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math: Consolidate internal erf/erfc tables 

The shared internal data definitions are consolidated in
s_erf_data.c and the erfc only one are moved to s_erfc_data.c.

Checked on x86_64-linux-gnu, aarch64-linux-gnu, and
powerpc64le-linux-gnu.

Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella 2025-10-10 15:15:31 -03:00
parent acaad9ab06
commit fc419290f9
7 changed files with 2066 additions and 3083 deletions
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2
math/Makefile
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@ -363,6 +363,8 @@ type-double-routines := \
math_err \
s_asincosh_data \
s_atanh_data \
s_erf_data \
s_erfc_data \
sincostab \
# type-double-routines

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sysdeps/ieee754/dbl-64/s_erf.c
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sysdeps/ieee754/dbl-64/s_erf_data.c Normal file
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sysdeps/ieee754/dbl-64/s_erf_data.h Normal file
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@ -0,0 +1,56 @@
/* Common data for erf/erfc.
Copyright (c) 2023-2025 Paul Zimmermann
The original version of this file was copied from the CORE-MATH
project (file src/binary64/erf/erf.c, revision 384ed01d).
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#ifndef _S_ERF_DATA_H
#define _S_ERF_DATA_H
extern const double __erf_data_c0[] attribute_hidden;
#define C0 __erf_data_c0
extern const double __erf_data_C[94][13] attribute_hidden;
#define C __erf_data_C
extern const double __erf_data_C2[47][27] attribute_hidden;
#define C2 __erf_data_C2
extern const double __erf_data_T1[][2] attribute_hidden;
#define T1 __erf_data_T1
extern const double __erf_data_T2[][2] attribute_hidden;
#define T2 __erf_data_T2
extern const double __erf_data_Q_1[] attribute_hidden;
#define Q_1 __erf_data_Q_1
extern const double __erf_data_exceptions_tiny[][3] attribute_hidden;
#define EXCEPTIONS_TINY __erf_data_exceptions_tiny
extern const size_t __erf_data_exceptions_tiny_len attribute_hidden;
#define EXCEPTIONS_TINY_LEN __erf_data_exceptions_tiny_len
extern const double __erf_data_p[] attribute_hidden;
#define P __erf_data_p
extern const double __erf_data_exceptions[][3] attribute_hidden;
#define EXCEPTIONS __erf_data_exceptions
extern const size_t __erf_data_exceptions_len attribute_hidden;
#define EXCEPTIONS_LEN __erf_data_exceptions_len
#endif

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sysdeps/ieee754/dbl-64/s_erfc.c
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/* Data definitions for erfc implementation.
Copyright (c) 2022-2025 Alexei Sibidanov, Paul Zimmermann, Tom Hubrecht and
Claude-Pierre Jeannerod.
The original version of this file was copied from the CORE-MATH
project (file src/binary64/erf/erf.c, revision 384ed01d).
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#include "s_erfc_data.h"
/* the following contains polynomials generated by Sollya for
erfc(1/x)*exp(1/x^2), over various ranges.
Polynomials are of degree 23, with only odd coefficients, of type double
except the degree-1 one which is a double-double.
