Add probabability distribution utility code.
Add probabability distribution utility code that enables generation of random deviates drawn from normal, Chi-square, and Gamma distributions. Fix format strings in several of the assert_* macros (remove a %s). Clean up header issues; it's critical that system headers are not included after internal definitions potentially do things like: #define inline Fix the build system to incorporate header dependencies for the test library C files.
This commit is contained in:
Jason Evans
parent
80061b6df0
commit
b1941c6150
16
Makefile.in
16
Makefile.in
@ -103,12 +103,11 @@ DOCS_XML := $(objroot)doc/jemalloc$(install_suffix).xml
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DOCS_HTML := $(DOCS_XML:$(objroot)%.xml=$(srcroot)%.html)
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DOCS_MAN3 := $(DOCS_XML:$(objroot)%.xml=$(srcroot)%.3)
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DOCS := $(DOCS_HTML) $(DOCS_MAN3)
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C_TESTLIB_SRCS := $(srcroot)test/src/SFMT.c $(srcroot)test/src/test.c \
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$(srcroot)test/src/thread.c
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C_TESTLIB_SRCS := $(srcroot)test/src/math.c $(srcroot)test/src/SFMT.c \
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$(srcroot)test/src/test.c $(srcroot)test/src/thread.c
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C_UTIL_INTEGRATION_SRCS := $(srcroot)src/util.c
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TESTS_UNIT := $(srcroot)test/unit/bitmap.c \
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$(srcroot)test/unit/SFMT.c \
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$(srcroot)test/unit/tsd.c
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TESTS_UNIT := $(srcroot)test/unit/bitmap.c $(srcroot)test/unit/math.c \
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$(srcroot)test/unit/SFMT.c $(srcroot)test/unit/tsd.c
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TESTS_INTEGRATION := $(srcroot)test/integration/aligned_alloc.c \
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$(srcroot)test/integration/allocated.c \
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$(srcroot)test/integration/ALLOCM_ARENA.c \
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@ -166,6 +165,7 @@ ifdef CC_MM
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-include $(C_OBJS:%.$(O)=%.d)
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-include $(C_PIC_OBJS:%.$(O)=%.d)
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-include $(C_JET_OBJS:%.$(O)=%.d)
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-include $(C_TESTLIB_OBJS:%.$(O)=%.d)
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-include $(TESTS_OBJS:%.$(O)=%.d)
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endif
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@ -227,15 +227,15 @@ $(STATIC_LIBS):
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$(objroot)test/unit/%$(EXE): $(objroot)test/unit/%.$(O) $(C_JET_OBJS) $(C_TESTLIB_UNIT_OBJS)
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@mkdir -p $(@D)
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$(CC) $(LDTARGET) $(filter %.$(O),$^) $(call RPATH,$(objroot)lib) $(LDFLAGS) $(LIBS) $(EXTRA_LDFLAGS)
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$(CC) $(LDTARGET) $(filter %.$(O),$^) $(call RPATH,$(objroot)lib) $(LDFLAGS) $(filter-out -lm,$(LIBS)) -lm $(EXTRA_LDFLAGS)
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$(objroot)test/integration/%$(EXE): $(objroot)test/integration/%.$(O) $(C_TESTLIB_INTEGRATION_OBJS) $(C_UTIL_INTEGRATION_OBJS) $(objroot)lib/$(LIBJEMALLOC).$(IMPORTLIB)
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@mkdir -p $(@D)
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$(CC) $(LDTARGET) $(filter %.$(O),$^) $(call RPATH,$(objroot)lib) $(objroot)lib/$(LIBJEMALLOC).$(IMPORTLIB) $(LDFLAGS) $(filter -lpthread,$(LIBS)) $(EXTRA_LDFLAGS)
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$(CC) $(LDTARGET) $(filter %.$(O),$^) $(call RPATH,$(objroot)lib) $(objroot)lib/$(LIBJEMALLOC).$(IMPORTLIB) $(LDFLAGS) $(filter-out -lm,$(filter -lpthread,$(LIBS))) -lm $(EXTRA_LDFLAGS)
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$(objroot)test/stress/%$(EXE): $(objroot)test/stress/%.$(O) $(C_JET_OBJS) $(C_TESTLIB_STRESS_OBJS) $(objroot)lib/$(LIBJEMALLOC).$(IMPORTLIB)
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@mkdir -p $(@D)
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$(CC) $(LDTARGET) $(filter %.$(O),$^) $(call RPATH,$(objroot)lib) $(objroot)lib/$(LIBJEMALLOC).$(IMPORTLIB) $(LDFLAGS) $(LIBS) $(EXTRA_LDFLAGS)
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$(CC) $(LDTARGET) $(filter %.$(O),$^) $(call RPATH,$(objroot)lib) $(objroot)lib/$(LIBJEMALLOC).$(IMPORTLIB) $(LDFLAGS) $(filter-out -lm,$(LIBS)) -lm $(EXTRA_LDFLAGS)
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build_lib_shared: $(DSOS)
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build_lib_static: $(STATIC_LIBS)
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@ -37,6 +37,7 @@
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#define ZU(z) ((size_t)z)
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#define QU(q) ((uint64_t)q)
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#define QI(q) ((int64_t)q)
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#ifndef __DECONST
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# define __DECONST(type, var) ((type)(uintptr_t)(const void *)(var))
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@ -355,7 +355,7 @@ prof_sample_threshold_update(prof_tdata_t *prof_tdata)
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* Luc Devroye
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* Springer-Verlag, New York, 1986
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* pp 500
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* (http://cg.scs.carleton.ca/~luc/rnbookindex.html)
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* (http://luc.devroye.org/rnbookindex.html)
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*/
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prng64(r, 53, prof_tdata->prng_state,
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UINT64_C(6364136223846793005), UINT64_C(1442695040888963407));
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@ -66,32 +66,6 @@
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#ifndef SFMT_H
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#define SFMT_H
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#include <stdio.h>
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#include <stdlib.h>
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#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)
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#include <inttypes.h>
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#elif defined(_MSC_VER) || defined(__BORLANDC__)
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typedef unsigned int uint32_t;
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typedef unsigned __int64 uint64_t;
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#define inline __inline
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#else
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#include <inttypes.h>
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#if defined(__GNUC__)
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#define inline __inline__
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#endif
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#endif
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#ifndef PRIu64
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#if defined(_MSC_VER) || defined(__BORLANDC__)
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#define PRIu64 "I64u"
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#define PRIx64 "I64x"
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#else
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#define PRIu64 "llu"
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#define PRIx64 "llx"
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#endif
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#endif
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#if defined(__GNUC__)
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#define ALWAYSINLINE __attribute__((always_inline))
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#else
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@ -1,6 +1,14 @@
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#include <stdlib.h>
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#include <stdbool.h>
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#include <string.h>
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#include <inttypes.h>
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#include <math.h>
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#ifdef _WIN32
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# include <windows.h>
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#else
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# include <pthread.h>
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#endif
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/******************************************************************************/
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/*
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@ -37,6 +45,13 @@
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#include "test/jemalloc_test_defs.h"
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#if defined(HAVE_ALTIVEC) && !defined(__APPLE__)
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# include <altivec.h>
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#endif
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#ifdef HAVE_SSE2
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# include <emmintrin.h>
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#endif
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/******************************************************************************/
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/*
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* For unit tests, expose all public and private interfaces.
