LIB: fast_log2: simplify loop while keeping it auto vectorizable

Signed-off-by: Stefan Westerfeld <[email protected]>

Author: swesterfeld

lib/smmath.hh

@@ -585,36 +585,29 @@ union FloatIEEE754 {
 extern inline void
 fast_log2 (float *values, int n_values)
 {
-  const int block_size = 4096; // guarantee fixed amount of stack space
-  int fexp[block_size];
-  while (n_values)
+  /* this loop is written in a way that both, gcc and clang should auto vectorize it */
+  for (int k = 0; k < n_values; k++)
     {
-      int todo = std::min (n_values, block_size);
-      int *values_i = reinterpret_cast<int *> (values);
-      for (int k = 0; k < todo; k++)
-        {
-          const int EXPONENT_MASK = 0x7F800000;
-          fexp[k] = (values_i[k] >> 23) - FloatIEEE754::BIAS;                      // extract exponent without bias (rely on sign bit == 0)
-          values_i[k] = (values_i[k] & ~EXPONENT_MASK) | FloatIEEE754::BIAS << 23; // reset exponent to 2^0 so v_float is mantissa in [1..2]
-        }
-      for (int k = 0; k < todo; k++)
-        {
-          float r, x = values[k] - 1.0f;
-          // x=[0..1]; r = log2 (x + 1);
-          // h=0.0113916; // offset to reduce error at origin
-          // f=(1/log(2)) * log(x+1); dom=[0-h;1+h]; p=remez(f, 6, dom, 1);
-          // p = p - p(0); // discard non-0 offset
-          // err=p-f; plot(err,[0;1]); plot(f,p,dom); // result in sollya
-          r = x *  -0.0259366993544709205147977455165000143561553284592936f;
-          r = x * (+0.122047857676447181074792747820717519424533931189428f + r);
-          r = x * (-0.27814297685064327713977752916286528359628147166014f + r);
-          r = x * (+0.45764712300320092992105460899527194244236573556309f + r);
-          r = x * (-0.71816105664624015087225994551041120290062342459945f + r);
-          r = x * (+1.44254540258782520489769598315182363877204824648687f + r);
-          values[k] = fexp[k] + r; // log2 (i) + log2 (x)
-        }
-      values += todo;
-      n_values -= todo;
+      const int EXPONENT_MASK = 0x7F800000;
+      int iv;
+      memcpy (&iv, &values[k], sizeof (float));              // iv = *(int *) &values[k]
+      int fexp = (iv >> 23) - FloatIEEE754::BIAS;            // extract exponent without bias (rely on sign bit == 0)
+      iv = (iv & ~EXPONENT_MASK) | FloatIEEE754::BIAS << 23; // reset exponent to 2^0 so v_float is mantissa in [1..2]
+      float r, x;
+      memcpy (&x, &iv, sizeof (float));                      // x = *(float *) &iv;
+      x -= 1;
+      // x=[0..1]; r = log2 (x + 1);
+      // h=0.0113916; // offset to reduce error at origin
+      // f=(1/log(2)) * log(x+1); dom=[0-h;1+h]; p=remez(f, 6, dom, 1);
+      // p = p - p(0); // discard non-0 offset
+      // err=p-f; plot(err,[0;1]); plot(f,p,dom); // result in sollya
+      r = x *  -0.0259366993544709205147977455165000143561553284592936f;
+      r = x * (+0.122047857676447181074792747820717519424533931189428f + r);
+      r = x * (-0.27814297685064327713977752916286528359628147166014f + r);
+      r = x * (+0.45764712300320092992105460899527194244236573556309f + r);
+      r = x * (-0.71816105664624015087225994551041120290062342459945f + r);
+      r = x * (+1.44254540258782520489769598315182363877204824648687f + r);
+      values[k] = fexp + r; // log2 (i) + log2 (x)
     }
 }
 ////////////// end: code based on log2 code from Anklang/ASE by Tim Janik