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