Add a utility library for downconverting to fp16.
authorSteinar H. Gunderson <sgunderson@bigfoot.com>
Sun, 9 Mar 2014 16:24:00 +0000 (17:24 +0100)
committerSteinar H. Gunderson <sgunderson@bigfoot.com>
Sun, 9 Mar 2014 16:25:46 +0000 (17:25 +0100)
ATI's drivers don't do this properly by themselves, so we want to
do it on our side. Adapted from some code I wrote a few years ago.

Makefile.in
fp16.cpp [new file with mode: 0644]
fp16.h [new file with mode: 0644]
fp16_test.cpp [new file with mode: 0644]

index 7b1698e..7d4a645 100644 (file)
@@ -68,9 +68,9 @@ UNTESTED_EFFECTS += multiply_effect
 EFFECTS = $(TESTED_EFFECTS) $(UNTESTED_EFFECTS)
 
 # Unit tests.
-TESTS=effect_chain_test $(TESTED_INPUTS:=_test) $(TESTED_EFFECTS:=_test)
+TESTS=effect_chain_test fp16_test $(TESTED_INPUTS:=_test) $(TESTED_EFFECTS:=_test)
 
-LIB_OBJS=effect_util.o util.o widgets.o effect.o effect_chain.o init.o resource_pool.o $(INPUTS:=.o) $(EFFECTS:=.o)
+LIB_OBJS=effect_util.o util.o widgets.o effect.o effect_chain.o init.o resource_pool.o fp16.o $(INPUTS:=.o) $(EFFECTS:=.o)
 
 # Default target:
 all: libmovit.la $(TESTS)
diff --git a/fp16.cpp b/fp16.cpp
new file mode 100644 (file)
index 0000000..3738f5c
--- /dev/null
+++ b/fp16.cpp
@@ -0,0 +1,240 @@
+#include "fp16.h"
+
+namespace movit {
+namespace {
+
+union fp64 {
+       double f;
+       unsigned long long ll;
+};
+
+template<class FP16_INT_T,
+         int FP16_BIAS, int FP16_MANTISSA_BITS, int FP16_EXPONENT_BITS, int FP16_MAX_EXPONENT,
+         int FP64_BIAS, int FP64_MANTISSA_BITS, int FP64_EXPONENT_BITS, int FP64_MAX_EXPONENT>
+inline double fp_upconvert(FP16_INT_T x)
+{
+       int sign = x >> (FP16_MANTISSA_BITS + FP16_EXPONENT_BITS);
+       int exponent = (x & ((1ULL << (FP16_MANTISSA_BITS + FP16_EXPONENT_BITS)) - 1)) >> FP16_MANTISSA_BITS;
+       unsigned long long mantissa = x & ((1ULL << FP16_MANTISSA_BITS) - 1);
+
+       int sign64;
+       int exponent64;
+       unsigned long long mantissa64;
+
+       if (exponent == 0) {
+               /* 
+                * Denormals, or zero. Zero is still zero, denormals become
+                * ordinary numbers.
+                */
+               if (mantissa == 0) {
+                       sign64 = sign;
+                       exponent64 = 0;
+                       mantissa64 = 0;
+               } else {
+                       sign64 = sign;
+                       exponent64 = FP64_BIAS - FP16_BIAS;
+                       mantissa64 = mantissa << (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS + 1);
+
+                       /* Normalize the number. */
+                       while ((mantissa64 & (1ULL << FP64_MANTISSA_BITS)) == 0) {
+                               --exponent64;
+                               mantissa64 <<= 1;
+                       }
+
+                       /* Clear the now-implicit one-bit. */
+                       mantissa64 &= ~(1ULL << FP64_MANTISSA_BITS);
+               }
+       } else if (exponent == FP16_MAX_EXPONENT) {
+               /*
+                * Infinities or NaN (mantissa=0 => infinity, otherwise NaN).
+                * We don't care much about NaNs, so let us just make sure we
+                * keep the first bit (which signals signalling/non-signalling
+                * in many implementations).
+                */
+               sign64 = sign;
+               exponent64 = FP64_MAX_EXPONENT;
+               mantissa64 = mantissa << (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+       } else {
+               sign64 = sign;
+
+               /* Up-conversion is simple. Just re-bias the exponent... */
+               exponent64 = exponent + FP64_BIAS - FP16_BIAS;
+
+               /* ...and convert the mantissa. */
+               mantissa64 = mantissa << (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+       }
+
+       union fp64 nx;
+       nx.ll = ((unsigned long long)sign64 << (FP64_MANTISSA_BITS + FP64_EXPONENT_BITS))
+           | ((unsigned long long)exponent64 << FP64_MANTISSA_BITS)
+           | mantissa64;
+       return nx.f;
+}
+               
+unsigned long long shift_right_with_round(unsigned long long x, unsigned shift)
+{
+       /* shifts >= 64 need to be special-cased */
+       if (shift > 64) {
+               return 0;
+       } else if (shift == 64) {
+               if (x > (1ULL << 63)) {
+                       return 1;
+               } else {
+                       return 0;
+               }
+       }
+
+       unsigned long long round_part = x & ((1ULL << shift) - 1);
+       if (round_part < (1ULL << (shift - 1))) {
+               /* round down */
+               x >>= shift;
+       } else if (round_part > (1ULL << (shift - 1))) {
+               /* round up */
+               x >>= shift;
+               ++x;
+       } else {
+               /* round to nearest even number */
+               x >>= shift;
+               if ((x & 1) != 0) {
+                       ++x;
+               }
+       }
+       return x;
+}
+
+template<class FP16_INT_T,
+         int FP16_BIAS, int FP16_MANTISSA_BITS, int FP16_EXPONENT_BITS, int FP16_MAX_EXPONENT,
+         int FP64_BIAS, int FP64_MANTISSA_BITS, int FP64_EXPONENT_BITS, int FP64_MAX_EXPONENT>
+inline FP16_INT_T fp_downconvert(double x)
+{
+       union fp64 nx;
+       nx.f = x;
+       unsigned long long f = nx.ll;
+       int sign = f >> (FP64_MANTISSA_BITS + FP64_EXPONENT_BITS);
+       int exponent = (f & ((1ULL << (FP64_MANTISSA_BITS + FP64_EXPONENT_BITS)) - 1)) >> FP64_MANTISSA_BITS;
+       unsigned long long mantissa = f & ((1ULL << FP64_MANTISSA_BITS) - 1);
+
+       int sign16;
+       int exponent16;
+       unsigned long long mantissa16;
+
+       if (exponent == 0) {
+               /*
+                * Denormals, or zero. The largest possible 64-bit
+                * denormal is about +- 2^-1022, and the smallest possible
+                * 16-bit denormal is +- 2^-24. Thus, we can safely
+                * just set all of these to zero (but keep the sign bit).
+                */
+               sign16 = sign;
+               exponent16 = 0;
+               mantissa16 = 0;
+       } else if (exponent == FP64_MAX_EXPONENT) {
+               /*
+                * Infinities or NaN (mantissa=0 => infinity, otherwise NaN).
+                * We don't care much about NaNs, so let us just keep the first
+                * bit (which signals signalling/ non-signalling) and make sure 
+                * that we don't coerce NaNs down to infinities.
+                */
+               if (mantissa == 0) {
+                       sign16 = sign;
+                       exponent16 = FP16_MAX_EXPONENT;
+                       mantissa16 = 0;
+               } else {
+                       sign16 = sign;  /* undefined */
+                       exponent16 = FP16_MAX_EXPONENT;
+                       mantissa16 = mantissa >> (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+                       if (mantissa16 == 0) {
+                               mantissa16 = 1;
+                       }
+               }
+       } else {
+               /* Re-bias the exponent, and check if we will create a denormal. */
+               exponent16 = exponent + FP16_BIAS - FP64_BIAS;
+               if (exponent16 <= 0) {
+                       int shift_amount = FP64_MANTISSA_BITS - FP16_MANTISSA_BITS - exponent16 + 1;
+                       sign16 = sign;
+                       exponent16 = 0;
+                       mantissa16 = shift_right_with_round(mantissa | (1ULL << FP64_MANTISSA_BITS), shift_amount);
+
+                       /*
+                        * We could actually have rounded back into the lowest possible non-denormal
+                        * here, so check for that.
+                        */
+                       if (mantissa16 == (1ULL << FP16_MANTISSA_BITS)) {
+                               exponent16 = 1;
+                               mantissa16 = 0;
+                       }
+               } else {
+                       /*
+                        * First, round off the mantissa, since that could change
+                        * the exponent. We use standard IEEE 754r roundTiesToEven
+                        * mode.
+                        */
+                       sign16 = sign;
+                       mantissa16 = shift_right_with_round(mantissa, FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+
+                       /* Check if we overflowed and need to increase the exponent. */
+                       if (mantissa16 == (1ULL << FP16_MANTISSA_BITS)) {
+                               ++exponent16;
+                               mantissa16 = 0;
+                       }
+
+                       /* Finally, check for overflow, and create +- inf if we need to. */
+                       if (exponent16 >= FP16_MAX_EXPONENT) {
+                               exponent16 = FP16_MAX_EXPONENT;
+                               mantissa16 = 0;
+                       }
+               }
+       }
+
+       return (sign16 << (FP16_MANTISSA_BITS + FP16_EXPONENT_BITS))
+           | (exponent16 << FP16_MANTISSA_BITS)
+           | mantissa16;
+}
+
+const int FP64_BIAS = 1023;
+const int FP64_MANTISSA_BITS = 52;
+const int FP64_EXPONENT_BITS = 11;
+const int FP64_MAX_EXPONENT = (1 << FP64_EXPONENT_BITS) - 1;
+
+const int FP32_BIAS = 127;
+const int FP32_MANTISSA_BITS = 23;
+const int FP32_EXPONENT_BITS = 8;
+const int FP32_MAX_EXPONENT = (1 << FP32_EXPONENT_BITS) - 1;
+
+const int FP16_BIAS = 15;
+const int FP16_MANTISSA_BITS = 10;
+const int FP16_EXPONENT_BITS = 5;
+const int FP16_MAX_EXPONENT = (1 << FP16_EXPONENT_BITS) - 1;
+
+}  // namespace
+
+double fp16_to_fp64(fp16_int_t x)
+{
+       return fp_upconvert<fp16_int_t,
+              FP16_BIAS, FP16_MANTISSA_BITS, FP16_EXPONENT_BITS, FP16_MAX_EXPONENT,
+              FP64_BIAS, FP64_MANTISSA_BITS, FP64_EXPONENT_BITS, FP64_MAX_EXPONENT>(x);
+}
+
+fp16_int_t fp64_to_fp16(double x)
+{
+       return fp_downconvert<fp16_int_t,
+              FP16_BIAS, FP16_MANTISSA_BITS, FP16_EXPONENT_BITS, FP16_MAX_EXPONENT,
+              FP64_BIAS, FP64_MANTISSA_BITS, FP64_EXPONENT_BITS, FP64_MAX_EXPONENT>(x);
+}
+
+double fp32_to_fp64(fp32_int_t x)
+{
+       return fp_upconvert<fp32_int_t,
+              FP32_BIAS, FP32_MANTISSA_BITS, FP32_EXPONENT_BITS, FP32_MAX_EXPONENT,
+              FP64_BIAS, FP64_MANTISSA_BITS, FP64_EXPONENT_BITS, FP64_MAX_EXPONENT>(x);
+}
+
+fp32_int_t fp64_to_fp32(double x)
+{
+       return fp_downconvert<fp32_int_t,
+              FP32_BIAS, FP32_MANTISSA_BITS, FP32_EXPONENT_BITS, FP32_MAX_EXPONENT,
+              FP64_BIAS, FP64_MANTISSA_BITS, FP64_EXPONENT_BITS, FP64_MAX_EXPONENT>(x);
+}
+
+}  // namespace
diff --git a/fp16.h b/fp16.h
new file mode 100644 (file)
index 0000000..9f7eff9
--- /dev/null
+++ b/fp16.h
@@ -0,0 +1,27 @@
+#ifndef _MOVIT_FP16_H
+#define _MOVIT_FP16_H 1
+
+// Code for converting to and from fp16 (from fp64), without any particular
+// machine support, with proper IEEE round-to-even behavior (and correct
+// handling of NaNs and infinities). This is needed because some OpenGL
+// drivers don't properly round off when asked to convert data themselves.
