Update fallback rsqrt implementation to use optimal constants.

include/core/SkFloatingPoint.h

 
 /*
  * Copyright 2006 The Android Open Source Project
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 
 
 #ifndef SkFloatingPoint_DEFINED
@@ skipping 133 matching lines @@
 #define SK_FloatNegativeInfinity    (*SkTCast<const float*>(&gIEEENegativeInfinity))
 
 // Fast, approximate inverse square root.
 // Compare to name-brand "1.0f / sk_float_sqrt(x)".  Should be around 10x faster on SSE, 2x on NEON.
 static inline float sk_float_rsqrt(const float x) {
 // We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
 // it at compile time.  This is going to be too fast to productively hide behind a function pointer.
 //
 // We do one step of Newton's method to refine the estimates in the NEON and null paths.  No
 // refinement is faster, but very innacurate.  Two steps is more accurate, but slower than 1/sqrt.
+//
+// Optimized constants in the null path courtesy of http://rrrola.wz.cz/inv_sqrt.html
 #if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
     return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
 #elif defined(SK_ARM_HAS_NEON)
     // Get initial estimate.
     const float32x2_t xx = vdup_n_f32(x);  // Clever readers will note we're doing everything 2x.
     float32x2_t estimate = vrsqrte_f32(xx);
 
     // One step of Newton's method to refine.
     const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
     estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
     return vget_lane_f32(estimate, 0);  // 1 will work fine too; the answer's in both places.
 #else
     // Get initial estimate.
     int i = *SkTCast<int*>(&x);
-    i = 0x5f3759df - (i>>1);
+    i = 0x5F1FFFF9 - (i>>1);
     float estimate = *SkTCast<float*>(&i);
 
     // One step of Newton's method to refine.
     const float estimate_sq = estimate*estimate;
-    estimate *= (1.5f-0.5f*x*estimate_sq);
+    estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
     return estimate;
 #endif
 }
 
 #endif