diff options
Diffstat (limited to 'src/math/coshl.c')
| -rw-r--r-- | src/math/coshl.c | 55 |
1 files changed, 27 insertions, 28 deletions
diff --git a/src/math/coshl.c b/src/math/coshl.c index 36b52c02..3ea56e00 100644 --- a/src/math/coshl.c +++ b/src/math/coshl.c @@ -23,7 +23,7 @@ * 2 * 22 <= x <= lnovft : coshl(x) := expl(x)/2 * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) - * ln2ovft < x : coshl(x) := huge*huge (overflow) + * ln2ovft < x : coshl(x) := inf (overflow) * * Special cases: * coshl(x) is |x| if x is +INF, -INF, or NaN. @@ -38,49 +38,48 @@ long double coshl(long double x) return cosh(x); } #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -static const long double huge = 1.0e4900L; - long double coshl(long double x) { - long double t,w; - int32_t ex; + union { + long double f; + struct{uint64_t m; uint16_t se; uint16_t pad;} i; + } u = {.f = x}; + unsigned ex = u.i.se & 0x7fff; + long double t; uint32_t mx,lx; - /* High word of |x|. */ - GET_LDOUBLE_WORDS(ex, mx, lx, x); - ex &= 0x7fff; - - /* x is INF or NaN */ - if (ex == 0x7fff) return x*x; + /* |x| */ + u.i.se = ex; + x = u.f; + mx = u.i.m >> 32; + lx = u.i.m; /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ - if (ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { - t = expm1l(fabsl(x)); - w = 1.0 + t; - if (ex < 0x3fbc) return w; /* cosh(tiny) = 1 */ - return 1.0+(t*t)/(w+w); + if (ex < 0x3fff-2 || (ex == 0x3fff-2 && mx < 0xb17217f7)) { + t = expm1l(x); + if (ex < 0x3fff-64) + return 1; + return 1 + t*t/(2*(1+t)); } /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ - if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { - t = expl(fabsl(x)); + if (ex < 0x3fff+4 || (ex == 0x3fff+4 && mx < 0xb0000000)) { + t = expl(x); return 0.5*t + 0.5/t; } /* |x| in [22, ln(maxdouble)] return 0.5*exp(|x|) */ - if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) - return 0.5*expl(fabsl(x)); + if (ex < 0x3fff+13 || (ex == 0x3fff+13 && mx < 0xb1700000)) + return 0.5*expl(x); /* |x| in [log(maxdouble), log(2*maxdouble)) */ - if (ex == 0x400c && (mx < 0xb174ddc0u || - (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) - { - w = expl(0.5*fabsl(x)); - t = 0.5*w; - return t*w; + if (ex == 0x3fff+13 && (mx < 0xb174ddc0 || + (mx == 0xb174ddc0 && lx < 0x31aec0eb))) { + t = expl(0.5*x); + return 0.5*t*t; } - /* |x| >= log(2*maxdouble), cosh(x) overflow */ - return huge*huge; + /* |x| >= log(2*maxdouble) or nan */ + return x*0x1p16383L; } #endif |