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@ -60,7 +75,6 @@
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# define JEMALLOC_N(n) @private_namespace@##n
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# include "jemalloc/internal/private_namespace.h"
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# include <inttypes.h>
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# include <stdarg.h>
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# include <errno.h>
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# define JEMALLOC_H_TYPES
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@ -109,6 +123,7 @@
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/*
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* Common test utilities.
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*/
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#include "test/math.h"
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#include "test/test.h"
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#include "test/thread.h"
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#define MEXP 19937
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311
test/include/test/math.h
Normal file
311
test/include/test/math.h
Normal file
@ -0,0 +1,311 @@
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#ifndef JEMALLOC_ENABLE_INLINE
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double ln_gamma(double x);
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double i_gamma(double x, double p, double ln_gamma_p);
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double pt_norm(double p);
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double pt_chi2(double p, double df, double ln_gamma_df_2);
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double pt_gamma(double p, double shape, double scale, double ln_gamma_shape);
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#endif
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#if (defined(JEMALLOC_ENABLE_INLINE) || defined(MATH_C_))
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/*
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* Compute the natural log of Gamma(x), accurate to 10 decimal places.
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*
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* This implementation is based on:
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*
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* Pike, M.C., I.D. Hill (1966) Algorithm 291: Logarithm of Gamma function
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* [S14]. Communications of the ACM 9(9):684.
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*/
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JEMALLOC_INLINE double
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ln_gamma(double x)
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{
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double f, z;
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assert(x > 0.0);
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if (x < 7.0) {
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f = 1.0;
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z = x;
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while (z < 7.0) {
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f *= z;
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z += 1.0;
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}
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x = z;
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f = -log(f);
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} else
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f = 0.0;
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z = 1.0 / (x * x);
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return (f + (x-0.5) * log(x) - x + 0.918938533204673 +
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(((-0.000595238095238 * z + 0.000793650793651) * z -
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0.002777777777778) * z + 0.083333333333333) / x);
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}
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/*
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* Compute the incomplete Gamma ratio for [0..x], where p is the shape
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* parameter, and ln_gamma_p is ln_gamma(p).
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*
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* This implementation is based on:
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*
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* Bhattacharjee, G.P. (1970) Algorithm AS 32: The incomplete Gamma integral.
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* Applied Statistics 19:285-287.
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*/
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JEMALLOC_INLINE double
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i_gamma(double x, double p, double ln_gamma_p)
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{
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double acu, factor, oflo, gin, term, rn, a, b, an, dif;
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double pn[6];
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unsigned i;
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assert(p > 0.0);
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assert(x >= 0.0);
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if (x == 0.0)
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return (0.0);
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acu = 1.0e-10;
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oflo = 1.0e30;
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gin = 0.0;
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factor = exp(p * log(x) - x - ln_gamma_p);
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if (x <= 1.0 || x < p) {
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/* Calculation by series expansion. */
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gin = 1.0;
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term = 1.0;
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rn = p;
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while (true) {
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rn += 1.0;
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term *= x / rn;
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gin += term;
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if (term <= acu) {
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gin *= factor / p;
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return (gin);
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}
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}
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} else {
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/* Calculation by continued fraction. */
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a = 1.0 - p;
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b = a + x + 1.0;
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term = 0.0;
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pn[0] = 1.0;
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pn[1] = x;
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pn[2] = x + 1.0;
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pn[3] = x * b;
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gin = pn[2] / pn[3];
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while (true) {
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a += 1.0;
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b += 2.0;
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term += 1.0;
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an = a * term;
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for (i = 0; i < 2; i++)
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pn[i+4] = b * pn[i+2] - an * pn[i];
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if (pn[5] != 0.0) {
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rn = pn[4] / pn[5];
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dif = fabs(gin - rn);
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if (dif <= acu && dif <= acu * rn) {
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gin = 1.0 - factor * gin;
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return (gin);
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}
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gin = rn;
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}
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for (i = 0; i < 4; i++)
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pn[i] = pn[i+2];
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if (fabs(pn[4]) >= oflo) {
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for (i = 0; i < 4; i++)
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pn[i] /= oflo;
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}
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}
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}
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}
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/*
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* Given a value p in [0..1] of the lower tail area of the normal distribution,
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* compute the limit on the definite integral from [-inf..z] that satisfies p,
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* accurate to 16 decimal places.
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*
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* This implementation is based on:
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*
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* Wichura, M.J. (1988) Algorithm AS 241: The percentage points of the normal
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* distribution. Applied Statistics 37(3):477-484.
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*/
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JEMALLOC_INLINE double
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pt_norm(double p)
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{
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double q, r, ret;
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assert(p > 0.0 && p < 1.0);
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q = p - 0.5;
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if (fabs(q) <= 0.425) {
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/* p close to 1/2. */
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r = 0.180625 - q * q;
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return (q * (((((((2.5090809287301226727e3 * r +
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3.3430575583588128105e4) * r + 6.7265770927008700853e4) * r
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+ 4.5921953931549871457e4) * r + 1.3731693765509461125e4) *
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r + 1.9715909503065514427e3) * r + 1.3314166789178437745e2)
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* r + 3.3871328727963666080e0) /
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(((((((5.2264952788528545610e3 * r +
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2.8729085735721942674e4) * r + 3.9307895800092710610e4) * r
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+ 2.1213794301586595867e4) * r + 5.3941960214247511077e3) *
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r + 6.8718700749205790830e2) * r + 4.2313330701600911252e1)
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* r + 1.0));
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} else {
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if (q < 0.0)
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r = p;
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else
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r = 1.0 - p;
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assert(r > 0.0);
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r = sqrt(-log(r));
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if (r <= 5.0) {
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/* p neither close to 1/2 nor 0 or 1. */
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r -= 1.6;
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ret = ((((((((7.74545014278341407640e-4 * r +
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2.27238449892691845833e-2) * r +
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2.41780725177450611770e-1) * r +
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1.27045825245236838258e0) * r +
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3.64784832476320460504e0) * r +
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5.76949722146069140550e0) * r +
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4.63033784615654529590e0) * r +
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1.42343711074968357734e0) /
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(((((((1.05075007164441684324e-9 * r +
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5.47593808499534494600e-4) * r +
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1.51986665636164571966e-2)
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* r + 1.48103976427480074590e-1) * r +
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6.89767334985100004550e-1) * r +
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1.67638483018380384940e0) * r +
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2.05319162663775882187e0) * r + 1.0));
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} else {
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/* p near 0 or 1. */
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r -= 5.0;
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ret = ((((((((2.01033439929228813265e-7 * r +
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2.71155556874348757815e-5) * r +
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1.24266094738807843860e-3) * r +
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2.65321895265761230930e-2) * r +
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2.96560571828504891230e-1) * r +
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1.78482653991729133580e0) * r +
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5.46378491116411436990e0) * r +
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6.65790464350110377720e0) /
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(((((((2.04426310338993978564e-15 * r +
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1.42151175831644588870e-7) * r +
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1.84631831751005468180e-5) * r +
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7.86869131145613259100e-4) * r +
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1.48753612908506148525e-2) * r +
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1.36929880922735805310e-1) * r +
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5.99832206555887937690e-1)
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* r + 1.0));
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}
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if (q < 0.0)
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ret = -ret;
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return (ret);
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}
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}
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/*
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* Given a value p in [0..1] of the lower tail area of the Chi^2 distribution
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* with df degrees of freedom, where ln_gamma_df_2 is ln_gamma(df/2.0), compute
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* the upper limit on the definite integral from [0..z] that satisfies p,
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* accurate to 12 decimal places.
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*
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* This implementation is based on:
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*
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* Best, D.J., D.E. Roberts (1975) Algorithm AS 91: The percentage points of
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* the Chi^2 distribution. Applied Statistics 24(3):385-388.
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*
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* Shea, B.L. (1991) Algorithm AS R85: A remark on AS 91: The percentage
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* points of the Chi^2 distribution. Applied Statistics 40(1):233-235.
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*/
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JEMALLOC_INLINE double
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pt_chi2(double p, double df, double ln_gamma_df_2)
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{
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double e, aa, xx, c, ch, a, q, p1, p2, t, x, b, s1, s2, s3, s4, s5, s6;
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unsigned i;
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assert(p >= 0.0 && p < 1.0);
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assert(df > 0.0);
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e = 5.0e-7;
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aa = 0.6931471805;
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xx = 0.5 * df;
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c = xx - 1.0;
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if (df < -1.24 * log(p)) {
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/* Starting approximation for small Chi^2. */
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ch = pow(p * xx * exp(ln_gamma_df_2 + xx * aa), 1.0 / xx);
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if (ch - e < 0.0)
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return (ch);
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} else {
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if (df > 0.32) {
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x = pt_norm(p);
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/*
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* Starting approximation using Wilson and Hilferty
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* estimate.
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*/
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p1 = 0.222222 / df;
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ch = df * pow(x * sqrt(p1) + 1.0 - p1, 3.0);
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/* Starting approximation for p tending to 1. */
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if (ch > 2.2 * df + 6.0) {
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ch = -2.0 * (log(1.0 - p) - c * log(0.5 * ch) +
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ln_gamma_df_2);
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}
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} else {
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ch = 0.4;
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a = log(1.0 - p);
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while (true) {
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q = ch;
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p1 = 1.0 + ch * (4.67 + ch);
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p2 = ch * (6.73 + ch * (6.66 + ch));
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t = -0.5 + (4.67 + 2.0 * ch) / p1 - (6.73 + ch
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* (13.32 + 3.0 * ch)) / p2;
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ch -= (1.0 - exp(a + ln_gamma_df_2 + 0.5 * ch +
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c * aa) * p2 / p1) / t;
|
||||
if (fabs(q / ch - 1.0) - 0.01 <= 0.0)
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
for (i = 0; i < 20; i++) {
|
||||
/* Calculation of seven-term Taylor series. */
|
||||
q = ch;
|
||||
p1 = 0.5 * ch;
|
||||
if (p1 < 0.0)
|
||||
return (-1.0);
|
||||
p2 = p - i_gamma(p1, xx, ln_gamma_df_2);
|
||||
t = p2 * exp(xx * aa + ln_gamma_df_2 + p1 - c * log(ch));
|
||||
b = t / ch;
|
||||
a = 0.5 * t - b * c;
|
||||
s1 = (210.0 + a * (140.0 + a * (105.0 + a * (84.0 + a * (70.0 +
|
||||
60.0 * a))))) / 420.0;
|
||||
s2 = (420.0 + a * (735.0 + a * (966.0 + a * (1141.0 + 1278.0 *
|
||||
a)))) / 2520.0;
|
||||
s3 = (210.0 + a * (462.0 + a * (707.0 + 932.0 * a))) / 2520.0;
|
||||
s4 = (252.0 + a * (672.0 + 1182.0 * a) + c * (294.0 + a *
|
||||
(889.0 + 1740.0 * a))) / 5040.0;
|
||||
s5 = (84.0 + 264.0 * a + c * (175.0 + 606.0 * a)) / 2520.0;
|
||||
s6 = (120.0 + c * (346.0 + 127.0 * c)) / 5040.0;
|
||||
ch += t * (1.0 + 0.5 * t * s1 - b * c * (s1 - b * (s2 - b * (s3
|
||||
- b * (s4 - b * (s5 - b * s6))))));
|
||||
if (fabs(q / ch - 1.0) <= e)
|
||||
break;
|
||||
}
|
||||
|
||||
return (ch);
|
||||
}
|
||||
|
||||
/*
|
||||
* Given a value p in [0..1] and Gamma distribution shape and scale parameters,
|
||||
* compute the upper limit on the definite integeral from [0..z] that satisfies
|
||||
* p.
