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.zig");
8const math = std.math;
9const expect = std.testing.expect;
10
11/// Returns 2 raised to the power of x (2^x).
12///
13/// Special Cases:
14///  - exp2(+inf) = +inf
15///  - exp2(nan)  = nan
16pub fn exp2(x: anytype) @TypeOf(x) {
17    const T = @TypeOf(x);
18    return switch (T) {
19        f32 => exp2_32(x),
20        f64 => exp2_64(x),
21        else => @compileError("exp2 not implemented for " ++ @typeName(T)),
22    };
23}
24
25const exp2ft = [_]f64{
26    0x1.6a09e667f3bcdp-1,
27    0x1.7a11473eb0187p-1,
28    0x1.8ace5422aa0dbp-1,
29    0x1.9c49182a3f090p-1,
30    0x1.ae89f995ad3adp-1,
31    0x1.c199bdd85529cp-1,
32    0x1.d5818dcfba487p-1,
33    0x1.ea4afa2a490dap-1,
34    0x1.0000000000000p+0,
35    0x1.0b5586cf9890fp+0,
36    0x1.172b83c7d517bp+0,
37    0x1.2387a6e756238p+0,
38    0x1.306fe0a31b715p+0,
39    0x1.3dea64c123422p+0,
40    0x1.4bfdad5362a27p+0,
41    0x1.5ab07dd485429p+0,
42};
43
44fn exp2_32(x: f32) f32 {
45    const tblsiz = @intCast(u32, exp2ft.len);
46    const redux: f32 = 0x1.8p23 / @intToFloat(f32, tblsiz);
47    const P1: f32 = 0x1.62e430p-1;
48    const P2: f32 = 0x1.ebfbe0p-3;
49    const P3: f32 = 0x1.c6b348p-5;
50    const P4: f32 = 0x1.3b2c9cp-7;
51
52    var u = @bitCast(u32, x);
53    const ix = u & 0x7FFFFFFF;
54
55    // |x| > 126
56    if (ix > 0x42FC0000) {
57        // nan
58        if (ix > 0x7F800000) {
59            return x;
60        }
61        // x >= 128
62        if (u >= 0x43000000 and u < 0x80000000) {
63            return x * 0x1.0p127;
64        }
65        // x < -126
66        if (u >= 0x80000000) {
67            if (u >= 0xC3160000 or u & 0x000FFFF != 0) {
68                math.doNotOptimizeAway(-0x1.0p-149 / x);
69            }
70            // x <= -150
71            if (u >= 0x3160000) {
72                return 0;
73            }
74        }
75    }
76    // |x| <= 0x1p-25
77    else if (ix <= 0x33000000) {
78        return 1.0 + x;
79    }
80
81    // NOTE: musl relies on unsafe behaviours which are replicated below
82    // (addition/bit-shift overflow). Appears that this produces the
83    // intended result but should confirm how GCC/Clang handle this to ensure.