+//
+// These routines are not particularly fast.
+
+namespace movit {
+
+typedef unsigned int fp32_int_t;
+typedef unsigned short fp16_int_t;
+
+double fp16_to_fp64(fp16_int_t x);
+fp16_int_t fp64_to_fp16(double x);
+
+// These are not very useful by themselves, but are implemented using the same
+// code as the fp16 ones (just with different constants), so they are useful
+// for verifying against the FPU in unit tests.
+double fp32_to_fp64(fp32_int_t x);
+fp32_int_t fp64_to_fp32(double x);
+
+}  // namespace movit
+
+#endif  // _MOVIT_FP16_H
diff --git a/fp16_test.cpp b/fp16_test.cpp
new file mode 100644 (file)
index 0000000..d5d7fc0
--- /dev/null
@@ -0,0 +1,80 @@
+#include "fp16.h"
+
+#include <math.h>
+#include <gtest/gtest.h>
+
+namespace movit {
+
+TEST(FP16Test, Simple) {
+       EXPECT_EQ(0x0000, fp64_to_fp16(0.0));
+       EXPECT_DOUBLE_EQ(0.0, fp16_to_fp64(0x0000));
+
+       EXPECT_EQ(0x3c00, fp64_to_fp16(1.0));
+       EXPECT_DOUBLE_EQ(1.0, fp16_to_fp64(0x3c00));
+
+       EXPECT_EQ(0x3555, fp64_to_fp16(1.0 / 3.0));
+       EXPECT_DOUBLE_EQ(0.333251953125, fp16_to_fp64(0x3555));
+}
+
+TEST(FP16Test, NaN) {
+       EXPECT_EQ(0xfe00, fp64_to_fp16(0.0 / 0.0));
+       EXPECT_TRUE(isnan(fp16_to_fp64(0xfe00)));
+}
+
+union fp64 {
+       double f;
+       unsigned long long ll;
+};
+union fp32 {
+       float f;
+       unsigned int u;
+};
+
+// Randomly test a large number of fp64 -> fp32 conversions, comparing
+// against the FPU.
+TEST(FP16Test, FP32ReferenceDownconvert) {
+       srand(12345);
+
+       for (int i = 0; i < 1000000; ++i) {
+               unsigned r1 = rand();
+               unsigned r2 = rand();
+               unsigned r3 = rand();
+               union fp64 src;
+               union fp32 reference, result;
+
+               src.ll = (((unsigned long long)r1) << 33) ^ ((unsigned long long)r2 << 16) ^ r3;
+               reference.f = float(src.f);
+               result.u = fp64_to_fp32(src.f);
+
+               EXPECT_EQ(isnan(result.f), isnan(reference.f));
+               if (!isnan(result.f)) {
+                       EXPECT_EQ(result.u, reference.u)
+                           << src.f << " got rounded to " << result.u << " (" << result.f << ")";
+               }
+       }
+}
+
+// Randomly test a large number of fp32 -> fp64 conversions, comparing
+// against the FPU.
+TEST(FP16Test, FP32ReferenceUpconvert) {
+       srand(12345);
+
+       for (int i = 0; i < 1000000; ++i) {
+               unsigned r1 = rand();
+               unsigned r2 = rand();
+               union fp32 src;
+               union fp64 reference, result;
+
+               src.u = ((unsigned long long)r1 << 16) ^ r2;
+               reference.f = double(src.f);
+               result.f = fp32_to_fp64(src.u);
+
+               EXPECT_EQ(isnan(result.f), isnan(reference.f));
+               if (!isnan(result.f)) {
+                       EXPECT_EQ(result.ll, reference.ll)
+                           << src.f << " got converted to " << result.ll << " (" << result.f << ")";
+               }
+       }
+}
+
+}  // namespace movit