|
||||
*/
|
||||
JEMALLOC_INLINE double
|
||||
pt_gamma(double p, double shape, double scale, double ln_gamma_shape)
|
||||
{
|
||||
|
||||
return (pt_chi2(p, shape * 2.0, ln_gamma_shape) * 0.5 * scale);
|
||||
}
|
||||
#endif
|
||||
@ -131,7 +131,7 @@
|
||||
if (!(a_ == true)) { \
|
||||
p_test_fail( \
|
||||
"%s:%s:%d: Failed assertion: " \
|
||||
"(%s) == true --> %s != true: %s\n", \
|
||||
"(%s) == true --> %s != true: ", \
|
||||
__func__, __FILE__, __LINE__, \
|
||||
#a, a_ ? "true" : "false", fmt); \
|
||||
} \
|
||||
@ -141,7 +141,7 @@
|
||||
if (!(a_ == false)) { \
|
||||
p_test_fail( \
|
||||
"%s:%s:%d: Failed assertion: " \
|
||||
"(%s) == false --> %s != false: %s\n", \
|
||||
"(%s) == false --> %s != false: ", \
|
||||
__func__, __FILE__, __LINE__, \
|
||||
#a, a_ ? "true" : "false", fmt); \
|
||||
} \
|
||||
@ -152,7 +152,7 @@
|
||||
p_test_fail( \
|
||||
"%s:%s:%d: Failed assertion: " \
|
||||
"(%s) same as (%s) --> " \
|
||||
"\"%s\" differs from \"%s\": %s\n", \
|
||||
"\"%s\" differs from \"%s\": ", \
|
||||
__func__, __FILE__, __LINE__, #a, #b, a, b, fmt); \
|
||||
} \
|
||||
} while (0)
|
||||
@ -161,7 +161,7 @@
|
||||
p_test_fail( \
|
||||
"%s:%s:%d: Failed assertion: " \
|
||||
"(%s) differs from (%s) --> " \
|
||||
"\"%s\" same as \"%s\": %s\n", \
|
||||
"\"%s\" same as \"%s\": ", \
|
||||
__func__, __FILE__, __LINE__, #a, #b, a, b, fmt); \
|
||||
} \
|
||||
} while (0)
|
||||
|
||||
@ -1,10 +1,7 @@
|
||||
|
||||
/* Abstraction layer for threading in tests */
|
||||
#ifdef _WIN32
|
||||
#include <windows.h>
|
||||
typedef HANDLE je_thread_t;
|
||||
#else
|
||||
#include <pthread.h>
|
||||
typedef pthread_t je_thread_t;
|
||||
#endif
|
||||
|
||||
|
||||
@ -65,9 +65,6 @@
|
||||
128-bit SIMD data type for Altivec, SSE2 or standard C
|
||||
------------------------------------------------------*/
|
||||
#if defined(HAVE_ALTIVEC)
|
||||
#if !defined(__APPLE__)
|
||||
#include <altivec.h>
|
||||
#endif
|
||||
/** 128-bit data structure */
|
||||
union W128_T {
|
||||
vector unsigned int s;
|
||||
@ -77,8 +74,6 @@ union W128_T {
|
||||
typedef union W128_T w128_t;
|
||||
|
||||
#elif defined(HAVE_SSE2)
|
||||
#include <emmintrin.h>
|
||||
|
||||
/** 128-bit data structure */
|
||||
union W128_T {
|
||||
__m128i si;
|
||||
|
||||
2
test/src/math.c
Normal file
2
test/src/math.c
Normal file
@ -0,0 +1,2 @@
|
||||
#define MATH_C_
|
||||
#include "test/jemalloc_test.h"
|
||||
388
test/unit/math.c
Normal file
388
test/unit/math.c
Normal file
@ -0,0 +1,388 @@
|
||||
#include "test/jemalloc_test.h"
|
||||
|
||||
#define MAX_REL_ERR 1.0e-9
|
||||
#define MAX_ABS_ERR 1.0e-9
|
||||
|
||||
static bool
|
||||
double_eq_rel(double a, double b, double max_rel_err, double max_abs_err)
|
||||
{
|
||||
double rel_err;
|
||||
|
||||
if (fabs(a - b) < max_abs_err)
|
||||
return (true);
|
||||
rel_err = (fabs(b) > fabs(a)) ? fabs((a-b)/b) : fabs((a-b)/a);
|
||||
return (rel_err < max_rel_err);
|
||||
}
|
||||
|
||||
static uint64_t
|
||||
factorial(unsigned x)
|
||||
{
|
||||
uint64_t ret = 1;
|
||||
unsigned i;
|
||||
|
||||
for (i = 2; i <= x; i++)
|
||||
ret *= (uint64_t)i;
|
||||
|
||||
return (ret);
|
||||
}
|
||||
|
||||
TEST_BEGIN(test_ln_gamma_factorial)
|
||||
{
|
||||
unsigned x;
|
||||
|
||||
/* exp(ln_gamma(x)) == (x-1)! for integer x. */
|
||||
for (x = 1; x <= 21; x++) {
|
||||
assert_true(double_eq_rel(exp(ln_gamma(x)),
|
||||
(double)factorial(x-1), MAX_REL_ERR, MAX_ABS_ERR),
|
||||
"Incorrect factorial result for x=%u", x);
|
||||
}
|
||||
}
|
||||
TEST_END
|
||||
|
||||
/* Expected ln_gamma([0.0..100.0] increment=0.25). */
|
||||
static const double ln_gamma_misc_expected[] = {
|
||||
INFINITY,
|
||||
1.28802252469807743, 0.57236494292470008, 0.20328095143129538,
|
||||
0.00000000000000000, -0.09827183642181320, -0.12078223763524518,
|
||||
-0.08440112102048555, 0.00000000000000000, 0.12487171489239651,
|
||||
0.28468287047291918, 0.47521466691493719, 0.69314718055994529,
|
||||
0.93580193110872523, 1.20097360234707429, 1.48681557859341718,
|
||||
1.79175946922805496, 2.11445692745037128, 2.45373657084244234,
|
||||
2.80857141857573644, 3.17805383034794575, 3.56137591038669710,
|
||||
3.95781396761871651, 4.36671603662228680, 4.78749174278204581,
|
||||
5.21960398699022932, 5.66256205985714178, 6.11591589143154568,
|
||||
6.57925121201010121, 7.05218545073853953, 7.53436423675873268,
|
||||
8.02545839631598312, 8.52516136106541467, 9.03318691960512332,
|
||||
9.54926725730099690, 10.07315123968123949, 10.60460290274525086,
|
||||
11.14340011995171231, 11.68933342079726856, 12.24220494005076176,
|
||||
12.80182748008146909, 13.36802367147604720, 13.94062521940376342,
|
||||
14.51947222506051816, 15.10441257307551943, 15.69530137706046524,
|
||||
16.29200047656724237, 16.89437797963419285, 17.50230784587389010,
|
||||
18.11566950571089407, 18.73434751193644843, 19.35823122022435427,
|
||||
