diff options
Diffstat (limited to 'math')
| -rw-r--r-- | math/Makefile | 6 | ||||
| -rw-r--r-- | math/atest-exp2.c | 240 | ||||
| -rw-r--r-- | math/libm-test.c | 3 | ||||
| -rw-r--r-- | math/math_private.h | 3 | ||||
| -rw-r--r-- | math/test-reduce.c | 207 |
5 files changed, 457 insertions, 2 deletions
diff --git a/math/Makefile b/math/Makefile index 62619111c9..bc54d57c43 100644 --- a/math/Makefile +++ b/math/Makefile @@ -51,7 +51,7 @@ libm-calls = e_acos e_acosh e_asin e_atan2 e_atanh e_cosh e_exp e_fmod \ s_floor s_frexp s_ilogb s_ldexp s_log1p s_logb \ s_modf s_nextafter s_rint s_scalbn s_significand \ s_sin s_tan s_tanh w_acos w_acosh w_asin \ - w_atan2 w_atanh w_cosh w_drem w_exp w_fmod w_gamma \ + w_atan2 w_atanh w_cosh w_drem w_exp w_exp2 w_fmod w_gamma \ w_hypot w_j0 w_j1 w_jn w_lgamma w_lgamma_r \ w_log w_log10 w_pow w_remainder w_scalb w_sinh w_sqrt \ s_signbit s_fpclassify s_fmax s_fmin s_fdim s_nan s_trunc \ @@ -78,7 +78,7 @@ distribute += $(long-c-yes:=.c) # Rules for the test suite. tests = test-float test-double $(test-longdouble-$(long-double-fcts)) \ test-ifloat test-idouble test-matherr test-fenv \ - atest-exp atest-sincos + atest-exp atest-sincos atest-exp2 # test-reduce # We do the `long double' tests only if this data type is available and # distrinct from `double'. test-longdouble-yes = test-ldouble test-ildoubl @@ -93,8 +93,10 @@ LDLIBS-test-float = math/libm LDLIBS-test-double = math/libm LDLIBS-test-ldouble = math/libm LDLIBS-test-matherr = math/libm +LDLIBS-test-reduce = math/libm LDLIBS-atest-exp = math/libm LDLIBS-atest-sincos = math/libm +LDLIBS-atest-exp2 = math/libm distribute += libm-test.c diff --git a/math/atest-exp2.c b/math/atest-exp2.c new file mode 100644 index 0000000000..95e72aa507 --- /dev/null +++ b/math/atest-exp2.c @@ -0,0 +1,240 @@ +/* Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +#include <stdio.h> +#include <math.h> +#include <gmp.h> +#include <string.h> +#include <limits.h> +#include <assert.h> +#include <stdlib.h> + +#define PRINT_ERRORS 0 + +#define TOL 80 +#define N2 18 +#define FRAC (32*4) + +#define mpbpl (CHAR_BIT * sizeof (mp_limb_t)) +#define SZ (FRAC / mpbpl + 1) +typedef mp_limb_t mp1[SZ], mp2[SZ * 2]; + +/* This string has 101 hex digits. */ +static const char exp1[102] = "2" /* point */ +"b7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a7" +"84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07"; +static const char exp_m1[102] = "0" /* point */ +"5e2d58d8b3bcdf1abadec7829054f90dda9805aab56c773330" +"24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea"; + +static const char hexdig[] = "0123456789abcdef"; + +void +print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base) +{ + unsigned int i; + mp1 tx; + + memcpy (tx, x, sizeof (mp1)); + if (base == 16) + fputs ("0x", stdout); + assert (x[SZ-1] < base); + fputc (hexdig[x[SZ - 1]], stdout); + fputc ('.', stdout); + for (i = 0; i < dp; i++) + { + tx[SZ - 1] = 0; + mpn_mul_1 (tx, tx, SZ, base); + assert (tx[SZ - 1] < base); + fputc (hexdig[tx[SZ - 1]], stdout); + } +} + +void +read_mpn_hex(mp_limb_t *x, const char *str) +{ + int i; + + memset (x, 0, sizeof (mp1)); + for (i = -1; i < 100 && i < FRAC / 4; ++i) + x[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, str[i + 1]) - hexdig + << (FRAC - i * 4 - 4) % mpbpl); +} + +static mp_limb_t *get_log2(void) __attribute__((const)); +static mp_limb_t * +get_log2(void) +{ + static mp1 log2_m; + static int log2_m_inited = 0; + static const char log2[102] = "0" /* point */ + "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a" + "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e"; + + if (!log2_m_inited) + { + read_mpn_hex (log2_m, log2); + log2_m_inited = 1; + } + return log2_m; +} + +/* Compute e^x. */ +void +exp_mpn (mp1 ex, mp1 x) +{ + unsigned int n; + mp1 xp; + mp2 tmp; + mp_limb_t chk, round; + mp1 tol; + + memset (xp, 0, sizeof (mp1)); + memset (ex, 0, sizeof (mp1)); + xp[FRAC / mpbpl] = 1 << FRAC % mpbpl; + memset (tol, 0, sizeof (mp1)); + tol[(FRAC - TOL) / mpbpl] = 1 << (FRAC - TOL) % mpbpl; + + n = 0; + + do + { + /* Calculate sum(x^n/n!) until the next term is sufficiently small. */ + + mpn_mul_n (tmp, xp, x, SZ); + assert(tmp[SZ * 2 - 1] == 0); + if (n > 0) + round = mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n); + chk = mpn_add_n (ex, ex, xp, SZ); + assert (chk == 0); + ++n; + assert (n < 80); /* Catch too-high TOL. */ + } + while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0); +} + +/* Calculate 2^x. */ +void +exp2_mpn (mp1 ex, mp1 x) +{ + mp2 tmp; + mpn_mul_n (tmp, x, get_log2 (), SZ); + assert(tmp[SZ * 2 - 1] == 0); + exp_mpn (ex, tmp + FRAC / mpbpl); +} + + +static int +mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE) +{ + int i, j; + for (i = SIZE - 1; i > 0; --i) + if (SRC_PTR[i] != 0) + break; + for (j = mpbpl - 1; j > 0; --j) + if ((SRC_PTR[i] & 1 << j) != 0) + break; + + return i * 32 + j; +} + +int +main (void) +{ + mp1 ex, x, xt, e2, e3; + int i; + int errors = 0; + int failures = 0; + mp1 maxerror; + int maxerror_s = 0; + const double sf = pow (2, mpbpl); + + /* assert(mpbpl == mp_bits_per_limb); */ + assert(FRAC / mpbpl * mpbpl == FRAC); + + memset (maxerror, 0, sizeof (mp1)); + memset (xt, 0, sizeof (mp1)); + xt[(FRAC - N2) / mpbpl] = 1 << (FRAC - N2) % mpbpl; + + for (i = 0; i < (1 << N2); ++i) + { + int e2s, e3s, j; + double de2; + + mpn_mul_1 (x, xt, SZ, i); + exp2_mpn (ex, x); + de2 = exp2 (i / (double) (1 << N2)); + for (j = SZ - 1; j >= 0; --j) + { + e2[j] = (mp_limb_t) de2; + de2 = (de2 - e2[j]) * sf; + } + if (mpn_cmp (ex, e2, SZ) >= 0) + mpn_sub_n (e3, ex, e2, SZ); + else + mpn_sub_n (e3, e2, ex, SZ); + + e2s = mpn_bitsize (e2, SZ); + e3s = mpn_bitsize (e3, SZ); + if (e3s > 1 && e2s - e3s < 54) + { +#if PRINT_ERRORS + printf ("%06x ", i * (0x100000 / (1 << N2))); + print_mpn_fp (ex, (FRAC / 4) + 1, 16); + putchar ('\n'); + fputs (" ",stdout); + print_mpn_fp (e2, (FRAC / 4) + 1, 16); + putchar ('\n'); + printf (" %c ", + e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P'); + print_mpn_fp (e3, (FRAC / 4) + 1, 16); + putchar ('\n'); +#endif + errors += (e2s - e3s == 53); + failures += (e2s - e3s < 53); + } + if (e3s >= maxerror_s + && mpn_cmp (e3, maxerror, SZ) > 0) + { + memcpy (maxerror, e3, sizeof (mp1)); + maxerror_s = e3s; + } + } + + /* Check exp_mpn against precomputed value of exp(1). */ + memset (x, 0, sizeof (mp1)); + x[FRAC / mpbpl] = 1 << FRAC % mpbpl; + exp_mpn (ex, x); + read_mpn_hex (e2, exp1); + if (mpn_cmp (ex, e2, SZ) >= 0) + mpn_sub_n (e3, ex, e2, SZ); + else + mpn_sub_n (e3, e2, ex, SZ); + + printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors, + errors * 100.0 / (double) (1 << N2)); + fputs ("maximum error: ", stdout); + print_mpn_fp (maxerror, (FRAC / 4) + 1, 16); + putchar ('\n'); + fputs ("error in exp(1): ", stdout); + print_mpn_fp (e3, (FRAC / 4) + 1, 16); + putchar ('\n'); + + return failures == 0 ? 0 : 1; +} diff --git a/math/libm-test.c b/math/libm-test.c index da1de8385f..2075adcb59 100644 --- a/math/libm-test.c +++ b/math/libm-test.c @@ -1114,6 +1114,9 @@ exp2_test (void) check_isinfp ("exp2 (+inf) == +inf", FUNC(exp2) (plus_infty)); check ("exp2 (-inf) == 0", FUNC(exp2) (minus_infty), 0); check ("exp2 (10) == 1024", FUNC(exp2) (10), 1024); + check ("exp2 (-1) == 0.5", FUNC(exp2) (-1), 0.5); + check_isinfp ("exp2 (1e6) == +inf", FUNC(exp2) (1e6)); + check ("exp2 (-1e6) == 0", FUNC(exp2) (-1e6), 0); } diff --git a/math/math_private.h b/math/math_private.h index 74b729d419..4b3b5be3bf 100644 --- a/math/math_private.h +++ b/math/math_private.h @@ -252,6 +252,7 @@ extern double __ieee754_atanh __P((double)); extern double __ieee754_asin __P((double)); extern double __ieee754_atan2 __P((double,double)); extern double __ieee754_exp __P((double)); +extern double __ieee754_exp2 __P((double)); extern double __ieee754_cosh __P((double)); extern double __ieee754_fmod __P((double,double)); extern double __ieee754_pow __P((double,double)); @@ -290,6 +291,7 @@ extern float __ieee754_atanhf __P((float)); extern float __ieee754_asinf __P((float)); extern float __ieee754_atan2f __P((float,float)); extern float __ieee754_expf __P((float)); +extern float __ieee754_exp2f __P((float)); extern float __ieee754_coshf __P((float)); extern float __ieee754_fmodf __P((float,float)); extern float __ieee754_powf __P((float,float)); @@ -327,6 +329,7 @@ extern long double __ieee754_atanhl __P((long double)); extern long double __ieee754_asinl __P((long double)); extern long double __ieee754_atan2l __P((long double,long double)); extern long double __ieee754_expl __P((long double)); +extern long double __ieee754_exp2l __P((long double)); extern long double __ieee754_coshl __P((long double)); extern long double __ieee754_fmodl __P((long double,long double)); extern long double __ieee754_powl __P((long double,long double)); diff --git a/math/test-reduce.c b/math/test-reduce.c new file mode 100644 index 0000000000..5149ead341 --- /dev/null +++ b/math/test-reduce.c @@ -0,0 +1,207 @@ +/* Copyright (C) 1997 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* This is a generic program for comparing two precisions of a one-input + mathematical function. It is amazingly good at detecting when GCC + folds constants improperly. */ + +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <math.h> +#include <ieee754.h> +#include <fenv.h> +#include <stdio.h> +#include <stdlib.h> +#include <time.h> + +#define TSMALL float +#define RSMALL(rfun) ({ unsigned rnum = (rfun); *(float *) &rnum; }) +#define TBIG double +#define XDIFF (24) +#define REDUCE(x) \ + ({ union ieee754_float u = { x }; u.ieee.exponent = 0x80; x = u.f; }) +#define ABS(x) fabs(x) + +#define string_0(x) #x +#define string_1(x) string_0(x) +#define TBIG_NAME string_1(TBIG) +#define TSMALL_NAME string_1(TSMALL) + +#define R_NEAREST 1 +#define R_ZERO 2 +#define R_UP 4 +#define R_DOWN 8 +#define R_ALL (R_NEAREST|R_ZERO|R_UP|R_DOWN) +static fenv_t rmodes[4]; +static const char * const rmnames[4] = +{ "near","zero","+Inf","-Inf" }; + +static int quiet = 0; + +#ifdef FE_ALL_INVALID +static const int invalid_exceptions = (FE_ALL_INVALID + | FE_INVALID | FE_DIVBYZERO); +#else +static const int invalid_exceptions = (FE_INVALID | FE_DIVBYZERO); +#endif + +static int +checkit (char *fname, + TSMALL (*fsmall) (TSMALL), TBIG (*fbig) (TBIG), + unsigned smalltries, unsigned largetries) +{ + unsigned int i, nerrors = 0, nwarn; + + int tryone (TSMALL fval) + { + int rmode; + int excepts, exceptsb; + TSMALL fres; + TBIG fvalb, fresb, diff; + char warn; + + fvalb = (TBIG) fval; + + for (rmode = 0; rmode < 4; ++rmode) + { + fesetenv (rmodes + rmode); + fres = fsmall (fval); + excepts = fetestexcept (invalid_exceptions); + fesetenv (rmodes + rmode); + fresb = fbig (fvalb); + exceptsb = fetestexcept (invalid_exceptions); + + if (excepts != exceptsb) + { + unsigned char *fvp = (unsigned char *) &fval; + size_t j; + + printf ("%s(", fname); + for (j = 0; j < sizeof (TSMALL); j++) + printf ("%02x", fvp[j]); + printf ("),%s: exceptions %s: %08x, %s: %08x\n", + rmnames[rmode], + TBIG_NAME, exceptsb, TSMALL_NAME, excepts); + if (++nerrors > 10) + return 1; + } + + diff = ABS (fres - (TSMALL) fresb); + if (fres == (TSMALL) fresb + || isnan (fres) && isnan (fresb) + || logb (fresb) - logb (diff) < XDIFF - 1) + continue; + + if (logb (fresb) - logb (diff) < XDIFF) + { + if (++nwarn > 10 || quiet) + continue; + warn = 'w'; + } + else + { + if (++nerrors > 10) + return 1; + warn = 'e'; + } + + { + TSMALL fresbs = (TSMALL) fresb; + unsigned char *fvp = (unsigned char *) &fval; + unsigned char *frp = (unsigned char *) &fres; + unsigned char *frpb = (unsigned char *) &fresb; + unsigned char *frpbs = (unsigned char *) &fresbs; + size_t j; + + printf ("%s(",fname); + for (j = 0; j < sizeof (TSMALL); ++j) + printf ("%02x", fvp[j]); + printf ("),%s: %s ", rmnames[rmode], TBIG_NAME); + for (j = 0; j < sizeof (TBIG); ++j) + printf ("%02x", frpb[j]); + printf (" ("); + for (j = 0; j < sizeof (TSMALL); ++j) + printf ("%02x", frpbs[j]); + printf ("), %s ", TSMALL_NAME); + for (j = 0; j < sizeof (TSMALL); ++j) + printf ("%02x", frp[j]); + printf (" %c\n", warn); + } + } + return 0; + } + + nwarn = 0; + for (i = 0; i < smalltries; i++) + { + TSMALL fval; + + fval = RSMALL (rand () ^ rand () << 16); + REDUCE (fval); + if (tryone (fval)) + break; + } + + printf ("%s-small: %d errors, %d (%0.2f%%) inaccuracies\n", + fname, nerrors, nwarn, + nwarn * 0.25 / ((double) smalltries)); + + nwarn = 0; + for (i = 0; i < largetries; ++i) + { + TSMALL fval; + + fval = RSMALL (rand () ^ rand () << 16); + if (tryone (fval)) + break; + } + + printf ("%s-large: %d errors, %d (%0.2f%%) inaccuracies\n", + fname, nerrors, nwarn, + nwarn * 0.25 / ((double) largetries)); + return nerrors == 0; +} + +int +main (void) +{ + int r; + + _LIB_VERSION = _IEEE_; + + /* Set up environments for rounding modes. */ + fesetenv (FE_DFL_ENV); + fesetround (FE_TONEAREST); + fegetenv (rmodes + 0); + fesetround (FE_TOWARDSZERO); + fegetenv (rmodes + 1); + fesetround (FE_UPWARD); + fegetenv (rmodes + 2); + fesetround (FE_DOWNWARD); + fegetenv (rmodes + 3); + + /* Seed the RNG. */ + srand (time (0)); + + /* Do it. */ + r = checkit ("exp2", exp2f, exp2, 1 << 20, 1 << 15); + r &= checkit ("exp", expf, exp, 1 << 20, 1 << 15); + return r ? 0 : 1; +} |