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
7const std = @import("std");
8const builtin = @import("builtin");
9const arch = builtin.cpu.arch;
10const math = std.math;
11const mem = std.mem;
12const expect = std.testing.expect;
13const expectEqual = std.testing.expectEqual;
14const compiler_rt = @import("../compiler_rt.zig");
15const symbol = compiler_rt.symbol;
16
17comptime {
18 symbol(&__exp2h, "__exp2h");
19 symbol(&exp2f, "exp2f");
20 symbol(&exp2, "exp2");
21 symbol(&__exp2x, "__exp2x");
22 symbol(&exp2q, "exp2f128");
23 symbol(&exp2l, "exp2l");
24}
25
26fn __exp2h(x: compiler_rt.f16.Abi) callconv(.c) compiler_rt.f16.Abi {
27 return compiler_rt.f16.toAbi(exp2_f16(compiler_rt.f16.fromAbi(x)));
28}
29pub fn exp2_f16(x: f16) f16 {
30 // TODO: more efficient implementation
31 return @floatCast(exp2_f32(x));
32}
33
34fn exp2f(x: compiler_rt.f32.Abi) callconv(.c) compiler_rt.f32.Abi {
35 return compiler_rt.f32.toAbi(exp2_f32(compiler_rt.f32.fromAbi(x)));
36}
37pub fn exp2_f32(x: f32) f32 {
38 const tblsiz: u32 = @intCast(exp2ft.len);
39 const redux: f32 = 0x1.8p23 / @as(f32, @floatFromInt(tblsiz));
40 const P1: f32 = 0x1.62e430p-1;
41 const P2: f32 = 0x1.ebfbe0p-3;
42 const P3: f32 = 0x1.c6b348p-5;
43 const P4: f32 = 0x1.3b2c9cp-7;
44
45 const u: u32 = @bitCast(x);
46 const ix = u & 0x7FFFFFFF;
47
48 // |x| > 126
49 if (ix > 0x42FC0000) {
50 // nan
51 if (ix > 0x7F800000) {
52 return x;
53 }
54 // x >= 128
55 if (u >= 0x43000000 and u < 0x80000000) {
56 return x * 0x1.0p127;
57 }
58 // x < -126
59 if (u >= 0x80000000) {
60 if (u >= 0xC3160000 or u & 0x000FFFF != 0) {
61 if (compiler_rt.want_float_exceptions) mem.doNotOptimizeAway(-0x1.0p-149 / x);
62 }
63 // x <= -150
64 if (u >= 0xC3160000) {
65 return 0;
66 }
67 }
68 }
69 // |x| <= 0x1p-25
70 else if (ix <= 0x33000000) {
71 return 1.0 + x;
72 }
73
74 // NOTE: musl relies on unsafe behaviours which are replicated below
75 // (addition/bit-shift overflow). Appears that this produces the
76 // intended result but should confirm how GCC/Clang handle this to ensure.
77
78 var uf = x + redux;
79 var i_0: u32 = @bitCast(uf);
80 i_0 +%= tblsiz / 2;
81
82 const k = i_0 / tblsiz;
83 const uk: f64 = @bitCast(@as(u64, 0x3FF + k) << 52);
84 i_0 &= tblsiz - 1;
85 uf -= redux;
86
87 const z: f64 = x - uf;
88 var r: f64 = exp2ft[@intCast(i_0)];
89 const t: f64 = r * z;
90 r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4);
91 return @floatCast(r * uk);
92}
93
94fn exp2(x: compiler_rt.f64.Abi) callconv(.c) compiler_rt.f64.Abi {
95 return compiler_rt.f64.toAbi(exp2_f64(compiler_rt.f64.fromAbi(x)));
96}
97pub fn exp2_f64(x: f64) f64 {
98 const tblsiz: u32 = @intCast(exp2dt.len / 2);
99 const redux: f64 = 0x1.8p52 / @as(f64, @floatFromInt(tblsiz));
100 const P1: f64 = 0x1.62e42fefa39efp-1;
101 const P2: f64 = 0x1.ebfbdff82c575p-3;
102 const P3: f64 = 0x1.c6b08d704a0a6p-5;
103 const P4: f64 = 0x1.3b2ab88f70400p-7;
104 const P5: f64 = 0x1.5d88003875c74p-10;
105
106 const ux: u64 = @bitCast(x);
107 const ix = @as(u32, @intCast(ux >> 32)) & 0x7FFFFFFF;
108
109 // TODO: This should be handled beneath.
