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Unified Diff: fusl/src/math/powl.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/powl.c
diff --git a/fusl/src/math/powl.c b/fusl/src/math/powl.c
index 5b6da07b2efcce53795ec80da4a787208a2cb733..d7737b01b1b50ee60200244153a74d29706dd004 100644
--- a/fusl/src/math/powl.c
+++ b/fusl/src/math/powl.c
@@ -70,9 +70,8 @@
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
-long double powl(long double x, long double y)
-{
- return pow(x, y);
+long double powl(long double x, long double y) {
+ return pow(x, y);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
@@ -83,91 +82,61 @@ long double powl(long double x, long double y)
* on the domain 2^(-1/32) - 1 <= x <= 2^(1/32) - 1
*/
static const long double P[] = {
- 8.3319510773868690346226E-4L,
- 4.9000050881978028599627E-1L,
- 1.7500123722550302671919E0L,
- 1.4000100839971580279335E0L,
+ 8.3319510773868690346226E-4L, 4.9000050881978028599627E-1L,
+ 1.7500123722550302671919E0L, 1.4000100839971580279335E0L,
};
static const long double Q[] = {
-/* 1.0000000000000000000000E0L,*/
- 5.2500282295834889175431E0L,
- 8.4000598057587009834666E0L,
- 4.2000302519914740834728E0L,
+ /* 1.0000000000000000000000E0L,*/
+ 5.2500282295834889175431E0L, 8.4000598057587009834666E0L,
+ 4.2000302519914740834728E0L,
};
/* A[i] = 2^(-i/32), rounded to IEEE long double precision.
* If i is even, A[i] + B[i/2] gives additional accuracy.
*/
static const long double A[33] = {
- 1.0000000000000000000000E0L,
- 9.7857206208770013448287E-1L,
- 9.5760328069857364691013E-1L,
- 9.3708381705514995065011E-1L,
- 9.1700404320467123175367E-1L,
- 8.9735453750155359320742E-1L,
- 8.7812608018664974155474E-1L,
- 8.5930964906123895780165E-1L,
- 8.4089641525371454301892E-1L,
- 8.2287773907698242225554E-1L,
- 8.0524516597462715409607E-1L,
- 7.8799042255394324325455E-1L,
- 7.7110541270397041179298E-1L,
- 7.5458221379671136985669E-1L,
- 7.3841307296974965571198E-1L,
- 7.2259040348852331001267E-1L,
- 7.0710678118654752438189E-1L,
- 6.9195494098191597746178E-1L,
- 6.7712777346844636413344E-1L,
- 6.6261832157987064729696E-1L,
- 6.4841977732550483296079E-1L,
- 6.3452547859586661129850E-1L,
- 6.2092890603674202431705E-1L,
- 6.0762367999023443907803E-1L,
- 5.9460355750136053334378E-1L,
- 5.8186242938878875689693E-1L,
- 5.6939431737834582684856E-1L,
- 5.5719337129794626814472E-1L,
- 5.4525386633262882960438E-1L,
- 5.3357020033841180906486E-1L,
- 5.2213689121370692017331E-1L,
- 5.1094857432705833910408E-1L,
- 5.0000000000000000000000E-1L,
+ 1.0000000000000000000000E0L, 9.7857206208770013448287E-1L,
+ 9.5760328069857364691013E-1L, 9.3708381705514995065011E-1L,
+ 9.1700404320467123175367E-1L, 8.9735453750155359320742E-1L,
+ 8.7812608018664974155474E-1L, 8.5930964906123895780165E-1L,
+ 8.4089641525371454301892E-1L, 8.2287773907698242225554E-1L,
+ 8.0524516597462715409607E-1L, 7.8799042255394324325455E-1L,
+ 7.7110541270397041179298E-1L, 7.5458221379671136985669E-1L,
+ 7.3841307296974965571198E-1L, 7.2259040348852331001267E-1L,
+ 7.0710678118654752438189E-1L, 6.9195494098191597746178E-1L,
+ 6.7712777346844636413344E-1L, 6.6261832157987064729696E-1L,
+ 6.4841977732550483296079E-1L, 6.3452547859586661129850E-1L,
+ 6.2092890603674202431705E-1L, 6.0762367999023443907803E-1L,
+ 5.9460355750136053334378E-1L, 5.8186242938878875689693E-1L,
+ 5.6939431737834582684856E-1L, 5.5719337129794626814472E-1L,
+ 5.4525386633262882960438E-1L, 5.3357020033841180906486E-1L,
+ 5.2213689121370692017331E-1L, 5.1094857432705833910408E-1L,
+ 5.0000000000000000000000E-1L,
};
static const long double B[17] = {
- 0.0000000000000000000000E0L,
- 2.6176170809902549338711E-20L,
--1.0126791927256478897086E-20L,
- 1.3438228172316276937655E-21L,
- 1.2207982955417546912101E-20L,
--6.3084814358060867200133E-21L,
- 1.3164426894366316434230E-20L,
--1.8527916071632873716786E-20L,
- 1.8950325588932570796551E-20L,
- 1.5564775779538780478155E-20L,
- 6.0859793637556860974380E-21L,
--2.0208749253662532228949E-20L,
- 1.4966292219224761844552E-20L,
- 3.3540909728056476875639E-21L,
--8.6987564101742849540743E-22L,
--1.2327176863327626135542E-20L,
- 0.0000000000000000000000E0L,
+ 0.0000000000000000000000E0L, 2.6176170809902549338711E-20L,
+ -1.0126791927256478897086E-20L, 1.3438228172316276937655E-21L,
+ 1.2207982955417546912101E-20L, -6.3084814358060867200133E-21L,
+ 1.3164426894366316434230E-20L, -1.8527916071632873716786E-20L,
+ 1.8950325588932570796551E-20L, 1.5564775779538780478155E-20L,
+ 6.0859793637556860974380E-21L, -2.0208749253662532228949E-20L,
+ 1.4966292219224761844552E-20L, 3.3540909728056476875639E-21L,
+ -8.6987564101742849540743E-22L, -1.2327176863327626135542E-20L,
+ 0.0000000000000000000000E0L,
};
/* 2^x = 1 + x P(x),
* on the interval -1/32 <= x <= 0
*/
static const long double R[] = {
- 1.5089970579127659901157E-5L,
- 1.5402715328927013076125E-4L,
- 1.3333556028915671091390E-3L,
- 9.6181291046036762031786E-3L,
- 5.5504108664798463044015E-2L,
- 2.4022650695910062854352E-1L,
- 6.9314718055994530931447E-1L,
+ 1.5089970579127659901157E-5L, 1.5402715328927013076125E-4L,
+ 1.3333556028915671091390E-3L, 9.6181291046036762031786E-3L,
+ 5.5504108664798463044015E-2L, 2.4022650695910062854352E-1L,
+ 6.9314718055994530931447E-1L,
};
-#define MEXP (NXT*16384.0L)
+#define MEXP (NXT * 16384.0L)
/* The following if denormal numbers are supported, else -MEXP: */
-#define MNEXP (-NXT*(16384.0L+64.0L))
+#define MNEXP (-NXT * (16384.0L + 64.0L))
/* log2(e) - 1 */
#define LOG2EA 0.44269504088896340735992L
@@ -191,231 +160,228 @@ static const volatile long double twom10000 = 0x1p-10000L;
static long double reducl(long double);
static long double powil(long double, int);
-long double powl(long double x, long double y)
-{
- /* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
- int i, nflg, iyflg, yoddint;
- long e;
- volatile long double z=0;
- long double w=0, W=0, Wa=0, Wb=0, ya=0, yb=0, u=0;
-
- /* make sure no invalid exception is raised by nan comparision */
- if (isnan(x)) {
- if (!isnan(y) && y == 0.0)
- return 1.0;
- return x;
- }
- if (isnan(y)) {
- if (x == 1.0)
- return 1.0;
- return y;
- }
- if (x == 1.0)
- return 1.0; /* 1**y = 1, even if y is nan */
- if (x == -1.0 && !isfinite(y))
- return 1.0; /* -1**inf = 1 */
