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Diffstat (limited to 'arm-fm-22k/lib_src/eas_math.h')
| -rw-r--r-- | arm-fm-22k/lib_src/eas_math.h | 412 |
1 files changed, 412 insertions, 0 deletions
diff --git a/arm-fm-22k/lib_src/eas_math.h b/arm-fm-22k/lib_src/eas_math.h new file mode 100644 index 0000000..719270b --- /dev/null +++ b/arm-fm-22k/lib_src/eas_math.h @@ -0,0 +1,412 @@ +/*----------------------------------------------------------------------------
+ *
+ * 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
+
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