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Unified Diff: fusl/src/math/fma.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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Index: fusl/src/math/fma.c
diff --git a/fusl/src/math/fma.c b/fusl/src/math/fma.c
index b4e685bc45f2efd7fa57cceec19b71d642d3768d..cec9e3b490188c541ee95a3a0a304135793e2c7d 100644
--- a/fusl/src/math/fma.c
+++ b/fusl/src/math/fma.c
@@ -1,168 +1,170 @@
#include <fenv.h>
#include "libm.h"
-#if LDBL_MANT_DIG==64 && LDBL_MAX_EXP==16384
+#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
/* exact add, assumes exponent_x >= exponent_y */
-static void add(long double *hi, long double *lo, long double x, long double y)
-{
- long double r;
-
- r = x + y;
- *hi = r;
- r -= x;
- *lo = y - r;
+static void add(long double* hi,
+ long double* lo,
+ long double x,
+ long double y) {
+ long double r;
+
+ r = x + y;
+ *hi = r;
+ r -= x;
+ *lo = y - r;
}
/* exact mul, assumes no over/underflow */
-static void mul(long double *hi, long double *lo, long double x, long double y)
-{
- static const long double c = 1.0 + 0x1p32L;
- long double cx, xh, xl, cy, yh, yl;
-
- cx = c*x;
- xh = (x - cx) + cx;
- xl = x - xh;
- cy = c*y;
- yh = (y - cy) + cy;
- yl = y - yh;
- *hi = x*y;
- *lo = (xh*yh - *hi) + xh*yl + xl*yh + xl*yl;
+static void mul(long double* hi,
+ long double* lo,
+ long double x,
+ long double y) {
+ static const long double c = 1.0 + 0x1p32L;
+ long double cx, xh, xl, cy, yh, yl;
+
+ cx = c * x;
+ xh = (x - cx) + cx;
+ xl = x - xh;
+ cy = c * y;
+ yh = (y - cy) + cy;
+ yl = y - yh;
+ *hi = x * y;
+ *lo = (xh * yh - *hi) + xh * yl + xl * yh + xl * yl;
}
/*
assume (long double)(hi+lo) == hi
-return an adjusted hi so that rounding it to double (or less) precision is correct
+return an adjusted hi so that rounding it to double (or less) precision is
+correct
*/
-static long double adjust(long double hi, long double lo)
-{
- union ldshape uhi, ulo;
-
- if (lo == 0)
- return hi;
- uhi.f = hi;
- if (uhi.i.m & 0x3ff)
- return hi;
- ulo.f = lo;
- if ((uhi.i.se & 0x8000) == (ulo.i.se & 0x8000))
- uhi.i.m++;
- else {
- /* handle underflow and take care of ld80 implicit msb */
- if (uhi.i.m << 1 == 0) {
- uhi.i.m = 0;
- uhi.i.se--;
- }
- uhi.i.m--;
- }
- return uhi.f;
+static long double adjust(long double hi, long double lo) {
+ union ldshape uhi, ulo;
+
+ if (lo == 0)
+ return hi;
+ uhi.f = hi;
+ if (uhi.i.m & 0x3ff)
+ return hi;
+ ulo.f = lo;
+ if ((uhi.i.se & 0x8000) == (ulo.i.se & 0x8000))
+ uhi.i.m++;
+ else {
+ /* handle underflow and take care of ld80 implicit msb */
+ if (uhi.i.m << 1 == 0) {
+ uhi.i.m = 0;
+ uhi.i.se--;
+ }
+ uhi.i.m--;
+ }
+ return uhi.f;
}
-/* adjusted add so the result is correct when rounded to double (or less) precision */
-static long double dadd(long double x, long double y)
-{
- add(&x, &y, x, y);
- return adjust(x, y);
+/* adjusted add so the result is correct when rounded to double (or less)
+ * precision */
+static long double dadd(long double x, long double y) {
+ add(&x, &y, x, y);
+ return adjust(x, y);
}
-/* adjusted mul so the result is correct when rounded to double (or less) precision */
-static long double dmul(long double x, long double y)
-{
- mul(&x, &y, x, y);
- return adjust(x, y);
+/* adjusted mul so the result is correct when rounded to double (or less)
+ * precision */
+static long double dmul(long double x, long double y) {
+ mul(&x, &y, x, y);
+ return adjust(x, y);
}
-static int getexp(long double x)
-{
- union ldshape u;
- u.f = x;
- return u.i.se & 0x7fff;
+static int getexp(long double x) {
+ union ldshape u;
+ u.f = x;
+ return u.i.se & 0x7fff;
}
-double fma(double x, double y, double z)
-{
- PRAGMA_STDC_FENV_ACCESS_ON
- long double hi, lo1, lo2, xy;
- int round, ez, exy;
-
- /* handle +-inf,nan */
- if (!isfinite(x) || !isfinite(y))
- return x*y + z;
- if (!isfinite(z))
- return z;
- /* handle +-0 */
- if (x == 0.0 || y == 0.0)
- return x*y + z;
- round = fegetround();
- if (z == 0.0) {
- if (round == FE_TONEAREST)
- return dmul(x, y);
- return x*y;
- }
-
- /* exact mul and add require nearest rounding */
- /* spurious inexact exceptions may be raised */
- fesetround(FE_TONEAREST);
