mirror of
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Make quality improvements
- Write some more unit tests - memcpy() on ARM is now faster - Address the Musl complex math FIXME comments - Some libm funcs like pow() now support setting errno - Import the latest and greatest math functions from ARM - Use more accurate atan2f() and log1pf() implementations - atoi() and atol() will no longer saturate or clobber errno
This commit is contained in:
Justine Tunney
parent
af8f2bd19f
commit
592f6ebc20
122 changed files with 6305 additions and 3859 deletions
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@ -1,177 +1,120 @@
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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
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│ vi: set et ft=c ts=8 sts=2 sw=2 fenc=utf-8 :vi │
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/*-*- 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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│ Optimized Routines │
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│ Copyright (c) 1999-2022, Arm Limited. │
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│ FreeBSD lib/msun/src/s_asinhl.c │
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│ Converted to ldbl by David Schultz <das@FreeBSD.ORG> and Bruce D. Evans. │
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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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│ Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. │
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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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│ 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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│ 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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│ Copyright (c) 1992-2023 The FreeBSD Project. │
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│ │
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│ Redistribution and use in source and binary forms, with or without │
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│ modification, are permitted provided that the following conditions │
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│ are met: │
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│ 1. Redistributions of source code must retain the above copyright │
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│ notice, this list of conditions and the following disclaimer. │
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│ 2. Redistributions in binary form must reproduce the above copyright │
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│ notice, this list of conditions and the following disclaimer in the │
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│ documentation and/or other materials provided with the distribution. │
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│ │
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│ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND │
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│ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE │
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│ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE │
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│ ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE │
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│ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL │
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│ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS │
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│ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) │
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│ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT │
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│ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY │
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│ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF │
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│ SUCH DAMAGE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/intrin/likely.h"
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#include "libc/math.h"
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#include "libc/tinymath/atanf_common.internal.h"
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#include "libc/tinymath/internal.h"
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__static_yoink("arm_optimized_routines_notice");
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#include "libc/tinymath/freebsd.internal.h"
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__static_yoink("freebsd_libm_notice");
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__static_yoink("fdlibm_notice");
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#define Pi (0x1.921fb6p+1f)
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#define PiOver2 (0x1.921fb6p+0f)
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#define PiOver4 (0x1.921fb6p-1f)
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#define SignMask (0x80000000)
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static volatile float
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tiny = 1.0e-30;
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static const float
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zero = 0.0,
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pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
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pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
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pi = 3.1415927410e+00; /* 0x40490fdb */
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static volatile float
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pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */
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/* We calculate atan2f by P(n/d), where n and d are similar to the input
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arguments, and P is a polynomial. The polynomial may underflow.
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POLY_UFLOW_BOUND is the lower bound of the difference in exponents of n and d
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for which P underflows, and is used to special-case such inputs. */
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#define POLY_UFLOW_BOUND 24
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static inline int32_t
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biased_exponent (float f)
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{
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uint32_t fi = asuint (f);
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int32_t ex = (int32_t) ((fi & 0x7f800000) >> 23);
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if (UNLIKELY (ex == 0))
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{
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/* Subnormal case - we still need to get the exponent right for subnormal
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numbers as division may take us back inside the normal range. */
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return ex - __builtin_clz (fi << 9);
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}
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return ex;
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}
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/* Fast implementation of scalar atan2f. Largest observed error is
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2.88ulps in [99.0, 101.0] x [99.0, 101.0]:
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atan2f(0x1.9332d8p+6, 0x1.8cb6c4p+6) got 0x1.964646p-1
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want 0x1.964640p-1. */
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/**
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* Returns arc tangent of 𝑦/𝑥.
