mirror of git://sourceware.org/git/glibc.git
New generic sincosf
This implementation is based on generic s_sinf.c and s_cosf.c. Tested on s390x, powerpc64le and powerpc32.
This commit is contained in:
Rajalakshmi Srinivasaraghavan
parent
93930ea935
commit
984ae9967b
10
ChangeLog
10
ChangeLog
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@ -1,3 +1,13 @@
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2017-12-16 Rajalakshmi Srinivasaraghavan <raji@linux.vnet.ibm.com>
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* sysdeps/ieee754/flt-32/s_cosf.c: Move reduced() and
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constants to s_sincosf.h file.
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* sysdeps/ieee754/flt-32/s_sinf.c: Likewise.
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* sysdeps/ieee754/flt-32/s_sincosf.c: New
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implementation.
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* sysdeps/ieee754/flt-32/s_sincosf.h:
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New file.
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2017-12-12 Carlos O'Donell <carlos@redhat.com>
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2017-12-12 Carlos O'Donell <carlos@redhat.com>
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[BZ #14681]
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[BZ #14681]
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@ -20,6 +20,7 @@
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#include <math.h>
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#include <math.h>
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#include <math_private.h>
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#include <math_private.h>
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#include <libm-alias-float.h>
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#include <libm-alias-float.h>
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#include "s_sincosf.h"
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#ifndef COSF
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#ifndef COSF
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# define COSF_FUNC __cosf
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# define COSF_FUNC __cosf
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@ -27,95 +28,6 @@
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# define COSF_FUNC COSF
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# define COSF_FUNC COSF
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#endif
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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 cos, range 2^-27 - 2^-5. */
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static const double CC0 = -0x1.fffffff5cc6fdp-2;
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static const double CC1 = 0x1.55514b178dac5p-5;
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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 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 cosine 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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the sign of the result. */
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static inline float
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reduced (double theta, unsigned int n)
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{
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double sign, cx;
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const double theta2 = theta * theta;
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/* Determine positive or negative primary interval. */
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n += 2;
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sign = ones[(n >> 2) & 1];
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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 cosf() 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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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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}
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else
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{
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/* Here cosf() 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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cx = C3 + theta2 * C4;
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cx = C2 + theta2 * cx;
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cx = C1 + theta2 * cx;
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cx = C0 + theta2 * cx;
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cx = 1. + theta2 * cx;
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}
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return sign * cx;
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}
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float
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float
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COSF_FUNC (float x)
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COSF_FUNC (float x)
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{
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{
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@ -161,7 +73,7 @@ COSF_FUNC (float x)
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pio2_table must go to 5 (9 / 2 + 1). */
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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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unsigned int n = (abstheta * inv_PI_4) + 1;
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theta = abstheta - pio2_table[n / 2];
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theta = abstheta - pio2_table[n / 2];
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return reduced (theta, n);
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return reduced_cos (theta, n);
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}
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}
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else if (isless (abstheta, INFINITY))
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else if (isless (abstheta, INFINITY))
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{
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{
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@ -171,7 +83,7 @@ COSF_FUNC (float x)
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double x = n / 2;
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double x = n / 2;
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theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
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theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
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/* Argument reduction needed. */
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/* Argument reduction needed. */
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return reduced (theta, n);
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return reduced_cos (theta, n);
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}
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}
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else /* |theta| >= 2^23. */
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else /* |theta| >= 2^23. */
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{
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{
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@ -199,7 +111,7 @@ COSF_FUNC (float x)
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e += c;
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e += c;
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e += d;
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e += d;
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e *= M_PI_4;
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e *= M_PI_4;
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return reduced (e, l + 1);
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return reduced_cos (e, l + 1);
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}
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}
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else
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else
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{
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{
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@ -209,14 +121,14 @@ COSF_FUNC (float x)
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if (e <= 1.0)
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if (e <= 1.0)
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{
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{
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e *= M_PI_4;
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e *= M_PI_4;
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return reduced (e, l + 1);
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return reduced_cos (e, l + 1);
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}
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}
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else
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else
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{
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{
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l++;
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l++;
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e -= 2.0;
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e -= 2.0;
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e *= M_PI_4;
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e *= M_PI_4;
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return reduced (e, l + 1);
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return reduced_cos (e, l + 1);
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}
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}
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}
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}
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}
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}
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@ -1,7 +1,6 @@
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/* Compute sine and cosine of argument.
