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GNU C Library master sources branch master updated. glibc-2.21-540-ga8e2112
- From: jsm28 at sourceware dot org
- To: glibc-cvs at sourceware dot org
- Date: 25 Jun 2015 21:46:56 -0000
- Subject: GNU C Library master sources branch master updated. glibc-2.21-540-ga8e2112
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http://sourceware.org/git/gitweb.cgi?p=glibc.git;a=commitdiff;h=a8e2112ae3e57fae592d84af2936a61d6239a248
commit a8e2112ae3e57fae592d84af2936a61d6239a248
Author: Joseph Myers <joseph@codesourcery.com>
Date: Thu Jun 25 21:46:02 2015 +0000
Use round-to-nearest internally in jn, test with ALL_RM_TEST (bug 18602).
Some existing jn tests, if run in non-default rounding modes, produce
errors above those accepted in glibc, which causes problems for moving
tests of jn to use ALL_RM_TEST. This patch makes jn set rounding
to-nearest internally, as was done for yn some time ago, then computes
the appropriate underflowing value for results that underflowed to
zero in to-nearest, and moves the tests to ALL_RM_TEST. It does
nothing about the general inaccuracy of Bessel function
implementations in glibc, though it should make jn more accurate on
average in non-default rounding modes through reduced error
accumulation. The recomputation of results that underflowed to zero
should as a side-effect fix some cases of bug 16559, where jn just
used an exact zero, but that is *not* the goal of this patch and other
cases of that bug remain unfixed.
(Most of the changes in the patch are reindentation to add new scopes
for SET_RESTORE_ROUND*.)
Tested for x86_64, x86, powerpc and mips64.
[BZ #16559]
[BZ #18602]
* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Set
round-to-nearest internally then recompute results that
underflowed to zero in the original rounding mode.
* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
* sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
* sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise
* math/libm-test.inc (jn_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
diff --git a/ChangeLog b/ChangeLog
index be0be0f..b61ea3c 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,18 @@
+2015-06-25 Joseph Myers <joseph@codesourcery.com>
+
+ [BZ #16559]
+ [BZ #18602]
+ * sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Set
+ round-to-nearest internally then recompute results that
+ underflowed to zero in the original rounding mode.
+ * sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
+ * sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise
+ * math/libm-test.inc (jn_test): Use ALL_RM_TEST.
+ * sysdeps/i386/fpu/libm-test-ulps: Update.
+ * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
2015-06-25 Andrew Senkevich <andrew.senkevich@intel.com>
* NEWS: Fixed description of link with vector math library.
diff --git a/NEWS b/NEWS
index c9be0e4..24f8c27 100644
--- a/NEWS
+++ b/NEWS
@@ -25,7 +25,7 @@ Version 2.22
18498, 18507, 18512, 18513, 18519, 18520, 18522, 18527, 18528, 18529,
18530, 18532, 18533, 18534, 18536, 18539, 18540, 18542, 18544, 18545,
18546, 18547, 18549, 18553, 18558, 18569, 18583, 18585, 18586, 18593,
- 18594.
+ 18594, 18602.
* Cache information can be queried via sysconf() function on s390 e.g. with
_SC_LEVEL1_ICACHE_SIZE as argument.
diff --git a/math/libm-test.inc b/math/libm-test.inc
index da8f8ca..9e402ab 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -7486,9 +7486,7 @@ static const struct test_if_f_data jn_test_data[] =
static void
jn_test (void)
{
- START (jn,, 0);
- RUN_TEST_LOOP_if_f (jn, jn_test_data, );
- END;
+ ALL_RM_TEST (jn, 0, jn_test_data, RUN_TEST_LOOP_if_f, END);
}
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index c9b565f..5a2af00 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1613,6 +1613,30 @@ ifloat: 3
ildouble: 4
ldouble: 4
+Function: "jn_downward":
+double: 2
+float: 3
+idouble: 2
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+Function: "jn_towardzero":
+double: 2
+float: 3
+idouble: 2
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: "jn_upward":
+double: 2
+float: 3
+idouble: 2
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
Function: "lgamma":
double: 1
float: 1
diff --git a/sysdeps/ieee754/dbl-64/e_jn.c b/sysdeps/ieee754/dbl-64/e_jn.c
index 900737c..b0ddd5e 100644
--- a/sysdeps/ieee754/dbl-64/e_jn.c
+++ b/sysdeps/ieee754/dbl-64/e_jn.c
@@ -52,7 +52,7 @@ double
__ieee754_jn (int n, double x)
{
int32_t i, hx, ix, lx, sgn;
- double a, b, temp, di;
+ double a, b, temp, di, ret;
double z, w;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
@@ -75,14 +75,16 @@ __ieee754_jn (int n, double x)
return (__ieee754_j1 (x));
sgn = (n & 1) & (hx >> 31); /* even n -- 0, odd n -- sign(x) */
x = fabs (x);
- if (__glibc_unlikely ((ix | lx) == 0 || ix >= 0x7ff00000))
- /* if x is 0 or inf */
- b = zero;
- else if ((double) n <= x)
- {
- /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
- if (ix >= 0x52D00000) /* x > 2**302 */
- { /* (x >> n**2)
+ {
+ SET_RESTORE_ROUND (FE_TONEAREST);
+ if (__glibc_unlikely ((ix | lx) == 0 || ix >= 0x7ff00000))
+ /* if x is 0 or inf */
+ return sgn == 1 ? -zero : zero;
+ else if ((double) n <= x)
+ {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if (ix >= 0x52D00000) /* x > 2**302 */
+ { /* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
@@ -95,152 +97,156 @@ __ieee754_jn (int n, double x)
* 2 -s+c -c-s
* 3 s+c c-s
*/
- double s;
- double c;
- __sincos (x, &s, &c);
- switch (n & 3)
- {
- case 0: temp = c + s; break;
- case 1: temp = -c + s; break;
- case 2: temp = -c - s; break;
- case 3: temp = c - s; break;
- }
- b = invsqrtpi * temp / __ieee754_sqrt (x);
- }
- else
- {
- a = __ieee754_j0 (x);
- b = __ieee754_j1 (x);
- for (i = 1; i < n; i++)
- {
- temp = b;
- b = b * ((double) (i + i) / x) - a; /* avoid underflow */
- a = temp;
- }
- }
- }
- else
- {
- if (ix < 0x3e100000) /* x < 2**-29 */
- { /* x is tiny, return the first Taylor expansion of J(n,x)
+ double s;
+ double c;
+ __sincos (x, &s, &c);
+ switch (n & 3)
+ {
+ case 0: temp = c + s; break;
+ case 1: temp = -c + s; break;
+ case 2: temp = -c - s; break;
+ case 3: temp = c - s; break;
+ }
+ b = invsqrtpi * temp / __ieee754_sqrt (x);
+ }
+ else
+ {
+ a = __ieee754_j0 (x);
+ b = __ieee754_j1 (x);
+ for (i = 1; i < n; i++)
+ {
+ temp = b;
+ b = b * ((double) (i + i) / x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ }
+ else
+ {
+ if (ix < 0x3e100000) /* x < 2**-29 */
+ { /* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
- if (n > 33) /* underflow */
- b = zero;
- else
- {
- temp = x * 0.5; b = temp;
- for (a = one, i = 2; i <= n; i++)
- {
- a *= (double) i; /* a = n! */
- b *= temp; /* b = (x/2)^n */
- }
- b = b / a;
- }
- }
- else
- {
- /* use backward recurrence */
- /* x x^2 x^2
- * J(n,x)/J(n-1,x) = ---- ------ ------ .....
- * 2n - 2(n+1) - 2(n+2)
- *
- * 1 1 1
- * (for large x) = ---- ------ ------ .....
- * 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
- * x x x
- *
- * Let w = 2n/x and h=2/x, then the above quotient
- * is equal to the continued fraction:
- * 1
- * = -----------------------
- * 1
- * w - -----------------
- * 1
- * w+h - ---------
- * w+2h - ...
- *
- * To determine how many terms needed, let
- * Q(0) = w, Q(1) = w(w+h) - 1,
- * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
- */
- /* determine k */
- double t, v;
- double q0, q1, h, tmp; int32_t k, m;
- w = (n + n) / (double) x; h = 2.0 / (double) x;
- q0 = w; z = w + h; q1 = w * z - 1.0; k = 1;
- while (q1 < 1.0e9)
- {
- k += 1; z += h;
- tmp = z * q1 - q0;
- q0 = q1;
- q1 = tmp;
- }
- m = n + n;
- for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
- t = one / (i / x - t);
- a = t;
- b = one;
- /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
- * Hence, if n*(log(2n/x)) > ...
- * single 8.8722839355e+01
- * double 7.09782712893383973096e+02
- * long double 1.1356523406294143949491931077970765006170e+04
- * then recurrent value may overflow and the result is
- * likely underflow to zero
- */
- tmp = n;
- v = two / x;
- tmp = tmp * __ieee754_log (fabs (v * tmp));
- if (tmp < 7.09782712893383973096e+02)
- {
- for (i = n - 1, di = (double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- }
- }
- else
- {
- for (i = n - 1, di = (double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- /* scale b to avoid spurious overflow */
- if (b > 1e100)
- {
- a /= b;
- t /= b;
- b = one;
- }
- }
- }
- /* j0() and j1() suffer enormous loss of precision at and
- * near zero; however, we know that their zero points never
- * coincide, so just choose the one further away from zero.
- */
- z = __ieee754_j0 (x);
- w = __ieee754_j1 (x);
- if (fabs (z) >= fabs (w))
- b = (t * z / b);
- else
- b = (t * w / a);
- }
- }
- if (sgn == 1)
- return -b;
- else
- return b;
+ if (n > 33) /* underflow */
+ b = zero;
+ else
+ {
+ temp = x * 0.5; b = temp;
+ for (a = one, i = 2; i <= n; i++)
+ {
+ a *= (double) i; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ }
+ b = b / a;
+ }
+ }
+ else
+ {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ double t, v;
+ double q0, q1, h, tmp; int32_t k, m;
+ w = (n + n) / (double) x; h = 2.0 / (double) x;
+ q0 = w; z = w + h; q1 = w * z - 1.0; k = 1;
+ while (q1 < 1.0e9)
+ {
+ k += 1; z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ m = n + n;
+ for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
+ t = one / (i / x - t);
+ a = t;
+ b = one;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = n;
+ v = two / x;
+ tmp = tmp * __ieee754_log (fabs (v * tmp));
+ if (tmp < 7.09782712893383973096e+02)
+ {
+ for (i = n - 1, di = (double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ }
+ }
+ else
+ {
+ for (i = n - 1, di = (double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ /* scale b to avoid spurious overflow */
+ if (b > 1e100)
+ {
+ a /= b;
+ t /= b;
+ b = one;
+ }
+ }
+ }
+ /* j0() and j1() suffer enormous loss of precision at and
+ * near zero; however, we know that their zero points never
+ * coincide, so just choose the one further away from zero.
+ */
+ z = __ieee754_j0 (x);
+ w = __ieee754_j1 (x);
+ if (fabs (z) >= fabs (w))
+ b = (t * z / b);
+ else
+ b = (t * w / a);
+ }
+ }
+ if (sgn == 1)
+ ret = -b;
+ else
+ ret = b;
+ }
+ if (ret == 0)
+ ret = __copysign (DBL_MIN, ret) * DBL_MIN;
+ return ret;
}
strong_alias (__ieee754_jn, __jn_finite)
diff --git a/sysdeps/ieee754/flt-32/e_jnf.c b/sysdeps/ieee754/flt-32/e_jnf.c
index dc4b371..ec5a81b 100644
--- a/sysdeps/ieee754/flt-32/e_jnf.c
+++ b/sysdeps/ieee754/flt-32/e_jnf.c
@@ -27,6 +27,8 @@ static const float zero = 0.0000000000e+00;
float
__ieee754_jnf(int n, float x)
{
+ float ret;
+ {
int32_t i,hx,ix, sgn;
float a, b, temp, di;
float z, w;
@@ -47,8 +49,9 @@ __ieee754_jnf(int n, float x)
if(n==1) return(__ieee754_j1f(x));
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
x = fabsf(x);
+ SET_RESTORE_ROUNDF (FE_TONEAREST);
if(__builtin_expect(ix==0||ix>=0x7f800000, 0)) /* if x is 0 or inf */
- b = zero;
+ return sgn == 1 ? -zero : zero;
else if((float)n<=x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
a = __ieee754_j0f(x);
@@ -163,7 +166,11 @@ __ieee754_jnf(int n, float x)
b = (t * w / a);
}
}
- if(sgn==1) return -b; else return b;
+ if(sgn==1) ret = -b; else ret = b;
+ }
+ if (ret == 0)
+ ret = __copysignf (FLT_MIN, ret) * FLT_MIN;
+ return ret;
}
strong_alias (__ieee754_jnf, __jnf_finite)
diff --git a/sysdeps/ieee754/ldbl-128/e_jnl.c b/sysdeps/ieee754/ldbl-128/e_jnl.c
index 422623f..14d65ff 100644
--- a/sysdeps/ieee754/ldbl-128/e_jnl.c
+++ b/sysdeps/ieee754/ldbl-128/e_jnl.c
@@ -73,7 +73,7 @@ __ieee754_jnl (int n, long double x)
{
u_int32_t se;
int32_t i, ix, sgn;
- long double a, b, temp, di;
+ long double a, b, temp, di, ret;
long double z, w;
ieee854_long_double_shape_type u;
@@ -106,192 +106,198 @@ __ieee754_jnl (int n, long double x)
sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */
x = fabsl (x);
- if (x == 0.0L || ix >= 0x7fff0000) /* if x is 0 or inf */
- b = zero;
- else if ((long double) n <= x)
- {
- /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
- if (ix >= 0x412D0000)
- { /* x > 2**302 */
+ {
+ SET_RESTORE_ROUNDL (FE_TONEAREST);
+ if (x == 0.0L || ix >= 0x7fff0000) /* if x is 0 or inf */
+ return sgn == 1 ? -zero : zero;
+ else if ((long double) n <= x)
+ {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if (ix >= 0x412D0000)
+ { /* x > 2**302 */
- /* ??? Could use an expansion for large x here. */
+ /* ??? Could use an expansion for large x here. */
- /* (x >> n**2)
- * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
- * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
- *
- * n sin(xn)*sqt2 cos(xn)*sqt2
- * ----------------------------------
- * 0 s-c c+s
- * 1 -s-c -c+s
- * 2 -s+c -c-s
- * 3 s+c c-s
- */
- long double s;
- long double c;
- __sincosl (x, &s, &c);
- switch (n & 3)
- {
- case 0:
- temp = c + s;
- break;
- case 1:
- temp = -c + s;
- break;
- case 2:
- temp = -c - s;
- break;
- case 3:
- temp = c - s;
- break;
- }
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
- }
- else
- {
- a = __ieee754_j0l (x);
- b = __ieee754_j1l (x);
- for (i = 1; i < n; i++)
- {
- temp = b;
- b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
- a = temp;
- }
- }
- }
- else
- {
- if (ix < 0x3fc60000)
- { /* x < 2**-57 */
- /* x is tiny, return the first Taylor expansion of J(n,x)
- * J(n,x) = 1/n!*(x/2)^n - ...
- */
- if (n >= 400) /* underflow, result < 10^-4952 */
- b = zero;
- else
- {
- temp = x * 0.5;
- b = temp;
- for (a = one, i = 2; i <= n; i++)
- {
- a *= (long double) i; /* a = n! */
- b *= temp; /* b = (x/2)^n */
- }
- b = b / a;
- }
- }
- else
- {
- /* use backward recurrence */
- /* x x^2 x^2
- * J(n,x)/J(n-1,x) = ---- ------ ------ .....
- * 2n - 2(n+1) - 2(n+2)
- *
- * 1 1 1
- * (for large x) = ---- ------ ------ .....
- * 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
- * x x x
- *
- * Let w = 2n/x and h=2/x, then the above quotient
- * is equal to the continued fraction:
- * 1
- * = -----------------------
- * 1
- * w - -----------------
- * 1
- * w+h - ---------
- * w+2h - ...
- *
- * To determine how many terms needed, let
- * Q(0) = w, Q(1) = w(w+h) - 1,
- * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
- */
- /* determine k */
- long double t, v;
- long double q0, q1, h, tmp;
- int32_t k, m;
- w = (n + n) / (long double) x;
- h = 2.0L / (long double) x;
- q0 = w;
- z = w + h;
- q1 = w * z - 1.0L;
- k = 1;
- while (q1 < 1.0e17L)
- {
- k += 1;
- z += h;
- tmp = z * q1 - q0;
- q0 = q1;
- q1 = tmp;
- }
- m = n + n;
- for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
- t = one / (i / x - t);
- a = t;
- b = one;
- /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
- * Hence, if n*(log(2n/x)) > ...
- * single 8.8722839355e+01
- * double 7.09782712893383973096e+02
- * long double 1.1356523406294143949491931077970765006170e+04
- * then recurrent value may overflow and the result is
- * likely underflow to zero
- */
- tmp = n;
- v = two / x;
- tmp = tmp * __ieee754_logl (fabsl (v * tmp));
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ long double s;
+ long double c;
+ __sincosl (x, &s, &c);
+ switch (n & 3)
+ {
+ case 0:
+ temp = c + s;
+ break;
+ case 1:
+ temp = -c + s;
+ break;
+ case 2:
+ temp = -c - s;
+ break;
+ case 3:
+ temp = c - s;
+ break;
+ }
+ b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ }
+ else
+ {
+ a = __ieee754_j0l (x);
+ b = __ieee754_j1l (x);
+ for (i = 1; i < n; i++)
+ {
+ temp = b;
+ b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ }
+ else
+ {
+ if (ix < 0x3fc60000)
+ { /* x < 2**-57 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if (n >= 400) /* underflow, result < 10^-4952 */
+ b = zero;
+ else
+ {
+ temp = x * 0.5;
+ b = temp;
+ for (a = one, i = 2; i <= n; i++)
+ {
+ a *= (long double) i; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ }
+ b = b / a;
+ }
+ }
+ else
+ {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ long double t, v;
+ long double q0, q1, h, tmp;
+ int32_t k, m;
+ w = (n + n) / (long double) x;
+ h = 2.0L / (long double) x;
+ q0 = w;
+ z = w + h;
+ q1 = w * z - 1.0L;
+ k = 1;
+ while (q1 < 1.0e17L)
+ {
+ k += 1;
+ z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ m = n + n;
+ for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
+ t = one / (i / x - t);
+ a = t;
+ b = one;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = n;
+ v = two / x;
+ tmp = tmp * __ieee754_logl (fabsl (v * tmp));
- if (tmp < 1.1356523406294143949491931077970765006170e+04L)
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- }
- }
- else
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- /* scale b to avoid spurious overflow */
- if (b > 1e100L)
- {
- a /= b;
- t /= b;
- b = one;
- }
- }
- }
- /* j0() and j1() suffer enormous loss of precision at and
- * near zero; however, we know that their zero points never
- * coincide, so just choose the one further away from zero.
- */
- z = __ieee754_j0l (x);
- w = __ieee754_j1l (x);
- if (fabsl (z) >= fabsl (w))
- b = (t * z / b);
- else
- b = (t * w / a);
- }
- }
- if (sgn == 1)
- return -b;
- else
- return b;
+ if (tmp < 1.1356523406294143949491931077970765006170e+04L)
+ {
+ for (i = n - 1, di = (long double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ }
+ }
+ else
+ {
+ for (i = n - 1, di = (long double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ /* scale b to avoid spurious overflow */
+ if (b > 1e100L)
+ {
+ a /= b;
+ t /= b;
+ b = one;
+ }
+ }
+ }
+ /* j0() and j1() suffer enormous loss of precision at and
+ * near zero; however, we know that their zero points never
+ * coincide, so just choose the one further away from zero.
+ */
+ z = __ieee754_j0l (x);
+ w = __ieee754_j1l (x);
+ if (fabsl (z) >= fabsl (w))
+ b = (t * z / b);
+ else
+ b = (t * w / a);
+ }
+ }
+ if (sgn == 1)
+ ret = -b;
+ else
+ ret = b;
+ }
+ if (ret == 0)
+ ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN;
+ return ret;
}
strong_alias (__ieee754_jnl, __jnl_finite)
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
index d2b9318..5d0a2b5 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
@@ -73,7 +73,7 @@ __ieee754_jnl (int n, long double x)
{
uint32_t se, lx;
int32_t i, ix, sgn;
- long double a, b, temp, di;
+ long double a, b, temp, di, ret;
long double z, w;
double xhi;
@@ -106,192 +106,198 @@ __ieee754_jnl (int n, long double x)
sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */
x = fabsl (x);
- if (x == 0.0L || ix >= 0x7ff00000) /* if x is 0 or inf */
- b = zero;
- else if ((long double) n <= x)
- {
- /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
- if (ix >= 0x52d00000)
- { /* x > 2**302 */
+ {
+ SET_RESTORE_ROUNDL (FE_TONEAREST);
+ if (x == 0.0L || ix >= 0x7ff00000) /* if x is 0 or inf */
+ return sgn == 1 ? -zero : zero;
+ else if ((long double) n <= x)
+ {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if (ix >= 0x52d00000)
+ { /* x > 2**302 */
- /* ??? Could use an expansion for large x here. */
+ /* ??? Could use an expansion for large x here. */
- /* (x >> n**2)
- * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
- * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
- *
- * n sin(xn)*sqt2 cos(xn)*sqt2
- * ----------------------------------
- * 0 s-c c+s
- * 1 -s-c -c+s
- * 2 -s+c -c-s
- * 3 s+c c-s
- */
- long double s;
- long double c;
- __sincosl (x, &s, &c);
- switch (n & 3)
- {
- case 0:
- temp = c + s;
- break;
- case 1:
- temp = -c + s;
- break;
- case 2:
- temp = -c - s;
- break;
- case 3:
- temp = c - s;
- break;
- }
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
- }
- else
- {
- a = __ieee754_j0l (x);
- b = __ieee754_j1l (x);
- for (i = 1; i < n; i++)
- {
- temp = b;
- b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
- a = temp;
- }
- }
- }
- else
- {
- if (ix < 0x3e100000)
- { /* x < 2**-29 */
- /* x is tiny, return the first Taylor expansion of J(n,x)
- * J(n,x) = 1/n!*(x/2)^n - ...
- */
- if (n >= 33) /* underflow, result < 10^-300 */
- b = zero;
- else
- {
- temp = x * 0.5;
- b = temp;
- for (a = one, i = 2; i <= n; i++)
- {
- a *= (long double) i; /* a = n! */
- b *= temp; /* b = (x/2)^n */
- }
- b = b / a;
- }
- }
- else
- {
- /* use backward recurrence */
- /* x x^2 x^2
- * J(n,x)/J(n-1,x) = ---- ------ ------ .....
- * 2n - 2(n+1) - 2(n+2)
- *
- * 1 1 1
- * (for large x) = ---- ------ ------ .....
- * 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
- * x x x
- *
- * Let w = 2n/x and h=2/x, then the above quotient
- * is equal to the continued fraction:
- * 1
- * = -----------------------
- * 1
- * w - -----------------
- * 1
- * w+h - ---------
- * w+2h - ...
- *
- * To determine how many terms needed, let
- * Q(0) = w, Q(1) = w(w+h) - 1,
- * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
- */
- /* determine k */
- long double t, v;
- long double q0, q1, h, tmp;
- int32_t k, m;
- w = (n + n) / (long double) x;
- h = 2.0L / (long double) x;
- q0 = w;
- z = w + h;
- q1 = w * z - 1.0L;
- k = 1;
- while (q1 < 1.0e17L)
- {
- k += 1;
- z += h;
- tmp = z * q1 - q0;
- q0 = q1;
- q1 = tmp;
- }
- m = n + n;
- for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
- t = one / (i / x - t);
- a = t;
- b = one;
- /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
- * Hence, if n*(log(2n/x)) > ...
- * single 8.8722839355e+01
- * double 7.09782712893383973096e+02
- * long double 1.1356523406294143949491931077970765006170e+04
- * then recurrent value may overflow and the result is
- * likely underflow to zero
- */
- tmp = n;
- v = two / x;
- tmp = tmp * __ieee754_logl (fabsl (v * tmp));
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ long double s;
+ long double c;
+ __sincosl (x, &s, &c);
+ switch (n & 3)
+ {
+ case 0:
+ temp = c + s;
+ break;
+ case 1:
+ temp = -c + s;
+ break;
+ case 2:
+ temp = -c - s;
+ break;
+ case 3:
+ temp = c - s;
+ break;
+ }
+ b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ }
+ else
+ {
+ a = __ieee754_j0l (x);
+ b = __ieee754_j1l (x);
+ for (i = 1; i < n; i++)
+ {
+ temp = b;
+ b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ }
+ else
+ {
+ if (ix < 0x3e100000)
+ { /* x < 2**-29 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if (n >= 33) /* underflow, result < 10^-300 */
+ b = zero;
+ else
+ {
+ temp = x * 0.5;
+ b = temp;
+ for (a = one, i = 2; i <= n; i++)
+ {
+ a *= (long double) i; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ }
+ b = b / a;
+ }
+ }
+ else
+ {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ long double t, v;
+ long double q0, q1, h, tmp;
+ int32_t k, m;
+ w = (n + n) / (long double) x;
+ h = 2.0L / (long double) x;
+ q0 = w;
+ z = w + h;
+ q1 = w * z - 1.0L;
+ k = 1;
+ while (q1 < 1.0e17L)
+ {
+ k += 1;
+ z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ m = n + n;
+ for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
+ t = one / (i / x - t);
+ a = t;
+ b = one;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = n;
+ v = two / x;
+ tmp = tmp * __ieee754_logl (fabsl (v * tmp));
- if (tmp < 1.1356523406294143949491931077970765006170e+04L)
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- }
- }
- else
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- /* scale b to avoid spurious overflow */
- if (b > 1e100L)
- {
- a /= b;
- t /= b;
- b = one;
- }
- }
- }
- /* j0() and j1() suffer enormous loss of precision at and
- * near zero; however, we know that their zero points never
- * coincide, so just choose the one further away from zero.
- */
- z = __ieee754_j0l (x);
- w = __ieee754_j1l (x);
- if (fabsl (z) >= fabsl (w))
- b = (t * z / b);
- else
- b = (t * w / a);
- }
- }
- if (sgn == 1)
- return -b;
- else
- return b;
+ if (tmp < 1.1356523406294143949491931077970765006170e+04L)
+ {
+ for (i = n - 1, di = (long double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ }
+ }
+ else
+ {
+ for (i = n - 1, di = (long double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ /* scale b to avoid spurious overflow */
+ if (b > 1e100L)
+ {
+ a /= b;
+ t /= b;
+ b = one;
+ }
+ }
+ }
+ /* j0() and j1() suffer enormous loss of precision at and
+ * near zero; however, we know that their zero points never
+ * coincide, so just choose the one further away from zero.
+ */
+ z = __ieee754_j0l (x);
+ w = __ieee754_j1l (x);
+ if (fabsl (z) >= fabsl (w))
+ b = (t * z / b);
+ else
+ b = (t * w / a);
+ }
+ }
+ if (sgn == 1)
+ ret = -b;
+ else
+ ret = b;
+ }
+ if (ret == 0)
+ ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN;
+ return ret;
}
strong_alias (__ieee754_jnl, __jnl_finite)
diff --git a/sysdeps/ieee754/ldbl-96/e_jnl.c b/sysdeps/ieee754/ldbl-96/e_jnl.c
index a666808..49c9c42 100644
--- a/sysdeps/ieee754/ldbl-96/e_jnl.c
+++ b/sysdeps/ieee754/ldbl-96/e_jnl.c
@@ -71,7 +71,7 @@ __ieee754_jnl (int n, long double x)
{
u_int32_t se, i0, i1;
int32_t i, ix, sgn;
- long double a, b, temp, di;
+ long double a, b, temp, di, ret;
long double z, w;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
@@ -96,195 +96,201 @@ __ieee754_jnl (int n, long double x)
return (__ieee754_j1l (x));
sgn = (n & 1) & (se >> 15); /* even n -- 0, odd n -- sign(x) */
x = fabsl (x);
- if (__glibc_unlikely ((ix | i0 | i1) == 0 || ix >= 0x7fff))
- /* if x is 0 or inf */
- b = zero;
- else if ((long double) n <= x)
- {
- /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
- if (ix >= 0x412D)
- { /* x > 2**302 */
+ {
+ SET_RESTORE_ROUNDL (FE_TONEAREST);
+ if (__glibc_unlikely ((ix | i0 | i1) == 0 || ix >= 0x7fff))
+ /* if x is 0 or inf */
+ return sgn == 1 ? -zero : zero;
+ else if ((long double) n <= x)
+ {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if (ix >= 0x412D)
+ { /* x > 2**302 */
- /* ??? This might be a futile gesture.
- If x exceeds X_TLOSS anyway, the wrapper function
- will set the result to zero. */
+ /* ??? This might be a futile gesture.
+ If x exceeds X_TLOSS anyway, the wrapper function
+ will set the result to zero. */
- /* (x >> n**2)
- * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
- * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
- *
- * n sin(xn)*sqt2 cos(xn)*sqt2
- * ----------------------------------
- * 0 s-c c+s
- * 1 -s-c -c+s
- * 2 -s+c -c-s
- * 3 s+c c-s
- */
- long double s;
- long double c;
- __sincosl (x, &s, &c);
- switch (n & 3)
- {
- case 0:
- temp = c + s;
- break;
- case 1:
- temp = -c + s;
- break;
- case 2:
- temp = -c - s;
- break;
- case 3:
- temp = c - s;
- break;
- }
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
- }
- else
- {
- a = __ieee754_j0l (x);
- b = __ieee754_j1l (x);
- for (i = 1; i < n; i++)
- {
- temp = b;
- b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
- a = temp;
- }
- }
- }
- else
- {
- if (ix < 0x3fde)
- { /* x < 2**-33 */
- /* x is tiny, return the first Taylor expansion of J(n,x)
- * J(n,x) = 1/n!*(x/2)^n - ...
- */
- if (n >= 400) /* underflow, result < 10^-4952 */
- b = zero;
- else
- {
- temp = x * 0.5;
- b = temp;
- for (a = one, i = 2; i <= n; i++)
- {
- a *= (long double) i; /* a = n! */
- b *= temp; /* b = (x/2)^n */
- }
- b = b / a;
- }
- }
- else
- {
- /* use backward recurrence */
- /* x x^2 x^2
- * J(n,x)/J(n-1,x) = ---- ------ ------ .....
- * 2n - 2(n+1) - 2(n+2)
- *
- * 1 1 1
- * (for large x) = ---- ------ ------ .....
- * 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
- * x x x
- *
- * Let w = 2n/x and h=2/x, then the above quotient
- * is equal to the continued fraction:
- * 1
- * = -----------------------
- * 1
- * w - -----------------
- * 1
- * w+h - ---------
- * w+2h - ...
- *
- * To determine how many terms needed, let
- * Q(0) = w, Q(1) = w(w+h) - 1,
- * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
- */
- /* determine k */
- long double t, v;
- long double q0, q1, h, tmp;
- int32_t k, m;
- w = (n + n) / (long double) x;
- h = 2.0L / (long double) x;
- q0 = w;
- z = w + h;
- q1 = w * z - 1.0L;
- k = 1;
- while (q1 < 1.0e11L)
- {
- k += 1;
- z += h;
- tmp = z * q1 - q0;
- q0 = q1;
- q1 = tmp;
- }
- m = n + n;
- for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
- t = one / (i / x - t);
- a = t;
- b = one;
- /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
- * Hence, if n*(log(2n/x)) > ...
- * single 8.8722839355e+01
- * double 7.09782712893383973096e+02
- * long double 1.1356523406294143949491931077970765006170e+04
- * then recurrent value may overflow and the result is
- * likely underflow to zero
- */
- tmp = n;
- v = two / x;
- tmp = tmp * __ieee754_logl (fabsl (v * tmp));
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ long double s;
+ long double c;
+ __sincosl (x, &s, &c);
+ switch (n & 3)
+ {
+ case 0:
+ temp = c + s;
+ break;
+ case 1:
+ temp = -c + s;
+ break;
+ case 2:
+ temp = -c - s;
+ break;
+ case 3:
+ temp = c - s;
+ break;
+ }
+ b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ }
+ else
+ {
+ a = __ieee754_j0l (x);
+ b = __ieee754_j1l (x);
+ for (i = 1; i < n; i++)
+ {
+ temp = b;
+ b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ }
+ else
+ {
+ if (ix < 0x3fde)
+ { /* x < 2**-33 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if (n >= 400) /* underflow, result < 10^-4952 */
+ b = zero;
+ else
+ {
+ temp = x * 0.5;
+ b = temp;
+ for (a = one, i = 2; i <= n; i++)
+ {
+ a *= (long double) i; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ }
+ b = b / a;
+ }
+ }
+ else
+ {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ long double t, v;
+ long double q0, q1, h, tmp;
+ int32_t k, m;
+ w = (n + n) / (long double) x;
+ h = 2.0L / (long double) x;
+ q0 = w;
+ z = w + h;
+ q1 = w * z - 1.0L;
+ k = 1;
+ while (q1 < 1.0e11L)
+ {
+ k += 1;
+ z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ m = n + n;
+ for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
+ t = one / (i / x - t);
+ a = t;
+ b = one;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = n;
+ v = two / x;
+ tmp = tmp * __ieee754_logl (fabsl (v * tmp));
- if (tmp < 1.1356523406294143949491931077970765006170e+04L)
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- }
- }
- else
- {
- for (i = n - 1, di = (long double) (i + i); i > 0; i--)
- {
- temp = b;
- b *= di;
- b = b / x - a;
- a = temp;
- di -= two;
- /* scale b to avoid spurious overflow */
- if (b > 1e100L)
- {
- a /= b;
- t /= b;
- b = one;
- }
- }
- }
- /* j0() and j1() suffer enormous loss of precision at and
- * near zero; however, we know that their zero points never
- * coincide, so just choose the one further away from zero.
- */
- z = __ieee754_j0l (x);
- w = __ieee754_j1l (x);
- if (fabsl (z) >= fabsl (w))
- b = (t * z / b);
- else
- b = (t * w / a);
- }
- }
- if (sgn == 1)
- return -b;
- else
- return b;
+ if (tmp < 1.1356523406294143949491931077970765006170e+04L)
+ {
+ for (i = n - 1, di = (long double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ }
+ }
+ else
+ {
+ for (i = n - 1, di = (long double) (i + i); i > 0; i--)
+ {
+ temp = b;
+ b *= di;
+ b = b / x - a;
+ a = temp;
+ di -= two;
+ /* scale b to avoid spurious overflow */
+ if (b > 1e100L)
+ {
+ a /= b;
+ t /= b;
+ b = one;
+ }
+ }
+ }
+ /* j0() and j1() suffer enormous loss of precision at and
+ * near zero; however, we know that their zero points never
+ * coincide, so just choose the one further away from zero.
+ */
+ z = __ieee754_j0l (x);
+ w = __ieee754_j1l (x);
+ if (fabsl (z) >= fabsl (w))
+ b = (t * z / b);
+ else
+ b = (t * w / a);
+ }
+ }
+ if (sgn == 1)
+ ret = -b;
+ else
+ ret = b;
+ }
+ if (ret == 0)
+ ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN;
+ return ret;
}
strong_alias (__ieee754_jnl, __jnl_finite)
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 48d11a6..12d0c5a 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1767,6 +1767,30 @@ ifloat: 4
ildouble: 4
ldouble: 4
+Function: "jn_downward":
+double: 5
+float: 5
+idouble: 5
+ifloat: 5
+ildouble: 4
+ldouble: 4
+
+Function: "jn_towardzero":
+double: 5
+float: 5
+idouble: 5
+ifloat: 5
+ildouble: 5
+ldouble: 5
+
+Function: "jn_upward":
+double: 5
+float: 5
+idouble: 5
+ifloat: 5
+ildouble: 5
+ldouble: 5
+
Function: "lgamma":
double: 2
float: 2
-----------------------------------------------------------------------
Summary of changes:
ChangeLog | 15 ++
NEWS | 2 +-
math/libm-test.inc | 4 +-
sysdeps/i386/fpu/libm-test-ulps | 24 +++
sysdeps/ieee754/dbl-64/e_jn.c | 312 +++++++++++++++--------------
sysdeps/ieee754/flt-32/e_jnf.c | 11 +-
sysdeps/ieee754/ldbl-128/e_jnl.c | 374 +++++++++++++++++-----------------
sysdeps/ieee754/ldbl-128ibm/e_jnl.c | 374 +++++++++++++++++-----------------
sysdeps/ieee754/ldbl-96/e_jnl.c | 380 ++++++++++++++++++-----------------
sysdeps/x86_64/fpu/libm-test-ulps | 24 +++
10 files changed, 806 insertions(+), 714 deletions(-)
hooks/post-receive
--
GNU C Library master sources