19.98721449566188468, 20.62119544270163018, 21.26007615624470048,
|
||||
21.90376249182879320, 22.55216385312342098, 23.20519299513386002,
|
||||
23.86276584168908954, 24.52480131594137802, 25.19122118273868338,
|
||||
25.86194990184851861, 26.53691449111561340, 27.21604439872720604,
|
||||
27.89927138384089389, 28.58652940490193828, 29.27775451504081516,
|
||||
29.97288476399884871, 30.67186010608067548, 31.37462231367769050,
|
||||
32.08111489594735843, 32.79128302226991565, 33.50507345013689076,
|
||||
34.22243445715505317, 34.94331577687681545, 35.66766853819134298,
|
||||
36.39544520803305261, 37.12659953718355865, 37.86108650896109395,
|
||||
38.59886229060776230, 39.33988418719949465, 40.08411059791735198,
|
||||
40.83150097453079752, 41.58201578195490100, 42.33561646075348506,
|
||||
43.09226539146988699, 43.85192586067515208, 44.61456202863158893,
|
||||
45.38013889847690052, 46.14862228684032885, 46.91997879580877395,
|
||||
47.69417578616628361, 48.47118135183522014, 49.25096429545256882,
|
||||
50.03349410501914463, 50.81874093156324790, 51.60667556776436982,
|
||||
52.39726942748592364, 53.19049452616926743, 53.98632346204390586,
|
||||
54.78472939811231157, 55.58568604486942633, 56.38916764371992940,
|
||||
57.19514895105859864, 58.00360522298051080, 58.81451220059079787,
|
||||
59.62784609588432261, 60.44358357816834371, 61.26170176100199427,
|
||||
62.08217818962842927, 62.90499082887649962, 63.73011805151035958,
|
||||
64.55753862700632340, 65.38723171073768015, 66.21917683354901385,
|
||||
67.05335389170279825, 67.88974313718154008, 68.72832516833013017,
|
||||
69.56908092082363737, 70.41199165894616385, 71.25703896716800045,
|
||||
72.10420474200799390, 72.95347118416940191, 73.80482079093779646,
|
||||
74.65823634883015814, 75.51370092648485866, 76.37119786778275454,
|
||||
77.23071078519033961, 78.09222355331530707, 78.95572030266725960,
|
||||
79.82118541361435859, 80.68860351052903468, 81.55795945611502873,
|
||||
82.42923834590904164, 83.30242550295004378, 84.17750647261028973,
|
||||
85.05446701758152983, 85.93329311301090456, 86.81397094178107920,
|
||||
87.69648688992882057, 88.58082754219766741, 89.46697967771913795,
|
||||
90.35493026581838194, 91.24466646193963015, 92.13617560368709292,
|
||||
93.02944520697742803, 93.92446296229978486, 94.82121673107967297,
|
||||
95.71969454214321615, 96.61988458827809723, 97.52177522288820910,
|
||||
98.42535495673848800, 99.33061245478741341, 100.23753653310367895,
|
||||
101.14611615586458981, 102.05634043243354370, 102.96819861451382394,
|
||||
103.88168009337621811, 104.79677439715833032, 105.71347118823287303,
|
||||
106.63176026064346047, 107.55163153760463501, 108.47307506906540198,
|
||||
109.39608102933323153, 110.32063971475740516, 111.24674154146920557,
|
||||
112.17437704317786995, 113.10353686902013237, 114.03421178146170689,
|
||||
114.96639265424990128, 115.90007047041454769, 116.83523632031698014,
|
||||
117.77188139974506953, 118.70999700805310795, 119.64957454634490830,
|
||||
120.59060551569974962, 121.53308151543865279, 122.47699424143097247,
|
||||
123.42233548443955726, 124.36909712850338394, 125.31727114935689826,
|
||||
126.26684961288492559, 127.21782467361175861, 128.17018857322420899,
|
||||
129.12393363912724453, 130.07905228303084755, 131.03553699956862033,
|
||||
131.99338036494577864, 132.95257503561629164, 133.91311374698926784,
|
||||
134.87498931216194364, 135.83819462068046846, 136.80272263732638294,
|
||||
137.76856640092901785, 138.73571902320256299, 139.70417368760718091,
|
||||
140.67392364823425055, 141.64496222871400732, 142.61728282114600574,
|
||||
143.59087888505104047, 144.56574394634486680, 145.54187159633210058,
|
||||
146.51925549072063859, 147.49788934865566148, 148.47776695177302031,
|
||||
149.45888214327129617, 150.44122882700193600, 151.42480096657754984,
|
||||
152.40959258449737490, 153.39559776128982094, 154.38281063467164245,
|
||||
155.37122539872302696, 156.36083630307879844, 157.35163765213474107,
|
||||
158.34362380426921391, 159.33678917107920370, 160.33112821663092973,
|
||||
161.32663545672428995, 162.32330545817117695, 163.32113283808695314,
|
||||
164.32011226319519892, 165.32023844914485267, 166.32150615984036790,
|
||||
167.32391020678358018, 168.32744544842768164, 169.33210678954270634,
|
||||
170.33788918059275375, 171.34478761712384198, 172.35279713916281707,
|
||||
173.36191283062726143, 174.37212981874515094, 175.38344327348534080,
|
||||
176.39584840699734514, 177.40934047306160437, 178.42391476654847793,
|
||||
179.43956662288721304, 180.45629141754378111, 181.47408456550741107,
|
||||
182.49294152078630304, 183.51285777591152737, 184.53382886144947861,
|
||||
185.55585034552262869, 186.57891783333786861, 187.60302696672312095,
|
||||
188.62817342367162610, 189.65435291789341932, 190.68156119837468054,
|
||||
191.70979404894376330, 192.73904728784492590, 193.76931676731820176,
|
||||
194.80059837318714244, 195.83288802445184729, 196.86618167288995096,
|
||||
197.90047530266301123, 198.93576492992946214, 199.97204660246373464,
|
||||
201.00931639928148797, 202.04757043027063901, 203.08680483582807597,
|
||||
204.12701578650228385, 205.16819948264117102, 206.21035215404597807,
|
||||
207.25347005962987623, 208.29754948708190909, 209.34258675253678916,
|
||||
210.38857820024875878, 211.43552020227099320, 212.48340915813977858,
|
||||
213.53224149456323744, 214.58201366511514152, 215.63272214993284592,
|
||||
216.68436345542014010, 217.73693411395422004, 218.79043068359703739,
|
||||
219.84484974781133815, 220.90018791517996988, 221.95644181913033322,
|
||||
223.01360811766215875, 224.07168349307951871, 225.13066465172661879,
|
||||
226.19054832372759734, 227.25133126272962159, 228.31301024565024704,
|
||||
229.37558207242807384, 230.43904356577689896, 231.50339157094342113,
|
||||
232.56862295546847008, 233.63473460895144740, 234.70172344281823484,
|
||||
235.76958639009222907, 236.83832040516844586, 237.90792246359117712,
|
||||
238.97838956183431947, 240.04971871708477238, 241.12190696702904802,
|
||||
242.19495136964280846, 243.26884900298270509, 244.34359696498191283,
|
||||
245.41919237324782443, 246.49563236486270057, 247.57291409618682110,
|
||||
248.65103474266476269, 249.72999149863338175, 250.80978157713354904,
|
||||
251.89040220972316320, 252.97185064629374551, 254.05412415488834199,
|
||||
255.13722002152300661, 256.22113555000953511, 257.30586806178126835,
|
||||
258.39141489572085675, 259.47777340799029844, 260.56494097186322279,
|
||||
261.65291497755913497, 262.74169283208021852, 263.83127195904967266,
|
||||
264.92164979855277807, 266.01282380697938379, 267.10479145686849733,
|
||||
268.19755023675537586, 269.29109765101975427, 270.38543121973674488,
|
||||
271.48054847852881721, 272.57644697842033565, 273.67312428569374561,
|
||||
274.77057798174683967, 275.86880566295326389, 276.96780494052313770,
|
||||
278.06757344036617496, 279.16810880295668085, 280.26940868320008349,
|
||||
281.37147075030043197, 282.47429268763045229, 283.57787219260217171,
|
||||
284.68220697654078322, 285.78729476455760050, 286.89313329542699194,
|
||||
287.99972032146268930, 289.10705360839756395, 290.21513093526289140,
|
||||
291.32395009427028754, 292.43350889069523646, 293.54380514276073200,
|
||||
294.65483668152336350, 295.76660135076059532, 296.87909700685889902,
|
||||
297.99232151870342022, 299.10627276756946458, 300.22094864701409733,
|
||||
301.33634706277030091, 302.45246593264130297, 303.56930318639643929,
|
||||
304.68685676566872189, 305.80512462385280514, 306.92410472600477078,
|
||||
308.04379504874236773, 309.16419358014690033, 310.28529831966631036,
|
||||
311.40710727801865687, 312.52961847709792664, 313.65282994987899201,
|
||||
314.77673974032603610, 315.90134590329950015, 317.02664650446632777,
|
||||
318.15263962020929966, 319.27932333753892635, 320.40669575400545455,
|
||||
321.53475497761127144, 322.66349912672620803, 323.79292633000159185,
|
||||
324.92303472628691452, 326.05382246454587403, 327.18528770377525916,
|
||||
328.31742861292224234, 329.45024337080525356, 330.58373016603343331,
|
||||
331.71788719692847280, 332.85271267144611329, 333.98820480709991898,
|
||||
335.12436183088397001, 336.26118197919845443, 337.39866349777429377,
|
||||
338.53680464159958774, 339.67560367484657036, 340.81505887079896411,
|
||||
341.95516851178109619, 343.09593088908627578, 344.23734430290727460,
|
||||
345.37940706226686416, 346.52211748494903532, 347.66547389743118401,
|
||||
348.80947463481720661, 349.95411804077025408, 351.09940246744753267,
|
||||
352.24532627543504759, 353.39188783368263103, 354.53908551944078908,
|
||||
355.68691771819692349, 356.83538282361303118, 357.98447923746385868,
|
||||
359.13420536957539753
|
||||
};
|
||||
|
||||
TEST_BEGIN(test_ln_gamma_misc)
|
||||
{
|
||||
unsigned i;
|
||||
|
||||
for (i = 1; i < sizeof(ln_gamma_misc_expected)/sizeof(double); i++) {
|
||||
double x = (double)i * 0.25;
|
||||
assert_true(double_eq_rel(ln_gamma(x),
|
||||
ln_gamma_misc_expected[i], MAX_REL_ERR, MAX_ABS_ERR),
|
||||
"Incorrect ln_gamma result for i=%u", i);
|
||||
}
|
||||
}
|
||||
TEST_END
|
||||
|
||||
/* Expected pt_norm([0.01..0.99] increment=0.01). */
|
||||
static const double pt_norm_expected[] = {
|
||||
-INFINITY,
|
||||
-2.32634787404084076, -2.05374891063182252, -1.88079360815125085,
|
||||
-1.75068607125216946, -1.64485362695147264, -1.55477359459685305,
|
||||
-1.47579102817917063, -1.40507156030963221, -1.34075503369021654,
|
||||
-1.28155156554460081, -1.22652812003661049, -1.17498679206608991,
|
||||
-1.12639112903880045, -1.08031934081495606, -1.03643338949378938,
|
||||
-0.99445788320975281, -0.95416525314619416, -0.91536508784281390,
|
||||
-0.87789629505122846, -0.84162123357291418, -0.80642124701824025,
|
||||
