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957c61cbbf
This change upgrades to GCC 12.3 and GNU binutils 2.42. The GNU linker appears to have changed things so that only a single de-duplicated str table is present in the binary, and it gets placed wherever the linker wants, regardless of what the linker script says. To cope with that we need to stop using .ident to embed licenses. As such, this change does significant work to revamp how third party licenses are defined in the codebase, using `.section .notice,"aR",@progbits`. This new GCC 12.3 toolchain has support for GNU indirect functions. It lets us support __target_clones__ for the first time. This is used for optimizing the performance of libc string functions such as strlen and friends so far on x86, by ensuring AVX systems favor a second codepath that uses VEX encoding. It shaves some latency off certain operations. It's a useful feature to have for scientific computing for the reasons explained by the test/libcxx/openmp_test.cc example which compiles for fifteen different microarchitectures. Thanks to the upgrades, it's now also possible to use newer instruction sets, such as AVX512FP16, VNNI. Cosmo now uses the %gs register on x86 by default for TLS. Doing it is helpful for any program that links `cosmo_dlopen()`. Such programs had to recompile their binaries at startup to change the TLS instructions. That's not great, since it means every page in the executable needs to be faulted. The work of rewriting TLS-related x86 opcodes, is moved to fixupobj.com instead. This is great news for MacOS x86 users, since we previously needed to morph the binary every time for that platform but now that's no longer necessary. The only platforms where we need fixup of TLS x86 opcodes at runtime are now Windows, OpenBSD, and NetBSD. On Windows we morph TLS to point deeper into the TIB, based on a TlsAlloc assignment, and on OpenBSD/NetBSD we morph %gs back into %fs since the kernels do not allow us to specify a value for the %gs register. OpenBSD users are now required to use APE Loader to run Cosmo binaries and assimilation is no longer possible. OpenBSD kernel needs to change to allow programs to specify a value for the %gs register, or it needs to stop marking executable pages loaded by the kernel as mimmutable(). This release fixes __constructor__, .ctor, .init_array, and lastly the .preinit_array so they behave the exact same way as glibc. We no longer use hex constants to define math.h symbols like M_PI.
334 lines
14 KiB
C
334 lines
14 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
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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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__static_yoink("musl_libc_notice");
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__static_yoink("fdlibm_notice");
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/* origin: FreeBSD /usr/src/lib/msun/src/s_erf.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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/* double erf(double x)
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* double erfc(double x)
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* x
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* 2 |\
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* erf(x) = --------- | exp(-t*t)dt
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* sqrt(pi) \|
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* 0
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*
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* erfc(x) = 1-erf(x)
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* Note that
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* erf(-x) = -erf(x)
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* erfc(-x) = 2 - erfc(x)
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*
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* Method:
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* 1. For |x| in [0, 0.84375]
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* erf(x) = x + x*R(x^2)
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* erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
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* = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
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* where R = P/Q where P is an odd poly of degree 8 and
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* Q is an odd poly of degree 10.
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* -57.90
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* | R - (erf(x)-x)/x | <= 2
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*
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*
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* Remark. The formula is derived by noting
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* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
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* and that
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* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
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* is close to one. The interval is chosen because the fix
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* point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
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* near 0.6174), and by some experiment, 0.84375 is chosen to
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* guarantee the error is less than one ulp for erf.
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*
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* 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
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* c = 0.84506291151 rounded to single (24 bits)
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* erf(x) = sign(x) * (c + P1(s)/Q1(s))
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* erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
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* 1+(c+P1(s)/Q1(s)) if x < 0
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* |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
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* Remark: here we use the taylor series expansion at x=1.
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* erf(1+s) = erf(1) + s*Poly(s)
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* = 0.845.. + P1(s)/Q1(s)
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* That is, we use rational approximation to approximate
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* erf(1+s) - (c = (single)0.84506291151)
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* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
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* where
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* P1(s) = degree 6 poly in s
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* Q1(s) = degree 6 poly in s
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*
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* 3. For x in [1.25,1/0.35(~2.857143)],
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* erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
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* erf(x) = 1 - erfc(x)
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* where
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* R1(z) = degree 7 poly in z, (z=1/x^2)
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* S1(z) = degree 8 poly in z
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*
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* 4. For x in [1/0.35,28]
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* erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
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* = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
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* = 2.0 - tiny (if x <= -6)
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* erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
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* erf(x) = sign(x)*(1.0 - tiny)
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* where
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* R2(z) = degree 6 poly in z, (z=1/x^2)
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* S2(z) = degree 7 poly in z
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*
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* Note1:
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* To compute exp(-x*x-0.5625+R/S), let s be a single
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* precision number and s := x; then
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* -x*x = -s*s + (s-x)*(s+x)
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* exp(-x*x-0.5626+R/S) =
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* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
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* Note2:
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* Here 4 and 5 make use of the asymptotic series
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* exp(-x*x)
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* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
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* x*sqrt(pi)
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* We use rational approximation to approximate
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* g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
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* Here is the error bound for R1/S1 and R2/S2
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* |R1/S1 - f(x)| < 2**(-62.57)
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* |R2/S2 - f(x)| < 2**(-61.52)
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*
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* 5. For inf > x >= 28
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* erf(x) = sign(x) *(1 - tiny) (raise inexact)
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* erfc(x) = tiny*tiny (raise underflow) if x > 0
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* = 2 - tiny if x<0
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*
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* 7. Special case:
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* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
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* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
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* erfc/erf(NaN) is NaN
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*/
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static const double
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erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
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/*
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* Coefficients for approximation to erf on [0,0.84375]
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*/
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efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
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pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
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pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
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pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
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pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
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pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
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qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
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qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
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qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
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qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
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qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
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/*
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* Coefficients for approximation to erf in [0.84375,1.25]
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*/
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pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
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pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
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pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
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pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
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pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
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pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
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pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
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qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
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qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
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qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
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qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
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qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
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qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
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/*
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* Coefficients for approximation to erfc in [1.25,1/0.35]
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*/
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ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
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ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
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ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
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ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
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ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
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ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
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ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
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ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
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sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
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sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
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sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
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sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
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sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
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sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
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sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
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sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
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/*
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* Coefficients for approximation to erfc in [1/.35,28]
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*/
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rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
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rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
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rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
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rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
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rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
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rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
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rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
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sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
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sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
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sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
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sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
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sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
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sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
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sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
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#define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
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#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
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#define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
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#define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f
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#define INSERT_WORDS(d,hi,lo) \
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do { \
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(d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
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} while (0)
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#define GET_HIGH_WORD(hi,d) \
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do { \
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(hi) = asuint64(d) >> 32; \
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} while (0)
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#define GET_LOW_WORD(lo,d) \
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do { \
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(lo) = (uint32_t)asuint64(d); \
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} while (0)
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#define SET_HIGH_WORD(d,hi) \
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INSERT_WORDS(d, hi, (uint32_t)asuint64(d))
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#define SET_LOW_WORD(d,lo) \
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INSERT_WORDS(d, asuint64(d)>>32, lo)
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static double erfc1(double x)
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{
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double_t s,P,Q;
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s = fabs(x) - 1;
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P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
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Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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return 1 - erx - P/Q;
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}
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static double erfc2(uint32_t ix, double x)
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{
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double_t s,R,S;
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double z;
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if (ix < 0x3ff40000) /* |x| < 1.25 */
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return erfc1(x);
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x = fabs(x);
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s = 1/(x*x);
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if (ix < 0x4006db6d) { /* |x| < 1/.35 ~ 2.85714 */
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R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
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ra5+s*(ra6+s*ra7))))));
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S = 1.0+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
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sa5+s*(sa6+s*(sa7+s*sa8)))))));
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} else { /* |x| > 1/.35 */
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R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
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rb5+s*rb6)))));
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S = 1.0+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
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sb5+s*(sb6+s*sb7))))));
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}
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z = x;
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SET_LOW_WORD(z,0);
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return exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S)/x;
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}
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/**
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* Returns error function of 𝑥.
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*/
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double erf(double x)
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{
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double r,s,z,y;
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uint32_t ix;
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int sign;
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GET_HIGH_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7ff00000) {
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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return 1-2*sign + 1/x;
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}
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if (ix < 0x3feb0000) { /* |x| < 0.84375 */
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if (ix < 0x3e300000) { /* |x| < 2**-28 */
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/* avoid underflow */
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return 0.125*(8*x + efx8*x);
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}
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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return x + x*y;
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}
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if (ix < 0x40180000) /* 0.84375 <= |x| < 6 */
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y = 1 - erfc2(ix,x);
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else
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y = 1 - 0x1p-1022;
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return sign ? -y : y;
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}
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/**
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* Returns complementary error function of 𝑥.
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*/
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double erfc(double x)
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{
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double r,s,z,y;
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uint32_t ix;
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int sign;
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GET_HIGH_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7ff00000) {
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/* erfc(nan)=nan, erfc(+-inf)=0,2 */
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return 2*sign + 1/x;
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}
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if (ix < 0x3feb0000) { /* |x| < 0.84375 */
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if (ix < 0x3c700000) /* |x| < 2**-56 */
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return 1.0 - x;
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
|
||
if (sign || ix < 0x3fd00000) { /* x < 1/4 */
|
||
return 1.0 - (x+x*y);
|
||
}
|
||
return 0.5 - (x - 0.5 + x*y);
|
||
}
|
||
if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */
|
||
return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
|
||
}
|
||
return sign ? 2 - 0x1p-1022 : 0x1p-1022*0x1p-1022;
|
||
}
|
||
|
||
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
|
||
__weak_reference(erf, erfl);
|
||
__weak_reference(erfc, erfcl);
|
||
#endif
|