110 if (math.isNan(x)) {
111 return math.nan(f64);
112 }
113
114 // |x| >= 1022 or nan
115 if (ix >= 0x408FF000) {
116 // x >= 1024 or nan
117 if (ix >= 0x40900000 and ux >> 63 == 0) {
118 return if (compiler_rt.want_float_exceptions) x * 0x1p1023 else std.math.inf(f64);
119 }
120 // -inf or -nan
121 if (ix >= 0x7FF00000) {
122 return -1 / x;
123 }
124 // x <= -1022
125 if (ux >> 63 != 0) {
126 // underflow
127 if (x <= -1075 or x - 0x1.0p52 + 0x1.0p52 != x) {
128 if (compiler_rt.want_float_exceptions) mem.doNotOptimizeAway(@as(f32, @floatCast(-0x1.0p-149 / x)));
129 }
130 if (x <= -1075) {
131 return 0;
132 }
133 }
134 }
135 // |x| < 0x1p-54
136 else if (ix < 0x3C900000) {
137 return 1.0 + x;
138 }
139
140 // NOTE: musl relies on unsafe behaviours which are replicated below
141 // (addition overflow, division truncation, casting). Appears that this
142 // produces the intended result but should confirm how GCC/Clang handle this
143 // to ensure.
144
145 // reduce x
146 var uf: f64 = x + redux;
147 // NOTE: musl performs an implicit 64-bit to 32-bit u32 truncation here
148 var i_0: u32 = @truncate(@as(u64, @bitCast(uf)));
149 i_0 +%= tblsiz / 2;
150
151 const k: u32 = i_0 / tblsiz * tblsiz;
152 const ik: i32 = @divTrunc(@as(i32, @bitCast(k)), tblsiz);
153 i_0 %= tblsiz;
154 uf -= redux;
155
156 // r = exp2(y) = exp2t[i_0] * p(z - eps[i])
157 var z: f64 = x - uf;
158 const t: f64 = exp2dt[@intCast(2 * i_0)];
159 z -= exp2dt[@intCast(2 * i_0 + 1)];
160 const r: f64 = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
161
162 return math.scalbn(r, ik);
163}
164
165fn __exp2x(x: compiler_rt.f80.Abi) callconv(.c) compiler_rt.f80.Abi {
166 return compiler_rt.f80.toAbi(exp2_f80(compiler_rt.f80.fromAbi(x)));
167}
168pub fn exp2_f80(x: f80) f80 {
169 // TODO: more efficient implementation
170 return @floatCast(exp2_f128(x));
171}
172
173fn exp2q(x: compiler_rt.f128.Abi) callconv(.c) compiler_rt.f128.Abi {
174 return compiler_rt.f128.toAbi(exp2_f128(compiler_rt.f128.fromAbi(x)));
175}
176pub const exp2_f128 = @import("exp_f128.zig").exp2;
177
178pub fn exp2l(x: c_longdouble) callconv(.c) c_longdouble {
179 switch (@typeInfo(c_longdouble).float.bits) {
180 64 => return exp2_f64(x),
181 80 => return exp2_f80(x),
182 128 => return exp2_f128(x),
183 else => comptime unreachable,
184 }
185}
186
187const exp2ft = [_]f64{
188 0x1.6a09e667f3bcdp-1,
189 0x1.7a11473eb0187p-1,
190 0x1.8ace5422aa0dbp-1,
191 0x1.9c49182a3f090p-1,
192 0x1.ae89f995ad3adp-1,
193 0x1.c199bdd85529cp-1,
194 0x1.d5818dcfba487p-1,
195 0x1.ea4afa2a490dap-1,
196 0x1.0000000000000p+0,
197 0x1.0b5586cf9890fp+0,
