libgcc/config/avr/libf7/libf7-const.def

/* Copyright (C) 2019-2021 Free Software Foundation, Inc.

   This file is part of LIBF7, which is part of GCC.

   GCC is free software; you can redistribute it and/or modify it under
   the terms of the GNU General Public License as published by the Free
   Software Foundation; either version 3, or (at your option) any later
   version.

   GCC is distributed in the hope that it will be useful, but WITHOUT ANY
   WARRANTY; without even the implied warranty of MERCHANTABILITY or
   FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
   for more details.

   Under Section 7 of GPL version 3, you are granted additional
   permissions described in the GCC Runtime Library Exception, version
   3.1, as published by the Free Software Foundation.

   You should have received a copy of the GNU General Public License and
   a copy of the GCC Runtime Library Exception along with this program;
   see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
   <http://www.gnu.org/licenses/>.  */

#ifndef ONLY_CONST_WITH_ID
#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_1_2_)
F7_CONST_DEF (1_2,  0,  0x80,0,0,0,0,0,0,   -1)
#endif /* 1/2 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_1_)
F7_CONST_DEF (1,    0,  0x80,0,0,0,0,0,0,   0)
#endif /* 1 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_2_)
F7_CONST_DEF (2,    0,  0x80,0,0,0,0,0,0,   1)
#endif /* 2 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_1_3_)
F7_CONST_DEF (1_3,  0,  0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xab, -2)
#endif /* 1/3 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_1_ln2_)
F7_CONST_DEF (1_ln2,  0,  0xb8,0xaa,0x3b,0x29,0x5c,0x17,0xf1, 0)
#endif /* 1 / ln2 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_1_ln10_)
F7_CONST_DEF (1_ln10,  0,  0xde,0x5b,0xd8,0xa9,0x37,0x28,0x72, -2)
#endif /* 1 / ln10 */
#endif /* const with ID */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_m1_)
F7_CONST_DEF (m1,   1,  0x80,0,0,0,0,0,0,   0)
#endif /* -1 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_pi_)
F7_CONST_DEF (pi,   0,  0xc9,0x0f,0xda,0xa2,0x21,0x68,0xc2, 1)
#endif /* pi */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_ln2_)
F7_CONST_DEF (ln2,  0,  0xb1,0x72,0x17,0xf7,0xd1,0xcf,0x7a, -1)
#endif /* ln2 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_ln10_)
F7_CONST_DEF (ln10,  0,  0x93,0x5d,0x8d,0xdd,0xaa,0xa8,0xac, 1)
#endif /* ln10 */

#if defined IN_LIBF7_H || defined (F7MOD_const_) || defined (F7MOD_const_sqrt2_)
F7_CONST_DEF (sqrt2,    0,  0xb5,0x04,0xf3,0x33,0xf9,0xde,0x65, 0)
#endif /* sqrt2 */

#if !defined (IN_LIBF7_H) && !defined (F7MOD_const_)

#if defined (F7MOD_logx_)
// 2.00000000000000000287938058543222037939 + 0.666666666666667653654896829047862109605x + 0.399999999996639180070480580779767357622x^2 + 0.285714286985476106491309914245597720749x^3 + 0.222222024077476110197597399876978069272x^4 + 0.181833876328594532366358057253631240618x^5 + 0.153181571233880298729095145342556944283x^6 + 0.147580071554569676223389696418304199218x^7
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 1)
F7_CONST_DEF (X, 0, 0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xf2, -1)
F7_CONST_DEF (X, 0, 0xcc,0xcc,0xcc,0xcc,0xc5,0x68,0xd4, -2)
F7_CONST_DEF (X, 0, 0x92,0x49,0x24,0x9d,0x34,0x85,0x25, -2)
F7_CONST_DEF (X, 0, 0xe3,0x8e,0x2b,0x97,0x74,0x69,0xb3, -3)
F7_CONST_DEF (X, 0, 0xba,0x32,0xa8,0xe0,0x8b,0x7d,0xcc, -3)
F7_CONST_DEF (X, 0, 0x9c,0xdb,0xa1,0x3b,0x32,0x98,0x9a, -3)
F7_CONST_DEF (X, 0, 0x97,0x1f,0x3a,0xf3,0x79,0x0d,0xc8, -3)