With p=T[i], the degree-1 coefficient is p[0] + p[1],
the degree-3 coefficient is p[2], ...,
the degree-23 coefficient is p[12]. In each line, the value is comment is
the relative error bound given by Sollya. */
const double __erfc_data_T[6][13] = {
{ 0x1.20dd750429b6dp-1, 0x1.1a1feb75a48a8p-57, -0x1.20dd750429b6cp-2,
0x1.b14c2f863e403p-2, -0x1.0ecf9db3af35dp+0, 0x1.d9eb53ca6eeedp+1,
-0x1.0a945830d95c8p+4, 0x1.6e8a963e2f1f5p+6, -0x1.29b7ccc8f396fp+9,
0x1.15e716e83c27ep+12, -0x1.1cfdcfbcaf22ap+15, 0x1.1986cc7a7e8fep+18,
-0x1.71f7540590a91p+20 }, /* asympt0.sollya,
[0x1.2ce37fb080c7dp-5,0x1.d5p-4], 2^-74.788,
|p'/p| < 27.2 */
{ 0x1.20dd750429ae7p-1, 0x1.63da89e801fd4p-55, -0x1.20dd750400795p-2,
0x1.b14c2f57c490cp-2, -0x1.0ecf95c8c9014p+0, 0x1.d9e981f2321efp+1,
-0x1.0a81482de1506p+4, 0x1.6d662420a604bp+6, -0x1.233c96fff7772p+9,
0x1.f5d62018d3e37p+11, -0x1.9ae55e955445p+14, 0x1.052901e10d139p+17,
-0x1.66465df1385fp+18 }, /* asympt1.sollya,
[0x1.d5p-4,0x1.59da6ca291ba6p-3], 2^-72.938,
|p'/p| < 8.63 */
{ 0x1.20dd75041e3fcp-1, -0x1.c9b491c4920fcp-56, -0x1.20dd74e5f1526p-2,
0x1.b14c1d35a40ep-2, -0x1.0ecdecd30e86bp+0, 0x1.d9b4e7f725263p+1,
-0x1.0958b5ca8fb39p+4, 0x1.63e3179bf609cp+6, -0x1.06bbd1cd2d0fdp+9,
0x1.7b66eb6d1d2f2p+11, -0x1.ce5a4b1afab75p+13, 0x1.8b5c6ae6f773cp+15,
-0x1.5475860326f86p+16 }, /* asympt2.sollya,
[0x1.59da6ca291ba6p-3,0x1.bcp-3], 2^-72.15,
|p'/p| < 5.77 */
{ 0x1.20dd75025cfe9p-1, 0x1.5a92eef32fb2p-58, -0x1.20dd71eb9d4e7p-2,
0x1.b14af4c25db28p-2, -0x1.0ebc78a22b3d8p+0, 0x1.d85287a0b3399p+1,
-0x1.045f751e5ca1dp+4, 0x1.4a0d87ddea589p+6, -0x1.ac6a0981d1eeep+8,
0x1.f44822f567956p+10, -0x1.cba372de71349p+12, 0x1.1a4a19f550ca4p+14,
-0x1.52a580455ed79p+14 }, /* asympt3.sollya, [0x1.bcp-3,0x1.0cp-2],
2^-71.804, |p'/p| < 4.42 */
{ 0x1.20dd74eb31d84p-1, -0x1.39c4054b7c09p-59, -0x1.20dd561af98c4p-2,
0x1.b1435165d9df1p-2, -0x1.0e6b60308e94p+0, 0x1.d3ce30c140882p+1,
-0x1.f2083e404c299p+3, 0x1.20f113d89b42ap+6, -0x1.41433ebd89f19p+8,
0x1.2f35b6a3154f6p+10, -0x1.b020a4313cf3bp+11, 0x1.90f07e92da7eep+12,
-0x1.6565e1d7665c3p+12 }, /* asympt4.sollya, [0x1.0cp-2,0x1.38p-2],
2^-71.811, |p'/p| < 3.60 */
{ 0x1.20dd744b3517bp-1, -0x1.f77ab25e01ab4p-57, -0x1.20dcc62ec4024p-2,
0x1.b125bfa4f66c1p-2, -0x1.0d80e6538197p+0, 0x1.ca11fbcfa65b2p+1,
-0x1.cd9eaffb88315p+3, 0x1.e010db42e0da7p+5, -0x1.c5c85250ef6a3p+7,
0x1.5e118d9c1eeafp+9, -0x1.8d74be13d3d3p+10, 0x1.211b1b2b5ac83p+11,
-0x1.900be759fc663p+10 }, /* asympt5.sollya, [0x1.38p-2,0x1.63p-2],
2^-71.841, |p'/p| < 3.04 */
};
/* the following is a degree-19 polynomial approximating exp(x) for
1/sqrt(2) <= x <= sqrt(2) with relative error bounded by 2^-104.311
(see file exp_accurate.sollya).
Coefficients of degree 0-7 are double-double and stored first,
coefficients of degree 8-19 are double and follow. */
const double __erfc_data_E2[] = {
0x1p+0,
-0x1p-105, // degree 0
0x1p+0,
-0x1.e2p-100, // degree 1
0x1p-1,
0x1.3cp-95, // degree 2
0x1.5555555555555p-3,
0x1.55555555c78d9p-57, // degree 3
0x1.5555555555555p-5,
0x1.55555545616e2p-59, // degree 4
0x1.1111111111111p-7,
0x1.11110121fc314p-63, // degree 5
0x1.6c16c16c16c17p-10,
-0x1.f49e06ee3a56ep-65, // degree 6
0x1.a01a01a01a01ap-13,
0x1.b053e1eeab9cp-73, // degree 7
0x1.a01a01a01a01ap-16, // degree 8
0x1.71de3a556c733p-19, // degree 9
0x1.27e4fb7789f66p-22, // degree 10
0x1.ae64567f54abep-26, // degree 11
0x1.1eed8eff8958bp-29, // degree 12
0x1.6124613837216p-33, // degree 13
0x1.93974aaf26a57p-37, // degree 14
0x1.ae7f4fd6d0bd9p-41, // degree 15
0x1.ae7e982620b25p-45, // degree 16
0x1.94e4ca59460d8p-49, // degree 17
0x1.69a2a4b7ef36dp-53, // degree 18
0x1.abfe1602308c9p-57, // degree 19
};
/* The following are polynomial approximations for erfc(1/x)*exp(1/x^2)
over various intervals covering [0x1.2ce37fb080c7dp-5,0x1.2b81f34bfce36p-1].
Polynomials have only odd coefficients, with the first six coefficients
(degree 1 to 11) being double-double, the remaining coefficients double.
*/
const double __erfc_data_Tacc[10][30]
= {
{ 0x1.20dd750429b6dp-1, 0x1.1ae3a912b08fp-57,
-0x1.20dd750429b6dp-2, -0x1.1ae34c0606d68p-58,
0x1.b14c2f863e924p-2, -0x1.96c0f4c848fc8p-56,
-0x1.0ecf9db3e71b6p+0, 0x1.45d756bd288bp-57,
0x1.d9eb53fad4672p+1, -0x1.c61629de9adf2p-53,
-0x1.0a945f3d147eap+4, 0x1.8fec5ad7ece2p-52,
0x1.6e8c02f27ca6dp+6, -0x1.29d1c21c363ep+9,
0x1.17349b70be627p+12, -0x1.28a6bb4686182p+15,
0x1.602d1662523cap+18, -0x1.ccae7625c4111p+21,
0x1.4237d064f6e0dp+25, -0x1.b1e5466ca3a2fp+28,
0x1.90ae06a0f6cc1p+31 }, /* asympt_acc0.sollya:
[0x1.2ce37fb080c7dp-5,0x1.45p-4], degree
29, relerr <= 2^-107.71 */
{ 0x1.20dd750429b6dp-1, 0x1.1adaa62435c1p-57,
-0x1.20dd750429b6dp-2, -0x1.41516126827c8p-59,
0x1.b14c2f863e90bp-2, 0x1.a535780ba5ed4p-56,
-0x1.0ecf9db3e65d6p+0, -0x1.089edde27ad07p-54,
0x1.d9eb53fa52f2p+1, -0x1.bc9737e9464acp-53,
-0x1.0a945f2cd7621p+4, -0x1.589f28b700332p-51,
0x1.6e8bffd7e194ep+6, -0x1.29d18716876e2p+9,
0x1.17312abe1825p+12, -0x1.287e73592805cp+15,
0x1.5ebf7394a39c1p+18, -0x1.c2f14d46d0cf9p+21,
0x1.2af3d256f955ep+25, -0x1.7041659ebd7aap+28,
