1 /*----------------------------------------------------------------------------
2  *
3  * File:
4  * eas_math.h
5  *
6  * Contents and purpose:
7  * Contains common math routines for the various audio engines.
8  *
9  *
10  * Copyright Sonic Network Inc. 2005
11 
12  * Licensed under the Apache License, Version 2.0 (the "License");
13  * you may not use this file except in compliance with the License.
14  * You may obtain a copy of the License at
15  *
16  *      http://www.apache.org/licenses/LICENSE-2.0
17  *
18  * Unless required by applicable law or agreed to in writing, software
19  * distributed under the License is distributed on an "AS IS" BASIS,
20  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
21  * See the License for the specific language governing permissions and
22  * limitations under the License.
23  *
24  *----------------------------------------------------------------------------
25  * Revision Control:
26  *   $Revision: 584 $
27  *   $Date: 2007-03-08 09:49:24 -0800 (Thu, 08 Mar 2007) $
28  *----------------------------------------------------------------------------
29 */
30 
31 #ifndef _EAS_MATH_H
32 #define _EAS_MATH_H
33 
34 #include <stdint.h>
35 
36 /** coefs for pan, generates sin, cos */
37 #define COEFF_PAN_G2    -27146      /* -0.82842712474619 = 2 - 4/sqrt(2) */
38 #define COEFF_PAN_G0    23170       /* 0.707106781186547 = 1/sqrt(2) */
39 
40 /*
41 coefficients for approximating
42 2^x = gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3
43 where x is a int.frac number representing number of octaves.
44 Actually, we approximate only the 2^(frac) using the power series
45 and implement the 2^(int) as a shift, so that
46 2^x == 2^(int.frac) == 2^(int) * 2^(fract)
47     == (gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3) << (int)
48 
49 The gn2toX.. were generated using a best fit for a 3rd
50 order polynomial, instead of taking the coefficients from
51 a truncated Taylor (or Maclaurin?) series.
52 */
53 
54 #define GN2_TO_X0   32768   /*  1                   */
55 #define GN2_TO_X1   22833   /*  0.696807861328125   */
56 #define GN2_TO_X2   7344    /*  0.22412109375       */
57 #define GN2_TO_X3   2588    /*  0.0789794921875     */
58 
59 /*----------------------------------------------------------------------------
60  * Fixed Point Math
61  *----------------------------------------------------------------------------
62  * These macros are used for fixed point multiplies. If the processor
63  * supports fixed point multiplies, replace these macros with inline
64  * assembly code to improve performance.
65  *----------------------------------------------------------------------------
66 */
67 
68 /* Fixed point multiply 0.15 x 0.15 = 0.15 returned as 32-bits */
69 #define FMUL_15x15(a,b) \
70     /*lint -e(704) <avoid multiply for performance>*/ \
71     (((int32_t)(a) * (int32_t)(b)) >> 15)
72 
73 /* Fixed point multiply 0.7 x 0.7 = 0.15 returned as 32-bits */
74 #define FMUL_7x7(a,b) \
75     /*lint -e(704) <avoid multiply for performance>*/ \
76     (((int32_t)(a) * (int32_t)(b) ) << 1)
77 
78 /* Fixed point multiply 0.8 x 0.8 = 0.15 returned as 32-bits */
79 #define FMUL_8x8(a,b) \
80     /*lint -e(704) <avoid multiply for performance>*/ \
81     (((int32_t)(a) * (int32_t)(b) ) >> 1)
82 
83 /* Fixed point multiply 0.8 x 1.15 = 0.15 returned as 32-bits */
84 #define FMUL_8x15(a,b) \
85     /*lint -e(704) <avoid divide for performance>*/ \
86     (((int32_t)((a) << 7) * (int32_t)(b)) >> 15)
87 
88 /* macros for fractional phase accumulator */
89 /*
90 Note: changed the _U32 to _I32 on 03/14/02. This should not
91 affect the phase calculations, and should allow us to reuse these
92 macros for other audio sample related math.
93 */
94 #define HARDWARE_BIT_WIDTH      32
95 
96 #define NUM_PHASE_INT_BITS      1
97 #define NUM_PHASE_FRAC_BITS     15
98 
99 #define PHASE_FRAC_MASK         (uint32_t) ((0x1L << NUM_PHASE_FRAC_BITS) -1)
100 
101 #define GET_PHASE_INT_PART(x)   (uint32_t)((uint32_t)(x) >> NUM_PHASE_FRAC_BITS)
102 #define GET_PHASE_FRAC_PART(x)  (uint32_t)((uint32_t)(x) & PHASE_FRAC_MASK)
103 
104 #define DEFAULT_PHASE_FRAC      0
105 #define DEFAULT_PHASE_INT       0
106 
107 /*
108 Linear interpolation calculates:
109 output = (1-frac) * sample[n] + (frac) * sample[n+1]
110 
111 where conceptually  0 <= frac < 1
112 
113 For a fixed point implementation, frac is actually an integer value
114 with an implied binary point one position to the left. The value of
115 one (unity) is given by PHASE_ONE
116 one half and one quarter are useful for 4-point linear interp.