-0.77219321418868492, -0.73884684918521371, -0.70630256284008752,
|
||||
-0.67448975019608171, -0.64334540539291685, -0.61281299101662701,
|
||||
-0.58284150727121620, -0.55338471955567281, -0.52440051270804067,
|
||||
-0.49585034734745320, -0.46769879911450812, -0.43991316567323380,
|
||||
-0.41246312944140462, -0.38532046640756751, -0.35845879325119373,
|
||||
-0.33185334643681652, -0.30548078809939738, -0.27931903444745404,
|
||||
-0.25334710313579978, -0.22754497664114931, -0.20189347914185077,
|
||||
-0.17637416478086135, -0.15096921549677725, -0.12566134685507399,
|
||||
-0.10043372051146975, -0.07526986209982976, -0.05015358346473352,
|
||||
-0.02506890825871106, 0.00000000000000000, 0.02506890825871106,
|
||||
0.05015358346473366, 0.07526986209982990, 0.10043372051146990,
|
||||
0.12566134685507413, 0.15096921549677739, 0.17637416478086146,
|
||||
0.20189347914185105, 0.22754497664114931, 0.25334710313579978,
|
||||
0.27931903444745404, 0.30548078809939738, 0.33185334643681652,
|
||||
0.35845879325119373, 0.38532046640756762, 0.41246312944140484,
|
||||
0.43991316567323391, 0.46769879911450835, 0.49585034734745348,
|
||||
0.52440051270804111, 0.55338471955567303, 0.58284150727121620,
|
||||
0.61281299101662701, 0.64334540539291685, 0.67448975019608171,
|
||||
0.70630256284008752, 0.73884684918521371, 0.77219321418868492,
|
||||
0.80642124701824036, 0.84162123357291441, 0.87789629505122879,
|
||||
0.91536508784281423, 0.95416525314619460, 0.99445788320975348,
|
||||
1.03643338949378938, 1.08031934081495606, 1.12639112903880045,
|
||||
1.17498679206608991, 1.22652812003661049, 1.28155156554460081,
|
||||
1.34075503369021654, 1.40507156030963265, 1.47579102817917085,
|
||||
1.55477359459685394, 1.64485362695147308, 1.75068607125217102,
|
||||
1.88079360815125041, 2.05374891063182208, 2.32634787404084076
|
||||
};
|
||||
|
||||
TEST_BEGIN(test_pt_norm)
|
||||
{
|
||||
unsigned i;
|
||||
|
||||
for (i = 1; i < sizeof(pt_norm_expected)/sizeof(double); i++) {
|
||||
double p = (double)i * 0.01;
|
||||
assert_true(double_eq_rel(pt_norm(p), pt_norm_expected[i],
|
||||
MAX_REL_ERR, MAX_ABS_ERR),
|
||||
"Incorrect pt_norm result for i=%u", i);
|
||||
}
|
||||
}
|
||||
TEST_END
|
||||
|
||||
/*
|
||||
* Expected pt_chi2(p=[0.01..0.99] increment=0.07,
|
||||
* df={0.1, 1.1, 10.1, 100.1, 1000.1}).
|
||||
*/
|
||||
static const double pt_chi2_df[] = {0.1, 1.1, 10.1, 100.1, 1000.1};
|
||||
static const double pt_chi2_expected[] = {
|
||||
1.168926411457320e-40, 1.347680397072034e-22, 3.886980416666260e-17,
|
||||
8.245951724356564e-14, 2.068936347497604e-11, 1.562561743309233e-09,
|
||||
5.459543043426564e-08, 1.114775688149252e-06, 1.532101202364371e-05,
|
||||
1.553884683726585e-04, 1.239396954915939e-03, 8.153872320255721e-03,
|
||||
4.631183739647523e-02, 2.473187311701327e-01, 2.175254800183617e+00,
|
||||
|
||||
0.0003729887888876379, 0.0164409238228929513, 0.0521523015190650113,
|
||||
0.1064701372271216612, 0.1800913735793082115, 0.2748704281195626931,
|
||||
0.3939246282787986497, 0.5420727552260817816, 0.7267265822221973259,
|
||||
0.9596554296000253670, 1.2607440376386165326, 1.6671185084541604304,
|
||||
2.2604828984738705167, 3.2868613342148607082, 6.9298574921692139839,
|
||||
|
||||
2.606673548632508, 4.602913725294877, 5.646152813924212,
|
||||
6.488971315540869, 7.249823275816285, 7.977314231410841,
|
||||
8.700354939944047, 9.441728024225892, 10.224338321374127,
|
||||
11.076435368801061, 12.039320937038386, 13.183878752697167,
|
||||
14.657791935084575, 16.885728216339373, 23.361991680031817,
|
||||
|
||||
70.14844087392152, 80.92379498849355, 85.53325420085891,
|
||||
88.94433120715347, 91.83732712857017, 94.46719943606301,
|
||||
96.96896479994635, 99.43412843510363, 101.94074719829733,
|
||||
104.57228644307247, 107.43900093448734, 110.71844673417287,
|
||||
114.76616819871325, 120.57422505959563, 135.92318818757556,
|
||||
|
||||
899.0072447849649, 937.9271278858220, 953.8117189560207,
|
||||
965.3079371501154, 974.8974061207954, 983.4936235182347,
|
||||
991.5691170518946, 999.4334123954690, 1007.3391826856553,
|
||||
1015.5445154999951, 1024.3777075619569, 1034.3538789836223,
|
||||
1046.4872561869577, 1063.5717461999654, 1107.0741966053859
|
||||
};
|
||||
|
||||
TEST_BEGIN(test_pt_chi2)
|
||||
{
|
||||
unsigned i, j;
|
||||
unsigned e = 0;
|
||||
|
||||
for (i = 0; i < sizeof(pt_chi2_df)/sizeof(double); i++) {
|
||||
double df = pt_chi2_df[i];
|
||||
double ln_gamma_df = ln_gamma(df * 0.5);
|
||||
for (j = 1; j < 100; j += 7) {
|
||||
double p = (double)j * 0.01;
|
||||
assert_true(double_eq_rel(pt_chi2(p, df, ln_gamma_df),
|
||||
pt_chi2_expected[e], MAX_REL_ERR, MAX_ABS_ERR),
|
||||
"Incorrect pt_chi2 result for i=%u, j=%u", i, j);
|
||||
e++;
|
||||
}
|
||||
}
|
||||
}
|
||||
TEST_END
|
||||
|
||||
/*
|
||||
* Expected pt_gamma(p=[0.1..0.99] increment=0.07,
|
||||
* shape=[0.5..3.0] increment=0.5).
