| /*---------------------------------------------------------------------------- |
| * |
| * 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 |
| |