198 0x1.172b83c7d517bp+0,
199 0x1.2387a6e756238p+0,
200 0x1.306fe0a31b715p+0,
201 0x1.3dea64c123422p+0,
202 0x1.4bfdad5362a27p+0,
203 0x1.5ab07dd485429p+0,
204};
205
206const exp2dt = [_]f64{
207 // exp2(z + eps) eps
208 0x1.6a09e667f3d5dp-1, 0x1.9880p-44,
209 0x1.6b052fa751744p-1, 0x1.8000p-50,
210 0x1.6c012750bd9fep-1, -0x1.8780p-45,
211 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46,
212 0x1.6dfb23c651a29p-1, -0x1.8000p-50,
213 0x1.6ef9298593ae3p-1, -0x1.c000p-52,
214 0x1.6ff7df9519386p-1, -0x1.fd80p-45,
215 0x1.70f7466f42da3p-1, -0x1.c880p-45,
216 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46,
217 0x1.72f8286eacf05p-1, -0x1.8300p-44,
218 0x1.73f9a48a58152p-1, -0x1.0c00p-47,
219 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45,
220 0x1.75feb564267f1p-1, 0x1.3e00p-47,
221 0x1.77024b1ab6d48p-1, -0x1.7d00p-45,
222 0x1.780694fde5d38p-1, -0x1.d000p-50,
223 0x1.790b938ac1d00p-1, 0x1.3000p-49,
224 0x1.7a11473eb0178p-1, -0x1.d000p-49,
225 0x1.7b17b0976d060p-1, 0x1.0400p-45,
226 0x1.7c1ed0130c133p-1, 0x1.0000p-53,
227 0x1.7d26a62ff8636p-1, -0x1.6900p-45,
228 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47,
229 0x1.7f3878491c3e8p-1, -0x1.4580p-45,
230 0x1.80427543e1b4ep-1, 0x1.3000p-44,
231 0x1.814d2add1071ap-1, 0x1.f000p-47,
232 0x1.82589994ccd7ep-1, -0x1.1c00p-45,
233 0x1.8364c1eb942d0p-1, 0x1.9d00p-45,
234 0x1.8471a4623cab5p-1, 0x1.7100p-43,
235 0x1.857f4179f5bbcp-1, 0x1.2600p-45,
236 0x1.868d99b4491afp-1, -0x1.2c40p-44,
237 0x1.879cad931a395p-1, -0x1.3000p-45,
238 0x1.88ac7d98a65b8p-1, -0x1.a800p-45,
239 0x1.89bd0a4785800p-1, -0x1.d000p-49,
240 0x1.8ace5422aa223p-1, 0x1.3280p-44,
241 0x1.8be05bad619fap-1, 0x1.2b40p-43,
242 0x1.8cf3216b54383p-1, -0x1.ed00p-45,
243 0x1.8e06a5e08664cp-1, -0x1.0500p-45,
244 0x1.8f1ae99157807p-1, 0x1.8280p-45,
245 0x1.902fed0282c0ep-1, -0x1.cb00p-46,
246 0x1.9145b0b91ff96p-1, -0x1.5e00p-47,
247 0x1.925c353aa2ff9p-1, 0x1.5400p-48,
248 0x1.93737b0cdc64ap-1, 0x1.7200p-46,
249 0x1.948b82b5f98aep-1, -0x1.9000p-47,
250 0x1.95a44cbc852cbp-1, 0x1.5680p-45,
251 0x1.96bdd9a766f21p-1, -0x1.6d00p-44,
252 0x1.97d829fde4e2ap-1, -0x1.1000p-47,
253 0x1.98f33e47a23a3p-1, 0x1.d000p-45,
254 0x1.9a0f170ca0604p-1, -0x1.8a40p-44,
255 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44,
256 0x1.9c49182a3f15bp-1, 0x1.6b80p-45,
257 0x1.9d674194bb8c5p-1, -0x1.c000p-49,
258 0x1.9e86319e3238ep-1, 0x1.7d00p-46,
259 0x1.9fa5e8d07f302p-1, 0x1.6400p-46,
260 0x1.a0c667b5de54dp-1, -0x1.5000p-48,
261 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47,
262 0x1.a309bec4a2e27p-1, 0x1.ad80p-45,