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*/
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float
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atan2f (float y, float x)
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atan2f(float y, float x)
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{
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uint32_t ix = asuint (x);
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uint32_t iy = asuint (y);
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float z;
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int32_t k,m,hx,hy,ix,iy;
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uint32_t sign_x = ix & SignMask;
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uint32_t sign_y = iy & SignMask;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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GET_FLOAT_WORD(hy,y);
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iy = hy&0x7fffffff;
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if((ix>0x7f800000)||
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(iy>0x7f800000)) /* x or y is NaN */
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return nan_mix(x, y);
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if(hx==0x3f800000) return atanf(y); /* x=1.0 */
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m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
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uint32_t iax = ix & ~SignMask;
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uint32_t iay = iy & ~SignMask;
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/* x or y is NaN. */
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if ((iax > 0x7f800000) || (iay > 0x7f800000))
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return x + y;
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/* m = 2 * sign(x) + sign(y). */
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uint32_t m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
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/* The following follows glibc ieee754 implementation, except
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that we do not use +-tiny shifts (non-nearest rounding mode). */
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int32_t exp_diff = biased_exponent (x) - biased_exponent (y);
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/* Special case for (x, y) either on or very close to the x axis. Either y =
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0, or y is tiny and x is huge (difference in exponents >=
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POLY_UFLOW_BOUND). In the second case, we only want to use this special
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case when x is negative (i.e. quadrants 2 or 3). */
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if (UNLIKELY (iay == 0 || (exp_diff >= POLY_UFLOW_BOUND && m >= 2)))
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{
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switch (m)
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{
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case 0:
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case 1:
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return y; /* atan(+-0,+anything)=+-0. */
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case 2:
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return Pi; /* atan(+0,-anything) = pi. */
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case 3:
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return -Pi; /* atan(-0,-anything) =-pi. */
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}
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}
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/* Special case for (x, y) either on or very close to the y axis. Either x =
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0, or x is tiny and y is huge (difference in exponents >=
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POLY_UFLOW_BOUND). */
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if (UNLIKELY (iax == 0 || exp_diff <= -POLY_UFLOW_BOUND))
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return sign_y ? -PiOver2 : PiOver2;
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/* x is INF. */
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if (iax == 0x7f800000)
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{
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if (iay == 0x7f800000)
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{
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switch (m)
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{
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case 0:
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return PiOver4; /* atan(+INF,+INF). */
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case 1:
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return -PiOver4; /* atan(-INF,+INF). */
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case 2:
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return 3.0f * PiOver4; /* atan(+INF,-INF). */
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case 3:
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return -3.0f * PiOver4; /* atan(-INF,-INF). */
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/* when y = 0 */
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if(iy==0) {
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switch(m) {
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case 0:
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case 1: return y; /* atan(+-0,+anything)=+-0 */
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case 2: return pi+tiny;/* atan(+0,-anything) = pi */
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case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
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}
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}
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else
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{
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switch (m)
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{
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case 0:
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return 0.0f; /* atan(+...,+INF). */
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case 1:
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return -0.0f; /* atan(-...,+INF). */
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case 2:
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return Pi; /* atan(+...,-INF). */
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case 3:
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return -Pi; /* atan(-...,-INF). */
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/* when x = 0 */
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if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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/* when x is INF */
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if(ix==0x7f800000) {
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if(iy==0x7f800000) {
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switch(m) {
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case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
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case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
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case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
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case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
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}
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} else {
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switch(m) {
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case 0: return zero ; /* atan(+...,+INF) */
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case 1: return -zero ; /* atan(-...,+INF) */
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case 2: return pi+tiny ; /* atan(+...,-INF) */
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case 3: return -pi-tiny ; /* atan(-...,-INF) */
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}
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}
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}
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}
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/* y is INF. */
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if (iay == 0x7f800000)
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return sign_y ? -PiOver2 : PiOver2;
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/* when y is INF */
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if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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uint32_t sign_xy = sign_x ^ sign_y;
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float ax = asfloat (iax);
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float ay = asfloat (iay);
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bool pred_aygtax = (ay > ax);
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/* Set up z for call to atanf. */
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float n = pred_aygtax ? -ax : ay;
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float d = pred_aygtax ? ay : ax;
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float z = n / d;
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float ret;
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if (UNLIKELY (m < 2 && exp_diff >= POLY_UFLOW_BOUND))
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{
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/* If (x, y) is very close to x axis and x is positive, the polynomial
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will underflow and evaluate to z. */
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ret = z;
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}
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else
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{
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/* Work out the correct shift. */
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float shift = sign_x ? -2.0f : 0.0f;
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shift = pred_aygtax ? shift + 1.0f : shift;
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shift *= PiOver2;
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ret = eval_poly (z, z, shift);
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}
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/* Account for the sign of x and y. */
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return asfloat (asuint (ret) ^ sign_xy);
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/* compute y/x */
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k = (iy-ix)>>23;
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if(k > 26) { /* |y/x| > 2**26 */
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z=pi_o_2+(float)0.5*pi_lo;
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m&=1;
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}
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else if(k<-26&&hx<0) z=0.0; /* 0 > |y|/x > -2**-26 */
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else z=atanf(fabsf(y/x)); /* safe to do y/x */
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switch (m) {
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case 0: return z ; /* atan(+,+) */
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case 1: return -z ; /* atan(-,+) */
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case 2: return pi-(z-pi_lo);/* atan(+,-) */
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default: /* case 3 */
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return (z-pi_lo)-pi;/* atan(-,-) */
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}
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}
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