- if (y == 0.0)
- return 1.0; /* x**0 = 1, even if x is nan */
- if (y == 1.0)
- return x;
- if (y >= LDBL_MAX) {
- if (x > 1.0 || x < -1.0)
- return INFINITY;
- if (x != 0.0)
- return 0.0;
- }
- if (y <= -LDBL_MAX) {
- if (x > 1.0 || x < -1.0)
- return 0.0;
- if (x != 0.0 || y == -INFINITY)
- return INFINITY;
- }
- if (x >= LDBL_MAX) {
- if (y > 0.0)
- return INFINITY;
- return 0.0;
- }
-
- w = floorl(y);
-
- /* Set iyflg to 1 if y is an integer. */
- iyflg = 0;
- if (w == y)
- iyflg = 1;
-
- /* Test for odd integer y. */
- yoddint = 0;
- if (iyflg) {
- ya = fabsl(y);
- ya = floorl(0.5 * ya);
- yb = 0.5 * fabsl(w);
- if( ya != yb )
- yoddint = 1;
- }
-
- if (x <= -LDBL_MAX) {
- if (y > 0.0) {
- if (yoddint)
- return -INFINITY;
- return INFINITY;
- }
- if (y < 0.0) {
- if (yoddint)
- return -0.0;
- return 0.0;
- }
- }
- nflg = 0; /* (x<0)**(odd int) */
- if (x <= 0.0) {
- if (x == 0.0) {
- if (y < 0.0) {
- if (signbit(x) && yoddint)
- /* (-0.0)**(-odd int) = -inf, divbyzero */
- return -1.0/0.0;
- /* (+-0.0)**(negative) = inf, divbyzero */
- return 1.0/0.0;
- }
- if (signbit(x) && yoddint)
- return -0.0;
- return 0.0;
- }
- if (iyflg == 0)
- return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */
- /* (x<0)**(integer) */
- if (yoddint)
- nflg = 1; /* negate result */
- x = -x;
- }
- /* (+integer)**(integer) */
- if (iyflg && floorl(x) == x && fabsl(y) < 32768.0) {
- w = powil(x, (int)y);
- return nflg ? -w : w;
- }
-
- /* separate significand from exponent */
- x = frexpl(x, &i);
- e = i;
-
- /* find significand in antilog table A[] */
- i = 1;
- if (x <= A[17])
- i = 17;
- if (x <= A[i+8])
- i += 8;
- if (x <= A[i+4])
- i += 4;
- if (x <= A[i+2])
- i += 2;
- if (x >= A[1])
- i = -1;
- i += 1;
-
- /* Find (x - A[i])/A[i]
- * in order to compute log(x/A[i]):
- *
- * log(x) = log( a x/a ) = log(a) + log(x/a)
- *
- * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
- */
- x -= A[i];
- x -= B[i/2];
- x /= A[i];
-
- /* rational approximation for log(1+v):
- *
- * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
- */
- z = x*x;
- w = x * (z * __polevll(x, P, 3) / __p1evll(x, Q, 3));
- w = w - 0.5*z;
-
- /* Convert to base 2 logarithm:
- * multiply by log2(e) = 1 + LOG2EA
- */
- z = LOG2EA * w;
- z += w;
- z += LOG2EA * x;
- z += x;
-
- /* Compute exponent term of the base 2 logarithm. */
- w = -i;
- w /= NXT;
- w += e;
- /* Now base 2 log of x is w + z. */
-
- /* Multiply base 2 log by y, in extended precision. */
-
- /* separate y into large part ya
- * and small part yb less than 1/NXT
- */
- ya = reducl(y);
- yb = y - ya;
-
- /* (w+z)(ya+yb)
- * = w*ya + w*yb + z*y
- */
- F = z * y + w * yb;
- Fa = reducl(F);
- Fb = F - Fa;
-
- G = Fa + w * ya;
- Ga = reducl(G);
- Gb = G - Ga;
-
- H = Fb + Gb;
- Ha = reducl(H);
- w = (Ga + Ha) * NXT;
-
- /* Test the power of 2 for overflow */
- if (w > MEXP)
- return huge * huge; /* overflow */
- if (w < MNEXP)
- return twom10000 * twom10000; /* underflow */
-
- e = w;
- Hb = H - Ha;
-
- if (Hb > 0.0) {
- e += 1;
- Hb -= 1.0/NXT; /*0.0625L;*/
- }
-
- /* Now the product y * log2(x) = Hb + e/NXT.
- *
- * Compute base 2 exponential of Hb,
- * where -0.0625 <= Hb <= 0.
- */
- z = Hb * __polevll(Hb, R, 6); /* z = 2**Hb - 1 */
-
- /* Express e/NXT as an integer plus a negative number of (1/NXT)ths.
- * Find lookup table entry for the fractional power of 2.
- */
- if (e < 0)
- i = 0;
- else
- i = 1;
- i = e/NXT + i;
- e = NXT*i - e;
- w = A[e];
- z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
- z = z + w;
- z = scalbnl(z, i); /* multiply by integer power of 2 */
-
- if (nflg)
- z = -z;
- return z;
+long double powl(long double x, long double y) {
+ /* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
+ int i, nflg, iyflg, yoddint;
+ long e;
+ volatile long double z = 0;
+ long double w = 0, W = 0, Wa = 0, Wb = 0, ya = 0, yb = 0, u = 0;
+
+ /* make sure no invalid exception is raised by nan comparision */
+ if (isnan(x)) {
+ if (!isnan(y) && y == 0.0)
+ return 1.0;
+ return x;
+ }
+ if (isnan(y)) {
+ if (x == 1.0)
+ return 1.0;
+ return y;
+ }
+ if (x == 1.0)
+ return 1.0; /* 1**y = 1, even if y is nan */
+ if (x == -1.0 && !isfinite(y))
+ return 1.0; /* -1**inf = 1 */
+ if (y == 0.0)
+ return 1.0; /* x**0 = 1, even if x is nan */
+ if (y == 1.0)
+ return x;
+ if (y >= LDBL_MAX) {
+ if (x > 1.0 || x < -1.0)
+ return INFINITY;
+ if (x != 0.0)
+ return 0.0;
+ }
+ if (y <= -LDBL_MAX) {
+ if (x > 1.0 || x < -1.0)
+ return 0.0;
+ if (x != 0.0 || y == -INFINITY)
+ return INFINITY;
+ }
+ if (x >= LDBL_MAX) {
+ if (y > 0.0)
+ return INFINITY;
+ return 0.0;
+ }
+
+ w = floorl(y);
+
+ /* Set iyflg to 1 if y is an integer. */
+ iyflg = 0;
+ if (w == y)
+ iyflg = 1;
+
+ /* Test for odd integer y. */
+ yoddint = 0;
+ if (iyflg) {
+ ya = fabsl(y);
+ ya = floorl(0.5 * ya);
+ yb = 0.5 * fabsl(w);
+ if (ya != yb)
+ yoddint = 1;
+ }
+
+ if (x <= -LDBL_MAX) {
+ if (y > 0.0) {
+ if (yoddint)
+ return -INFINITY;
+ return INFINITY;
+ }
+ if (y < 0.0) {
+ if (yoddint)
+ return -0.0;
+ return 0.0;
+ }
+ }
+ nflg = 0; /* (x<0)**(odd int) */
+ if (x <= 0.0) {
+ if (x == 0.0) {
+ if (y < 0.0) {
+ if (signbit(x) && yoddint)
+ /* (-0.0)**(-odd int) = -inf, divbyzero */
+ return -1.0 / 0.0;
+ /* (+-0.0)**(negative) = inf, divbyzero */
+ return 1.0 / 0.0;
+ }
+ if (signbit(x) && yoddint)
+ return -0.0;
+ return 0.0;
+ }
+ if (iyflg == 0)
+ return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */
+ /* (x<0)**(integer) */
+ if (yoddint)
+ nflg = 1; /* negate result */
+ x = -x;
+ }
+ /* (+integer)**(integer) */
+ if (iyflg && floorl(x) == x && fabsl(y) < 32768.0) {
+ w = powil(x, (int)y);
+ return nflg ? -w : w;
+ }
+
+ /* separate significand from exponent */
+ x = frexpl(x, &i);
+ e = i;
+
+ /* find significand in antilog table A[] */
+ i = 1;
+ if (x <= A[17])
+ i = 17;
+ if (x <= A[i + 8])
+ i += 8;
+ if (x <= A[i + 4])
+ i += 4;
+ if (x <= A[i + 2])
+ i += 2;
+ if (x >= A[1])
+ i = -1;
+ i += 1;
+
+ /* Find (x - A[i])/A[i]
+ * in order to compute log(x/A[i]):
+ *
+ * log(x) = log( a x/a ) = log(a) + log(x/a)
+ *
+ * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
+ */
+ x -= A[i];
+ x -= B[i / 2];
+ x /= A[i];
+
+ /* rational approximation for log(1+v):
+ *
+ * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
+ */
+ z = x * x;
+ w = x * (z * __polevll(x, P, 3) / __p1evll(x, Q, 3));
+ w = w - 0.5 * z;
+
+ /* Convert to base 2 logarithm:
+ * multiply by log2(e) = 1 + LOG2EA
+ */
+ z = LOG2EA * w;
+ z += w;
+ z += LOG2EA * x;
+ z += x;
+
+ /* Compute exponent term of the base 2 logarithm. */
+ w = -i;
+ w /= NXT;
+ w += e;
+ /* Now base 2 log of x is w + z. */
+
+ /* Multiply base 2 log by y, in extended precision. */
+
+ /* separate y into large part ya
+ * and small part yb less than 1/NXT
+ */
+ ya = reducl(y);
+ yb = y - ya;
+
+ /* (w+z)(ya+yb)
+ * = w*ya + w*yb + z*y
+ */
+ F = z * y + w * yb;
+ Fa = reducl(F);
+ Fb = F - Fa;
+
+ G = Fa + w * ya;
+ Ga = reducl(G);
+ Gb = G - Ga;
+
+ H = Fb + Gb;
+ Ha = reducl(H);
+ w = (Ga + Ha) * NXT;
+
+ /* Test the power of 2 for overflow */
+ if (w > MEXP)
+ return huge * huge; /* overflow */
+ if (w < MNEXP)
+ return twom10000 * twom10000; /* underflow */
+
+ e = w;
+ Hb = H - Ha;
+
+ if (Hb > 0.0) {
+ e += 1;
+ Hb -= 1.0 / NXT; /*0.0625L;*/
+ }
+
+ /* Now the product y * log2(x) = Hb + e/NXT.
+ *
+ * Compute base 2 exponential of Hb,
+ * where -0.0625 <= Hb <= 0.
+ */
+ z = Hb * __polevll(Hb, R, 6); /* z = 2**Hb - 1 */
+
+ /* Express e/NXT as an integer plus a negative number of (1/NXT)ths.
+ * Find lookup table entry for the fractional power of 2.