0x1.6039c232e2f71p+31, -0x1.70ca15c5a07cbp+33 }, /* asympt_acc1.sollya:
[0x1.45p-4,0x1.e0p-4],
degree 31, relerr
<= 2^-106.203 */
{ 0x1.20dd750429b6dp-1, 0x1.d3c35b5d3741p-58,
-0x1.20dd750429b56p-2, -0x1.c028415f6f81bp-56,
0x1.b14c2f863c1cfp-2, 0x1.1bb0de6470dbcp-58,
-0x1.0ecf9db33c363p+0, 0x1.0f8068459eb16p-55,
0x1.d9eb53b9ce57bp+1, 0x1.20cce33e7d84ap-53,
-0x1.0a945aa2ec4fap+4, -0x1.f6e0fcd7c603p-50,
0x1.6e8b824d2bfaap+6, -0x1.29cc372a6d0bp+9,
0x1.1703a99ddd429p+12, -0x1.2749f9a267cc6p+15,
0x1.5856a17271849p+18, -0x1.a8bcb4ba9753fp+21,
0x1.035dcce88294p+25, -0x1.1e5d8c5e6e043p+28,
0x1.fe3b4f365386ep+30, -0x1.398fdef2b98fep+33,
0x1.84234d4f4ea12p+34 }, /* asympt_acc2.sollya:
[0x1.e0p-4,0x1.3fp-3], degree 33, relerr
<= 2^-105.859 */
{ 0x1.20dd750429b6ap-1, 0x1.ae622b765e9fdp-55,
-0x1.20dd750428f0ep-2, 0x1.03c6c67d69513p-56,
0x1.b14c2f8563e8ep-2, 0x1.766a6bd7aa89cp-57,
-0x1.0ecf9d8dedd48p+0, 0x1.0af52e90336e3p-54,
0x1.d9eb4aad086fep+1, 0x1.640d371d54a19p-53,
-0x1.0a93f1d01cfep+4, -0x1.68dbd8d9c522cp-51,
0x1.6e842e9fd5898p+6, -0x1.299886ef1fb8p+9,
0x1.15e0f0162c9ap+12, -0x1.222dbc6b04cd8p+15,
0x1.460268db1ebdfp+18, -0x1.74f53ce065fb3p+21,
0x1.961ca8553f87p+24, -0x1.8788395d13798p+27,
0x1.35e37b25d0e81p+30, -0x1.707b7457c8f5ep+32,
0x1.1ff852df1c023p+34, -0x1.b75d0ec56e2cdp+34 }, /* asympt_acc3.sollya:
[0x1.3fp-3,0x1.95p-3],
degree 35, relerr
<= 2^-105.557 */
{ 0x1.20dd750429a8fp-1, -0x1.66d8dda59bceap-56,
-0x1.20dd7503fdbabp-2, 0x1.707bdffc2b3fep-57,
0x1.b14c2f6526025p-2, -0x1.7fa4bb954114p-61,
-0x1.0ecf99c417d45p+0, -0x1.748645ef7af94p-54,
0x1.d9eaa9c712a7dp+1, 0x1.79e478994ebb4p-53,
-0x1.0a8ef11fbf141p+4, 0x1.b5c72d69f8954p-52,
0x1.6e4653e0455b1p+6, -0x1.286909448e6cfp+9,
0x1.113424ce76821p+12, -0x1.1346d859e76dep+15,
0x1.1f9f6cf2293bfp+18, -0x1.258e6e3b337dbp+21,
0x1.14029ecd465fbp+24, -0x1.c530df5337a6fp+26,
0x1.34bc4bbccd336p+29, -0x1.4a37c52641688p+31,
0x1.019707cec2974p+33, -0x1.031fe736ea169p+34,
0x1.f6b3003de3ddfp+33 }, /* asympt_acc4.sollya:
[0x1.95p-3,0x1.f5p-3], degree 37, relerr
<= 2^-105.539 */
{ 0x1.20dd75042756bp-1, 0x1.4ad9178b5691p-55,
-0x1.20dd74feda9e8p-2, -0x1.8141c70bbc8d6p-56,
0x1.b14c2cb128467p-2, -0x1.09aebaa106821p-56,
-0x1.0ecf603921a0bp+0, 0x1.7d3cb5bceaf0bp-54,
0x1.d9e3e1751ca59p+1, 0x1.6622ae564267p-56,
-0x1.0a686af57f547p+4, 0x1.083b320aff6b6p-51,
0x1.6cf0b6c027326p+6, -0x1.23afcb69443d3p+9,
0x1.03ab450d9f1b9p+12, -0x1.e74cdb76bcab4p+14,