- mul(&xy, &lo1, x, y);
- exy = getexp(xy);
- ez = getexp(z);
- if (ez > exy) {
- add(&hi, &lo2, z, xy);
- } else if (ez > exy - 12) {
- add(&hi, &lo2, xy, z);
- if (hi == 0) {
- /*
- xy + z is 0, but it should be calculated with the
- original rounding mode so the sign is correct, if the
- compiler does not support FENV_ACCESS ON it does not
- know about the changed rounding mode and eliminates
- the xy + z below without the volatile memory access
- */
- volatile double z_;
- fesetround(round);
- z_ = z;
- return (xy + z_) + lo1;
- }
- } else {
- /*
- ez <= exy - 12
- the 12 extra bits (1guard, 11round+sticky) are needed so with
- lo = dadd(lo1, lo2)
- elo <= ehi - 11, and we use the last 10 bits in adjust so
- dadd(hi, lo)
- gives correct result when rounded to double
- */
- hi = xy;
- lo2 = z;
- }
- /*
- the result is stored before return for correct precision and exceptions
-
- one corner case is when the underflow flag should be raised because
- the precise result is an inexact subnormal double, but the calculated
- long double result is an exact subnormal double
- (so rounding to double does not raise exceptions)
-
- in nearest rounding mode dadd takes care of this: the last bit of the
- result is adjusted so rounding sees an inexact value when it should
-
- in non-nearest rounding mode fenv is used for the workaround
- */
- fesetround(round);
- if (round == FE_TONEAREST)
- z = dadd(hi, dadd(lo1, lo2));
- else {
+double fma(double x, double y, double z) {
+ PRAGMA_STDC_FENV_ACCESS_ON
+ long double hi, lo1, lo2, xy;
+ int round, ez, exy;
+
+ /* handle +-inf,nan */
+ if (!isfinite(x) || !isfinite(y))
+ return x * y + z;
+ if (!isfinite(z))
+ return z;
+ /* handle +-0 */
+ if (x == 0.0 || y == 0.0)
+ return x * y + z;
+ round = fegetround();
+ if (z == 0.0) {
+ if (round == FE_TONEAREST)
+ return dmul(x, y);
+ return x * y;
+ }
+
+ /* exact mul and add require nearest rounding */
+ /* spurious inexact exceptions may be raised */
+ fesetround(FE_TONEAREST);
+ mul(&xy, &lo1, x, y);
+ exy = getexp(xy);
+ ez = getexp(z);
+ if (ez > exy) {
+ add(&hi, &lo2, z, xy);
+ } else if (ez > exy - 12) {
+ add(&hi, &lo2, xy, z);
+ if (hi == 0) {
+ /*
+ xy + z is 0, but it should be calculated with the
+ original rounding mode so the sign is correct, if the
+ compiler does not support FENV_ACCESS ON it does not
+ know about the changed rounding mode and eliminates
+ the xy + z below without the volatile memory access
+ */
+ volatile double z_;
+ fesetround(round);
+ z_ = z;
+ return (xy + z_) + lo1;
+ }
+ } else {
+ /*
+ ez <= exy - 12
+ the 12 extra bits (1guard, 11round+sticky) are needed so with
+ lo = dadd(lo1, lo2)
+ elo <= ehi - 11, and we use the last 10 bits in adjust so
+ dadd(hi, lo)
+ gives correct result when rounded to double
+ */
+ hi = xy;
+ lo2 = z;
+ }
+ /*
+ the result is stored before return for correct precision and exceptions
+
+ one corner case is when the underflow flag should be raised because
+ the precise result is an inexact subnormal double, but the calculated
+ long double result is an exact subnormal double
+ (so rounding to double does not raise exceptions)
+
+ in nearest rounding mode dadd takes care of this: the last bit of the
+ result is adjusted so rounding sees an inexact value when it should
+
+ in non-nearest rounding mode fenv is used for the workaround
+ */
+ fesetround(round);
+ if (round == FE_TONEAREST)
+ z = dadd(hi, dadd(lo1, lo2));
+ else {
#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
- int e = fetestexcept(FE_INEXACT);
- feclearexcept(FE_INEXACT);
+ int e = fetestexcept(FE_INEXACT);
+ feclearexcept(FE_INEXACT);
#endif
- z = hi + (lo1 + lo2);
+ z = hi + (lo1 + lo2);
#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
- if (getexp(z) < 0x3fff-1022 && fetestexcept(FE_INEXACT))
- feraiseexcept(FE_UNDERFLOW);
- else if (e)
- feraiseexcept(FE_INEXACT);
+ if (getexp(z) < 0x3fff - 1022 && fetestexcept(FE_INEXACT))
+ feraiseexcept(FE_UNDERFLOW);
+ else if (e)
+ feraiseexcept(FE_INEXACT);
#endif
- }
- return z;
+ }
+ return z;
}
#else
/* origin: FreeBSD /usr/src/lib/msun/src/s_fma.c */
@@ -198,8 +200,8 @@ double fma(double x, double y, double z)
* bits of the result.
