2023-05-03 01:35:25 +00:00
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/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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2023-12-13 07:28:11 +00:00
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│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
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2023-05-03 01:35:25 +00:00
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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#include "libc/tinymath/internal.h"
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#include "libc/tinymath/ldshape.internal.h"
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2023-05-15 23:32:10 +00:00
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#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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2023-05-03 01:35:25 +00:00
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asm(".ident\t\"\\n\\n\
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fdlibm (fdlibm license)\\n\
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Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2014 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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2023-05-09 04:38:30 +00:00
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// clang-format off
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2023-05-03 01:35:25 +00:00
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/* origin: FreeBSD /usr/src/lib/msun/src/s_atanl.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* See comments in atan.c.
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* Converted to long double by David Schultz <das@FreeBSD.ORG>.
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*/
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#if LDBL_MANT_DIG == 64
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#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | (u.i.m>>55 & 0xff))
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static const long double atanhi[] = {
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4.63647609000806116202e-01L,
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7.85398163397448309628e-01L,
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9.82793723247329067960e-01L,
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1.57079632679489661926e+00L,
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};
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static const long double atanlo[] = {
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1.18469937025062860669e-20L,
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-1.25413940316708300586e-20L,
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2.55232234165405176172e-20L,
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-2.50827880633416601173e-20L,
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};
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static const long double aT[] = {
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3.33333333333333333017e-01L,
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-1.99999999999999632011e-01L,
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1.42857142857046531280e-01L,
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-1.11111111100562372733e-01L,
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9.09090902935647302252e-02L,
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-7.69230552476207730353e-02L,
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6.66661718042406260546e-02L,
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-5.88158892835030888692e-02L,
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5.25499891539726639379e-02L,
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-4.70119845393155721494e-02L,
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4.03539201366454414072e-02L,
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-2.91303858419364158725e-02L,
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1.24822046299269234080e-02L,
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};
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static long double T_even(long double x)
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{
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return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
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x * (aT[8] + x * (aT[10] + x * aT[12])))));
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}
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static long double T_odd(long double x)
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{
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return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
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x * (aT[9] + x * aT[11]))));
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}
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#elif LDBL_MANT_DIG == 113
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#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | u.i.top>>8)
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static const long double atanhi[] = {
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4.63647609000806116214256231461214397e-01L,
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7.85398163397448309615660845819875699e-01L,
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9.82793723247329067985710611014666038e-01L,
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1.57079632679489661923132169163975140e+00L,
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};
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static const long double atanlo[] = {
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4.89509642257333492668618435220297706e-36L,
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2.16795253253094525619926100651083806e-35L,
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-2.31288434538183565909319952098066272e-35L,
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4.33590506506189051239852201302167613e-35L,
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};
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static const long double aT[] = {
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3.33333333333333333333333333333333125e-01L,
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-1.99999999999999999999999999999180430e-01L,
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1.42857142857142857142857142125269827e-01L,
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-1.11111111111111111111110834490810169e-01L,
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9.09090909090909090908522355708623681e-02L,
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-7.69230769230769230696553844935357021e-02L,
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6.66666666666666660390096773046256096e-02L,
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-5.88235294117646671706582985209643694e-02L,
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5.26315789473666478515847092020327506e-02L,
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-4.76190476189855517021024424991436144e-02L,
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4.34782608678695085948531993458097026e-02L,
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-3.99999999632663469330634215991142368e-02L,
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3.70370363987423702891250829918659723e-02L,
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-3.44827496515048090726669907612335954e-02L,
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3.22579620681420149871973710852268528e-02L,
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-3.03020767654269261041647570626778067e-02L,
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2.85641979882534783223403715930946138e-02L,
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-2.69824879726738568189929461383741323e-02L,
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2.54194698498808542954187110873675769e-02L,
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-2.35083879708189059926183138130183215e-02L,
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2.04832358998165364349957325067131428e-02L,
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-1.54489555488544397858507248612362957e-02L,
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8.64492360989278761493037861575248038e-03L,
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-2.58521121597609872727919154569765469e-03L,
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};
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static long double T_even(long double x)
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{
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return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * (aT[8] +
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x * (aT[10] + x * (aT[12] + x * (aT[14] + x * (aT[16] +
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x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
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}
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static long double T_odd(long double x)
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{
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return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * (aT[9] +
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x * (aT[11] + x * (aT[13] + x * (aT[15] + x * (aT[17] +
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x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
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}
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#endif
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/**
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* Returns arc tangent of 𝑥.
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*
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* 1 3 1 5 1 7 1 9 1 11
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* atan(𝑥) = 𝑥 - - 𝑥 + - 𝑥 - - 𝑥 + - 𝑥 - -- 𝑥 ...
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* 3 5 7 9 11
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*
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* @param 𝑥 is an 80-bit long double passed on stack in 16-bytes
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* @return result of computation on FPU stack in %st
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* @define atan(𝑥) = Σₙ₌₀₋∞ 2²ⁿ(𝑛!)²/(𝟸𝑛+𝟷)!(𝑥²ⁿ⁺¹/(𝑥²+𝟷)ⁿ⁺¹)
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*/
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long double atanl(long double x)
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{
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union ldshape u = {x};
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long double w, s1, s2, z;
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int id;
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unsigned e = u.i.se & 0x7fff;
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unsigned sign = u.i.se >> 15;
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unsigned expman;
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if (e >= 0x3fff + LDBL_MANT_DIG + 1) { /* if |x| is large, atan(x)~=pi/2 */
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if (isnan(x))
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return x;
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return sign ? -atanhi[3] : atanhi[3];
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}
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/* Extract the exponent and the first few bits of the mantissa. */
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expman = EXPMAN(u);
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if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
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if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { /* if |x| is small, atanl(x)~=x */
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/* raise underflow if subnormal */
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if (e == 0)
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FORCE_EVAL((float)x);
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return x;
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}
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id = -1;
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} else {
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x = fabsl(x);
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if (expman < (0x3fff << 8) + 0x30) { /* |x| < 1.1875 */
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if (expman < ((0x3fff - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
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id = 0;
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x = (2.0*x-1.0)/(2.0+x);
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} else { /* 11/16 <= |x| < 19/16 */
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id = 1;
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x = (x-1.0)/(x+1.0);
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}
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} else {
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if (expman < ((0x3fff + 1) << 8) + 0x38) { /* |x| < 2.4375 */
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id = 2;
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x = (x-1.5)/(1.0+1.5*x);
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} else { /* 2.4375 <= |x| */
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id = 3;
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x = -1.0/x;
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}
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}
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}
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/* end of argument reduction */
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z = x*x;
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w = z*z;
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/* break sum aT[i]z**(i+1) into odd and even poly */
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s1 = z*T_even(w);
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s2 = w*T_odd(w);
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if (id < 0)
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return x - x*(s1+s2);
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z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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return sign ? -z : z;
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}
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2023-05-15 23:32:10 +00:00
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#endif /* long double is long */
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