117 */
118 #define PHASE_ONE               (int32_t) (0x1L << NUM_PHASE_FRAC_BITS)
119 
120 /*
121  Multiply the signed audio sample by the unsigned fraction.
122 -  a is the signed audio sample
123 -  b is the unsigned fraction (cast to signed int as long as coef
124     uses (n-1) or less bits, where n == hardware bit width)
125 */
126 #define MULT_AUDIO_COEF(audio,coef)         /*lint -e704 <avoid divide for performance>*/ \
127             (int32_t)(                                  \
128             (                                           \
129                 ((int32_t)(audio)) * ((int32_t)(coef))  \
130             )                                           \
131             >> NUM_PHASE_FRAC_BITS                      \
132                                         )               \
133                                         /* lint +704 <restore checking>*/
134 
135 /* wet / dry calculation macros */
136 #define NUM_WET_DRY_FRAC_BITS       7   // 15
137 #define NUM_WET_DRY_INT_BITS        9   // 1
138 
139 /* define a 1.0 */
140 #define WET_DRY_ONE                 (int32_t) ((0x1L << NUM_WET_DRY_FRAC_BITS))
141 #define WET_DRY_MINUS_ONE           (int32_t) (~WET_DRY_ONE)
142 #define WET_DRY_FULL_SCALE          (int32_t) (WET_DRY_ONE - 1)
143 
144 #define MULT_AUDIO_WET_DRY_COEF(audio,coef) /*lint -e(702) <avoid divide for performance>*/ \
145             (int32_t)(                                      \
146             (                                               \
147                 ((int32_t)(audio)) * ((int32_t)(coef))      \
148             )                                               \
149             >> NUM_WET_DRY_FRAC_BITS                        \
150                                                      )
151 
152 /* Envelope 1 (EG1) calculation macros */
153 #define NUM_EG1_INT_BITS            1
154 #define NUM_EG1_FRAC_BITS           15
155 
156 /* the max positive gain used in the synth for EG1 */
157 /* SYNTH_FULL_SCALE_EG1_GAIN must match the value in the dls2eas
158 converter, otherwise, the values we read from the .eas file are bogus. */
159 #define SYNTH_FULL_SCALE_EG1_GAIN   (int32_t) ((0x1L << NUM_EG1_FRAC_BITS) -1)
160 
161 /* define a 1.0 */
162 #define EG1_ONE                     (int32_t) ((0x1L << NUM_EG1_FRAC_BITS))
163 #define EG1_MINUS_ONE               (int32_t) (~SYNTH_FULL_SCALE_EG1_GAIN)
164 
165 #define EG1_HALF                    (int32_t) (EG1_ONE/2)
166 #define EG1_MINUS_HALF              (int32_t) (EG1_MINUS_ONE/2)
167 
168 /*
169 We implement the EG1 using a linear gain value, which means that the
170 attack segment is handled by incrementing (adding) the linear gain.
171 However, EG1 treats the Decay, Sustain, and Release differently than
172 the Attack portion. For Decay, Sustain, and Release, the gain is
173 linear on dB scale, which is equivalent to exponential damping on
174 a linear scale. Because we use a linear gain for EG1, we implement
175 the Decay and Release as multiplication (instead of incrementing
176 as we did for the attack segment).
177 Therefore, we need the following macro to implement the multiplication
178 (i.e., exponential damping) during the Decay and Release segments of
179 the EG1
180 */
181 #define MULT_EG1_EG1(gain,damping)      /*lint -e(704) <avoid divide for performance>*/ \
182             (int32_t)(                                      \
183             (                                               \
184                 ((int32_t)(gain)) * ((int32_t)(damping))    \
185             )                                               \
186             >> NUM_EG1_FRAC_BITS                            \
187                                         )
188 
189 // Use the following macro specifically for the filter, when multiplying
190 // the b1 coefficient. The 0 <= |b1| < 2, which therefore might overflow
191 // in certain conditions because we store b1 as a 1.15 value.
