1 /* 2 * Shared data between erf and erfc. 3 * 4 * Copyright (c) 2019-2020, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "math_config.h" 9 10 /* 11 Minimax approximation of erf 12 */ 13 const struct erf_data __erf_data = { 14 .erf_poly_A = { 15 #if ERF_POLY_A_NCOEFFS == 10 16 0x1.06eba8214db68p-3, -0x1.812746b037948p-2, 0x1.ce2f21a03872p-4, 17 -0x1.b82ce30e6548p-6, 0x1.565bcc360a2f2p-8, -0x1.c02d812bc979ap-11, 18 0x1.f99bddfc1ebe9p-14, -0x1.f42c457cee912p-17, 0x1.b0e414ec20ee9p-20, 19 -0x1.18c47fd143c5ep-23 20 #endif 21 }, 22 /* Rational approximation on [0x1p-28, 0.84375] */ 23 .erf_ratio_N_A = { 24 0x1.06eba8214db68p-3, -0x1.4cd7d691cb913p-2, -0x1.d2a51dbd7194fp-6, 25 -0x1.7a291236668e4p-8, -0x1.8ead6120016acp-16 26 }, 27 .erf_ratio_D_A = { 28 0x1.97779cddadc09p-2, 0x1.0a54c5536cebap-4, 0x1.4d022c4d36b0fp-8, 29 0x1.15dc9221c1a1p-13, -0x1.09c4342a2612p-18 30 }, 31 /* Rational approximation on [0.84375, 1.25] */ 32 .erf_ratio_N_B = { 33 -0x1.359b8bef77538p-9, 0x1.a8d00ad92b34dp-2, -0x1.7d240fbb8c3f1p-2, 34 0x1.45fca805120e4p-2, -0x1.c63983d3e28ecp-4, 0x1.22a36599795ebp-5, 35 -0x1.1bf380a96073fp-9 36 }, 37 .erf_ratio_D_B = { 38 0x1.b3e6618eee323p-4, 0x1.14af092eb6f33p-1, 0x1.2635cd99fe9a7p-4, 39 0x1.02660e763351fp-3, 0x1.bedc26b51dd1cp-7, 0x1.88b545735151dp-7 40 }, 41 .erfc_poly_C = { 42 #if ERFC_POLY_C_NCOEFFS == 16 43 /* Generated using Sollya::remez(f(c*x+d), deg, [(a-d)/c;(b-d)/c], 1, 1e-16), [|D ...|] with deg=15 a=1.25 b=2 c=1 d=1.25 */ 44 0x1.3bcd133aa0ffcp-4, -0x1.e4652fadcb702p-3, 0x1.2ebf3dcca0446p-2, 45 -0x1.571d01c62d66p-3, 0x1.93a9a8f5b3413p-8, 0x1.8281cbcc2cd52p-5, 46 -0x1.5cffd86b4de16p-6, -0x1.db4ccf595053ep-9, 0x1.757cbf8684edap-8, 47 -0x1.ce7dfd2a9e56ap-11, -0x1.99ee3bc5a3263p-11, 0x1.3c57cf9213f5fp-12, 48 0x1.60692996bf254p-14, -0x1.6e44cb7c1fa2ap-14, 0x1.9d4484ac482b2p-16, 49 -0x1.578c9e375d37p-19 50 #endif 51 }, 52 .erfc_poly_D = { 53 #if ERFC_POLY_D_NCOEFFS == 18 54 /* Generated using Sollya::remez(f(c*x+d), deg, [(a-d)/c;(b-d)/c], 1, 1e-16), [|D ...|] with deg=17 a=2 b=3.25 c=2 d=2 */ 55 0x1.328f5ec350e5p-8, -0x1.529b9e8cf8e99p-5, 0x1.529b9e8cd9e71p-3, 56 -0x1.8b0ae3a023bf2p-2, 0x1.1a2c592599d82p-1, -0x1.ace732477e494p-2, 57 -0x1.e1a06a27920ffp-6, 0x1.bae92a6d27af6p-2, -0x1.a15470fcf5ce7p-2, 58 0x1.bafe45d18e213p-6, 0x1.0d950680d199ap-2, -0x1.8c9481e8f22e3p-3, 59 -0x1.158450ed5c899p-4, 0x1.c01f2973b44p-3, -0x1.73ed2827546a7p-3, 60 0x1.47733687d1ff7p-4, -0x1.2dec70d00b8e1p-6, 0x1.a947ab83cd4fp-10 61 #endif 62 }, 63 .erfc_poly_E = { 64 #if ERFC_POLY_E_NCOEFFS == 14 65 /* Generated using Sollya::remez(f(c*x+d), deg, [(a-d)/c;(b-d)/c], 1, 1e-16), [|D ...|] with deg=13 a=3.25 b=4 c=1 d=3.25 */ 66 0x1.20c13035539e4p-18, -0x1.e9b5e8d16df7ep-16, 0x1.8de3cd4733bf9p-14, 67 -0x1.9aa48beb8382fp-13, 0x1.2c7d713370a9fp-12, -0x1.490b12110b9e2p-12, 68 0x1.1459c5d989d23p-12, -0x1.64b28e9f1269p-13, 0x1.57c76d9d05cf8p-14, 69 -0x1.bf271d9951cf8p-16, 0x1.db7ea4d4535c9p-19, 0x1.91c2e102d5e49p-20, 70 -0x1.e9f0826c2149ep-21, 0x1.60eebaea236e1p-23 71 #endif 72 }, 73 .erfc_poly_F = { 74 #if ERFC_POLY_F_NCOEFFS == 17 75 /* Generated using Sollya::remez(f(c*x+d), deg, [(a-d)/c;(b-d)/c], 1, 1e-16), [|D ...|] with deg=16 a=4 b=5.90625 c=2 d=4 */ 76 0x1.08ddd130d1fa6p-26, -0x1.10b146f59ff06p-22, 0x1.10b135328b7b2p-19, 77 -0x1.6039988e7575fp-17, 0x1.497d365e19367p-15, -0x1.da48d9afac83ep-14, 78 0x1.1024c9b1fbb48p-12, -0x1.fc962e7066272p-12, 0x1.87297282d4651p-11, 79 -0x1.f057b255f8c59p-11, 0x1.0228d0eee063p-10, -0x1.b1b21b84ec41cp-11, 80 0x1.1ead8ae9e1253p-11, -0x1.1e708fba37fccp-12, 0x1.9559363991edap-14, 81 -0x1.68c827b783d9cp-16, 0x1.2ec4adeccf4a2p-19 82 #endif 83 } 84 }; 85 86