0x1.c671b60e607f1p+17, -0x1.8f1376d324ce4p+20,
0x1.3b64276234676p+23, -0x1.aff0ce13c5a8ep+25,
0x1.ef20247251e87p+27, -0x1.c9f5662f721f6p+29,
0x1.4687858e185e1p+31, -0x1.4fa507be073c2p+32,
0x1.b99ac35ee4accp+32, -0x1.16cb585ee3fa9p+32 }, /* asympt_acc5.sollya:
[0x1.f5p-3,0x1.31p-2],
degree 39, relerr
<= 2^-105.722 */
{ 0x1.20dd7503e730dp-1, 0x1.4e524a098a467p-55,
-0x1.20dd7498fa6b2p-2, 0x1.60a4e27751c8p-61,
0x1.b14c061bd2a0cp-2, 0x1.95a8f847d2fc2p-57,
-0x1.0ecd0f11b8c7dp+0, -0x1.4126deea76061p-54,
0x1.d9b1344463548p+1, 0x1.fe09a4eca9b0ep-53,
-0x1.0996ea52a87edp+4, -0x1.924f920db26cp-53,
0x1.67a2264b556bp+6, -0x1.15dfc2c86b6b5p+9,
0x1.ccc291b62efe4p+11, -0x1.81375a78e746ap+14,
0x1.33a6f15546329p+17, -0x1.c1e9dc121601p+19,
0x1.2397ea3d43fdap+22, -0x1.4661e5b2ea512p+24,
0x1.3412367ca5d45p+26, -0x1.de56b9d7f37c4p+27,
0x1.2851d9722146dp+29, -0x1.19027baf0c3fep+30,
0x1.7e7b8b6ab58acp+30, -0x1.4c446d56aaf22p+30,
0x1.1492190400505p+29 }, /* asympt_acc6.sollya:
[0x1.31p-2,0x1.71p-2], degree 41, relerr
<= 2^-105.433 */
{ 0x1.20dd74ff10852p-1, 0x1.a32f26deff875p-55,
-0x1.20dd6f06c491cp-2, 0x1.70c16e1793358p-56,
0x1.b14a7d5e7fd4ap-2, 0x1.479998b54db5bp-56,
-0x1.0ebbdb3889c5fp+0, -0x1.59b853e11369cp-56,
0x1.d89dd249d7ef8p+1, -0x1.4b5edf0c8c314p-55,
-0x1.06526fb386114p+4, -0x1.40d04eed7c7ep-55,
0x1.57ff657e429cep+6, -0x1.ef63e90d3863p+8,
0x1.6d4f34c4ea3dap+11, -0x1.04542b9e36a54p+14,
0x1.577bf19097738p+16, -0x1.9702fe47c736dp+18,
0x1.a7ae12b54fdc6p+20, -0x1.7ca3f0f7c4fa9p+22,
0x1.225d983963cbfp+24, -0x1.71a6eac612f9ep+25,
0x1.8086324225e1ep+26, -0x1.3de68670a7716p+27,
0x1.91674de4dcbe9p+27, -0x1.6b44cc15b76c2p+27,
0x1.a36dae0f30d8p+26, -0x1.cffc1747ea3dcp+24 }, /* asympt_acc7.sollya:
[0x1.71p-2,0x1.bcp-2],
degree 43, relerr
<= 2^-105.629 */
{ 0x1.20dd74ba8f3p-1, -0x1.9dd256871d21p-58,
-0x1.20dd3593675bcp-2, 0x1.ec0e7ffa91ad9p-56,
0x1.b13eef86a077ap-2, -0x1.4fb5d78d411b8p-56,
-0x1.0e5cf52a11f3ap+0, -0x1.51f36c779dc8cp-55,
0x1.d4417a08b39d5p+1, 0x1.1be9fb5956638p-54,
-0x1.f91b9f6ce80c3p+3, -0x1.c9c99dd42829cp-51,
0x1.356439f45bb43p+6, -0x1.8c0ca12819b48p+8,
0x1.efcad2ecd6671p+10, -0x1.21b0af6fc1039p+13,
0x1.327d215ee30c9p+15, -0x1.1fabda96167bp+17,
0x1.d82e4373b315dp+18, -0x1.4ed9e2ff591e9p+20,
0x1.95c85dcd8eab5p+21, -0x1.9f016f0a3d62ap+22,
0x1.60e89d918b96fp+23, -0x1.e97be202cba64p+23,
0x1.0d8a081619793p+24, -0x1.c5422b4fcfc65p+23,
