flang/unittests/Runtime/Numeric.cpp

   1 //===-- flang/unittests/Runtime/Numeric.cpp ---------------------*- C++ -*-===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8
   9 #include "flang/Runtime/numeric.h"
  10 #include "gtest/gtest.h"
  11 #include "flang/Common/float128.h"
  12 #include <cmath>
  13 #include <limits>
  14
  15 using namespace Fortran::runtime;
  16 using Fortran::common::TypeCategory;
  17 template <int KIND> using Int = CppTypeFor<TypeCategory::Integer, KIND>;
  18 template <int KIND> using Real = CppTypeFor<TypeCategory::Real, KIND>;
  19
  20 // Simple tests of numeric intrinsic functions using examples from Fortran 2018
  21
  22 TEST(Numeric, Ceiling) {
  23   EXPECT_EQ(RTNAME(Ceiling4_4)(Real<4>{3.7}), 4);
  24   EXPECT_EQ(RTNAME(Ceiling8_8)(Real<8>{-3.7}), -3);
  25   EXPECT_EQ(RTNAME(Ceiling4_1)(Real<4>{0}), 0);
  26 }
  27
  28 TEST(Numeric, Floor) {
  29   EXPECT_EQ(RTNAME(Floor4_4)(Real<4>{3.7}), 3);
  30   EXPECT_EQ(RTNAME(Floor8_8)(Real<8>{-3.7}), -4);
  31   EXPECT_EQ(RTNAME(Floor4_1)(Real<4>{0}), 0);
  32 }
  33
  34 TEST(Numeric, Erfc_scaled) {
  35   EXPECT_NEAR(RTNAME(ErfcScaled4)(Real<4>{20.0}), 0.02817434874, 1.0e-8);
  36   EXPECT_NEAR(RTNAME(ErfcScaled8)(Real<8>{20.0}), 0.02817434874, 1.0e-11);
  37 #if HAS_FLOAT80
  38   EXPECT_NEAR(RTNAME(ErfcScaled10)(Real<10>{20.0}), 0.02817434874, 1.0e-8);
  39 #endif
  40 }
  41
  42 TEST(Numeric, Exponent) {
  43   EXPECT_EQ(RTNAME(Exponent4_4)(Real<4>{0}), 0);
  44   EXPECT_EQ(RTNAME(Exponent4_8)(Real<4>{1.0}), 1);
  45   EXPECT_EQ(RTNAME(Exponent8_4)(Real<8>{4.1}), 3);
  46   EXPECT_EQ(RTNAME(Exponent8_8)(std::numeric_limits<Real<8>>::infinity()),
  47       std::numeric_limits<Int<8>>::max());
  48   EXPECT_EQ(RTNAME(Exponent8_8)(std::numeric_limits<Real<8>>::quiet_NaN()),
  49       std::numeric_limits<Int<8>>::max());
  50 }
  51
  52 TEST(Numeric, Fraction) {
  53   EXPECT_EQ(RTNAME(Fraction4)(Real<4>{0}), 0);
  54   EXPECT_EQ(RTNAME(Fraction8)(Real<8>{3.0}), 0.75);
  55   EXPECT_TRUE(
  56       std::isnan(RTNAME(Fraction4)(std::numeric_limits<Real<4>>::infinity())));
  57   EXPECT_TRUE(
  58       std::isnan(RTNAME(Fraction8)(std::numeric_limits<Real<8>>::quiet_NaN())));
  59 }
  60
  61 TEST(Numeric, IsNaN) {
  62   EXPECT_FALSE(RTNAME(IsNaN4)(Real<4>{0}));
  63   EXPECT_FALSE(RTNAME(IsNaN8)(std::numeric_limits<Real<8>>::infinity()));
  64   EXPECT_TRUE(RTNAME(IsNaN8)(std::numeric_limits<Real<8>>::quiet_NaN()));
  65 }
  66
  67 TEST(Numeric, Mod) {
  68   EXPECT_EQ(RTNAME(ModInteger1)(Int<1>{8}, Int<1>(5)), 3);
  69   EXPECT_EQ(RTNAME(ModInteger4)(Int<4>{-8}, Int<4>(5)), -3);
  70   EXPECT_EQ(RTNAME(ModInteger2)(Int<2>{8}, Int<2>(-5)), 3);
  71   EXPECT_EQ(RTNAME(ModInteger8)(Int<8>{-8}, Int<8>(-5)), -3);
  72   EXPECT_EQ(RTNAME(ModReal4)(Real<4>{8.0}, Real<4>(5.0)), 3.0);
  73   EXPECT_EQ(RTNAME(ModReal4)(Real<4>{-8.0}, Real<4>(5.0)), -3.0);
  74   EXPECT_EQ(RTNAME(ModReal8)(Real<8>{8.0}, Real<8>(-5.0)), 3.0);
  75   EXPECT_EQ(RTNAME(ModReal8)(Real<8>{-8.0}, Real<8>(-5.0)), -3.0);
  76   EXPECT_EQ(
  77       RTNAME(ModReal4)(Real<4>{0.5}, std::numeric_limits<Real<4>>::infinity()),
  78       0.5);
  79   EXPECT_EQ(
  80       RTNAME(ModReal4)(Real<4>{-0.5}, std::numeric_limits<Real<4>>::infinity()),
  81       -0.5);
  82   EXPECT_EQ(
  83       RTNAME(ModReal4)(Real<4>{0.5}, -std::numeric_limits<Real<4>>::infinity()),
  84       0.5);
  85   EXPECT_EQ(RTNAME(ModReal4)(
  86                 Real<4>{-0.5}, -std::numeric_limits<Real<4>>::infinity()),
  87       -0.5);
  88   EXPECT_EQ(
  89       RTNAME(ModReal8)(Real<8>{0.5}, std::numeric_limits<Real<8>>::infinity()),
  90       0.5);
  91   EXPECT_EQ(
  92       RTNAME(ModReal8)(Real<8>{-0.5}, std::numeric_limits<Real<8>>::infinity()),
  93       -0.5);
  94   EXPECT_EQ(
  95       RTNAME(ModReal8)(Real<8>{0.5}, -std::numeric_limits<Real<8>>::infinity()),
  96       0.5);
  97   EXPECT_EQ(RTNAME(ModReal8)(
  98                 Real<8>{-0.5}, -std::numeric_limits<Real<8>>::infinity()),
  99       -0.5);
 100 }
 101
 102 TEST(Numeric, Modulo) {
 103   EXPECT_EQ(RTNAME(ModuloInteger1)(Int<1>{8}, Int<1>(5)), 3);
 104   EXPECT_EQ(RTNAME(ModuloInteger4)(Int<4>{-8}, Int<4>(5)), 2);
 105   EXPECT_EQ(RTNAME(ModuloInteger2)(Int<2>{8}, Int<2>(-5)), -2);
 106   EXPECT_EQ(RTNAME(ModuloInteger8)(Int<8>{-8}, Int<8>(-5)), -3);
 107   EXPECT_EQ(RTNAME(ModuloReal4)(Real<4>{8.0}, Real<4>(5.0)), 3.0);
 108   EXPECT_EQ(RTNAME(ModuloReal4)(Real<4>{-8.0}, Real<4>(5.0)), 2.0);
 109   EXPECT_EQ(RTNAME(ModuloReal8)(Real<8>{8.0}, Real<8>(-5.0)), -2.0);
 110   EXPECT_EQ(RTNAME(ModuloReal8)(Real<8>{-8.0}, Real<8>(-5.0)), -3.0);
 111   // MODULO(x, INF) == NaN
 112   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal4)(
 113       Real<4>{0.5}, std::numeric_limits<Real<4>>::infinity())));
 114   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal4)(
 115       Real<4>{-0.5}, std::numeric_limits<Real<4>>::infinity())));
 116   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal4)(
 117       Real<4>{0.5}, -std::numeric_limits<Real<4>>::infinity())));
 118   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal4)(
 119       Real<4>{-0.5}, -std::numeric_limits<Real<4>>::infinity())));
 120   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal8)(
 121       Real<8>{-0.5}, std::numeric_limits<Real<8>>::infinity())));
 122   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal8)(
 123       Real<8>{0.5}, std::numeric_limits<Real<8>>::infinity())));
 124   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal8)(
 125       Real<8>{-0.5}, -std::numeric_limits<Real<8>>::infinity())));
 126   EXPECT_TRUE(std::isnan(RTNAME(ModuloReal8)(
 127       Real<8>{0.5}, -std::numeric_limits<Real<8>>::infinity())));
 128   // MODULO(x, y) for integer values of x and y with 0 remainder.
 129   EXPECT_EQ(RTNAME(ModuloReal4)(Real<4>{5.0}, Real<4>(1.0)), 0.0);
 130   EXPECT_EQ(RTNAME(ModuloReal4)(Real<4>{5.0}, Real<4>(-1.0)), -0.0);
 131   EXPECT_EQ(RTNAME(ModuloReal4)(Real<4>{-5.0}, Real<4>(1.0)), 0.0);
 132   EXPECT_EQ(RTNAME(ModuloReal4)(Real<4>{-5.0}, Real<4>(-1.0)), -0.0);
 133 }
 134
 135 TEST(Numeric, Nearest) {
 136   EXPECT_EQ(RTNAME(Nearest4)(Real<4>{0}, true),
 137       std::numeric_limits<Real<4>>::denorm_min());
 138   EXPECT_EQ(RTNAME(Nearest4)(Real<4>{3.0}, true),
 139       Real<4>{3.0} + std::ldexp(Real<4>{1.0}, -22));
 140   EXPECT_EQ(RTNAME(Nearest8)(Real<8>{1.0}, true),
 141       Real<8>{1.0} + std::ldexp(Real<8>{1.0}, -52));
 142   EXPECT_EQ(RTNAME(Nearest8)(Real<8>{1.0}, false),
 143       Real<8>{1.0} - 0.5 * std::ldexp(Real<8>{1.0}, -52));
 144 }
 145
 146 TEST(Numeric, Nint) {
 147   EXPECT_EQ(RTNAME(Nint4_4)(Real<4>{2.783}), 3);
 148   EXPECT_EQ(RTNAME(Nint8_4)(Real<8>{-2.783}), -3);
 149   EXPECT_EQ(RTNAME(Nint4_4)(Real<4>{2.5}), 3);
 150   EXPECT_EQ(RTNAME(Nint8_4)(Real<8>{-2.5}), -3);
 151   EXPECT_EQ(RTNAME(Nint8_8)(Real<8>{0}), 0);
 152 }
 153
 154 TEST(Numeric, RRSpacing) {
 155   EXPECT_EQ(RTNAME(RRSpacing8)(Real<8>{0}), 0);
 156   EXPECT_EQ(RTNAME(RRSpacing4)(Real<4>{-3.0}), 0.75 * (1 << 24));
 157   EXPECT_EQ(RTNAME(RRSpacing8)(Real<8>{-3.0}), 0.75 * (std::int64_t{1} << 53));
 158   EXPECT_TRUE(
 159       std::isnan(RTNAME(RRSpacing4)(std::numeric_limits<Real<4>>::infinity())));
 160   EXPECT_TRUE(std::isnan(
 161       RTNAME(RRSpacing8)(std::numeric_limits<Real<8>>::quiet_NaN())));
 162 }
 163
 164 TEST(Numeric, Scale) {
 165   EXPECT_EQ(RTNAME(Scale4)(Real<4>{0}, 0), 0);
 166   EXPECT_EQ(RTNAME(Scale4)(Real<4>{1.0}, 0), 1.0);
 167   EXPECT_EQ(RTNAME(Scale4)(Real<4>{1.0}, 1), 2.0);
 168   EXPECT_EQ(RTNAME(Scale4)(Real<4>{1.0}, -1), 0.5);
 169   EXPECT_TRUE(
 170       std::isinf(RTNAME(Scale4)(std::numeric_limits<Real<4>>::infinity(), 1)));
 171   EXPECT_TRUE(
 172       std::isnan(RTNAME(Scale8)(std::numeric_limits<Real<8>>::quiet_NaN(), 1)));
 173 }
 174
 175 TEST(Numeric, SetExponent) {
 176   EXPECT_EQ(RTNAME(SetExponent4)(Real<4>{0}, 0), 0);
 177   EXPECT_EQ(RTNAME(SetExponent8)(Real<8>{0}, 666), 0);
