summaryrefslogtreecommitdiffstats
path: root/third_party/rust/libm/src/math/exp2.rs
diff options
context:
space:
mode:
authorDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-19 00:47:55 +0000
committerDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-19 00:47:55 +0000
commit26a029d407be480d791972afb5975cf62c9360a6 (patch)
treef435a8308119effd964b339f76abb83a57c29483 /third_party/rust/libm/src/math/exp2.rs
parentInitial commit. (diff)
downloadfirefox-26a029d407be480d791972afb5975cf62c9360a6.tar.xz
firefox-26a029d407be480d791972afb5975cf62c9360a6.zip
Adding upstream version 124.0.1.upstream/124.0.1
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'third_party/rust/libm/src/math/exp2.rs')
-rw-r--r--third_party/rust/libm/src/math/exp2.rs394
1 files changed, 394 insertions, 0 deletions
diff --git a/third_party/rust/libm/src/math/exp2.rs b/third_party/rust/libm/src/math/exp2.rs
new file mode 100644
index 0000000000..e0e385df2e
--- /dev/null
+++ b/third_party/rust/libm/src/math/exp2.rs
@@ -0,0 +1,394 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_exp2.c */
+//-
+// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions
+// are met:
+// 1. Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+// 2. Redistributions in binary form must reproduce the above copyright
+// notice, this list of conditions and the following disclaimer in the
+// documentation and/or other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+// SUCH DAMAGE.
+
+use super::scalbn;
+
+const TBLSIZE: usize = 256;
+
+#[cfg_attr(rustfmt, rustfmt_skip)]
+static TBL: [u64; TBLSIZE * 2] = [
+ // exp2(z + eps) eps
+ 0x3fe6a09e667f3d5d, 0x3d39880000000000,
+ 0x3fe6b052fa751744, 0x3cd8000000000000,
+ 0x3fe6c012750bd9fe, 0xbd28780000000000,
+ 0x3fe6cfdcddd476bf, 0x3d1ec00000000000,
+ 0x3fe6dfb23c651a29, 0xbcd8000000000000,
+ 0x3fe6ef9298593ae3, 0xbcbc000000000000,
+ 0x3fe6ff7df9519386, 0xbd2fd80000000000,
+ 0x3fe70f7466f42da3, 0xbd2c880000000000,
+ 0x3fe71f75e8ec5fc3, 0x3d13c00000000000,
+ 0x3fe72f8286eacf05, 0xbd38300000000000,
+ 0x3fe73f9a48a58152, 0xbd00c00000000000,
+ 0x3fe74fbd35d7ccfc, 0x3d2f880000000000,
+ 0x3fe75feb564267f1, 0x3d03e00000000000,
+ 0x3fe77024b1ab6d48, 0xbd27d00000000000,
+ 0x3fe780694fde5d38, 0xbcdd000000000000,
+ 0x3fe790b938ac1d00, 0x3ce3000000000000,
+ 0x3fe7a11473eb0178, 0xbced000000000000,
+ 0x3fe7b17b0976d060, 0x3d20400000000000,
+ 0x3fe7c1ed0130c133, 0x3ca0000000000000,
+ 0x3fe7d26a62ff8636, 0xbd26900000000000,
+ 0x3fe7e2f336cf4e3b, 0xbd02e00000000000,
+ 0x3fe7f3878491c3e8, 0xbd24580000000000,
+ 0x3fe80427543e1b4e, 0x3d33000000000000,
+ 0x3fe814d2add1071a, 0x3d0f000000000000,
+ 0x3fe82589994ccd7e, 0xbd21c00000000000,
+ 0x3fe8364c1eb942d0, 0x3d29d00000000000,
+ 0x3fe8471a4623cab5, 0x3d47100000000000,
+ 0x3fe857f4179f5bbc, 0x3d22600000000000,
+ 0x3fe868d99b4491af, 0xbd32c40000000000,
+ 0x3fe879cad931a395, 0xbd23000000000000,
+ 0x3fe88ac7d98a65b8, 0xbd2a800000000000,
+ 0x3fe89bd0a4785800, 0xbced000000000000,
+ 0x3fe8ace5422aa223, 0x3d33280000000000,
+ 0x3fe8be05bad619fa, 0x3d42b40000000000,
+ 0x3fe8cf3216b54383, 0xbd2ed00000000000,
+ 0x3fe8e06a5e08664c, 0xbd20500000000000,
+ 0x3fe8f1ae99157807, 0x3d28280000000000,
+ 0x3fe902fed0282c0e, 0xbd1cb00000000000,
+ 0x3fe9145b0b91ff96, 0xbd05e00000000000,
+ 0x3fe925c353aa2ff9, 0x3cf5400000000000,
+ 0x3fe93737b0cdc64a, 0x3d17200000000000,
+ 0x3fe948b82b5f98ae, 0xbd09000000000000,
+ 0x3fe95a44cbc852cb, 0x3d25680000000000,
+ 0x3fe96bdd9a766f21, 0xbd36d00000000000,
+ 0x3fe97d829fde4e2a, 0xbd01000000000000,
+ 0x3fe98f33e47a23a3, 0x3d2d000000000000,
+ 0x3fe9a0f170ca0604, 0xbd38a40000000000,
+ 0x3fe9b2bb4d53ff89, 0x3d355c0000000000,
+ 0x3fe9c49182a3f15b, 0x3d26b80000000000,
+ 0x3fe9d674194bb8c5, 0xbcec000000000000,
+ 0x3fe9e86319e3238e, 0x3d17d00000000000,
+ 0x3fe9fa5e8d07f302, 0x3d16400000000000,
+ 0x3fea0c667b5de54d, 0xbcf5000000000000,
+ 0x3fea1e7aed8eb8f6, 0x3d09e00000000000,
+ 0x3fea309bec4a2e27, 0x3d2ad80000000000,
+ 0x3fea42c980460a5d, 0xbd1af00000000000,
+ 0x3fea5503b23e259b, 0x3d0b600000000000,
+ 0x3fea674a8af46213, 0x3d38880000000000,
+ 0x3fea799e1330b3a7, 0x3d11200000000000,
+ 0x3fea8bfe53c12e8d, 0x3d06c00000000000,
+ 0x3fea9e6b5579fcd2, 0xbd29b80000000000,
+ 0x3feab0e521356fb8, 0x3d2b700000000000,
+ 0x3feac36bbfd3f381, 0x3cd9000000000000,
+ 0x3fead5ff3a3c2780, 0x3ce4000000000000,
+ 0x3feae89f995ad2a3, 0xbd2c900000000000,
+ 0x3feafb4ce622f367, 0x3d16500000000000,
+ 0x3feb0e07298db790, 0x3d2fd40000000000,
+ 0x3feb20ce6c9a89a9, 0x3d12700000000000,
+ 0x3feb33a2b84f1a4b, 0x3d4d470000000000,
+ 0x3feb468415b747e7, 0xbd38380000000000,
+ 0x3feb59728de5593a, 0x3c98000000000000,
+ 0x3feb6c6e29f1c56a, 0x3d0ad00000000000,
+ 0x3feb7f76f2fb5e50, 0x3cde800000000000,
+ 0x3feb928cf22749b2, 0xbd04c00000000000,
+ 0x3feba5b030a10603, 0xbd0d700000000000,
+ 0x3febb8e0b79a6f66, 0x3d0d900000000000,
+ 0x3febcc1e904bc1ff, 0x3d02a00000000000,
+ 0x3febdf69c3f3a16f, 0xbd1f780000000000,
+ 0x3febf2c25bd71db8, 0xbd10a00000000000,
+ 0x3fec06286141b2e9, 0xbd11400000000000,
+ 0x3fec199bdd8552e0, 0x3d0be00000000000,
+ 0x3fec2d1cd9fa64ee, 0xbd09400000000000,
+ 0x3fec40ab5fffd02f, 0xbd0ed00000000000,
+ 0x3fec544778fafd15, 0x3d39660000000000,
+ 0x3fec67f12e57d0cb, 0xbd1a100000000000,
+ 0x3fec7ba88988c1b6, 0xbd58458000000000,
+ 0x3fec8f6d9406e733, 0xbd1a480000000000,
+ 0x3feca3405751c4df, 0x3ccb000000000000,
+ 0x3fecb720dcef9094, 0x3d01400000000000,
+ 0x3feccb0f2e6d1689, 0x3cf0200000000000,
+ 0x3fecdf0b555dc412, 0x3cf3600000000000,
+ 0x3fecf3155b5bab3b, 0xbd06900000000000,
+ 0x3fed072d4a0789bc, 0x3d09a00000000000,
+ 0x3fed1b532b08c8fa, 0xbd15e00000000000,
+ 0x3fed2f87080d8a85, 0x3d1d280000000000,
+ 0x3fed43c8eacaa203, 0x3d01a00000000000,
+ 0x3fed5818dcfba491, 0x3cdf000000000000,
+ 0x3fed6c76e862e6a1, 0xbd03a00000000000,
+ 0x3fed80e316c9834e, 0xbd0cd80000000000,
+ 0x3fed955d71ff6090, 0x3cf4c00000000000,
+ 0x3feda9e603db32ae, 0x3cff900000000000,
+ 0x3fedbe7cd63a8325, 0x3ce9800000000000,
+ 0x3fedd321f301b445, 0xbcf5200000000000,
+ 0x3fede7d5641c05bf, 0xbd1d700000000000,
+ 0x3fedfc97337b9aec, 0xbd16140000000000,
+ 0x3fee11676b197d5e, 0x3d0b480000000000,
+ 0x3fee264614f5a3e7, 0x3d40ce0000000000,
+ 0x3fee3b333b16ee5c, 0x3d0c680000000000,
+ 0x3fee502ee78b3fb4, 0xbd09300000000000,
+ 0x3fee653924676d68, 0xbce5000000000000,
+ 0x3fee7a51fbc74c44, 0xbd07f80000000000,
+ 0x3fee8f7977cdb726, 0xbcf3700000000000,
+ 0x3feea4afa2a490e8, 0x3ce5d00000000000,
+ 0x3feeb9f4867ccae4, 0x3d161a0000000000,
+ 0x3feecf482d8e680d, 0x3cf5500000000000,
+ 0x3feee4aaa2188514, 0x3cc6400000000000,
+ 0x3feefa1bee615a13, 0xbcee800000000000,
+ 0x3fef0f9c1cb64106, 0xbcfa880000000000,
+ 0x3fef252b376bb963, 0xbd2c900000000000,
+ 0x3fef3ac948dd7275, 0x3caa000000000000,
+ 0x3fef50765b6e4524, 0xbcf4f00000000000,
+ 0x3fef6632798844fd, 0x3cca800000000000,
+ 0x3fef7bfdad9cbe38, 0x3cfabc0000000000,
+ 0x3fef91d802243c82, 0xbcd4600000000000,
+ 0x3fefa7c1819e908e, 0xbd0b0c0000000000,
+ 0x3fefbdba3692d511, 0xbcc0e00000000000,
+ 0x3fefd3c22b8f7194, 0xbd10de8000000000,
+ 0x3fefe9d96b2a23ee, 0x3cee430000000000,
+ 0x3ff0000000000000, 0x0,
+ 0x3ff00b1afa5abcbe, 0xbcb3400000000000,
+ 0x3ff0163da9fb3303, 0xbd12170000000000,
+ 0x3ff02168143b0282, 0x3cba400000000000,
+ 0x3ff02c9a3e77806c, 0x3cef980000000000,
+ 0x3ff037d42e11bbca, 0xbcc7400000000000,
+ 0x3ff04315e86e7f89, 0x3cd8300000000000,
+ 0x3ff04e5f72f65467, 0xbd1a3f0000000000,
+ 0x3ff059b0d315855a, 0xbd02840000000000,
+ 0x3ff0650a0e3c1f95, 0x3cf1600000000000,
+ 0x3ff0706b29ddf71a, 0x3d15240000000000,
+ 0x3ff07bd42b72a82d, 0xbce9a00000000000,