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/* Compute sine and cosine of argument.
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Copyright (C) 1997-2017 Free Software Foundation, Inc.
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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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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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The GNU C Library is free software; you can redistribute it and/or
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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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modify it under the terms of the GNU Lesser General Public
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#include <errno.h>
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#include <errno.h>
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#include <math.h>
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#include <math.h>
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#include <math_private.h>
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#include <math_private.h>
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#include <libm-alias-float.h>
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#include <libm-alias-float.h>
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#include "s_sincosf.h"
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#ifndef SINCOSF
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#ifndef SINCOSF
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# define SINCOSF_FUNC __sincosf
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# define SINCOSF_FUNC __sincosf
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void
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void
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SINCOSF_FUNC (float x, float *sinx, float *cosx)
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SINCOSF_FUNC (float x, float *sinx, float *cosx)
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{
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{
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int32_t ix;
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double cx;
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double theta = x;
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/* High word of x. */
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double abstheta = fabs (theta);
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GET_FLOAT_WORD (ix, x);
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/* If |x|< Pi/4. */
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if (isless (abstheta, M_PI_4))
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/* |x| ~< pi/4 */
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ix &= 0x7fffffff;
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if (ix <= 0x3f490fd8)
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{
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{
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*sinx = __kernel_sinf (x, 0.0, 0);
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if (abstheta >= 0x1p-5) /* |x| >= 2^-5. */
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*cosx = __kernel_cosf (x, 0.0);
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}
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else if (ix>=0x7f800000)
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{
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/* sin(Inf or NaN) is NaN */
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*sinx = *cosx = x - x;
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if (ix == 0x7f800000)
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__set_errno (EDOM);
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}
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else
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{
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/* Argument reduction needed. */
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float y[2];
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int n;
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n = __ieee754_rem_pio2f (x, y);
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switch (n & 3)
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{
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{
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case 0:
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const double theta2 = theta * theta;
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*sinx = __kernel_sinf (y[0], y[1], 1);
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/* Chebyshev polynomial of the form for sin and cos. */
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*cosx = __kernel_cosf (y[0], y[1]);
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cx = C3 + theta2 * C4;
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break;
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cx = C2 + theta2 * cx;
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case 1:
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cx = C1 + theta2 * cx;
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*sinx = __kernel_cosf (y[0], y[1]);
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cx = C0 + theta2 * cx;
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*cosx = -__kernel_sinf (y[0], y[1], 1);
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cx = 1.0 + theta2 * cx;
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break;
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*cosx = cx;
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case 2:
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cx = S3 + theta2 * S4;
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*sinx = -__kernel_sinf (y[0], y[1], 1);
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cx = S2 + theta2 * cx;
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*cosx = -__kernel_cosf (y[0], y[1]);
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cx = S1 + theta2 * cx;
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break;
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cx = S0 + theta2 * cx;
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default:
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cx = theta + theta * theta2 * cx;
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*sinx = -__kernel_cosf (y[0], y[1]);
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*sinx = cx;
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*cosx = __kernel_sinf (y[0], y[1], 1);
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}
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break;
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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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for cos: 1.0+x^2*(CC0+x^3*CC1). */
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const double theta2 = theta * theta;
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cx = CC0 + theta * theta2 * CC1;
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cx = 1.0 + theta2 * cx;
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*cosx = cx;
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cx = SS0 + theta2 * SS1;
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cx = theta + theta * theta2 * cx;
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*sinx = 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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*sinx = theta - (theta * SMALL);
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else
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*sinx = theta;
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*cosx = 1.0 - abstheta;
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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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*sinx = reduced_sin (theta, n, signbit);
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*cosx = reduced_cos (theta, n);
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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 = (abstheta - x * PI_2_hi) - x * PI_2_lo;
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/* Argument reduction needed. */
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*sinx = reduced_sin (theta, n, signbit);
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*cosx = reduced_cos (theta, n);
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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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*sinx = reduced_sin (e, l + 1, signbit);
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*cosx = reduced_cos (e, l + 1);
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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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*sinx = reduced_sin (e, l + 1, signbit);
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*cosx = reduced_cos (e, l + 1);
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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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*sinx = reduced_sin (e, l + 1, signbit);
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*cosx = reduced_cos (e, l + 1);
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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/cos(Inf or NaN) is NaN. */
|
||||||
|
*sinx = *cosx = x - x;
|
||||||
|
if (ix == 0x7f800000)
|
||||||
|
__set_errno (EDOM);
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
|
||||||
|
|
@ -0,0 +1,155 @@
|
||||||
|
/* Used by sinf, cosf and sincosf functions.