263 0x1.a42c980460a5dp-1, -0x1.af00p-46,
264 0x1.a5503b23e259bp-1, 0x1.b600p-47,
265 0x1.a674a8af46213p-1, 0x1.8880p-44,
266 0x1.a799e1330b3a7p-1, 0x1.1200p-46,
267 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47,
268 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45,
269 0x1.ab0e521356fb8p-1, 0x1.b700p-45,
270 0x1.ac36bbfd3f381p-1, 0x1.9000p-50,
271 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49,
272 0x1.ae89f995ad2a3p-1, -0x1.c900p-45,
273 0x1.afb4ce622f367p-1, 0x1.6500p-46,
274 0x1.b0e07298db790p-1, 0x1.fd40p-45,
275 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46,
276 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43,
277 0x1.b468415b747e7p-1, -0x1.8380p-44,
278 0x1.b59728de5593ap-1, 0x1.8000p-54,
279 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47,
280 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50,
281 0x1.b928cf22749b2p-1, -0x1.4c00p-47,
282 0x1.ba5b030a10603p-1, -0x1.d700p-47,
283 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47,
284 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47,
285 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46,
286 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46,
287 0x1.c06286141b2e9p-1, -0x1.1400p-46,
288 0x1.c199bdd8552e0p-1, 0x1.be00p-47,
289 0x1.c2d1cd9fa64eep-1, -0x1.9400p-47,
290 0x1.c40ab5fffd02fp-1, -0x1.ed00p-47,
291 0x1.c544778fafd15p-1, 0x1.9660p-44,
292 0x1.c67f12e57d0cbp-1, -0x1.a100p-46,
293 0x1.c7ba88988c1b6p-1, -0x1.8458p-42,
294 0x1.c8f6d9406e733p-1, -0x1.a480p-46,
295 0x1.ca3405751c4dfp-1, 0x1.b000p-51,
296 0x1.cb720dcef9094p-1, 0x1.1400p-47,
297 0x1.ccb0f2e6d1689p-1, 0x1.0200p-48,
298 0x1.cdf0b555dc412p-1, 0x1.3600p-48,
299 0x1.cf3155b5bab3bp-1, -0x1.6900p-47,
300 0x1.d072d4a0789bcp-1, 0x1.9a00p-47,
301 0x1.d1b532b08c8fap-1, -0x1.5e00p-46,
302 0x1.d2f87080d8a85p-1, 0x1.d280p-46,
303 0x1.d43c8eacaa203p-1, 0x1.1a00p-47,
304 0x1.d5818dcfba491p-1, 0x1.f000p-50,
305 0x1.d6c76e862e6a1p-1, -0x1.3a00p-47,
306 0x1.d80e316c9834ep-1, -0x1.cd80p-47,
307 0x1.d955d71ff6090p-1, 0x1.4c00p-48,
308 0x1.da9e603db32aep-1, 0x1.f900p-48,
309 0x1.dbe7cd63a8325p-1, 0x1.9800p-49,
310 0x1.dd321f301b445p-1, -0x1.5200p-48,
311 0x1.de7d5641c05bfp-1, -0x1.d700p-46,
312 0x1.dfc97337b9aecp-1, -0x1.6140p-46,
313 0x1.e11676b197d5ep-1, 0x1.b480p-47,
314 0x1.e264614f5a3e7p-1, 0x1.0ce0p-43,
315 0x1.e3b333b16ee5cp-1, 0x1.c680p-47,
316 0x1.e502ee78b3fb4p-1, -0x1.9300p-47,
317 0x1.e653924676d68p-1, -0x1.5000p-49,
318 0x1.e7a51fbc74c44p-1, -0x1.7f80p-47,
319 0x1.e8f7977cdb726p-1, -0x1.3700p-48,
320 0x1.ea4afa2a490e8p-1, 0x1.5d00p-49,
321 0x1.eb9f4867ccae4p-1, 0x1.61a0p-46,