+ 0x3ff0874518759bd0, 0x3ce6400000000000,
+ 0x3ff092bdf66607c8, 0xbd00780000000000,
+ 0x3ff09e3ecac6f383, 0xbc98000000000000,
+ 0x3ff0a9c79b1f3930, 0x3cffa00000000000,
+ 0x3ff0b5586cf988fc, 0xbcfac80000000000,
+ 0x3ff0c0f145e46c8a, 0x3cd9c00000000000,
+ 0x3ff0cc922b724816, 0x3d05200000000000,
+ 0x3ff0d83b23395dd8, 0xbcfad00000000000,
+ 0x3ff0e3ec32d3d1f3, 0x3d1bac0000000000,
+ 0x3ff0efa55fdfa9a6, 0xbd04e80000000000,
+ 0x3ff0fb66affed2f0, 0xbd0d300000000000,
+ 0x3ff1073028d7234b, 0x3cf1500000000000,
+ 0x3ff11301d0125b5b, 0x3cec000000000000,
+ 0x3ff11edbab5e2af9, 0x3d16bc0000000000,
+ 0x3ff12abdc06c31d5, 0x3ce8400000000000,
+ 0x3ff136a814f2047d, 0xbd0ed00000000000,
+ 0x3ff1429aaea92de9, 0x3ce8e00000000000,
+ 0x3ff14e95934f3138, 0x3ceb400000000000,
+ 0x3ff15a98c8a58e71, 0x3d05300000000000,
+ 0x3ff166a45471c3df, 0x3d03380000000000,
+ 0x3ff172b83c7d5211, 0x3d28d40000000000,
+ 0x3ff17ed48695bb9f, 0xbd05d00000000000,
+ 0x3ff18af9388c8d93, 0xbd1c880000000000,
+ 0x3ff1972658375d66, 0x3d11f00000000000,
+ 0x3ff1a35beb6fcba7, 0x3d10480000000000,
+ 0x3ff1af99f81387e3, 0xbd47390000000000,
+ 0x3ff1bbe084045d54, 0x3d24e40000000000,
+ 0x3ff1c82f95281c43, 0xbd0a200000000000,
+ 0x3ff1d4873168b9b2, 0x3ce3800000000000,
+ 0x3ff1e0e75eb44031, 0x3ceac00000000000,
+ 0x3ff1ed5022fcd938, 0x3d01900000000000,
+ 0x3ff1f9c18438cdf7, 0xbd1b780000000000,
+ 0x3ff2063b88628d8f, 0x3d2d940000000000,
+ 0x3ff212be3578a81e, 0x3cd8000000000000,
+ 0x3ff21f49917ddd41, 0x3d2b340000000000,
+ 0x3ff22bdda2791323, 0x3d19f80000000000,
+ 0x3ff2387a6e7561e7, 0xbd19c80000000000,
+ 0x3ff2451ffb821427, 0x3d02300000000000,
+ 0x3ff251ce4fb2a602, 0xbd13480000000000,
+ 0x3ff25e85711eceb0, 0x3d12700000000000,
+ 0x3ff26b4565e27d16, 0x3d11d00000000000,
+ 0x3ff2780e341de00f, 0x3d31ee0000000000,
+ 0x3ff284dfe1f5633e, 0xbd14c00000000000,
+ 0x3ff291ba7591bb30, 0xbd13d80000000000,
+ 0x3ff29e9df51fdf09, 0x3d08b00000000000,
+ 0x3ff2ab8a66d10e9b, 0xbd227c0000000000,
+ 0x3ff2b87fd0dada3a, 0x3d2a340000000000,
+ 0x3ff2c57e39771af9, 0xbd10800000000000,
+ 0x3ff2d285a6e402d9, 0xbd0ed00000000000,
+ 0x3ff2df961f641579, 0xbcf4200000000000,
+ 0x3ff2ecafa93e2ecf, 0xbd24980000000000,
+ 0x3ff2f9d24abd8822, 0xbd16300000000000,
+ 0x3ff306fe0a31b625, 0xbd32360000000000,
+ 0x3ff31432edeea50b, 0xbd70df8000000000,
+ 0x3ff32170fc4cd7b8, 0xbd22480000000000,
+ 0x3ff32eb83ba8e9a2, 0xbd25980000000000,
+ 0x3ff33c08b2641766, 0x3d1ed00000000000,
+ 0x3ff3496266e3fa27, 0xbcdc000000000000,
+ 0x3ff356c55f929f0f, 0xbd30d80000000000,