0x1.1131a9dc6aed1p+23, -0x1.a457d9dced257p+21,
0x1.3605e980e8b86p+19 }, /* asympt_acc8.sollya:
[0x1.bcp-2,0x1.0bp-1], degree 45, relerr
<= 2^-105.064 */
{ 0x1.20dd7319d4d25p-1, 0x1.2b02992c3b7abp-55,
-0x1.20dc29c13ab1bp-2, -0x1.d78d79b4ad767p-56,
0x1.b115a57b5ab13p-2, -0x1.aa8c45be0aa2ep-57,
-0x1.0d58ec437efd7p+0, -0x1.994f00a15e85p-58,
0x1.cb1742e229f23p+1, -0x1.8000471d54399p-53,
-0x1.d99a5edf7b946p+3, -0x1.af76ed7e35cdep-52,
0x1.0a8b71058eb28p+6, -0x1.2d88289da5bfcp+8,
0x1.43ddf24168edbp+10, -0x1.3e9dfc38b6d1ap+12,
0x1.18d4df97ab3dfp+14, -0x1.b550fc62dcab5p+15,
0x1.29cb71f116ed1p+17, -0x1.5fc9cc4e854e3p+18,
0x1.65915fd0567b1p+19, -0x1.35eb5fca0e46dp+20,
0x1.c5261ecc0d789p+20, -0x1.138932dc4eafcp+21,
0x1.117d4eb18facdp+21, -0x1.af96163e35ecap+20,
0x1.0454a3a63c766p+20, -0x1.c2ebc1d39b44ap+18,
0x1.f3327698e0e6bp+16, -0x1.094febc3dff35p+14 }, /* asympt_acc9.sollya:
[0x1.0bp-1,0x1.2b81f34bfce36p-1],
degree 47, relerr
<= 2^-117.075 */
};
const double __erfc_data_exceptions[22][3] = {
{ 0x1.4a42b163f7a7dp+3, 0x1.183d60a1f7e3cp-158, -0x1.fffffffffffffp-212 },
{ 0x1.a631d4bc7f56bp+3, 0x1.3f07281bb43aep-256, -0x1p-309 },
{ 0x1.1b2588f5d972ep+4, 0x1.2923609150ffp-457, -0x1.ffffffffffffdp-511 },
{ 0x1.1d41cb671cad3p+4, 0x1.5c4d8d179be8cp-464, -0x1.fffffffffffffp-518 },
{ 0x1.48de452fb1a15p+4, 0x1.3c2a1264045adp-615, 0x1.fffffffffffffp-669 },
{ 0x1.bb1ef58eda44p+0, 0x1.d6d259cb81801p-7, 0x1.387cbdb500a5ep-114 },
{ 0x1.0ca37ce17afa6p+1, 0x1.88cc1284157f5p-9, 0x1.6fd53d489a2c1p-120 },
{ 0x1.1cb6b0f91a4ccp+1, 0x1.b2639c7a46899p-10, 0x1.f8111f4b0ab0fp-114 },
{ 0x1.d1e19af184c6ep+0, 0x1.49bf1937979edp-7, 0x1.c1b55587c1381p-112 },
{ 0x1.37994c710a4d2p+1, 0x1.2df150139d8eap-11, 0x1.d46afcc14563p-114 },
{ 0x1.8966f65d9a1a1p+1, 0x1.d01a8497b522dp-17, 0x1.c935c97d5bfe4p-121 },
{ 0x1.9f4a466c51bb5p+2, 0x1.a3d059f3770b9p-65, 0x1.3f16dde099b74p-167 },
{ 0x1.164f857d1749cp+3, 0x1.e35102e39e989p-114, 0x1.32b4c82bbb9e3p-219 },
{ 0x1.76957728f1f31p+1, 0x1.251dea1afe1adp-15, -0x1.155995aa5bae6p-119 },
{ 0x1.651c78cec84f6p+2, 0x1.af9d1df8b5e8p-49, -0x1.fe39e86292256p-153 },
{ 0x1.77d0f07e113dcp+3, 0x1.8b93f18b3cdc6p-204, 0x1.6ffd370fba52ap-307 },
{ 0x1.ef72633933d36p+2, 0x1.aee3861d8657ep-91, -0x1.00ca47f3ced2ap-194 },
{ 0x1.391f434b53d18p+4, 0x1.44e8c50fa25e9p-558, -0x1.15aa7b49bc597p-662 },
{ 0x1.b8940788b825dp+0, 0x1.e97eaf1080bffp-7, 0x1.38836346525eap-107 },
