libm: sync with upstream.
There's potential here to maybe lose some/all of builtins.cpp, but I'll
look at that separately later.
Test: treehugger
Change-Id: I2c2bc1d0753affdd214daeb09fa1ac7cd73db347
diff --git a/libm/Android.bp b/libm/Android.bp
index 83f40c2..43d82d5 100644
--- a/libm/Android.bp
+++ b/libm/Android.bp
@@ -30,8 +30,6 @@
whole_static_libs: ["libarm-optimized-routines-math"],
srcs: [
- "upstream-freebsd/lib/msun/bsdsrc/b_exp.c",
- "upstream-freebsd/lib/msun/bsdsrc/b_log.c",
"upstream-freebsd/lib/msun/bsdsrc/b_tgamma.c",
"upstream-freebsd/lib/msun/src/catrig.c",
"upstream-freebsd/lib/msun/src/catrigf.c",
@@ -112,6 +110,7 @@
"upstream-freebsd/lib/msun/src/s_copysign.c",
"upstream-freebsd/lib/msun/src/s_copysignf.c",
"upstream-freebsd/lib/msun/src/s_cos.c",
+ "upstream-freebsd/lib/msun/src/s_cospi.c",
"upstream-freebsd/lib/msun/src/s_cpow.c",
"upstream-freebsd/lib/msun/src/s_cpowf.c",
"upstream-freebsd/lib/msun/src/s_cpowl.c",
@@ -177,6 +176,7 @@
"upstream-freebsd/lib/msun/src/s_significand.c",
"upstream-freebsd/lib/msun/src/s_significandf.c",
"upstream-freebsd/lib/msun/src/s_sin.c",
+ "upstream-freebsd/lib/msun/src/s_sinpi.c",
"upstream-freebsd/lib/msun/src/s_sincos.c",
"upstream-freebsd/lib/msun/src/s_tan.c",
"upstream-freebsd/lib/msun/src/s_tanf.c",
diff --git a/libm/NOTICE b/libm/NOTICE
index 0c37b2b..64d253a 100644
--- a/libm/NOTICE
+++ b/libm/NOTICE
@@ -689,6 +689,14 @@
-------------------------------------------------------------------
+Copyright (c) 2005-2020 Rich Felker, et al.
+
+
+Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
+for all contributors to musl.
+
+-------------------------------------------------------------------
+
Copyright (c) 2007 David Schultz
All rights reserved.
@@ -1173,6 +1181,32 @@
-------------------------------------------------------------------
+Copyright (c) 2017 Steven G. Kargl
+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 unmodified, 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 ``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 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.
+
+-------------------------------------------------------------------
+
From: @(#)s_ilogb.c 5.1 93/09/24
====================================================
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
diff --git a/libm/freebsd-compat.h b/libm/freebsd-compat.h
index f400f2a..7accc55 100644
--- a/libm/freebsd-compat.h
+++ b/libm/freebsd-compat.h
@@ -39,3 +39,7 @@
// Similarly rename _scan_nan.
#define _scan_nan __libm_scan_nan
+
+// FreeBSD exports these in <math.h> but we don't.
+double cospi(double);
+double sinpi(double);
diff --git a/libm/upstream-freebsd/lib/msun/bsdsrc/b_exp.c b/libm/upstream-freebsd/lib/msun/bsdsrc/b_exp.c
index 89a2905..c667293 100644
--- a/libm/upstream-freebsd/lib/msun/bsdsrc/b_exp.c
+++ b/libm/upstream-freebsd/lib/msun/bsdsrc/b_exp.c
@@ -33,7 +33,6 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
-
/* EXP(X)
* RETURN THE EXPONENTIAL OF X
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
@@ -41,14 +40,14 @@
* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
*
* Required system supported functions:
- * scalb(x,n)
+ * ldexp(x,n)
* copysign(x,y)
- * finite(x)
+ * isfinite(x)
*
* Method:
* 1. Argument Reduction: given the input x, find r and integer k such
* that
- * x = k*ln2 + r, |r| <= 0.5*ln2 .
+ * x = k*ln2 + r, |r| <= 0.5*ln2.
* r will be represented as r := z+c for better accuracy.
*
* 2. Compute exp(r) by
@@ -69,105 +68,59 @@
* with 1,156,000 random arguments on a VAX, the maximum observed
* error was 0.869 ulps (units in the last place).
*/
+static const double
+ p1 = 1.6666666666666660e-01, /* 0x3fc55555, 0x55555553 */
+ p2 = -2.7777777777564776e-03, /* 0xbf66c16c, 0x16c0ac3c */
+ p3 = 6.6137564717940088e-05, /* 0x3f11566a, 0xb5c2ba0d */
+ p4 = -1.6534060280704225e-06, /* 0xbebbbd53, 0x273e8fb7 */
+ p5 = 4.1437773411069054e-08; /* 0x3e663f2a, 0x09c94b6c */
-#include "mathimpl.h"
+static const double
+ ln2hi = 0x1.62e42fee00000p-1, /* High 32 bits round-down. */
+ ln2lo = 0x1.a39ef35793c76p-33; /* Next 53 bits round-to-nearst. */
-static const double p1 = 0x1.555555555553ep-3;
-static const double p2 = -0x1.6c16c16bebd93p-9;
-static const double p3 = 0x1.1566aaf25de2cp-14;
-static const double p4 = -0x1.bbd41c5d26bf1p-20;
-static const double p5 = 0x1.6376972bea4d0p-25;
-static const double ln2hi = 0x1.62e42fee00000p-1;
-static const double ln2lo = 0x1.a39ef35793c76p-33;
-static const double lnhuge = 0x1.6602b15b7ecf2p9;
-static const double lntiny = -0x1.77af8ebeae354p9;
-static const double invln2 = 0x1.71547652b82fep0;
-
-#if 0
-double exp(x)
-double x;
-{
- double z,hi,lo,c;
- int k;
-
-#if !defined(vax)&&!defined(tahoe)
- if(x!=x) return(x); /* x is NaN */
-#endif /* !defined(vax)&&!defined(tahoe) */
- if( x <= lnhuge ) {
- if( x >= lntiny ) {
-
- /* argument reduction : x --> x - k*ln2 */
-
- k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
-
- /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
-
- hi=x-k*ln2hi;
- x=hi-(lo=k*ln2lo);
-
- /* return 2^k*[1+x+x*c/(2+c)] */
- z=x*x;
- c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
- return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
-
- }
- /* end of x > lntiny */
-
- else
- /* exp(-big#) underflows to zero */
- if(finite(x)) return(scalb(1.0,-5000));
-
- /* exp(-INF) is zero */
- else return(0.0);
- }
- /* end of x < lnhuge */
-
- else
- /* exp(INF) is INF, exp(+big#) overflows to INF */
- return( finite(x) ? scalb(1.0,5000) : x);
-}
-#endif
+static const double
+ lnhuge = 0x1.6602b15b7ecf2p9, /* (DBL_MAX_EXP + 9) * log(2.) */
+ lntiny = -0x1.77af8ebeae354p9, /* (DBL_MIN_EXP - 53 - 10) * log(2.) */
+ invln2 = 0x1.71547652b82fep0; /* 1 / log(2.) */
/* returns exp(r = x + c) for |c| < |x| with no overlap. */
-double __exp__D(x, c)
-double x, c;
+static double
+__exp__D(double x, double c)
{
- double z,hi,lo;
+ double hi, lo, z;
int k;
- if (x != x) /* x is NaN */
+ if (x != x) /* x is NaN. */
return(x);
- if ( x <= lnhuge ) {
- if ( x >= lntiny ) {
- /* argument reduction : x --> x - k*ln2 */
- z = invln2*x;
- k = z + copysign(.5, x);
+ if (x <= lnhuge) {
+ if (x >= lntiny) {
+ /* argument reduction: x --> x - k*ln2 */
+ z = invln2 * x;
+ k = z + copysign(0.5, x);
- /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
+ /*
+ * Express (x + c) - k * ln2 as hi - lo.
+ * Let x = hi - lo rounded.
+ */
+ hi = x - k * ln2hi; /* Exact. */
+ lo = k * ln2lo - c;
+ x = hi - lo;
- hi=(x-k*ln2hi); /* Exact. */
- x= hi - (lo = k*ln2lo-c);
- /* return 2^k*[1+x+x*c/(2+c)] */
- z=x*x;
- c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
- c = (x*c)/(2.0-c);
+ /* Return 2^k*[1+x+x*c/(2+c)] */
+ z = x * x;
+ c = x - z * (p1 + z * (p2 + z * (p3 + z * (p4 +
+ z * p5))));
+ c = (x * c) / (2 - c);
- return scalb(1.+(hi-(lo - c)), k);
+ return (ldexp(1 + (hi - (lo - c)), k));
+ } else {
+ /* exp(-INF) is 0. exp(-big) underflows to 0. */
+ return (isfinite(x) ? ldexp(1., -5000) : 0);
}
- /* end of x > lntiny */
-
- else
- /* exp(-big#) underflows to zero */
- if(finite(x)) return(scalb(1.0,-5000));
-
- /* exp(-INF) is zero */
- else return(0.0);
- }
- /* end of x < lnhuge */
-
- else
+ } else
/* exp(INF) is INF, exp(+big#) overflows to INF */
- return( finite(x) ? scalb(1.0,5000) : x);
+ return (isfinite(x) ? ldexp(1., 5000) : x);
}
diff --git a/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c b/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c
index c164dfa..9d09ac7 100644
--- a/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c
+++ b/libm/upstream-freebsd/lib/msun/bsdsrc/b_log.c
@@ -33,10 +33,6 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
-#include <math.h>
-
-#include "mathimpl.h"
-
/* Table-driven natural logarithm.
