de-proc sk_float_rsqrt

include/private/SkFloatingPoint.h

Index: include/private/SkFloatingPoint.h
diff --git a/include/private/SkFloatingPoint.h b/include/private/SkFloatingPoint.h
index f7ee816b12005a6377a34016e35f878696a1e270..ffed5c07471709e3dd188e3a8d572fcbd7e6b7cd 100644
--- a/include/private/SkFloatingPoint.h
+++ b/include/private/SkFloatingPoint.h
@@ -127,20 +127,28 @@ extern const uint32_t gIEEENegativeInfinity;
 #define SK_FloatInfinity            (*SkTCast<const float*>(&gIEEEInfinity))
 #define SK_FloatNegativeInfinity    (*SkTCast<const float*>(&gIEEENegativeInfinity))
 
-// We forward declare this to break an #include cycle.
-// (SkScalar -> SkFloatingPoint -> SkOpts.h -> SkXfermode -> SkColor -> SkScalar)
-namespace SkOpts { extern float (*rsqrt)(float); }
+static inline float sk_float_rsqrt_portable(float x) {
+    // Get initial estimate.
+    int i = *SkTCast<int*>(&x);
+    i = 0x5F1FFFF9 - (i>>1);
+    float estimate = *SkTCast<float*>(&i);
+
+    // One step of Newton's method to refine.
+    const float estimate_sq = estimate*estimate;
+    estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
+    return estimate;
+}
 
 // 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) {
+static inline float sk_float_rsqrt(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
+// We do one step of Newton's method to refine the estimates in the NEON and portable 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
+// Optimized constants in the portable 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)
@@ -153,8 +161,7 @@ static inline float sk_float_rsqrt(const float x) {
     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
-    // Perhaps runtime-detected NEON, or a portable fallback.
-    return SkOpts::rsqrt(x);
+    return sk_float_rsqrt_portable(x);
 #endif
 }