diff options
| -rw-r--r-- | math/auto-libm-test-in | 2 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_j0f.c | 17 |
2 files changed, 18 insertions, 1 deletions
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in index 4414e54d93..5d488a8711 100644 --- a/math/auto-libm-test-in +++ b/math/auto-libm-test-in @@ -5748,6 +5748,8 @@ j0 0x1p16382 j0 0x1p16383 # the next value generates larger error bounds on x86_64 (binary32) j0 0x2.602774p+0 xfail-rounding:ibm128-libgcc +# the next value exercises the flt-32 code path for x >= 2^127 +j0 0x8.2f4ecp+124 j1 -1.0 j1 0.0 diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c index c89b9f2688..5d29611eb7 100644 --- a/sysdeps/ieee754/flt-32/e_j0f.c +++ b/sysdeps/ieee754/flt-32/e_j0f.c @@ -55,7 +55,22 @@ __ieee754_j0f(float x) z = -__cosf(x+x); if ((s*c)<zero) cc = z/ss; else ss = z/cc; - } + } else { + /* We subtract (exactly) a value x0 such that + cos(x0)+sin(x0) is very near to 0, and use the identity + sin(x-x0) = sin(x)*cos(x0)-cos(x)*sin(x0) to get + sin(x) + cos(x) with extra accuracy. */ + float x0 = 0xe.d4108p+124f; + float y = x - x0; /* exact */ + /* sin(y) = sin(x)*cos(x0)-cos(x)*sin(x0) */ + z = __sinf (y); + float eps = 0x1.5f263ep-24f; + /* cos(x0) ~ -sin(x0) + eps */ + z += eps * __cosf (x); + /* now z ~ (sin(x)-cos(x))*cos(x0) */ + float cosx0 = -0xb.504f3p-4f; + cc = z / cosx0; + } /* * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |