diff options
Diffstat (limited to 'sysdeps/ieee754/flt-32/s_cosf.c')
| -rw-r--r-- | sysdeps/ieee754/flt-32/s_cosf.c | 161 |
1 files changed, 49 insertions, 112 deletions
diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c index 061264d259..13b5ffead8 100644 --- a/sysdeps/ieee754/flt-32/s_cosf.c +++ b/sysdeps/ieee754/flt-32/s_cosf.c @@ -1,5 +1,5 @@ /* Compute cosine of argument. - Copyright (C) 2017-2018 Free Software Foundation, Inc. + Copyright (C) 2018 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 @@ -16,10 +16,11 @@ License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ -#include <errno.h> +#include <stdint.h> #include <math.h> -#include <math_private.h> +#include <math-barriers.h> #include <libm-alias-float.h> +#include "math_config.h" #include "s_sincosf.h" #ifndef COSF @@ -28,121 +29,57 @@ # define COSF_FUNC COSF #endif +/* Fast cosf implementation. Worst-case ULP is 0.5607, maximum relative + error is 0.5303 * 2^-23. A single-step range reduction is used for + small values. Large inputs have their range reduced using fast integer + arithmetic. +*/ float -COSF_FUNC (float x) +COSF_FUNC (float y) { - double theta = x; - double abstheta = fabs (theta); - if (isless (abstheta, M_PI_4)) + double x = y; + double s; + int n; + const sincos_t *p = &__sincosf_table[0]; + + if (abstop12 (y) < abstop12 (pio4)) + { + double x2 = x * x; + + if (__glibc_unlikely (abstop12 (y) < abstop12 (0x1p-12f))) + return 1.0f; + + return sinf_poly (x, x2, p, 1); + } + else if (__glibc_likely (abstop12 (y) < abstop12 (120.0f))) { - 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; - } - 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; - } + x = reduce_fast (x, p, &n); + + /* Setup the signs for sin and cos. */ + s = p->sign[n & 3]; + + if (n & 2) + p = &__sincosf_table[1]; + + return sinf_poly (x * s, x * x, p, n ^ 1); } - else /* |theta| >= Pi/4. */ + else if (abstop12 (y) < abstop12 (INFINITY)) { - 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_cos (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_cos (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_cos (e, l + 1); - } - else - { - e += b; - e += c; - e += d; - if (e <= 1.0) - { - e *= M_PI_4; - return reduced_cos (e, l + 1); - } - else - { - l++; - e -= 2.0; - e *= M_PI_4; - return reduced_cos (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; - } + uint32_t xi = asuint (y); + int sign = xi >> 31; + + x = reduce_large (xi, &n); + + /* Setup signs for sin and cos - include original sign. */ + s = p->sign[(n + sign) & 3]; + + if ((n + sign) & 2) + p = &__sincosf_table[1]; + + return sinf_poly (x * s, x * x, p, n ^ 1); } + else + return __math_invalidf (y); } #ifndef COSF |