diff options
| -rw-r--r-- | src/math/cosh.c | 41 | ||||
| -rw-r--r-- | src/math/coshf.c | 37 | ||||
| -rw-r--r-- | src/math/coshl.c | 55 |
3 files changed, 63 insertions, 70 deletions
diff --git a/src/math/cosh.c b/src/math/cosh.c index a1f7dbc7..2fcdea8f 100644 --- a/src/math/cosh.c +++ b/src/math/cosh.c @@ -23,7 +23,7 @@ * 2 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) - * ln2ovft < x : cosh(x) := huge*huge (overflow) + * ln2ovft < x : cosh(x) := inf (overflow) * * Special cases: * cosh(x) is |x| if x is +INF, -INF, or NaN. @@ -32,43 +32,40 @@ #include "libm.h" -static const double huge = 1.0e300; - double cosh(double x) { - double t, w; - int32_t ix; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; + union {double f; uint64_t i;} u = {.f = x}; + uint32_t ix; + double t; - /* x is INF or NaN */ - if (ix >= 0x7ff00000) - return x*x; + /* |x| */ + u.i &= (uint64_t)-1/2; + x = u.f; + ix = u.i >> 32; /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if (ix < 0x3fd62e43) { - t = expm1(fabs(x)); - w = 1.0+t; + t = expm1(x); if (ix < 0x3c800000) - return w; /* cosh(tiny) = 1 */ - return 1.0 + (t*t)/(w+w); + return 1; + return 1 + t*t/(2*(1+t)); } /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */ if (ix < 0x40360000) { - t = exp(fabs(x)); + t = exp(x); return 0.5*t + 0.5/t; } /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ - if (ix < 0x40862E42) - return 0.5*exp(fabs(x)); + if (ix < 0x40862e42) + return 0.5*exp(x); /* |x| in [log(maxdouble), overflowthresold] */ - if (ix <= 0x408633CE) - return __expo2(fabs(x)); + if (ix <= 0x408633ce) + return __expo2(x); - /* |x| > overflowthresold, cosh(x) overflow */ - return huge*huge; + /* overflow (or nan) */ + x *= 0x1p1023; + return x; } diff --git a/src/math/coshf.c b/src/math/coshf.c index 97318f10..2bed1258 100644 --- a/src/math/coshf.c +++ b/src/math/coshf.c @@ -15,43 +15,40 @@ #include "libm.h" -static const float huge = 1.0e30; - float coshf(float x) { - float t, w; - int32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; + union {float f; uint32_t i;} u = {.f = x}; + uint32_t ix; + float t; - /* x is INF or NaN */ - if (ix >= 0x7f800000) - return x*x; + /* |x| */ + u.i &= 0x7fffffff; + x = u.f; + ix = u.i; /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if (ix < 0x3eb17218) { - t = expm1f(fabsf(x)); - w = 1.0f+t; - if (ix<0x39800000) - return 1.0f; /* cosh(tiny) = 1 */ - return 1.0f + (t*t)/(w+w); + t = expm1f(x); + if (ix < 0x39800000) + return 1; + return 1 + t*t/(2*(1+t)); } /* |x| in [0.5*ln2,9], return (exp(|x|)+1/exp(|x|))/2; */ if (ix < 0x41100000) { - t = expf(fabsf(x)); + t = expf(x); return 0.5f*t + 0.5f/t; } /* |x| in [9, log(maxfloat)] return 0.5f*exp(|x|) */ if (ix < 0x42b17217) - return 0.5f*expf(fabsf(x)); + return 0.5f*expf(x); /* |x| in [log(maxfloat), overflowthresold] */ if (ix <= 0x42b2d4fc) - return __expo2f(fabsf(x)); + return __expo2f(x); - /* |x| > overflowthresold, cosh(x) overflow */ - return huge*huge; + /* |x| > overflowthresold or nan */ + x *= 0x1p127f; + return x; } 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 |