*
* This code was derived, with minor modifications, from:
@@ -44,25 +40,27 @@
* Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
* Math Software, vol 16. no 4, pp 378-400, Dec 1990).
*
- * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
+ * Calculates log(2^m*F*(1+f/F)), |f/F| <= 1/256,
* where F = j/128 for j an integer in [0, 128].
*
* log(2^m) = log2_hi*m + log2_tail*m
- * since m is an integer, the dominant term is exact.
+ * The leading term is exact, because m is an integer,
* m has at most 10 digits (for subnormal numbers),
* and log2_hi has 11 trailing zero bits.
*
- * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
+ * log(F) = logF_hi[j] + logF_lo[j] is in table below.
* logF_hi[] + 512 is exact.
*
* log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
- * the leading term is calculated to extra precision in two
+ *
+ * The leading term is calculated to extra precision in two
* parts, the larger of which adds exactly to the dominant
* m and F terms.
+ *
* There are two cases:
- * 1. when m, j are non-zero (m | j), use absolute
+ * 1. When m and j are non-zero (m | j), use absolute
* precision for the leading term.
- * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
+ * 2. When m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
* In this case, use a relative precision of 24 bits.
* (This is done differently in the original paper)
*
@@ -70,11 +68,21 @@
* 0 return signalling -Inf
* neg return signalling NaN
* +Inf return +Inf
-*/
+ */
#define N 128
-/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
+/*
+ * Coefficients in the polynomial approximation of log(1+f/F).
+ * Domain of x is [0,1./256] with 2**(-64.187) precision.
+ */
+static const double
+ A1 = 8.3333333333333329e-02, /* 0x3fb55555, 0x55555555 */
+ A2 = 1.2499999999943598e-02, /* 0x3f899999, 0x99991a98 */
+ A3 = 2.2321527525957776e-03; /* 0x3f624929, 0xe24e70be */
+
+/*
+ * Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
* Used for generation of extend precision logarithms.
* The constant 35184372088832 is 2^45, so the divide is exact.
* It ensures correct reading of logF_head, even for inaccurate
@@ -82,12 +90,7 @@
* right answer for integers less than 2^53.)
* Values for log(F) were generated using error < 10^-57 absolute
* with the bc -l package.
-*/
-static double A1 = .08333333333333178827;
-static double A2 = .01250000000377174923;
-static double A3 = .002232139987919447809;
-static double A4 = .0004348877777076145742;
-
+ */
static double logF_head[N+1] = {
0.,
.007782140442060381246,
@@ -351,118 +354,51 @@
.00000000000025144230728376072,
-.00000000000017239444525614834
};
-
-#if 0
-double
-#ifdef _ANSI_SOURCE
-log(double x)
-#else
-log(x) double x;
-#endif
-{
- int m, j;
- double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
- volatile double u1;
-
- /* Catch special cases */
- if (x <= 0)
- if (x == zero) /* log(0) = -Inf */
- return (-one/zero);
- else /* log(neg) = NaN */
- return (zero/zero);
- else if (!finite(x))
- return (x+x); /* x = NaN, Inf */
-
- /* Argument reduction: 1 <= g < 2; x/2^m = g; */
- /* y = F*(1 + f/F) for |f| <= 2^-8 */
-
- m = logb(x);
- g = ldexp(x, -m);
- if (m == -1022) {
- j = logb(g), m += j;
- g = ldexp(g, -j);
- }
- j = N*(g-1) + .5;
- F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */
- f = g - F;
-
- /* Approximate expansion for log(1+f/F) ~= u + q */
- g = 1/(2*F+f);
- u = 2*f*g;
- v = u*u;
- q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
-
- /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8,
- * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
- * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
- */
- if (m | j)
- u1 = u + 513, u1 -= 513;
-
- /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero;
- * u1 = u to 24 bits.
- */
- else
- u1 = u, TRUNC(u1);
- u2 = (2.0*(f - F*u1) - u1*f) * g;
- /* u1 + u2 = 2f/(2F+f) to extra precision. */
-
- /* log(x) = log(2^m*F*(1+f/F)) = */
- /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */
- /* (exact) + (tiny) */
-
- u1 += m*logF_head[N] + logF_head[j]; /* exact */
- u2 = (u2 + logF_tail[j]) + q; /* tiny */
- u2 += logF_tail[N]*m;
- return (u1 + u2);
-}
-#endif
-
/*
* Extra precision variant, returning struct {double a, b;};
- * log(x) = a+b to 63 bits, with a rounded to 26 bits.
+ * log(x) = a+b to 63 bits, with 'a' rounded to 24 bits.
*/
-struct Double
-#ifdef _ANSI_SOURCE
+static struct Double
__log__D(double x)
-#else
-__log__D(x) double x;
-#endif
{
int m, j;
- double F, f, g, q, u, v, u2;
- volatile double u1;
+ double F, f, g, q, u, v, u1, u2;
struct Double r;
- /* Argument reduction: 1 <= g < 2; x/2^m = g; */
- /* y = F*(1 + f/F) for |f| <= 2^-8 */
-
- m = logb(x);
- g = ldexp(x, -m);
+ /*
+ * Argument reduction: 1 <= g < 2; x/2^m = g;
+ * y = F*(1 + f/F) for |f| <= 2^-8
+ */
+ g = frexp(x, &m);
+ g *= 2;
+ m--;
if (m == -1022) {
- j = logb(g), m += j;
+ j = ilogb(g);
+ m += j;
g = ldexp(g, -j);
}
- j = N*(g-1) + .5;
- F = (1.0/N) * j + 1;
+ j = N * (g - 1) + 0.5;
+ F = (1. / N) * j + 1;
f = g - F;
- g = 1/(2*F+f);
- u = 2*f*g;
- v = u*u;
- q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
- if (m | j)
- u1 = u + 513, u1 -= 513;
- else
- u1 = u, TRUNC(u1);
- u2 = (2.0*(f - F*u1) - u1*f) * g;
+ g = 1 / (2 * F + f);
+ u = 2 * f * g;
+ v = u * u;
+ q = u * v * (A1 + v * (A2 + v * A3));
+ if (m | j) {
+ u1 = u + 513;
+ u1 -= 513;
+ } else {
+ u1 = (float)u;
+ }
+ u2 = (2 * (f - F * u1) - u1 * f) * g;
- u1 += m*logF_head[N] + logF_head[j];
+ u1 += m * logF_head[N] + logF_head[j];
- u2 += logF_tail[j]; u2 += q;
- u2 += logF_tail[N]*m;
- r.a = u1 + u2; /* Only difference is here */
- TRUNC(r.a);
+ u2 += logF_tail[j];
+ u2 += q;
+ u2 += logF_tail[N] * m;
+ r.a = (float)(u1 + u2); /* Only difference is here. */
r.b = (u1 - r.a) + u2;
return (r);
}
diff --git a/libm/upstream-freebsd/lib/msun/bsdsrc/b_tgamma.c b/libm/upstream-freebsd/lib/msun/bsdsrc/b_tgamma.c
index 5cb1f93..493ced3 100644
--- a/libm/upstream-freebsd/lib/msun/bsdsrc/b_tgamma.c
+++ b/libm/upstream-freebsd/lib/msun/bsdsrc/b_tgamma.c
@@ -29,37 +29,46 @@
* SUCH DAMAGE.
*/
+/*
+ * The original code, FreeBSD's old svn r93211, contained the following
+ * attribution:
+ *
+ * This code by P. McIlroy, Oct 1992;
+ *
+ * The financial support of UUNET Communications Services is greatfully
+ * acknowledged.
+ *
+ * The algorithm remains, but the code has been re-arranged to facilitate
+ * porting to other precisions.
+ */
+
/* @(#)gamma.c 8.1 (Berkeley) 6/4/93 */
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
+#include <float.h>
+
+#include "math.h"
+#include "math_private.h"
+
+/* Used in b_log.c and below. */
+struct Double {
+ double a;
+ double b;
+};
+
+#include "b_log.c"
+#include "b_exp.c"
+
/*
- * This code by P. McIlroy, Oct 1992;
+ * The range is broken into several subranges. Each is handled by its
+ * helper functions.
*
- * The financial support of UUNET Communications Services is greatfully
- * acknowledged.
- */
-
-#include <math.h>
-#include "mathimpl.h"
-
-/* METHOD:
- * x < 0: Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x))
- * At negative integers, return NaN and raise invalid.
- *
- * x < 6.5:
- * Use argument reduction G(x+1) = xG(x) to reach the
- * range [1.066124,2.066124]. Use a rational
- * approximation centered at the minimum (x0+1) to
- * ensure monotonicity.
- *
- * x >= 6.5: Use the asymptotic approximation (Stirling's formula)
- * adjusted for equal-ripples:
- *
- * log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + 1/x*P(1/(x*x))
- *
- * Keep extra precision in multiplying (x-.5)(log(x)-1), to
- * avoid premature round-off.
+ * x >= 6.0: large_gam(x)
+ * 6.0 > x >= xleft: small_gam(x) where xleft = 1 + left + x0.
+ * xleft > x > iota: smaller_gam(x) where iota = 1e-17.
+ * iota > x > -itoa: Handle x near 0.
+ * -iota > x : neg_gam
*
* Special values:
* -Inf: return NaN and raise invalid;
@@ -77,201 +86,224 @@
* Maximum observed error < 4ulp in 1,000,000 trials.
*/
-static double neg_gam(double);
-static double small_gam(double);
-static double smaller_gam(double);
-static struct Double large_gam(double);
-static struct Double ratfun_gam(double, double);
-
-/*
- * Rational approximation, A0 + x*x*P(x)/Q(x), on the interval
- * [1.066.., 2.066..] accurate to 4.25e-19.
- */
-#define LEFT -.3955078125 /* left boundary for rat. approx */
-#define x0 .461632144968362356785 /* xmin - 1 */
-
-#define a0_hi 0.88560319441088874992
-#define a0_lo -.00000000000000004996427036469019695
-#define P0 6.21389571821820863029017800727e-01
-#define P1 2.65757198651533466104979197553e-01
-#define P2 5.53859446429917461063308081748e-03
-#define P3 1.38456698304096573887145282811e-03
-#define P4 2.40659950032711365819348969808e-03
-#define Q0 1.45019531250000000000000000000e+00
-#define Q1 1.06258521948016171343454061571e+00
-#define Q2 -2.07474561943859936441469926649e-01
-#define Q3 -1.46734131782005422506287573015e-01
-#define Q4 3.07878176156175520361557573779e-02
-#define Q5 5.12449347980666221336054633184e-03
-#define Q6 -1.76012741431666995019222898833e-03
-#define Q7 9.35021023573788935372153030556e-05
-#define Q8 6.13275507472443958924745652239e-06
/*
* Constants for large x approximation (x in [6, Inf])
* (Accurate to 2.8*10^-19 absolute)
*/
-#define lns2pi_hi 0.418945312500000
-#define lns2pi_lo -.000006779295327258219670263595
-#define Pa0 8.33333333333333148296162562474e-02
-#define Pa1 -2.77777777774548123579378966497e-03
-#define Pa2 7.93650778754435631476282786423e-04
-#define Pa3 -5.95235082566672847950717262222e-04
-#define Pa4 8.41428560346653702135821806252e-04
-#define Pa5 -1.89773526463879200348872089421e-03
-#define Pa6 5.69394463439411649408050664078e-03
-#define Pa7 -1.44705562421428915453880392761e-02
-static const double zero = 0., one = 1.0, tiny = 1e-300;
-
-double
-tgamma(x)
- double x;
-{
- struct Double u;
-
- if (x >= 6) {
- if(x > 171.63)
- return (x / zero);
- u = large_gam(x);
- return(__exp__D(u.a, u.b));
- } else if (x >= 1.0 + LEFT + x0)
- return (small_gam(x));
- else if (x > 1.e-17)
- return (smaller_gam(x));
- else if (x > -1.e-17) {
- if (x != 0.0)
- u.a = one - tiny; /* raise inexact */
- return (one/x);
- } else if (!finite(x))
- return (x - x); /* x is NaN or -Inf */
- else
- return (neg_gam(x));
-}
+static const double zero = 0.;
+static const volatile double tiny = 1e-300;
/*
+ * x >= 6
+ *
+ * Use the asymptotic approximation (Stirling's formula) adjusted fof
+ * equal-ripples:
+ *
+ * log(G(x)) ~= (x-0.5)*(log(x)-1) + 0.5(log(2*pi)-1) + 1/x*P(1/(x*x))
+ *
+ * Keep extra precision in multiplying (x-.5)(log(x)-1), to avoid
+ * premature round-off.
+ *
* Accurate to max(ulp(1/128) absolute, 2^-66 relative) error.
*/
-static struct Double
-large_gam(x)
- double x;
-{
- double z, p;
- struct Double t, u, v;
+static const double
+ ln2pi_hi = 0.41894531250000000,
+ ln2pi_lo = -6.7792953272582197e-6,
+ Pa0 = 8.3333333333333329e-02, /* 0x3fb55555, 0x55555555 */
+ Pa1 = -2.7777777777735404e-03, /* 0xbf66c16c, 0x16c145ec */
+ Pa2 = 7.9365079044114095e-04, /* 0x3f4a01a0, 0x183de82d */
+ Pa3 = -5.9523715464225254e-04, /* 0xbf438136, 0x0e681f62 */
+ Pa4 = 8.4161391899445698e-04, /* 0x3f4b93f8, 0x21042a13 */
+ Pa5 = -1.9065246069191080e-03, /* 0xbf5f3c8b, 0x357cb64e */
+ Pa6 = 5.9047708485785158e-03, /* 0x3f782f99, 0xdaf5d65f */
+ Pa7 = -1.6484018705183290e-02; /* 0xbf90e12f, 0xc4fb4df0 */
- z = one/(x*x);
- p = Pa0+z*(Pa1+z*(Pa2+z*(Pa3+z*(Pa4+z*(Pa5+z*(Pa6+z*Pa7))))));
- p = p/x;
+static struct Double
+large_gam(double x)
+{
+ double p, z, thi, tlo, xhi, xlo;
+ struct Double u;
+
+ z = 1 / (x * x);
+ p = Pa0 + z * (Pa1 + z * (Pa2 + z * (Pa3 + z * (Pa4 + z * (Pa5 +
+ z * (Pa6 + z * Pa7))))));
+ p = p / x;
u = __log__D(x);
- u.a -= one;
- v.a = (x -= .5);
- TRUNC(v.a);
- v.b = x - v.a;
- t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */
- t.b = v.b*u.a + x*u.b;
- /* return t.a + t.b + lns2pi_hi + lns2pi_lo + p */
- t.b += lns2pi_lo; t.b += p;
- u.a = lns2pi_hi + t.b; u.a += t.a;
- u.b = t.a - u.a;
- u.b += lns2pi_hi; u.b += t.b;
+ u.a -= 1;
+
+ /* Split (x - 0.5) in high and low parts. */
+ x -= 0.5;
+ xhi = (float)x;
+ xlo = x - xhi;
+
+ /* Compute t = (x-.5)*(log(x)-1) in extra precision. */
+ thi = xhi * u.a;
+ tlo = xlo * u.a + x * u.b;
+
+ /* Compute thi + tlo + ln2pi_hi + ln2pi_lo + p. */
+ tlo += ln2pi_lo;
+ tlo += p;
+ u.a = ln2pi_hi + tlo;
+ u.a += thi;
+ u.b = thi - u.a;
+ u.b += ln2pi_hi;
+ u.b += tlo;
return (u);
}
/*
+ * Rational approximation, A0 + x * x * P(x) / Q(x), on the interval
+ * [1.066.., 2.066..] accurate to 4.25e-19.
+ *
+ * Returns r.a + r.b = a0 + (z + c)^2 * p / q, with r.a truncated.
+ */
+static const double
+#if 0
+ a0_hi = 8.8560319441088875e-1,
+ a0_lo = -4.9964270364690197e-17,
+#else
+ a0_hi = 8.8560319441088875e-01, /* 0x3fec56dc, 0x82a74aef */
+ a0_lo = -4.9642368725563397e-17, /* 0xbc8c9deb, 0xaa64afc3 */
+#endif
+ P0 = 6.2138957182182086e-1,
+ P1 = 2.6575719865153347e-1,
+ P2 = 5.5385944642991746e-3,
+ P3 = 1.3845669830409657e-3,
+ P4 = 2.4065995003271137e-3,
+ Q0 = 1.4501953125000000e+0,
+ Q1 = 1.0625852194801617e+0,
+ Q2 = -2.0747456194385994e-1,
+ Q3 = -1.4673413178200542e-1,
+ Q4 = 3.0787817615617552e-2,
+ Q5 = 5.1244934798066622e-3,
+ Q6 = -1.7601274143166700e-3,
+ Q7 = 9.3502102357378894e-5,
+ Q8 = 6.1327550747244396e-6;
+
+static struct Double
+ratfun_gam(double z, double c)
+{
+ double p, q, thi, tlo;
+ struct Double r;
+
+ q = Q0 + z * (Q1 + z * (Q2 + z * (Q3 + z * (Q4 + z * (Q5 +
+ z * (Q6 + z * (Q7 + z * Q8)))))));
+ p = P0 + z * (P1 + z * (P2 + z * (P3 + z * P4)));
+ p = p / q;
+
+ /* Split z into high and low parts. */
+ thi = (float)z;
+ tlo = (z - thi) + c;
+ tlo *= (thi + z);
+
+ /* Split (z+c)^2 into high and low parts. */
+ thi *= thi;
+ q = thi;
+ thi = (float)thi;
+ tlo += (q - thi);
+
+ /* Split p/q into high and low parts. */
+ r.a = (float)p;
+ r.b = p - r.a;
+
+ tlo = tlo * p + thi * r.b + a0_lo;
+ thi *= r.a; /* t = (z+c)^2*(P/Q) */
+ r.a = (float)(thi + a0_hi);
+ r.b = ((a0_hi - r.a) + thi) + tlo;
+ return (r); /* r = a0 + t */
+}
+/*
+ * x < 6
+ *
+ * Use argument reduction G(x+1) = xG(x) to reach the range [1.066124,
+ * 2.066124]. Use a rational approximation centered at the minimum
+ * (x0+1) to ensure monotonicity.
+ *
* Good to < 1 ulp. (provably .90 ulp; .87 ulp on 1,000,000 runs.)
* It also has correct monotonicity.
