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0242c9f9e6
The libm size improvement built with gcc-14, "--enable-stack-protector=strong --enable-bind-now=yes --enable-fortify-source=2": Before: 582292 844 12 583148 8e5ec aarch64-linux-gnu/math/libm.so 975133 1076 12 976221 ee55d x86_64-linux-gnu/math/libm.so 1203586 5608 368 1209562 1274da powerpc64le-linux-gnu/math/libm.so After: 581972 844 12 582828 8e4ac aarch64-linux-gnu/math/libm.so 974941 1076 12 976029 ee49d x86_64-linux-gnu/math/libm.so 1203394 5608 368 1209370 12741a powerpc64le-linux-gnu/math/libm.so Reviewed-by: Andreas K. Huettel <dilfridge@gentoo.org>
119 lines
3.7 KiB
C
119 lines
3.7 KiB
C
/* Correctly-rounded arc-sine function for binary32 value.
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Copyright (c) 2023-2024 Alexei Sibidanov.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/asin/asinf.c, revision bc385c2).
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#include <stdint.h>
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#include <errno.h>
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#include <libm-alias-finite.h>
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#include "math_config.h"
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#include "s_asincosf_data.h"
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static __attribute__ ((noinline)) float
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as_special (float x)
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{
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uint32_t ax = asuint (x) << 1;
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if (ax > (0xffu << 24))
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return x + x; /* nan */
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return __math_invalidf (0.0);
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}
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static double
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poly12 (double z, const double *c)
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{
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double z2 = z * z;
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double z4 = z2 * z2;
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double c0 = c[0] + z * c[1];
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double c2 = c[2] + z * c[3];
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double c4 = c[4] + z * c[5];
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double c6 = c[6] + z * c[7];
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double c8 = c[8] + z * c[9];
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double c10 = c[10] + z * c[11];
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c0 += c2 * z2;
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c4 += c6 * z2;
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c8 += z2 * c10;
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c0 += z4 * (c4 + z4 * c8);
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return c0;
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}
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float
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__ieee754_asinf (float x)
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{
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const double pi2 = 0x1.921fb54442d18p+0;
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double xs = x;
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double r;
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uint32_t ax = asuint (x) << 1;
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if (__glibc_unlikely (ax > 0x7f << 24))
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return as_special(x);
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if (__glibc_likely (ax < 0x7ec29000u))
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{
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if (__glibc_unlikely (ax < 115 << 24))
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return fmaf (x, 0x1p-25, x);
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static const double b[] =
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{
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0x1.0000000000005p+0, 0x1.55557aeca105dp-3, 0x1.3314ec3db7d12p-4,
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0x1.775738a5a6f92p-5, 0x1.5d5f7ce1c8538p-8, 0x1.605c6d58740fp-2,
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-0x1.5728b732d73c6p+1, 0x1.f152170f151ebp+3, -0x1.f962ea3ca992ep+5,
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0x1.71971e17375ap+7, -0x1.860512b4ba23p+8, 0x1.26a3b8d4bdb14p+9,
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-0x1.36f2ea5698b51p+9, 0x1.b3d722aebfa2ep+8, -0x1.6cf89703b1289p+7,
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0x1.1518af6a65e2dp+5
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};
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double z = xs;
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double z2 = z * z;
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double z4 = z2 * z2;
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double z8 = z4 * z4;
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double z16 = z8 * z8;
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r = z * ((((b[0] + z2 * b[1]) + z4 * (b[2] + z2 * b[3]))
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+ z8 * ((b[4] + z2 * b[5]) + z4 * (b[6] + z2 * b[7])))
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+ z16 * (((b[8] + z2 * b[9]) + z4 * (b[10] + z2 * b[11]))
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+ z8 * ((b[12] + z2 * b[13])
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+ z4 * (b[14] + z2 * b[15]))));
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float ub = r;
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float lb = r - z * 0x1.efa8ebp-31;
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if (ub == lb)
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return ub;
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}
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if (ax < (0x7eu << 24))
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{
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double z = xs;
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double z2 = z * z;
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double c0 = poly12 (z2, C0);
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r = z + (z * z2) * c0;
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}
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else
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{
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if (__glibc_unlikely (ax == 0x7e55688au))
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return copysignf (0x1.75b8a2p-1f, x) + copysignf (0x1p-26f, x);
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if (__glibc_unlikely (ax == 0x7e107434u))
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return copysignf (0x1.1f4b64p-1f, x) + copysignf (0x1p-26f, x);
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double bx = fabs (xs);
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double z = 1.0 - bx;
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double s = sqrt (z);
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r = pi2 - s * poly12 (z, C1);
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r = copysign (r, xs);
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}
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return r;
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}
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libm_alias_finite (__ieee754_asinf, __asinf)
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