|
||||||
|
Copyright (C) 2017 Free Software Foundation, Inc.
|
||||||
|
This file is part of the GNU C Library.
|
||||||
|
|
||||||
|
The GNU C Library is free software; you can redistribute it and/or
|
||||||
|
modify it under the terms of the GNU Lesser General Public
|
||||||
|
License as published by the Free Software Foundation; either
|
||||||
|
version 2.1 of the License, or (at your option) any later version.
|
||||||
|
|
||||||
|
The GNU C Library is distributed in the hope that it will be useful,
|
||||||
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||||
|
Lesser General Public License for more details.
|
||||||
|
|
||||||
|
You should have received a copy of the GNU Lesser General Public
|
||||||
|
License along with the GNU C Library; if not, see
|
||||||
|
<http://www.gnu.org/licenses/>. */
|
||||||
|
|
||||||
|
/* Chebyshev constants for cos, range -PI/4 - PI/4. */
|
||||||
|
static const double C0 = -0x1.ffffffffe98aep-2;
|
||||||
|
static const double C1 = 0x1.55555545c50c7p-5;
|
||||||
|
static const double C2 = -0x1.6c16b348b6874p-10;
|
||||||
|
static const double C3 = 0x1.a00eb9ac43ccp-16;
|
||||||
|
static const double C4 = -0x1.23c97dd8844d7p-22;
|
||||||
|
|
||||||
|
/* Chebyshev constants for sin, range -PI/4 - PI/4. */
|
||||||
|
static const double S0 = -0x1.5555555551cd9p-3;
|
||||||
|
static const double S1 = 0x1.1111110c2688bp-7;
|
||||||
|
static const double S2 = -0x1.a019f8b4bd1f9p-13;
|
||||||
|
static const double S3 = 0x1.71d7264e6b5b4p-19;
|
||||||
|
static const double S4 = -0x1.a947e1674b58ap-26;
|
||||||
|
|
||||||
|
/* Chebyshev constants for sin, range 2^-27 - 2^-5. */
|
||||||
|
static const double SS0 = -0x1.555555543d49dp-3;
|
||||||
|
static const double SS1 = 0x1.110f475cec8c5p-7;
|
||||||
|
|
||||||
|
/* Chebyshev constants for cos, range 2^-27 - 2^-5. */
|
||||||
|
static const double CC0 = -0x1.fffffff5cc6fdp-2;
|
||||||
|
static const double CC1 = 0x1.55514b178dac5p-5;
|
||||||
|
|
||||||
|
/* PI/2 with 98 bits of accuracy. */
|
||||||
|
static const double PI_2_hi = 0x1.921fb544p+0;
|
||||||
|
static const double PI_2_lo = 0x1.0b4611a626332p-34;
|
||||||
|
|
||||||
|
static const double SMALL = 0x1p-50; /* 2^-50. */
|
||||||
|
static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
|
||||||
|
|
||||||
|
#define FLOAT_EXPONENT_SHIFT 23
|
||||||
|
#define FLOAT_EXPONENT_BIAS 127
|
||||||
|
|
||||||
|
static const double pio2_table[] = {
|
||||||
|
0 * M_PI_2,
|
||||||
|
1 * M_PI_2,
|
||||||
|
2 * M_PI_2,
|
||||||
|
3 * M_PI_2,
|
||||||
|
4 * M_PI_2,
|
||||||
|
5 * M_PI_2
|
||||||
|
};
|
||||||
|
|
||||||
|
static const double invpio4_table[] = {
|
||||||
|
0x0p+0,
|
||||||
|
0x1.45f306cp+0,
|
||||||
|
0x1.c9c882ap-28,
|
||||||
|
0x1.4fe13a8p-58,
|
||||||
|
0x1.f47d4dp-85,
|
||||||
|
0x1.bb81b6cp-112,
|
||||||
|
0x1.4acc9ep-142,
|
||||||
|
0x1.0e4107cp-169
|
||||||
|
};
|
||||||
|
|
||||||
|
static const double ones[] = { 1.0, -1.0 };
|
||||||
|
|
||||||
|
/* Compute the sine value using Chebyshev polynomials where
|
||||||
|
THETA is the range reduced absolute value of the input
|
||||||
|
and it is less than Pi/4,
|
||||||
|
N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
|
||||||
|
whether a sine or cosine approximation is more accurate and
|
||||||
|
SIGNBIT is used to add the correct sign after the Chebyshev
|
||||||
|
polynomial is computed. */
|
||||||
|
static inline float
|
||||||
|
reduced_sin (const double theta, const unsigned int n,
|
||||||
|
const unsigned int signbit)
|
||||||
|
{
|
||||||
|
double sx;
|
||||||
|
const double theta2 = theta * theta;
|
||||||
|
/* We are operating on |x|, so we need to add back the original
|
||||||
|
signbit for sinf. */
|
||||||
|
double sign;
|
||||||
|
/* Determine positive or negative primary interval. */
|
||||||
|
sign = ones[((n >> 2) & 1) ^ signbit];
|
||||||
|
/* Are we in the primary interval of sin or cos? */
|
||||||
|
if ((n & 2) == 0)
|
||||||
|
{
|
||||||
|
/* Here sinf() is calculated using sin Chebyshev polynomial:
|
||||||
|
x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
|
||||||
|
sx = S3 + theta2 * S4; /* S3+x^2*S4. */
|
||||||
|
sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */
|
||||||
|
sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
|
||||||
|
sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
|
||||||
|
sx = theta + theta * theta2 * sx;
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
/* Here sinf() is calculated using cos Chebyshev polynomial:
|
||||||
|
1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
|
||||||
|
sx = C3 + theta2 * C4; /* C3+x^2*C4. */
|
||||||
|
sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */
|
||||||
|
sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */
|
||||||
|
sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */
|
||||||
|
sx = 1.0 + theta2 * sx;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Add in the signbit and assign the result. */
|
||||||
|
return sign * sx;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Compute the cosine value using Chebyshev polynomials where
|
||||||
|
THETA is the range reduced absolute value of the input
|
||||||
|
and it is less than Pi/4,
|
||||||
|
N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
|
||||||
|
whether a sine or cosine approximation is more accurate and
|
||||||
|
the sign of the result. */
|
||||||
|
static inline float
|
||||||
|
reduced_cos (double theta, unsigned int n)
|
||||||
|
{
|
||||||
|
double sign, cx;
|
||||||
|
const double theta2 = theta * theta;
|
||||||
|
|
||||||
|
/* Determine positive or negative primary interval. */
|
||||||
|
n += 2;
|
||||||
|
sign = ones[(n >> 2) & 1];
|
||||||
|
|
||||||
|
/* Are we in the primary interval of sin or cos? */
|
||||||
|
if ((n & 2) == 0)
|
||||||
|
{
|
||||||
|
/* Here cosf() is calculated using sin Chebyshev polynomial:
|
||||||
|
x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
|
||||||
|
cx = S3 + theta2 * S4;
|
||||||
|
cx = S2 + theta2 * cx;
|
||||||
|
cx = S1 + theta2 * cx;
|
||||||
|
cx = S0 + theta2 * cx;
|
||||||
|
cx = theta + theta * theta2 * cx;
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
/* Here cosf() is calculated using cos Chebyshev polynomial:
|
||||||
|
1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
|
||||||
|
cx = C3 + theta2 * C4;
|
||||||
|
cx = C2 + theta2 * cx;
|
||||||
|
cx = C1 + theta2 * cx;
|
||||||
|
cx = C0 + theta2 * cx;
|
||||||
|
cx = 1. + theta2 * cx;
|
||||||
|
}
|
||||||
|
return sign * cx;
