mirror of
https://github.com/jart/cosmopolitan.git
synced 2024-05-18 03:22:40 +00:00
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.
475 lines
19 KiB
C
475 lines
19 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
|
|
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
|
|
╚──────────────────────────────────────────────────────────────────────────────╝
|
|
│ │
|
|
│ Musl Libc │
|
|
│ Copyright © 2005-2014 Rich Felker, et al. │
|
|
│ │
|
|
│ 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 "libc/math.h"
|
|
#include "libc/tinymath/kernel.internal.h"
|
|
__static_yoink("musl_libc_notice");
|
|
__static_yoink("fdlibm_notice");
|
|
|
|
#pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
|
|
|
|
|
|
/* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.c */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
/*
|
|
* __rem_pio2_large(x,y,e0,nx,prec)
|
|
* double x[],y[]; int e0,nx,prec;
|
|
*
|
|
* __rem_pio2_large return the last three digits of N with
|
|
* y = x - N*pi/2
|
|
* so that |y| < pi/2.
|
|
*
|
|
* The method is to compute the integer (mod 8) and fraction parts of
|
|
* (2/pi)*x without doing the full multiplication. In general we
|
|
* skip the part of the product that are known to be a huge integer (
|
|
* more accurately, = 0 mod 8 ). Thus the number of operations are
|
|
* independent of the exponent of the input.
|
|
*
|
|
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
|
|
*
|
|
* Input parameters:
|
|
* x[] The input value (must be positive) is broken into nx
|
|
* pieces of 24-bit integers in double precision format.
|
|
* x[i] will be the i-th 24 bit of x. The scaled exponent
|
|
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
|
|
* match x's up to 24 bits.
|
|
*
|
|
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
|
|
* e0 = ilogb(z)-23
|
|
* z = scalbn(z,-e0)
|
|
* for i = 0,1,2
|
|
* x[i] = floor(z)
|
|
* z = (z-x[i])*2**24
|
|
*
|
|
*
|
|
* y[] output result in an array of double precision numbers.
|
|
* The dimension of y[] is:
|
|
* 24-bit precision 1
|
|
* 53-bit precision 2
|
|
* 64-bit precision 2
|
|
* 113-bit precision 3
|
|
* The actual value is the sum of them. Thus for 113-bit
|
|
* precision, one may have to do something like:
|
|
*
|
|
* long double t,w,r_head, r_tail;
|
|
* t = (long double)y[2] + (long double)y[1];
|
|
* w = (long double)y[0];
|
|
* r_head = t+w;
|
|
* r_tail = w - (r_head - t);
|
|
*
|
|
* e0 The exponent of x[0]. Must be <= 16360 or you need to
|
|
* expand the ipio2 table.
|
|
*
|
|
* nx dimension of x[]
|
|
*
|
|
* prec an integer indicating the precision:
|
|
* 0 24 bits (single)
|
|
* 1 53 bits (double)
|
|
* 2 64 bits (extended)
|
|
* 3 113 bits (quad)
|
|
*
|
|
* External function:
|
|
* double scalbn(), floor();
|
|
*
|
|
*
|
|
* Here is the description of some local variables:
|
|
*
|
|
* jk jk+1 is the initial number of terms of ipio2[] needed
|
|
* in the computation. The minimum and recommended value
|
|
* for jk is 3,4,4,6 for single, double, extended, and quad.
|
|
* jk+1 must be 2 larger than you might expect so that our
|
|
* recomputation test works. (Up to 24 bits in the integer
|
|
* part (the 24 bits of it that we compute) and 23 bits in
|
|
* the fraction part may be lost to cancellation before we
|
|
* recompute.)
|
|
*
|
|
* jz local integer variable indicating the number of
|
|
* terms of ipio2[] used.
|
|
*
|
|
* jx nx - 1
|
|
*
|
|
* jv index for pointing to the suitable ipio2[] for the
|
|
* computation. In general, we want
|
|
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
|
|
* is an integer. Thus
|
|
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
|
|
* Hence jv = max(0,(e0-3)/24).
|
|
*
|
|
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
|
|
*
|
|
* q[] double array with integral value, representing the
|
|
* 24-bits chunk of the product of x and 2/pi.
|
|
*
|
|
* q0 the corresponding exponent of q[0]. Note that the
|
|
* exponent for q[i] would be q0-24*i.
|
|
*
|
|
* PIo2[] double precision array, obtained by cutting pi/2
|
|
* into 24 bits chunks.
|
|
*
|
|
* f[] ipio2[] in floating point
|
|
*
|
|
* iq[] integer array by breaking up q[] in 24-bits chunk.
|
|
*
|
|
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
|
|
*
|
|
* ih integer. If >0 it indicates q[] is >= 0.5, hence
|
|
* it also indicates the *sign* of the result.
|
|
*
|
|
*/
|
|
/*
|
|
* Constants:
|
|
* The hexadecimal values are the intended ones for the following
|
|
* constants. The decimal values may be used, provided that the
|
|
* compiler will convert from decimal to binary accurately enough
|
|
* to produce the hexadecimal values shown.
|
|
*/
|
|
|
|
static const int init_jk[] = {3,4,4,6}; /* initial value for jk */
|
|
|
|
/*
|
|
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
|
*
|
|
* integer array, contains the (24*i)-th to (24*i+23)-th
|
|
* bit of 2/pi after binary point. The corresponding
|
|
* floating value is
|
|
*
|
|
* ipio2[i] * 2^(-24(i+1)).
|
|
*
|
|
* NB: This table must have at least (e0-3)/24 + jk terms.
|
|
* For quad precision (e0 <= 16360, jk = 6), this is 686.
|
|
*/
|
|
static const int32_t ipio2[] = {
|
|
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
|
|
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
|
|
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
|
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
|
|
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
|
|
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
|
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
|
|
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
|
|
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
|
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
|
|
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
|
|
#if LDBL_MAX_EXP > 1024
|
|
0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6,
|
|
0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2,
|
|
0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35,
|
|
0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30,
|
|
0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C,
|
|
0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4,
|
|
0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770,
|
|
0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7,
|
|
0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19,
|
|
0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522,
|
|
0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16,
|
|
0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6,
|
|
0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E,
|
|
0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48,
|
|
0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3,
|
|
0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF,
|
|
0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55,
|
|
0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612,
|
|
0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929,
|
|
0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC,
|
|
0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B,
|
|
0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C,
|
|
0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4,
|
|
0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB,
|
|
0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC,
|
|
0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C,
|
|
0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F,
|
|
0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5,
|
|
0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437,
|
|
0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B,
|
|
0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA,
|
|
0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD,
|
|
0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3,
|
|
0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3,
|
|
0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717,
|
|
0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F,
|
|
0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61,
|
|
0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB,
|
|
0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51,
|
|
0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0,
|
|
0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C,
|
|
0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6,
|
|
0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC,
|
|
0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED,
|
|
0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328,
|
|
0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D,
|
|
0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0,
|
|
0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B,
|
|
0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4,
|
|
0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3,
|
|
0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F,
|
|
0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD,
|
|
0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B,
|
|
0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4,
|
|
0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761,
|
|
0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31,
|
|
0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30,
|
|
0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262,
|
|
0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E,
|
|
0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1,
|
|
0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C,
|
|
0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4,
|
|
0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08,
|
|
0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196,
|
|
0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9,
|
|
0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4,
|
|
0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC,
|
|
0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C,
|
|
0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0,
|
|
0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C,
|
|
0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0,
|
|
0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC,
|
|
0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22,
|
|
0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893,
|
|
0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7,
|
|
0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5,
|
|
0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F,
|
|
0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4,
|
|
0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF,
|
|
0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B,
|
|
0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2,
|
|
0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138,
|
|
0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E,
|
|
0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569,
|
|
0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34,
|
|
0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9,
|
|
0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D,
|
|
0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F,
|
|
0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855,
|
|
0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569,
|
|
0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B,
|
|
0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE,
|
|
0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41,
|
|
0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49,
|
|
0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F,
|
|
0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110,
|
|
0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8,
|
|
0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365,
|
|
0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A,
|
|
0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270,
|
|
0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5,
|
|
0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616,
|
|
0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B,
|
|
0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0,
|
|
#endif
|
|
};
|
|
|
|
static const double PIo2[] = {
|
|
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
|
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
|
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
|
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
|
|
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
|
|
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
|
|
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
|
|
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
|
|
};
|
|
|
|
int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec)
|
|
{
|
|
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
|
double z,fw,f[20],fq[20],q[20];
|
|
|
|
/* initialize jk*/
|
|
jk = init_jk[prec];
|
|
jp = jk;
|
|
|
|
/* determine jx,jv,q0, note that 3>q0 */
|
|
jx = nx-1;
|
|
jv = (e0-3)/24; if(jv<0) jv=0;
|
|
q0 = e0-24*(jv+1);
|
|
|
|
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
|
j = jv-jx; m = jx+jk;
|
|
for (i=0; i<=m; i++,j++)
|
|
f[i] = j<0 ? 0.0 : (double)ipio2[j];
|
|
|
|
/* compute q[0],q[1],...q[jk] */
|
|
for (i=0; i<=jk; i++) {
|
|
for (j=0,fw=0.0; j<=jx; j++)
|
|
fw += x[j]*f[jx+i-j];
|
|
q[i] = fw;
|
|
}
|
|
|
|
jz = jk;
|
|
recompute:
|
|
/* distill q[] into iq[] reversingly */
|
|
for (i=0,j=jz,z=q[jz]; j>0; i++,j--) {
|
|
fw = (double)(int32_t)(0x1p-24*z);
|
|
iq[i] = (int32_t)(z - 0x1p24*fw);
|
|
z = q[j-1]+fw;
|
|
}
|
|
|
|
/* compute n */
|
|
z = scalbn(z,q0); /* actual value of z */
|
|
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
|
|
n = (int32_t)z;
|
|
z -= (double)n;
|
|
ih = 0;
|
|
if (q0 > 0) { /* need iq[jz-1] to determine n */
|
|
i = iq[jz-1]>>(24-q0); n += i;
|
|
iq[jz-1] -= i<<(24-q0);
|
|
ih = iq[jz-1]>>(23-q0);
|
|
}
|
|
else if (q0 == 0) ih = iq[jz-1]>>23;
|
|
else if (z >= 0.5) ih = 2;
|
|
|
|
if (ih > 0) { /* q > 0.5 */
|
|
n += 1; carry = 0;
|
|
for (i=0; i<jz; i++) { /* compute 1-q */
|
|
j = iq[i];
|
|
if (carry == 0) {
|
|
if (j != 0) {
|
|
carry = 1;
|
|
iq[i] = 0x1000000 - j;
|
|
}
|
|
} else
|
|
iq[i] = 0xffffff - j;
|
|
}
|
|
if (q0 > 0) { /* rare case: chance is 1 in 12 */
|
|
switch(q0) {
|
|
case 1:
|
|
iq[jz-1] &= 0x7fffff; break;
|
|
case 2:
|
|
iq[jz-1] &= 0x3fffff; break;
|
|
}
|
|
}
|
|
if (ih == 2) {
|
|
z = 1.0 - z;
|
|
if (carry != 0)
|
|
z -= scalbn(1.0,q0);
|
|
}
|
|
}
|
|
|
|
/* check if recomputation is needed */
|
|
if (z == 0.0) {
|
|
j = 0;
|
|
for (i=jz-1; i>=jk; i--) j |= iq[i];
|
|
if (j == 0) { /* need recomputation */
|
|
for (k=1; iq[jk-k]==0; k++); /* k = no. of terms needed */
|
|
|
|
for (i=jz+1; i<=jz+k; i++) { /* add q[jz+1] to q[jz+k] */
|
|
f[jx+i] = (double)ipio2[jv+i];
|
|
for (j=0,fw=0.0; j<=jx; j++)
|
|
fw += x[j]*f[jx+i-j];
|
|
q[i] = fw;
|
|
}
|
|
jz += k;
|
|
goto recompute;
|
|
}
|
|
}
|
|
|
|
/* chop off zero terms */
|
|
if (z == 0.0) {
|
|
jz -= 1;
|
|
q0 -= 24;
|
|
while (iq[jz] == 0) {
|
|
jz--;
|
|
q0 -= 24;
|
|
}
|
|
} else { /* break z into 24-bit if necessary */
|
|
z = scalbn(z,-q0);
|
|
if (z >= 0x1p24) {
|
|
fw = (double)(int32_t)(0x1p-24*z);
|
|
iq[jz] = (int32_t)(z - 0x1p24*fw);
|
|
jz += 1;
|
|
q0 += 24;
|
|
iq[jz] = (int32_t)fw;
|
|
} else
|
|
iq[jz] = (int32_t)z;
|
|
}
|
|
|
|
/* convert integer "bit" chunk to floating-point value */
|
|
fw = scalbn(1.0,q0);
|
|
for (i=jz; i>=0; i--) {
|
|
q[i] = fw*(double)iq[i];
|
|
fw *= 0x1p-24;
|
|
}
|
|
|
|
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
|
for(i=jz; i>=0; i--) {
|
|
for (fw=0.0,k=0; k<=jp && k<=jz-i; k++)
|
|
fw += PIo2[k]*q[i+k];
|
|
fq[jz-i] = fw;
|
|
}
|
|
|
|
/* compress fq[] into y[] */
|
|
switch(prec) {
|
|
case 0:
|
|
fw = 0.0;
|
|
for (i=jz; i>=0; i--)
|
|
fw += fq[i];
|
|
y[0] = ih==0 ? fw : -fw;
|
|
break;
|
|
case 1:
|
|
case 2:
|
|
fw = 0.0;
|
|
for (i=jz; i>=0; i--)
|
|
fw += fq[i];
|
|
// TODO: drop excess precision here once double_t is used
|
|
fw = (double)fw;
|
|
y[0] = ih==0 ? fw : -fw;
|
|
fw = fq[0]-fw;
|
|
for (i=1; i<=jz; i++)
|
|
fw += fq[i];
|
|
y[1] = ih==0 ? fw : -fw;
|
|
break;
|
|
case 3: /* painful */
|
|
for (i=jz; i>0; i--) {
|
|
fw = fq[i-1]+fq[i];
|
|
fq[i] += fq[i-1]-fw;
|
|
fq[i-1] = fw;
|
|
}
|
|
for (i=jz; i>1; i--) {
|
|
fw = fq[i-1]+fq[i];
|
|
fq[i] += fq[i-1]-fw;
|
|
fq[i-1] = fw;
|
|
}
|
|
for (fw=0.0,i=jz; i>=2; i--)
|
|
fw += fq[i];
|
|
if (ih==0) {
|
|
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
|
} else {
|
|
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
|
}
|
|
}
|
|
return n&7;
|
|
}
|