Add float-to-half (binary16) conversion functions.

Based on code by Fabian Giesen at
https://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/.

These will be needed for creating binary16 textures from floating point data.

BUG=skia:3103

Review URL: https://codereview.chromium.org/760753003

gyp/core.gypi

@@ -101,6 +101,8 @@
         '<(skia_src_path)/core/SkGlyphCache.h',
         '<(skia_src_path)/core/SkGlyphCache_Globals.h',
         '<(skia_src_path)/core/SkGraphics.cpp',
+        '<(skia_src_path)/core/SkHalf.cpp',
+        '<(skia_src_path)/core/SkHalf.h',
         '<(skia_src_path)/core/SkInstCnt.cpp',
         '<(skia_src_path)/core/SkImageFilter.cpp',
         '<(skia_src_path)/core/SkImageInfo.cpp',

src/core/SkHalf.cpp

@@ -0,0 +1,97 @@
+/*
+ * Copyright 2014 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+#include "SkHalf.h"
+#include "SkFloatBits.h"
+
+uint16_t halfMantissa(SkHalf h) {
+    return h & 0x03ff;
+}
+
+uint16_t halfExponent(SkHalf h) {
+    return (h >> 10) & 0x001f;
+}
+
+uint16_t halfSign(SkHalf h) {
+    return h >> 15;
+}
+
+union FloatUIntUnion {
+    uint32_t fUInt;    // this must come first for the initializations below to work
+    float    fFloat;
+};
+
+// based on Fabien Giesen's float_to_half_fast3()
+// see https://gist.github.com/rygorous/2156668
+SkHalf SkFloatToHalf(float f) {
+    static const uint32_t f32infty = { 255 << 23 };
+    static const uint32_t f16infty = { 31 << 23 };
+    static const FloatUIntUnion magic = { 15 << 23 };
+    static const uint32_t sign_mask = 0x80000000u;
+    static const uint32_t round_mask = ~0xfffu;
+    SkHalf o = 0;
+    
+    FloatUIntUnion floatUnion;
+    floatUnion.fFloat = f;
+    
+    uint32_t sign = floatUnion.fUInt & sign_mask;
+    floatUnion.fUInt ^= sign;
+    
+    // NOTE all the integer compares in this function can be safely
+    // compiled into signed compares since all operands are below
+    // 0x80000000. Important if you want fast straight SSE2 code
+    // (since there's no unsigned PCMPGTD).
+    
+    // Inf or NaN (all exponent bits set)
+    if (floatUnion.fUInt >= f32infty)
+        // NaN->qNaN and Inf->Inf
+        o = (floatUnion.fUInt > f32infty) ? 0x7e00 : 0x7c00;
+    // (De)normalized number or zero
+    else {
+        floatUnion.fUInt &= round_mask;
+        floatUnion.fFloat *= magic.fFloat;
+        floatUnion.fUInt -= round_mask;
+        // Clamp to signed infinity if overflowed
+        if (floatUnion.fUInt > f16infty) {
+            floatUnion.fUInt = f16infty;
+        }
+        
+        o = floatUnion.fUInt >> 13; // Take the bits!
+    }
+    
+    o |= sign >> 16;
+    return o;
+}
+
+// based on Fabien Giesen's half_to_float_fast2()
+// see https://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/
+float SkHalfToFloat(SkHalf h) {
+    static const FloatUIntUnion magic = { 126 << 23 };
+    FloatUIntUnion o;
+    
+    if (halfExponent(h) == 0)
+    {
+        // Zero / Denormal
+        o.fUInt = magic.fUInt + halfMantissa(h);
+        o.fFloat -= magic.fFloat;
+    }
+    else
+    {
+        // Set mantissa
+        o.fUInt = halfMantissa(h) << 13;
+        // Set exponent
+        if (halfExponent(h) == 0x1f)
+            // Inf/NaN
+            o.fUInt |= (255 << 23);
+        else
+            o.fUInt |= ((127 - 15 + halfExponent(h)) << 23);
+    }
+    
+    // Set sign
+    o.fUInt |= (halfSign(h) << 31);
+    return o.fFloat;
+}