|
||||||
|
}
|
||||||
|
|
@ -20,6 +20,7 @@
|
||||||
#include <math.h>
|
#include <math.h>
|
||||||
#include <math_private.h>
|
#include <math_private.h>
|
||||||
#include <libm-alias-float.h>
|
#include <libm-alias-float.h>
|
||||||
|
#include "s_sincosf.h"
|
||||||
|
|
||||||
#ifndef SINF
|
#ifndef SINF
|
||||||
# define SINF_FUNC __sinf
|
# define SINF_FUNC __sinf
|
||||||
|
|
@ -27,100 +28,6 @@
|
||||||
# define SINF_FUNC SINF
|
# define SINF_FUNC SINF
|
||||||
#endif
|
#endif
|
||||||
|
|
||||||
/* Chebyshev constants for cos, range -PI/4 - PI/4. */
|
|
||||||
static const double C0 = -0x1.ffffffffe98aep-2;
|
|
||||||
static const double C1 = 0x1.55555545c50c7p-5;
|
|
||||||
static const double C2 = -0x1.6c16b348b6874p-10;
|
|
||||||
static const double C3 = 0x1.a00eb9ac43ccp-16;
|
|
||||||
static const double C4 = -0x1.23c97dd8844d7p-22;
|
|
||||||
|
|
||||||
/* Chebyshev constants for sin, range -PI/4 - PI/4. */
|
|
||||||
static const double S0 = -0x1.5555555551cd9p-3;
|
|
||||||
static const double S1 = 0x1.1111110c2688bp-7;
|
|
||||||
static const double S2 = -0x1.a019f8b4bd1f9p-13;
|
|
||||||
static const double S3 = 0x1.71d7264e6b5b4p-19;
|
|
||||||
static const double S4 = -0x1.a947e1674b58ap-26;
|
|
||||||
|
|
||||||
/* Chebyshev constants for sin, range 2^-27 - 2^-5. */
|
|
||||||
static const double SS0 = -0x1.555555543d49dp-3;
|
|
||||||
static const double SS1 = 0x1.110f475cec8c5p-7;
|
|
||||||
|
|
||||||
/* PI/2 with 98 bits of accuracy. */
|
|
||||||
static const double PI_2_hi = -0x1.921fb544p+0;
|
|
||||||
static const double PI_2_lo = -0x1.0b4611a626332p-34;
|
|
||||||
|
|
||||||
static const double SMALL = 0x1p-50; /* 2^-50. */
|
|
||||||
static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
|
|
||||||
|
|
||||||
#define FLOAT_EXPONENT_SHIFT 23
|
|
||||||
#define FLOAT_EXPONENT_BIAS 127
|
|
||||||
|
|
||||||
static const double pio2_table[] = {
|
|
||||||
0 * M_PI_2,
|
|
||||||
1 * M_PI_2,
|
|
||||||
2 * M_PI_2,
|
|
||||||
3 * M_PI_2,
|
|
||||||
4 * M_PI_2,
|
|
||||||
5 * M_PI_2
|
|
||||||
};
|
|
||||||
|
|
||||||
static const double invpio4_table[] = {
|
|
||||||
0x0p+0,
|
|
||||||
0x1.45f306cp+0,
|
|
||||||
0x1.c9c882ap-28,
|
|
||||||
0x1.4fe13a8p-58,
|
|
||||||
0x1.f47d4dp-85,
|
|
||||||
0x1.bb81b6cp-112,
|
|
||||||
0x1.4acc9ep-142,
|
|
||||||
0x1.0e4107cp-169
|
|
||||||
};
|
|
||||||
|
|
||||||
static const double ones[] = { 1.0, -1.0 };
|
|
||||||
|
|
||||||
/* Compute the sine value using Chebyshev polynomials where
|
|
||||||
THETA is the range reduced absolute value of the input
|
|
||||||
and it is less than Pi/4,
|
|
||||||
N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
|
|
||||||
whether a sine or cosine approximation is more accurate and
|
|
||||||
SIGNBIT is used to add the correct sign after the Chebyshev
|
|
||||||
polynomial is computed. */
|
|
||||||
static inline float
|
|
||||||
reduced (const double theta, const unsigned int n,
|
|
||||||
const unsigned int signbit)
|
|
||||||
{
|
|
||||||
double sx;
|
|
||||||
const double theta2 = theta * theta;
|
|
||||||
/* We are operating on |x|, so we need to add back the original
|
|
||||||
signbit for sinf. */
|
|
||||||
double sign;
|
|
||||||
/* Determine positive or negative primary interval. */
