gtests/HexFloat.cpp

   1 // Copyright (c) 2015-2016 The Khronos Group Inc.
   2 //
   3 // Licensed under the Apache License, Version 2.0 (the "License");
   4 // you may not use this file except in compliance with the License.
   5 // You may obtain a copy of the License at
   6 //
   7 //     http://www.apache.org/licenses/LICENSE-2.0
   8 //
   9 // Unless required by applicable law or agreed to in writing, software
  10 // distributed under the License is distributed on an "AS IS" BASIS,
  11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  12 // See the License for the specific language governing permissions and
  13 // limitations under the License.
  14
  15 #include <cfloat>
  16 #include <cmath>
  17 #include <cstdio>
  18 #include <sstream>
  19 #include <string>
  20 #include <tuple>
  21
  22 #include <gmock/gmock.h>
  23 #include "SPIRV/hex_float.h"
  24
  25 namespace {
  26 using ::testing::Eq;
  27 using spvutils::BitwiseCast;
  28 using spvutils::Float16;
  29 using spvutils::FloatProxy;
  30 using spvutils::HexFloat;
  31 using spvutils::ParseNormalFloat;
  32
  33 // In this file "encode" means converting a number into a string,
  34 // and "decode" means converting a string into a number.
  35
  36 using HexFloatTest =
  37     ::testing::TestWithParam<std::pair<FloatProxy<float>, std::string>>;
  38 using DecodeHexFloatTest =
  39     ::testing::TestWithParam<std::pair<std::string, FloatProxy<float>>>;
  40 using HexDoubleTest =
  41     ::testing::TestWithParam<std::pair<FloatProxy<double>, std::string>>;
  42 using DecodeHexDoubleTest =
  43     ::testing::TestWithParam<std::pair<std::string, FloatProxy<double>>>;
  44
  45 // Hex-encodes a float value.
  46 template <typename T>
  47 std::string EncodeViaHexFloat(const T& value) {
  48   std::stringstream ss;
  49   ss << spvutils::HexFloat<T>(value);
  50   return ss.str();
  51 }
  52
  53 // The following two tests can't be DRY because they take different parameter
  54 // types.
  55
  56 TEST_P(HexFloatTest, EncodeCorrectly) {
  57   EXPECT_THAT(EncodeViaHexFloat(GetParam().first), Eq(GetParam().second));
  58 }
  59
  60 TEST_P(HexDoubleTest, EncodeCorrectly) {
  61   EXPECT_THAT(EncodeViaHexFloat(GetParam().first), Eq(GetParam().second));
  62 }
  63
  64 // Decodes a hex-float string.
  65 template <typename T>
  66 FloatProxy<T> Decode(const std::string& str) {
  67   spvutils::HexFloat<FloatProxy<T>> decoded(0.f);
  68   EXPECT_TRUE((std::stringstream(str) >> decoded).eof());
  69   return decoded.value();
  70 }
  71
  72 TEST_P(HexFloatTest, DecodeCorrectly) {
  73   EXPECT_THAT(Decode<float>(GetParam().second), Eq(GetParam().first));
  74 }
  75
  76 TEST_P(HexDoubleTest, DecodeCorrectly) {
  77   EXPECT_THAT(Decode<double>(GetParam().second), Eq(GetParam().first));
  78 }
  79
  80 INSTANTIATE_TEST_SUITE_P(
  81     Float32Tests, HexFloatTest,
  82     ::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
  83         {0.f, "0x0p+0"},
  84         {1.f, "0x1p+0"},
  85         {2.f, "0x1p+1"},
  86         {3.f, "0x1.8p+1"},
  87         {0.5f, "0x1p-1"},
  88         {0.25f, "0x1p-2"},
  89         {0.75f, "0x1.8p-1"},
  90         {-0.f, "-0x0p+0"},
  91         {-1.f, "-0x1p+0"},
  92         {-0.5f, "-0x1p-1"},
  93         {-0.25f, "-0x1p-2"},
  94         {-0.75f, "-0x1.8p-1"},
  95
  96         // Larger numbers
  97         {512.f, "0x1p+9"},
  98         {-512.f, "-0x1p+9"},
  99         {1024.f, "0x1p+10"},
 100         {-1024.f, "-0x1p+10"},
 101         {1024.f + 8.f, "0x1.02p+10"},
 102         {-1024.f - 8.f, "-0x1.02p+10"},
 103
 104         // Small numbers
 105         {1.0f / 512.f, "0x1p-9"},
 106         {1.0f / -512.f, "-0x1p-9"},
 107         {1.0f / 1024.f, "0x1p-10"},
 108         {1.0f / -1024.f, "-0x1p-10"},
 109         {1.0f / 1024.f + 1.0f / 8.f, "0x1.02p-3"},
 110         {1.0f / -1024.f - 1.0f / 8.f, "-0x1.02p-3"},
 111
 112         // lowest non-denorm
 113         {float(ldexp(1.0f, -126)), "0x1p-126"},
 114         {float(ldexp(-1.0f, -126)), "-0x1p-126"},
 115
 116         // Denormalized values
 117         {float(ldexp(1.0f, -127)), "0x1p-127"},
 118         {float(ldexp(1.0f, -127) / 2.0f), "0x1p-128"},
 119         {float(ldexp(1.0f, -127) / 4.0f), "0x1p-129"},
 120         {float(ldexp(1.0f, -127) / 8.0f), "0x1p-130"},
 121         {float(ldexp(-1.0f, -127)), "-0x1p-127"},
 122         {float(ldexp(-1.0f, -127) / 2.0f), "-0x1p-128"},
 123         {float(ldexp(-1.0f, -127) / 4.0f), "-0x1p-129"},
 124         {float(ldexp(-1.0f, -127) / 8.0f), "-0x1p-130"},
 125
 126         {float(ldexp(1.0, -127) + (ldexp(1.0, -127) / 2.0f)), "0x1.8p-127"},
 127         {float(ldexp(1.0, -127) / 2.0 + (ldexp(1.0, -127) / 4.0f)),
 128          "0x1.8p-128"},
 129
 130     })));
 131
 132 INSTANTIATE_TEST_SUITE_P(
 133     Float32NanTests, HexFloatTest,
 134     ::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
 135         // Various NAN and INF cases
 136         {uint32_t(0xFF800000), "-0x1p+128"},         // -inf
 137         {uint32_t(0x7F800000), "0x1p+128"},          // inf
 138         {uint32_t(0xFFC00000), "-0x1.8p+128"},       // -nan
 139         {uint32_t(0xFF800100), "-0x1.0002p+128"},    // -nan
 140         {uint32_t(0xFF800c00), "-0x1.0018p+128"},    // -nan
 141         {uint32_t(0xFF80F000), "-0x1.01ep+128"},     // -nan
 142         {uint32_t(0xFFFFFFFF), "-0x1.fffffep+128"},  // -nan
 143         {uint32_t(0x7FC00000), "0x1.8p+128"},        // +nan
 144         {uint32_t(0x7F800100), "0x1.0002p+128"},     // +nan
 145         {uint32_t(0x7f800c00), "0x1.0018p+128"},     // +nan
 146         {uint32_t(0x7F80F000), "0x1.01ep+128"},      // +nan
 147         {uint32_t(0x7FFFFFFF), "0x1.fffffep+128"},   // +nan
 148     })));
 149
 150 INSTANTIATE_TEST_SUITE_P(
 151     Float64Tests, HexDoubleTest,
 152     ::testing::ValuesIn(
 153         std::vector<std::pair<FloatProxy<double>, std::string>>({
