de-proc sk_float_rsqrt

include/private/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 109 matching lines @@
 #define sk_double_ceil2int(x)       (int)ceil(x)
 
 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))
 
-// We forward declare this to break an #include cycle.
-// (SkScalar -> SkFloatingPoint -> SkOpts.h -> SkXfermode -> SkColor -> SkScalar)
-namespace SkOpts { extern float (*rsqrt)(float); }
-
 // 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
+// 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)
     // 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
-    // Perhaps runtime-detected NEON, or a portable fallback.
-    return SkOpts::rsqrt(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;
 #endif
 }
 
 // This is the number of significant digits we can print in a string such that when we read that
 // string back we get the floating point number we expect.  The minimum value C requires is 6, but
 // most compilers support 9
 #ifdef FLT_DECIMAL_DIG
 #define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG
 #else
 #define SK_FLT_DECIMAL_DIG 9
 #endif
 
 #endif