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-rw-r--r--lib/mlibc/options/ansi/musl-generic-math/fmal.c293
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diff --git a/lib/mlibc/options/ansi/musl-generic-math/fmal.c b/lib/mlibc/options/ansi/musl-generic-math/fmal.c
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--- a/lib/mlibc/options/ansi/musl-generic-math/fmal.c
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-/* 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