 178   EXPECT_EQ(RTNAME(SetExponent8)(Real<8>{3.0}, 0), 0.75);
 179   EXPECT_EQ(RTNAME(SetExponent4)(Real<4>{1.0}, 0), 0.5);
 180   EXPECT_EQ(RTNAME(SetExponent4)(Real<4>{1.0}, 1), 1.0);
 181   EXPECT_EQ(RTNAME(SetExponent4)(Real<4>{1.0}, -1), 0.25);
 182   EXPECT_TRUE(std::isnan(
 183       RTNAME(SetExponent4)(std::numeric_limits<Real<4>>::infinity(), 1)));
 184   EXPECT_TRUE(std::isnan(
 185       RTNAME(SetExponent8)(std::numeric_limits<Real<8>>::quiet_NaN(), 1)));
 186 }
 187
 188 TEST(Numeric, SelectedIntKind) {
 189   std::int8_t r0 = 1;
 190   std::int16_t r1 = 3;
 191   std::int32_t r2 = 8;
 192   std::int64_t r3 = 10;
 193   std::int32_t r4 = -10;
 194   std::int32_t r5 = 100;
 195   EXPECT_EQ(RTNAME(SelectedIntKind)(__FILE__, __LINE__, &r0, 1), 1);
 196   EXPECT_EQ(RTNAME(SelectedIntKind)(__FILE__, __LINE__, &r1, 2), 2);
 197   EXPECT_EQ(RTNAME(SelectedIntKind)(__FILE__, __LINE__, &r2, 4), 4);
 198   EXPECT_EQ(RTNAME(SelectedIntKind)(__FILE__, __LINE__, &r3, 8), 8);
 199   EXPECT_EQ(RTNAME(SelectedIntKind)(__FILE__, __LINE__, &r4, 4), 1);
 200   EXPECT_EQ(RTNAME(SelectedIntKind)(__FILE__, __LINE__, &r5, 4), -1);
 201 }
 202
 203 TEST(Numeric, SelectedRealKind) {
 204   std::int8_t p_s = 1;
 205   std::int16_t p[11] = {-10, 1, 1, 4, 50, 1, 1, 4, 1, 1, 50};
 206   std::int32_t r[11] = {-1, 1, 1, 1, 2, 1, 20, 20, 100, 5000, 5000};
 207   std::int64_t d[11] = {2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2};
 208   EXPECT_EQ(RTNAME(SelectedRealKind)(
 209                 __FILE__, __LINE__, &p[0], 2, &r[0], 4, &d[0], 8),
 210       2);
 211   EXPECT_EQ(RTNAME(SelectedRealKind)(
 212                 __FILE__, __LINE__, &p[1], 2, &r[1], 4, &d[1], 8),
 213       -5);
 214   EXPECT_EQ(RTNAME(SelectedRealKind)(
 215                 __FILE__, __LINE__, &p[2], 2, &r[2], 4, &d[2], 8),
 216       2);
 217   EXPECT_EQ(RTNAME(SelectedRealKind)(
 218                 __FILE__, __LINE__, &p[3], 2, &r[3], 4, &d[3], 8),
 219       4);
 220   EXPECT_EQ(RTNAME(SelectedRealKind)(
 221                 __FILE__, __LINE__, &p[4], 2, &r[4], 4, &d[4], 8),
 222       -1);
 223   EXPECT_EQ(RTNAME(SelectedRealKind)(
 224                 __FILE__, __LINE__, &p[5], 2, &r[5], 4, &d[5], 8),