+ */
+ if (e < 0)
+ i = 0;
+ else
+ i = 1;
+ i = e / NXT + i;
+ e = NXT * i - e;
+ w = A[e];
+ z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
+ z = z + w;
+ z = scalbnl(z, i); /* multiply by integer power of 2 */
+
+ if (nflg)
+ z = -z;
+ return z;
}
-
/* Find a multiple of 1/NXT that is within 1/NXT of x. */
-static long double reducl(long double x)
-{
- long double t;
-
- t = x * NXT;
- t = floorl(t);
- t = t / NXT;
- return t;
+static long double reducl(long double x) {
+ long double t;
+
+ t = x * NXT;
+ t = floorl(t);
+ t = t / NXT;
+ return t;
}
/*
@@ -450,73 +416,71 @@ static long double reducl(long double x)
* Returns MAXNUM on overflow, zero on underflow.
*/
-static long double powil(long double x, int nn)
-{
- long double ww, y;
- long double s;
- int n, e, sign, lx;
-
- if (nn == 0)
- return 1.0;
-
- if (nn < 0) {
- sign = -1;
- n = -nn;
- } else {
- sign = 1;
- n = nn;
- }
-
- /* Overflow detection */
-
- /* Calculate approximate logarithm of answer */
- s = x;
- s = frexpl( s, &lx);
- e = (lx - 1)*n;
- if ((e == 0) || (e > 64) || (e < -64)) {
- s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L);
- s = (2.9142135623730950L * s - 0.5 + lx) * nn * LOGE2L;
- } else {
- s = LOGE2L * e;
- }
-
- if (s > MAXLOGL)
- return huge * huge; /* overflow */
-
- if (s < MINLOGL)
- return twom10000 * twom10000; /* underflow */
- /* Handle tiny denormal answer, but with less accuracy
- * since roundoff error in 1.0/x will be amplified.
- * The precise demarcation should be the gradual underflow threshold.
- */
- if (s < -MAXLOGL+2.0) {
- x = 1.0/x;
- sign = -sign;
- }
-
- /* First bit of the power */
- if (n & 1)
- y = x;
- else
- y = 1.0;
-
- ww = x;
- n >>= 1;
- while (n) {
- ww = ww * ww; /* arg to the 2-to-the-kth power */
- if (n & 1) /* if that bit is set, then include in product */
- y *= ww;
- n >>= 1;
- }
-
- if (sign < 0)
- y = 1.0/y;
- return y;
+static long double powil(long double x, int nn) {
+ long double ww, y;
+ long double s;
+ int n, e, sign, lx;
+
+ if (nn == 0)
+ return 1.0;
+
+ if (nn < 0) {
+ sign = -1;
+ n = -nn;
+ } else {
+ sign = 1;
+ n = nn;
+ }
+
+ /* Overflow detection */
+
+ /* Calculate approximate logarithm of answer */
+ s = x;
+ s = frexpl(s, &lx);
+ e = (lx - 1) * n;
+ if ((e == 0) || (e > 64) || (e < -64)) {
+ s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L);
+ s = (2.9142135623730950L * s - 0.5 + lx) * nn * LOGE2L;
+ } else {
+ s = LOGE2L * e;
+ }
+
+ if (s > MAXLOGL)
+ return huge * huge; /* overflow */
+
+ if (s < MINLOGL)
+ return twom10000 * twom10000; /* underflow */
+ /* Handle tiny denormal answer, but with less accuracy
+ * since roundoff error in 1.0/x will be amplified.
+ * The precise demarcation should be the gradual underflow threshold.
+ */
+ if (s < -MAXLOGL + 2.0) {
+ x = 1.0 / x;
+ sign = -sign;
+ }
+
+ /* First bit of the power */
+ if (n & 1)
+ y = x;
+ else
+ y = 1.0;
+
+ ww = x;
+ n >>= 1;
+ while (n) {
+ ww = ww * ww; /* arg to the 2-to-the-kth power */
+ if (n & 1) /* if that bit is set, then include in product */
+ y *= ww;
+ n >>= 1;
+ }
+
+ if (sign < 0)
+ y = 1.0 / y;
+ return y;
}
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
// TODO: broken implementation to make things compile
-long double powl(long double x, long double y)
-{
- return pow(x, y);
+long double powl(long double x, long double y) {
+ return pow(x, y);
}
#endif
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