exp2.zig (20924B) - Raw
1 // Ported from musl, which is licensed under the MIT license: 2 // https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT 3 // 4 // https://git.musl-libc.org/cgit/musl/tree/src/math/exp2f.c 5 // https://git.musl-libc.org/cgit/musl/tree/src/math/exp2.c 6 7 const std = @import("std"); 8 const builtin = @import("builtin"); 9 const arch = builtin.cpu.arch; 10 const math = std.math; 11 const mem = std.mem; 12 const expect = std.testing.expect; 13 const expectEqual = std.testing.expectEqual; 14 const common = @import("common.zig"); 15 16 pub const panic = common.panic; 17 18 comptime { 19 @export(&__exp2h, .{ .name = "__exp2h", .linkage = common.linkage, .visibility = common.visibility }); 20 @export(&exp2f, .{ .name = "exp2f", .linkage = common.linkage, .visibility = common.visibility }); 21 @export(&exp2, .{ .name = "exp2", .linkage = common.linkage, .visibility = common.visibility }); 22 @export(&__exp2x, .{ .name = "__exp2x", .linkage = common.linkage, .visibility = common.visibility }); 23 if (common.want_ppc_abi) { 24 @export(&exp2q, .{ .name = "exp2f128", .linkage = common.linkage, .visibility = common.visibility }); 25 } 26 @export(&exp2q, .{ .name = "exp2q", .linkage = common.linkage, .visibility = common.visibility }); 27 @export(&exp2l, .{ .name = "exp2l", .linkage = common.linkage, .visibility = common.visibility }); 28 } 29 30 pub fn __exp2h(x: f16) callconv(.c) f16 { 31 // TODO: more efficient implementation 32 return @floatCast(exp2f(x)); 33 } 34 35 pub fn exp2f(x: f32) callconv(.c) f32 { 36 const tblsiz: u32 = @intCast(exp2ft.len); 37 const redux: f32 = 0x1.8p23 / @as(f32, @floatFromInt(tblsiz)); 38 const P1: f32 = 0x1.62e430p-1; 39 const P2: f32 = 0x1.ebfbe0p-3; 40 const P3: f32 = 0x1.c6b348p-5; 41 const P4: f32 = 0x1.3b2c9cp-7; 42 43 const u: u32 = @bitCast(x); 44 const ix = u & 0x7FFFFFFF; 45 46 // |x| > 126 47 if (ix > 0x42FC0000) { 48 // nan 49 if (ix > 0x7F800000) { 50 return x; 51 } 52 // x >= 128 53 if (u >= 0x43000000 and u < 0x80000000) { 54 return x * 0x1.0p127; 55 } 56 // x < -126 57 if (u >= 0x80000000) { 58 if (u >= 0xC3160000 or u & 0x000FFFF != 0) { 59 if (common.want_float_exceptions) mem.doNotOptimizeAway(-0x1.0p-149 / x); 60 } 61 // x <= -150 62 if (u >= 0xC3160000) { 63 return 0; 64 } 65 } 66 } 67 // |x| <= 0x1p-25 68 else if (ix <= 0x33000000) { 69 return 1.0 + x; 70 } 71 72 // NOTE: musl relies on unsafe behaviours which are replicated below 73 // (addition/bit-shift overflow). Appears that this produces the 74 // intended result but should confirm how GCC/Clang handle this to ensure. 