Split rsqrt into rsqrt{0,1,2}, with increasing cost and precision on ARM

src/opts/SkNx_neon.h

 /*
  * Copyright 2015 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 
 #ifndef SkNx_neon_DEFINED
 #define SkNx_neon_DEFINED
 
@@ skipping 63 matching lines @@
     Nb operator == (const SkNf& o) const { return vceq_f32(fVec, o.fVec); }
     Nb operator  < (const SkNf& o) const { return vclt_f32(fVec, o.fVec); }
     Nb operator  > (const SkNf& o) const { return vcgt_f32(fVec, o.fVec); }
     Nb operator <= (const SkNf& o) const { return vcle_f32(fVec, o.fVec); }
     Nb operator >= (const SkNf& o) const { return vcge_f32(fVec, o.fVec); }
     Nb operator != (const SkNf& o) const { return vmvn_u32(vceq_f32(fVec, o.fVec)); }
 
     static SkNf Min(const SkNf& l, const SkNf& r) { return vmin_f32(l.fVec, r.fVec); }
     static SkNf Max(const SkNf& l, const SkNf& r) { return vmax_f32(l.fVec, r.fVec); }
 
-    SkNf rsqrt() const {
-        float32x2_t est0 = vrsqrte_f32(fVec),
-                    est1 = vmul_f32(vrsqrts_f32(fVec, vmul_f32(est0, est0)), est0);
-        return est1;
+    SkNf rsqrt0() const { return vrsqrte_f32(fVec); }
+    SkNf rsqrt1() const {
+        float32x2_t est0 = this->rsqrt0().fVec;
+        return vmul_f32(vrsqrts_f32(fVec, vmul_f32(est0, est0)), est0);
+    }
+    SkNf rsqrt2() const {
+        float32x2_t est1 = this->rsqrt1().fVec;
+        return vmul_f32(vrsqrts_f32(fVec, vmul_f32(est1, est1)), est1);
     }
 
     SkNf sqrt() const {
     #if defined(SK_CPU_ARM64)
         return vsqrt_f32(fVec);
     #else
-        float32x2_t est1 = this->rsqrt().fVec,
-        // An extra step of Newton's method to refine the estimate of 1/sqrt(this).
-                    est2 = vmul_f32(vrsqrts_f32(fVec, vmul_f32(est1, est1)), est1);
-        return vmul_f32(fVec, est2);
+        return *this * this->rsqrt2();
     #endif
     }
 
     template <int k> float kth() const {
         SkASSERT(0 <= k && k < 2);
         return vget_lane_f32(fVec, k&1);
     }
 
 private:
     float32x2_t fVec;
@@ skipping 36 matching lines @@
     Nb operator <= (const SkNf& o) const { return vcleq_f64(fVec, o.fVec); }
     Nb operator >= (const SkNf& o) const { return vcgeq_f64(fVec, o.fVec); }
     Nb operator != (const SkNf& o) const {
         return vreinterpretq_u64_u32(vmvnq_u32(vreinterpretq_u32_u64(vceqq_f64(fVec, o.fVec))));
     }
 
     static SkNf Min(const SkNf& l, const SkNf& r) { return vminq_f64(l.fVec, r.fVec); }
     static SkNf Max(const SkNf& l, const SkNf& r) { return vmaxq_f64(l.fVec, r.fVec); }
 
     SkNf  sqrt() const { return vsqrtq_f64(fVec);  }
-    SkNf rsqrt() const {
-        float64x2_t est0 = vrsqrteq_f64(fVec),
-                    est1 = vmulq_f64(vrsqrtsq_f64(fVec, vmulq_f64(est0, est0)), est0);
-        return est1;
+
+    SkNf rsqrt0() const { return vrsqrteq_f64(fVec); }
+    SkNf rsqrt1() const {
+        float64x2_t est0 = this->rsqrt0().fVec;
+        return vmulq_f64(vrsqrtsq_f64(fVec, vmulq_f64(est0, est0)), est0);
+    }
+    SkNf rsqrt2() const {
+        float64x2_t est1 = this->rsqrt1().fVec;
+        return vmulq_f64(vrsqrtsq_f64(fVec, vmulq_f64(est1, est1)), est1);
     }
 
     SkNf approxInvert() const {
         float64x2_t est0 = vrecpeq_f64(fVec),
                     est1 = vmulq_f64(vrecpsq_f64(est0, fVec), est0);
         return est1;
     }
 
     SkNf invert() const {
         float64x2_t est1 = this->approxInvert().fVec,
@@ skipping 94 matching lines @@
     Nb operator == (const SkNf& o) const { return vceqq_f32(fVec, o.fVec); }
     Nb operator  < (const SkNf& o) const { return vcltq_f32(fVec, o.fVec); }
     Nb operator  > (const SkNf& o) const { return vcgtq_f32(fVec, o.fVec); }
     Nb operator <= (const SkNf& o) const { return vcleq_f32(fVec, o.fVec); }
     Nb operator >= (const SkNf& o) const { return vcgeq_f32(fVec, o.fVec); }
     Nb operator != (const SkNf& o) const { return vmvnq_u32(vceqq_f32(fVec, o.fVec)); }
 
     static SkNf Min(const SkNf& l, const SkNf& r) { return vminq_f32(l.fVec, r.fVec); }
     static SkNf Max(const SkNf& l, const SkNf& r) { return vmaxq_f32(l.fVec, r.fVec); }
 
-    SkNf rsqrt() const {
-        float32x4_t est0 = vrsqrteq_f32(fVec),
-                    est1 = vmulq_f32(vrsqrtsq_f32(fVec, vmulq_f32(est0, est0)), est0);
-        return est1;
+    SkNf rsqrt0() const { return vrsqrteq_f32(fVec); }
+    SkNf rsqrt1() const {
+        float32x4_t est0 = this->rsqrt0().fVec;
+        return vmulq_f32(vrsqrtsq_f32(fVec, vmulq_f32(est0, est0)), est0);
+    }
+    SkNf rsqrt2() const {
+        float32x4_t est1 = this->rsqrt1().fVec;
+        return vmulq_f32(vrsqrtsq_f32(fVec, vmulq_f32(est1, est1)), est1);
     }
 
     SkNf sqrt() const {
     #if defined(SK_CPU_ARM64)
         return vsqrtq_f32(fVec);
     #else
-        float32x4_t est1 = this->rsqrt().fVec,
-        // An extra step of Newton's method to refine the estimate of 1/sqrt(this).
-                    est2 = vmulq_f32(vrsqrtsq_f32(fVec, vmulq_f32(est1, est1)), est1);
-        return vmulq_f32(fVec, est2);
+        return *this * this->rsqrt2();
     #endif
     }
 
     template <int k> float kth() const {
         SkASSERT(0 <= k && k < 4);
         return vgetq_lane_f32(fVec, k&3);
     }
 
 protected:
     float32x4_t fVec;
 };
 
 #endif//SkNx_neon_DEFINED