84
85    var uf = x + redux;
86    var i_0 = @bitCast(u32, uf);
87    i_0 +%= tblsiz / 2;
88
89    const k = i_0 / tblsiz;
90    const uk = @bitCast(f64, @as(u64, 0x3FF + k) << 52);
91    i_0 &= tblsiz - 1;
92    uf -= redux;
93
94    const z: f64 = x - uf;
95    var r: f64 = exp2ft[@intCast(usize, i_0)];
96    const t: f64 = r * z;
97    r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4);
98    return @floatCast(f32, r * uk);
99}
100
101const exp2dt = [_]f64{
102    //  exp2(z + eps)          eps
103    0x1.6a09e667f3d5dp-1, 0x1.9880p-44,
104    0x1.6b052fa751744p-1, 0x1.8000p-50,
105    0x1.6c012750bd9fep-1, -0x1.8780p-45,
106    0x1.6cfdcddd476bfp-1, 0x1.ec00p-46,
107    0x1.6dfb23c651a29p-1, -0x1.8000p-50,
108    0x1.6ef9298593ae3p-1, -0x1.c000p-52,
109    0x1.6ff7df9519386p-1, -0x1.fd80p-45,
110    0x1.70f7466f42da3p-1, -0x1.c880p-45,
111    0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46,
112    0x1.72f8286eacf05p-1, -0x1.8300p-44,
113    0x1.73f9a48a58152p-1, -0x1.0c00p-47,
114    0x1.74fbd35d7ccfcp-1, 0x1.f880p-45,
115    0x1.75feb564267f1p-1, 0x1.3e00p-47,
116    0x1.77024b1ab6d48p-1, -0x1.7d00p-45,
117    0x1.780694fde5d38p-1, -0x1.d000p-50,
118    0x1.790b938ac1d00p-1, 0x1.3000p-49,
119    0x1.7a11473eb0178p-1, -0x1.d000p-49,
120    0x1.7b17b0976d060p-1, 0x1.0400p-45,
121    0x1.7c1ed0130c133p-1, 0x1.0000p-53,
122    0x1.7d26a62ff8636p-1, -0x1.6900p-45,
123    0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47,
124    0x1.7f3878491c3e8p-1, -0x1.4580p-45,
125    0x1.80427543e1b4ep-1, 0x1.3000p-44,
126    0x1.814d2add1071ap-1, 0x1.f000p-47,
127    0x1.82589994ccd7ep-1, -0x1.1c00p-45,
128    0x1.8364c1eb942d0p-1, 0x1.9d00p-45,
129    0x1.8471a4623cab5p-1, 0x1.7100p-43,
130    0x1.857f4179f5bbcp-1, 0x1.2600p-45,
131    0x1.868d99b4491afp-1, -0x1.2c40p-44,
132    0x1.879cad931a395p-1, -0x1.3000p-45,
133    0x1.88ac7d98a65b8p-1, -0x1.a800p-45,
134    0x1.89bd0a4785800p-1, -0x1.d000p-49,
135    0x1.8ace5422aa223p-1, 0x1.3280p-44,
136    0x1.8be05bad619fap-1, 0x1.2b40p-43,
137    0x1.8cf3216b54383p-1, -0x1.ed00p-45,
138    0x1.8e06a5e08664cp-1, -0x1.0500p-45,
139    0x1.8f1ae99157807p-1, 0x1.8280p-45,
140    0x1.902fed0282c0ep-1, -0x1.cb00p-46,
141    0x1.9145b0b91ff96p-1, -0x1.5e00p-47,
142    0x1.925c353aa2ff9p-1, 0x1.5400p-48,
143    0x1.93737b0cdc64ap-1, 0x1.7200p-46,
144    0x1.948b82b5f98aep-1, -0x1.9000p-47,
145    0x1.95a44cbc852cbp-1, 0x1.5680p-45,
146    0x1.96bdd9a766f21p-1, -0x1.6d00p-44,
147    0x1.97d829fde4e2ap-1, -0x1.1000p-47,