 154             {0., "0x0p+0"},
 155             {1., "0x1p+0"},
 156             {2., "0x1p+1"},
 157             {3., "0x1.8p+1"},
 158             {0.5, "0x1p-1"},
 159             {0.25, "0x1p-2"},
 160             {0.75, "0x1.8p-1"},
 161             {-0., "-0x0p+0"},
 162             {-1., "-0x1p+0"},
 163             {-0.5, "-0x1p-1"},
 164             {-0.25, "-0x1p-2"},
 165             {-0.75, "-0x1.8p-1"},
 166
 167             // Larger numbers
 168             {512., "0x1p+9"},
 169             {-512., "-0x1p+9"},
 170             {1024., "0x1p+10"},
 171             {-1024., "-0x1p+10"},
 172             {1024. + 8., "0x1.02p+10"},
 173             {-1024. - 8., "-0x1.02p+10"},
 174
 175             // Large outside the range of normal floats
 176             {ldexp(1.0, 128), "0x1p+128"},
 177             {ldexp(1.0, 129), "0x1p+129"},
 178             {ldexp(-1.0, 128), "-0x1p+128"},
 179             {ldexp(-1.0, 129), "-0x1p+129"},
 180             {ldexp(1.0, 128) + ldexp(1.0, 90), "0x1.0000000004p+128"},
 181             {ldexp(1.0, 129) + ldexp(1.0, 120), "0x1.008p+129"},
 182             {ldexp(-1.0, 128) + ldexp(1.0, 90), "-0x1.fffffffff8p+127"},
 183             {ldexp(-1.0, 129) + ldexp(1.0, 120), "-0x1.ffp+128"},
 184
 185             // Small numbers
 186             {1.0 / 512., "0x1p-9"},
 187             {1.0 / -512., "-0x1p-9"},
 188             {1.0 / 1024., "0x1p-10"},
 189             {1.0 / -1024., "-0x1p-10"},
 190             {1.0 / 1024. + 1.0 / 8., "0x1.02p-3"},
 191             {1.0 / -1024. - 1.0 / 8., "-0x1.02p-3"},
 192
 193             // Small outside the range of normal floats
 194             {ldexp(1.0, -128), "0x1p-128"},
 195             {ldexp(1.0, -129), "0x1p-129"},
 196             {ldexp(-1.0, -128), "-0x1p-128"},
 197             {ldexp(-1.0, -129), "-0x1p-129"},
 198             {ldexp(1.0, -128) + ldexp(1.0, -90), "0x1.0000000004p-90"},
 199             {ldexp(1.0, -129) + ldexp(1.0, -120), "0x1.008p-120"},
 200             {ldexp(-1.0, -128) + ldexp(1.0, -90), "0x1.fffffffff8p-91"},
 201             {ldexp(-1.0, -129) + ldexp(1.0, -120), "0x1.ffp-121"},
 202
 203             // lowest non-denorm
 204             {ldexp(1.0, -1022), "0x1p-1022"},
 205             {ldexp(-1.0, -1022), "-0x1p-1022"},
 206
 207             // Denormalized values
 208             {ldexp(1.0, -1023), "0x1p-1023"},
 209             {ldexp(1.0, -1023) / 2.0, "0x1p-1024"},
 210             {ldexp(1.0, -1023) / 4.0, "0x1p-1025"},
 211             {ldexp(1.0, -1023) / 8.0, "0x1p-1026"},
 212             {ldexp(-1.0, -1024), "-0x1p-1024"},
 213             {ldexp(-1.0, -1024) / 2.0, "-0x1p-1025"},
 214             {ldexp(-1.0, -1024) / 4.0, "-0x1p-1026"},
 215             {ldexp(-1.0, -1024) / 8.0, "-0x1p-1027"},
 216
 217             {ldexp(1.0, -1023) + (ldexp(1.0, -1023) / 2.0), "0x1.8p-1023"},
 218             {ldexp(1.0, -1023) / 2.0 + (ldexp(1.0, -1023) / 4.0),
 219              "0x1.8p-1024"},
 220
 221         })));
 222
 223 INSTANTIATE_TEST_SUITE_P(
 224     Float64NanTests, HexDoubleTest,
 225     ::testing::ValuesIn(std::vector<
 226                         std::pair<FloatProxy<double>, std::string>>({
 227         // Various NAN and INF cases
 228         {uint64_t(0xFFF0000000000000LL), "-0x1p+1024"},                //-inf
 229         {uint64_t(0x7FF0000000000000LL), "0x1p+1024"},                 //+inf
 230         {uint64_t(0xFFF8000000000000LL), "-0x1.8p+1024"},              // -nan
 231         {uint64_t(0xFFF0F00000000000LL), "-0x1.0fp+1024"},             // -nan
 232         {uint64_t(0xFFF0000000000001LL), "-0x1.0000000000001p+1024"},  // -nan
 233         {uint64_t(0xFFF0000300000000LL), "-0x1.00003p+1024"},          // -nan
 234         {uint64_t(0xFFFFFFFFFFFFFFFFLL), "-0x1.fffffffffffffp+1024"},  // -nan
 235         {uint64_t(0x7FF8000000000000LL), "0x1.8p+1024"},               // +nan
 236         {uint64_t(0x7FF0F00000000000LL), "0x1.0fp+1024"},              // +nan
 237         {uint64_t(0x7FF0000000000001LL), "0x1.0000000000001p+1024"},   // -nan
 238         {uint64_t(0x7FF0000300000000LL), "0x1.00003p+1024"},           // -nan
 239         {uint64_t(0x7FFFFFFFFFFFFFFFLL), "0x1.fffffffffffffp+1024"},   // -nan
 240     })));
 241
 242 TEST(HexFloatStreamTest, OperatorLeftShiftPreservesFloatAndFill) {
 243   std::stringstream s;
 244   s << std::setw(4) << std::oct << std::setfill('x') << 8 << " "
 245     << FloatProxy<float>(uint32_t(0xFF800100)) << " " << std::setw(4) << 9;
 246   EXPECT_THAT(s.str(), Eq(std::string("xx10 -0x1.0002p+128 xx11")));
 247 }
 248
 249 TEST(HexDoubleStreamTest, OperatorLeftShiftPreservesFloatAndFill) {
 250   std::stringstream s;
 251   s << std::setw(4) << std::oct << std::setfill('x') << 8 << " "
 252     << FloatProxy<double>(uint64_t(0x7FF0F00000000000LL)) << " " << std::setw(4)
 253     << 9;
 254   EXPECT_THAT(s.str(), Eq(std::string("xx10 0x1.0fp+1024 xx11")));
 255 }
 256
 257 TEST_P(DecodeHexFloatTest, DecodeCorrectly) {
 258   EXPECT_THAT(Decode<float>(GetParam().first), Eq(GetParam().second));
 259 }
 260
 261 TEST_P(DecodeHexDoubleTest, DecodeCorrectly) {
 262   EXPECT_THAT(Decode<double>(GetParam().first), Eq(GetParam().second));
 263 }
 264
 265 INSTANTIATE_TEST_SUITE_P(
 266     Float32DecodeTests, DecodeHexFloatTest,
 267     ::testing::ValuesIn(std::vector<std::pair<std::string, FloatProxy<float>>>({
 268         {"0x0p+000", 0.f},
 269         {"0x0p0", 0.f},
 270         {"0x0p-0", 0.f},
 271
 272         // flush to zero cases
 273         {"0x1p-500", 0.f},  // Exponent underflows.
 274         {"-0x1p-500", -0.f},
 275         {"0x0.00000000001p-126", 0.f},  // Fraction causes underflow.
 276         {"-0x0.0000000001p-127", -0.f},
 277         {"-0x0.01p-142", -0.f},  // Fraction causes additional underflow.
 278         {"0x0.01p-142", 0.f},
 279
 280         // Some floats that do not encode the same way as they decode.
 281         {"0x2p+0", 2.f},
 282         {"0xFFp+0", 255.f},
 283         {"0x0.8p+0", 0.5f},
 284         {"0x0.4p+0", 0.25f},
 285     })));
 286
 287 INSTANTIATE_TEST_SUITE_P(
 288     Float32DecodeInfTests, DecodeHexFloatTest,
 289     ::testing::ValuesIn(std::vector<std::pair<std::string, FloatProxy<float>>>({
 290         // inf cases
 291         {"-0x1p+128", uint32_t(0xFF800000)},   // -inf
 292         {"0x32p+127", uint32_t(0x7F800000)},   // inf
 293         {"0x32p+500", uint32_t(0x7F800000)},   // inf
 294         {"-0x32p+127", uint32_t(0xFF800000)},  // -inf
 295     })));
 296
 297 INSTANTIATE_TEST_SUITE_P(
 298     Float64DecodeTests, DecodeHexDoubleTest,
 299     ::testing::ValuesIn(
 300         std::vector<std::pair<std::string, FloatProxy<double>>>({
 301             {"0x0p+000", 0.},
 302             {"0x0p0", 0.},
 303             {"0x0p-0", 0.},
 304
 305             // flush to zero cases
 306             {"0x1p-5000", 0.},  // Exponent underflows.
 307             {"-0x1p-5000", -0.},
 308             {"0x0.0000000000000001p-1023", 0.},  // Fraction causes underflow.
 309             {"-0x0.000000000000001p-1024", -0.},
 310             {"-0x0.01p-1090", -0.f},  // Fraction causes additional underflow.
 311             {"0x0.01p-1090", 0.},
 312
 313             // Some floats that do not encode the same way as they decode.
 314             {"0x2p+0", 2.},
 315             {"0xFFp+0", 255.},
 316             {"0x0.8p+0", 0.5},
 317             {"0x0.4p+0", 0.25},
 318         })));
 319
 320 INSTANTIATE_TEST_SUITE_P(
 321     Float64DecodeInfTests, DecodeHexDoubleTest,
 322     ::testing::ValuesIn(
 323         std::vector<std::pair<std::string, FloatProxy<double>>>({
 324             // inf cases
 325             {"-0x1p+1024", uint64_t(0xFFF0000000000000)},   // -inf
 326             {"0x32p+1023", uint64_t(0x7FF0000000000000)},   // inf
 327             {"0x32p+5000", uint64_t(0x7FF0000000000000)},   // inf
 328             {"-0x32p+1023", uint64_t(0xFFF0000000000000)},  // -inf
 329         })));
 330
 331 TEST(FloatProxy, ValidConversion) {
 332   EXPECT_THAT(FloatProxy<float>(1.f).getAsFloat(), Eq(1.0f));
 333   EXPECT_THAT(FloatProxy<float>(32.f).getAsFloat(), Eq(32.0f));
 334   EXPECT_THAT(FloatProxy<float>(-1.f).getAsFloat(), Eq(-1.0f));
 335   EXPECT_THAT(FloatProxy<float>(0.f).getAsFloat(), Eq(0.0f));
 336   EXPECT_THAT(FloatProxy<float>(-0.f).getAsFloat(), Eq(-0.0f));
 337   EXPECT_THAT(FloatProxy<float>(1.2e32f).getAsFloat(), Eq(1.2e32f));
 338
 339   EXPECT_TRUE(std::isinf(FloatProxy<float>(uint32_t(0xFF800000)).getAsFloat()));
 340   EXPECT_TRUE(std::isinf(FloatProxy<float>(uint32_t(0x7F800000)).getAsFloat()));
 341   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFFC00000)).getAsFloat()));
 342   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF800100)).getAsFloat()));
 343   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF800c00)).getAsFloat()));
 344   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF80F000)).getAsFloat()));
 345   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFFFFFFFF)).getAsFloat()));
 346   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7FC00000)).getAsFloat()));
 347   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7F800100)).getAsFloat()));
 348   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7f800c00)).getAsFloat()));
 349   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7F80F000)).getAsFloat()));
 350   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7FFFFFFF)).getAsFloat()));
 351
 352   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800000)).data(), Eq(0xFF800000u));
 353   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F800000)).data(), Eq(0x7F800000u));
 354   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFFC00000)).data(), Eq(0xFFC00000u));
 355   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800100)).data(), Eq(0xFF800100u));
 356   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800c00)).data(), Eq(0xFF800c00u));
 357   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF80F000)).data(), Eq(0xFF80F000u));
 358   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFFFFFFFF)).data(), Eq(0xFFFFFFFFu));
 359   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7FC00000)).data(), Eq(0x7FC00000u));
 360   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F800100)).data(), Eq(0x7F800100u));
 361   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7f800c00)).data(), Eq(0x7f800c00u));
 362   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F80F000)).data(), Eq(0x7F80F000u));
 363   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7FFFFFFF)).data(), Eq(0x7FFFFFFFu));
 364 }
 365
 366 TEST(FloatProxy, Nan) {
 367   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFFC00000)).isNan());
 368   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF800100)).isNan());
 369   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF800c00)).isNan());
 370   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF80F000)).isNan());
 371   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFFFFFFFF)).isNan());
 372   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7FC00000)).isNan());
 373   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7F800100)).isNan());
 374   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7f800c00)).isNan());
 375   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7F80F000)).isNan());
 376   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7FFFFFFF)).isNan());
 377 }
 378
 379 TEST(FloatProxy, Negation) {
 380   EXPECT_THAT((-FloatProxy<float>(1.f)).getAsFloat(), Eq(-1.0f));
 381   EXPECT_THAT((-FloatProxy<float>(0.f)).getAsFloat(), Eq(-0.0f));
 382
 383   EXPECT_THAT((-FloatProxy<float>(-1.f)).getAsFloat(), Eq(1.0f));
 384   EXPECT_THAT((-FloatProxy<float>(-0.f)).getAsFloat(), Eq(0.0f));
 385
 386   EXPECT_THAT((-FloatProxy<float>(32.f)).getAsFloat(), Eq(-32.0f));
 387   EXPECT_THAT((-FloatProxy<float>(-32.f)).getAsFloat(), Eq(32.0f));
 388
 389   EXPECT_THAT((-FloatProxy<float>(1.2e32f)).getAsFloat(), Eq(-1.2e32f));
 390   EXPECT_THAT((-FloatProxy<float>(-1.2e32f)).getAsFloat(), Eq(1.2e32f));
 391
 392   EXPECT_THAT(
 393       (-FloatProxy<float>(std::numeric_limits<float>::infinity())).getAsFloat(),
 394       Eq(-std::numeric_limits<float>::infinity()));
 395   EXPECT_THAT((-FloatProxy<float>(-std::numeric_limits<float>::infinity()))
 396                   .getAsFloat(),
 397               Eq(std::numeric_limits<float>::infinity()));
 398 }
 399
 400 // Test conversion of FloatProxy values to strings.
 401 //
 402 // In previous cases, we always wrapped the FloatProxy value in a HexFloat
 403 // before conversion to a string.  In the following cases, the FloatProxy
 404 // decides for itself whether to print as a regular number or as a hex float.
 405
 406 using FloatProxyFloatTest =
 407     ::testing::TestWithParam<std::pair<FloatProxy<float>, std::string>>;
 408 using FloatProxyDoubleTest =
 409     ::testing::TestWithParam<std::pair<FloatProxy<double>, std::string>>;
 410
 411 // Converts a float value to a string via a FloatProxy.
 412 template <typename T>
 413 std::string EncodeViaFloatProxy(const T& value) {
 414   std::stringstream ss;
 415   ss << value;
 416   return ss.str();
 417 }
 418
 419 // Converts a floating point string so that the exponent prefix
 420 // is 'e', and the exponent value does not have leading zeros.
 421 // The Microsoft runtime library likes to write things like "2.5E+010".
 422 // Convert that to "2.5e+10".
 423 // We don't care what happens to strings that are not floating point
 424 // strings.
 425 std::string NormalizeExponentInFloatString(std::string in) {
 426   std::string result;
 427   // Reserve one spot for the terminating null, even when the sscanf fails.
 428   std::vector<char> prefix(in.size() + 1);
 429   char e;
 430   char plus_or_minus;
 431   int exponent;  // in base 10
 432   if ((4 == std::sscanf(in.c_str(), "%[-+.0123456789]%c%c%d", prefix.data(), &e,
 433                         &plus_or_minus, &exponent)) &&
 434       (e == 'e' || e == 'E') &&
 435       (plus_or_minus == '-' || plus_or_minus == '+')) {
 436     // It looks like a floating point value with exponent.
 437     std::stringstream out;
 438     out << prefix.data() << 'e' << plus_or_minus << exponent;
 439     result = out.str();
 440   } else {
 441     result = in;
 442   }
 443   return result;
 444 }
 445
 446 TEST(NormalizeFloat, Sample) {
 447   EXPECT_THAT(NormalizeExponentInFloatString(""), Eq(""));
 448   EXPECT_THAT(NormalizeExponentInFloatString("1e-12"), Eq("1e-12"));
 449   EXPECT_THAT(NormalizeExponentInFloatString("1E+14"), Eq("1e+14"));
 450   EXPECT_THAT(NormalizeExponentInFloatString("1e-0012"), Eq("1e-12"));
 451   EXPECT_THAT(NormalizeExponentInFloatString("1.263E+014"), Eq("1.263e+14"));
 452 }
 453
 454 // The following two tests can't be DRY because they take different parameter
 455 // types.
 456 TEST_P(FloatProxyFloatTest, EncodeCorrectly) {
 457   EXPECT_THAT(
 458       NormalizeExponentInFloatString(EncodeViaFloatProxy(GetParam().first)),
 459       Eq(GetParam().second));
 460 }
 461
 462 TEST_P(FloatProxyDoubleTest, EncodeCorrectly) {
 463   EXPECT_THAT(
 464       NormalizeExponentInFloatString(EncodeViaFloatProxy(GetParam().first)),
 465       Eq(GetParam().second));
 466 }
 467
 468 INSTANTIATE_TEST_SUITE_P(
 469     Float32Tests, FloatProxyFloatTest,
 470     ::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
 471         // Zero
 472         {0.f, "0"},
 473         // Normal numbers
 474         {1.f, "1"},
 475         {-0.25f, "-0.25"},
 476         {1000.0f, "1000"},
 477
 478         // Still normal numbers, but with large magnitude exponents.
 479         {float(ldexp(1.f, 126)), "8.50706e+37"},
 480         {float(ldexp(-1.f, -126)), "-1.17549e-38"},
 481
 482         // denormalized values are printed as hex floats.
 483         {float(ldexp(1.0f, -127)), "0x1p-127"},
 484         {float(ldexp(1.5f, -128)), "0x1.8p-128"},
 485         {float(ldexp(1.25, -129)), "0x1.4p-129"},
 486         {float(ldexp(1.125, -130)), "0x1.2p-130"},
 487         {float(ldexp(-1.0f, -127)), "-0x1p-127"},
 488         {float(ldexp(-1.0f, -128)), "-0x1p-128"},
 489         {float(ldexp(-1.0f, -129)), "-0x1p-129"},
 490         {float(ldexp(-1.5f, -130)), "-0x1.8p-130"},
 491
 492         // NaNs
 493         {FloatProxy<float>(uint32_t(0xFFC00000)), "-0x1.8p+128"},
 494         {FloatProxy<float>(uint32_t(0xFF800100)), "-0x1.0002p+128"},
 495
 496         {std::numeric_limits<float>::infinity(), "0x1p+128"},
 497         {-std::numeric_limits<float>::infinity(), "-0x1p+128"},
 498     })));
 499
 500 INSTANTIATE_TEST_SUITE_P(
 501     Float64Tests, FloatProxyDoubleTest,
 502     ::testing::ValuesIn(
 503         std::vector<std::pair<FloatProxy<double>, std::string>>({
 504             {0., "0"},
 505             {1., "1"},
 506             {-0.25, "-0.25"},
 507             {1000.0, "1000"},
 508
 509             // Large outside the range of normal floats
 510             {ldexp(1.0, 128), "3.40282366920938e+38"},
 511             {ldexp(1.5, 129), "1.02084710076282e+39"},
 512             {ldexp(-1.0, 128), "-3.40282366920938e+38"},
 513             {ldexp(-1.5, 129), "-1.02084710076282e+39"},
 514
 515             // Small outside the range of normal floats
 516             {ldexp(1.5, -129), "2.20405190779179e-39"},
 517             {ldexp(-1.5, -129), "-2.20405190779179e-39"},
 518
 519             // lowest non-denorm
 520             {ldexp(1.0, -1022), "2.2250738585072e-308"},
 521             {ldexp(-1.0, -1022), "-2.2250738585072e-308"},
 522
 523             // Denormalized values
 524             {ldexp(1.125, -1023), "0x1.2p-1023"},
 525             {ldexp(-1.375, -1024), "-0x1.6p-1024"},
 526
 527             // NaNs
 528             {uint64_t(0x7FF8000000000000LL), "0x1.8p+1024"},
 529             {uint64_t(0xFFF0F00000000000LL), "-0x1.0fp+1024"},
 530
 531             // Infinity
 532             {std::numeric_limits<double>::infinity(), "0x1p+1024"},
 533             {-std::numeric_limits<double>::infinity(), "-0x1p+1024"},
 534
 535         })));
 536
 537 // double is used so that unbiased_exponent can be used with the output
 538 // of ldexp directly.
 539 int32_t unbiased_exponent(double f) {
 540   return spvutils::HexFloat<spvutils::FloatProxy<float>>(
 541       static_cast<float>(f)).getUnbiasedNormalizedExponent();
 542 }
 543
 544 int16_t unbiased_half_exponent(uint16_t f) {
 545   return spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>(f)
 546       .getUnbiasedNormalizedExponent();
 547 }
 548
 549 TEST(HexFloatOperationTest, UnbiasedExponent) {
 550   // Float cases
 551   EXPECT_EQ(0, unbiased_exponent(ldexp(1.0f, 0)));
 552   EXPECT_EQ(-32, unbiased_exponent(ldexp(1.0f, -32)));
 553   EXPECT_EQ(42, unbiased_exponent(ldexp(1.0f, 42)));
 554   EXPECT_EQ(125, unbiased_exponent(ldexp(1.0f, 125)));
 555   // Saturates to 128
 556   EXPECT_EQ(128, unbiased_exponent(ldexp(1.0f, 256)));
 557
 558   EXPECT_EQ(-100, unbiased_exponent(ldexp(1.0f, -100)));
 559   EXPECT_EQ(-127, unbiased_exponent(ldexp(1.0f, -127))); // First denorm
 560   EXPECT_EQ(-128, unbiased_exponent(ldexp(1.0f, -128)));
 561   EXPECT_EQ(-129, unbiased_exponent(ldexp(1.0f, -129)));
 562   EXPECT_EQ(-140, unbiased_exponent(ldexp(1.0f, -140)));
 563   // Smallest representable number
 564   EXPECT_EQ(-126 - 23, unbiased_exponent(ldexp(1.0f, -126 - 23)));
 565   // Should get rounded to 0 first.
 566   EXPECT_EQ(0, unbiased_exponent(ldexp(1.0f, -127 - 23)));
 567
 568   // Float16 cases
 569   // The exponent is represented in the bits 0x7C00
 570   // The offset is -15
 571   EXPECT_EQ(0, unbiased_half_exponent(0x3C00));
 572   EXPECT_EQ(3, unbiased_half_exponent(0x4800));
 573   EXPECT_EQ(-1, unbiased_half_exponent(0x3800));
 574   EXPECT_EQ(-14, unbiased_half_exponent(0x0400));
 575   EXPECT_EQ(16, unbiased_half_exponent(0x7C00));
 576   EXPECT_EQ(10, unbiased_half_exponent(0x6400));
 577
 578   // Smallest representable number
 579   EXPECT_EQ(-24, unbiased_half_exponent(0x0001));
 580 }
 581
 582 // Creates a float that is the sum of 1/(2 ^ fractions[i]) for i in factions
 583 float float_fractions(const std::vector<uint32_t>& fractions) {
 584   float f = 0;
 585   for(int32_t i: fractions) {
 586     f += std::ldexp(1.0f, -i);
 587   }
 588   return f;
 589 }
 590
 591 // Returns the normalized significand of a HexFloat<FloatProxy<float>>
 592 // that was created by calling float_fractions with the input fractions,
 593 // raised to the power of exp.
 594 uint32_t normalized_significand(const std::vector<uint32_t>& fractions, uint32_t exp) {
 595   return spvutils::HexFloat<spvutils::FloatProxy<float>>(
 596              static_cast<float>(ldexp(float_fractions(fractions), exp)))
 597       .getNormalizedSignificand();
 598 }
 599
 600 // Sets the bits from MSB to LSB of the significand part of a float.
 601 // For example 0 would set the bit 23 (counting from LSB to MSB),
 602 // and 1 would set the 22nd bit.
 603 uint32_t bits_set(const std::vector<uint32_t>& bits) {
 604   const uint32_t top_bit = 1u << 22u;
 605   uint32_t val= 0;
 606   for(uint32_t i: bits) {
 607     val |= top_bit >> i;
 608   }
 609   return val;
 610 }
 611
 612 // The same as bits_set but for a Float16 value instead of 32-bit floating
 613 // point.
 614 uint16_t half_bits_set(const std::vector<uint32_t>& bits) {
 615   const uint32_t top_bit = 1u << 9u;
 616   uint32_t val= 0;
 617   for(uint32_t i: bits) {
 618     val |= top_bit >> i;
 619   }
 620   return static_cast<uint16_t>(val);
 621 }
 622
 623 TEST(HexFloatOperationTest, NormalizedSignificand) {
 624   // For normalized numbers (the following) it should be a simple matter
 625   // of getting rid of the top implicit bit
 626   EXPECT_EQ(bits_set({}), normalized_significand({0}, 0));
 627   EXPECT_EQ(bits_set({0}), normalized_significand({0, 1}, 0));
 628   EXPECT_EQ(bits_set({0, 1}), normalized_significand({0, 1, 2}, 0));
 629   EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 0));
 630   EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 32));
 631   EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 126));
 632
 633   // For denormalized numbers we expect the normalized significand to
 634   // shift as if it were normalized. This means, in practice that the
 635   // top_most set bit will be cut off. Looks very similar to above (on purpose)
 636   EXPECT_EQ(bits_set({}), normalized_significand({0}, -127));
 637   EXPECT_EQ(bits_set({3}), normalized_significand({0, 4}, -128));
 638   EXPECT_EQ(bits_set({3}), normalized_significand({0, 4}, -127));
 639   EXPECT_EQ(bits_set({}), normalized_significand({22}, -127));
 640   EXPECT_EQ(bits_set({0}), normalized_significand({21, 22}, -127));
 641 }
 642
 643 // Returns the 32-bit floating point value created by
 644 // calling setFromSignUnbiasedExponentAndNormalizedSignificand
 645 // on a HexFloat<FloatProxy<float>>
 646 float set_from_sign(bool negative, int32_t unbiased_exponent,
 647                    uint32_t significand, bool round_denorm_up) {
 648   spvutils::HexFloat<spvutils::FloatProxy<float>>  f(0.f);
 649   f.setFromSignUnbiasedExponentAndNormalizedSignificand(
 650       negative, unbiased_exponent, significand, round_denorm_up);
 651   return f.value().getAsFloat();
 652 }
 653
 654 TEST(HexFloatOperationTests,
 655      SetFromSignUnbiasedExponentAndNormalizedSignificand) {
 656
 657   EXPECT_EQ(1.f, set_from_sign(false, 0, 0, false));
 658
 659   // Tests insertion of various denormalized numbers with and without round up.
 660   EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)), set_from_sign(false, -149, 0, false));
 661   EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)), set_from_sign(false, -149, 0, true));
 662   EXPECT_EQ(0.f, set_from_sign(false, -150, 1, false));
 663   EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)), set_from_sign(false, -150, 1, true));
 664
 665   EXPECT_EQ(ldexp(1.0f, -127), set_from_sign(false, -127, 0, false));
 666   EXPECT_EQ(ldexp(1.0f, -128), set_from_sign(false, -128, 0, false));
 667   EXPECT_EQ(float_fractions({0, 1, 2, 5}),
 668             set_from_sign(false, 0, bits_set({0, 1, 4}), false));
 669   EXPECT_EQ(ldexp(float_fractions({0, 1, 2, 5}), -32),
 670             set_from_sign(false, -32, bits_set({0, 1, 4}), false));
 671   EXPECT_EQ(ldexp(float_fractions({0, 1, 2, 5}), -128),
 672             set_from_sign(false, -128, bits_set({0, 1, 4}), false));
 673
 674   // The negative cases from above.
 675   EXPECT_EQ(-1.f, set_from_sign(true, 0, 0, false));
 676   EXPECT_EQ(-ldexp(1.0, -127), set_from_sign(true, -127, 0, false));
 677   EXPECT_EQ(-ldexp(1.0, -128), set_from_sign(true, -128, 0, false));
 678   EXPECT_EQ(-float_fractions({0, 1, 2, 5}),
 679             set_from_sign(true, 0, bits_set({0, 1, 4}), false));
 680   EXPECT_EQ(-ldexp(float_fractions({0, 1, 2, 5}), -32),
 681             set_from_sign(true, -32, bits_set({0, 1, 4}), false));
 682   EXPECT_EQ(-ldexp(float_fractions({0, 1, 2, 5}), -128),
 683             set_from_sign(true, -128, bits_set({0, 1, 4}), false));
 684 }
 685
 686 TEST(HexFloatOperationTests, NonRounding) {
 687   // Rounding from 32-bit hex-float to 32-bit hex-float should be trivial,
 688   // except in the denorm case which is a bit more complex.
 689   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 690   bool carry_bit = false;
 691
 692   spvutils::round_direction rounding[] = {
 693       spvutils::kRoundToZero,
 694       spvutils::kRoundToNearestEven,
 695       spvutils::kRoundToPositiveInfinity,
 696       spvutils::kRoundToNegativeInfinity};
 697
 698   // Everything fits, so this should be straight-forward
 699   for (spvutils::round_direction round : rounding) {
 700     EXPECT_EQ(bits_set({}), HF(0.f).getRoundedNormalizedSignificand<HF>(
 701                                 round, &carry_bit));
 702     EXPECT_FALSE(carry_bit);
 703
 704     EXPECT_EQ(bits_set({0}),
 705               HF(float_fractions({0, 1}))
 706                   .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 707     EXPECT_FALSE(carry_bit);
 708
 709     EXPECT_EQ(bits_set({1, 3}),
 710               HF(float_fractions({0, 2, 4}))
 711                   .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 712     EXPECT_FALSE(carry_bit);
 713
 714     EXPECT_EQ(
 715         bits_set({0, 1, 4}),
 716         HF(static_cast<float>(-ldexp(float_fractions({0, 1, 2, 5}), -128)))
 717             .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 718     EXPECT_FALSE(carry_bit);
 719
 720     EXPECT_EQ(
 721         bits_set({0, 1, 4, 22}),
 722         HF(static_cast<float>(float_fractions({0, 1, 2, 5, 23})))
 723             .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 724     EXPECT_FALSE(carry_bit);
 725   }
 726 }
 727
 728 struct RoundSignificandCase {
 729   float source_float;
 730   std::pair<int16_t, bool> expected_results;
 731   spvutils::round_direction round;
 732 };
 733
 734 using HexFloatRoundTest =
 735     ::testing::TestWithParam<RoundSignificandCase>;
 736
 737 TEST_P(HexFloatRoundTest, RoundDownToFP16) {
 738   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 739   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 740
 741   HF input_value(GetParam().source_float);
 742   bool carry_bit = false;
 743   EXPECT_EQ(GetParam().expected_results.first,
 744             input_value.getRoundedNormalizedSignificand<HF16>(
 745                 GetParam().round, &carry_bit));
 746   EXPECT_EQ(carry_bit, GetParam().expected_results.second);
 747 }
 748
 749 // clang-format off
 750 INSTANTIATE_TEST_SUITE_P(F32ToF16, HexFloatRoundTest,
 751   ::testing::ValuesIn(std::vector<RoundSignificandCase>(
 752   {
 753     {float_fractions({0}), std::make_pair(half_bits_set({}), false), spvutils::kRoundToZero},
 754     {float_fractions({0}), std::make_pair(half_bits_set({}), false), spvutils::kRoundToNearestEven},
 755     {float_fractions({0}), std::make_pair(half_bits_set({}), false), spvutils::kRoundToPositiveInfinity},
 756     {float_fractions({0}), std::make_pair(half_bits_set({}), false), spvutils::kRoundToNegativeInfinity},
 757     {float_fractions({0, 1}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToZero},
 758
 759     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToZero},
 760     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToPositiveInfinity},
 761     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToNegativeInfinity},
 762     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToNearestEven},
 763
 764     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToZero},
 765     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 8}), false), spvutils::kRoundToPositiveInfinity},
 766     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToNegativeInfinity},
 767     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 8}), false), spvutils::kRoundToNearestEven},
 768
 769     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToZero},
 770     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToPositiveInfinity},
 771     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToNegativeInfinity},
 772     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToNearestEven},
 773
 774     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToZero},
 775     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToPositiveInfinity},
 776     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToNegativeInfinity},
 777     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToNearestEven},
 778
 779     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToZero},
 780     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToPositiveInfinity},
 781     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToNegativeInfinity},
 782     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToNearestEven},
 783
 784     // Carries
 785     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), false), spvutils::kRoundToZero},
 786     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({}), true), spvutils::kRoundToPositiveInfinity},
 787     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), false), spvutils::kRoundToNegativeInfinity},
 788     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({}), true), spvutils::kRoundToNearestEven},
 789
 790     // Cases where original number was denorm. Note: this should have no effect
 791     // the number is pre-normalized.
 792     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -128)), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToZero},
 793     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -129)), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToPositiveInfinity},
 794     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -131)), std::make_pair(half_bits_set({0}), false), spvutils::kRoundToNegativeInfinity},
 795     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -130)), std::make_pair(half_bits_set({0, 9}), false), spvutils::kRoundToNearestEven},
 796   })));
 797 // clang-format on
 798
 799 struct UpCastSignificandCase {
 800   uint16_t source_half;
 801   uint32_t expected_result;
 802 };
 803
 804 using HexFloatRoundUpSignificandTest =
 805     ::testing::TestWithParam<UpCastSignificandCase>;
 806 TEST_P(HexFloatRoundUpSignificandTest, Widening) {
 807   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 808   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 809   bool carry_bit = false;
 810
 811   spvutils::round_direction rounding[] = {
 812       spvutils::kRoundToZero,
 813       spvutils::kRoundToNearestEven,
 814       spvutils::kRoundToPositiveInfinity,
 815       spvutils::kRoundToNegativeInfinity};
 816
 817   // Everything fits, so everything should just be bit-shifts.
 818   for (spvutils::round_direction round : rounding) {
 819     carry_bit = false;
 820     HF16 input_value(GetParam().source_half);
 821     EXPECT_EQ(
 822         GetParam().expected_result,
 823         input_value.getRoundedNormalizedSignificand<HF>(round, &carry_bit))
 824         << std::hex << "0x"
 825         << input_value.getRoundedNormalizedSignificand<HF>(round, &carry_bit)
 826         << "  0x" << GetParam().expected_result;
 827     EXPECT_FALSE(carry_bit);
 828   }
 829 }
 830
 831 INSTANTIATE_TEST_SUITE_P(F16toF32, HexFloatRoundUpSignificandTest,
 832   // 0xFC00 of the source 16-bit hex value cover the sign and the exponent.
 833   // They are ignored for this test.
 834   ::testing::ValuesIn(std::vector<UpCastSignificandCase>(
 835   {
 836     {0x3F00, 0x600000},
 837     {0x0F00, 0x600000},
 838     {0x0F01, 0x602000},
 839     {0x0FFF, 0x7FE000},
 840   })));
 841
 842 struct DownCastTest {
 843   float source_float;
 844   uint16_t expected_half;
 845   std::vector<spvutils::round_direction> directions;
 846 };
 847
 848 std::string get_round_text(spvutils::round_direction direction) {
 849 #define CASE(round_direction) \
 850   case round_direction:      \
 851     return #round_direction
 852
 853   switch (direction) {
 854     CASE(spvutils::kRoundToZero);
 855     CASE(spvutils::kRoundToPositiveInfinity);
 856     CASE(spvutils::kRoundToNegativeInfinity);
 857     CASE(spvutils::kRoundToNearestEven);
 858   }
 859 #undef CASE
 860   return "";
 861 }
 862
 863 using HexFloatFP32To16Tests = ::testing::TestWithParam<DownCastTest>;
 864
 865 TEST_P(HexFloatFP32To16Tests, NarrowingCasts) {
 866   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 867   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 868   HF f(GetParam().source_float);
 869   for (auto round : GetParam().directions) {
 870     HF16 half(0);
 871     f.castTo(half, round);
 872     EXPECT_EQ(GetParam().expected_half, half.value().getAsFloat().get_value())
 873         << get_round_text(round) << "  " << std::hex
 874         << spvutils::BitwiseCast<uint32_t>(GetParam().source_float)
 875         << " cast to: " << half.value().getAsFloat().get_value();
 876   }
 877 }
 878
 879 const uint16_t positive_infinity = 0x7C00;
 880 const uint16_t negative_infinity = 0xFC00;
 881
 882 INSTANTIATE_TEST_SUITE_P(F32ToF16, HexFloatFP32To16Tests,
 883   ::testing::ValuesIn(std::vector<DownCastTest>(
 884   {
 885     // Exactly representable as half.
 886     {0.f, 0x0, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 887     {-0.f, 0x8000, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 888     {1.0f, 0x3C00, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 889     {-1.0f, 0xBC00, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 890
 891     {float_fractions({0, 1, 10}) , 0x3E01, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 892     {-float_fractions({0, 1, 10}) , 0xBE01, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 893     {static_cast<float>(ldexp(float_fractions({0, 1, 10}), 3)), 0x4A01, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 894     {static_cast<float>(-ldexp(float_fractions({0, 1, 10}), 3)), 0xCA01, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 895
 896
 897     // Underflow
 898     {static_cast<float>(ldexp(1.0f, -25)), 0x0, {spvutils::kRoundToZero, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 899     {static_cast<float>(ldexp(1.0f, -25)), 0x1, {spvutils::kRoundToPositiveInfinity}},
 900     {static_cast<float>(-ldexp(1.0f, -25)), 0x8000, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNearestEven}},
 901     {static_cast<float>(-ldexp(1.0f, -25)), 0x8001, {spvutils::kRoundToNegativeInfinity}},
 902     {static_cast<float>(ldexp(1.0f, -24)), 0x1, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 903
 904     // Overflow
 905     {static_cast<float>(ldexp(1.0f, 16)), positive_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 906     {static_cast<float>(ldexp(1.0f, 18)), positive_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 907     {static_cast<float>(ldexp(1.3f, 16)), positive_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 908     {static_cast<float>(-ldexp(1.0f, 16)), negative_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 909     {static_cast<float>(-ldexp(1.0f, 18)), negative_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 910     {static_cast<float>(-ldexp(1.3f, 16)), negative_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 911
 912     // Transfer of Infinities
 913     {std::numeric_limits<float>::infinity(), positive_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 914     {-std::numeric_limits<float>::infinity(), negative_infinity, {spvutils::kRoundToZero, spvutils::kRoundToPositiveInfinity, spvutils::kRoundToNegativeInfinity, spvutils::kRoundToNearestEven}},
 915
 916     // Nans are below because we cannot test for equality.
 917   })));
 918
 919 struct UpCastCase{
 920   uint16_t source_half;
 921   float expected_float;
 922 };
 923
 924 using HexFloatFP16To32Tests = ::testing::TestWithParam<UpCastCase>;
 925 TEST_P(HexFloatFP16To32Tests, WideningCasts) {
 926   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 927   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 928   HF16 f(GetParam().source_half);
 929
 930   spvutils::round_direction rounding[] = {
 931       spvutils::kRoundToZero,
 932       spvutils::kRoundToNearestEven,
 933       spvutils::kRoundToPositiveInfinity,
 934       spvutils::kRoundToNegativeInfinity};
 935
 936   // Everything fits, so everything should just be bit-shifts.
 937   for (spvutils::round_direction round : rounding) {
 938     HF flt(0.f);
 939     f.castTo(flt, round);
 940     EXPECT_EQ(GetParam().expected_float, flt.value().getAsFloat())
 941         << get_round_text(round) << "  " << std::hex
 942         << spvutils::BitwiseCast<uint16_t>(GetParam().source_half)
 943         << " cast to: " << flt.value().getAsFloat();
 944   }
 945 }
 946
 947 INSTANTIATE_TEST_SUITE_P(F16ToF32, HexFloatFP16To32Tests,
 948   ::testing::ValuesIn(std::vector<UpCastCase>(
 949   {
 950     {0x0000, 0.f},
 951     {0x8000, -0.f},
 952     {0x3C00, 1.0f},
 953     {0xBC00, -1.0f},
 954     {0x3F00, float_fractions({0, 1, 2})},
 955     {0xBF00, -float_fractions({0, 1, 2})},
 956     {0x3F01, float_fractions({0, 1, 2, 10})},
 957     {0xBF01, -float_fractions({0, 1, 2, 10})},
 958
 959     // denorm
 960     {0x0001, static_cast<float>(ldexp(1.0, -24))},
 961     {0x0002, static_cast<float>(ldexp(1.0, -23))},
 962     {0x8001, static_cast<float>(-ldexp(1.0, -24))},
 963     {0x8011, static_cast<float>(-ldexp(1.0, -20) + -ldexp(1.0, -24))},
 964
 965     // inf
 966     {0x7C00, std::numeric_limits<float>::infinity()},
 967     {0xFC00, -std::numeric_limits<float>::infinity()},
 968   })));
 969
 970 TEST(HexFloatOperationTests, NanTests) {
 971   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 972   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 973   spvutils::round_direction rounding[] = {
 974       spvutils::kRoundToZero,
 975       spvutils::kRoundToNearestEven,
 976       spvutils::kRoundToPositiveInfinity,
 977       spvutils::kRoundToNegativeInfinity};
 978
 979   // Everything fits, so everything should just be bit-shifts.
 980   for (spvutils::round_direction round : rounding) {
 981     HF16 f16(0);
 982     HF f(0.f);
 983     HF(std::numeric_limits<float>::quiet_NaN()).castTo(f16, round);
 984     EXPECT_TRUE(f16.value().isNan());
 985     HF(std::numeric_limits<float>::signaling_NaN()).castTo(f16, round);
 986     EXPECT_TRUE(f16.value().isNan());
 987
 988     HF16(0x7C01).castTo(f, round);
 989     EXPECT_TRUE(f.value().isNan());
 990     HF16(0x7C11).castTo(f, round);
 991     EXPECT_TRUE(f.value().isNan());
 992     HF16(0xFC01).castTo(f, round);
 993     EXPECT_TRUE(f.value().isNan());
 994     HF16(0x7C10).castTo(f, round);
 995     EXPECT_TRUE(f.value().isNan());
 996     HF16(0xFF00).castTo(f, round);
 997     EXPECT_TRUE(f.value().isNan());
 998   }
 999 }
1000
1001 // A test case for parsing good and bad HexFloat<FloatProxy<T>> literals.
1002 template <typename T>
1003 struct FloatParseCase {
1004   std::string literal;
1005   bool negate_value;
1006   bool expect_success;
1007   HexFloat<FloatProxy<T>> expected_value;
1008 };
1009
1010 using ParseNormalFloatTest = ::testing::TestWithParam<FloatParseCase<float>>;
1011
1012 TEST_P(ParseNormalFloatTest, Samples) {
1013   std::stringstream input(GetParam().literal);
1014   HexFloat<FloatProxy<float>> parsed_value(0.0f);
1015   ParseNormalFloat(input, GetParam().negate_value, parsed_value);
1016   EXPECT_NE(GetParam().expect_success, input.fail())
1017       << " literal: " << GetParam().literal
1018       << " negate: " << GetParam().negate_value;
1019   if (GetParam().expect_success) {
1020     EXPECT_THAT(parsed_value.value(), Eq(GetParam().expected_value.value()))
1021         << " literal: " << GetParam().literal
1022         << " negate: " << GetParam().negate_value;
1023   }
1024 }
1025
1026 // Returns a FloatParseCase with expected failure.
1027 template <typename T>
1028 FloatParseCase<T> BadFloatParseCase(std::string literal, bool negate_value,
1029                                     T expected_value) {
1030   HexFloat<FloatProxy<T>> proxy_expected_value(expected_value);
1031   return FloatParseCase<T>{literal, negate_value, false, proxy_expected_value};
1032 }
1033
1034 // Returns a FloatParseCase that should successfully parse to a given value.
1035 template <typename T>
1036 FloatParseCase<T> GoodFloatParseCase(std::string literal, bool negate_value,
1037                                      T expected_value) {
1038   HexFloat<FloatProxy<T>> proxy_expected_value(expected_value);
1039   return FloatParseCase<T>{literal, negate_value, true, proxy_expected_value};
1040 }
1041
1042 INSTANTIATE_TEST_SUITE_P(
1043     FloatParse, ParseNormalFloatTest,
1044     ::testing::ValuesIn(std::vector<FloatParseCase<float>>{
1045         // Failing cases due to trivially incorrect syntax.
1046         BadFloatParseCase("abc", false, 0.0f),
1047         BadFloatParseCase("abc", true, 0.0f),
1048
1049         // Valid cases.
1050         GoodFloatParseCase("0", false, 0.0f),
1051         GoodFloatParseCase("0.0", false, 0.0f),
1052         GoodFloatParseCase("-0.0", false, -0.0f),
1053         GoodFloatParseCase("2.0", false, 2.0f),
1054         GoodFloatParseCase("-2.0", false, -2.0f),
1055         GoodFloatParseCase("+2.0", false, 2.0f),
1056         // Cases with negate_value being true.
1057         GoodFloatParseCase("0.0", true, -0.0f),
1058         GoodFloatParseCase("2.0", true, -2.0f),
1059
1060         // When negate_value is true, we should not accept a
1061         // leading minus or plus.
1062         BadFloatParseCase("-0.0", true, 0.0f),
1063         BadFloatParseCase("-2.0", true, 0.0f),
1064         BadFloatParseCase("+0.0", true, 0.0f),
1065         BadFloatParseCase("+2.0", true, 0.0f),
1066
1067         // Overflow is an error for 32-bit float parsing.
1068         BadFloatParseCase("1e40", false, FLT_MAX),
1069         BadFloatParseCase("1e40", true, -FLT_MAX),
1070         BadFloatParseCase("-1e40", false, -FLT_MAX),
1071         // We can't have -1e40 and negate_value == true since
1072         // that represents an original case of "--1e40" which
1073         // is invalid.