192 // Instead, we could store b1 as b1p (b1' == b1 "prime") where
193 // b1p == b1/2, thus ensuring no potential overflow for b1p because
194 // 0 <= |b1p| < 1
195 // However, during the filter calculation, we must account for the fact
196 // that we are using b1p instead of b1, and thereby multiply by
197 // an extra factor of 2. Rather than multiply by an extra factor of 2,
198 // we can instead shift the result right by one less, hence the
199 // modified shift right value of (NUM_EG1_FRAC_BITS -1)
200 #define MULT_EG1_EG1_X2(gain,damping)       /*lint -e(702) <avoid divide for performance>*/ \
201             (int32_t)(                                      \
202             (                                               \
203                 ((int32_t)(gain)) * ((int32_t)(damping))    \
204             )                                               \
205             >> (NUM_EG1_FRAC_BITS -1)                       \
206                                         )
207 
208 #define SATURATE_EG1(x)     /*lint -e{734} saturation operation */              \
209     ((int32_t)(x) > SYNTH_FULL_SCALE_EG1_GAIN)  ? (SYNTH_FULL_SCALE_EG1_GAIN) : \
210     ((int32_t)(x) < EG1_MINUS_ONE)              ? (EG1_MINUS_ONE) : (x);
211 
212 
213 /* use "digital cents" == "dents" instead of cents */
214 /* we coudl re-use the phase frac macros, but if we do,
215 we must change the phase macros to cast to _I32 instead of _U32,
216 because using a _U32 cast causes problems when shifting the exponent
217 for the 2^x calculation, because right shift a negative values MUST
218 be sign extended, or else the 2^x calculation is wrong */
219 
220 /* use "digital cents" == "dents" instead of cents */
221 #define NUM_DENTS_FRAC_BITS     12
222 #define NUM_DENTS_INT_BITS      (HARDWARE_BIT_WIDTH - NUM_DENTS_FRAC_BITS)
223 
224 #define DENTS_FRAC_MASK             (int32_t) ((0x1L << NUM_DENTS_FRAC_BITS) -1)
225 
226 #define GET_DENTS_INT_PART(x)       /*lint -e(704) <avoid divide for performance>*/ \
227                             (int32_t)((int32_t)(x) >> NUM_DENTS_FRAC_BITS)
228 
229 #define GET_DENTS_FRAC_PART(x)  (int32_t)((int32_t)(x) & DENTS_FRAC_MASK)
230 
231 #define DENTS_ONE               (int32_t) (0x1L << NUM_DENTS_FRAC_BITS)
232 
233 /* use CENTS_TO_DENTS to convert a value in cents to dents */
234 #define CENTS_TO_DENTS (int32_t) (DENTS_ONE * (0x1L << NUM_EG1_FRAC_BITS) / 1200L)                          \
235 
236 
237 /*
238 For gain, the LFO generates a value that modulates in terms
239 of dB. However, we use a linear gain value, so we must convert
240 the LFO value in dB to a linear gain. Normally, we would use
241 linear gain = 10^x, where x = LFO value in dB / 20.
242 Instead, we implement 10^x using our 2^x approximation.
243 because
244 
245   10^x = 2^(log2(10^x)) = 2^(x * log2(10))
246 
247 so we need to multiply by log2(10) which is just a constant.
248 Ah, but just wait -- our 2^x actually doesn't exactly implement
249 2^x, but it actually assumes that the input is in cents, and within
250 the 2^x approximation converts its input from cents to octaves
251 by dividing its input by 1200.
252 
253 So, in order to convert the LFO gain value in dB to something
254 that our existing 2^x approximation can use, multiply the LFO gain
255 by log2(10) * 1200 / 20
256 
257 The divide by 20 helps convert dB to linear gain, and we might
258 as well incorporate that operation into this conversion.
