diff options
Diffstat (limited to 'sysdeps')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/e_j0l.c | 68 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/e_j1l.c | 69 |
2 files changed, 79 insertions, 58 deletions
diff --git a/sysdeps/ieee754/ldbl-128/e_j0l.c b/sysdeps/ieee754/ldbl-128/e_j0l.c index 1b18289588..9e7880c49d 100644 --- a/sysdeps/ieee754/ldbl-128/e_j0l.c +++ b/sysdeps/ieee754/ldbl-128/e_j0l.c @@ -700,6 +700,25 @@ __ieee754_j0l (long double x) return p; } + /* X = x - pi/4 + cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) + = 1/sqrt(2) * (cos(x) + sin(x)) + sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) + = 1/sqrt(2) * (sin(x) - cos(x)) + sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = s - c; + cc = s + c; + z = -__cosl (xx + xx); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + + if (xx > 0x1p256L) + return ONEOSQPI * cc / __ieee754_sqrtl (xx); + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -761,21 +780,6 @@ __ieee754_j0l (long double x) p = 1.0L + z * p; q = z * xinv * q; q = q - 0.125L * xinv; - /* X = x - pi/4 - cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) - = 1/sqrt(2) * (cos(x) + sin(x)) - sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) - = 1/sqrt(2) * (sin(x) - cos(x)) - sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - cf. Fdlibm. */ - __sincosl (xx, &s, &c); - ss = s - c; - cc = s + c; - z = -__cosl (xx + xx); - if ((s * c) < 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); return z; } @@ -843,6 +847,25 @@ long double return p; } + /* X = x - pi/4 + cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) + = 1/sqrt(2) * (cos(x) + sin(x)) + sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) + = 1/sqrt(2) * (sin(x) - cos(x)) + sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + cf. Fdlibm. */ + __sincosl (x, &s, &c); + ss = s - c; + cc = s + c; + z = -__cosl (x + x); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + + if (xx > 0x1p256L) + return ONEOSQPI * ss / __ieee754_sqrtl (x); + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -904,21 +927,6 @@ long double p = 1.0L + z * p; q = z * xinv * q; q = q - 0.125L * xinv; - /* X = x - pi/4 - cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) - = 1/sqrt(2) * (cos(x) + sin(x)) - sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) - = 1/sqrt(2) * (sin(x) - cos(x)) - sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - cf. Fdlibm. */ - __sincosl (x, &s, &c); - ss = s - c; - cc = s + c; - z = -__cosl (x + x); - if ((s * c) < 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x); return z; } diff --git a/sysdeps/ieee754/ldbl-128/e_j1l.c b/sysdeps/ieee754/ldbl-128/e_j1l.c index f16343b26b..95e01a39cc 100644 --- a/sysdeps/ieee754/ldbl-128/e_j1l.c +++ b/sysdeps/ieee754/ldbl-128/e_j1l.c @@ -706,6 +706,29 @@ __ieee754_j1l (long double x) return p; } + /* X = x - 3 pi/4 + cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) + = 1/sqrt(2) * (-cos(x) + sin(x)) + sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) + = -1/sqrt(2) * (sin(x) + cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = -s - c; + cc = s - c; + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + + if (xx > 0x1p256L) + { + z = ONEOSQPI * cc / __ieee754_sqrtl (xx); + if (x < 0) + z = -z; + return z; + } + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -767,20 +790,6 @@ __ieee754_j1l (long double x) p = 1.0L + z * p; q = z * q; q = q * xinv + 0.375L * xinv; - /* X = x - 3 pi/4 - cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) - = 1/sqrt(2) * (-cos(x) + sin(x)) - sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) - = -1/sqrt(2) * (sin(x) + cos(x)) - cf. Fdlibm. */ - __sincosl (xx, &s, &c); - ss = -s - c; - cc = s - c; - z = __cosl (xx + xx); - if ((s * c) > 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); if (x < 0) z = -z; @@ -850,6 +859,24 @@ __ieee754_y1l (long double x) return p; } + /* X = x - 3 pi/4 + cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) + = 1/sqrt(2) * (-cos(x) + sin(x)) + sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) + = -1/sqrt(2) * (sin(x) + cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = -s - c; + cc = s - c; + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + + if (xx > 0x1p256L) + return ONEOSQPI * ss / __ieee754_sqrtl (xx); + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -911,20 +938,6 @@ __ieee754_y1l (long double x) p = 1.0L + z * p; q = z * q; q = q * xinv + 0.375L * xinv; - /* X = x - 3 pi/4 - cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) - = 1/sqrt(2) * (-cos(x) + sin(x)) - sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) - = -1/sqrt(2) * (sin(x) + cos(x)) - cf. Fdlibm. */ - __sincosl (xx, &s, &c); - ss = -s - c; - cc = s - c; - z = __cosl (xx + xx); - if ((s * c) > 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx); return z; } |