Add sk_float_rsqrt with SSE + NEON fast paths.

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 78 matching lines @@
     #define sk_float_ceil2int(x)    (int)sk_float_ceil(x)
 #endif
 
 extern const uint32_t gIEEENotANumber;
 extern const uint32_t gIEEEInfinity;
 extern const uint32_t gIEEENegativeInfinity;
 
 #define SK_FloatNaN                 (*SkTCast<const float*>(&gIEEENotANumber))
 #define SK_FloatInfinity            (*SkTCast<const float*>(&gIEEEInfinity))
 #define SK_FloatNegativeInfinity    (*SkTCast<const float*>(&gIEEENegativeInfinity))
+
+#if defined(__SSE__)
+#include <xmmintrin.h>
+#elif defined(__ARM_NEON__)
+#include <arm_neon.h>
 #endif
+
+// 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.
+#if defined(__SSE__)
+    float result;
+    _mm_store_ss(&result, _mm_rsqrt_ss(_mm_set_ss(x)));
+    return result;
+#elif defined(__ARM_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);
+    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);
+    return estimate;
+#endif
+}
+
+#endif