = NEG16(x); |
| } |
| x = SUB16(16384,x); |
| |
| x = x >> 1; |
| sq = MULT16_16_Q13(x, ADD16(A1, MULT16_16_Q13(x, ADD16(A2, MULT16_16_Q13(x, (A3)))))); |
| ret = spx_sqrt(SHL32(EXTEND32(sq),13)); |
| |
| /*ret = spx_sqrt(67108864*(-1.6129e-04 + 2.0104e+00*f + 2.7373e-01*f*f + 1.8136e-01*f*f*f));*/ |
| if (s) |
| ret = SUB16(25736,ret); |
| return ret; |
| } |
| |
| |
| #define K1 8192 |
| #define K2 -4096 |
| #define K3 340 |
| #define K4 -10 |
| |
| static inline spx_word16_t spx_cos(spx_word16_t x) |
| { |
| spx_word16_t x2; |
| |
| if (x<12868) |
| { |
| x2 = MULT16_16_P13(x,x); |
| return ADD32(K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3, MULT16_16_P13(K4, x2)))))); |
| } else { |
| x = SUB16(25736,x); |
| x2 = MULT16_16_P13(x,x); |
| return SUB32(-K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3, MULT16_16_P13(K4, x2)))))); |
| } |
| } |
| |
| #define L1 32767 |
| #define L2 -7651 |
| #define L3 8277 |
| #define L4 -626 |
| |
| static inline spx_word16_t _spx_cos_pi_2(spx_word16_t x) |
| { |
| spx_word16_t 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)))))))); |
| } |
| |
| static inline spx_word16_t spx_cos_norm(spx_word32_t 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 _spx_cos_pi_2(EXTRACT16(x)); |
| } else { |
| return NEG32(_spx_cos_pi_2(EXTRACT16(65536-x))); |
| } |
| } else { |
| if (x&0x0000ffff) |
| return 0; |
| else if (x&0x0001ffff) |
| return -32767; |
| else |
| return 32767; |
| } |
| } |
| |
| /* |
| K0 = 1 |
| K1 = log(2) |
| K2 = 3-4*log(2) |
| K3 = 3*log(2) - 2 |
| */ |
| #define D0 16384 |
| #define D1 11356 |
| #define D2 3726 |
| #define D3 1301 |
| /* Input in Q11 format, output in Q16 */ |
| static inline spx_word32_t spx_exp2(spx_word16_t x) |
| { |
| int integer; |
| spx_word16_t frac; |
| integer = SHR16(x,11); |
| if (integer>14) |
| return 0x7fffffff; |
| else if (integer < -15) |
| return 0; |
| frac = SHL16(x-SHL16(integer,11),3); |
| frac = ADD16(D0, MULT16_16_Q14(frac, ADD16(D1, MULT16_16_Q14(frac, ADD16(D2 , MULT16_16_Q14(D3,frac)))))); |
| return VSHR32(EXTEND32(frac), -integer-2); |
| } |
| |
| /* Input in Q11 format, output in Q16 */ |
| static inline spx_word32_t spx_exp(spx_word16_t x) |
| { |
| if (x>21290) |
| return 0x7fffffff; |
| else if (x<-21290) |
| return 0; |
| else |
| return spx_exp2(MULT16_16_P14(23637,x)); |
| } |
| #define M1 32767 |
| #define M2 -21 |
| #define M3 -11943 |
| #define M4 4936 |
| |
| static inline spx_word16_t spx_atan01(spx_word16_t 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 |
| |
| /* Input in Q15, output in Q14 */ |
| static inline spx_word16_t spx_atan(spx_word32_t x) |
| { |
| if (x <= 32767) |
| { |
| return SHR16(spx_atan01(x),1); |
| } else { |
| int e = spx_ilog2(x); |
| if (e>=29) |
| return 25736; |
| x = DIV32_16(SHL32(EXTEND32(32767),29-e), EXTRACT16(SHR32(x, e-14))); |
| return SUB16(25736, SHR16(spx_atan01(x),1)); |
| } |
| } |
| #else |
| |
| #ifndef M_PI |
| #define M_PI 3.14159265358979323846 /* pi */ |
| #endif |
| |
| #define C1 0.9999932946f |
| #define C2 -0.4999124376f |
| #define C3 0.0414877472f |
| #define C4 -0.0012712095f |
| |
| |
| #define SPX_PI_2 1.5707963268 |
| static inline spx_word16_t spx_cos(spx_word16_t x) |
| { |
| if (x<SPX_PI_2) |
| { |
| x *= x; |
| return C1 + x*(C2+x*(C3+C4*x)); |
| } else { |
| x = M_PI-x; |
| x *= x; |
| return NEG16(C1 + x*(C2+x*(C3+C4*x))); |
| } |
| } |
| |
| #endif |
| |
| |
| #endif |