 225       2);
 226   EXPECT_EQ(RTNAME(SelectedRealKind)(
 227                 __FILE__, __LINE__, &p[6], 2, &r[6], 4, &d[6], 8),
 228       3);
 229   EXPECT_EQ(RTNAME(SelectedRealKind)(
 230                 __FILE__, __LINE__, &p[7], 2, &r[7], 4, &d[7], 8),
 231       4);
 232   EXPECT_EQ(RTNAME(SelectedRealKind)(
 233                 __FILE__, __LINE__, &p[8], 2, &r[8], 4, &d[8], 8),
 234       8);
 235   EXPECT_EQ(RTNAME(SelectedRealKind)(
 236                 __FILE__, __LINE__, &p[9], 2, &r[9], 4, &d[9], 8),
 237       -2);
 238   EXPECT_EQ(RTNAME(SelectedRealKind)(
 239                 __FILE__, __LINE__, &p[10], 2, &r[10], 4, &d[10], 8),
 240       -3);
 241   EXPECT_EQ(
 242       RTNAME(SelectedRealKind)(__FILE__, __LINE__, &p_s, 1, &r[0], 4, &d[0], 8),
 243       2);
 244   EXPECT_EQ(RTNAME(SelectedRealKind)(
 245                 __FILE__, __LINE__, nullptr, 0, &r[0], 4, &d[0], 8),
 246       2);
 247   EXPECT_EQ(RTNAME(SelectedRealKind)(
 248                 __FILE__, __LINE__, &p[0], 2, nullptr, 0, &d[0], 8),
 249       2);
 250   EXPECT_EQ(RTNAME(SelectedRealKind)(
 251                 __FILE__, __LINE__, &p[0], 2, &r[0], 4, nullptr, 0),
 252       2);
 253 }
 254
 255 TEST(Numeric, Spacing) {
 256   EXPECT_EQ(RTNAME(Spacing8)(Real<8>{0}), std::numeric_limits<Real<8>>::min());
 257   EXPECT_EQ(RTNAME(Spacing4)(Real<4>{3.0}), std::ldexp(Real<4>{1.0}, -22));
 258   EXPECT_TRUE(
 259       std::isnan(RTNAME(Spacing4)(std::numeric_limits<Real<4>>::infinity())));
 260   EXPECT_TRUE(
 261       std::isnan(RTNAME(Spacing8)(std::numeric_limits<Real<8>>::quiet_NaN())));
 262   EXPECT_EQ(RTNAME(Spacing2By4)(Real<4>{3.0}), std::ldexp(Real<4>{1.0}, -9));
 263   EXPECT_EQ(RTNAME(Spacing2By4)(Real<4>{0.0}), Real<4>{0.00006103515625E-04});
 264   EXPECT_EQ(RTNAME(Spacing3By4)(Real<4>{3.0}), std::ldexp(Real<4>{1.0}, -6));
 265   EXPECT_EQ(
 266       RTNAME(Spacing3By4)(Real<4>{0.0}), std::numeric_limits<Real<4>>::min());
 267 }
 268
 269 TEST(Numeric, FPowI) {
 270   EXPECT_EQ(RTNAME(FPow4i)(Real<4>{0}, Int<4>{0}), Real<4>{1});
 271   EXPECT_EQ(RTNAME(FPow4i)(Real<4>{0.3}, Int<4>{0}), Real<4>{1});
 272   EXPECT_EQ(RTNAME(FPow4i)(Real<4>{2}, Int<4>{-1}), Real<4>{0.5});