148    0x1.98f33e47a23a3p-1, 0x1.d000p-45,
149    0x1.9a0f170ca0604p-1, -0x1.8a40p-44,
150    0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44,
151    0x1.9c49182a3f15bp-1, 0x1.6b80p-45,
152    0x1.9d674194bb8c5p-1, -0x1.c000p-49,
153    0x1.9e86319e3238ep-1, 0x1.7d00p-46,
154    0x1.9fa5e8d07f302p-1, 0x1.6400p-46,
155    0x1.a0c667b5de54dp-1, -0x1.5000p-48,
156    0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47,
157    0x1.a309bec4a2e27p-1, 0x1.ad80p-45,
158    0x1.a42c980460a5dp-1, -0x1.af00p-46,
159    0x1.a5503b23e259bp-1, 0x1.b600p-47,
160    0x1.a674a8af46213p-1, 0x1.8880p-44,
161    0x1.a799e1330b3a7p-1, 0x1.1200p-46,
162    0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47,
163    0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45,
164    0x1.ab0e521356fb8p-1, 0x1.b700p-45,
165    0x1.ac36bbfd3f381p-1, 0x1.9000p-50,
166    0x1.ad5ff3a3c2780p-1, 0x1.4000p-49,
167    0x1.ae89f995ad2a3p-1, -0x1.c900p-45,
168    0x1.afb4ce622f367p-1, 0x1.6500p-46,
169    0x1.b0e07298db790p-1, 0x1.fd40p-45,
170    0x1.b20ce6c9a89a9p-1, 0x1.2700p-46,
171    0x1.b33a2b84f1a4bp-1, 0x1.d470p-43,
172    0x1.b468415b747e7p-1, -0x1.8380p-44,
173    0x1.b59728de5593ap-1, 0x1.8000p-54,
174    0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47,
175    0x1.b7f76f2fb5e50p-1, 0x1.e800p-50,
176    0x1.b928cf22749b2p-1, -0x1.4c00p-47,
177    0x1.ba5b030a10603p-1, -0x1.d700p-47,
178    0x1.bb8e0b79a6f66p-1, 0x1.d900p-47,
179    0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47,
180    0x1.bdf69c3f3a16fp-1, -0x1.f780p-46,
181    0x1.bf2c25bd71db8p-1, -0x1.0a00p-46,
182    0x1.c06286141b2e9p-1, -0x1.1400p-46,
183    0x1.c199bdd8552e0p-1, 0x1.be00p-47,
184    0x1.c2d1cd9fa64eep-1, -0x1.9400p-47,
185    0x1.c40ab5fffd02fp-1, -0x1.ed00p-47,
186    0x1.c544778fafd15p-1, 0x1.9660p-44,
187    0x1.c67f12e57d0cbp-1, -0x1.a100p-46,
188    0x1.c7ba88988c1b6p-1, -0x1.8458p-42,
189    0x1.c8f6d9406e733p-1, -0x1.a480p-46,
190    0x1.ca3405751c4dfp-1, 0x1.b000p-51,
191    0x1.cb720dcef9094p-1, 0x1.1400p-47,
192    0x1.ccb0f2e6d1689p-1, 0x1.0200p-48,
193    0x1.cdf0b555dc412p-1, 0x1.3600p-48,
194    0x1.cf3155b5bab3bp-1, -0x1.6900p-47,
195    0x1.d072d4a0789bcp-1, 0x1.9a00p-47,
196    0x1.d1b532b08c8fap-1, -0x1.5e00p-46,
197    0x1.d2f87080d8a85p-1, 0x1.d280p-46,
198    0x1.d43c8eacaa203p-1, 0x1.1a00p-47,
199    0x1.d5818dcfba491p-1, 0x1.f000p-50,
200    0x1.d6c76e862e6a1p-1, -0x1.3a00p-47,
201    0x1.d80e316c9834ep-1, -0x1.cd80p-47,
