diff options
Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/cbrt.c')
| -rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/cbrt.c | 103 |
1 files changed, 0 insertions, 103 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/cbrt.c b/lib/mlibc/options/ansi/musl-generic-math/cbrt.c deleted file mode 100644 index 7599d3e..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/cbrt.c +++ /dev/null @@ -1,103 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrt.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * 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. - * ==================================================== - * - * Optimized by Bruce D. Evans. - */ -/* cbrt(x) - * Return cube root of x - */ - -#include <math.h> -#include <stdint.h> - -static const uint32_t -B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */ -B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ - -/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */ -static const double -P0 = 1.87595182427177009643, /* 0x3ffe03e6, 0x0f61e692 */ -P1 = -1.88497979543377169875, /* 0xbffe28e0, 0x92f02420 */ -P2 = 1.621429720105354466140, /* 0x3ff9f160, 0x4a49d6c2 */ -P3 = -0.758397934778766047437, /* 0xbfe844cb, 0xbee751d9 */ -P4 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */ - -double cbrt(double x) -{ - union {double f; uint64_t i;} u = {x}; - double_t r,s,t,w; - uint32_t hx = u.i>>32 & 0x7fffffff; - - if (hx >= 0x7ff00000) /* cbrt(NaN,INF) is itself */ - return x+x; - - /* - * Rough cbrt to 5 bits: - * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3) - * where e is integral and >= 0, m is real and in [0, 1), and "/" and - * "%" are integer division and modulus with rounding towards minus - * infinity. The RHS is always >= the LHS and has a maximum relative - * error of about 1 in 16. Adding a bias of -0.03306235651 to the - * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE - * floating point representation, for finite positive normal values, - * ordinary integer divison of the value in bits magically gives - * almost exactly the RHS of the above provided we first subtract the - * exponent bias (1023 for doubles) and later add it back. We do the - * subtraction virtually to keep e >= 0 so that ordinary integer - * division rounds towards minus infinity; this is also efficient. - */ - if (hx < 0x00100000) { /* zero or subnormal? */ - u.f = x*0x1p54; - hx = u.i>>32 & 0x7fffffff; - if (hx == 0) - return x; /* cbrt(0) is itself */ - hx = hx/3 + B2; - } else - hx = hx/3 + B1; - u.i &= 1ULL<<63; - u.i |= (uint64_t)hx << 32; - t = u.f; - - /* - * New cbrt to 23 bits: - * cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x) - * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r) - * to within 2**-23.5 when |r - 1| < 1/10. The rough approximation - * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this - * gives us bounds for r = t**3/x. - * - * Try to optimize for parallel evaluation as in __tanf.c. - */ - r = (t*t)*(t/x); - t = t*((P0+r*(P1+r*P2))+((r*r)*r)*(P3+r*P4)); - - /* - * Round t away from zero to 23 bits (sloppily except for ensuring that - * the result is larger in magnitude than cbrt(x) but not much more than - * 2 23-bit ulps larger). With rounding towards zero, the error bound - * would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps - * in the rounded t, the infinite-precision error in the Newton - * approximation barely affects third digit in the final error - * 0.667; the error in the rounded t can be up to about 3 23-bit ulps - * before the final error is larger than 0.667 ulps. - */ - u.f = t; - u.i = (u.i + 0x80000000) & 0xffffffffc0000000ULL; - t = u.f; - - /* one step Newton iteration to 53 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 */ - return t; -} |