75 76 var uf = x + redux; 77 var i_0: u32 = @bitCast(uf); 78 i_0 +%= tblsiz / 2; 79 80 const k = i_0 / tblsiz; 81 const uk: f64 = @bitCast(@as(u64, 0x3FF + k) << 52); 82 i_0 &= tblsiz - 1; 83 uf -= redux; 84 85 const z: f64 = x - uf; 86 var r: f64 = exp2ft[@intCast(i_0)]; 87 const t: f64 = r * z; 88 r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4); 89 return @floatCast(r * uk); 90 } 91 92 pub fn exp2(x: f64) callconv(.c) f64 { 93 const tblsiz: u32 = @intCast(exp2dt.len / 2); 94 const redux: f64 = 0x1.8p52 / @as(f64, @floatFromInt(tblsiz)); 95 const P1: f64 = 0x1.62e42fefa39efp-1; 96 const P2: f64 = 0x1.ebfbdff82c575p-3; 97 const P3: f64 = 0x1.c6b08d704a0a6p-5; 98 const P4: f64 = 0x1.3b2ab88f70400p-7; 99 const P5: f64 = 0x1.5d88003875c74p-10; 100 101 const ux: u64 = @bitCast(x); 102 const ix = @as(u32, @intCast(ux >> 32)) & 0x7FFFFFFF; 103 104 // TODO: This should be handled beneath. 105 if (math.isNan(x)) { 106 return math.nan(f64); 107 } 108 109 // |x| >= 1022 or nan 110 if (ix >= 0x408FF000) { 111 // x >= 1024 or nan 112 if (ix >= 0x40900000 and ux >> 63 == 0) { 113 math.raiseOverflow(); 114 return math.inf(f64); 115 } 116 // -inf or -nan 117 if (ix >= 0x7FF00000) { 118 return -1 / x; 119 } 120 // x <= -1022 121 if (ux >> 63 != 0) { 122 // underflow 123 if (x <= -1075 or x - 0x1.0p52 + 0x1.0p52 != x) { 124 if (common.want_float_exceptions) mem.doNotOptimizeAway(@as(f32, @floatCast(-0x1.0p-149 / x))); 125 } 126 if (x <= -1075) { 127 return 0; 128 } 129 } 130 } 131 // |x| < 0x1p-54 132 else if (ix < 0x3C900000) { 133 return 1.0 + x; 134 } 135 136 // NOTE: musl relies on unsafe behaviours which are replicated below 137 // (addition overflow, division truncation, casting). Appears that this 138 // produces the intended result but should confirm how GCC/Clang handle this 139 // to ensure. 140 141 // reduce x 142 var uf: f64 = x + redux; 143 // NOTE: musl performs an implicit 64-bit to 32-bit u32 truncation here 144 var i_0: u32 = @truncate(@as(u64, @bitCast(uf))); 145 i_0 +%= tblsiz / 2; 146 147 const k: u32 = i_0 / tblsiz * tblsiz; 148 const ik: i32 = @divTrunc(@as(i32, @bitCast(k)), tblsiz); 149 i_0 %= tblsiz; 150 uf -= redux; 151 152 // r = exp2(y) = exp2t[i_0] * p(z - eps[i]) 153 var z: f64 = x - uf; 154 const t: f64 = exp2dt[@intCast(2 * i_0)]; 155 z -= exp2dt[@intCast(2 * i_0 + 1)]; 156 const r: f64 = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); 157 158 return math.scalbn(r, ik); 159 } 160 161 pub fn __exp2x(x: f80) callconv(.c) f80 { 162 // TODO: more efficient implementation 163 return @floatCast(exp2q(x)); 164 } 165 166 pub fn exp2q(x: f128) callconv(.c) f128 { 167 // TODO: more correct implementation 168 return exp2(@floatCast(x)); 169 } 170 171 pub fn exp2l(x: c_longdouble) callconv(.c) c_longdouble { 172 switch (@typeInfo(c_longdouble).float.bits) { 173 16 => return __exp2h(x), 174 32 => return exp2f(x), 175 64 => return exp2(x), 176 80 => return __exp2x(x), 177 128 => return exp2q(x), 178 else => @compileError("unreachable"), 179 } 180 } 181 182 const exp2ft = [_]f64{ 183 0x1.6a09e667f3bcdp-1, 184 0x1.7a11473eb0187p-1, 185 0x1.8ace5422aa0dbp-1, 186 0x1.9c49182a3f090p-1, 187 0x1.ae89f995ad3adp-1, 188 0x1.c199bdd85529cp-1, 189 0x1.d5818dcfba487p-1, 190 0x1.ea4afa2a490dap-1, 191 0x1.0000000000000p+0, 192 0x1.0b5586cf9890fp+0, 193 0x1.172b83c7d517bp+0, 194 0x1.2387a6e756238p+0, 195 0x1.306fe0a31b715p+0, 196 0x1.3dea64c123422p+0, 197 0x1.4bfdad5362a27p+0, 198 0x1.5ab07dd485429p+0, 199 }; 200 201 const exp2dt = [_]f64{ 202 // exp2(z + eps) eps 203 0x1.6a09e667f3d5dp-1, 0x1.9880p-44, 204 0x1.6b052fa751744p-1, 0x1.8000p-50, 205 0x1.6c012750bd9fep-1, -0x1.8780p-45, 206 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, 207 0x1.6dfb23c651a29p-1, -0x1.8000p-50, 208 0x1.6ef9298593ae3p-1, -0x1.c000p-52, 209 0x1.6ff7df9519386p-1, -0x1.fd80p-45, 210 0x1.70f7466f42da3p-1, -0x1.c880p-45, 211 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, 212 0x1.72f8286eacf05p-1, -0x1.8300p-44, 213 0x1.73f9a48a58152p-1, -0x1.0c00p-47, 214 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, 215 0x1.75feb564267f1p-1, 0x1.3e00p-47, 216 0x1.77024b1ab6d48p-1, -0x1.7d00p-45, 217 0x1.780694fde5d38p-1, -0x1.d000p-50, 218 0x1.790b938ac1d00p-1, 0x1.3000p-49, 219 0x1.7a11473eb0178p-1, -0x1.d000p-49, 220 0x1.7b17b0976d060p-1, 0x1.0400p-45, 221 0x1.7c1ed0130c133p-1, 0x1.0000p-53, 222 0x1.7d26a62ff8636p-1, -0x1.6900p-45, 223 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, 224 0x1.7f3878491c3e8p-1, -0x1.4580p-45, 225 0x1.80427543e1b4ep-1, 0x1.3000p-44, 226 0x1.814d2add1071ap-1, 0x1.f000p-47, 227 0x1.82589994ccd7ep-1, -0x1.1c00p-45, 228 0x1.8364c1eb942d0p-1, 0x1.9d00p-45, 229 0x1.8471a4623cab5p-1, 0x1.7100p-43, 230 0x1.857f4179f5bbcp-1, 0x1.2600p-45, 231 0x1.868d99b4491afp-1, -0x1.2c40p-44, 232 0x1.879cad931a395p-1, -0x1.3000p-45, 233 0x1.88ac7d98a65b8p-1, -0x1.a800p-45, 234 0x1.89bd0a4785800p-1, -0x1.d000p-49, 235 0x1.8ace5422aa223p-1, 0x1.3280p-44, 236 0x1.8be05bad619fap-1, 0x1.2b40p-43, 237 0x1.8cf3216b54383p-1, -0x1.ed00p-45, 238 0x1.8e06a5e08664cp-1, -0x1.0500p-45, 239 0x1.8f1ae99157807p-1, 0x1.8280p-45, 240 0x1.902fed0282c0ep-1, -0x1.cb00p-46, 241 0x1.9145b0b91ff96p-1, -0x1.5e00p-47, 242 0x1.925c353aa2ff9p-1, 0x1.5400p-48, 243 0x1.93737b0cdc64ap-1, 0x1.7200p-46, 244 0x1.948b82b5f98aep-1, -0x1.9000p-47, 245 0x1.95a44cbc852cbp-1, 0x1.5680p-45, 246 0x1.96bdd9a766f21p-1, -0x1.6d00p-44, 247 