| /* Copyright (C) 2005 Jean-Marc Valin */ |
| /** |
| @file pseudofloat.h |
| @brief Pseudo-floating point |
| * This header file provides a lightweight floating point type for |
| * use on fixed-point platforms when a large dynamic range is |
| * required. The new type is not compatible with the 32-bit IEEE format, |
| * it is not even remotely as accurate as 32-bit floats, and is not |
| * even guaranteed to produce even remotely correct results for code |
| * other than Speex. It makes all kinds of shortcuts that are acceptable |
| * for Speex, but may not be acceptable for your application. You're |
| * quite welcome to reuse this code and improve it, but don't assume |
| * it works out of the box. Most likely, it doesn't. |
| */ |
| /* |
| 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 PSEUDOFLOAT_H |
| #define PSEUDOFLOAT_H |
| |
| #include "arch.h" |
| #include "os_support.h" |
| #include "math_approx.h" |
| #include <math.h> |
| |
| #ifdef FIXED_POINT |
| |
| typedef struct { |
| spx_int16_t m; |
| spx_int16_t e; |
| } spx_float_t; |
| |
| static const spx_float_t FLOAT_ZERO = {0,0}; |
| static const spx_float_t FLOAT_ONE = {16384,-14}; |
| static const spx_float_t FLOAT_HALF = {16384,-15}; |
| |
| #define MIN(a,b) ((a)<(b)?(a):(b)) |
| static inline spx_float_t PSEUDOFLOAT(spx_int32_t x) |
| { |
| int e=0; |
| int sign=0; |
| if (x<0) |
| { |
| sign = 1; |
| x = -x; |
| } |
| if (x==0) |
| { |
| spx_float_t r = {0,0}; |
| return r; |
| } |
| e = spx_ilog2(ABS32(x))-14; |
| x = VSHR32(x, e); |
| if (sign) |
| { |
| spx_float_t r; |
| r.m = -x; |
| r.e = e; |
| return r; |
| } |
| else |
| { |
| spx_float_t r; |
| r.m = x; |
| r.e = e; |
| return r; |
| } |
| } |
| |
| |
| static inline spx_float_t FLOAT_ADD(spx_float_t a, spx_float_t b) |
| { |
| spx_float_t r; |
| if (a.m==0) |
| return b; |
| else if (b.m==0) |
| return a; |
| if ((a).e > (b).e) |
| { |
| r.m = ((a).m>>1) + ((b).m>>MIN(15,(a).e-(b).e+1)); |
| r.e = (a).e+1; |
| } |
| else |
| { |
| r.m = ((b).m>>1) + ((a).m>>MIN(15,(b).e-(a).e+1)); |
| r.e = (b).e+1; |
| } |
| if (r.m>0) |
| { |
| if (r.m<16384) |
| { |
| r.m<<=1; |
| r.e-=1; |
| } |
| } else { |
| if (r.m>-16384) |
| { |
| r.m<<=1; |
| r.e-=1; |
| } |
| } |
| /*printf ("%f + %f = %f\n", REALFLOAT(a), REALFLOAT(b), REALFLOAT(r));*/ |
| return r; |
| } |
| |
| static inline spx_float_t FLOAT_SUB(spx_float_t a, spx_float_t b) |
| { |
| spx_float_t r; |
| if (a.m==0) |
| return b; |
| else if (b.m==0) |
| return a; |
| if ((a).e > (b).e) |