src/core/SkHalf.h

@@ -0,0 +1,22 @@
+/*
+ * Copyright 2014 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+#ifndef SkHalf_DEFINED
+#define SkHalf_DEFINED
+
+#include "SkTypes.h"
+
+// 16-bit floating point value
+// format is 1 bit sign, 5 bits exponent, 10 bits mantissa
+// only used for storage
+typedef uint16_t SkHalf;
+
+// convert between half and single precision floating point
+float SkHalfToFloat(SkHalf h);
+SkHalf SkFloatToHalf(float f);
+
+#endif

tests/MathTest.cpp

@@ -9,6 +9,7 @@
 #include "SkEndian.h"
 #include "SkFloatBits.h"
 #include "SkFloatingPoint.h"
+#include "SkHalf.h"
 #include "SkMathPriv.h"
 #include "SkPoint.h"
 #include "SkRandom.h"
@@ -326,6 +327,61 @@ static void unittest_isfinite(skiatest::Reporter* reporter) {
     REPORTER_ASSERT(reporter,  SkScalarIsFinite(0));
 }
 
+static void unittest_half(skiatest::Reporter* reporter) {
+    static const float gFloats[] = {
+        0.f, 1.f, 0.5f, 0.499999f, 0.5000001f, 1.f/3,
+        -0.f, -1.f, -0.5f, -0.499999f, -0.5000001f, -1.f/3
+    };
+
+    for (size_t i = 0; i < SK_ARRAY_COUNT(gFloats); ++i) {
+        SkHalf h = SkFloatToHalf(gFloats[i]);
+        float f = SkHalfToFloat(h);
+        REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, gFloats[i]));
+    }
+
+    // check some special values
+    union FloatUnion {
+        uint32_t fU;
+        float    fF;
+    };
+
+    static const FloatUnion largestPositiveHalf = { ((142 << 23) | (1023 << 13)) };
+    SkHalf h = SkFloatToHalf(largestPositiveHalf.fF);
+    float f = SkHalfToFloat(h);
+    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, largestPositiveHalf.fF));
+
+    static const FloatUnion largestNegativeHalf = { (1u << 31) | (142u << 23) | (1023u << 13) };
+    h = SkFloatToHalf(largestNegativeHalf.fF);
+    f = SkHalfToFloat(h);
+    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, largestNegativeHalf.fF));
+
+    static const FloatUnion smallestPositiveHalf = { 102 << 23 };
+    h = SkFloatToHalf(smallestPositiveHalf.fF);
+    f = SkHalfToFloat(h);
+    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, smallestPositiveHalf.fF));
+
+    static const FloatUnion overflowHalf = { ((143 << 23) | (1023 << 13)) };
+    h = SkFloatToHalf(overflowHalf.fF);
+    f = SkHalfToFloat(h);
+    REPORTER_ASSERT(reporter, !SkScalarIsFinite(f) );
+
+    static const FloatUnion underflowHalf = { 101 << 23 };
+    h = SkFloatToHalf(underflowHalf.fF);
+    f = SkHalfToFloat(h);
+    REPORTER_ASSERT(reporter, f == 0.0f );
+
+    static const FloatUnion inf32 = { 255 << 23 };
+    h = SkFloatToHalf(inf32.fF);
+    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_muldiv255(skiatest::Reporter* reporter) {
     for (int a = 0; a <= 255; a++) {
         for (int b = 0; b <= 255; b++) {
@@ -464,6 +520,7 @@ DEF_TEST(Math, reporter) {
 
     unittest_fastfloat(reporter);
     unittest_isfinite(reporter);
+    unittest_half(reporter);
 
     for (i = 0; i < 10000; i++) {
         SkFixed numer = rand.nextS();