322 0x1.ecf482d8e680dp-1, 0x1.5500p-48,
323 0x1.ee4aaa2188514p-1, 0x1.6400p-51,
324 0x1.efa1bee615a13p-1, -0x1.e800p-49,
325 0x1.f0f9c1cb64106p-1, -0x1.a880p-48,
326 0x1.f252b376bb963p-1, -0x1.c900p-45,
327 0x1.f3ac948dd7275p-1, 0x1.a000p-53,
328 0x1.f50765b6e4524p-1, -0x1.4f00p-48,
329 0x1.f6632798844fdp-1, 0x1.a800p-51,
330 0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48,
331 0x1.f91d802243c82p-1, -0x1.4600p-50,
332 0x1.fa7c1819e908ep-1, -0x1.b0c0p-47,
333 0x1.fbdba3692d511p-1, -0x1.0e00p-51,
334 0x1.fd3c22b8f7194p-1, -0x1.0de8p-46,
335 0x1.fe9d96b2a23eep-1, 0x1.e430p-49,
336 0x1.0000000000000p+0, 0x0.0000p+0,
337 0x1.00b1afa5abcbep+0, -0x1.3400p-52,
338 0x1.0163da9fb3303p+0, -0x1.2170p-46,
339 0x1.02168143b0282p+0, 0x1.a400p-52,
340 0x1.02c9a3e77806cp+0, 0x1.f980p-49,
341 0x1.037d42e11bbcap+0, -0x1.7400p-51,
342 0x1.04315e86e7f89p+0, 0x1.8300p-50,
343 0x1.04e5f72f65467p+0, -0x1.a3f0p-46,
344 0x1.059b0d315855ap+0, -0x1.2840p-47,
345 0x1.0650a0e3c1f95p+0, 0x1.1600p-48,
346 0x1.0706b29ddf71ap+0, 0x1.5240p-46,
347 0x1.07bd42b72a82dp+0, -0x1.9a00p-49,
348 0x1.0874518759bd0p+0, 0x1.6400p-49,
349 0x1.092bdf66607c8p+0, -0x1.0780p-47,
350 0x1.09e3ecac6f383p+0, -0x1.8000p-54,
351 0x1.0a9c79b1f3930p+0, 0x1.fa00p-48,
352 0x1.0b5586cf988fcp+0, -0x1.ac80p-48,
353 0x1.0c0f145e46c8ap+0, 0x1.9c00p-50,
354 0x1.0cc922b724816p+0, 0x1.5200p-47,
355 0x1.0d83b23395dd8p+0, -0x1.ad00p-48,
356 0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46,
357 0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47,
358 0x1.0fb66affed2f0p+0, -0x1.d300p-47,
359 0x1.1073028d7234bp+0, 0x1.1500p-48,
360 0x1.11301d0125b5bp+0, 0x1.c000p-49,
361 0x1.11edbab5e2af9p+0, 0x1.6bc0p-46,
362 0x1.12abdc06c31d5p+0, 0x1.8400p-49,
363 0x1.136a814f2047dp+0, -0x1.ed00p-47,
364 0x1.1429aaea92de9p+0, 0x1.8e00p-49,
365 0x1.14e95934f3138p+0, 0x1.b400p-49,
366 0x1.15a98c8a58e71p+0, 0x1.5300p-47,
367 0x1.166a45471c3dfp+0, 0x1.3380p-47,
368 0x1.172b83c7d5211p+0, 0x1.8d40p-45,
369 0x1.17ed48695bb9fp+0, -0x1.5d00p-47,
370 0x1.18af9388c8d93p+0, -0x1.c880p-46,
371 0x1.1972658375d66p+0, 0x1.1f00p-46,
372 0x1.1a35beb6fcba7p+0, 0x1.0480p-46,
373 0x1.1af99f81387e3p+0, -0x1.7390p-43,
374 0x1.1bbe084045d54p+0, 0x1.4e40p-45,
375 0x1.1c82f95281c43p+0, -0x1.a200p-47,
376 0x1.1d4873168b9b2p+0, 0x1.3800p-49,
377 0x1.1e0e75eb44031p+0, 0x1.ac00p-49,
378 0x1.1ed5022fcd938p+0, 0x1.1900p-47,
379 0x1.1f9c18438cdf7p+0, -0x1.b780p-46,
380 0x1.2063b88628d8fp+0, 0x1.d940p-45,
381 0x1.212be3578a81ep+0, 0x1.8000p-50,
382 0x1.21f49917ddd41p+0, 0x1.b340p-45,
383 0x1.22bdda2791323p+0, 0x1.9f80p-46,
384 0x1.2387a6e7561e7p+0, -0x1.9c80p-46,
