diff options
Diffstat (limited to 'sysdeps')
| -rw-r--r-- | sysdeps/ieee754/flt-32/s_cosf.c | 254 |
1 files changed, 214 insertions, 40 deletions
diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c index 5ed0bcaba3..ac6d044449 100644 --- a/sysdeps/ieee754/flt-32/s_cosf.c +++ b/sysdeps/ieee754/flt-32/s_cosf.c @@ -1,21 +1,20 @@ -/* 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 $"; -#endif +/* Compute cosine of argument. + Copyright (C) 2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ #include <errno.h> #include <math.h> @@ -28,35 +27,210 @@ static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $"; # 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 |