0x1.97d829fde4e2ap-1, -0x1.1000p-47, 248 0x1.98f33e47a23a3p-1, 0x1.d000p-45, 249 0x1.9a0f170ca0604p-1, -0x1.8a40p-44, 250 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44, 251 0x1.9c49182a3f15bp-1, 0x1.6b80p-45, 252 0x1.9d674194bb8c5p-1, -0x1.c000p-49, 253 0x1.9e86319e3238ep-1, 0x1.7d00p-46, 254 0x1.9fa5e8d07f302p-1, 0x1.6400p-46, 255 0x1.a0c667b5de54dp-1, -0x1.5000p-48, 256 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47, 257 0x1.a309bec4a2e27p-1, 0x1.ad80p-45, 258 0x1.a42c980460a5dp-1, -0x1.af00p-46, 259 0x1.a5503b23e259bp-1, 0x1.b600p-47, 260 0x1.a674a8af46213p-1, 0x1.8880p-44, 261 0x1.a799e1330b3a7p-1, 0x1.1200p-46, 262 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47, 263 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45, 264 0x1.ab0e521356fb8p-1, 0x1.b700p-45, 265 0x1.ac36bbfd3f381p-1, 0x1.9000p-50, 266 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49, 267 0x1.ae89f995ad2a3p-1, -0x1.c900p-45, 268 0x1.afb4ce622f367p-1, 0x1.6500p-46, 269 0x1.b0e07298db790p-1, 0x1.fd40p-45, 270 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46, 271 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43, 272 0x1.b468415b747e7p-1, -0x1.8380p-44, 273 0x1.b59728de5593ap-1, 0x1.8000p-54, 274 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47, 275 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50, 276 0x1.b928cf22749b2p-1, -0x1.4c00p-47, 277 0x1.ba5b030a10603p-1, -0x1.d700p-47, 278 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47, 279 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47, 280 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46, 281 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46, 282 0x1.c06286141b2e9p-1, -0x1.1400p-46, 283 0x1.c199bdd8552e0p-1, 0x1.be00p-47, 284 0x1.c2d1cd9fa64eep-1, -0x1.9400p-47, 285 0x1.c40ab5fffd02fp-1, -0x1.ed00p-47, 286 0x1.c544778fafd15p-1, 0x1.9660p-44, 287 0x1.c67f12e57d0cbp-1, -0x1.a100p-46, 288 0x1.c7ba88988c1b6p-1, -0x1.8458p-42, 289 0x1.c8f6d9406e733p-1, -0x1.a480p-46, 290 0x1.ca3405751c4dfp-1, 0x1.b000p-51, 291 0x1.cb720dcef9094p-1, 0x1.1400p-47, 292 0x1.ccb0f2e6d1689p-1, 0x1.0200p-48, 293 0x1.cdf0b555dc412p-1, 0x1.3600p-48, 294 0x1.cf3155b5bab3bp-1, -0x1.6900p-47, 295 0x1.d072d4a0789bcp-1, 0x1.9a00p-47, 296 0x1.d1b532b08c8fap-1, -0x1.5e00p-46, 297 0x1.d2f87080d8a85p-1, 0x1.d280p-46, 298 0x1.d43c8eacaa203p-1, 0x1.1a00p-47, 299 0x1.d5818dcfba491p-1, 0x1.f000p-50, 300 0x1.d6c76e862e6a1p-1, -0x1.3a00p-47, 301 0x1.d80e316c9834ep-1, -0x1.cd80p-47, 302 0x1.d955d71ff6090p-1, 0x1.4c00p-48, 303 0x1.da9e603db32aep-1, 0x1.f900p-48, 304 0x1.dbe7cd63a8325p-1, 0x1.9800p-49, 305 0x1.dd321f301b445p-1, -0x1.5200p-48, 306 