385 0x1.2451ffb821427p+0, 0x1.2300p-47,
386 0x1.251ce4fb2a602p+0, -0x1.3480p-46,
387 0x1.25e85711eceb0p+0, 0x1.2700p-46,
388 0x1.26b4565e27d16p+0, 0x1.1d00p-46,
389 0x1.2780e341de00fp+0, 0x1.1ee0p-44,
390 0x1.284dfe1f5633ep+0, -0x1.4c00p-46,
391 0x1.291ba7591bb30p+0, -0x1.3d80p-46,
392 0x1.29e9df51fdf09p+0, 0x1.8b00p-47,
393 0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45,
394 0x1.2b87fd0dada3ap+0, 0x1.a340p-45,
395 0x1.2c57e39771af9p+0, -0x1.0800p-46,
396 0x1.2d285a6e402d9p+0, -0x1.ed00p-47,
397 0x1.2df961f641579p+0, -0x1.4200p-48,
398 0x1.2ecafa93e2ecfp+0, -0x1.4980p-45,
399 0x1.2f9d24abd8822p+0, -0x1.6300p-46,
400 0x1.306fe0a31b625p+0, -0x1.2360p-44,
401 0x1.31432edeea50bp+0, -0x1.0df8p-40,
402 0x1.32170fc4cd7b8p+0, -0x1.2480p-45,
403 0x1.32eb83ba8e9a2p+0, -0x1.5980p-45,
404 0x1.33c08b2641766p+0, 0x1.ed00p-46,
405 0x1.3496266e3fa27p+0, -0x1.c000p-50,
406 0x1.356c55f929f0fp+0, -0x1.0d80p-44,
407 0x1.36431a2de88b9p+0, 0x1.2c80p-45,
408 0x1.371a7373aaa39p+0, 0x1.0600p-45,
409 0x1.37f26231e74fep+0, -0x1.6600p-46,
410 0x1.38cae6d05d838p+0, -0x1.ae00p-47,
411 0x1.39a401b713ec3p+0, -0x1.4720p-43,
412 0x1.3a7db34e5a020p+0, 0x1.8200p-47,
413 0x1.3b57fbfec6e95p+0, 0x1.e800p-44,
414 0x1.3c32dc313a8f2p+0, 0x1.f800p-49,
415 0x1.3d0e544ede122p+0, -0x1.7a00p-46,
416 0x1.3dea64c1234bbp+0, 0x1.6300p-45,
417 0x1.3ec70df1c4eccp+0, -0x1.8a60p-43,
418 0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44,
419 0x1.40822c367a0bbp+0, 0x1.5b80p-45,
420 0x1.4160a21f72e95p+0, 0x1.ec00p-46,
421 0x1.423fb27094646p+0, -0x1.3600p-46,
422 0x1.431f5d950a920p+0, 0x1.3980p-45,
423 0x1.43ffa3f84b9ebp+0, 0x1.a000p-48,
424 0x1.44e0860618919p+0, -0x1.6c00p-48,
425 0x1.45c2042a7d201p+0, -0x1.bc00p-47,
426 0x1.46a41ed1d0016p+0, -0x1.2800p-46,
427 0x1.4786d668b3326p+0, 0x1.0e00p-44,
428 0x1.486a2b5c13c00p+0, -0x1.d400p-45,
429 0x1.494e1e192af04p+0, 0x1.c200p-47,
430 0x1.4a32af0d7d372p+0, -0x1.e500p-46,
431 0x1.4b17dea6db801p+0, 0x1.7800p-47,
432 0x1.4bfdad53629e1p+0, -0x1.3800p-46,
433 0x1.4ce41b817c132p+0, 0x1.0800p-47,
434 0x1.4dcb299fddddbp+0, 0x1.c700p-45,
435 0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46,
436 0x1.4f9b2769d2d02p+0, 0x1.9200p-46,
437 0x1.508417f4531c1p+0, -0x1.8c00p-47,
438 0x1.516daa2cf662ap+0, -0x1.a000p-48,
439 0x1.5257de83f51eap+0, 0x1.a080p-43,
440 0x1.5342b569d4edap+0, -0x1.6d80p-45,
441 0x1.542e2f4f6ac1ap+0, -0x1.2440p-44,
442 0x1.551a4ca5d94dbp+0, 0x1.83c0p-43,
443 0x1.56070dde9116bp+0, 0x1.4b00p-45,
444 0x1.56f4736b529dep+0, 0x1.15a0p-43,
445 0x1.57e27dbe2c40ep+0, -0x1.9e00p-45,
446 0x1.58d12d497c76fp+0, -0x1.3080p-45,
