Update fallback rsqrt implementation to use optimal constants.

tests/MathTest.cpp

 /*
  * Copyright 2011 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 
 #include "SkColorPriv.h"
 #include "SkEndian.h"
 #include "SkFloatBits.h"
@@ skipping 364 matching lines @@
     f = SkHalfToFloat(h);
     REPORTER_ASSERT(reporter, !SkScalarIsFinite(f) );
 
     static const FloatUnion nan32 = { 255 << 23 | 1 };
     h = SkFloatToHalf(nan32.fF);
     f = SkHalfToFloat(h);
     REPORTER_ASSERT(reporter, SkScalarIsNaN(f) );
 
 }
 
+static void test_rsqrt(skiatest::Reporter* reporter) {
+    const float maxRelativeError = 6.50196699e-4f;
+
+    // test close to 0 up to 1
+    float input = 0.000001f;
+    for (int i = 0; i < 1000; ++i) {
+        float exact = 1.0f/sk_float_sqrt(input);
+        float estimate = sk_float_rsqrt(input);
+        float relativeError = sk_float_abs(exact - estimate)/exact;
+        REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
+        input += 0.001f;
+    }
+
+    // test 1 to ~100
+    input = 1.0f;
+    for (int i = 0; i < 1000; ++i) {
+        float exact = 1.0f/sk_float_sqrt(input);
+        float estimate = sk_float_rsqrt(input);
+        float relativeError = sk_float_abs(exact - estimate)/exact;
+        REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
+        input += 0.01f;
+    }
+
+    // test some big numbers
+    input = 1000000.0f;
+    for (int i = 0; i < 100; ++i) {
+        float exact = 1.0f/sk_float_sqrt(input);
+        float estimate = sk_float_rsqrt(input);
+        float relativeError = sk_float_abs(exact - estimate)/exact;
+        REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
+        input += 754326.f;
+    }
+}
+
 static void test_muldiv255(skiatest::Reporter* reporter) {
     for (int a = 0; a <= 255; a++) {
         for (int b = 0; b <= 255; b++) {
             int ab = a * b;
             float s = ab / 255.0f;
             int round = (int)floorf(s + 0.5f);
             int trunc = (int)floorf(s);
 
             int iround = SkMulDiv255Round(a, b);
             int itrunc = SkMulDiv255Trunc(a, b);
@@ skipping 119 matching lines @@
     {
         SkFixed result = SkFixedDiv(100, 100);
         REPORTER_ASSERT(reporter, result == SK_Fixed1);
         result = SkFixedDiv(1, SK_Fixed1);
         REPORTER_ASSERT(reporter, result == 1);
     }
 
     unittest_fastfloat(reporter);
     unittest_isfinite(reporter);
     unittest_half(reporter);
+    test_rsqrt(reporter);
 
     for (i = 0; i < 10000; i++) {
         SkFixed numer = rand.nextS();
         SkFixed denom = rand.nextS();
         SkFixed result = SkFixedDiv(numer, denom);
         int64_t check = ((int64_t)numer << 16) / denom;
 
         (void)SkCLZ(numer);
         (void)SkCLZ(denom);
 
@@ skipping 120 matching lines @@
     test_divmod<int16_t>(r);
 }
 
 DEF_TEST(divmod_s32, r) {
     test_divmod<int32_t>(r);
 }
 
 DEF_TEST(divmod_s64, r) {
     test_divmod<int64_t>(r);
 }