| /*---------------------------------------------------------------------------- | |
| * | |
| * File: | |
| * eas_math.h | |
| * | |
| * Contents and purpose: | |
| * Contains common math routines for the various audio engines. | |
| * | |
| * | |
| * Copyright Sonic Network Inc. 2005 | |
| * Licensed under the Apache License, Version 2.0 (the "License"); | |
| * you may not use this file except in compliance with the License. | |
| * You may obtain a copy of the License at | |
| * | |
| * http://www.apache.org/licenses/LICENSE-2.0 | |
| * | |
| * Unless required by applicable law or agreed to in writing, software | |
| * distributed under the License is distributed on an "AS IS" BASIS, | |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
| * See the License for the specific language governing permissions and | |
| * limitations under the License. | |
| * | |
| *---------------------------------------------------------------------------- | |
| * Revision Control: | |
| * $Revision: 584 $ | |
| * $Date: 2007-03-08 09:49:24 -0800 (Thu, 08 Mar 2007) $ | |
| *---------------------------------------------------------------------------- | |
| */ | |
| #ifndef _EAS_MATH_H | |
| #define _EAS_MATH_H | |
| /** coefs for pan, generates sin, cos */ | |
| #define COEFF_PAN_G2 -27146 /* -0.82842712474619 = 2 - 4/sqrt(2) */ | |
| #define COEFF_PAN_G0 23170 /* 0.707106781186547 = 1/sqrt(2) */ | |
| /* | |
| coefficients for approximating | |
| 2^x = gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3 | |
| where x is a int.frac number representing number of octaves. | |
| Actually, we approximate only the 2^(frac) using the power series | |
| and implement the 2^(int) as a shift, so that | |
| 2^x == 2^(int.frac) == 2^(int) * 2^(fract) | |
| == (gn2toX0 + gn2toX1*x + gn2toX2*x^2 + gn2toX3*x^3) << (int) | |
| The gn2toX.. were generated using a best fit for a 3rd | |
| order polynomial, instead of taking the coefficients from | |
| a truncated Taylor (or Maclaurin?) series. | |
| */ | |
| #define GN2_TO_X0 32768 /* 1 */ | |
| #define GN2_TO_X1 22833 /* 0.696807861328125 */ | |
| #define GN2_TO_X2 7344 /* 0.22412109375 */ | |
| #define GN2_TO_X3 2588 /* 0.0789794921875 */ | |
| /*---------------------------------------------------------------------------- | |
| * Fixed Point Math | |
| *---------------------------------------------------------------------------- | |
| * These macros are used for fixed point multiplies. If the processor | |
| * supports fixed point multiplies, replace these macros with inline | |
| * assembly code to improve performance. | |
| *---------------------------------------------------------------------------- | |
| */ | |
| /* Fixed point multiply 0.15 x 0.15 = 0.15 returned as 32-bits */ | |
| #define FMUL_15x15(a,b) \ | |
| /*lint -e(704) <avoid multiply for performance>*/ \ | |
| (((EAS_I32)(a) * (EAS_I32)(b)) >> 15) | |
| /* Fixed point multiply 0.7 x 0.7 = 0.15 returned as 32-bits */ | |
| #define FMUL_7x7(a,b) \ | |
| /*lint -e(704) <avoid multiply for performance>*/ \ | |
| (((EAS_I32)(a) * (EAS_I32)(b) ) << 1) | |