 273   EXPECT_EQ(RTNAME(FPow4i)(Real<4>{0.5}, Int<4>{-1}), Real<4>{2});
 274   EXPECT_EQ(RTNAME(FPow4i)(Real<4>{-3}, Int<4>{3}), Real<4>{-27});
 275   EXPECT_EQ(RTNAME(FPow4i)(Real<4>{-2}, Int<4>{-3}), Real<4>{-0.125});
 276
 277   EXPECT_EQ(RTNAME(FPow4k)(Real<4>{0}, Int<8>{0}), Real<4>{1});
 278   EXPECT_EQ(RTNAME(FPow4k)(Real<4>{0.3}, Int<8>{0}), Real<4>{1});
 279   EXPECT_EQ(RTNAME(FPow4k)(Real<4>{2}, Int<8>{-1}), Real<4>{0.5});
 280   EXPECT_EQ(RTNAME(FPow4k)(Real<4>{0.5}, Int<8>{-1}), Real<4>{2});
 281   EXPECT_EQ(RTNAME(FPow4k)(Real<4>{-3}, Int<8>{3}), Real<4>{-27});
 282   EXPECT_EQ(RTNAME(FPow4k)(Real<4>{-2}, Int<8>{-3}), Real<4>{-0.125});
 283
 284   EXPECT_EQ(RTNAME(FPow8i)(Real<8>{0}, Int<4>{0}), Real<8>{1});
 285   EXPECT_EQ(RTNAME(FPow8i)(Real<8>{0.3}, Int<4>{0}), Real<8>{1});
 286   EXPECT_EQ(RTNAME(FPow8i)(Real<8>{2}, Int<4>{-1}), Real<8>{0.5});
 287   EXPECT_EQ(RTNAME(FPow8i)(Real<8>{0.5}, Int<4>{-1}), Real<8>{2});
 288   EXPECT_EQ(RTNAME(FPow8i)(Real<8>{-3}, Int<4>{3}), Real<8>{-27});
 289   EXPECT_EQ(RTNAME(FPow8i)(Real<8>{-2}, Int<4>{-3}), Real<8>{-0.125});
 290
 291   EXPECT_EQ(RTNAME(FPow8k)(Real<8>{0}, Int<8>{0}), Real<8>{1});
 292   EXPECT_EQ(RTNAME(FPow8k)(Real<8>{0.3}, Int<8>{0}), Real<8>{1});
 293   EXPECT_EQ(RTNAME(FPow8k)(Real<8>{2}, Int<8>{-1}), Real<8>{0.5});
 294   EXPECT_EQ(RTNAME(FPow8k)(Real<8>{0.5}, Int<8>{-1}), Real<8>{2});
 295   EXPECT_EQ(RTNAME(FPow8k)(Real<8>{-3}, Int<8>{3}), Real<8>{-27});
 296   EXPECT_EQ(RTNAME(FPow8k)(Real<8>{-2}, Int<8>{-3}), Real<8>{-0.125});
 297
 298 #if HAS_FLOAT80
 299   EXPECT_EQ(RTNAME(FPow10i)(Real<10>{0}, Int<4>{0}), Real<10>{1});
 300   EXPECT_EQ(RTNAME(FPow10i)(Real<10>{0.3}, Int<4>{0}), Real<10>{1});
 301   EXPECT_EQ(RTNAME(FPow10i)(Real<10>{2}, Int<4>{-1}), Real<10>{0.5});
 302   EXPECT_EQ(RTNAME(FPow10i)(Real<10>{0.5}, Int<4>{-1}), Real<10>{2});
 303   EXPECT_EQ(RTNAME(FPow10i)(Real<10>{-3}, Int<4>{3}), Real<10>{-27});
 304   EXPECT_EQ(RTNAME(FPow10i)(Real<10>{-2}, Int<4>{-3}), Real<10>{-0.125});
 305
 306   EXPECT_EQ(RTNAME(FPow10k)(Real<10>{0}, Int<8>{0}), Real<10>{1});
 307   EXPECT_EQ(RTNAME(FPow10k)(Real<10>{0.3}, Int<8>{0}), Real<10>{1});