*/
struct dd {
- double hi;
- double lo;
+ double hi;
+ double lo;
};
/*
@@ -207,15 +209,14 @@ struct dd {
* that both a and b are finite, but make no assumptions about their relative
* magnitudes.
*/
-static inline struct dd dd_add(double a, double b)
-{
- struct dd ret;
- double s;
-
- ret.hi = a + b;
- s = ret.hi - a;
- ret.lo = (a - (ret.hi - s)) + (b - s);
- return (ret);
+static inline struct dd dd_add(double a, double b) {
+ struct dd ret;
+ double s;
+
+ ret.hi = a + b;
+ s = ret.hi - a;
+ ret.lo = (a - (ret.hi - s)) + (b - s);
+ return (ret);
}
/*
@@ -229,22 +230,24 @@ static inline struct dd dd_add(double a, double b)
* J. Coonen. An Implementation Guide to a Proposed Standard for
* Floating-Point Arithmetic. Computer, vol. 13, no. 1, Jan 1980.
*/
-static inline double add_adjusted(double a, double b)
-{
- struct dd sum;
- union {double f; uint64_t i;} uhi, ulo;
-
- sum = dd_add(a, b);
- if (sum.lo != 0) {
- uhi.f = sum.hi;
- if ((uhi.i & 1) == 0) {
- /* hibits += (int)copysign(1.0, sum.hi * sum.lo) */
- ulo.f = sum.lo;
- uhi.i += 1 - ((uhi.i ^ ulo.i) >> 62);
- sum.hi = uhi.f;
- }
- }
- return (sum.hi);
+static inline double add_adjusted(double a, double b) {
+ struct dd sum;
+ union {
+ double f;
+ uint64_t i;
+ } uhi, ulo;
+
+ sum = dd_add(a, b);
+ if (sum.lo != 0) {
+ uhi.f = sum.hi;
+ if ((uhi.i & 1) == 0) {
+ /* hibits += (int)copysign(1.0, sum.hi * sum.lo) */
+ ulo.f = sum.lo;
+ uhi.i += 1 - ((uhi.i ^ ulo.i) >> 62);
+ sum.hi = uhi.f;
+ }
+ }
+ return (sum.hi);
}
/*
@@ -252,35 +255,37 @@ static inline double add_adjusted(double a, double b)
* that the result will be subnormal, and care is taken to ensure that
* double rounding does not occur.
*/
-static inline double add_and_denormalize(double a, double b, int scale)
-{
- struct dd sum;
- union {double f; uint64_t i;} uhi, ulo;
- int bits_lost;
-
- 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) {
- uhi.f = sum.hi;
- bits_lost = -((int)(uhi.i >> 52) & 0x7ff) - scale + 1;
- if ((bits_lost != 1) ^ (int)(uhi.i & 1)) {
- /* hibits += (int)copysign(1.0, sum.hi * sum.lo) */
- ulo.f = sum.lo;
- uhi.i += 1 - (((uhi.i ^ ulo.i) >> 62) & 2);
- sum.hi = uhi.f;
- }
- }
- return scalbn(sum.hi, scale);
+static inline double add_and_denormalize(double a, double b, int scale) {
+ struct dd sum;
+ union {
+ double f;
+ uint64_t i;
+ } uhi, ulo;
+ int bits_lost;
+
+ 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) {
+ uhi.f = sum.hi;
+ bits_lost = -((int)(uhi.i >> 52) & 0x7ff) - scale + 1;
+ if ((bits_lost != 1) ^ (int)(uhi.i & 1)) {
+ /* hibits += (int)copysign(1.0, sum.hi * sum.lo) */
+ ulo.f = sum.lo;
+ uhi.i += 1 - (((uhi.i ^ ulo.i) >> 62) & 2);
+ sum.hi = uhi.f;
+ }
+ }
+ return scalbn(sum.hi, scale);
}
/*
@@ -288,28 +293,27 @@ static inline double add_and_denormalize(double a, double b, int scale)
* 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(double a, double b)
-{
- static const double split = 0x1p27 + 1.0;
- struct dd ret;
- 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);
+static inline struct dd dd_mul(double a, double b) {
+ static const double split = 0x1p27 + 1.0;
+ struct dd ret;
+ 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);
}
/*
@@ -329,132 +333,131 @@ static inline struct dd dd_mul(double a, double b)
* Hardware instructions should be used on architectures that support it,
* since this implementation will likely be several times slower.