{ 0x1.16ffd71e2d8c6p+2, 0x1.834e2899c5506p-31, -0x1.b7516e4549528p-135 },
{ 0x1.7fa5439251a75p+1, 0x1.7923ec231992dp-16, -0x1.74f633ea13fecp-121 },
{ 0x1.a8fb2b7ef1f8p+2, 0x1.c1b9f4cda246bp-68, 0x1.6fce2e1cae1a5p-171 },
};
const double __erfc_data_exceptions_accurate[17][3] = {
{ -0x1.c5bf891b4ef6bp-54, 0x1.0000000000001p+0, -0x1.fffffffffffffp-54 },
{ -0x1.fe777a3eb8d58p-51, 0x1.0000000000005p+0, -0x1.fffffffffffffp-54 },
{ -0x1.d3ed8564296e6p-49, 0x1.0000000000011p+0, -0x1.fffffffffffffp-54 },
{ -0x1.29c5b1f9ebd1ep-49, 0x1.000000000000bp+0, -0x1.fffffffffffffp-54 },
{ -0x1.e9327fd17121fp-48, 0x1.0000000000023p+0, -0x1.fffffffffffffp-54 },
{ -0x1.941e961c5253bp-48, 0x1.000000000001dp+0, -0x1.fffffffffffffp-54 },
{ -0x1.3f0aac6733857p-48, 0x1.0000000000017p+0, -0x1.fffffffffffffp-54 },
{ -0x1.dc87cb831c792p-37, 0x1.0000000010cdbp+0, -0x1.fffffffffffffp-54 },
{ -0x1.b71f3a10691d9p-37, 0x1.000000000f7bfp+0, -0x1.fffffffffffffp-54 },
{ -0x1.cea935ba73f4cp-32, 0x1.000000020a0e9p+0, 0x1.fffffffffffffp-54 },
{ -0x1.abaf3b436049ep-25, 0x1.000000f14b8e3p+0, 0x1.fffffffffffffp-54 },
{ -0x1.d4c18d3599cbep-19, 0x1.0000421de806fp+0, -0x1.fffffffffffffp-54 },
{ -0x1.607b67e03b83bp-15, 0x1.00031b7780fe5p+0, -0x1.fffffffffffffp-54 },
{ -0x1.4a943c917ed26p-12, 0x1.0017504bc67c1p+0, 0x1.fffffffffffffp-54 },
{ -0x1.106c2cd5ea6c3p-9, 0x1.0099b29fab8cfp+0, 0x1.fffffffffffffp-54 },
{ -0x1.d4af8adb90116p-4, 0x1.20e8e5d1e73ffp+0, 0x1.ffffffffffffep-54 },
{ -0x1.f9a4a209ca0e4p+0, 0x1.feaa166e384c9p+0, 0x1.ffffffffffffep-54 },
};
const double __erfc_data_exceptions_accurate_2[29][3] = {
{ 0x1.c5bf891b4ef6bp-55, 0x1.fffffffffffffp-1, 0x1.ffffffffffffep-55 },
{ 0x1.fe777a3eb8d58p-52, 0x1.ffffffffffffbp-1, 0x1.ffffffffffffep-55 },
{ 0x1.29c5b1f9ebd1ep-50, 0x1.ffffffffffff5p-1, 0x1.ffffffffffffep-55 },
{ 0x1.d3ed8564296e6p-50, 0x1.fffffffffffefp-1, 0x1.ffffffffffffep-55 },
{ 0x1.3f0aac6733857p-49, 0x1.fffffffffffe9p-1, 0x1.fffffffffffffp-55 },
{ 0x1.941e961c5253bp-49, 0x1.fffffffffffe3p-1, 0x1.fffffffffffffp-55 },
{ 0x1.e9327fd17121fp-49, 0x1.fffffffffffddp-1, 0x1.fffffffffffffp-55 },
{ 0x1.b71f3a10691d9p-38, 0x1.fffffffff0841p-1, -0x1.ffffffffffffep-55 },
{ 0x1.dc87cb831c792p-38, 0x1.ffffffffef325p-1, 0x1.fffffffffffffp-55 },
{ 0x1.52b18fe8fbad1p-36, 0x1.ffffffffd03a7p-1, -0x1.ffffffffffffep-55 },
{ 0x1.cf0ed5959b276p-28, 0x1.ffffffbeafd79p-1, -0x1.fffffffffffffp-55 },
{ 0x1.6af79a30bbf3cp-27, 0x1.ffffff999bdd3p-1, 0x1.fffffffffffffp-55 },
{ 0x1.dd48360dd7824p-26, 0x1.fffffef2b8f0dp-1, 0x1.fffffffffffffp-55 },
{ 0x1.40757fba82477p-24, 0x1.fffffd2ccd30dp-1, -0x1.fffffffffffffp-55 },
{ 0x1.8bc46e0d85524p-9, 0x1.fe416cffa803dp-1, -0x1.fffffffffffffp-55 },
{ 0x1.d4af8adb90116p-4, 0x1.be2e345c31801p-1, 0x1.ea7fa18173ab8p-106 },
{ 0x1.3229110bf9d66p-2, 0x1.5847806aef94bp-1, 0x1.fffffffffffffp-55 },
{ 0x1.a93059aabe4bcp-1, 0x1.ebfa1229d0dcep-3, 0x1.99b4b80fd9415p-107 },
{ 0x1.bc466342a2296p-1, 0x1.c2153a8529156p-3, -0x1.088fb70829f71p-107 },
{ 0x1.eef77c6caae18p-1, 0x1.5f61e96f60783p-3, -0x1.ffffffffffffdp-57 },
{ 0x1.fd5d9d8c9ef66p-1, 0x1.468ba052c2fep-3, -0x1.03fa708a553b3p-105 },
{ 0x1.23c67ff8b8a0ap+0, 0x1.b640be5efa2e3p-4, -0x1.b9a66b42d916p-107 },
{ 0x1.3a013a3c71e92p+0, 0x1.5329743c2c15cp-4, 0x1.7766eb5263404p-109 },
{ 0x1.589bbd3ae5489p+0, 0x1.d2847b1409248p-5, 0x1.57b4a906bc605p-107 },
{ 0x1.757fe152a87c9p+0, 0x1.402acce35d833p-5, 0x1.d38ccfa0c1d6bp-108 },
{ 0x1.7749479e598d3p+0, 0x1.3891521afe3e3p-5, 0x1.8b8423c82ad72p-108 },
{ 0x1.9a3a5f5f28f3p+0, 0x1.80040c25bab9p-6, -0x1.a8686704bdb14p-108 },
{ 0x1.a44869b34ea46p+0, 0x1.4bb609c105c2dp-6, -0x1.9182dae766fc4p-109 },
{ 0x1.af08ae30c9364p+0, 0x1.1ac47852096cbp-6, -0x1.fffffffffffdap-60 },
};

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/* Data definitions for erfc implementation.
Copyright (c) 2022-2025 Alexei Sibidanov, Paul Zimmermann, Tom Hubrecht and
Claude-Pierre Jeannerod.
The original version of this file was copied from the CORE-MATH
project (file src/binary64/erf/erf.c, revision 384ed01d).
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#ifndef _S_ERFC_DATA_H
#define _S_ERFC_DATA_H
extern const double __erfc_data_T[6][13] attribute_hidden;
#define T __erfc_data_T
extern const double __erfc_data_E2[] attribute_hidden;
#define E2 __erfc_data_E2
extern const double __erfc_data_Tacc[10][30] attribute_hidden;
#define Tacc __erfc_data_Tacc
extern const double __erfc_data_exceptions[22][3] attribute_hidden;
#define EXCEPTIONS_ERFC __erfc_data_exceptions
extern const double __erfc_data_exceptions_accurate[17][3] attribute_hidden;
#define EXCEPTIONS_ACCURATE_ERFC __erfc_data_exceptions_accurate
extern const double __erfc_data_exceptions_accurate_2[29][3] attribute_hidden;
#define EXCEPTIONS_ACCURATE_ERFC_2 __erfc_data_exceptions_accurate_2
#endif