447 0x1.59c0827ff0b4cp+0, 0x1.dec0p-43,
448 0x1.5ab07dd485427p+0, -0x1.4000p-51,
449 0x1.5ba11fba87af4p+0, 0x1.0080p-44,
450 0x1.5c9268a59460bp+0, -0x1.6c80p-45,
451 0x1.5d84590998e3fp+0, 0x1.69a0p-43,
452 0x1.5e76f15ad20e1p+0, -0x1.b400p-46,
453 0x1.5f6a320dcebcap+0, 0x1.7700p-46,
454 0x1.605e1b976dcb8p+0, 0x1.6f80p-45,
455 0x1.6152ae6cdf715p+0, 0x1.1000p-47,
456 0x1.6247eb03a5531p+0, -0x1.5d00p-46,
457 0x1.633dd1d1929b5p+0, -0x1.2d00p-46,
458 0x1.6434634ccc313p+0, -0x1.a800p-49,
459 0x1.652b9febc8efap+0, -0x1.8600p-45,
460 0x1.6623882553397p+0, 0x1.1fe0p-40,
461 0x1.671c1c708328ep+0, -0x1.7200p-44,
462 0x1.68155d44ca97ep+0, 0x1.6800p-49,
463 0x1.690f4b19e9471p+0, -0x1.9780p-45,
464};
465
466test "exp2f() special" {
467 try expectEqual(exp2_f32(0.0), 1.0);
468 try expectEqual(exp2_f32(-0.0), 1.0);
469 try expectEqual(exp2_f32(1.0), 2.0);
470 try expectEqual(exp2_f32(-1.0), 0.5);
471 try expectEqual(exp2_f32(math.inf(f32)), math.inf(f32));
472 try expect(math.isPositiveZero(exp2_f32(-math.inf(f32))));
473 try expect(math.isNan(exp2_f32(math.nan(f32))));
474 try expect(math.isNan(exp2_f32(math.snan(f32))));
475}
476
477test "exp2f() sanity" {
478 try expectEqual(exp2_f32(-0x1.0223a0p+3), 0x1.e8d134p-9);
479 try expectEqual(exp2_f32(0x1.161868p+2), 0x1.453672p+4);
480 try expectEqual(exp2_f32(-0x1.0c34b4p+3), 0x1.890ca0p-9);
481 try expectEqual(exp2_f32(-0x1.a206f0p+2), 0x1.622d4ep-7);
482 try expectEqual(exp2_f32(0x1.288bbcp+3), 0x1.340ecep+9);
483 try expectEqual(exp2_f32(0x1.52efd0p-1), 0x1.950eeep+0);
484 try expectEqual(exp2_f32(-0x1.a05cc8p-2), 0x1.824056p-1);
485 try expectEqual(exp2_f32(0x1.1f9efap-1), 0x1.79dfa2p+0);
486 try expectEqual(exp2_f32(0x1.8c5db0p-1), 0x1.b5ceacp+0);
487 try expectEqual(exp2_f32(-0x1.5b86eap-1), 0x1.3fd8bap-1);
488}
489
490test "exp2f() boundary" {
491 try expectEqual(exp2_f32(0x1.fffffep+6), 0x1.ffff4ep+127); // The last value before the result gets infinite
492 try expectEqual(exp2_f32(0x1p+7), math.inf(f32)); // The first value that gives infinite result
493 try expectEqual(exp2_f32(-0x1.2bccccp+7), 0x1p-149); // The last value before the result flushes to zero
494 try expectEqual(exp2_f32(-0x1.2cp+7), 0); // The first value at which the result flushes to zero
495 try expectEqual(exp2_f32(-0x1.f8p+6), 0x1p-126); // The last value before the result flushes to subnormal
496 try expectEqual(exp2_f32(-0x1.f80002p+6), 0x1.ffff50p-127); // The first value for which the result flushes to subnormal
497 try expectEqual(exp2_f32(0x1.fffffep+127), math.inf(f32)); // Max input value
498 try expectEqual(exp2_f32(0x1p-149), 1); // Min positive input value
