diff options
Diffstat (limited to 'sin.c')
| -rw-r--r-- | sin.c | 70 |
1 files changed, 35 insertions, 35 deletions
@@ -69,40 +69,40 @@ mpfr_sin (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) for (;;) { /* first perform argument reduction modulo 2*Pi (if needed), - also helps to determine the sign of sin(x) */ + also helps to determine the sign of sin(x) */ if (expx >= 2) /* If Pi < x < 4, we need to reduce too, to determine - the sign of sin(x). For 2 <= |x| < Pi, we could avoid - the reduction. */ - { - reduce = 1; - mpfr_set_prec (c, expx + m - 1); - mpfr_set_prec (xr, m); - mpfr_const_pi (c, GMP_RNDN); - mpfr_mul_2ui (c, c, 1, GMP_RNDN); - mpfr_remainder (xr, x, c, GMP_RNDN); - /* The analysis is similar to that of cos.c: - |xr - x - 2kPi| <= 2^(2-m). Thus we can decide the sign - of sin(x) if xr is at distance at least 2^(2-m) of both - 0 and +/-Pi. */ - mpfr_div_2ui (c, c, 1, GMP_RNDN); - /* Since c approximates Pi with an error <= 2^(2-expx-m) <= 2^(-m), - it suffices to check that c - |xr| >= 2^(2-m). */ - if (MPFR_SIGN (xr) > 0) - mpfr_sub (c, c, xr, GMP_RNDZ); - else - mpfr_add (c, c, xr, GMP_RNDZ); - if (MPFR_IS_ZERO(xr) || MPFR_EXP(xr) < (mp_exp_t) 3 - (mp_exp_t) m - || MPFR_EXP(c) < (mp_exp_t) 3 - (mp_exp_t) m) - goto ziv_next; - - /* |xr - x - 2kPi| <= 2^(2-m), thus |sin(xr) - sin(x)| <= 2^(2-m) */ - xx = xr; - } + the sign of sin(x). For 2 <= |x| < Pi, we could avoid + the reduction. */ + { + reduce = 1; + mpfr_set_prec (c, expx + m - 1); + mpfr_set_prec (xr, m); + mpfr_const_pi (c, GMP_RNDN); + mpfr_mul_2ui (c, c, 1, GMP_RNDN); + mpfr_remainder (xr, x, c, GMP_RNDN); + /* The analysis is similar to that of cos.c: + |xr - x - 2kPi| <= 2^(2-m). Thus we can decide the sign + of sin(x) if xr is at distance at least 2^(2-m) of both + 0 and +/-Pi. */ + mpfr_div_2ui (c, c, 1, GMP_RNDN); + /* Since c approximates Pi with an error <= 2^(2-expx-m) <= 2^(-m), + it suffices to check that c - |xr| >= 2^(2-m). */ + if (MPFR_SIGN (xr) > 0) + mpfr_sub (c, c, xr, GMP_RNDZ); + else + mpfr_add (c, c, xr, GMP_RNDZ); + if (MPFR_IS_ZERO(xr) || MPFR_EXP(xr) < (mp_exp_t) 3 - (mp_exp_t) m + || MPFR_EXP(c) < (mp_exp_t) 3 - (mp_exp_t) m) + goto ziv_next; + + /* |xr - x - 2kPi| <= 2^(2-m), thus |sin(xr) - sin(x)| <= 2^(2-m) */ + xx = xr; + } else /* the input argument is already reduced */ - { - reduce = 0; - xx = x; - } + { + reduce = 0; + xx = x; + } sign = MPFR_SIGN(xx); /* now that the argument is reduced, precision m is enough */ @@ -125,9 +125,9 @@ mpfr_sin (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) else { /* the absolute error on c is at most 2^(3-m-EXP(c)), - plus 2^(2-m) if there was an argument reduction. - Since EXP(c) <= 1, 3-m-EXP(c) >= 2-m, thus the error - is at most 2^(3-m-EXP(c)) in case of argument reduction. */ + plus 2^(2-m) if there was an argument reduction. + Since EXP(c) <= 1, 3-m-EXP(c) >= 2-m, thus the error + is at most 2^(3-m-EXP(c)) in case of argument reduction. */ err = 2 * MPFR_GET_EXP (c) + (mp_exp_t) m - 3 - (reduce != 0); if (mpfr_can_round (c, err, GMP_RNDN, GMP_RNDZ, precy + (rnd_mode == GMP_RNDN))) |