SkHalfToFloat_01 / SkFloatToHalf_01

These are basically inlined, 4-at-a-time versions of our existing functions,
but cut down to avoid any work that's only necessary outside [0,1].

Both f16 and f32 denorms should work fine modulo the usual ARMv7 NEON denorm==zero caveat.

In exchange for a little speed, f32->f16 does not round properly.
Instead it truncates, so it's never off by more than 1 bit.

Support for finite values >1 or <0 is straightforward to add back.
>1 might already work as-is.

Getting close to _u16 performance:
    micros   	bench
    261.13  	xferu64_bw_1_opaque_u16
   1833.51  	xferu64_bw_1_alpha_u16
   2762.32 ?	xferu64_aa_1_opaque_u16
   3334.29  	xferu64_aa_1_alpha_u16
    249.78  	xferu64_bw_1_opaque_f16
   3383.18  	xferu64_bw_1_alpha_f16
   4214.72  	xferu64_aa_1_opaque_f16
   4701.19  	xferu64_aa_1_alpha_f16

BUG=skia:
GOLD_TRYBOT_URL= https://gold.skia.org/search2?unt=true&query=source_type%3Dgm&master=false&issue=1685133005

Review URL: https://codereview.chromium.org/1685133005

src/core/SkHalf.h

@@ -8,6 +8,7 @@
 #ifndef SkHalf_DEFINED
 #define SkHalf_DEFINED
 
+#include "SkNx.h"
 #include "SkTypes.h"
 
 // 16-bit floating point value
@@ -23,4 +24,66 @@ typedef uint16_t SkHalf;
 float SkHalfToFloat(SkHalf h);
 SkHalf SkFloatToHalf(float f);
 
+// Convert between half and single precision floating point, but pull any dirty
+// trick we can to make it faster as long as it's correct enough for values in [0,1].
+static inline     Sk4f SkHalfToFloat_01(uint64_t);
+static inline uint64_t SkFloatToHalf_01(const Sk4f&);
+
+// ~~~~~~~~~~~ impl ~~~~~~~~~~~~~~ //
+
+// Like the serial versions in SkHalf.cpp, these are based on
+// https://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/
+
+// TODO: NEON versions
+static inline Sk4f SkHalfToFloat_01(uint64_t hs) {
+#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE2
+    // Load our 16-bit floats into the bottom 16 bits of each 32-bit lane, with zeroes on top.
+    __m128i h = _mm_unpacklo_epi16(_mm_loadl_epi64((const __m128i*)&hs), _mm_setzero_si128());
+
+    // Fork into two paths, depending on whether the 16-bit float is denormalized.
+    __m128 is_denorm = _mm_castsi128_ps(_mm_cmplt_epi32(h, _mm_set1_epi32(0x0400)));
+
+    // TODO: figure out, explain
+    const __m128 half = _mm_set1_ps(0.5f);
+    __m128 denorm = _mm_sub_ps(_mm_or_ps(_mm_castsi128_ps(h), half), half);
+
+    // If we're normalized, just shift ourselves so the exponent/mantissa dividing line
+    // is correct, then re-bias the exponent from 15 to 127.
+    __m128 norm = _mm_castsi128_ps(_mm_add_epi32(_mm_slli_epi32(h, 13),
+                                                 _mm_set1_epi32((127-15) << 23)));
+
+    return _mm_or_ps(_mm_and_ps   (is_denorm, denorm),
+                     _mm_andnot_ps(is_denorm, norm));
+#else
+    float fs[4];
+    for (int i = 0; i < 4; i++) {
+        fs[i] = SkHalfToFloat(hs >> (i*16));
+    }
+    return Sk4f::Load(fs);
+#endif
+}
+
+static inline uint64_t SkFloatToHalf_01(const Sk4f& fs) {
+#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE2
+    // Scale our floats down by a tiny power of 2 to pull up our mantissa bits,
+    // then shift back down to 16-bit float layout.  This doesn't round, so can be 1 bit small.
+    // TODO: understand better.  Why this scale factor?
+    const __m128 scale = _mm_castsi128_ps(_mm_set1_epi32(15 << 23));
+    __m128i h = _mm_srli_epi32(_mm_castps_si128(_mm_mul_ps(fs.fVec, scale)), 13);
+
+    uint64_t r;
+    _mm_storel_epi64((__m128i*)&r, _mm_packs_epi32(h,h));
+    return r;
+#else
+    SkHalf hs[4];
+    for (int i = 0; i < 4; i++) {
+        hs[i] = SkFloatToHalf(fs[i]);
+    }
+    return (uint64_t)hs[3] << 48
+         | (uint64_t)hs[2] << 32
+         | (uint64_t)hs[1] << 16
+         | (uint64_t)hs[0] <<  0;
+#endif
+}
+
 #endif

