diff options
Diffstat (limited to 'sysdeps/ieee754/flt-32/s_sincosf.c')
| -rw-r--r-- | sysdeps/ieee754/flt-32/s_sincosf.c | 196 |
1 files changed, 64 insertions, 132 deletions
diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c index d4a5a1b22c..f7e3245097 100644 --- a/sysdeps/ieee754/flt-32/s_sincosf.c +++ b/sysdeps/ieee754/flt-32/s_sincosf.c @@ -1,5 +1,5 @@ /* Compute sine and 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 @@ -17,9 +17,11 @@ <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 SINCOSF @@ -28,141 +30,71 @@ # define SINCOSF_FUNC SINCOSF #endif +/* Fast sincosf 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. */ void -SINCOSF_FUNC (float x, float *sinx, float *cosx) +SINCOSF_FUNC (float y, float *sinp, float *cosp) { - double cx; - double theta = x; - double abstheta = fabs (theta); - /* If |x|< Pi/4. */ - 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))) + { + /* Force underflow for tiny y. */ + if (__glibc_unlikely (abstop12 (y) < abstop12 (0x1p-126f))) + math_force_eval ((float)x2); + *sinp = y; + *cosp = 1.0f; + return; + } + + sincosf_poly (x, x2, p, 0, sinp, cosp); + } + else if (abstop12 (y) < abstop12 (120.0f)) { - if (abstheta >= 0x1p-5) /* |x| >= 2^-5. */ - { - const double theta2 = theta * theta; - /* Chebyshev polynomial of the form for sin and cos. */ - cx = C3 + theta2 * C4; - cx = C2 + theta2 * cx; - cx = C1 + theta2 * cx; - cx = C0 + theta2 * cx; - cx = 1.0 + theta2 * cx; - *cosx = cx; - cx = S3 + theta2 * S4; - cx = S2 + theta2 * cx; - cx = S1 + theta2 * cx; - cx = S0 + theta2 * cx; - cx = theta + theta * theta2 * cx; - *sinx = cx; - } - else if (abstheta >= 0x1p-27) /* |x| >= 2^-27. */ - { - /* A simpler Chebyshev approximation is close enough for this range: - for sin: x+x^3*(SS0+x^2*SS1) - for cos: 1.0+x^2*(CC0+x^3*CC1). */ - const double theta2 = theta * theta; - cx = CC0 + theta * theta2 * CC1; - cx = 1.0 + theta2 * cx; - *cosx = cx; - cx = SS0 + theta2 * SS1; - cx = theta + theta * theta2 * cx; - *sinx = cx; - } - else - { - /* Handle some special cases. */ - if (theta) - *sinx = theta - (theta * SMALL); - else - *sinx = theta; - *cosx = 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]; + + sincosf_poly (x * s, x * x, p, n, sinp, cosp); } - else /* |x| >= Pi/4. */ + else if (__glibc_likely (abstop12 (y) < abstop12 (INFINITY))) { - unsigned int signbit = isless (x, 0); - if (isless (abstheta, 9 * M_PI_4)) /* |x| < 9*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]; - *sinx = reduced_sin (theta, n, signbit); - *cosx = reduced_cos (theta, n); - } - else if (isless (abstheta, INFINITY)) - { - if (abstheta < 0x1p+23) /* |x| < 2^23. */ - { - 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. */ - *sinx = reduced_sin (theta, n, signbit); - *cosx = reduced_cos (theta, n); - } - else /* |x| >= 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; - *sinx = reduced_sin (e, l + 1, signbit); - *cosx = reduced_cos (e, l + 1); - } - else - { - e += b; - e += c; - e += d; - if (e <= 1.0) - { - e *= M_PI_4; - *sinx = reduced_sin (e, l + 1, signbit); - *cosx = reduced_cos (e, l + 1); - } - else - { - l++; - e -= 2.0; - e *= M_PI_4; - *sinx = reduced_sin (e, l + 1, signbit); - *cosx = reduced_cos (e, l + 1); - } - } - } - } - else - { - int32_t ix; - /* High word of x. */ - GET_FLOAT_WORD (ix, abstheta); - /* sin/cos(Inf or NaN) is NaN. */ - *sinx = *cosx = x - x; - if (ix == 0x7f800000) - __set_errno (EDOM); - } + 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]; + + sincosf_poly (x * s, x * x, p, n, sinp, cosp); + } + else + { + /* Return NaN if Inf or NaN for both sin and cos. */ + *sinp = *cosp = y - y; +#if WANT_ERRNO + /* Needed to set errno for +-Inf, the add is a hack to work + around a gcc register allocation issue: just passing y + affects code generation in the fast path (PR86901). */ + __math_invalidf (y + y); +#endif } } |