*/
-double fma(double x, double y, double z)
-{
- #pragma STDC FENV_ACCESS ON
- 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 = frexp(x, &ex);
- ys = frexp(y, &ey);
- zs = frexp(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 < -DBL_MANT_DIG) {
+double fma(double x, double y, double z) {
+#pragma STDC FENV_ACCESS ON
+ 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 = frexp(x, &ex);
+ ys = frexp(y, &ey);
+ zs = frexp(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 < -DBL_MANT_DIG) {
#ifdef FE_INEXACT
- feraiseexcept(FE_INEXACT);
+ feraiseexcept(FE_INEXACT);
#endif
#ifdef FE_UNDERFLOW
- if (!isnormal(z))
- feraiseexcept(FE_UNDERFLOW);
+ if (!isnormal(z))
+ feraiseexcept(FE_UNDERFLOW);
#endif
- switch (oround) {
- default: /* FE_TONEAREST */
- return (z);
+ 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 (nextafter(z, 0));
+ case FE_TOWARDZERO:
+ if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
+ return (z);
+ else
+ return (nextafter(z, 0));
#endif
#ifdef FE_DOWNWARD
- case FE_DOWNWARD:
- if (x > 0.0 ^ y < 0.0)
- return (z);
- else
- return (nextafter(z, -INFINITY));
+ case FE_DOWNWARD:
+ if (x > 0.0 ^ y < 0.0)
+ return (z);
+ else
+ return (nextafter(z, -INFINITY));
#endif
#ifdef FE_UPWARD
- case FE_UPWARD:
- if (x > 0.0 ^ y < 0.0)
- return (nextafter(z, INFINITY));
- else
- return (z);
+ case FE_UPWARD:
+ if (x > 0.0 ^ y < 0.0)
+ return (nextafter(z, INFINITY));
+ else
+ return (z);
#endif
- }
- }
- if (spread <= DBL_MANT_DIG * 2)
- zs = scalbn(zs, -spread);
- else
- zs = copysign(DBL_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 double vzs = zs; /* XXX gcc CSE bug workaround */
- return xy.hi + vzs + scalbn(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 properly, example in downward rounding:
- * fma(0x1.000000001p-1000, 0x1.000000001p-30, -0x1p-1066)
- */
- double ret;
+ }
+ }
+ if (spread <= DBL_MANT_DIG * 2)
+ zs = scalbn(zs, -spread);
+ else
+ zs = copysign(DBL_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 double vzs = zs; /* XXX gcc CSE bug workaround */
+ return xy.hi + vzs + scalbn(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 properly, example in downward rounding:
+ * fma(0x1.000000001p-1000, 0x1.000000001p-30, -0x1p-1066)
+ */
+ double ret;
#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
- int e = fetestexcept(FE_INEXACT);
- feclearexcept(FE_INEXACT);
+ int e = fetestexcept(FE_INEXACT);
+ feclearexcept(FE_INEXACT);
#endif
- fesetround(oround);
- adj = r.lo + xy.lo;
- ret = scalbn(r.hi + adj, spread);
+ fesetround(oround);
+ adj = r.lo + xy.lo;
+ ret = scalbn(r.hi + adj, spread);
#if defined(FE_INEXACT) && defined(FE_UNDERFLOW)
- if (ilogb(ret) < -1022 && fetestexcept(FE_INEXACT))
- feraiseexcept(FE_UNDERFLOW);
- else if (e)
- feraiseexcept(FE_INEXACT);
+ if (ilogb(ret) < -1022 && fetestexcept(FE_INEXACT))
+ feraiseexcept(FE_UNDERFLOW);
+ else if (e)
+ feraiseexcept(FE_INEXACT);
#endif
- return ret;
- }
-
- adj = add_adjusted(r.lo, xy.lo);
- if (spread + ilogb(r.hi) > -1023)
- return scalbn(r.hi + adj, spread);
- else
- return add_and_denormalize(r.hi, adj, spread);
+ return ret;
+ }
+
+ adj = add_adjusted(r.lo, xy.lo);
+ if (spread + ilogb(r.hi) > -1023)
+ return scalbn(r.hi + adj, spread);
+ else
+ return add_and_denormalize(r.hi, adj, spread);
}
#endif

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