-/* s_cosf.c -- float version of s_cos.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $";
-#endif
+/* Compute cosine of argument.
+ 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/>. */
#include <errno.h>
#include <math.h>
# define COSF_FUNC COSF
#endif
-float COSF_FUNC(float x)
+/* 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 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 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 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 (double theta, unsigned int n)
{
- float y[2],z=0.0;
- int32_t n,ix;
+ double sign, cx;
+ const double theta2 = theta * theta;
- GET_FLOAT_WORD(ix,x);
+ /* Determine positive or negative primary interval. */
+ n += 2;
+ sign = ones[(n >> 2) & 1];
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
+ /* 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;
+}
- /* cos(Inf or NaN) is NaN */
- else if (ix>=0x7f800000) {
- if (ix == 0x7f800000)
- __set_errno (EDOM);
- return x-x;
+float
+COSF_FUNC (float x)
+{
+ double theta = x;
+ double abstheta = fabs (theta);
+ if (isless (abstheta, M_PI_4))
+ {
+ double cx;
+ if (abstheta >= 0x1p-5)
+ {
+ const double theta2 = theta * theta;
+ /* Chebyshev polynomial of the form for cos:
+ * 1 + 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 cx;
}
-
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,y);
- switch(n&3) {
- case 0: return __kernel_cosf(y[0],y[1]);
- case 1: return -__kernel_sinf(y[0],y[1],1);
- case 2: return -__kernel_cosf(y[0],y[1]);
- default:
- return __kernel_sinf(y[0],y[1],1);
+ else if (abstheta >= 0x1p-27)
+ {
+ /* A simpler Chebyshev approximation is close enough for this range:
+ * 1 + x^2 (CC0 + x^3 * CC1). */
+ const double theta2 = theta * theta;
+ cx = CC0 + theta * theta2 * CC1;
+ cx = 1.0 + theta2 * cx;
+ return cx;
+ }
+ else
+ {
+ /* For small enough |theta|, this is close enough. */
+ return 1.0 - abstheta;
+ }
+ }
+ else /* |theta| >= Pi/4. */
+ {
+ if (isless (abstheta, 9 * M_PI_4))
+ {
+ /* There are cases where FE_UPWARD rounding mode can
+ produce a result of abstheta * inv_PI_4 == 9,
+ where abstheta < 9pi/4, so the domain for
+ pio2_table must go to 5 (9 / 2 + 1). */
+ unsigned int n = (abstheta * inv_PI_4) + 1;
+ theta = abstheta - pio2_table[n / 2];
+ return reduced (theta, n);
+ }
+ else if (isless (abstheta, INFINITY))
+ {
+ if (abstheta < 0x1p+23)
+ {
+ unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
+ double x = n / 2;
+ theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
+ /* Argument reduction needed. */
+ return reduced (theta, n);
+ }
+ else /* |theta| >= 2^23. */
+ {
+ x = fabsf (x);
+ int exponent;
+ GET_FLOAT_WORD (exponent, x);
+ exponent = (exponent >> FLOAT_EXPONENT_SHIFT)
+ - FLOAT_EXPONENT_BIAS;
+ exponent += 3;
+ exponent /= 28;
+ double a = invpio4_table[exponent] * x;
+ double b = invpio4_table[exponent + 1] * x;
+ double c = invpio4_table[exponent + 2] * x;
+ double d = invpio4_table[exponent + 3] * x;
+ uint64_t l = a;
+ l &= ~0x7;
+ a -= l;
+ double e = a + b;
+ l = e;
+ e = a - l;
+ if (l & 1)
+ {
+ e -= 1.0;
+ e += b;
+ e += c;
+ e += d;
+ e *= M_PI_4;
+ return reduced (e, l + 1);
+ }
+ else
+ {
+ e += b;
+ e += c;
+ e += d;
+ if (e <= 1.0)
+ {
+ e *= M_PI_4;
+ return reduced (e, l + 1);
+ }
+ else
+ {
+ l++;
+ e -= 2.0;
+ e *= M_PI_4;
+ return reduced (e, l + 1);
+ }
+ }
}
}
+ else
+ {
+ int32_t ix;
+ GET_FLOAT_WORD (ix, abstheta);
+ /* cos(Inf or NaN) is NaN. */
+ if (ix == 0x7f800000) /* Inf. */
+ __set_errno (EDOM);
+ return x - x;
+ }
+ }
}
#ifndef COSF
projects / thirdparty / glibc.git / commitdiff