+ 0x3ff36431a2de88b9, 0x3d22c80000000000,
+ 0x3ff371a7373aaa39, 0x3d20600000000000,
+ 0x3ff37f26231e74fe, 0xbd16600000000000,
+ 0x3ff38cae6d05d838, 0xbd0ae00000000000,
+ 0x3ff39a401b713ec3, 0xbd44720000000000,
+ 0x3ff3a7db34e5a020, 0x3d08200000000000,
+ 0x3ff3b57fbfec6e95, 0x3d3e800000000000,
+ 0x3ff3c32dc313a8f2, 0x3cef800000000000,
+ 0x3ff3d0e544ede122, 0xbd17a00000000000,
+ 0x3ff3dea64c1234bb, 0x3d26300000000000,
+ 0x3ff3ec70df1c4ecc, 0xbd48a60000000000,
+ 0x3ff3fa4504ac7e8c, 0xbd3cdc0000000000,
+ 0x3ff40822c367a0bb, 0x3d25b80000000000,
+ 0x3ff4160a21f72e95, 0x3d1ec00000000000,
+ 0x3ff423fb27094646, 0xbd13600000000000,
+ 0x3ff431f5d950a920, 0x3d23980000000000,
+ 0x3ff43ffa3f84b9eb, 0x3cfa000000000000,
+ 0x3ff44e0860618919, 0xbcf6c00000000000,
+ 0x3ff45c2042a7d201, 0xbd0bc00000000000,
+ 0x3ff46a41ed1d0016, 0xbd12800000000000,
+ 0x3ff4786d668b3326, 0x3d30e00000000000,
+ 0x3ff486a2b5c13c00, 0xbd2d400000000000,
+ 0x3ff494e1e192af04, 0x3d0c200000000000,
+ 0x3ff4a32af0d7d372, 0xbd1e500000000000,
+ 0x3ff4b17dea6db801, 0x3d07800000000000,
+ 0x3ff4bfdad53629e1, 0xbd13800000000000,
+ 0x3ff4ce41b817c132, 0x3d00800000000000,
+ 0x3ff4dcb299fddddb, 0x3d2c700000000000,
+ 0x3ff4eb2d81d8ab96, 0xbd1ce00000000000,
+ 0x3ff4f9b2769d2d02, 0x3d19200000000000,
+ 0x3ff508417f4531c1, 0xbd08c00000000000,
+ 0x3ff516daa2cf662a, 0xbcfa000000000000,
+ 0x3ff5257de83f51ea, 0x3d4a080000000000,
+ 0x3ff5342b569d4eda, 0xbd26d80000000000,
+ 0x3ff542e2f4f6ac1a, 0xbd32440000000000,
+ 0x3ff551a4ca5d94db, 0x3d483c0000000000,
+ 0x3ff56070dde9116b, 0x3d24b00000000000,
+ 0x3ff56f4736b529de, 0x3d415a0000000000,
+ 0x3ff57e27dbe2c40e, 0xbd29e00000000000,
+ 0x3ff58d12d497c76f, 0xbd23080000000000,
+ 0x3ff59c0827ff0b4c, 0x3d4dec0000000000,
+ 0x3ff5ab07dd485427, 0xbcc4000000000000,
+ 0x3ff5ba11fba87af4, 0x3d30080000000000,
+ 0x3ff5c9268a59460b, 0xbd26c80000000000,
+ 0x3ff5d84590998e3f, 0x3d469a0000000000,
+ 0x3ff5e76f15ad20e1, 0xbd1b400000000000,
+ 0x3ff5f6a320dcebca, 0x3d17700000000000,
+ 0x3ff605e1b976dcb8, 0x3d26f80000000000,
+ 0x3ff6152ae6cdf715, 0x3d01000000000000,
+ 0x3ff6247eb03a5531, 0xbd15d00000000000,
+ 0x3ff633dd1d1929b5, 0xbd12d00000000000,
+ 0x3ff6434634ccc313, 0xbcea800000000000,
+ 0x3ff652b9febc8efa, 0xbd28600000000000,
+ 0x3ff6623882553397, 0x3d71fe0000000000,
+ 0x3ff671c1c708328e, 0xbd37200000000000,
+ 0x3ff68155d44ca97e, 0x3ce6800000000000,
+ 0x3ff690f4b19e9471, 0xbd29780000000000,
+];
+
+// exp2(x): compute the base 2 exponential of x
+//
+// Accuracy: Peak error < 0.503 ulp for normalized results.