 308   EXPECT_EQ(RTNAME(FPow10k)(Real<10>{2}, Int<8>{-1}), Real<10>{0.5});
 309   EXPECT_EQ(RTNAME(FPow10k)(Real<10>{0.5}, Int<8>{-1}), Real<10>{2});
 310   EXPECT_EQ(RTNAME(FPow10k)(Real<10>{-3}, Int<8>{3}), Real<10>{-27});
 311   EXPECT_EQ(RTNAME(FPow10k)(Real<10>{-2}, Int<8>{-3}), Real<10>{-0.125});
 312 #endif
 313 #if HAS_LDBL128 || HAS_FLOAT128
 314   EXPECT_EQ(RTNAME(FPow16i)(Real<16>{0}, Int<4>{0}), Real<16>{1});
 315   EXPECT_EQ(RTNAME(FPow16i)(Real<16>{0.3}, Int<4>{0}), Real<16>{1});
 316   EXPECT_EQ(RTNAME(FPow16i)(Real<16>{2}, Int<4>{-1}), Real<16>{0.5});
 317   EXPECT_EQ(RTNAME(FPow16i)(Real<16>{0.5}, Int<4>{-1}), Real<16>{2});
 318   EXPECT_EQ(RTNAME(FPow16i)(Real<16>{-3}, Int<4>{3}), Real<16>{-27});
 319   EXPECT_EQ(RTNAME(FPow16i)(Real<16>{-2}, Int<4>{-3}), Real<16>{-0.125});
 320
 321   EXPECT_EQ(RTNAME(FPow16k)(Real<16>{0}, Int<8>{0}), Real<16>{1});
 322   EXPECT_EQ(RTNAME(FPow16k)(Real<16>{0.3}, Int<8>{0}), Real<16>{1});
 323   EXPECT_EQ(RTNAME(FPow16k)(Real<16>{2}, Int<8>{-1}), Real<16>{0.5});
 324   EXPECT_EQ(RTNAME(FPow16k)(Real<16>{0.5}, Int<8>{-1}), Real<16>{2});
 325   EXPECT_EQ(RTNAME(FPow16k)(Real<16>{-3}, Int<8>{3}), Real<16>{-27});
 326   EXPECT_EQ(RTNAME(FPow16k)(Real<16>{-2}, Int<8>{-3}), Real<16>{-0.125});
 327 #endif
 328
 329   // Test some extreme values.
 330   if (sizeof(double) == sizeof(std::uint64_t)) {
 331     // (0x3FF0000000000001 ** -2147483648) ~ 0x3FEFFFFF00000401
 332     double base;
 333     *reinterpret_cast<std::uint64_t *>(&base) = 4607182418800017409ULL;
 334     double result;
 335     *reinterpret_cast<std::uint64_t *>(&result) = 4607182414505051137ULL;
 336     EXPECT_TRUE(std::abs(RTNAME(FPow8i)(Real<8>{base},
 337                              Int<4>{std::numeric_limits<Int<4>>::min()}) -
 338                     Real<8>{result}) < 0.00000000001);
 339
 340     // (0x3FF0000000000001 ** 4294967296ULL) ~ 0x3FF00001000007FF
 341     *reinterpret_cast<std::uint64_t *>(&base) = 4607182418800017409ULL;
 342     *reinterpret_cast<std::uint64_t *>(&result) = 4607182423094986751ULL;
 343     EXPECT_TRUE(std::abs(RTNAME(FPow8k)(Real<8>{base}, Int<8>{4294967296ULL}) -
 344                     Real<8>{result}) < 0.00000000001);
 345   }
 346 }