259 Of course, we need to keep some fractional bits, so multiply
260 the constant by NUM_EG1_FRAC_BITS
261 */
262 
263 /* use LFO_GAIN_TO_CENTS to convert the LFO gain value to cents */
264 #if 0
265 #define DOUBLE_LOG2_10  (double) (3.32192809488736) /* log2(10) */
266 
267 #define DOUBLE_LFO_GAIN_TO_CENTS    (double)                \
268     (                                                       \
269                 (DOUBLE_LOG2_10) *                          \
270                 1200.0  /                                   \
271                 20.0                                        \
272     )
273 
274 #define LFO_GAIN_TO_CENTS   (int32_t)                       \
275     (                                                       \
276                 DOUBLE_LFO_GAIN_TO_CENTS *                  \
277                 (0x1L << NUM_EG1_FRAC_BITS)                 \
278     )
279 #endif
280 
281 #define LFO_GAIN_TO_CENTS (int32_t) (1671981156L >> (23 - NUM_EG1_FRAC_BITS))
282 
283 
284 #define MULT_DENTS_COEF(dents,coef)     /*lint -e704 <avoid divide for performance>*/   \
285             (int32_t)(                                  \
286             (                                           \
287                 ((int32_t)(dents)) * ((int32_t)(coef))  \
288             )                                           \
289             >> NUM_DENTS_FRAC_BITS                      \
290                                         )               \
291                                         /* lint +e704 <restore checking>*/
292 
293 /* we use 16-bits in the PC per audio sample */
294 #define BITS_PER_AUDIO_SAMPLE   16
295 
296 /* we define 1 as 1.0 - 1 LSbit */
297 #define DISTORTION_ONE          (int32_t)((0x1L << (BITS_PER_AUDIO_SAMPLE-1)) -1)
298 #define DISTORTION_MINUS_ONE    (int32_t)(~DISTORTION_ONE)
299 
300 /* drive coef is given as int.frac */
301 #define NUM_DRIVE_COEF_INT_BITS     1
302 #define NUM_DRIVE_COEF_FRAC_BITS    4
303 
304 #define MULT_AUDIO_DRIVE(audio,drive)       /*lint -e(702) <avoid divide for performance>*/ \
305             (int32_t)   (                               \
306             (                                           \
307                 ((int32_t)(audio)) * ((int32_t)(drive)) \
308             )                                           \
309             >> NUM_DRIVE_COEF_FRAC_BITS                 \
310                                                 )
311 
312 #define MULT_AUDIO_AUDIO(audio1,audio2)         /*lint -e(702) <avoid divide for performance>*/ \
313             (int32_t)   (                                   \
314             (                                               \
315                 ((int32_t)(audio1)) * ((int32_t)(audio2))   \
316             )                                               \
317             >> (BITS_PER_AUDIO_SAMPLE-1)                    \
318                                                     )
319 
320 #define SATURATE(x)                                                         \
321     ((((int32_t)(x)) > DISTORTION_ONE)      ? (DISTORTION_ONE) :            \
322     (((int32_t)(x)) < DISTORTION_MINUS_ONE) ? (DISTORTION_MINUS_ONE) :  ((int32_t)(x)));
323 
324 
325 
326 /*----------------------------------------------------------------------------
327  * EAS_Calculate2toX()
328  *----------------------------------------------------------------------------
329  * Purpose:
330  * Calculate 2^x
331  *
332  * Inputs:
333  * nCents -     measured in cents
334  *
335  * Outputs:
336  * nResult - int.frac result (where frac has NUM_DENTS_FRAC_BITS)
337  *
338  * Side Effects:
339  *
340  *----------------------------------------------------------------------------
341 */
342 EAS_I32 EAS_Calculate2toX (EAS_I32 nCents);
343 
344 /*----------------------------------------------------------------------------
345  * EAS_LogToLinear16()
346  *----------------------------------------------------------------------------
347  * Purpose:
348  * Transform log value to linear gain multiplier using piece-wise linear
349  * approximation
350  *
351  * Inputs:
352  * nGain - log scale value in 20.10 format. Even though gain is normally
353  * stored in 6.10 (16-bit) format we use 32-bit numbers here to eliminate
354  * the need for saturation checking when combining gain values.
355  *
356  * Outputs:
357  * Returns a 16-bit linear value approximately equal to 2^(nGain/1024)
358  *
359  * Side Effects:
360  *
361  *----------------------------------------------------------------------------
362 */
363 EAS_U16 EAS_LogToLinear16 (EAS_I32 nGain);
364 
365 /*----------------------------------------------------------------------------
366  * EAS_VolumeToGain()
367  *----------------------------------------------------------------------------
368  * Purpose:
369  * Transform volume control in 1dB increments to gain multiplier
370  *
371  * Inputs:
372  * volume - 100 = 0dB, 99 = -1dB, 0 = -inf
373  *
374  * Outputs:
375  * Returns a 16-bit linear value
376  *----------------------------------------------------------------------------
377 */
378 EAS_I16 EAS_VolumeToGain (EAS_INT volume);
379 
380 /*----------------------------------------------------------------------------
381  * EAS_fsqrt()
382  *----------------------------------------------------------------------------
383  * Purpose:
384  * Calculates the square root of a 32-bit fixed point value
385  *
386  * Inputs:
387  * n = value of interest
388  *
389  * Outputs:
390  * returns the square root of n
391  *
392  *----------------------------------------------------------------------------
393 */
394 EAS_U16 EAS_fsqrt (EAS_U32 n);
395 
396 /*----------------------------------------------------------------------------
397  * EAS_flog2()
398  *----------------------------------------------------------------------------
399  * Purpose:
400  * Calculates the log2 of a 32-bit fixed point value
401  *
402  * Inputs:
403  * n = value of interest
404  *
405  * Outputs:
406  * returns the log2 of n
407  *
408  *----------------------------------------------------------------------------
409 */
410 EAS_I32 EAS_flog2 (EAS_U32 n);
411 
412 #endif
413 
414