1074   }));
1075
1076 using ParseNormalFloat16Test =
1077     ::testing::TestWithParam<FloatParseCase<Float16>>;
1078
1079 TEST_P(ParseNormalFloat16Test, Samples) {
1080   std::stringstream input(GetParam().literal);
1081   HexFloat<FloatProxy<Float16>> parsed_value(0);
1082   ParseNormalFloat(input, GetParam().negate_value, parsed_value);
1083   EXPECT_NE(GetParam().expect_success, input.fail())
1084       << " literal: " << GetParam().literal
1085       << " negate: " << GetParam().negate_value;
1086   if (GetParam().expect_success) {
1087     EXPECT_THAT(parsed_value.value(), Eq(GetParam().expected_value.value()))
1088         << " literal: " << GetParam().literal
1089         << " negate: " << GetParam().negate_value;
1090   }
1091 }
1092
1093 INSTANTIATE_TEST_SUITE_P(
1094     Float16Parse, ParseNormalFloat16Test,
1095     ::testing::ValuesIn(std::vector<FloatParseCase<Float16>>{
1096         // Failing cases due to trivially incorrect syntax.
1097         BadFloatParseCase<Float16>("abc", false, uint16_t{0}),
1098         BadFloatParseCase<Float16>("abc", true, uint16_t{0}),
1099
1100         // Valid cases.
1101         GoodFloatParseCase<Float16>("0", false, uint16_t{0}),
1102         GoodFloatParseCase<Float16>("0.0", false, uint16_t{0}),
1103         GoodFloatParseCase<Float16>("-0.0", false, uint16_t{0x8000}),
1104         GoodFloatParseCase<Float16>("2.0", false, uint16_t{0x4000}),
1105         GoodFloatParseCase<Float16>("-2.0", false, uint16_t{0xc000}),
1106         GoodFloatParseCase<Float16>("+2.0", false, uint16_t{0x4000}),
1107         // Cases with negate_value being true.
1108         GoodFloatParseCase<Float16>("0.0", true, uint16_t{0x8000}),
1109         GoodFloatParseCase<Float16>("2.0", true, uint16_t{0xc000}),
1110
1111         // When negate_value is true, we should not accept a leading minus or
1112         // plus.
1113         BadFloatParseCase<Float16>("-0.0", true, uint16_t{0}),
1114         BadFloatParseCase<Float16>("-2.0", true, uint16_t{0}),
1115         BadFloatParseCase<Float16>("+0.0", true, uint16_t{0}),
1116         BadFloatParseCase<Float16>("+2.0", true, uint16_t{0}),
1117     }));
1118
1119 // A test case for detecting infinities.
1120 template <typename T>
1121 struct OverflowParseCase {
1122   std::string input;
1123   bool expect_success;
1124   T expected_value;
1125 };
1126
1127 using FloatProxyParseOverflowFloatTest =
1128     ::testing::TestWithParam<OverflowParseCase<float>>;
1129
1130 TEST_P(FloatProxyParseOverflowFloatTest, Sample) {
1131   std::istringstream input(GetParam().input);
1132   HexFloat<FloatProxy<float>> value(0.0f);
1133   input >> value;
1134   EXPECT_NE(GetParam().expect_success, input.fail());
1135   if (GetParam().expect_success) {
1136     EXPECT_THAT(value.value().getAsFloat(), GetParam().expected_value);
1137   }
1138 }
1139
1140 INSTANTIATE_TEST_SUITE_P(
1141     FloatOverflow, FloatProxyParseOverflowFloatTest,
1142     ::testing::ValuesIn(std::vector<OverflowParseCase<float>>({
1143         {"0", true, 0.0f},
1144         {"0.0", true, 0.0f},
1145         {"1.0", true, 1.0f},
1146         {"1e38", true, 1e38f},
1147         {"-1e38", true, -1e38f},
1148         {"1e40", false, FLT_MAX},
1149         {"-1e40", false, -FLT_MAX},
1150         {"1e400", false, FLT_MAX},
1151         {"-1e400", false, -FLT_MAX},
1152     })));
1153
1154 using FloatProxyParseOverflowDoubleTest =
1155     ::testing::TestWithParam<OverflowParseCase<double>>;
1156
1157 TEST_P(FloatProxyParseOverflowDoubleTest, Sample) {
1158   std::istringstream input(GetParam().input);
1159   HexFloat<FloatProxy<double>> value(0.0);
1160   input >> value;
1161   EXPECT_NE(GetParam().expect_success, input.fail());
1162   if (GetParam().expect_success) {
1163     EXPECT_THAT(value.value().getAsFloat(), Eq(GetParam().expected_value));
1164   }
1165 }
1166
1167 INSTANTIATE_TEST_SUITE_P(
1168     DoubleOverflow, FloatProxyParseOverflowDoubleTest,
1169     ::testing::ValuesIn(std::vector<OverflowParseCase<double>>({
1170         {"0", true, 0.0},
1171         {"0.0", true, 0.0},
1172         {"1.0", true, 1.0},
1173         {"1e38", true, 1e38},
1174         {"-1e38", true, -1e38},
1175         {"1e40", true, 1e40},
1176         {"-1e40", true, -1e40},
1177         {"1e400", false, DBL_MAX},
1178         {"-1e400", false, -DBL_MAX},
1179     })));
1180
1181 using FloatProxyParseOverflowFloat16Test =
1182     ::testing::TestWithParam<OverflowParseCase<uint16_t>>;
1183
1184 TEST_P(FloatProxyParseOverflowFloat16Test, Sample) {
1185   std::istringstream input(GetParam().input);
1186   HexFloat<FloatProxy<Float16>> value(0);
1187   input >> value;
1188   EXPECT_NE(GetParam().expect_success, input.fail()) << " literal: "
1189                                                      << GetParam().input;
1190   if (GetParam().expect_success) {
1191     EXPECT_THAT(value.value().data(), Eq(GetParam().expected_value))
1192         << " literal: " << GetParam().input;
1193   }
1194 }
1195
1196 INSTANTIATE_TEST_SUITE_P(
1197     Float16Overflow, FloatProxyParseOverflowFloat16Test,
1198     ::testing::ValuesIn(std::vector<OverflowParseCase<uint16_t>>({
1199         {"0", true, uint16_t{0}},
1200         {"0.0", true, uint16_t{0}},
1201         {"1.0", true, uint16_t{0x3c00}},
1202         // Overflow for 16-bit float is an error, and returns max or
1203         // lowest value.
1204         {"1e38", false, uint16_t{0x7bff}},
1205         {"1e40", false, uint16_t{0x7bff}},
1206         {"1e400", false, uint16_t{0x7bff}},
1207         {"-1e38", false, uint16_t{0xfbff}},
1208         {"-1e40", false, uint16_t{0xfbff}},
1209         {"-1e400", false, uint16_t{0xfbff}},
1210     })));
1211
1212 TEST(FloatProxy, Max) {
1213   EXPECT_THAT(FloatProxy<Float16>::max().getAsFloat().get_value(),
1214               Eq(uint16_t{0x7bff}));
1215   EXPECT_THAT(FloatProxy<float>::max().getAsFloat(),
1216               Eq(std::numeric_limits<float>::max()));
1217   EXPECT_THAT(FloatProxy<double>::max().getAsFloat(),
1218               Eq(std::numeric_limits<double>::max()));
1219 }
1220
1221 TEST(FloatProxy, Lowest) {
1222   EXPECT_THAT(FloatProxy<Float16>::lowest().getAsFloat().get_value(),
1223               Eq(uint16_t{0xfbff}));
1224   EXPECT_THAT(FloatProxy<float>::lowest().getAsFloat(),
1225               Eq(std::numeric_limits<float>::lowest()));
1226   EXPECT_THAT(FloatProxy<double>::lowest().getAsFloat(),
1227               Eq(std::numeric_limits<double>::lowest()));
1228 }
1229
1230 // TODO(awoloszyn): Add fp16 tests and HexFloatTraits.
1231 }  // anonymous namespace