0x1.de7d5641c05bfp-1, -0x1.d700p-46, 307 0x1.dfc97337b9aecp-1, -0x1.6140p-46, 308 0x1.e11676b197d5ep-1, 0x1.b480p-47, 309 0x1.e264614f5a3e7p-1, 0x1.0ce0p-43, 310 0x1.e3b333b16ee5cp-1, 0x1.c680p-47, 311 0x1.e502ee78b3fb4p-1, -0x1.9300p-47, 312 0x1.e653924676d68p-1, -0x1.5000p-49, 313 0x1.e7a51fbc74c44p-1, -0x1.7f80p-47, 314 0x1.e8f7977cdb726p-1, -0x1.3700p-48, 315 0x1.ea4afa2a490e8p-1, 0x1.5d00p-49, 316 0x1.eb9f4867ccae4p-1, 0x1.61a0p-46, 317 0x1.ecf482d8e680dp-1, 0x1.5500p-48, 318 0x1.ee4aaa2188514p-1, 0x1.6400p-51, 319 0x1.efa1bee615a13p-1, -0x1.e800p-49, 320 0x1.f0f9c1cb64106p-1, -0x1.a880p-48, 321 0x1.f252b376bb963p-1, -0x1.c900p-45, 322 0x1.f3ac948dd7275p-1, 0x1.a000p-53, 323 0x1.f50765b6e4524p-1, -0x1.4f00p-48, 324 0x1.f6632798844fdp-1, 0x1.a800p-51, 325 0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48, 326 0x1.f91d802243c82p-1, -0x1.4600p-50, 327 0x1.fa7c1819e908ep-1, -0x1.b0c0p-47, 328 0x1.fbdba3692d511p-1, -0x1.0e00p-51, 329 0x1.fd3c22b8f7194p-1, -0x1.0de8p-46, 330 0x1.fe9d96b2a23eep-1, 0x1.e430p-49, 331 0x1.0000000000000p+0, 0x0.0000p+0, 332 0x1.00b1afa5abcbep+0, -0x1.3400p-52, 333 0x1.0163da9fb3303p+0, -0x1.2170p-46, 334 0x1.02168143b0282p+0, 0x1.a400p-52, 335 0x1.02c9a3e77806cp+0, 0x1.f980p-49, 336 0x1.037d42e11bbcap+0, -0x1.7400p-51, 337 0x1.04315e86e7f89p+0, 0x1.8300p-50, 338 0x1.04e5f72f65467p+0, -0x1.a3f0p-46, 339 0x1.059b0d315855ap+0, -0x1.2840p-47, 340 0x1.0650a0e3c1f95p+0, 0x1.1600p-48, 341 0x1.0706b29ddf71ap+0, 0x1.5240p-46, 342 0x1.07bd42b72a82dp+0, -0x1.9a00p-49, 343 0x1.0874518759bd0p+0, 0x1.6400p-49, 344 0x1.092bdf66607c8p+0, -0x1.0780p-47, 345 0x1.09e3ecac6f383p+0, -0x1.8000p-54, 346 0x1.0a9c79b1f3930p+0, 0x1.fa00p-48, 347 0x1.0b5586cf988fcp+0, -0x1.ac80p-48, 348 0x1.0c0f145e46c8ap+0, 0x1.9c00p-50, 349 0x1.0cc922b724816p+0, 0x1.5200p-47, 350 0x1.0d83b23395dd8p+0, -0x1.ad00p-48, 351 0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46, 352 0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47, 353 0x1.0fb66affed2f0p+0, -0x1.d300p-47, 354 0x1.1073028d7234bp+0, 0x1.1500p-48, 355 0x1.11301d0125b5bp+0, 0x1.c000p-49, 356 0x1.11edbab5e2af9p+0, 0x1.6bc0p-46, 357 0x1.12abdc06c31d5p+0, 0x1.8400p-49, 358 0x1.136a814f2047dp+0, -0x1.ed00p-47, 359 0x1.1429aaea92de9p+0, 0x1.8e00p-49, 360 0x1.14e95934f3138p+0, 0x1.b400p-49, 361 0x1.15a98c8a58e71p+0, 0x1.5300p-47, 362 0x1.166a45471c3dfp+0, 0x1.3380p-47, 363 0x1.172b83c7d5211p+0, 0x1.8d40p-45, 364 0x1.17ed48695bb9fp+0, -0x1.5d00p-47, 365 0x1.18af9388c8d93p+0, -0x1.c880p-46, 366 0x1.1972658375d66p+0, 0x1.1f00p-46, 367 0x1.1a35beb6fcba7p+0, 0x1.0480p-46, 368 0x1.1af99f81387e3p+0, -0x1.7390p-43, 369 0x1.1bbe084045d54p+0, 0x1.4e40p-45, 370 0x1.1c82f95281c43p+0, -0x1.a200p-47, 371 0x1.1d4873168b9b2p+0, 0x1.3800p-49, 372 0x1.1e0e75eb44031p+0, 0x1.ac00p-49, 373 0x1.1ed5022fcd938p+0, 0x1.1900p-47, 374 0x1.1f9c18438cdf7p+0, -0x1.b780p-46, 375 0x1.2063b88628d8fp+0, 0x1.d940p-45, 376 0x1.212be3578a81ep+0, 0x1.8000p-50, 377 0x1.21f49917ddd41p+0, 0x1.b340p-45, 378 0x1.22bdda2791323p+0, 0x1.9f80p-46, 379 0x1.2387a6e7561e7p+0, -0x1.9c80p-46, 380 0x1.2451ffb821427p+0, 0x1.2300p-47, 381 0x1.251ce4fb2a602p+0, -0x1.3480p-46, 382 0x1.25e85711eceb0p+0, 0x1.2700p-46, 383 0x1.26b4565e27d16p+0, 0x1.1d00p-46, 384 0x1.2780e341de00fp+0, 0x1.1ee0p-44, 385 0x1.284dfe1f5633ep+0, -0x1.4c00p-46, 386 0x1.291ba7591bb30p+0, -0x1.3d80p-46, 387 0x1.29e9df51fdf09p+0, 0x1.8b00p-47, 388 0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45, 389 0x1.2b87fd0dada3ap+0, 0x1.a340p-45, 390 0x1.2c57e39771af9p+0, -0x1.0800p-46, 391 0x1.2d285a6e402d9p+0, -0x1.ed00p-47, 392 0x1.2df961f641579p+0, -0x1.4200p-48, 393 0x1.2ecafa93e2ecfp+0, -0x1.4980p-45, 394 0x1.2f9d24abd8822p+0, -0x1.6300p-46, 395 0x1.306fe0a31b625p+0, -0x1.2360p-44, 396 0x1.31432edeea50bp+0, -0x1.0df8p-40, 397 0x1.32170fc4cd7b8p+0, -0x1.2480p-45, 398 0x1.32eb83ba8e9a2p+0, -0x1.5980p-45, 399 0x1.33c08b2641766p+0, 0x1.ed00p-46, 400 0x1.3496266e3fa27p+0, -0x1.c000p-50, 401 0x1.356c55f929f0fp+0, -0x1.0d80p-44, 402 0x1.36431a2de88b9p+0, 0x1.2c80p-45, 403 0x1.371a7373aaa39p+0, 0x1.0600p-45, 404 0x1.37f26231e74fep+0, -0x1.6600p-46, 405 0x1.38cae6d05d838p+0, -0x1.ae00p-47, 406 0x1.39a401b713ec3p+0, -0x1.4720p-43, 407 0x1.3a7db34e5a020p+0, 0x1.8200p-47, 408 0x1.3b57fbfec6e95p+0, 0x1.e800p-44, 409 0x1.3c32dc313a8f2p+0, 0x1.f800p-49, 410 0x1.3d0e544ede122p+0, -0x1.7a00p-46, 411 0x1.3dea64c1234bbp+0, 0x1.6300p-45, 412 0x1.3ec70df1c4eccp+0, -0x1.8a60p-43, 413 0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44, 414 0x1.40822c367a0bbp+0, 0x1.5b80p-45, 415 0x1.4160a21f72e95p+0, 0x1.ec00p-46, 416 0x1.423fb27094646p+0, -0x1.3600p-46, 417 0x1.431f5d950a920p+0, 0x1.3980p-45, 418 0x1.43ffa3f84b9ebp+0, 0x1.a000p-48, 419 0x1.44e0860618919p+0, -0x1.6c00p-48, 420 0x1.45c2042a7d201p+0, -0x1.bc00p-47, 421 0x1.46a41ed1d0016p+0, -0x1.2800p-46, 422 0x1.4786d668b3326p+0, 0x1.0e00p-44, 423 0x1.486a2b5c13c00p+0, -0x1.d400p-45, 424 0x1.494e1e192af04p+0, 0x1.c200p-47, 425 0x1.4a32af0d7d372p+0, -0x1.e500p-46, 426 0x1.4b17dea6db801p+0, 0x1.7800p-47, 427 0x1.4bfdad53629e1p+0, -0x1.3800p-46, 428 0x1.4ce41b817c132p+0, 0x1.0800p-47, 429 0x1.4dcb299fddddbp+0, 0x1.c700p-45, 430 0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46, 431 0x1.4f9b2769d2d02p+0, 0x1.9200p-46, 432 0x1.508417f4531c1p+0, -0x1.8c00p-47, 433 0x1.516daa2cf662ap+0, -0x1.a000p-48, 434 0x1.5257de83f51eap+0, 