| /* Fixed point multiply 0.8 x 0.8 = 0.15 returned as 32-bits */ | |
| #define FMUL_8x8(a,b) \ | |
| /*lint -e(704) <avoid multiply for performance>*/ \ | |
| (((EAS_I32)(a) * (EAS_I32)(b) ) >> 1) | |
| /* Fixed point multiply 0.8 x 1.15 = 0.15 returned as 32-bits */ | |
| #define FMUL_8x15(a,b) \ | |
| /*lint -e(704) <avoid divide for performance>*/ \ | |
| (((EAS_I32)((a) << 7) * (EAS_I32)(b)) >> 15) | |
| /* macros for fractional phase accumulator */ | |
| /* | |
| Note: changed the _U32 to _I32 on 03/14/02. This should not | |
| affect the phase calculations, and should allow us to reuse these | |
| macros for other audio sample related math. | |
| */ | |
| #define HARDWARE_BIT_WIDTH 32 | |
| #define NUM_PHASE_INT_BITS 1 | |
| #define NUM_PHASE_FRAC_BITS 15 | |
| #define PHASE_FRAC_MASK (EAS_U32) ((0x1L << NUM_PHASE_FRAC_BITS) -1) | |
| #define GET_PHASE_INT_PART(x) (EAS_U32)((EAS_U32)(x) >> NUM_PHASE_FRAC_BITS) | |
| #define GET_PHASE_FRAC_PART(x) (EAS_U32)((EAS_U32)(x) & PHASE_FRAC_MASK) | |
| #define DEFAULT_PHASE_FRAC 0 | |
| #define DEFAULT_PHASE_INT 0 | |
| /* | |
| Linear interpolation calculates: | |
| output = (1-frac) * sample[n] + (frac) * sample[n+1] | |
| where conceptually 0 <= frac < 1 | |
| For a fixed point implementation, frac is actually an integer value | |
| with an implied binary point one position to the left. The value of | |
| one (unity) is given by PHASE_ONE | |
| one half and one quarter are useful for 4-point linear interp. | |
| */ | |
| #define PHASE_ONE (EAS_I32) (0x1L << NUM_PHASE_FRAC_BITS) | |
| /* | |
| Multiply the signed audio sample by the unsigned fraction. | |
| - a is the signed audio sample | |
| - b is the unsigned fraction (cast to signed int as long as coef | |
| uses (n-1) or less bits, where n == hardware bit width) | |
| */ | |
| #define MULT_AUDIO_COEF(audio,coef) /*lint -e704 <avoid divide for performance>*/ \ | |
| (EAS_I32)( \ | |
| ( \ | |
| ((EAS_I32)(audio)) * ((EAS_I32)(coef)) \ | |
| ) \ | |
| >> NUM_PHASE_FRAC_BITS \ | |
| ) \ | |
| /* lint +704 <restore checking>*/ | |
| /* wet / dry calculation macros */ | |
| #define NUM_WET_DRY_FRAC_BITS 7 // 15 | |
| #define NUM_WET_DRY_INT_BITS 9 // 1 | |
| /* define a 1.0 */ | |
| #define WET_DRY_ONE (EAS_I32) ((0x1L << NUM_WET_DRY_FRAC_BITS)) | |
| #define WET_DRY_MINUS_ONE (EAS_I32) (~WET_DRY_ONE) | |
| #define WET_DRY_FULL_SCALE (EAS_I32) (WET_DRY_ONE - 1) | |
| #define MULT_AUDIO_WET_DRY_COEF(audio,coef) /*lint -e(702) <avoid divide for performance>*/ \ | |
| (EAS_I32)( \ | |
| ( \ | |
| ((EAS_I32)(audio)) * ((EAS_I32)(coef)) \ | |
| ) \ | |
| >> NUM_WET_DRY_FRAC_BITS \ | |
| ) | |
| /* Envelope 1 (EG1) calculation macros */ | |
| #define NUM_EG1_INT_BITS 1 | |
| #define NUM_EG1_FRAC_BITS 15 | |
| /* the max positive gain used in the synth for EG1 */ | |
| /* SYNTH_FULL_SCALE_EG1_GAIN must match the value in the dls2eas | |
| converter, otherwise, the values we read from the .eas file are bogus. */ | |
| #define SYNTH_FULL_SCALE_EG1_GAIN (EAS_I32) ((0x1L << NUM_EG1_FRAC_BITS) -1) | |
| /* define a 1.0 */ | |
| #define EG1_ONE (EAS_I32) ((0x1L << NUM_EG1_FRAC_BITS)) | |
| #define EG1_MINUS_ONE (EAS_I32) (~SYNTH_FULL_SCALE_EG1_GAIN) | |
| #define EG1_HALF (EAS_I32) (EG1_ONE/2) | |
| #define EG1_MINUS_HALF (EAS_I32) (EG1_MINUS_ONE/2) | |
| /* | |
| We implement the EG1 using a linear gain value, which means that the | |
| attack segment is handled by incrementing (adding) the linear gain. | |
| However, EG1 treats the Decay, Sustain, and Release differently than | |
| the Attack portion. For Decay, Sustain, and Release, the gain is | |
| linear on dB scale, which is equivalent to exponential damping on | |
| a linear scale. Because we use a linear gain for EG1, we implement | |
| the Decay and Release as multiplication (instead of incrementing | |
| as we did for the attack segment). | |
| Therefore, we need the following macro to implement the multiplication | |
| (i.e., exponential damping) during the Decay and Release segments of | |
| the EG1 | |
| */ | |
| #define MULT_EG1_EG1(gain,damping) /*lint -e(704) <avoid divide for performance>*/ \ | |
| (EAS_I32)( \ | |
| ( \ | |
| ((EAS_I32)(gain)) * ((EAS_I32)(damping)) \ | |
| ) \ | |
| >> NUM_EG1_FRAC_BITS \ | |
| ) | |
| // Use the following macro specifically for the filter, when multiplying | |
| // the b1 coefficient. The 0 <= |b1| < 2, which therefore might overflow | |
| // in certain conditions because we store b1 as a 1.15 value. | |
| // Instead, we could store b1 as b1p (b1' == b1 "prime") where | |
| // b1p == b1/2, thus ensuring no potential overflow for b1p because | |
| // 0 <= |b1p| < 1 | |
| // However, during the filter calculation, we must account for the fact | |
| // that we are using b1p instead of b1, and thereby multiply by | |
| // an extra factor of 2. Rather than multiply by an extra factor of 2, | |
| // we can instead shift the result right by one less, hence the | |
| // modified shift right value of (NUM_EG1_FRAC_BITS -1) | |
| #define MULT_EG1_EG1_X2(gain,damping) /*lint -e(702) <avoid divide for performance>*/ \ | |
| (EAS_I32)( \ | |
| ( \ | |
| ((EAS_I32)(gain)) * ((EAS_I32)(damping)) \ | |
| ) \ | |
| >> (NUM_EG1_FRAC_BITS -1) \ | |
| ) | |
| #define SATURATE_EG1(x) /*lint -e{734} saturation operation */ \ | |
| ((EAS_I32)(x) > SYNTH_FULL_SCALE_EG1_GAIN) ? (SYNTH_FULL_SCALE_EG1_GAIN) : \ | |
| ((EAS_I32)(x) < EG1_MINUS_ONE) ? (EG1_MINUS_ONE) : (x); | |
| /* use "digital cents" == "dents" instead of cents */ | |
| /* we coudl re-use the phase frac macros, but if we do, | |
| we must change the phase macros to cast to _I32 instead of _U32, | |
| because using a _U32 cast causes problems when shifting the exponent | |
| for the 2^x calculation, because right shift a negative values MUST | |
| be sign extended, or else the 2^x calculation is wrong */ | |
| /* use "digital cents" == "dents" instead of cents */ | |
| #define NUM_DENTS_FRAC_BITS 12 | |
| #define NUM_DENTS_INT_BITS (HARDWARE_BIT_WIDTH - NUM_DENTS_FRAC_BITS) | |
| #define DENTS_FRAC_MASK (EAS_I32) ((0x1L << NUM_DENTS_FRAC_BITS) -1) | |
| #define GET_DENTS_INT_PART(x) /*lint -e(704) <avoid divide for performance>*/ \ | |
| (EAS_I32)((EAS_I32)(x) >> NUM_DENTS_FRAC_BITS) | |
| #define GET_DENTS_FRAC_PART(x) (EAS_I32)((EAS_I32)(x) & DENTS_FRAC_MASK) | |
| #define DENTS_ONE (EAS_I32) (0x1L << NUM_DENTS_FRAC_BITS) | |
| /* use CENTS_TO_DENTS to convert a value in cents to dents */ | |
| #define CENTS_TO_DENTS (EAS_I32) (DENTS_ONE * (0x1L << NUM_EG1_FRAC_BITS) / 1200L) \ | |
| /* | |
| For gain, the LFO generates a value that modulates in terms | |
| of dB. However, we use a linear gain value, so we must convert | |
| the LFO value in dB to a linear gain. Normally, we would use | |
| linear gain = 10^x, where x = LFO value in dB / 20. | |
| Instead, we implement 10^x using our 2^x approximation. | |
| because | |
| 10^x = 2^(log2(10^x)) = 2^(x * log2(10)) | |
| so we need to multiply by log2(10) which is just a constant. | |
| Ah, but just wait -- our 2^x actually doesn't exactly implement | |
| 2^x, but it actually assumes that the input is in cents, and within | |
| the 2^x approximation converts its input from cents to octaves | |
| by dividing its input by 1200. | |
| So, in order to convert the LFO gain value in dB to something | |
| that our existing 2^x approximation can use, multiply the LFO gain | |
| by log2(10) * 1200 / 20 | |
| The divide by 20 helps convert dB to linear gain, and we might | |
| as well incorporate that operation into this conversion. | |
| Of course, we need to keep some fractional bits, so multiply | |
| the constant by NUM_EG1_FRAC_BITS | |
| */ | |
| /* use LFO_GAIN_TO_CENTS to convert the LFO gain value to cents */ | |
| #if 0 | |
| #define DOUBLE_LOG2_10 (double) (3.32192809488736) /* log2(10) */ | |
| #define DOUBLE_LFO_GAIN_TO_CENTS (double) \ | |
| ( \ | |
| (DOUBLE_LOG2_10) * \ | |
| 1200.0 / \ | |
| 20.0 \ | |
| ) | |
| #define LFO_GAIN_TO_CENTS (EAS_I32) \ | |
| ( \ | |
| DOUBLE_LFO_GAIN_TO_CENTS * \ | |
| (0x1L << NUM_EG1_FRAC_BITS) \ | |
| ) | |
| #endif | |
| #define LFO_GAIN_TO_CENTS (EAS_I32) (1671981156L >> (23 - NUM_EG1_FRAC_BITS)) | |
| #define MULT_DENTS_COEF(dents,coef) /*lint -e704 <avoid divide for performance>*/ \ | |
| (EAS_I32)( \ | |
| ( \ | |
| ((EAS_I32)(dents)) * ((EAS_I32)(coef)) \ | |
| ) \ | |
| >> NUM_DENTS_FRAC_BITS \ | |
| ) \ | |
| /* lint +e704 <restore checking>*/ | |
| /* we use 16-bits in the PC per audio sample */ | |
| #define BITS_PER_AUDIO_SAMPLE 16 | |
| /* we define 1 as 1.0 - 1 LSbit */ | |
| #define DISTORTION_ONE (EAS_I32)((0x1L << (BITS_PER_AUDIO_SAMPLE-1)) -1) | |
| #define DISTORTION_MINUS_ONE (EAS_I32)(~DISTORTION_ONE) | |
| /* drive coef is given as int.frac */ | |
| #define NUM_DRIVE_COEF_INT_BITS 1 | |
| #define NUM_DRIVE_COEF_FRAC_BITS 4 | |
| #define MULT_AUDIO_DRIVE(audio,drive) /*lint -e(702) <avoid divide for performance>*/ \ | |
| (EAS_I32) ( \ | |
| ( \ | |
| ((EAS_I32)(audio)) * ((EAS_I32)(drive)) \ | |
| ) \ | |
| >> NUM_DRIVE_COEF_FRAC_BITS \ | |
| ) | |
| #define MULT_AUDIO_AUDIO(audio1,audio2) /*lint -e(702) <avoid divide for performance>*/ \ | |
| (EAS_I32) ( \ | |
| ( \ | |
| ((EAS_I32)(audio1)) * ((EAS_I32)(audio2)) \ | |
| ) \ | |
| >> (BITS_PER_AUDIO_SAMPLE-1) \ | |
| ) | |
| #define SATURATE(x) \ | |
| ((((EAS_I32)(x)) > DISTORTION_ONE) ? (DISTORTION_ONE) : \ | |
| (((EAS_I32)(x)) < DISTORTION_MINUS_ONE) ? (DISTORTION_MINUS_ONE) : ((EAS_I32)(x))); | |
| /*---------------------------------------------------------------------------- | |
| * EAS_Calculate2toX() | |
| *---------------------------------------------------------------------------- | |
| * Purpose: | |
| * Calculate 2^x | |
| * | |
| * Inputs: | |
| * nCents - measured in cents | |
| * | |
| * Outputs: | |
| * nResult - int.frac result (where frac has NUM_DENTS_FRAC_BITS) | |
| * | |
| * Side Effects: | |
| * | |
| *---------------------------------------------------------------------------- | |
| */ | |
| EAS_I32 EAS_Calculate2toX (EAS_I32 nCents); | |
| /*---------------------------------------------------------------------------- | |
| * EAS_LogToLinear16() | |
| *---------------------------------------------------------------------------- | |
| * Purpose: | |
| * Transform log value to linear gain multiplier using piece-wise linear | |
| * approximation | |
| * | |
| * Inputs: | |
| * nGain - log scale value in 20.10 format. Even though gain is normally | |
| * stored in 6.10 (16-bit) format we use 32-bit numbers here to eliminate | |
| * the need for saturation checking when combining gain values. | |
| * | |
| * Outputs: | |
| * Returns a 16-bit linear value approximately equal to 2^(nGain/1024) | |
| * | |
| * Side Effects: | |
| * | |
| *---------------------------------------------------------------------------- | |
| */ | |
| EAS_U16 EAS_LogToLinear16 (EAS_I32 nGain); | |
| /*---------------------------------------------------------------------------- | |
| * EAS_VolumeToGain() | |
| *---------------------------------------------------------------------------- | |
| * Purpose: | |
| * Transform volume control in 1dB increments to gain multiplier | |
| * | |
| * Inputs: | |
| * volume - 100 = 0dB, 99 = -1dB, 0 = -inf | |
| * | |
| * Outputs: | |
| * Returns a 16-bit linear value | |
| *---------------------------------------------------------------------------- | |
| */ | |
| EAS_I16 EAS_VolumeToGain (EAS_INT volume); | |
| /*---------------------------------------------------------------------------- | |
| * EAS_fsqrt() | |
| *---------------------------------------------------------------------------- | |
| * Purpose: | |
| * Calculates the square root of a 32-bit fixed point value | |
| * | |
| * Inputs: | |
| * n = value of interest | |
| * | |
| * Outputs: | |
| * returns the square root of n | |
| * | |
| *---------------------------------------------------------------------------- | |
| */ | |
| EAS_U16 EAS_fsqrt (EAS_U32 n); | |
| /*---------------------------------------------------------------------------- | |
| * EAS_flog2() | |
| *---------------------------------------------------------------------------- | |
| * Purpose: | |
| * Calculates the log2 of a 32-bit fixed point value | |
| * | |
| * Inputs: | |
| * n = value of interest | |
| * | |
| * Outputs: | |
| * returns the log2 of n | |
| * | |
| *---------------------------------------------------------------------------- | |
| */ | |
| EAS_I32 EAS_flog2 (EAS_U32 n); | |
| #endif | |