*/
+static const double
+ left = -0.3955078125, /* left boundary for rat. approx */
+ x0 = 4.6163214496836236e-1; /* xmin - 1 */
+
static double
-small_gam(x)
- double x;
+small_gam(double x)
{
- double y, ym1, t;
+ double t, y, ym1;
struct Double yy, r;
- y = x - one;
- ym1 = y - one;
- if (y <= 1.0 + (LEFT + x0)) {
+
+ y = x - 1;
+ if (y <= 1 + (left + x0)) {
yy = ratfun_gam(y - x0, 0);
return (yy.a + yy.b);
}
- r.a = y;
- TRUNC(r.a);
- yy.a = r.a - one;
- y = ym1;
- yy.b = r.b = y - yy.a;
+
+ r.a = (float)y;
+ yy.a = r.a - 1;
+ y = y - 1 ;
+ r.b = yy.b = y - yy.a;
+
/* Argument reduction: G(x+1) = x*G(x) */
- for (ym1 = y-one; ym1 > LEFT + x0; y = ym1--, yy.a--) {
- t = r.a*yy.a;
- r.b = r.a*yy.b + y*r.b;
- r.a = t;
- TRUNC(r.a);
+ for (ym1 = y - 1; ym1 > left + x0; y = ym1--, yy.a--) {
+ t = r.a * yy.a;
+ r.b = r.a * yy.b + y * r.b;
+ r.a = (float)t;
r.b += (t - r.a);
}
+
/* Return r*tgamma(y). */
yy = ratfun_gam(y - x0, 0);
- y = r.b*(yy.a + yy.b) + r.a*yy.b;
- y += yy.a*r.a;
+ y = r.b * (yy.a + yy.b) + r.a * yy.b;
+ y += yy.a * r.a;
return (y);
}
/*
- * Good on (0, 1+x0+LEFT]. Accurate to 1ulp.
+ * Good on (0, 1+x0+left]. Accurate to 1 ulp.
*/
static double
-smaller_gam(x)
- double x;
+smaller_gam(double x)
{
- double t, d;
- struct Double r, xx;
- if (x < x0 + LEFT) {
- t = x, TRUNC(t);
- d = (t+x)*(x-t);
+ double d, rhi, rlo, t, xhi, xlo;
+ struct Double r;
+
+ if (x < x0 + left) {
+ t = (float)x;
+ d = (t + x) * (x - t);
t *= t;
- xx.a = (t + x), TRUNC(xx.a);
- xx.b = x - xx.a; xx.b += t; xx.b += d;
- t = (one-x0); t += x;
- d = (one-x0); d -= t; d += x;
- x = xx.a + xx.b;
+ xhi = (float)(t + x);
+ xlo = x - xhi;
+ xlo += t;
+ xlo += d;
+ t = 1 - x0;
+ t += x;
+ d = 1 - x0;
+ d -= t;
+ d += x;
+ x = xhi + xlo;
} else {
- xx.a = x, TRUNC(xx.a);
- xx.b = x - xx.a;
+ xhi = (float)x;
+ xlo = x - xhi;
t = x - x0;
- d = (-x0 -t); d += x;
+ d = - x0 - t;
+ d += x;
}
+
r = ratfun_gam(t, d);
- d = r.a/x, TRUNC(d);
- r.a -= d*xx.a; r.a -= d*xx.b; r.a += r.b;
- return (d + r.a/x);
+ d = (float)(r.a / x);
+ r.a -= d * xhi;
+ r.a -= d * xlo;
+ r.a += r.b;
+
+ return (d + r.a / x);
}
/*
- * returns (z+c)^2 * P(z)/Q(z) + a0
+ * x < 0
+ *
+ * Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x)).
+ * At negative integers, return NaN and raise invalid.
*/
-static struct Double
-ratfun_gam(z, c)
- double z, c;
-{
- double p, q;
- struct Double r, t;
-
- q = Q0 +z*(Q1+z*(Q2+z*(Q3+z*(Q4+z*(Q5+z*(Q6+z*(Q7+z*Q8)))))));
- p = P0 + z*(P1 + z*(P2 + z*(P3 + z*P4)));
-
- /* return r.a + r.b = a0 + (z+c)^2*p/q, with r.a truncated to 26 bits. */
- p = p/q;
- t.a = z, TRUNC(t.a); /* t ~= z + c */
- t.b = (z - t.a) + c;
- t.b *= (t.a + z);
- q = (t.a *= t.a); /* t = (z+c)^2 */
- TRUNC(t.a);
- t.b += (q - t.a);
- r.a = p, TRUNC(r.a); /* r = P/Q */
- r.b = p - r.a;
- t.b = t.b*p + t.a*r.b + a0_lo;
- t.a *= r.a; /* t = (z+c)^2*(P/Q) */
- r.a = t.a + a0_hi, TRUNC(r.a);
- r.b = ((a0_hi-r.a) + t.a) + t.b;
- return (r); /* r = a0 + t */
-}
-
static double
-neg_gam(x)
- double x;
+neg_gam(double x)
{
int sgn = 1;
struct Double lg, lsine;
@@ -280,23 +312,29 @@
y = ceil(x);
if (y == x) /* Negative integer. */
return ((x - x) / zero);
+
z = y - x;
if (z > 0.5)
- z = one - z;
- y = 0.5 * y;
+ z = 1 - z;
+
+ y = y / 2;
if (y == ceil(y))
sgn = -1;
- if (z < .25)
- z = sin(M_PI*z);
+
+ if (z < 0.25)
+ z = sinpi(z);
else
- z = cos(M_PI*(0.5-z));
+ z = cospi(0.5 - z);
+
/* Special case: G(1-x) = Inf; G(x) may be nonzero. */
if (x < -170) {
+
if (x < -190)
- return ((double)sgn*tiny*tiny);
- y = one - x; /* exact: 128 < |x| < 255 */
+ return (sgn * tiny * tiny);
+
+ y = 1 - x; /* exact: 128 < |x| < 255 */
lg = large_gam(y);
- lsine = __log__D(M_PI/z); /* = TRUNC(log(u)) + small */
+ lsine = __log__D(M_PI / z); /* = TRUNC(log(u)) + small */
lg.a -= lsine.a; /* exact (opposite signs) */
lg.b -= lsine.b;
y = -(lg.a + lg.b);
@@ -305,11 +343,58 @@
if (sgn < 0) y = -y;
return (y);
}
- y = one-x;
- if (one-y == x)
+
+ y = 1 - x;
+ if (1 - y == x)
y = tgamma(y);
else /* 1-x is inexact */
- y = -x*tgamma(-x);
+ y = - x * tgamma(-x);
+
if (sgn < 0) y = -y;
- return (M_PI / (y*z));
+ return (M_PI / (y * z));
}
+/*
+ * xmax comes from lgamma(xmax) - emax * log(2) = 0.
+ * static const float xmax = 35.040095f
+ * static const double xmax = 171.624376956302725;
+ * ld80: LD80C(0xdb718c066b352e20, 10, 1.75554834290446291689e+03L),
+ * ld128: 1.75554834290446291700388921607020320e+03L,
+ *
+ * iota is a sloppy threshold to isolate x = 0.
+ */
+static const double xmax = 171.624376956302725;
+static const double iota = 0x1p-56;
+
+double
+tgamma(double x)
+{
+ struct Double u;
+
+ if (x >= 6) {
+ if (x > xmax)
+ return (x / zero);
+ u = large_gam(x);
+ return (__exp__D(u.a, u.b));
+ }
+
+ if (x >= 1 + left + x0)
+ return (small_gam(x));
+
+ if (x > iota)
+ return (smaller_gam(x));
+
+ if (x > -iota) {
+ if (x != 0.)
+ u.a = 1 - tiny; /* raise inexact */
+ return (1 / x);
+ }
+
+ if (!isfinite(x))
+ return (x - x); /* x is NaN or -Inf */
+
+ return (neg_gam(x));
+}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(tgamma, tgammal);
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c b/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
index fe57773..422357b 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
+++ b/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
@@ -21,8 +21,8 @@
#include "math_private.h"
/*
- * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
- * |cos(x) - c(x))| < 2**-122.0
+ * Domain [-0.7854, 0.7854], range ~[-1.17e-39, 1.19e-39]:
+ * |cos(x) - c(x))| < 2**-129.3
*
* 113-bit precision requires more care than 64-bit precision, since
* simple methods give a minimax polynomial with coefficient for x^2
@@ -31,21 +31,19 @@
*/
static const double
one = 1.0;
-
static const long double
-C1 = 0.04166666666666666666666666666666658424671L,
-C2 = -0.001388888888888888888888888888863490893732L,
-C3 = 0.00002480158730158730158730158600795304914210L,
-C4 = -0.2755731922398589065255474947078934284324e-6L,
-C5 = 0.2087675698786809897659225313136400793948e-8L,
-C6 = -0.1147074559772972315817149986812031204775e-10L,
-C7 = 0.4779477332386808976875457937252120293400e-13L;
-
-static const double
-C8 = -0.1561920696721507929516718307820958119868e-15,
-C9 = 0.4110317413744594971475941557607804508039e-18,
-C10 = -0.8896592467191938803288521958313920156409e-21,
-C11 = 0.1601061435794535138244346256065192782581e-23;
+C1 = 4.16666666666666666666666666666666667e-02L,
+C2 = -1.38888888888888888888888888888888834e-03L,
+C3 = 2.48015873015873015873015873015446795e-05L,
+C4 = -2.75573192239858906525573190949988493e-07L,
+C5 = 2.08767569878680989792098886701451072e-09L,
+C6 = -1.14707455977297247136657111139971865e-11L,
+C7 = 4.77947733238738518870113294139830239e-14L,
+C8 = -1.56192069685858079920640872925306403e-16L,
+C9 = 4.11031762320473354032038893429515732e-19L,
+C10= -8.89679121027589608738005163931958096e-22L,
+C11= 1.61171797801314301767074036661901531e-24L,
+C12= -2.46748624357670948912574279501044295e-27L;
long double
__kernel_cosl(long double x, long double y)
@@ -54,7 +52,7 @@
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
- z*(C8+z*(C9+z*(C10+z*C11))))))))));
+ z*(C8+z*(C9+z*(C10+z*(C11+z*C12)))))))))));
hz = 0.5*z;
w = one-hz;
return w + (((one-w)-hz) + (z*r-x*y));
diff --git a/libm/upstream-freebsd/lib/msun/ld128/s_logl.c b/libm/upstream-freebsd/lib/msun/ld128/s_logl.c
index 93a2a7c..4774a27 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/s_logl.c
+++ b/libm/upstream-freebsd/lib/msun/ld128/s_logl.c
@@ -697,14 +697,15 @@
invln2_hi = 1.4426950402557850e0; /* 0x17154765000000.0p-52 */
static const long double
invln10_lo = 1.41498268538580090791605082294397000e-10L, /* 0x137287195355baaafad33dc323ee3.0p-145L */
-invln2_lo = 6.33178418956604368501892137426645911e-10L; /* 0x15c17f0bbbe87fed0691d3e88eb57.0p-143L */
+invln2_lo = 6.33178418956604368501892137426645911e-10L, /* 0x15c17f0bbbe87fed0691d3e88eb57.0p-143L */
+invln10_lo_plus_hi = invln10_lo + invln10_hi,
+invln2_lo_plus_hi = invln2_lo + invln2_hi;
long double
log10l(long double x)
{
struct ld r;
- long double lo;
- float hi;
+ long double hi, lo;
ENTERI();
DOPRINT_START(&x);
@@ -712,18 +713,17 @@
if (!r.lo_set)
RETURNPI(r.hi);
_2sumF(r.hi, r.lo);
- hi = r.hi;
+ hi = (float)r.hi;
lo = r.lo + (r.hi - hi);
RETURN2PI(invln10_hi * hi,
- (invln10_lo + invln10_hi) * lo + invln10_lo * hi);
+ invln10_lo_plus_hi * lo + invln10_lo * hi);
}
long double
log2l(long double x)
{
struct ld r;
- long double lo;
- float hi;
+ long double hi, lo;
ENTERI();
DOPRINT_START(&x);
@@ -731,10 +731,10 @@
if (!r.lo_set)
RETURNPI(r.hi);
_2sumF(r.hi, r.lo);
- hi = r.hi;
+ hi = (float)r.hi;
lo = r.lo + (r.hi - hi);
RETURN2PI(invln2_hi * hi,
- (invln2_lo + invln2_hi) * lo + invln2_lo * hi);
+ invln2_lo_plus_hi * lo + invln2_lo * hi);
}
#endif /* STRUCT_RETURN */
diff --git a/libm/upstream-freebsd/lib/msun/src/e_hypotl.c b/libm/upstream-freebsd/lib/msun/src/e_hypotl.c
index 9189b1f..fc43538 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_hypotl.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_hypotl.c
@@ -82,7 +82,7 @@
man_t manh, manl;
GET_LDBL_MAN(manh,manl,b);
if((manh|manl)==0) return a;
- t1=0;
+ t1=1;
SET_HIGH_WORD(t1,ESW(MAX_EXP-2)); /* t1=2^(MAX_EXP-2) */
b *= t1;
a *= t1;
diff --git a/libm/upstream-freebsd/lib/msun/src/e_powf.c b/libm/upstream-freebsd/lib/msun/src/e_powf.c
index 53f1d37..122da45 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_powf.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_powf.c
@@ -136,7 +136,7 @@
/* |y| is huge */
if(iy>0x4d000000) { /* if |y| > 2**27 */
/* over/underflow if x is not close to one */
- if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
+ if(ix<0x3f7ffff6) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
diff --git a/libm/upstream-freebsd/lib/msun/src/e_sqrt.c b/libm/upstream-freebsd/lib/msun/src/e_sqrt.c
index 12fb56e..37351a4 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_sqrt.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_sqrt.c
@@ -14,6 +14,18 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
+#include <float.h>
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef USE_BUILTIN_SQRT
+double
+__ieee754_sqrt(double x)
+{
+ return (__builtin_sqrt(x));
+}
+#else
/* __ieee754_sqrt(x)
* Return correctly rounded sqrt.
* ------------------------------------------
@@ -84,11 +96,6 @@
*---------------
*/
-#include <float.h>
-
-#include "math.h"
-#include "math_private.h"
-
static const double one = 1.0, tiny=1.0e-300;
double
@@ -187,6 +194,7 @@
INSERT_WORDS(z,ix0,ix1);
return z;
}
+#endif
#if (LDBL_MANT_DIG == 53)
__weak_reference(sqrt, sqrtl);
diff --git a/libm/upstream-freebsd/lib/msun/src/e_sqrtf.c b/libm/upstream-freebsd/lib/msun/src/e_sqrtf.c
index 7eba4d0..06e5d62 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_sqrtf.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_sqrtf.c
@@ -20,6 +20,13 @@
#include "math.h"
#include "math_private.h"
+#ifdef USE_BUILTIN_SQRTF
+float
+__ieee754_sqrtf(float x)
+{
+ return (__builtin_sqrtf(x));
+}
+#else
static const float one = 1.0, tiny=1.0e-30;
float
@@ -87,3 +94,4 @@
SET_FLOAT_WORD(z,ix);
return z;
}
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/k_cospi.h b/libm/upstream-freebsd/lib/msun/src/k_cospi.h
new file mode 100644
index 0000000..32985be
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/k_cospi.h
@@ -0,0 +1,44 @@
+/*-
+ * Copyright (c) 2017 Steven G. Kargl
+ * 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 unmodified, 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 ``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 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.
+ */
+
+/*
+ * The basic kernel for x in [0,0.25]. To use the kernel for cos(x), the
+ * argument to __kernel_cospi() must be multiplied by pi.
+ */
+
+static inline double
+__kernel_cospi(double x)
+{
+ double_t hi, lo;
+
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
+ hi *= pi_hi;
+ _2sumF(hi, lo);
+ return (__kernel_cos(hi, lo));
+}
+
diff --git a/libm/upstream-freebsd/lib/msun/src/k_sincosl.h b/libm/upstream-freebsd/lib/msun/src/k_sincosl.h
index 4d4dc69..6425f14 100644
--- a/libm/upstream-freebsd/lib/msun/src/k_sincosl.h
+++ b/libm/upstream-freebsd/lib/msun/src/k_sincosl.h
@@ -76,13 +76,6 @@
#elif LDBL_MANT_DIG == 113 /* ld128 version of k_sincosl.c. */
static const long double
-C1 = 0.04166666666666666666666666666666658424671L,
-C2 = -0.001388888888888888888888888888863490893732L,
-C3 = 0.00002480158730158730158730158600795304914210L,
-C4 = -0.2755731922398589065255474947078934284324e-6L,
-C5 = 0.2087675698786809897659225313136400793948e-8L,
-C6 = -0.1147074559772972315817149986812031204775e-10L,
-C7 = 0.4779477332386808976875457937252120293400e-13L,
S1 = -0.16666666666666666666666666666666666606732416116558L,
S2 = 0.0083333333333333333333333333333331135404851288270047L,
S3 = -0.00019841269841269841269841269839935785325638310428717L,
@@ -93,15 +86,25 @@
S8 = 0.28114572543451292625024967174638477283187397621303e-14L;
static const double
-C8 = -0.1561920696721507929516718307820958119868e-15,
-C9 = 0.4110317413744594971475941557607804508039e-18,
-C10 = -0.8896592467191938803288521958313920156409e-21,
-C11 = 0.1601061435794535138244346256065192782581e-23,
S9 = -0.82206352458348947812512122163446202498005154296863e-17,
S10 = 0.19572940011906109418080609928334380560135358385256e-19,
S11 = -0.38680813379701966970673724299207480965452616911420e-22,
S12 = 0.64038150078671872796678569586315881020659912139412e-25;
+static const long double
+C1 = 4.16666666666666666666666666666666667e-02L,
+C2 = -1.38888888888888888888888888888888834e-03L,
+C3 = 2.48015873015873015873015873015446795e-05L,
+C4 = -2.75573192239858906525573190949988493e-07L,
+C5 = 2.08767569878680989792098886701451072e-09L,
+C6 = -1.14707455977297247136657111139971865e-11L,
+C7 = 4.77947733238738518870113294139830239e-14L,
+C8 = -1.56192069685858079920640872925306403e-16L,
+C9 = 4.11031762320473354032038893429515732e-19L,
+C10= -8.89679121027589608738005163931958096e-22L,
+C11= 1.61171797801314301767074036661901531e-24L,
+C12= -2.46748624357670948912574279501044295e-27L;
+
static inline void
__kernel_sincosl(long double x, long double y, int iy, long double *sn,
long double *cs)
@@ -120,12 +123,12 @@
if (iy == 0)
*sn = x + v * (S1 + z * r);
else
- *cs = x - ((z * (y / 2 - v * r) - y) - v * S1);
+ *sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
hz = z / 2;
w = 1 - hz;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
- z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
+ z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * (C11+z*C12)))))))))));
*cs = w + (((1 - w) - hz) + (z * r - x * y));
}
diff --git a/libm/upstream-freebsd/lib/msun/src/k_sinpi.h b/libm/upstream-freebsd/lib/msun/src/k_sinpi.h
new file mode 100644
index 0000000..66152ba
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/k_sinpi.h
@@ -0,0 +1,43 @@
+/*-
+ * Copyright (c) 2017 Steven G. Kargl
+ * 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 unmodified, 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 ``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 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.
+ */
+
+/*
+ * The basic kernel for x in [0,0.25]. To use the kernel for sin(x), the
+ * argument to __kernel_sinpi() must be multiplied by pi.
+ */
+
+static inline double
+__kernel_sinpi(double x)
+{
+ double_t hi, lo;
+
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
+ hi *= pi_hi;
+ _2sumF(hi, lo);
+ return (__kernel_sin(hi, lo, 1));
+}
diff --git a/libm/upstream-freebsd/lib/msun/src/s_cexp.c b/libm/upstream-freebsd/lib/msun/src/s_cexp.c
index 2ef8ba1..a1f853e 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_cexp.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_cexp.c
@@ -30,6 +30,7 @@
__FBSDID("$FreeBSD$");
#include <complex.h>
+#include <float.h>
#include <math.h>
#include "math_private.h"
@@ -41,7 +42,7 @@
double complex
cexp(double complex z)
{
- double x, y, exp_x;
+ double c, exp_x, s, x, y;
uint32_t hx, hy, lx, ly;
x = creal(z);
@@ -55,8 +56,10 @@
return (CMPLX(exp(x), y));
EXTRACT_WORDS(hx, lx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
- if (((hx & 0x7fffffff) | lx) == 0)
- return (CMPLX(cos(y), sin(y)));
+ if (((hx & 0x7fffffff) | lx) == 0) {
+ sincos(y, &s, &c);
+ return (CMPLX(c, s));
+ }
if (hy >= 0x7ff00000) {
if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
@@ -86,6 +89,11 @@
* - x = NaN (spurious inexact exception from y)
*/
exp_x = exp(x);
- return (CMPLX(exp_x * cos(y), exp_x * sin(y)));
+ sincos(y, &s, &c);
+ return (CMPLX(exp_x * c, exp_x * s));
}
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(cexp, cexpl);
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/s_cexpf.c b/libm/upstream-freebsd/lib/msun/src/s_cexpf.c
index b815c99..d905b74 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_cexpf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_cexpf.c
@@ -41,7 +41,7 @@
float complex
cexpf(float complex z)
{
- float x, y, exp_x;
+ float c, exp_x, s, x, y;
uint32_t hx, hy;
x = crealf(z);
@@ -55,8 +55,10 @@
return (CMPLXF(expf(x), y));
GET_FLOAT_WORD(hx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
- if ((hx & 0x7fffffff) == 0)
- return (CMPLXF(cosf(y), sinf(y)));
+ if ((hx & 0x7fffffff) == 0) {
+ sincosf(y, &s, &c);
+ return (CMPLXF(c, s));
+ }
if (hy >= 0x7f800000) {
if ((hx & 0x7fffffff) != 0x7f800000) {
@@ -86,6 +88,7 @@
* - x = NaN (spurious inexact exception from y)
*/
exp_x = expf(x);
- return (CMPLXF(exp_x * cosf(y), exp_x * sinf(y)));
+ sincosf(y, &s, &c);
+ return (CMPLXF(exp_x * c, exp_x * s));
}
}
diff --git a/libm/upstream-freebsd/lib/msun/src/s_cosl.c b/libm/upstream-freebsd/lib/msun/src/s_cosl.c
index 46a2e86..3d06648 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_cosl.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_cosl.c
@@ -39,12 +39,17 @@
#include <ieeefp.h>
#endif
+#include "fpmath.h"
#include "math.h"
#include "math_private.h"
#if LDBL_MANT_DIG == 64
#include "../ld80/e_rem_pio2l.h"
+static const union IEEEl2bits
+pio4u = LD80C(0xc90fdaa22168c235, -00001, 7.85398163397448309628e-01L);
+#define pio4 (pio4u.e)
#elif LDBL_MANT_DIG == 113
#include "../ld128/e_rem_pio2l.h"
+long double pio4 = 7.85398163397448309615660845819875721e-1L;
#else
#error "Unsupported long double format"
#endif
@@ -71,7 +76,7 @@
ENTERI();
/* Optimize the case where x is already within range. */
- if (z.e < M_PI_4)
+ if (z.e < pio4)
RETURNI(__kernel_cosl(z.e, 0));
e0 = __ieee754_rem_pio2l(x, y);
diff --git a/libm/upstream-freebsd/lib/msun/src/s_cospi.c b/libm/upstream-freebsd/lib/msun/src/s_cospi.c
new file mode 100644
index 0000000..860219e
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/s_cospi.c
@@ -0,0 +1,152 @@
+/*-
+ * Copyright (c) 2017 Steven G. Kargl
+ * 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 unmodified, 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 ``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 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.
+ */
+
+/**
+ * cospi(x) computes cos(pi*x) without multiplication by pi (almost). First,
+ * note that cospi(-x) = cospi(x), so the algorithm considers only |x|. The
+ * method used depends on the magnitude of x.
+ *
+ * 1. For small |x|, cospi(x) = 1 with FE_INEXACT raised where a sloppy
+ * threshold is used. The threshold is |x| < 0x1pN with N = -(P/2+M).
+ * P is the precision of the floating-point type and M = 2 to 4.
+ *
+ * 2. For |x| < 1, argument reduction is not required and sinpi(x) is
+ * computed by calling a kernel that leverages the kernels for sin(x)
+ * ans cos(x). See k_sinpi.c and k_cospi.c for details.
+ *
+ * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
+ * |x| = j0 + r with j0 an integer and the remainder r satisfies
+ * 0 <= r < 1. With the given domain, a simplified inline floor(x)
+ * is used. Also, note the following identity
+ *
+ * cospi(x) = cos(pi*(j0+r))
+ * = cos(pi*j0) * cos(pi*r) - sin(pi*j0) * sin(pi*r)
+ * = cos(pi*j0) * cos(pi*r)
+ * = +-cospi(r)
+ *
+ * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1.
+ * cospi(r) is then computed via an appropriate kernel.
+ *
+ * 4. For |x| >= 0x1p(P-1), |x| is integral and cospi(x) = 1.
+ *
+ * 5. Special cases:
+ *
+ * cospi(+-0) = 1.
+ * cospi(n.5) = 0 for n an integer.
+ * cospi(+-inf) = nan. Raises the "invalid" floating-point exception.
+ * cospi(nan) = nan. Raises the "invalid" floating-point exception.
+ */
+
+#include <float.h>
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+#include "k_cospi.h"
+#include "k_sinpi.h"
+
+volatile static const double vzero = 0;
+
+double
+cospi(double x)
+{
+ double ax, c;
+ uint32_t hx, ix, j0, lx;
+
+ EXTRACT_WORDS(hx, lx, x);
+ ix = hx & 0x7fffffff;
+ INSERT_WORDS(ax, ix, lx);
+
+ if (ix < 0x3ff00000) { /* |x| < 1 */
+ if (ix < 0x3fd00000) { /* |x| < 0.25 */
+ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */
+ if ((int)ax == 0)
+ return (1);
+ }
+ return (__kernel_cospi(ax));
+ }
+
+ if (ix < 0x3fe00000) /* |x| < 0.5 */
+ c = __kernel_sinpi(0.5 - ax);
+ else if (ix < 0x3fe80000){ /* |x| < 0.75 */
+ if (ax == 0.5)
+ return (0);
+ c = -__kernel_sinpi(ax - 0.5);
+ } else
+ c = -__kernel_cospi(1 - ax);
+ return (c);
+ }
+
+ if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */
+ /* Determine integer part of ax. */
+ j0 = ((ix >> 20) & 0x7ff) - 0x3ff;
+ if (j0 < 20) {
+ ix &= ~(0x000fffff >> j0);
+ lx = 0;
+ } else {
+ lx &= ~((uint32_t)0xffffffff >> (j0 - 20));
+ }
+ INSERT_WORDS(x, ix, lx);
+
+ ax -= x;
+ EXTRACT_WORDS(ix, lx, ax);
+
+
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix < 0x3fd00000) /* |x| < 0.25 */
+ c = ix == 0 ? 1 : __kernel_cospi(ax);
+ else
+ c = __kernel_sinpi(0.5 - ax);
+ } else {
+ if (ix < 0x3fe80000) { /* |x| < 0.75 */
+ if (ax == 0.5)
+ return (0);
+ c = -__kernel_sinpi(ax - 0.5);
+ } else
+ c = -__kernel_cospi(1 - ax);
+ }
+
+ if (j0 > 30)
+ x -= 0x1p30;
+ j0 = (uint32_t)x;
+ return (j0 & 1 ? -c : c);
+ }
+
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p52 is always an even integer, so return 1.
+ */
+ return (1);
+}
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(cospi, cospil);
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/s_ctanh.c b/libm/upstream-freebsd/lib/msun/src/s_ctanh.c
index 88afeb5..e5840a1 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_ctanh.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_ctanh.c
@@ -111,11 +111,13 @@
}
/*
- * ctanh(x + I NaN) = d(NaN) + I d(NaN)
- * ctanh(x +- I Inf) = dNaN + I dNaN
+ * ctanh(+-0 + i NAN) = +-0 + i NaN
+ * ctanh(+-0 +- i Inf) = +-0 + i NaN
+ * ctanh(x + i NAN) = NaN + i NaN
+ * ctanh(x +- i Inf) = NaN + i NaN
*/
if (!isfinite(y))
- return (CMPLX(y - y, y - y));
+ return (CMPLX(x ? y - y : x, y - y));
/*
* ctanh(+-huge +- I y) ~= +-1 +- I 2sin(2y)/exp(2x), using the
diff --git a/libm/upstream-freebsd/lib/msun/src/s_ctanhf.c b/libm/upstream-freebsd/lib/msun/src/s_ctanhf.c
index d2bd0b6..c46f86d 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_ctanhf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_ctanhf.c
@@ -61,7 +61,7 @@
}
if (!isfinite(y))
- return (CMPLXF(y - y, y - y));
+ return (CMPLXF(ix ? y - y : x, y - y));
if (ix >= 0x41300000) { /* |x| >= 11 */
float exp_mx = expf(-fabsf(x));
diff --git a/libm/upstream-freebsd/lib/msun/src/s_fma.c b/libm/upstream-freebsd/lib/msun/src/s_fma.c
index 41a6424..95cffd0 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_fma.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_fma.c
@@ -35,6 +35,13 @@
#include "math_private.h"
+#ifdef USE_BUILTIN_FMA
+double
+fma(double x, double y, double z)
+{
+ return (__builtin_fma(x, y, z));
+}
+#else
/*
* A struct dd represents a floating-point number with twice the precision
* of a double. We maintain the invariant that "hi" stores the 53 high-order
@@ -284,6 +291,7 @@
else
return (add_and_denormalize(r.hi, adj, spread));
}
+#endif /* !USE_BUILTIN_FMA */
#if (LDBL_MANT_DIG == 53)
__weak_reference(fma, fmal);
diff --git a/libm/upstream-freebsd/lib/msun/src/s_fmaf.c b/libm/upstream-freebsd/lib/msun/src/s_fmaf.c
index 389cf1b..4591cc2 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_fmaf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_fmaf.c
@@ -34,6 +34,13 @@
#include "math.h"
#include "math_private.h"
+#ifdef USE_BUILTIN_FMAF
+float
+fmaf(float x, float y, float z)
+{
+ return (__builtin_fmaf(x, y, z));
+}
+#else
/*
* Fused multiply-add: Compute x * y + z with a single rounding error.
*
@@ -69,3 +76,4 @@
SET_LOW_WORD(adjusted_result, lr + 1);
return (adjusted_result);
}
+#endif /* !USE_BUILTIN_FMAF */
diff --git a/libm/upstream-freebsd/lib/msun/src/s_fmax.c b/libm/upstream-freebsd/lib/msun/src/s_fmax.c
index 0c234bc..b53b1e6 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_fmax.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_fmax.c
@@ -34,6 +34,13 @@
#include "fpmath.h"
+#ifdef USE_BUILTIN_FMAX
+double
+fmax(double x, double y)
+{
+ return (__builtin_fmax(x, y));
+}
+#else
double
fmax(double x, double y)
{
@@ -54,6 +61,7 @@
return (x > y ? x : y);
}
+#endif
#if (LDBL_MANT_DIG == 53)
__weak_reference(fmax, fmaxl);
diff --git a/libm/upstream-freebsd/lib/msun/src/s_fmaxf.c b/libm/upstream-freebsd/lib/msun/src/s_fmaxf.c
index 8e9d1ba..8d3d14f 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_fmaxf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_fmaxf.c
@@ -33,6 +33,13 @@
#include "fpmath.h"
+#ifdef USE_BUILTIN_FMAXF
+float
+fmaxf(float x, float y)
+{
+ return (__builtin_fmaxf(x, y));
+}
+#else
float
fmaxf(float x, float y)
{
@@ -53,3 +60,4 @@
return (x > y ? x : y);
}
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/s_fmin.c b/libm/upstream-freebsd/lib/msun/src/s_fmin.c
index d7f24c1..53f36c1 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_fmin.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_fmin.c
@@ -34,6 +34,13 @@
#include "fpmath.h"
+#ifdef USE_BUILTIN_FMIN
+double
+fmin(double x, double y)
+{
+ return (__builtin_fmin(x, y));
+}
+#else
double
fmin(double x, double y)
{
@@ -54,6 +61,7 @@
return (x < y ? x : y);
}
+#endif
#if (LDBL_MANT_DIG == 53)
__weak_reference(fmin, fminl);
diff --git a/libm/upstream-freebsd/lib/msun/src/s_fminf.c b/libm/upstream-freebsd/lib/msun/src/s_fminf.c
index 2583167..58b6a48 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_fminf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_fminf.c
@@ -33,6 +33,13 @@
#include "fpmath.h"
+#ifdef USE_BUILTIN_FMINF
+float
+fminf(float x, float y)
+{
+ return (__builtin_fminf(x, y));
+}
+#else
float
fminf(float x, float y)
{
@@ -53,3 +60,4 @@
return (x < y ? x : y);
}
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/s_lround.c b/libm/upstream-freebsd/lib/msun/src/s_lround.c
index 66d9183..1dd8e69 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_lround.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_lround.c
@@ -49,9 +49,11 @@
* that everything is in range. At compile time, INRANGE(x) should reduce to
* two floating-point comparisons in the former case, or TRUE otherwise.
*/
+static const type type_min = (type)DTYPE_MIN;
+static const type type_max = (type)DTYPE_MAX;
static const type dtype_min = (type)DTYPE_MIN - 0.5;
static const type dtype_max = (type)DTYPE_MAX + 0.5;
-#define INRANGE(x) (dtype_max - (type)DTYPE_MAX != 0.5 || \
+#define INRANGE(x) (dtype_max - type_max != 0.5 || \
((x) > dtype_min && (x) < dtype_max))
dtype
diff --git a/libm/upstream-freebsd/lib/msun/src/s_scalbn.c b/libm/upstream-freebsd/lib/msun/src/s_scalbn.c
index b048b05..2d4f7a3 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_scalbn.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_scalbn.c
@@ -1,66 +1,47 @@
-/* @(#)s_scalbn.c 5.1 93/09/24 */
/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2005-2020 Rich Felker, et al.
*
- * 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.
- * ====================================================
+ * SPDX-License-Identifier: MIT
+ *
+ * Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
+ * for all contributors to musl.
*/
-
-#include <sys/cdefs.h>
-__FBSDID("$FreeBSD$");
-
-/*
- * scalbn (double x, int n)
- * scalbn(x,n) returns x* 2**n computed by exponent
- * manipulation rather than by actually performing an
- * exponentiation or a multiplication.
- */
-
#include <float.h>
+#include <math.h>
+#include <stdint.h>
-#include "math.h"
-#include "math_private.h"
-
-static const double
-two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
-twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
-huge = 1.0e+300,
-tiny = 1.0e-300;
-
-double
-scalbn (double x, int n)
+double scalbn(double x, int n)
{
- int32_t k,hx,lx;
- EXTRACT_WORDS(hx,lx,x);
- k = (hx&0x7ff00000)>>20; /* extract exponent */
- if (k==0) { /* 0 or subnormal x */
- if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
- x *= two54;
- GET_HIGH_WORD(hx,x);
- k = ((hx&0x7ff00000)>>20) - 54;
- if (n< -50000) return tiny*x; /*underflow*/
- }
- if (k==0x7ff) return x+x; /* NaN or Inf */
- k = k+n;
- if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
- if (k > 0) /* normal result */
- {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
- if (k <= -54) {
- if (n > 50000) /* in case integer overflow in n+k */
- return huge*copysign(huge,x); /*overflow*/
- else
- return tiny*copysign(tiny,x); /*underflow*/
+ union {double f; uint64_t i;} u;
+ double_t y = x;
+
+ if (n > 1023) {
+ y *= 0x1p1023;
+ n -= 1023;
+ if (n > 1023) {
+ y *= 0x1p1023;
+ n -= 1023;
+ if (n > 1023)
+ n = 1023;
+ }
+ } else if (n < -1022) {
+ /* make sure final n < -53 to avoid double
+ rounding in the subnormal range */
+ y *= 0x1p-1022 * 0x1p53;
+ n += 1022 - 53;
+ if (n < -1022) {
+ y *= 0x1p-1022 * 0x1p53;
+ n += 1022 - 53;
+ if (n < -1022)
+ n = -1022;
+ }
}
- k += 54; /* subnormal result */
- SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
- return x*twom54;
+ u.i = (uint64_t)(0x3ff+n)<<52;
+ x = y * u.f;
+ return x;
}
-#if (LDBL_MANT_DIG == 53)
+#if (LDBL_MANT_DIG == 53) && !defined(scalbn)
__weak_reference(scalbn, ldexpl);
__weak_reference(scalbn, scalbnl);
#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/s_scalbnf.c b/libm/upstream-freebsd/lib/msun/src/s_scalbnf.c
index 21d001c..8cf1e01 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_scalbnf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_scalbnf.c
@@ -1,57 +1,41 @@
-/* s_scalbnf.c -- float version of s_scalbn.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2005-2020 Rich Felker, et al.
*
- * 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.
- * ====================================================
+ * SPDX-License-Identifier: MIT
+ *
+ * Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
+ * for all contributors to musl.
*/
+#include <math.h>
+#include <stdint.h>
-#include <sys/cdefs.h>
-__FBSDID("$FreeBSD$");
-
-#include "math.h"
-#include "math_private.h"
-
-static const float
-two25 = 3.355443200e+07, /* 0x4c000000 */
-twom25 = 2.9802322388e-08, /* 0x33000000 */
-huge = 1.0e+30,
-tiny = 1.0e-30;
-
-float
-scalbnf (float x, int n)
+float scalbnf(float x, int n)
{
- int32_t k,ix;
- GET_FLOAT_WORD(ix,x);
- k = (ix&0x7f800000)>>23; /* extract exponent */
- if (k==0) { /* 0 or subnormal x */
- if ((ix&0x7fffffff)==0) return x; /* +-0 */
- x *= two25;
- GET_FLOAT_WORD(ix,x);
- k = ((ix&0x7f800000)>>23) - 25;
- if (n< -50000) return tiny*x; /*underflow*/
- }
- if (k==0xff) return x+x; /* NaN or Inf */
- k = k+n;
- if (k > 0xfe) return huge*copysignf(huge,x); /* overflow */
- if (k > 0) /* normal result */
- {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;}
- if (k <= -25) {
- if (n > 50000) /* in case integer overflow in n+k */
- return huge*copysignf(huge,x); /*overflow*/
- else
- return tiny*copysignf(tiny,x); /*underflow*/
+ union {float f; uint32_t i;} u;
+ float_t y = x;
+
+ if (n > 127) {
+ y *= 0x1p127f;
+ n -= 127;
+ if (n > 127) {
+ y *= 0x1p127f;
+ n -= 127;
+ if (n > 127)
+ n = 127;
+ }
+ } else if (n < -126) {
+ y *= 0x1p-126f * 0x1p24f;
+ n += 126 - 24;
+ if (n < -126) {
+ y *= 0x1p-126f * 0x1p24f;
+ n += 126 - 24;
+ if (n < -126)
+ n = -126;
+ }
}
- k += 25; /* subnormal result */
- SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
- return x*twom25;
+ u.i = (uint32_t)(0x7f+n)<<23;
+ x = y * u.f;
+ return x;
}
__strong_reference(scalbnf, ldexpf);
diff --git a/libm/upstream-freebsd/lib/msun/src/s_scalbnl.c b/libm/upstream-freebsd/lib/msun/src/s_scalbnl.c
index 28b0cf9..6044c1b 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_scalbnl.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_scalbnl.c
@@ -1,71 +1,49 @@
-/* @(#)s_scalbn.c 5.1 93/09/24 */
/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2005-2020 Rich Felker, et al.
*
- * 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.
- * ====================================================
+ * SPDX-License-Identifier: MIT
+ *
+ * Please see https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
+ * for all contributors to musl.
*/
-
-#include <sys/cdefs.h>
-__FBSDID("$FreeBSD$");
-
+#include <math.h>
+#include <float.h>
+#include "math_private.h"
+#include "fpmath.h"
/*
* scalbnl (long double x, int n)
* scalbnl(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
-
-/*
- * We assume that a long double has a 15-bit exponent. On systems
- * where long double is the same as double, scalbnl() is an alias
- * for scalbn(), so we don't use this routine.
- */
-
-#include <float.h>
-#include <math.h>
-
-#include "fpmath.h"
-
-#if LDBL_MAX_EXP != 0x4000
-#error "Unsupported long double format"
-#endif
-
-static const long double
-huge = 0x1p16000L,
-tiny = 0x1p-16000L;
-
-long double
-scalbnl (long double x, int n)
+#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+long double scalbnl(long double x, int n)
{
union IEEEl2bits u;
- int k;
- u.e = x;
- k = u.bits.exp; /* extract exponent */
- if (k==0) { /* 0 or subnormal x */
- if ((u.bits.manh|u.bits.manl)==0) return x; /* +-0 */
- u.e *= 0x1p+128;
- k = u.bits.exp - 128;
- if (n< -50000) return tiny*x; /*underflow*/
- }
- if (k==0x7fff) return x+x; /* NaN or Inf */
- k = k+n;
- if (k >= 0x7fff) return huge*copysignl(huge,x); /* overflow */
- if (k > 0) /* normal result */
- {u.bits.exp = k; return u.e;}
- if (k <= -128) {
- if (n > 50000) /* in case integer overflow in n+k */
- return huge*copysign(huge,x); /*overflow*/
- else
- return tiny*copysign(tiny,x); /*underflow*/
- }
- k += 128; /* subnormal result */
- u.bits.exp = k;
- return u.e*0x1p-128;
-}
+ if (n > 16383) {
+ x *= 0x1p16383L;
+ n -= 16383;
+ if (n > 16383) {
+ x *= 0x1p16383L;
+ n -= 16383;
+ if (n > 16383)
+ n = 16383;
+ }
+ } else if (n < -16382) {
+ x *= 0x1p-16382L * 0x1p113L;
+ n += 16382 - 113;
+ if (n < -16382) {
+ x *= 0x1p-16382L * 0x1p113L;
+ n += 16382 - 113;
+ if (n < -16382)
+ n = -16382;
+ }
+ }
+ u.e = 1.0;
+ u.xbits.expsign = 0x3fff + n;
+ return x * u.e;
+}
__strong_reference(scalbnl, ldexpl);
+#endif
+
diff --git a/libm/upstream-freebsd/lib/msun/src/s_sincosl.c b/libm/upstream-freebsd/lib/msun/src/s_sincosl.c
index aef36c2..3dd3457 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_sincosl.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_sincosl.c
@@ -50,11 +50,10 @@
sincosl(long double x, long double *sn, long double *cs)
{
union IEEEl2bits z;
- int e0, sgn;
+ int e0;
long double y[2];
z.e = x;
- sgn = z.bits.sign;
z.bits.sign = 0;
ENTERV();
diff --git a/libm/upstream-freebsd/lib/msun/src/s_sinpi.c b/libm/upstream-freebsd/lib/msun/src/s_sinpi.c
new file mode 100644
index 0000000..858459a
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/s_sinpi.c
@@ -0,0 +1,169 @@
+/*-
+ * Copyright (c) 2017 Steven G. Kargl
+ * 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 unmodified, 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 ``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 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.
+ */
+
+/**
+ * sinpi(x) computes sin(pi*x) without multiplication by pi (almost). First,
+ * note that sinpi(-x) = -sinpi(x), so the algorithm considers only |x| and
+ * includes reflection symmetry by considering the sign of x on output. The
+ * method used depends on the magnitude of x.
+ *
+ * 1. For small |x|, sinpi(x) = pi * x where a sloppy threshold is used. The
+ * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the
+ * floating-point type and M = 2 to 4. To achieve high accuracy, pi is
+ * decomposed into high and low parts with the high part containing a
+ * number of trailing zero bits. x is also split into high and low parts.
+ *
+ * 2. For |x| < 1, argument reduction is not required and sinpi(x) is
+ * computed by calling a kernel that leverages the kernels for sin(x)
+ * ans cos(x). See k_sinpi.c and k_cospi.c for details.
+ *
+ * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
+ * |x| = j0 + r with j0 an integer and the remainder r satisfies
+ * 0 <= r < 1. With the given domain, a simplified inline floor(x)
+ * is used. Also, note the following identity
+ *
+ * sinpi(x) = sin(pi*(j0+r))
+ * = sin(pi*j0) * cos(pi*r) + cos(pi*j0) * sin(pi*r)
+ * = cos(pi*j0) * sin(pi*r)
+ * = +-sinpi(r)
+ *
+ * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1.
+ * sinpi(r) is then computed via an appropriate kernel.
+ *
+ * 4. For |x| >= 0x1p(P-1), |x| is integral and sinpi(x) = copysign(0,x).
+ *
+ * 5. Special cases:
+ *
+ * sinpi(+-0) = +-0
+ * sinpi(+-n) = +-0, for positive integers n.
+ * sinpi(+-inf) = nan. Raises the "invalid" floating-point exception.
+ * sinpi(nan) = nan. Raises the "invalid" floating-point exception.
+ */
+
+#include <float.h>
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+#include "k_cospi.h"
+#include "k_sinpi.h"
+
+volatile static const double vzero = 0;
+
+double
+sinpi(double x)
+{
+ double ax, hi, lo, s;
+ uint32_t hx, ix, j0, lx;
+
+ EXTRACT_WORDS(hx, lx, x);
+ ix = hx & 0x7fffffff;
+ INSERT_WORDS(ax, ix, lx);
+
+ if (ix < 0x3ff00000) { /* |x| < 1 */
+ if (ix < 0x3fd00000) { /* |x| < 0.25 */
+ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */
+ if (x == 0)
+ return (x);
+ /*
+ * To avoid issues with subnormal values,
+ * scale the computation and rescale on
+ * return.
+ */
+ INSERT_WORDS(hi, hx, 0);
+ hi *= 0x1p53;
+ lo = x * 0x1p53 - hi;
+ s = (pi_lo + pi_hi) * lo + pi_lo * hi +
+ pi_hi * hi;
+ return (s * 0x1p-53);
+ }
+
+ s = __kernel_sinpi(ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x3fe00000) /* |x| < 0.5 */
+ s = __kernel_cospi(0.5 - ax);
+ else if (ix < 0x3fe80000) /* |x| < 0.75 */
+ s = __kernel_cospi(ax - 0.5);
+ else
+ s = __kernel_sinpi(1 - ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */
+ /* Determine integer part of ax. */
+ j0 = ((ix >> 20) & 0x7ff) - 0x3ff;
+ if (j0 < 20) {
+ ix &= ~(0x000fffff >> j0);
+ lx = 0;
+ } else {
+ lx &= ~((uint32_t)0xffffffff >> (j0 - 20));
+ }
+ INSERT_WORDS(x, ix, lx);
+
+ ax -= x;
+ EXTRACT_WORDS(ix, lx, ax);
+
+ if (ix == 0)
+ s = 0;
+ else {
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix < 0x3fd00000) /* |x| < 0.25 */
+ s = __kernel_sinpi(ax);
+ else
+ s = __kernel_cospi(0.5 - ax);
+ } else {
+ if (ix < 0x3fe80000) /* |x| < 0.75 */
+ s = __kernel_cospi(ax - 0.5);
+ else
+ s = __kernel_sinpi(1 - ax);
+ }
+
+ if (j0 > 30)
+ x -= 0x1p30;
+ j0 = (uint32_t)x;
+ if (j0 & 1) s = -s;
+ }
+
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p52 is always an integer, so return +-0.
+ */
+ return (copysign(0, x));
+}
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(sinpi, sinpil);
+#endif
