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Diffstat (limited to '')
| -rw-r--r-- | libc-top-half/musl/src/math/cbrtl.c | 124 |
1 files changed, 124 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/cbrtl.c b/libc-top-half/musl/src/math/cbrtl.c new file mode 100644 index 0000000..ceff913 --- /dev/null +++ b/libc-top-half/musl/src/math/cbrtl.c @@ -0,0 +1,124 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtl.c */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * The argument reduction and testing for exceptional cases was + * written by Steven G. Kargl with input from Bruce D. Evans + * and David A. Schultz. + */ + +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double cbrtl(long double x) +{ + return cbrt(x); +} +#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 +static const unsigned B1 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */ + +long double cbrtl(long double x) +{ + union ldshape u = {x}, v; + union {float f; uint32_t i;} uft; + long double r, s, t, w; + double_t dr, dt, dx; + float_t ft; + int e = u.i.se & 0x7fff; + int sign = u.i.se & 0x8000; + + /* + * If x = +-Inf, then cbrt(x) = +-Inf. + * If x = NaN, then cbrt(x) = NaN. + */ + if (e == 0x7fff) + return x + x; + if (e == 0) { + /* Adjust subnormal numbers. */ + u.f *= 0x1p120; + e = u.i.se & 0x7fff; + /* If x = +-0, then cbrt(x) = +-0. */ + if (e == 0) + return x; + e -= 120; + } + e -= 0x3fff; + u.i.se = 0x3fff; + x = u.f; + switch (e % 3) { + case 1: + case -2: + x *= 2; + e--; + break; + case 2: + case -1: + x *= 4; + e -= 2; + break; + } + v.f = 1.0; + v.i.se = sign | (0x3fff + e/3); + + /* + * The following is the guts of s_cbrtf, with the handling of + * special values removed and extra care for accuracy not taken, + * but with most of the extra accuracy not discarded. + */ + + /* ~5-bit estimate: */ + uft.f = x; + uft.i = (uft.i & 0x7fffffff)/3 + B1; + ft = uft.f; + + /* ~16-bit estimate: */ + dx = x; + dt = ft; + dr = dt * dt * dt; + dt = dt * (dx + dx + dr) / (dx + dr + dr); + + /* ~47-bit estimate: */ + dr = dt * dt * dt; + dt = dt * (dx + dx + dr) / (dx + dr + dr); + +#if LDBL_MANT_DIG == 64 + /* + * dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8). + * Round it away from zero to 32 bits (32 so that t*t is exact, and + * away from zero for technical reasons). + */ + t = dt + (0x1.0p32L + 0x1.0p-31L) - 0x1.0p32; +#elif LDBL_MANT_DIG == 113 + /* + * Round dt away from zero to 47 bits. Since we don't trust the 47, + * add 2 47-bit ulps instead of 1 to round up. Rounding is slow and + * might be avoidable in this case, since on most machines dt will + * have been evaluated in 53-bit precision and the technical reasons + * for rounding up might not apply to either case in cbrtl() since + * dt is much more accurate than needed. + */ + t = dt + 0x2.0p-46 + 0x1.0p60L - 0x1.0p60; +#endif + + /* + * Final step Newton iteration to 64 or 113 bits with + * error < 0.667 ulps + */ + s = t*t; /* t*t is exact */ + r = x/s; /* error <= 0.5 ulps; |r| < |t| */ + w = t+t; /* t+t is exact */ + r = (r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */ + t = t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */ + + t *= v.f; + return t; +} +#endif |