202    0x1.d955d71ff6090p-1, 0x1.4c00p-48,
203    0x1.da9e603db32aep-1, 0x1.f900p-48,
204    0x1.dbe7cd63a8325p-1, 0x1.9800p-49,
205    0x1.dd321f301b445p-1, -0x1.5200p-48,
206    0x1.de7d5641c05bfp-1, -0x1.d700p-46,
207    0x1.dfc97337b9aecp-1, -0x1.6140p-46,
208    0x1.e11676b197d5ep-1, 0x1.b480p-47,
209    0x1.e264614f5a3e7p-1, 0x1.0ce0p-43,
210    0x1.e3b333b16ee5cp-1, 0x1.c680p-47,
211    0x1.e502ee78b3fb4p-1, -0x1.9300p-47,
212    0x1.e653924676d68p-1, -0x1.5000p-49,
213    0x1.e7a51fbc74c44p-1, -0x1.7f80p-47,
214    0x1.e8f7977cdb726p-1, -0x1.3700p-48,
215    0x1.ea4afa2a490e8p-1, 0x1.5d00p-49,
216    0x1.eb9f4867ccae4p-1, 0x1.61a0p-46,
217    0x1.ecf482d8e680dp-1, 0x1.5500p-48,
218    0x1.ee4aaa2188514p-1, 0x1.6400p-51,
219    0x1.efa1bee615a13p-1, -0x1.e800p-49,
220    0x1.f0f9c1cb64106p-1, -0x1.a880p-48,
221    0x1.f252b376bb963p-1, -0x1.c900p-45,
222    0x1.f3ac948dd7275p-1, 0x1.a000p-53,
223    0x1.f50765b6e4524p-1, -0x1.4f00p-48,
224    0x1.f6632798844fdp-1, 0x1.a800p-51,
225    0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48,
226    0x1.f91d802243c82p-1, -0x1.4600p-50,
227    0x1.fa7c1819e908ep-1, -0x1.b0c0p-47,
228    0x1.fbdba3692d511p-1, -0x1.0e00p-51,
229    0x1.fd3c22b8f7194p-1, -0x1.0de8p-46,
230    0x1.fe9d96b2a23eep-1, 0x1.e430p-49,
231    0x1.0000000000000p+0, 0x0.0000p+0,
232    0x1.00b1afa5abcbep+0, -0x1.3400p-52,
233    0x1.0163da9fb3303p+0, -0x1.2170p-46,
234    0x1.02168143b0282p+0, 0x1.a400p-52,
235    0x1.02c9a3e77806cp+0, 0x1.f980p-49,
236    0x1.037d42e11bbcap+0, -0x1.7400p-51,
237    0x1.04315e86e7f89p+0, 0x1.8300p-50,
238    0x1.04e5f72f65467p+0, -0x1.a3f0p-46,
239    0x1.059b0d315855ap+0, -0x1.2840p-47,
240    0x1.0650a0e3c1f95p+0, 0x1.1600p-48,
241    0x1.0706b29ddf71ap+0, 0x1.5240p-46,
242    0x1.07bd42b72a82dp+0, -0x1.9a00p-49,
243    0x1.0874518759bd0p+0, 0x1.6400p-49,
244    0x1.092bdf66607c8p+0, -0x1.0780p-47,
245    0x1.09e3ecac6f383p+0, -0x1.8000p-54,
246    0x1.0a9c79b1f3930p+0, 0x1.fa00p-48,
247    0x1.0b5586cf988fcp+0, -0x1.ac80p-48,
248    0x1.0c0f145e46c8ap+0, 0x1.9c00p-50,
249    0x1.0cc922b724816p+0, 0x1.5200p-47,
250    0x1.0d83b23395dd8p+0, -0x1.ad00p-48,
251    0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46,
252    0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47,
253    0x1.0fb66affed2f0p+0, -0x1.d300p-47,
254    0x1.1073028d7234bp+0, 0x1.1500p-48,
255    0x1.11301d0125b5bp+0, 0x1.c000p-49,
256    0x1.11edbab5e2af9p+0, 0x1.6bc0p-46,
257    0x1.12abdc06c31d5p+0, 0x1.8400p-49,
258    0x1.136a814f2047dp+0, -0x1.ed00p-47,
259    0x1.1429aaea92de9p+0, 0x1.8e00p-49,
260    0x1.14e95934f3138p+0, 0x1.b400p-49,
261    0x1.15a98c8a58e71p+0, 0x1.5300p-47,
262    0x1.166a45471c3dfp+0, 0x1.3380p-47,
263    0x1.172b83c7d5211p+0, 0x1.8d40p-45,
264    0x1.17ed48695bb9fp+0, -0x1.5d00p-47,
265    0x1.18af9388c8d93p+0, -0x1.c880p-46,
266    0x1.1972658375d66p+0, 0x1.1f00p-46,
267    0x1.1a35beb6fcba7p+0, 0x1.0480p-46,
268    0x1.1af99f81387e3p+0, -0x1.7390p-43,
269    0x1.1bbe084045d54p+0, 0x1.4e40p-45,
270    0x1.1c82f95281c43p+0, -0x1.a200p-47,
271    0x1.1d4873168b9b2p+0, 0x1.3800p-49,
272    0x1.1e0e75eb44031p+0, 0x1.ac00p-49,
273    0x1.1ed5022fcd938p+0, 0x1.1900p-47,
274    0x1.1f9c18438cdf7p+0, -0x1.b780p-46,
275    0x1.2063b88628d8fp+0, 0x1.d940p-45,
276    0x1.212be3578a81ep+0, 0x1.8000p-50,
277    0x1.21f49917ddd41p+0, 0x1.b340p-45,
278    0x1.22bdda2791323p+0, 0x1.9f80p-46,
279    0x1.2387a6e7561e7p+0, -0x1.9c80p-46,
280    0x1.2451ffb821427p+0, 0x1.2300p-47,
281    0x1.251ce4fb2a602p+0, -0x1.3480p-46,
282    0x1.25e85711eceb0p+0, 0x1.2700p-46,
283    0x1.26b4565e27d16p+0, 0x1.1d00p-46,
284    0x1.2780e341de00fp+0, 0x1.1ee0p-44,
285    0x1.284dfe1f5633ep+0, -0x1.4c00p-46,
286    0x1.291ba7591bb30p+0, -0x1.3d80p-46,
287    0x1.29e9df51fdf09p+0, 0x1.8b00p-47,
288    0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45,
289    0x1.2b87fd0dada3ap+0, 0x1.a340p-45,
290    0x1.2c57e39771af9p+0, -0x1.0800p-46,
291    0x1.2d285a6e402d9p+0, -0x1.ed00p-47,
292    0x1.2df961f641579p+0, -0x1.4200p-48,
293    0x1.2ecafa93e2ecfp+0, -0x1.4980p-45,
294    0x1.2f9d24abd8822p+0, -0x1.6300p-46,
295    0x1.306fe0a31b625p+0, -0x1.2360p-44,
296    0x1.31432edeea50bp+0, -0x1.0df8p-40,
297    0x1.32170fc4cd7b8p+0, -0x1.2480p-45,
298    0x1.32eb83ba8e9a2p+0, -0x1.5980p-45,
299    0x1.33c08b2641766p+0, 0x1.ed00p-46,
300    0x1.3496266e3fa27p+0, -0x1.c000p-50,
301    0x1.356c55f929f0fp+0, -0x1.0d80p-44,
302    0x1.36431a2de88b9p+0, 0x1.2c80p-45,
303    0x1.371a7373aaa39p+0, 0x1.0600p-45,
304    0x1.37f26231e74fep+0, -0x1.6600p-46,
305    0x1.38cae6d05d838p+0, -0x1.ae00p-47,
306    0x1.39a401b713ec3p+0, -0x1.4720p-43,
307    0x1.3a7db34e5a020p+0, 0x1.8200p-47,
308    0x1.3b57fbfec6e95p+0, 0x1.e800p-44,
309    0x1.3c32dc313a8f2p+0, 0x1.f800p-49,
310    0x1.3d0e544ede122p+0, -0x1.7a00p-46,
311    0x1.3dea64c1234bbp+0, 0x1.6300p-45,
312    0x1.3ec70df1c4eccp+0, -0x1.8a60p-43,
313    0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44,