0x1.a080p-43, 435 0x1.5342b569d4edap+0, -0x1.6d80p-45, 436 0x1.542e2f4f6ac1ap+0, -0x1.2440p-44, 437 0x1.551a4ca5d94dbp+0, 0x1.83c0p-43, 438 0x1.56070dde9116bp+0, 0x1.4b00p-45, 439 0x1.56f4736b529dep+0, 0x1.15a0p-43, 440 0x1.57e27dbe2c40ep+0, -0x1.9e00p-45, 441 0x1.58d12d497c76fp+0, -0x1.3080p-45, 442 0x1.59c0827ff0b4cp+0, 0x1.dec0p-43, 443 0x1.5ab07dd485427p+0, -0x1.4000p-51, 444 0x1.5ba11fba87af4p+0, 0x1.0080p-44, 445 0x1.5c9268a59460bp+0, -0x1.6c80p-45, 446 0x1.5d84590998e3fp+0, 0x1.69a0p-43, 447 0x1.5e76f15ad20e1p+0, -0x1.b400p-46, 448 0x1.5f6a320dcebcap+0, 0x1.7700p-46, 449 0x1.605e1b976dcb8p+0, 0x1.6f80p-45, 450 0x1.6152ae6cdf715p+0, 0x1.1000p-47, 451 0x1.6247eb03a5531p+0, -0x1.5d00p-46, 452 0x1.633dd1d1929b5p+0, -0x1.2d00p-46, 453 0x1.6434634ccc313p+0, -0x1.a800p-49, 454 0x1.652b9febc8efap+0, -0x1.8600p-45, 455 0x1.6623882553397p+0, 0x1.1fe0p-40, 456 0x1.671c1c708328ep+0, -0x1.7200p-44, 457 0x1.68155d44ca97ep+0, 0x1.6800p-49, 458 0x1.690f4b19e9471p+0, -0x1.9780p-45, 459 }; 460 461 test "exp2f() special" { 462 try expectEqual(exp2f(0.0), 1.0); 463 try expectEqual(exp2f(-0.0), 1.0); 464 try expectEqual(exp2f(1.0), 2.0); 465 try expectEqual(exp2f(-1.0), 0.5); 466 try expectEqual(exp2f(math.inf(f32)), math.inf(f32)); 467 try expect(math.isPositiveZero(exp2f(-math.inf(f32)))); 468 try expect(math.isNan(exp2f(math.nan(f32)))); 469 try expect(math.isNan(exp2f(math.snan(f32)))); 470 } 471 472 test "exp2f() sanity" { 473 try expectEqual(exp2f(-0x1.0223a0p+3), 0x1.e8d134p-9); 474 try expectEqual(exp2f(0x1.161868p+2), 0x1.453672p+4); 475 try expectEqual(exp2f(-0x1.0c34b4p+3), 0x1.890ca0p-9); 476 try expectEqual(exp2f(-0x1.a206f0p+2), 0x1.622d4ep-7); 477 try expectEqual(exp2f(0x1.288bbcp+3), 0x1.340ecep+9); 478 try expectEqual(exp2f(0x1.52efd0p-1), 0x1.950eeep+0); 479 try expectEqual(exp2f(-0x1.a05cc8p-2), 0x1.824056p-1); 480 try expectEqual(exp2f(0x1.1f9efap-1), 0x1.79dfa2p+0); 481 try expectEqual(exp2f(0x1.8c5db0p-1), 0x1.b5ceacp+0); 482 try expectEqual(exp2f(-0x1.5b86eap-1), 0x1.3fd8bap-1); 483 } 484 485 test "exp2f() boundary" { 486 try expectEqual(exp2f(0x1.fffffep+6), 0x1.ffff4ep+127); // The last value before the result gets infinite 487 try expectEqual(exp2f(0x1p+7), math.inf(f32)); // The first value that gives infinite result 488 try expectEqual(exp2f(-0x1.2bccccp+7), 0x1p-149); // The last value before the result flushes to zero 489 try expectEqual(exp2f(-0x1.2cp+7), 0); // The first value at which the result flushes to zero 490 try expectEqual(exp2f(-0x1.f8p+6), 0x1p-126); // The last value before the result flushes to subnormal 491 try expectEqual(exp2f(-0x1.f80002p+6), 0x1.ffff50p-127); // The first value