src/core/SkXfermodeU64.cpp

@@ -46,36 +46,15 @@ static uint64_t store_to_u16(const Sk4f& x4) {
     return value;
 }
 
-static Sk4f load_from_f16(uint64_t value) {
-    const uint16_t* u16 = reinterpret_cast<const uint16_t*>(&value);
-    float f4[4];
-    for (int i = 0; i < 4; ++i) {
-        f4[i] = SkHalfToFloat(u16[i]);
-    }
-    return Sk4f::Load(f4);
-}
-
-static uint64_t store_to_f16(const Sk4f& x4) {
-    uint64_t value;
-    uint16_t* u16 = reinterpret_cast<uint16_t*>(&value);
-
-    float f4[4];
-    x4.store(f4);
-    for (int i = 0; i < 4; ++i) {
-        u16[i] = SkFloatToHalf(f4[i]);
-    }
-    return value;
-}
-
 // Returns dst in its "natural" bias (either unit-float or 16bit int)
 //
 template <DstType D> Sk4f load_from_dst(uint64_t dst) {
-    return (D == kU16_Dst) ? load_from_u16(dst) : load_from_f16(dst);
+    return (D == kU16_Dst) ? load_from_u16(dst) : SkHalfToFloat_01(dst);
 }
 
 // Assumes x4 is already in the "natural" bias (either unit-float or 16bit int)
 template <DstType D> uint64_t store_to_dst(const Sk4f& x4) {
-    return (D == kU16_Dst) ? store_to_u16(x4) : store_to_f16(x4);
+    return (D == kU16_Dst) ? store_to_u16(x4) : SkFloatToHalf_01(x4);
 }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////

tests/Float16Test.cpp

@@ -10,6 +10,7 @@
 #include "SkHalf.h"
 #include "SkOpts.h"
 #include "SkPixmap.h"
+#include "SkRandom.h"
 
 static bool eq_within_half_float(float a, float b) {
     const float kTolerance = 1.0f / (1 << (8 + 10));
@@ -64,3 +65,37 @@ DEF_TEST(float_to_half, reporter) {
     SkOpts::half_to_float(fscratch, hs, 7);
     REPORTER_ASSERT(reporter, 0 == memcmp(fscratch, fs, sizeof(fs)));
 }
+
+DEF_TEST(HalfToFloat_01, r) {
+    for (uint16_t h = 0; h < 0x8000; h++) {
+        float f = SkHalfToFloat(h);
+        if (f >= 0 && f <= 1) {
+            REPORTER_ASSERT(r, SkHalfToFloat_01(h)[0] == f);
+            REPORTER_ASSERT(r, SkFloatToHalf_01(SkHalfToFloat_01(h)) == h);
+        }
+    }
+}
+
+DEF_TEST(FloatToHalf_01, r) {
+#if 0
+    for (uint32_t bits = 0; bits < 0x80000000; bits++) {
+#else
+    SkRandom rand;
+    for (int i = 0; i < 1000000; i++) {
+        uint32_t bits = rand.nextU();
+#endif
+        float f;
+        memcpy(&f, &bits, 4);
+        if (f >= 0 && f <= 1) {
+            uint16_t h1 = (uint16_t)SkFloatToHalf_01(Sk4f(f,0,0,0)),
+                     h2 = SkFloatToHalf(f);
+            bool ok = (h1 == h2 || h1 == h2-1);
+            REPORTER_ASSERT(r, ok);
+            if (!ok) {
+                SkDebugf("%08x (%d) -> %04x (%d), want %04x (%d)\n",
+                         bits, bits>>23, h1, h1>>10, h2, h2>>10);
+                break;
+            }
+        }
+    }
+}