| { |
| r.m = ((a).m>>1) - ((b).m>>MIN(15,(a).e-(b).e+1)); |
| r.e = (a).e+1; |
| } |
| else |
| { |
| r.m = ((a).m>>MIN(15,(b).e-(a).e+1)) - ((b).m>>1); |
| r.e = (b).e+1; |
| } |
| if (r.m>0) |
| { |
| if (r.m<16384) |
| { |
| r.m<<=1; |
| r.e-=1; |
| } |
| } else { |
| if (r.m>-16384) |
| { |
| r.m<<=1; |
| r.e-=1; |
| } |
| } |
| /*printf ("%f + %f = %f\n", REALFLOAT(a), REALFLOAT(b), REALFLOAT(r));*/ |
| return r; |
| } |
| |
| static inline int FLOAT_LT(spx_float_t a, spx_float_t b) |
| { |
| if (a.m==0) |
| return b.m>0; |
| else if (b.m==0) |
| return a.m<0; |
| if ((a).e > (b).e) |
| return ((a).m>>1) < ((b).m>>MIN(15,(a).e-(b).e+1)); |
| else |
| return ((b).m>>1) > ((a).m>>MIN(15,(b).e-(a).e+1)); |
| |
| } |
| |
| static inline int FLOAT_GT(spx_float_t a, spx_float_t b) |
| { |
| return FLOAT_LT(b,a); |
| } |
| |
| static inline spx_float_t FLOAT_MULT(spx_float_t a, spx_float_t b) |
| { |
| spx_float_t r; |
| r.m = (spx_int16_t)((spx_int32_t)(a).m*(b).m>>15); |
| r.e = (a).e+(b).e+15; |
| if (r.m>0) |
| { |
| if (r.m<16384) |
| { |
| r.m<<=1; |
| r.e-=1; |
| } |
| } else { |
| if (r.m>-16384) |
| { |
| r.m<<=1; |
| r.e-=1; |
| } |
| } |
| /*printf ("%f * %f = %f\n", REALFLOAT(a), REALFLOAT(b), REALFLOAT(r));*/ |
| return r; |
| } |
| |
| static inline spx_float_t FLOAT_AMULT(spx_float_t a, spx_float_t b) |
| { |
| spx_float_t r; |
| r.m = (spx_int16_t)((spx_int32_t)(a).m*(b).m>>15); |
| r.e = (a).e+(b).e+15; |
| return r; |
| } |
| |
| |
| static inline spx_float_t FLOAT_SHL(spx_float_t a, int b) |
| { |
| spx_float_t r; |
| r.m = a.m; |
| r.e = a.e+b; |
| return r; |
| } |
| |
| static inline spx_int16_t FLOAT_EXTRACT16(spx_float_t a) |
| { |
| if (a.e<0) |
| return EXTRACT16((EXTEND32(a.m)+(EXTEND32(1)<<(-a.e-1)))>>-a.e); |
| else |
| return a.m<<a.e; |
| } |
| |
| static inline spx_int32_t FLOAT_EXTRACT32(spx_float_t a) |
| { |
| if (a.e<0) |
| return (EXTEND32(a.m)+(EXTEND32(1)<<(-a.e-1)))>>-a.e; |
| else |
| return EXTEND32(a.m)<<a.e; |
| } |
| |
| static inline spx_int32_t FLOAT_MUL32(spx_float_t a, spx_word32_t b) |
| { |
| return VSHR32(MULT16_32_Q15(a.m, b),-a.e-15); |
| } |
| |
| static inline spx_float_t FLOAT_MUL32U(spx_word32_t a, spx_word32_t b) |
| { |
| int e1, e2; |
| spx_float_t r; |
| if (a==0 || b==0) |
| { |
| return FLOAT_ZERO; |
| } |
| e1 = spx_ilog2(ABS32(a)); |
| a = VSHR32(a, e1-14); |
| e2 = spx_ilog2(ABS32(b)); |
| b = VSHR32(b, e2-14); |
| r.m = MULT16_16_Q15(a,b); |
| r.e = e1+e2-13; |
| return r; |
| } |
| |