#elif defined (F7MOD_exp_)
#ifdef ARRAY_NAME
// Intended for |X| < ln2 / 8
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
// f(x) = (e^x - 1) / x  and  f -> 1 + x*f  by means of const_1 above.
// 0.99999999999999993104781692731238623644199 + 0.50000000000000018681311888335564572558345x + 0.16666666666696003026683736262180526042594x^2 + 0.041666666666489887893617892155331720764329x^3 + 0.0083333331383434741356242595738508060753717x^4 + 0.0013888889242082668539796357369837122917246x^5 + 0.00019845416752769938401628433087258224774248x^6 + 0.000024801569801689274979195020335136136418918x^7
F7_CONST_DEF (X, 0, 0xff,0xff,0xff,0xff,0xff,0xff,0xfb, -1)
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x0d, -1)
F7_CONST_DEF (X, 0, 0xaa,0xaa,0xaa,0xaa,0xab,0xf4,0xf7, -3)
F7_CONST_DEF (X, 0, 0xaa,0xaa,0xaa,0xaa,0xa7,0x8e,0x87, -5)
F7_CONST_DEF (X, 0, 0x88,0x88,0x88,0x52,0xef,0x57,0x81, -7)
F7_CONST_DEF (X, 0, 0xb6,0x0b,0x61,0x03,0xb6,0x6b,0x82, -10)
F7_CONST_DEF (X, 0, 0xd0,0x18,0x22,0x8c,0x6f,0xde,0x72, -13)
F7_CONST_DEF (X, 0, 0xd0,0x0c,0xf7,0x31,0x28,0xba,0xb5, -16)
#else
// Negative because f7_const_ln2 is ln2 rounded up.
F7_CONST_DEF (ln2_low, 1,	0xa8,0x6c,0x38,0x98,0xcf,0xf8,0x1a, -58)
#endif

#elif defined (F7MOD_atan_)

#if defined (MINIMAX_6_6_IN_0_1)
// https://www.mikrocontroller.net/topic/480840#6003520
#if defined (FOR_NUMERATOR)
// 1209.7470017580907217240715 + 3031.0745956115083044212807x + 2761.7198246138834959053784x^2 + 1114.1290728455183546172942x^3 + 192.5792014481559613474286x^4 + 11.3221594116764655236245x^5 + 0.09762721591717633036983x^6
// p = Poly ([Decimal('1209.7470017580907217240715'), Decimal('3031.0745956115083044212807'), Decimal('2761.7198246138834959053784'), Decimal('1114.1290728455183546172942'), Decimal('192.5792014481559613474286'), Decimal('11.3221594116764655236245'), Decimal('0.09762721591717633036983')])
F7_CONST_DEF (X, 0, 0x97,0x37,0xe7,0x70,0x3b,0x21,0xbc, 10)
F7_CONST_DEF (X, 0, 0xbd,0x71,0x31,0x8b,0x2a,0xfd,0xa7, 11)
F7_CONST_DEF (X, 0, 0xac,0x9b,0x84,0x66,0xd0,0x77,0xc4, 11)
F7_CONST_DEF (X, 0, 0x8b,0x44,0x21,0x5d,0x60,0x49,0xb2, 10)
F7_CONST_DEF (X, 0, 0xc0,0x94,0x46,0x8b,0xcd,0xa0,0x2d, 7)
F7_CONST_DEF (X, 0, 0xb5,0x27,0x90,0xa0,0x93,0xfb,0xfc, 3)
F7_CONST_DEF (X, 0, 0xc7,0xf0,0xc7,0x1c,0x82,0xab,0x23, -4)
#elif defined (FOR_DENOMINATOR)
// 1209.7470017580907287514197 + 3434.3235961975351716547069x + 3664.5449563283749893504796x^2 + 1821.6003392918464941509225x^3 + 423.0716464809047804524206x^4 + 39.9178842486537981501999x^5 + x^6
// q = Poly ([Decimal('1209.7470017580907287514197'), Decimal('3434.3235961975351716547069'), Decimal('3664.5449563283749893504796'), Decimal('1821.6003392918464941509225'), Decimal('423.0716464809047804524206'), Decimal('39.9178842486537981501999'), Decimal('1.0')])
F7_CONST_DEF (X, 0, 0x97,0x37,0xe7,0x70,0x3b,0x21,0xbc, 10)
F7_CONST_DEF (X, 0, 0xd6,0xa5,0x2d,0x73,0x34,0xd8,0x60, 11)
F7_CONST_DEF (X, 0, 0xe5,0x08,0xb8,0x24,0x20,0x81,0xe7, 11)
F7_CONST_DEF (X, 0, 0xe3,0xb3,0x35,0xfa,0xbf,0x1f,0x81, 10)
F7_CONST_DEF (X, 0, 0xd3,0x89,0x2b,0xb6,0x3e,0x2e,0x05, 8)
F7_CONST_DEF (X, 0, 0x9f,0xab,0xe9,0xd9,0x35,0xed,0x27, 5)
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
#endif

#elif defined (SWIFT_3_4)
// My [3,4] MiniMax
#if defined (FOR_NUMERATOR)
// 0.999999999999999998080178351225003952632 + 1.51597040589722809277543885223133087789x + 0.636928974763539784860899545005247736093x^2 + 0.0638944455799886571709448345524306512048x^3
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
F7_CONST_DEF (X, 0, 0xc2,0x0b,0x51,0x79,0x84,0x27,0x00, 0)
F7_CONST_DEF (X, 0, 0xa3,0x0d,0xc6,0xfc,0x7b,0xf5,0x5d, -1)
F7_CONST_DEF (X, 0, 0x82,0xdb,0x17,0x51,0x4b,0xfc,0xad, -4)
#elif defined (FOR_DENOMINATOR)
// 1 + 1.84930373923056200945453682584178320362x + 1.05336355450697082895016644607427716580x^2 + 0.188012025422931152047197803304030906006x^3 + 0.00507310235929401206762490897042543192106x^4
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
F7_CONST_DEF (X, 0, 0xec,0xb5,0xfc,0x24,0x2e,0xd1,0xc0, 0)
F7_CONST_DEF (X, 0, 0x86,0xd4,0x9d,0xf0,0xb3,0xef,0xb8, 0)
F7_CONST_DEF (X, 0, 0xc0,0x86,0x39,0x71,0xc8,0xeb,0x3d, -3)
F7_CONST_DEF (X, 0, 0xa6,0x3c,0x44,0x5c,0x78,0x87,0x2d, -8)
#else
F7_CONST_DEF (1_sqrt3,  0,  0x93,0xCD,0x3A,0x2C,0x81,0x98,0xE2, -1)
F7_CONST_DEF (pi_6, 0,  0x86,0x0a,0x91,0xc1,0x6b,0x9b,0x2c, -1)
#endif
#endif // which MiniMax

#elif defined (F7MOD_asinacos_)
// Relative error < 5.6E-18, quality = 1.00000037 (ideal = 1).
#if defined (FOR_NUMERATOR)
// 0.99999999999999999442491073135027586203 - 1.035234033892197627842731209x + 0.35290206232981519813422591897720574012x^2 - 0.04333483170641685705612351801x^3 + 0.0012557428614630796315205218507940285622x^4 + 0.0000084705471128435769021718764878041684288x^5
// p = Poly ([Decimal('0.99999999999999999442491073135027586203'), Decimal('-1.0352340338921976278427312087167692142'), Decimal('0.35290206232981519813422591897720574012'), Decimal('-0.043334831706416857056123518013656946650'), Decimal('0.0012557428614630796315205218507940285622'), Decimal('0.0000084705471128435769021718764878041684288')])
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
F7_CONST_DEF (X, 1, 0x84,0x82,0x8c,0x7f,0xa2,0xf6,0x65, 0)
F7_CONST_DEF (X, 0, 0xb4,0xaf,0x94,0x40,0xcb,0x86,0x69, -2)
F7_CONST_DEF (X, 1, 0xb1,0x7f,0xdd,0x4f,0x4e,0xbe,0x1d, -5)
F7_CONST_DEF (X, 0, 0xa4,0x97,0xbd,0x0b,0x59,0xc9,0x25, -10)
F7_CONST_DEF (X, 0, 0x8e,0x1c,0xb9,0x0b,0x50,0x6c,0xce, -17)
#elif defined (FOR_DENOMINATOR)
// 1 - 1.118567367225532923662371649x + 0.42736600959872448854098334016758333519x^2 - 0.06355588484963171659942148390x^3 + 0.0028820878185134035637440105959294542908x^4
// q = Poly ([Decimal('1'), Decimal('-1.1185673672255329236623716486696411533'), Decimal('0.42736600959872448854098334016758333519'), Decimal('-0.063555884849631716599421483898013782858'), Decimal('0.0028820878185134035637440105959294542908')])
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
F7_CONST_DEF (X, 1, 0x8f,0x2d,0x37,0x2a,0x4d,0xa1,0x57, 0)
F7_CONST_DEF (X, 0, 0xda,0xcf,0xb7,0xb5,0x4c,0x0d,0xee, -2)
F7_CONST_DEF (X, 1, 0x82,0x29,0x96,0x77,0x2e,0x19,0xc7, -4)
F7_CONST_DEF (X, 0, 0xbc,0xe1,0x68,0xec,0xba,0x20,0x29, -9)
#endif

#elif defined (F7MOD_sincos_)
#if defined (FOR_SIN)
// sin(sqrt(x)) / sqrt(x)  in  [0, pi^2/16] ~ [0, 0.6169].
// Error < 3.313E-18, quality@quot ~ 1.
// p = Poly ([Decimal('0.9999999999999999966879566228039012'), Decimal('-0.1666666666666661475365354492822562'), Decimal('0.008333333333320002444252560522892007'), Decimal('-0.0001984126982840212992698250499618594'), Decimal('0.000002755731329901509333692668814721451'), Decimal('-2.505070584638448064973439248538648E-8'), Decimal('1.589413637225924008237178592214358E-10')])
// 0.9999999999999999966879566228039012 - 0.1666666666666661475365354492822562x + 0.008333333333320002444252560522892007x^2 - 0.0001984126982840212992698250499618594x^3 + 0.000002755731329901509333692668814721451x^4 - 2.505070584638448064973439248538648E-8x^5 + 1.589413637225924008237178592214358E-10x^6
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
F7_CONST_DEF (X, 1, 0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0x15, -3)
F7_CONST_DEF (X, 0, 0x88,0x88,0x88,0x88,0x87,0x98,0x63, -7)
F7_CONST_DEF (X, 1, 0xd0,0x0d,0x00,0xcd,0xc9,0x7e,0x34, -13)
F7_CONST_DEF (X, 0, 0xb8,0xef,0x1a,0x8f,0x9e,0x91,0xa2, -19)
F7_CONST_DEF (X, 1, 0xd7,0x2f,0x15,0xb0,0x7c,0x11,0x7a, -26)
F7_CONST_DEF (X, 0, 0xae,0xc2,0x04,0x43,0x51,0x29,0xe8, -33)
#elif defined (FOR_COS)
// cos(sqrt(x))  in  [0, pi^2/16] ~ [0, 0.6169].
// Error < 3.6E-20, quality@quot ~ 1.
// p = Poly ([Decimal('0.999999999999999999964159204335255989833'), Decimal('-0.499999999999999992843598630174036090975'), Decimal('0.0416666666666664302574165741342831192783'), Decimal('-0.00138888888888589604372397206213200172560'), Decimal('0.0000248015872828994642415389301648196400167'), Decimal('-2.75573128656963697259081300852869272237E-7'), Decimal('2.08755551457127352241183195408105664857E-9'), Decimal('-1.13521232075810109334454849167561526185E-11')])
// 0.999999999999999999964159204335255989833 - 0.499999999999999992843598630174036090975x + 0.0416666666666664302574165741342831192783x^2 - 0.00138888888888589604372397206213200172560x^3 + 0.0000248015872828994642415389301648196400167x^4 - 2.75573128656963697259081300852869272237E-7x^5 + 2.08755551457127352241183195408105664857E-9x^6 - 1.13521232075810109334454849167561526185E-11x^7
F7_CONST_DEF (X, 0, 0x80,0x00,0x00,0x00,0x00,0x00,0x00, 0)
F7_CONST_DEF (X, 1, 0xff,0xff,0xff,0xff,0xff,0xff,0xff, -2)
F7_CONST_DEF (X, 0, 0xaa,0xaa,0xaa,0xaa,0xaa,0xa9,0x9a, -5)
F7_CONST_DEF (X, 1, 0xb6,0x0b,0x60,0xb6,0x09,0xb1,0x66, -10)
F7_CONST_DEF (X, 0, 0xd0,0x0d,0x00,0xcd,0x6b,0xb3,0xf0, -16)
F7_CONST_DEF (X, 1, 0x93,0xf2,0x7b,0x7f,0x10,0xce,0x3d, -22)
F7_CONST_DEF (X, 0, 0x8f,0x74,0xaa,0x3c,0xcf,0x51,0x3d, -29)
F7_CONST_DEF (X, 1, 0xc7,0xb5,0x6a,0xf8,0x0e,0x32,0x07, -37)
#else
F7_CONST_DEF (pi_low,0, 0xd3,0x13,0x19,0x8a,0x2e,0x03,0x70, 1 - F7_MANT_BITS-2)
#endif

#endif
#endif /* ! IN_LIBF7_H && ! F7MOD_const_ */