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94d80dfc73
This patch avoid an extra floating point to integer conversion in
reduced internal function for generic sinf by defining the sign as
double instead of integers.
There is no much difference on Haswell with GCC 7.2.1:
Before After
min 9.11 9.108
mean 21.982 21.9224
However H.J. Lu reported gains on Skylake:
Before:
"sinf": {
"": {
"duration": 3.4044e+10,
"iterations": 1.9942e+09,
"max": 141.106,
"min": 7.704,
"mean": 17.0715
}
}
After:
"sinf": {
"": {
"duration": 3.40665e+10,
"iterations": 2.03199e+09,
"max": 95.994,
"min": 7.704,
"mean": 16.765
}
}
Checked on x86_64-linux-gnu.
* sysdeps/ieee754/flt-32/s_sinf.c (ones): Define as double.
(reduced): Use ones as double instead of integer.
250 lines
7.1 KiB
C
250 lines
7.1 KiB
C
/* Compute sine of argument.
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Copyright (C) 2017 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <errno.h>
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#include <math.h>
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#include <math_private.h>
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#include <libm-alias-float.h>
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#ifndef SINF
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# define SINF_FUNC __sinf
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#else
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# define SINF_FUNC SINF
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#endif
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/* Chebyshev constants for cos, range -PI/4 - PI/4. */
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static const double C0 = -0x1.ffffffffe98aep-2;
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static const double C1 = 0x1.55555545c50c7p-5;
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static const double C2 = -0x1.6c16b348b6874p-10;
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static const double C3 = 0x1.a00eb9ac43ccp-16;
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static const double C4 = -0x1.23c97dd8844d7p-22;
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/* Chebyshev constants for sin, range -PI/4 - PI/4. */
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static const double S0 = -0x1.5555555551cd9p-3;
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static const double S1 = 0x1.1111110c2688bp-7;
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static const double S2 = -0x1.a019f8b4bd1f9p-13;
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static const double S3 = 0x1.71d7264e6b5b4p-19;
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static const double S4 = -0x1.a947e1674b58ap-26;
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/* Chebyshev constants for sin, range 2^-27 - 2^-5. */
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static const double SS0 = -0x1.555555543d49dp-3;
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static const double SS1 = 0x1.110f475cec8c5p-7;
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/* PI/2 with 98 bits of accuracy. */
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static const double PI_2_hi = -0x1.921fb544p+0;
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static const double PI_2_lo = -0x1.0b4611a626332p-34;
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static const double SMALL = 0x1p-50; /* 2^-50. */
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static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
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#define FLOAT_EXPONENT_SHIFT 23
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#define FLOAT_EXPONENT_BIAS 127
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static const double pio2_table[] = {
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0 * M_PI_2,
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1 * M_PI_2,
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2 * M_PI_2,
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3 * M_PI_2,
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4 * M_PI_2,
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5 * M_PI_2
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};
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static const double invpio4_table[] = {
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0x0p+0,
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0x1.45f306cp+0,
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0x1.c9c882ap-28,
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0x1.4fe13a8p-58,
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0x1.f47d4dp-85,
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0x1.bb81b6cp-112,
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0x1.4acc9ep-142,
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0x1.0e4107cp-169
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};
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static const double ones[] = { 1.0, -1.0 };
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/* Compute the sine value using Chebyshev polynomials where
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THETA is the range reduced absolute value of the input
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and it is less than Pi/4,
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N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
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whether a sine or cosine approximation is more accurate and
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SIGNBIT is used to add the correct sign after the Chebyshev
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polynomial is computed. */
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static inline float
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reduced (const double theta, const unsigned int n,
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const unsigned int signbit)
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{
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double sx;
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const double theta2 = theta * theta;
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/* We are operating on |x|, so we need to add back the original
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signbit for sinf. */
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double sign;
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/* Determine positive or negative primary interval. */
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sign = ones[((n >> 2) & 1) ^ signbit];
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/* Are we in the primary interval of sin or cos? */
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if ((n & 2) == 0)
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{
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/* Here sinf() is calculated using sin Chebyshev polynomial:
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x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
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sx = S3 + theta2 * S4; /* S3+x^2*S4. */
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sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */
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sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
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sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
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sx = theta + theta * theta2 * sx;
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}
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else
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{
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/* Here sinf() is calculated using cos Chebyshev polynomial:
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1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
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sx = C3 + theta2 * C4; /* C3+x^2*C4. */
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sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */
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sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */
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sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */
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sx = 1.0 + theta2 * sx;
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}
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/* Add in the signbit and assign the result. */
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return sign * sx;
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}
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float
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SINF_FUNC (float x)
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{
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double cx;
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double theta = x;
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double abstheta = fabs (theta);
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/* If |x|< Pi/4. */
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if (isless (abstheta, M_PI_4))
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{
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if (abstheta >= 0x1p-5) /* |x| >= 2^-5. */
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{
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const double theta2 = theta * theta;
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/* Chebyshev polynomial of the form for sin
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x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
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cx = S3 + theta2 * S4;
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cx = S2 + theta2 * cx;
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cx = S1 + theta2 * cx;
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cx = S0 + theta2 * cx;
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cx = theta + theta * theta2 * cx;
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return cx;
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}
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else if (abstheta >= 0x1p-27) /* |x| >= 2^-27. */
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{
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/* A simpler Chebyshev approximation is close enough for this range:
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for sin: x+x^3*(SS0+x^2*SS1). */
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const double theta2 = theta * theta;
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cx = SS0 + theta2 * SS1;
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cx = theta + theta * theta2 * cx;
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return cx;
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}
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else
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{
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/* Handle some special cases. */
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if (theta)
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return theta - (theta * SMALL);
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else
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return theta;
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}
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}
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else /* |x| >= Pi/4. */
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{
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unsigned int signbit = isless (x, 0);
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if (isless (abstheta, 9 * M_PI_4)) /* |x| < 9*Pi/4. */
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{
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/* There are cases where FE_UPWARD rounding mode can
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produce a result of abstheta * inv_PI_4 == 9,
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where abstheta < 9pi/4, so the domain for
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pio2_table must go to 5 (9 / 2 + 1). */
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unsigned int n = (abstheta * inv_PI_4) + 1;
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theta = abstheta - pio2_table[n / 2];
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return reduced (theta, n, signbit);
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}
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else if (isless (abstheta, INFINITY))
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{
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if (abstheta < 0x1p+23) /* |x| < 2^23. */
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{
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unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
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double x = n / 2;
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theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
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/* Argument reduction needed. */
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return reduced (theta, n, signbit);
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}
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else /* |x| >= 2^23. */
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{
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x = fabsf (x);
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int exponent;
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GET_FLOAT_WORD (exponent, x);
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exponent
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= (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
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exponent += 3;
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exponent /= 28;
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double a = invpio4_table[exponent] * x;
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double b = invpio4_table[exponent + 1] * x;
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double c = invpio4_table[exponent + 2] * x;
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double d = invpio4_table[exponent + 3] * x;
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uint64_t l = a;
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l &= ~0x7;
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a -= l;
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double e = a + b;
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l = e;
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e = a - l;
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if (l & 1)
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{
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e -= 1.0;
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e += b;
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e += c;
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e += d;
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e *= M_PI_4;
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return reduced (e, l + 1, signbit);
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}
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else
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{
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e += b;
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e += c;
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e += d;
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if (e <= 1.0)
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{
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e *= M_PI_4;
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return reduced (e, l + 1, signbit);
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}
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else
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{
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l++;
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e -= 2.0;
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e *= M_PI_4;
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return reduced (e, l + 1, signbit);
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}
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}
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}
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}
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else
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{
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int32_t ix;
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/* High word of x. */
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GET_FLOAT_WORD (ix, abstheta);
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/* Sin(Inf or NaN) is NaN. */
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if (ix == 0x7f800000)
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__set_errno (EDOM);
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return x - x;
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}
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}
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}
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#ifndef SINF
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libm_alias_float (__sin, sin)
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#endif
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