|
|
||||||
sign = ones[((n >> 2) & 1) ^ signbit];
|
|
||||||
/* Are we in the primary interval of sin or cos? */
|
|
||||||
if ((n & 2) == 0)
|
|
||||||
{
|
|
||||||
/* Here sinf() is calculated using sin Chebyshev polynomial:
|
|
||||||
x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
|
|
||||||
sx = S3 + theta2 * S4; /* S3+x^2*S4. */
|
|
||||||
sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */
|
|
||||||
sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
|
|
||||||
sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
|
|
||||||
sx = theta + theta * theta2 * sx;
|
|
||||||
}
|
|
||||||
else
|
|
||||||
{
|
|
||||||
/* Here sinf() is calculated using cos Chebyshev polynomial:
|
|
||||||
1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
|
|
||||||
sx = C3 + theta2 * C4; /* C3+x^2*C4. */
|
|
||||||
sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */
|
|
||||||
sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */
|
|
||||||
sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */
|
|
||||||
sx = 1.0 + theta2 * sx;
|
|
||||||
}
|
|
||||||
|
|
||||||
/* Add in the signbit and assign the result. */
|
|
||||||
return sign * sx;
|
|
||||||
}
|
|
||||||
|
|
||||||
float
|
float
|
||||||
SINF_FUNC (float x)
|
SINF_FUNC (float x)
|
||||||
{
|
{
|
||||||
|
|
@ -171,7 +78,7 @@ SINF_FUNC (float x)
|
||||||
pio2_table must go to 5 (9 / 2 + 1). */
|
pio2_table must go to 5 (9 / 2 + 1). */
|
||||||
unsigned int n = (abstheta * inv_PI_4) + 1;
|
unsigned int n = (abstheta * inv_PI_4) + 1;
|
||||||
theta = abstheta - pio2_table[n / 2];
|
theta = abstheta - pio2_table[n / 2];
|
||||||
return reduced (theta, n, signbit);
|
return reduced_sin (theta, n, signbit);
|
||||||
}
|
}
|
||||||
else if (isless (abstheta, INFINITY))
|
else if (isless (abstheta, INFINITY))
|
||||||
{
|
{
|
||||||
|
|
@ -179,9 +86,9 @@ SINF_FUNC (float x)
|
||||||
{
|
{
|
||||||
unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
|
unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
|
||||||
double x = n / 2;
|
double x = n / 2;
|
||||||
theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
|
theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
|
||||||
/* Argument reduction needed. */
|
/* Argument reduction needed. */
|
||||||
return reduced (theta, n, signbit);
|
return reduced_sin (theta, n, signbit);
|
||||||
}
|
}
|
||||||
else /* |x| >= 2^23. */
|
else /* |x| >= 2^23. */
|
||||||
{
|
{
|
||||||
|
|
@ -209,7 +116,7 @@ SINF_FUNC (float x)
|
||||||
e += c;
|
e += c;
|
||||||
e += d;
|
e += d;
|
||||||
e *= M_PI_4;
|
e *= M_PI_4;
|
||||||
return reduced (e, l + 1, signbit);
|
return reduced_sin (e, l + 1, signbit);
|
||||||
}
|
}
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
|
|
@ -219,14 +126,14 @@ SINF_FUNC (float x)
|
||||||
if (e <= 1.0)
|
if (e <= 1.0)
|
||||||
{
|
{
|
||||||
e *= M_PI_4;
|
e *= M_PI_4;
|
||||||
return reduced (e, l + 1, signbit);
|
return reduced_sin (e, l + 1, signbit);
|
||||||
}
|
}
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
l++;
|
l++;
|
||||||
e -= 2.0;
|
e -= 2.0;
|
||||||
e *= M_PI_4;
|
e *= M_PI_4;
|
||||||
return reduced (e, l + 1, signbit);
|
return reduced_sin (e, l + 1, signbit);
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue