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Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/fmal.c')
-rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/fmal.c | 293 |
1 files changed, 0 insertions, 293 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/fmal.c b/lib/mlibc/options/ansi/musl-generic-math/fmal.c deleted file mode 100644 index 4506aac..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/fmal.c +++ /dev/null @@ -1,293 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_fmal.c */ -/*- - * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG> - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "libm.h" -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double fmal(long double x, long double y, long double z) -{ - return fma(x, y, z); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#include <fenv.h> -#if LDBL_MANT_DIG == 64 -#define LASTBIT(u) (u.i.m & 1) -#define SPLIT (0x1p32L + 1) -#elif LDBL_MANT_DIG == 113 -#define LASTBIT(u) (u.i.lo & 1) -#define SPLIT (0x1p57L + 1) -#endif - -/* - * A struct dd represents a floating-point number with twice the precision - * of a long double. We maintain the invariant that "hi" stores the high-order - * bits of the result. - */ -struct dd { - long double hi; - long double lo; -}; - -/* - * Compute a+b exactly, returning the exact result in a struct dd. We assume - * that both a and b are finite, but make no assumptions about their relative - * magnitudes. - */ -static inline struct dd dd_add(long double a, long double b) -{ - struct dd ret; - long double s; - - ret.hi = a + b; - s = ret.hi - a; - ret.lo = (a - (ret.hi - s)) + (b - s); - return (ret); -} - -/* - * Compute a+b, with a small tweak: The least significant bit of the - * result is adjusted into a sticky bit summarizing all the bits that - * were lost to rounding. This adjustment negates the effects of double - * rounding when the result is added to another number with a higher - * exponent. For an explanation of round and sticky bits, see any reference - * on FPU design, e.g., - * - * J. Coonen. An Implementation Guide to a Proposed Standard for - * Floating-Point Arithmetic. Computer, vol. 13, no. 1, Jan 1980. - */ -static inline long double add_adjusted(long double a, long double b) -{ - struct dd sum; - union ldshape u; - - sum = dd_add(a, b); - if (sum.lo != 0) { - u.f = sum.hi; - if (!LASTBIT(u)) - sum.hi = nextafterl(sum.hi, INFINITY * sum.lo); - } - return (sum.hi); -} - -/* - * Compute ldexp(a+b, scale) with a single rounding error. It is assumed - * that the result will be subnormal, and care is taken to ensure that - * double rounding does not occur. - */ -static inline long double add_and_denormalize(long double a, long double b, int scale) -{ - struct dd sum; - int bits_lost; - union ldshape u; - - sum = dd_add(a, b); - - /* - * If we are losing at least two bits of accuracy to denormalization, - * then the first lost bit becomes a round bit, and we adjust the - * lowest bit of sum.hi to make it a sticky bit summarizing all the - * bits in sum.lo. With the sticky bit adjusted, the hardware will - * break any ties in the correct direction. - * - * If we are losing only one bit to denormalization, however, we must - * break the ties manually. - */ - if (sum.lo != 0) { - u.f = sum.hi; - bits_lost = -u.i.se - scale + 1; - if ((bits_lost != 1) ^ LASTBIT(u)) - sum.hi = nextafterl(sum.hi, INFINITY * sum.lo); - } - return scalbnl(sum.hi, scale); -} - -/* - * Compute a*b exactly, returning the exact result in a struct dd. We assume - * that both a and b are normalized, so no underflow or overflow will occur. - * The current rounding mode must be round-to-nearest. - */ -static inline struct dd dd_mul(long double a, long double b) -{ - struct dd ret; - long double ha, hb, la, lb, p, q; - - p = a * SPLIT; - ha = a - p; - ha += p; - la = a - ha; - - p = b * SPLIT; - hb = b - p; - hb += p; - lb = b - hb; - - p = ha * hb; - q = ha * lb + la * hb; - - ret.hi = p + q; - ret.lo = p - ret.hi + q + la * lb; - return (ret); -} - -/* - * Fused multiply-add: Compute x * y + z with a single rounding error. - * - * We use scaling to avoid overflow/underflow, along with the - * canonical precision-doubling technique adapted from: - * - * Dekker, T. A Floating-Point Technique for Extending the - * Available Precision. Numer. Math. 18, 224-242 (1971). - */ -long double fmal(long double x, long double y, long double z) -{ - #pragma STDC FENV_ACCESS ON - long double xs, ys, zs, adj; - struct dd xy, r; - int oround; - int ex, ey, ez; - int spread; - - /* - * Handle special cases. The order of operations and the particular - * return values here are crucial in handling special cases involving - * infinities, NaNs, overflows, and signed zeroes correctly. - */ - if (!isfinite(x) || !isfinite(y)) - return (x * y + z); - if (!isfinite(z)) - return (z); - if (x == 0.0 || y == 0.0) - return (x * y + z); - if (z == 0.0) - return (x * y); - - xs = frexpl(x, &ex); - ys = frexpl(y, &ey); - zs = frexpl(z, &ez); - oround = fegetround(); - spread = ex + ey - ez; - - /* - * If x * y and z are many orders of magnitude apart, the scaling - * will overflow, so we handle these cases specially. Rounding - * modes other than FE_TONEAREST are painful. - */ - if (spread < -LDBL_MANT_DIG) { -#ifdef FE_INEXACT - feraiseexcept(FE_INEXACT); -#endif -#ifdef FE_UNDERFLOW - if (!isnormal(z)) - feraiseexcept(FE_UNDERFLOW); -#endif - switch (oround) { - default: /* FE_TONEAREST */ - return (z); -#ifdef FE_TOWARDZERO - case FE_TOWARDZERO: - if (x > 0.0 ^ y < 0.0 ^ z < 0.0) - return (z); - else - return (nextafterl(z, 0)); -#endif -#ifdef FE_DOWNWARD - case FE_DOWNWARD: - if (x > 0.0 ^ y < 0.0) - return (z); - else - return (nextafterl(z, -INFINITY)); -#endif -#ifdef FE_UPWARD - case FE_UPWARD: - if (x > 0.0 ^ y < 0.0) - return (nextafterl(z, INFINITY)); - else - return (z); -#endif - } - } - if (spread <= LDBL_MANT_DIG * 2) - zs = scalbnl(zs, -spread); - else - zs = copysignl(LDBL_MIN, zs); - - fesetround(FE_TONEAREST); - - /* - * Basic approach for round-to-nearest: - * - * (xy.hi, xy.lo) = x * y (exact) - * (r.hi, r.lo) = xy.hi + z (exact) - * adj = xy.lo + r.lo (inexact; low bit is sticky) - * result = r.hi + adj (correctly rounded) - */ - xy = dd_mul(xs, ys); - r = dd_add(xy.hi, zs); - - spread = ex + ey; - - if (r.hi == 0.0) { - /* - * When the addends cancel to 0, ensure that the result has - * the correct sign. - */ - fesetround(oround); - volatile long double vzs = zs; /* XXX gcc CSE bug workaround */ - return xy.hi + vzs + scalbnl(xy.lo, spread); - } - - if (oround != FE_TONEAREST) { - /* - * There is no need to worry about double rounding in directed - * rounding modes. - * But underflow may not be raised correctly, example in downward rounding: - * fmal(0x1.0000000001p-16000L, 0x1.0000000001p-400L, -0x1p-16440L) - */ - long double ret; -#if defined(FE_INEXACT) && defined(FE_UNDERFLOW) - int e = fetestexcept(FE_INEXACT); - feclearexcept(FE_INEXACT); -#endif - fesetround(oround); - adj = r.lo + xy.lo; - ret = scalbnl(r.hi + adj, spread); -#if defined(FE_INEXACT) && defined(FE_UNDERFLOW) - if (ilogbl(ret) < -16382 && fetestexcept(FE_INEXACT)) - feraiseexcept(FE_UNDERFLOW); - else if (e) - feraiseexcept(FE_INEXACT); -#endif - return ret; - } - - adj = add_adjusted(r.lo, xy.lo); - if (spread + ilogbl(r.hi) > -16383) - return scalbnl(r.hi + adj, spread); - else - return add_and_denormalize(r.hi, adj, spread); -} -#endif |