Applies an ahead-of-time transformation to the exp table, and wraps it in a helper function.

Components/OPL2/Implementation/Tables.h

@@ -21,8 +21,17 @@ namespace OPL {
 */
 
 
-/// Defines the first quadrant of a sine curve, as calculated by round(-log(sin((x+0.5)*pi/256/2))/log(2)*256).
+/// Defines the first quadrant of 1024-unit negative log to the base two of  sine (that conveniently misses sin(0)).
-constexpr int log_sin[] = {
+///
+/// Expected branchless usage for a full 1024 unit output:
+///
+///	constexpr int multiplier[] = { 1, -1 };
+///	constexpr int mask[] = { 0, 255 };
+///
+/// value = exp( log_sin[angle & 255] ^ mask[(angle >> 8) & 1]) * multitplier[(angle >> 9) & 1]
+///
+/// ... where exp(x) = 2 ^ -x / 256
+constexpr int16_t log_sin[] = {
 	2137,	1731,	1543,	1419,	1326,	1252,	1190,	1137,
 	1091,	1050,	1013,	979,	949,	920,	894,	869,
 	846,	825,	804,	785,	767,	749,	732,	717,
@@ -57,42 +66,64 @@ constexpr int log_sin[] = {
 	0,		0,		0,		0,		0,		0,		0,		0
 };
 
-/// Defines exponentiation; to get exponential of x is (exp[x&255] + 1024) << (x >> 8)
+/*!
-constexpr int exp[] = {
+	@returns 2 ^ -x/256 in 0.10 fixed-point form.
-	0,		3,		6,		8,		11,		14,		17,		20,
+*/
-	22,		25,		28,		31,		34,		37,		40,		42,
+constexpr int exp(int x) {
-	45,		48,		51,		54,		57,		60,		63,		66,
+	/// A derivative of the exponent table in a real OPL2; mapped_exp[x] = (source[c ^ 0xff] << 1) | 0x800.
-	69,		72,		75,		78,		81,		84,		87,		90,
+	///
-	93,		96,		99,		102,	105,	108,	111,	114,
+	/// The ahead-of-time transformation represents fixed work the OPL2 does when reading its table
-	117,	120,	123,	126,	130,	133,	136,	139,
+	/// independent on the input.
-	142,	145,	148,	152,	155,	158,	161,	164,
+	///
-	168,	171,	174,	177,	181,	184,	187,	190,
+	/// The original table is a 0.10 fixed-point representation of 2^x - 1 with bit 10 implicitly set, where x is
-	194,	197,	200,	204,	207,	210,	214,	217,
+	/// in 0.8 fixed point.
-	220,	224,	227,	231,	234,	237,	241,	244,
+	///
-	248,	251,	255,	258,	262,	265,	268,	272,
+	/// Since the log_sin table represents sine in a negative base-2 logarithm, values from it would need
-	276,	279,	283,	286,	290,	293,	297,	300,
+	/// to be negatived before being put into the original table. That's haned with the ^ 0xff. The | 0x800 is to
-	304,	308,	311,	315,	318,	322,	326,	329,
+	/// set the implicit bit 10 (subject to the shift).
-	333,	337,	340,	344,	348,	352,	355,	359,
+	///
-	363,	367,	370,	374,	378,	382,	385,	389,
+	/// The shift by 1 is to allow the chip's exploitation of the recursive symmetry of the exponential table to
-	393,	397,	401,	405,	409,	412,	416,	420,
+	/// be achieved more easily. Specifically, to convert a logarithmic attenuation to a linear one, just perform:
-	424,	428,	432,	436,	440,	444,	448,	452,
+	///
-	456,	460,	464,	468,	472,	476,	480,	484,
+	///	result = mapped_exp[x & 0xff] >> (x >> 8)
-	488,	492,	496,	501,	505,	509,	513,	517,
+	constexpr int mapped_exp[] = {
-	521,	526,	530,	534,	538,	542,	547,	551,
+		4084,	4074,	4062,	4052,	4040,	4030,	4020,	4008,
-	555,	560,	564,	568,	572,	577,	581,	585,
+		3998,	3986,	3976,	3966,	3954,	3944,	3932,	3922,
-	590,	594,	599,	603,	607,	612,	616,	621,
+		3912,	3902,	3890,	3880,	3870,	3860,	3848,	3838,
-	625,	630,	634,	639,	643,	648,	652,	657,
+		3828,	3818,	3808,	3796,	3786,	3776,	3766,	3756,
-	661,	666,	670,	675,	680,	684,	689,	693,
+		3746,	3736,	3726,	3716,	3706,	3696,	3686,	3676,
-	698,	703,	708,	712,	717,	722,	726,	731,
+		3666,	3656,	3646,	3636,	3626,	3616,	3606,	3596,
-	736,	741,	745,	750,	755,	760,	765,	770,
+		3588,	3578,	3568,	3558,	3548,	3538,	3530,	3520,
-	774,	779,	784,	789,	794,	799,	804,	809,
+		3510,	3500,	3492,	3482,	3472,	3464,	3454,	3444,
-	814,	819,	824,	829,	834,	839,	844,	849,
+		3434,	3426,	3416,	3408,	3398,	3388,	3380,	3370,
-	854,	859,	864,	869,	874,	880,	885,	890,
+		3362,	3352,	3344,	3334,	3326,	3316,	3308,	3298,
-	895,	900,	906,	911,	916,	921,	927,	932,
+		3290,	3280,	3272,	3262,	3254,	3246,	3236,	3228,
-	937,	942,	948,	953,	959,	964,	969,	975,
+		3218,	3210,	3202,	3192,	3184,	3176,	3168,	3158,
-	980,	986,	991,	996,	1002,	1007,	1013,	1018
+		3150,	3142,	3132,	3124,	3116,	3108,	3100,	3090,
+		3082,	3074,	3066,	3058,	3050,	3040,	3032,	3024,
+		3016,	3008,	3000,	2992,	2984,	2976,	2968,	2960,
+		2952,	2944,	2936,	2928,	2920,	2912,	2904,	2896,
+		2888,	2880,	2872,	2866,	2858,	2850,	2842,	2834,
+		2826,	2818,	2812,	2804,	2796,	2788,	2782,	2774,
+		2766,	2758,	2752,	2744,	2736,	2728,	2722,	2714,
+		2706,	2700,	2692,	2684,	2678,	2670,	2664,	2656,
+		2648,	2642,	2634,	2628,	2620,	2614,	2606,	2600,
+		2592,	2584,	2578,	2572,	2564,	2558,	2550,	2544,
+		2536,	2530,	2522,	2516,	2510,	2502,	2496,	2488,
+		2482,	2476,	2468,	2462,	2456,	2448,	2442,	2436,
+		2428,	2422,	2416,	2410,	2402,	2396,	2390,	2384,
+		2376,	2370,	2364,	2358,	2352,	2344,	2338,	2332,
+		2326,	2320,	2314,	2308,	2300,	2294,	2288,	2282,
+		2276,	2270,	2264,	2258,	2252,	2246,	2240,	2234,
+		2228,	2222,	2216,	2210,	2204,	2198,	2192,	2186,
+		2180,	2174,	2168,	2162,	2156,	2150,	2144,	2138,
+		2132,	2128,	2122,	2116,	2110,	2104,	2098,	2092,
+		2088,	2082,	2076,	2070,	2064,	2060,	2054,	2048,
 	};
 
+	return mapped_exp[x & 0xff] >> (x >> 8);
+}
+
 /*
 
 	Credit for the fixed register lists goes to Nuke.YKT; I found them at: