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Update.
* sysdeps/ieee754/ldbl-96/e_jnl.c: New file. Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>. * sysdeps/i386/fpu/libm-test-ulps: Update for jnl and ynl introduction. * sysdeps/ia64/fpu/libm-test-ulps: Likewise.
This commit is contained in:
Ulrich Drepper
parent
00b16c4a62
commit
08b3d7ad68
@ -1,5 +1,11 @@
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2001-02-26 Ulrich Drepper <drepper@redhat.com>
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* sysdeps/ieee754/ldbl-96/e_jnl.c: New file.
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Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>.
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* sysdeps/i386/fpu/libm-test-ulps: Update for jnl and ynl introduction.
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* sysdeps/ia64/fpu/libm-test-ulps: Likewise.
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* posix/wordexp-test.c (testit): Remove warnings.
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* dlfcn/Makefile (distribute): Add modatexit.c and modcxaatexit.c.
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@ -1,3 +1,12 @@
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2001-02-20 Hans Boehm <hans_boehm@hp.com>
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* manager.c (manager_mask): Removed static vesion. Now always local
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to __pthread_manager().
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(manager_mask_all): Removed completely.
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(__pthread_manager): Remove manager_mask_all initialization.
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(pthread_handle_create): Remove code to set and reset signal mask
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around __clone2() calls.
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2001-02-17 Jakub Jelinek <jakub@redhat.com>
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* spinlock.c (__pthread_lock): Force lock->__status to be read from
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@ -88,13 +88,6 @@ static int main_thread_exiting;
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static pthread_t pthread_threads_counter;
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#ifdef NEED_SEPARATE_REGISTER_STACK
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/* Signal masks for the manager. These have to be global only when clone2
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is used since it's currently borken wrt signals in the child. */
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static sigset_t manager_mask; /* Manager normal signal mask */
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static sigset_t manager_mask_all; /* All bits set. */
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#endif
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/* Forward declarations */
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static int pthread_handle_create(pthread_t *thread, const pthread_attr_t *attr,
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@ -113,9 +106,7 @@ int __pthread_manager(void *arg)
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{
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int reqfd = (int) (long int) arg;
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struct pollfd ufd;
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#ifndef NEED_SEPARATE_REGISTER_STACK
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sigset_t manager_mask;
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#endif
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int n;
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struct pthread_request request;
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@ -133,9 +124,6 @@ int __pthread_manager(void *arg)
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if (__pthread_threads_debug && __pthread_sig_debug > 0)
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sigdelset(&manager_mask, __pthread_sig_debug);
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sigprocmask(SIG_SETMASK, &manager_mask, NULL);
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#ifdef NEED_SEPARATE_REGISTER_STACK
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sigfillset(&manager_mask_all);
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#endif
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/* Raise our priority to match that of main thread */
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__pthread_manager_adjust_prio(__pthread_main_thread->p_priority);
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/* Synchronize debugging of the thread manager */
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@ -583,17 +571,12 @@ static int pthread_handle_create(pthread_t *thread, const pthread_attr_t *attr,
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And there is some argument for changing the __clone2
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interface to pass sp and bsp instead, making it more IA64
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specific, but allowing stacks to grow outward from each
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other, to get less paging and fewer mmaps. Clone2
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currently can't take signals in the child right after
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process creation. Mask them in the child. It resets the
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mask once it starts up. */
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sigprocmask(SIG_SETMASK, &manager_mask_all, NULL);
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other, to get less paging and fewer mmaps. */
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pid = __clone2(pthread_start_thread_event,
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(void **)new_thread_bottom,
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(char *)new_thread - new_thread_bottom,
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CLONE_VM | CLONE_FS | CLONE_FILES | CLONE_SIGHAND |
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__pthread_sig_cancel, new_thread);
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sigprocmask(SIG_SETMASK, &manager_mask, NULL);
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#else
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pid = __clone(pthread_start_thread_event, (void **) new_thread,
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CLONE_VM | CLONE_FS | CLONE_FILES | CLONE_SIGHAND |
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@ -625,13 +608,11 @@ static int pthread_handle_create(pthread_t *thread, const pthread_attr_t *attr,
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if (pid == 0)
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{
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#ifdef NEED_SEPARATE_REGISTER_STACK
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sigprocmask(SIG_SETMASK, &manager_mask_all, NULL);
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pid = __clone2(pthread_start_thread,
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(void **)new_thread_bottom,
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(char *)new_thread - new_thread_bottom,
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CLONE_VM | CLONE_FS | CLONE_FILES | CLONE_SIGHAND |
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__pthread_sig_cancel, new_thread);
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sigprocmask(SIG_SETMASK, &manager_mask, NULL);
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#else
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pid = __clone(pthread_start_thread, (void **) new_thread,
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CLONE_VM | CLONE_FS | CLONE_FILES | CLONE_SIGHAND |
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@ -676,6 +676,8 @@ float: 1
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ifloat: 1
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double: 2
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idouble: 2
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ldouble: 2
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ildouble: 2
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Test "jn (0, 2.0) == 0.22389077914123566805":
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float: 1
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ifloat: 1
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@ -684,46 +686,66 @@ idouble: 1
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Test "jn (0, 8.0) == 0.17165080713755390609":
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float: 1
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "jn (1, 10.0) == 0.043472746168861436670":
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float: 1
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ifloat: 1
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double: 2
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idouble: 2
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ldouble: 2
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ildouble: 2
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Test "jn (1, 2.0) == 0.57672480775687338720":
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double: 1
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idouble: 1
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Test "jn (1, 8.0) == 0.23463634685391462438":
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float: 1
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "jn (10, -1.0) == 0.26306151236874532070e-9":
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float: 1
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "jn (10, 0.1) == 0.26905328954342155795e-19":
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double: 4
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float: 2
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idouble: 4
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ifloat: 2
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ldouble: 1
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ildouble: 1
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Test "jn (10, 0.7) == 0.75175911502153953928e-11":
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double: 4
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float: 1
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idouble: 4
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ifloat: 1
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ldouble: 2
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ildouble: 2
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Test "jn (10, 1.0) == 0.26306151236874532070e-9":
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float: 1
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "jn (10, 2.0) == 0.25153862827167367096e-6":
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float: 1
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ifloat: 1
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double: 2
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idouble: 2
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ldouble: 1
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ildouble: 1
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Test "jn (10, 10.0) == 0.20748610663335885770":
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float: 2
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ifloat: 2
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double: 4
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idouble: 4
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ldouble: 2
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ildouble: 2
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Test "jn (3, 0.1) == 0.000020820315754756261429":
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double: 1
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idouble: 1
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ldouble: 1
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ildouble: 1
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Test "jn (3, 0.7) == 0.0069296548267508408077":
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double: 2
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idouble: 2
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@ -737,6 +759,14 @@ float: 1
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ifloat: 1
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double: 3
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idouble: 3
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ldouble: 1
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ildouble: 1
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Test "jn (3, -1.0) == -0.019563353982668405919":
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ldouble: 1
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ildouble: 1
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Test "jn (3, 1.0) == 0.019563353982668405919":
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ldouble: 1
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ildouble: 1
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# lgamma
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Test "lgamma (-0.5) == log(2*sqrt(pi))":
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@ -972,6 +1002,8 @@ float: 1
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ifloat: 1
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double: 3
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idouble: 3
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ldouble: 2
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ildouble: 2
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Test "yn (0, 1.0) == 0.088256964215676957983":
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double: 2
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float: 1
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@ -990,16 +1022,22 @@ float: 1
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ifloat: 1
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double: 2
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idouble: 2
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ldouble: 1
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ildouble: 1
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Test "yn (0, 8.0) == 0.22352148938756622053":
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float: 1
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ifloat: 1
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double: 1
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idouble: 1
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ldouble: 1
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ildouble: 1
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Test "yn (1, 0.1) == -6.4589510947020269877":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "yn (1, 0.7) == -1.1032498719076333697":
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double: 1
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idouble: 1
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@ -1019,19 +1057,27 @@ double: 1
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float: 2
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idouble: 1
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ifloat: 2
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ldouble: 1
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ildouble: 1
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Test "yn (1, 8.0) == -0.15806046173124749426":
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float: 2
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ifloat: 2
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ldouble: 2
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ildouble: 2
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Test "yn (10, 0.1) == -0.11831335132045197885e19":
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double: 2
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float: 1
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idouble: 2
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ifloat: 1
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ldouble: 2
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ildouble: 2
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Test "yn (10, 0.7) == -0.42447194260703866924e10":
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double: 6
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float: 3
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idouble: 6
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ifloat: 3
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ldouble: 7
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ildouble: 7
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Test "yn (10, 1.0) == -0.12161801427868918929e9":
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double: 1
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float: 1
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@ -1047,14 +1093,20 @@ float: 1
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ifloat: 1
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double: 2
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idouble: 2
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ldouble: 1
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ildouble: 1
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Test "yn (3, 0.1) == -5099.3323786129048894":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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ldouble: 2
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ildouble: 2
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Test "yn (3, 0.7) == -15.819479052819633505":
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double: 2
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idouble: 2
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ldouble: 2
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ildouble: 2
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Test "yn (3, 2.0) == -1.1277837768404277861":
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float: 1
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ifloat: 1
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@ -1413,6 +1465,8 @@ double: 4
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float: 2
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idouble: 4
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ifloat: 2
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ldouble: 2
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ildouble: 2
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Function: "lgamma":
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double: 1
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@ -1515,5 +1569,7 @@ double: 6
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float: 3
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idouble: 6
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ifloat: 3
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ldouble: 7
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ildouble: 7
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# end of automatic generation
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@ -765,32 +765,46 @@ idouble: 1
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Test "jn (10, -1.0) == 0.26306151236874532070e-9":
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float: 1
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "jn (10, 0.1) == 0.26905328954342155795e-19":
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float: 4
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ifloat: 4
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double: 6
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idouble: 6
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ldouble: 1
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ildouble: 1
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Test "jn (10, 0.7) == 0.75175911502153953928e-11":
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double: 4
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float: 1
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idouble: 4
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ifloat: 1
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ldouble: 2
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ildouble: 2
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Test "jn (10, 1.0) == 0.26306151236874532070e-9":
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float: 1
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "jn (10, 2.0) == 0.25153862827167367096e-6":
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float: 3
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ifloat: 3
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double: 2
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idouble: 2
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ldouble: 1
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ildouble: 1
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Test "jn (10, 10.0) == 0.20748610663335885770":
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float: 2
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ifloat: 2
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double: 4
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idouble: 4
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ldouble: 2
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ildouble: 2
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Test "jn (3, 0.1) == 0.000020820315754756261429":
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double: 1
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idouble: 1
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ldouble: 1
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ildouble: 1
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Test "jn (3, 0.7) == 0.0069296548267508408077":
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float: 1
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ifloat: 1
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@ -806,6 +820,14 @@ float: 1
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ifloat: 1
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double: 3
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idouble: 3
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ldouble: 1
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ildouble: 1
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Test "jn (3, -1.0) == -0.019563353982668405919":
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ldouble: 1
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ildouble: 1
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Test "jn (3, 1.0) == 0.019563353982668405919":
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ldouble: 1
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ildouble: 1
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# lgamma
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Test "lgamma (-0.5) == log(2*sqrt(pi))":
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@ -1043,6 +1065,8 @@ float: 1
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ifloat: 1
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double: 2
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idouble: 2
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ldouble: 2
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ildouble: 2
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Test "yn (0, 1.0) == 0.088256964215676957983":
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double: 2
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float: 1
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@ -1066,6 +1090,8 @@ float: 1
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ifloat: 1
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double: 1
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idouble: 1
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ldouble: 2
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ildouble: 2
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Test "yn (1, 0.1) == -6.4589510947020269877":
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double: 1
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float: 1
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@ -1092,21 +1118,29 @@ double: 1
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float: 2
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idouble: 1
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ifloat: 2
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ldouble: 2
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ildouble: 2
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Test "yn (1, 8.0) == -0.15806046173124749426":
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float: 2
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ifloat: 2
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double: 1
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idouble: 1
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ldouble: 2
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ildouble: 2
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Test "yn (10, 0.1) == -0.11831335132045197885e19":
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double: 2
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float: 1
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idouble: 2
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ifloat: 1
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ldouble: 1
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ildouble: 1
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Test "yn (10, 0.7) == -0.42447194260703866924e10":
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double: 6
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float: 3
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idouble: 6
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ifloat: 3
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ldouble: 7
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ildouble: 7
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Test "yn (10, 1.0) == -0.12161801427868918929e9":
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float: 2
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ifloat: 2
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@ -1122,6 +1156,8 @@ float: 1
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ifloat: 1
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double: 3
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idouble: 3
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ldouble: 1
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ildouble: 1
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Test "yn (3, 0.1) == -5099.3323786129048894":
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double: 1
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float: 1
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@ -1132,6 +1168,8 @@ float: 1
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ifloat: 1
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double: 2
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idouble: 2
|
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ldouble: 3
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ildouble: 3
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Test "yn (3, 2.0) == -1.1277837768404277861":
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float: 1
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||||
ifloat: 1
|
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@ -1503,6 +1541,8 @@ float: 4
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ifloat: 4
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double: 6
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idouble: 6
|
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ldouble: 2
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||||
ildouble: 2
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||||
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Function: "lgamma":
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double: 1
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@ -1611,5 +1651,7 @@ double: 6
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float: 3
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idouble: 6
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ifloat: 3
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ldouble: 7
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ildouble: 7
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# end of automatic generation
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368
sysdeps/ieee754/ldbl-96/e_jnl.c
Normal file
368
sysdeps/ieee754/ldbl-96/e_jnl.c
Normal file
@ -0,0 +1,368 @@
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
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*
|
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* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
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* is preserved.
|
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* ====================================================
|
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*/
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|
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/* Modifications for long double contributed by
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Stephen L. Moshier <moshier@na-net.ornl.gov> */
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|
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/*
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* __ieee754_jn(n, x), __ieee754_yn(n, x)
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* floating point Bessel's function of the 1st and 2nd kind
|
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* of order n
|
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*
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* Special cases:
|
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* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
|
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* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
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* Note 2. About jn(n,x), yn(n,x)
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* For n=0, j0(x) is called,
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* for n=1, j1(x) is called,
|
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* for n<x, forward recursion us used starting
|
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* from values of j0(x) and j1(x).
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* for n>x, a continued fraction approximation to
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* j(n,x)/j(n-1,x) is evaluated and then backward
|
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* recursion is used starting from a supposed value
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* for j(n,x). The resulting value of j(0,x) is
|
||||
* compared with the actual value to correct the
|
||||
* supposed value of j(n,x).
|
||||
*
|
||||
* yn(n,x) is similar in all respects, except
|
||||
* that forward recursion is used for all
|
||||
* values of n>1.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const long double
|
||||
#else
|
||||
static long double
|
||||
#endif
|
||||
invsqrtpi = 5.64189583547756286948079e-1L, two = 2.0e0L, one = 1.0e0L;
|
||||
|
||||
#ifdef __STDC__
|
||||
static const long double zero = 0.0L;
|
||||
#else
|
||||
static long double zero = 0.0L;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
long double
|
||||
__ieee754_jnl (int n, long double x)
|
||||
#else
|
||||
long double
|
||||
__ieee754_jnl (n, x)
|
||||
int n;
|
||||
long double x;
|
||||
#endif
|
||||
{
|
||||
u_int32_t se, i0, i1;
|
||||
int32_t i, ix, sgn;
|
||||
long double a, b, temp, di;
|
||||
long double z, w;
|
||||
|
||||
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
|
||||
* Thus, J(-n,x) = J(n,-x)
|
||||
*/
|
||||
|
||||
GET_LDOUBLE_WORDS (se, i0, i1, x);
|
||||
ix = se & 0x7fff;
|
||||
|
||||
/* if J(n,NaN) is NaN */
|
||||
if ((ix == 0x7fff) && ((i0 & 0x7fffffff) != 0))
|
||||
return x + x;
|
||||
if (n < 0)
|
||||
{
|
||||
n = -n;
|
||||
x = -x;
|
||||
se ^= 0x8000;
|
||||
}
|
||||
if (n == 0)
|
||||
return (__ieee754_j0l (x));
|
||||
if (n == 1)
|
||||
return (__ieee754_j1l (x));
|
||||
sgn = (n & 1) & (se >> 15); /* even n -- 0, odd n -- sign(x) */
|
||||
x = fabsl (x);
|
||||
if ((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 */
|
||||
|
||||
/* ??? 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));
|
||||
|
||||
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;
|
||||
}
|
||||
}
|
||||
}
|
||||
b = (t * __ieee754_j0l (x) / b);
|
||||
}
|
||||
}
|
||||
if (sgn == 1)
|
||||
return -b;
|
||||
else
|
||||
return b;
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
long double
|
||||
__ieee754_ynl (int n, long double x)
|
||||
#else
|
||||
long double
|
||||
__ieee754_ynl (n, x)
|
||||
int n;
|
||||
long double x;
|
||||
#endif
|
||||
{
|
||||
u_int32_t se, i0, i1;
|
||||
int32_t i, ix;
|
||||
int32_t sign;
|
||||
long double a, b, temp;
|
||||
|
||||
|
||||
GET_LDOUBLE_WORDS (se, i0, i1, x);
|
||||
ix = se & 0x7fff;
|
||||
/* if Y(n,NaN) is NaN */
|
||||
if ((ix == 0x7fff) && ((i0 & 0x7fffffff) != 0))
|
||||
return x + x;
|
||||
if ((ix | i0 | i1) == 0)
|
||||
return -one / zero;
|
||||
if (se & 0x8000)
|
||||
return zero / zero;
|
||||
sign = 1;
|
||||
if (n < 0)
|
||||
{
|
||||
n = -n;
|
||||
sign = 1 - ((n & 1) << 1);
|
||||
}
|
||||
if (n == 0)
|
||||
return (__ieee754_y0l (x));
|
||||
if (n == 1)
|
||||
return (sign * __ieee754_y1l (x));
|
||||
if (ix == 0x7fff)
|
||||
return zero;
|
||||
if (ix >= 0x412D)
|
||||
{ /* x > 2**302 */
|
||||
|
||||
/* ??? See comment above on the possible futility of this. */
|
||||
|
||||
/* (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 = s - c;
|
||||
break;
|
||||
case 1:
|
||||
temp = -s - c;
|
||||
break;
|
||||
case 2:
|
||||
temp = -s + c;
|
||||
break;
|
||||
case 3:
|
||||
temp = s + c;
|
||||
break;
|
||||
}
|
||||
b = invsqrtpi * temp / __ieee754_sqrtl (x);
|
||||
}
|
||||
else
|
||||
{
|
||||
a = __ieee754_y0l (x);
|
||||
b = __ieee754_y1l (x);
|
||||
/* quit if b is -inf */
|
||||
GET_LDOUBLE_WORDS (se, i0, i1, b);
|
||||
for (i = 1; i < n && se != 0xffff; i++)
|
||||
{
|
||||
temp = b;
|
||||
b = ((long double) (i + i) / x) * b - a;
|
||||
GET_LDOUBLE_WORDS (se, i0, i1, b);
|
||||
a = temp;
|
||||
}
|
||||
}
|
||||
if (sign > 0)
|
||||
return b;
|
||||
else
|
||||
return -b;
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user