Changeset 0deeaad

Timestamp:

Oct 5, 2022, 5:20:54 PM (2 years ago)

Author:

Thierry Delisle <tdelisle@…>

Branches:

ADT, ast-experimental, master

Children:

815943f, d0a00a5a

Parents:

5f6b2c2

Message:

Added fixed point log2 calculation, which is not that useful but kind of cool.

File:

• libcfa/src/math.hfa (modified) (3 diffs)

libcfa/src/math.hfa

@@ -22 +22 @@
 
 #include "common.hfa"
+#include "bits/debug.hfa"
 
 //---------------------- General ----------------------
@@ -307 +308 @@
         // forall( T | { T ?+?( T, T ); T ?-?( T, T ); T ?%?( T, T ); } )
         // T ceiling_div( T n, T align ) { verify( is_pow2( align ) );return (n + (align - 1)) / align; }
-        
+
         // gcc notices the div/mod pair and saves both so only one div.
         signed char ceiling( signed char n, signed char align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
@@ -429 +430 @@
 } // distribution
 
+static inline unsigned long long log2_u32_32(unsigned long long val) {
+        enum {
+                TABLE_BITS = 6,
+                TABLE_SIZE = (1 << TABLE_BITS) + 2,
+        };
+        // for(i; TABLE_SIZE) {
+        //      table[i] = (unsigned long long)(log2(1.0 + i / pow(2, TABLE_BITS)) * pow(2, 32)));
+        // }
+        static const unsigned long long table[] = {
+                0x0000000000, 0x0005b9e5a1, 0x000b5d69ba, 0x0010eb389f,
+                0x001663f6fa, 0x001bc84240, 0x002118b119, 0x002655d3c4,
+                0x002b803473, 0x00309857a0, 0x00359ebc5b, 0x003a93dc98,
+                0x003f782d72, 0x00444c1f6b, 0x0049101eac, 0x004dc4933a,
+                0x005269e12f, 0x00570068e7, 0x005b888736, 0x006002958c,
+                0x00646eea24, 0x0068cdd829, 0x006d1fafdc, 0x007164beb4,
+                0x00759d4f80, 0x0079c9aa87, 0x007dea15a3, 0x0081fed45c,
+                0x0086082806, 0x008a064fd5, 0x008df988f4, 0x0091e20ea1,
+                0x0095c01a39, 0x009993e355, 0x009d5d9fd5, 0x00a11d83f4,
+                0x00a4d3c25e, 0x00a8808c38, 0x00ac241134, 0x00afbe7fa0,
+                0x00b3500472, 0x00b6d8cb53, 0x00ba58feb2, 0x00bdd0c7c9,
+                0x00c1404ead, 0x00c4a7ba58, 0x00c80730b0, 0x00cb5ed695,
+                0x00ceaecfea, 0x00d1f73f9c, 0x00d53847ac, 0x00d8720935,
+                0x00dba4a47a, 0x00ded038e6, 0x00e1f4e517, 0x00e512c6e5,
+                0x00e829fb69, 0x00eb3a9f01, 0x00ee44cd59, 0x00f148a170,
+                0x00f446359b, 0x00f73da38d, 0x00fa2f045e, 0x00fd1a708b,
+                0x0100000000, 0x0102dfca16,
+        };
+        _Static_assert((sizeof(table) / sizeof(table[0])) == TABLE_SIZE, "TABLE_SIZE should be accurate");
+        // starting from val = (2 ** i)*(1 + f) where 0 <= f < 1
+        // log identities mean log2(val) = log2((2 ** i)*(1 + f)) = log2(2**i) + log2(1+f)
+        //
+        // getting i is easy to do using builtin_clz (count leading zero)
+        //
+        // we want to calculate log2(1+f) independently to have a many bits of precision as possible.
+        //     val = (2 ** i)*(1 + f) = 2 ** i   +   f * 2 ** i
+        // isolating f we get
+        //     val - 2 ** i = f * 2 ** i
+        //     (val - 2 ** i) / 2 ** i = f
+        //
+        // we want to interpolate from the table to get the values
+        // and compromise by doing quadratic interpolation (rather than higher degree interpolation)
+        //
+        // for the interpolation we want to shift everything the fist sample point
+        // so our parabola becomes x = 0
+        // this further simplifies the equations
+        //
+        // the consequence is that we need f in 2 forms:
+        //  - finding the index of x0
+        //  - finding the distance between f and x0
+        //
+        // since sample points are equidistant we can significantly simplify the equations
+
+        // get i
+        const unsigned long long bits = sizeof(val) * __CHAR_BIT__;
+        const unsigned long long lz = __builtin_clzl(val);
+        const unsigned long long i = bits - 1 - lz;
+
+        // get the fractinal part as a u32.32
+        const unsigned long long frac = (val << (lz + 1)) >> 32;
+
+        // get high order bits for the index into the table
+        const unsigned long long idx0 = frac >> (32 - TABLE_BITS);
+
+        // get the x offset, i.e., the difference between the first sample point and the actual fractional part
+        const long long udx = frac - (idx0 << (32 - TABLE_BITS));
+        /* paranoid */ verify((idx0 + 2) < TABLE_SIZE);
+
+        const long long y0 = table[idx0 + 0];
+        const long long y1 = table[idx0 + 1];
+        const long long y2 = table[idx0 + 2];
+
+        // from there we can quadraticly interpolate to get the data, using the lagrange polynomial
+        // normally it would look like:
+        //     double r0 = y0 * ((x - x1) / (x0 - x1)) * ((x - x2) / (x0 - x2));
+        //     double r1 = y1 * ((x - x0) / (x1 - x0)) * ((x - x2) / (x1 - x2));
+        //     double r2 = y2 * ((x - x0) / (x2 - x0)) * ((x - x1) / (x2 - x1));
+        // but since the spacing between sample points is fixed, we can simplify it and extract common expressions
+        const long long f1 = (y1 - y0);
+        const long long f2 = (y2 - y0);
+        const long long a = f2 - (f1 * 2l);
+        const long long b = (f1 * 2l) - a;
+
+        // Now we can compute it in the form (ax + b)x + c (which avoid repeating steps)
+        long long sum = ((a*udx) >> (32 - TABLE_BITS))  + b;
+        sum = (sum*udx) >> (32 - TABLE_BITS + 1);
+        sum = y0 + sum;
+
+        return (i << 32) + (sum);
+}
+
 // Local Variables: //
 // mode: c //