+//
+// Method: (accurate tables)
+//
+// Reduce x:
+// x = k + y, for integer k and |y| <= 1/2.
+// Thus we have exp2(x) = 2**k * exp2(y).
+//
+// Reduce y:
+// y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE.
+// Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]),
+// with |z - eps[i]| <= 2**-9 + 2**-39 for the table used.
+//
+// We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via
+// a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61.
+// The values in exp2t[] and eps[] are chosen such that
+// exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such
+// that exp2t[i] is accurate to 2**-64.
+//
+// Note that the range of i is +-TBLSIZE/2, so we actually index the tables
+// by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are
+// virtual tables, interleaved in the real table tbl[].
+//
+// This method is due to Gal, with many details due to Gal and Bachelis:
+//
+// Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library
+// for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991).
+
+/// Exponential, base 2 (f64)
+///
+/// Calculate `2^x`, that is, 2 raised to the power `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp2(mut x: f64) -> f64 {
+ let redux = f64::from_bits(0x4338000000000000) / TBLSIZE as f64;
+ let p1 = f64::from_bits(0x3fe62e42fefa39ef);
+ let p2 = f64::from_bits(0x3fcebfbdff82c575);
+ let p3 = f64::from_bits(0x3fac6b08d704a0a6);
+ let p4 = f64::from_bits(0x3f83b2ab88f70400);
+ let p5 = f64::from_bits(0x3f55d88003875c74);
+
+ // double_t r, t, z;
+ // uint32_t ix, i0;
+ // union {double f; uint64_t i;} u = {x};
+ // union {uint32_t u; int32_t i;} k;
+ let x1p1023 = f64::from_bits(0x7fe0000000000000);
+ let x1p52 = f64::from_bits(0x4330000000000000);
+ let _0x1p_149 = f64::from_bits(0xb6a0000000000000);
+
+ /* Filter out exceptional cases. */
+ let ui = f64::to_bits(x);
+ let ix = ui >> 32 & 0x7fffffff;
+ if ix >= 0x408ff000 {
+ /* |x| >= 1022 or nan */
+ if ix >= 0x40900000 && ui >> 63 == 0 {
+ /* x >= 1024 or nan */
+ /* overflow */
+ x *= x1p1023;
+ return x;
+ }
+ if ix >= 0x7ff00000 {
+ /* -inf or -nan */
+ return -1.0 / x;
+ }
+ if ui >> 63 != 0 {
+ /* x <= -1022 */
+ /* underflow */
+ if x <= -1075.0 || x - x1p52 + x1p52 != x {
+ force_eval!((_0x1p_149 / x) as f32);
+ }
+ if x <= -1075.0 {
+ return 0.0;
+ }
+ }
+ } else if ix < 0x3c900000 {
+ /* |x| < 0x1p-54 */
+ return 1.0 + x;
+ }
+
+ /* Reduce x, computing z, i0, and k. */
+ let ui = f64::to_bits(x + redux);
+ let mut i0 = ui as u32;
+ i0 = i0.wrapping_add(TBLSIZE as u32 / 2);
+ let ku = i0 / TBLSIZE as u32 * TBLSIZE as u32;
+ let ki = div!(ku as i32, TBLSIZE as i32);
+ i0 %= TBLSIZE as u32;
+ let uf = f64::from_bits(ui) - redux;
+ let mut z = x - uf;
+
+ /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
+ let t = f64::from_bits(i!(TBL, 2 * i0 as usize)); /* exp2t[i0] */
+ z -= f64::from_bits(i!(TBL, 2 * i0 as usize + 1)); /* eps[i0] */
+ let r = t + t * z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * p5))));
+
+ scalbn(r, ki)
+}
+
+#[test]
+fn i0_wrap_test() {
+ let x = -3.0 / 256.0;
+ assert_eq!(exp2(x), f64::from_bits(0x3fefbdba3692d514));
+}