|
||||
*/
|
||||
static const double pt_gamma_shape[] = {0.5, 1.0, 1.5, 2.0, 2.5, 3.0};
|
||||
static const double pt_gamma_expected[] = {
|
||||
7.854392895485103e-05, 5.043466107888016e-03, 1.788288957794883e-02,
|
||||
3.900956150232906e-02, 6.913847560638034e-02, 1.093710833465766e-01,
|
||||
1.613412523825817e-01, 2.274682115597864e-01, 3.114117323127083e-01,
|
||||
4.189466220207417e-01, 5.598106789059246e-01, 7.521856146202706e-01,
|
||||
1.036125427911119e+00, 1.532450860038180e+00, 3.317448300510606e+00,
|
||||
|
||||
0.01005033585350144, 0.08338160893905107, 0.16251892949777497,
|
||||
0.24846135929849966, 0.34249030894677596, 0.44628710262841947,
|
||||
0.56211891815354142, 0.69314718055994529, 0.84397007029452920,
|
||||
1.02165124753198167, 1.23787435600161766, 1.51412773262977574,
|
||||
1.89711998488588196, 2.52572864430825783, 4.60517018598809091,
|
||||
|
||||
0.05741590094955853, 0.24747378084860744, 0.39888572212236084,
|
||||
0.54394139997444901, 0.69048812513915159, 0.84311389861296104,
|
||||
1.00580622221479898, 1.18298694218766931, 1.38038096305861213,
|
||||
1.60627736383027453, 1.87396970522337947, 2.20749220408081070,
|
||||
2.65852391865854942, 3.37934630984842244, 5.67243336507218476,
|
||||
|
||||
0.1485547402532659, 0.4657458011640391, 0.6832386130709406,
|
||||
0.8794297834672100, 1.0700752852474524, 1.2629614217350744,
|
||||
1.4638400448580779, 1.6783469900166610, 1.9132338090606940,
|
||||
2.1778589228618777, 2.4868823970010991, 2.8664695666264195,
|
||||
3.3724415436062114, 4.1682658512758071, 6.6383520679938108,
|
||||
|
||||
0.2771490383641385, 0.7195001279643727, 0.9969081732265243,
|
||||
1.2383497880608061, 1.4675206597269927, 1.6953064251816552,
|
||||
1.9291243435606809, 2.1757300955477641, 2.4428032131216391,
|
||||
2.7406534569230616, 3.0851445039665513, 3.5043101122033367,
|
||||
4.0575997065264637, 4.9182956424675286, 7.5431362346944937,
|
||||
|
||||
0.4360451650782932, 0.9983600902486267, 1.3306365880734528,
|
||||
1.6129750834753802, 1.8767241606994294, 2.1357032436097660,
|
||||
2.3988853336865565, 2.6740603137235603, 2.9697561737517959,
|
||||
3.2971457713883265, 3.6731795898504660, 4.1275751617770631,
|
||||
4.7230515633946677, 5.6417477865306020, 8.4059469148854635
|
||||
};
|
||||
|
||||
TEST_BEGIN(test_pt_gamma_shape)
|
||||
{
|
||||
unsigned i, j;
|
||||
unsigned e = 0;
|
||||
|
||||
for (i = 0; i < sizeof(pt_gamma_shape)/sizeof(double); i++) {
|
||||
double shape = pt_gamma_shape[i];
|
||||
double ln_gamma_shape = ln_gamma(shape);
|
||||
for (j = 1; j < 100; j += 7) {
|
||||
double p = (double)j * 0.01;
|
||||
assert_true(double_eq_rel(pt_gamma(p, shape, 1.0,
|
||||
ln_gamma_shape), pt_gamma_expected[e], MAX_REL_ERR,
|
||||
MAX_ABS_ERR),
|
||||
"Incorrect pt_gamma result for i=%u, j=%u", i, j);
|
||||
e++;
|
||||
}
|
||||
}
|
||||
}
|
||||
TEST_END
|
||||
|
||||
TEST_BEGIN(test_pt_gamma_scale)
|
||||
{
|
||||
double shape = 1.0;
|
||||
double ln_gamma_shape = ln_gamma(shape);
|
||||
|
||||
assert_true(double_eq_rel(
|
||||
pt_gamma(0.5, shape, 1.0, ln_gamma_shape) * 10.0,
|
||||
pt_gamma(0.5, shape, 10.0, ln_gamma_shape), MAX_REL_ERR,
|
||||
MAX_ABS_ERR),
|
||||
"Scale should be trivially equivalent to external multiplication");
|
||||
}
|
||||
TEST_END
|
||||
|
||||
int
|
||||
main(void)
|
||||
{
|
||||
|
||||
return (test(
|
||||
test_ln_gamma_factorial,
|
||||
test_ln_gamma_misc,
|
||||
test_pt_norm,
|
||||
test_pt_chi2,
|
||||
test_pt_gamma_shape,
|
||||
test_pt_gamma_scale));
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user