| /* Do NOT attempt to divide by a negative number */ |
| static inline spx_float_t FLOAT_DIV32_FLOAT(spx_word32_t a, spx_float_t b) |
| { |
| int e=0; |
| spx_float_t r; |
| if (a==0) |
| { |
| return FLOAT_ZERO; |
| } |
| e = spx_ilog2(ABS32(a))-spx_ilog2(b.m-1)-15; |
| a = VSHR32(a, e); |
| if (ABS32(a)>=SHL32(EXTEND32(b.m-1),15)) |
| { |
| a >>= 1; |
| e++; |
| } |
| r.m = DIV32_16(a,b.m); |
| r.e = e-b.e; |
| return r; |
| } |
| |
| |
| /* Do NOT attempt to divide by a negative number */ |
| static inline spx_float_t FLOAT_DIV32(spx_word32_t a, spx_word32_t b) |
| { |
| int e0=0,e=0; |
| spx_float_t r; |
| if (a==0) |
| { |
| return FLOAT_ZERO; |
| } |
| if (b>32767) |
| { |
| e0 = spx_ilog2(b)-14; |
| b = VSHR32(b, e0); |
| e0 = -e0; |
| } |
| e = spx_ilog2(ABS32(a))-spx_ilog2(b-1)-15; |
| a = VSHR32(a, e); |
| if (ABS32(a)>=SHL32(EXTEND32(b-1),15)) |
| { |
| a >>= 1; |
| e++; |
| } |
| e += e0; |
| r.m = DIV32_16(a,b); |
| r.e = e; |
| return r; |
| } |
| |
| /* Do NOT attempt to divide by a negative number */ |
| static inline spx_float_t FLOAT_DIVU(spx_float_t a, spx_float_t b) |
| { |
| int e=0; |
| spx_int32_t num; |
| spx_float_t r; |
| if (b.m<=0) |
| { |
| speex_warning_int("Attempted to divide by", b.m); |
| return FLOAT_ONE; |
| } |
| num = a.m; |
| a.m = ABS16(a.m); |
| while (a.m >= b.m) |
| { |
| e++; |
| a.m >>= 1; |
| } |
| num = num << (15-e); |
| r.m = DIV32_16(num,b.m); |
| r.e = a.e-b.e-15+e; |
| return r; |
| } |
| |
| static inline spx_float_t FLOAT_SQRT(spx_float_t a) |
| { |
| spx_float_t r; |
| spx_int32_t m; |
| m = SHL32(EXTEND32(a.m), 14); |
| r.e = a.e - 14; |
| if (r.e & 1) |
| { |
| r.e -= 1; |
| m <<= 1; |
| } |
| r.e >>= 1; |
| r.m = spx_sqrt(m); |
| return r; |
| } |
| |
| #else |
| |
| #define spx_float_t float |
| #define FLOAT_ZERO 0.f |
| #define FLOAT_ONE 1.f |
| #define FLOAT_HALF 0.5f |
| #define PSEUDOFLOAT(x) (x) |
| #define FLOAT_MULT(a,b) ((a)*(b)) |
| #define FLOAT_AMULT(a,b) ((a)*(b)) |
| #define FLOAT_MUL32(a,b) ((a)*(b)) |
| #define FLOAT_DIV32(a,b) ((a)/(b)) |
| #define FLOAT_EXTRACT16(a) (a) |
| #define FLOAT_EXTRACT32(a) (a) |
| #define FLOAT_ADD(a,b) ((a)+(b)) |
| #define FLOAT_SUB(a,b) ((a)-(b)) |
| #define REALFLOAT(x) (x) |
| #define FLOAT_DIV32_FLOAT(a,b) ((a)/(b)) |
| #define FLOAT_MUL32U(a,b) ((a)*(b)) |
| #define FLOAT_SHL(a,b) (a) |
| #define FLOAT_LT(a,b) ((a)<(b)) |
| #define FLOAT_GT(a,b) ((a)>(b)) |
| #define FLOAT_DIVU(a,b) ((a)/(b)) |
| #define FLOAT_SQRT(a) (spx_sqrt(a)) |
| |
| #endif |
| |
| #endif |