499 try expectEqual(exp2_f32(-0x1p-149), 1); // Min negative input value
500 try expectEqual(exp2_f32(0x1p-126), 1); // First positive subnormal input
501 try expectEqual(exp2_f32(-0x1p-126), 1); // First negative subnormal input
502}
503
504test "exp2() special" {
505 try expectEqual(exp2_f64(0.0), 1.0);
506 try expectEqual(exp2_f64(-0.0), 1.0);
507 try expectEqual(exp2_f64(1.0), 2.0);
508 try expectEqual(exp2_f64(-1.0), 0.5);
509 try expectEqual(exp2_f64(math.inf(f64)), math.inf(f64));
510 try expect(math.isPositiveZero(exp2_f64(-math.inf(f64))));
511 try expect(math.isNan(exp2_f64(math.nan(f64))));
512 try expect(math.isNan(exp2_f64(math.snan(f64))));
513}
514
515test "exp2() sanity" {
516 try expectEqual(exp2_f64(-0x1.02239f3c6a8f1p+3), 0x1.e8d13c396f452p-9);
517 try expectEqual(exp2_f64(0x1.161868e18bc67p+2), 0x1.4536746bb6f12p+4);
518 try expectEqual(exp2_f64(-0x1.0c34b3e01e6e7p+3), 0x1.890ca0c00b9a2p-9);
519 try expectEqual(exp2_f64(-0x1.a206f0a19dcc4p+2), 0x1.622d4b0ebc6c1p-7);
520 try expectEqual(exp2_f64(0x1.288bbb0d6a1e6p+3), 0x1.340ec7f3e607ep+9);
521 try expectEqual(exp2_f64(0x1.52efd0cd80497p-1), 0x1.950eef4bc5451p+0);
522 try expectEqual(exp2_f64(-0x1.a05cc754481d1p-2), 0x1.824056efc687cp-1);
523 try expectEqual(exp2_f64(0x1.1f9ef934745cbp-1), 0x1.79dfa14ab121ep+0);
524 try expectEqual(exp2_f64(0x1.8c5db097f7442p-1), 0x1.b5cead2247372p+0);
525 try expectEqual(exp2_f64(-0x1.5b86ea8118a0ep-1), 0x1.3fd8ba33216b9p-1);
526}
527
528test "exp2() boundary" {
529 try expectEqual(exp2_f64(0x1.fffffffffffffp+9), 0x1.ffffffffffd3ap+1023); // The last value before the result gets infinite
530 try expectEqual(exp2_f64(0x1p+10), math.inf(f64)); // The first value that gives infinite result
531 try expectEqual(exp2_f64(-0x1.0cbffffffffffp+10), 0x1p-1074); // The last value before the result flushes to zero
532 try expectEqual(exp2_f64(-0x1.0ccp+10), 0); // The first value at which the result flushes to zero
533 try expectEqual(exp2_f64(-0x1.ffp+9), 0x1p-1022); // The last value before the result flushes to subnormal
534 try expectEqual(exp2_f64(-0x1.ff00000000001p+9), 0x1.ffffffffffd3ap-1023); // The first value for which the result flushes to subnormal
535 try expectEqual(exp2_f64(0x1.fffffffffffffp+1023), math.inf(f64)); // Max input value
536 try expectEqual(exp2_f64(0x1p-1074), 1); // Min positive input value
537 try expectEqual(exp2_f64(-0x1p-1074), 1); // Min negative input value
538 try expectEqual(exp2_f64(0x1p-1022), 1); // First positive subnormal input
539 try expectEqual(exp2_f64(-0x1p-1022), 1); // First negative subnormal input
540}