for which the result flushes to subnormal 492 try expectEqual(exp2f(0x1.fffffep+127), math.inf(f32)); // Max input value 493 try expectEqual(exp2f(0x1p-149), 1); // Min positive input value 494 try expectEqual(exp2f(-0x1p-149), 1); // Min negative input value 495 try expectEqual(exp2f(0x1p-126), 1); // First positive subnormal input 496 try expectEqual(exp2f(-0x1p-126), 1); // First negative subnormal input 497 } 498 499 test "exp2() special" { 500 try expectEqual(exp2(0.0), 1.0); 501 try expectEqual(exp2(-0.0), 1.0); 502 try expectEqual(exp2(1.0), 2.0); 503 try expectEqual(exp2(-1.0), 0.5); 504 try expectEqual(exp2(math.inf(f64)), math.inf(f64)); 505 try expect(math.isPositiveZero(exp2(-math.inf(f64)))); 506 try expect(math.isNan(exp2(math.nan(f64)))); 507 try expect(math.isNan(exp2(math.snan(f64)))); 508 } 509 510 test "exp2() sanity" { 511 try expectEqual(exp2(-0x1.02239f3c6a8f1p+3), 0x1.e8d13c396f452p-9); 512 try expectEqual(exp2(0x1.161868e18bc67p+2), 0x1.4536746bb6f12p+4); 513 try expectEqual(exp2(-0x1.0c34b3e01e6e7p+3), 0x1.890ca0c00b9a2p-9); 514 try expectEqual(exp2(-0x1.a206f0a19dcc4p+2), 0x1.622d4b0ebc6c1p-7); 515 try expectEqual(exp2(0x1.288bbb0d6a1e6p+3), 0x1.340ec7f3e607ep+9); 516 try expectEqual(exp2(0x1.52efd0cd80497p-1), 0x1.950eef4bc5451p+0); 517 try expectEqual(exp2(-0x1.a05cc754481d1p-2), 0x1.824056efc687cp-1); 518 try expectEqual(exp2(0x1.1f9ef934745cbp-1), 0x1.79dfa14ab121ep+0); 519 try expectEqual(exp2(0x1.8c5db097f7442p-1), 0x1.b5cead2247372p+0); 520 try expectEqual(exp2(-0x1.5b86ea8118a0ep-1), 0x1.3fd8ba33216b9p-1); 521 } 522 523 test "exp2() boundary" { 524 try expectEqual(exp2(0x1.fffffffffffffp+9), 0x1.ffffffffffd3ap+1023); // The last value before the result gets infinite 525 try expectEqual(exp2(0x1p+10), math.inf(f64)); // The first value that gives infinite result 526 try expectEqual(exp2(-0x1.0cbffffffffffp+10), 0x1p-1074); // The last value before the result flushes to zero 527 try expectEqual(exp2(-0x1.0ccp+10), 0); // The first value at which the result flushes to zero 528 try expectEqual(exp2(-0x1.ffp+9), 0x1p-1022); // The last value before the result flushes to subnormal 529 try expectEqual(exp2(-0x1.ff00000000001p+9), 0x1.ffffffffffd3ap-1023); // The first value for which the result flushes to subnormal 530 try expectEqual(exp2(0x1.fffffffffffffp+1023), math.inf(f64)); // Max input value 531 try expectEqual(exp2(0x1p-1074), 1); // Min positive input value 532 try expectEqual(exp2(-0x1p-1074), 1); // Min negative input value 533 try expectEqual(exp2(0x1p-1022), 1); // First positive subnormal input 534 try expectEqual(exp2(-0x1p-1022), 1); // First negative subnormal input 535 }