314    0x1.40822c367a0bbp+0, 0x1.5b80p-45,
315    0x1.4160a21f72e95p+0, 0x1.ec00p-46,
316    0x1.423fb27094646p+0, -0x1.3600p-46,
317    0x1.431f5d950a920p+0, 0x1.3980p-45,
318    0x1.43ffa3f84b9ebp+0, 0x1.a000p-48,
319    0x1.44e0860618919p+0, -0x1.6c00p-48,
320    0x1.45c2042a7d201p+0, -0x1.bc00p-47,
321    0x1.46a41ed1d0016p+0, -0x1.2800p-46,
322    0x1.4786d668b3326p+0, 0x1.0e00p-44,
323    0x1.486a2b5c13c00p+0, -0x1.d400p-45,
324    0x1.494e1e192af04p+0, 0x1.c200p-47,
325    0x1.4a32af0d7d372p+0, -0x1.e500p-46,
326    0x1.4b17dea6db801p+0, 0x1.7800p-47,
327    0x1.4bfdad53629e1p+0, -0x1.3800p-46,
328    0x1.4ce41b817c132p+0, 0x1.0800p-47,
329    0x1.4dcb299fddddbp+0, 0x1.c700p-45,
330    0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46,
331    0x1.4f9b2769d2d02p+0, 0x1.9200p-46,
332    0x1.508417f4531c1p+0, -0x1.8c00p-47,
333    0x1.516daa2cf662ap+0, -0x1.a000p-48,
334    0x1.5257de83f51eap+0, 0x1.a080p-43,
335    0x1.5342b569d4edap+0, -0x1.6d80p-45,
336    0x1.542e2f4f6ac1ap+0, -0x1.2440p-44,
337    0x1.551a4ca5d94dbp+0, 0x1.83c0p-43,
338    0x1.56070dde9116bp+0, 0x1.4b00p-45,
339    0x1.56f4736b529dep+0, 0x1.15a0p-43,
340    0x1.57e27dbe2c40ep+0, -0x1.9e00p-45,
341    0x1.58d12d497c76fp+0, -0x1.3080p-45,
342    0x1.59c0827ff0b4cp+0, 0x1.dec0p-43,
343    0x1.5ab07dd485427p+0, -0x1.4000p-51,
344    0x1.5ba11fba87af4p+0, 0x1.0080p-44,
345    0x1.5c9268a59460bp+0, -0x1.6c80p-45,
346    0x1.5d84590998e3fp+0, 0x1.69a0p-43,
347    0x1.5e76f15ad20e1p+0, -0x1.b400p-46,
348    0x1.5f6a320dcebcap+0, 0x1.7700p-46,
349    0x1.605e1b976dcb8p+0, 0x1.6f80p-45,
350    0x1.6152ae6cdf715p+0, 0x1.1000p-47,
351    0x1.6247eb03a5531p+0, -0x1.5d00p-46,
352    0x1.633dd1d1929b5p+0, -0x1.2d00p-46,
353    0x1.6434634ccc313p+0, -0x1.a800p-49,
354    0x1.652b9febc8efap+0, -0x1.8600p-45,
355    0x1.6623882553397p+0, 0x1.1fe0p-40,
356    0x1.671c1c708328ep+0, -0x1.7200p-44,
357    0x1.68155d44ca97ep+0, 0x1.6800p-49,
358    0x1.690f4b19e9471p+0, -0x1.9780p-45,
359};
360
361fn exp2_64(x: f64) f64 {
362    const tblsiz: u32 = @intCast(u32, exp2dt.len / 2);
363    const redux: f64 = 0x1.8p52 / @intToFloat(f64, tblsiz);
364    const P1: f64 = 0x1.62e42fefa39efp-1;
365    const P2: f64 = 0x1.ebfbdff82c575p-3;
366    const P3: f64 = 0x1.c6b08d704a0a6p-5;
367    const P4: f64 = 0x1.3b2ab88f70400p-7;
368    const P5: f64 = 0x1.5d88003875c74p-10;
369
370    const ux = @bitCast(u64, x);
371    const ix = @intCast(u32, ux >> 32) & 0x7FFFFFFF;
372
373    // TODO: This should be handled beneath.
374    if (math.isNan(x)) {
375        return math.nan(f64);
376    }
377
378    // |x| >= 1022 or nan
379    if (ix >= 0x408FF000) {
380        // x >= 1024 or nan
381        if (ix >= 0x40900000 and ux >> 63 == 0) {
382            math.raiseOverflow();
383            return math.inf(f64);
384        }
385        // -inf or -nan
386        if (ix >= 0x7FF00000) {
387            return -1 / x;
388        }
389        // x <= -1022
390        if (ux >> 63 != 0) {
391            // underflow
392            if (x <= -1075 or x - 0x1.0p52 + 0x1.0p52 != x) {
393                math.doNotOptimizeAway(@floatCast(f32, -0x1.0p-149 / x));
394            }
395            if (x <= -1075) {
396                return 0;
397            }
398        }
399    }
400    // |x| < 0x1p-54
401    else if (ix < 0x3C900000) {
402        return 1.0 + x;
403    }
404
405    // NOTE: musl relies on unsafe behaviours which are replicated below
406    // (addition overflow, division truncation, casting). Appears that this
407    // produces the intended result but should confirm how GCC/Clang handle this
408    // to ensure.
409
410    // reduce x
411    var uf: f64 = x + redux;
412    // NOTE: musl performs an implicit 64-bit to 32-bit u32 truncation here
413    var i_0: u32 = @truncate(u32, @bitCast(u64, uf));
414    i_0 +%= tblsiz / 2;
415
416    const k: u32 = i_0 / tblsiz * tblsiz;
417    const ik: i32 = @divTrunc(@bitCast(i32, k), tblsiz);
418    i_0 %= tblsiz;
419    uf -= redux;
420
421    // r = exp2(y) = exp2t[i_0] * p(z - eps[i])
422    var z: f64 = x - uf;
423    const t: f64 = exp2dt[@intCast(usize, 2 * i_0)];
424    z -= exp2dt[@intCast(usize, 2 * i_0 + 1)];
425    const r: f64 = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
426
427    return math.scalbn(r, ik);
428}
429
430test "math.exp2" {
431    try expect(exp2(@as(f32, 0.8923)) == exp2_32(0.8923));
432    try expect(exp2(@as(f64, 0.8923)) == exp2_64(0.8923));
433}
434
435test "math.exp2_32" {
436    const epsilon = 0.000001;
437
438    try expect(exp2_32(0.0) == 1.0);
439    try expect(math.approxEqAbs(f32, exp2_32(0.2), 1.148698, epsilon));
440    try expect(math.approxEqAbs(f32, exp2_32(0.8923), 1.856133, epsilon));
441    try expect(math.approxEqAbs(f32, exp2_32(1.5), 2.828427, epsilon));
442    try expect(math.approxEqAbs(f32, exp2_32(37.45), 187747237888, epsilon));
443    try expect(math.approxEqAbs(f32, exp2_32(-1), 0.5, epsilon));
444}
445
446test "math.exp2_64" {
447    const epsilon = 0.000001;
448
449    try expect(exp2_64(0.0) == 1.0);
450    try expect(math.approxEqAbs(f64, exp2_64(0.2), 1.148698, epsilon));
451    try expect(math.approxEqAbs(f64, exp2_64(0.8923), 1.856133, epsilon));
452    try expect(math.approxEqAbs(f64, exp2_64(1.5), 2.828427, epsilon));
453    try expect(math.approxEqAbs(f64, exp2_64(-1), 0.5, epsilon));
454    try expect(math.approxEqAbs(f64, exp2_64(-0x1.a05cc754481d1p-2), 0x1.824056efc687cp-1, epsilon));
455}
456
457test "math.exp2_32.special" {
458    try expect(math.isPositiveInf(exp2_32(math.inf(f32))));
459    try expect(math.isNan(exp2_32(math.nan(f32))));
460}
461
462test "math.exp2_64.special" {
463    try expect(math.isPositiveInf(exp2_64(math.inf(f64))));
464    try expect(math.isNan(exp2_64(math.nan(f64))));
465}
466