diff options
Diffstat (limited to 'math')
| -rw-r--r-- | math/Makefile | 11 | ||||
| -rw-r--r-- | math/atest-exp.c | 191 | ||||
| -rw-r--r-- | math/atest-sincos.c | 275 | ||||
| -rw-r--r-- | math/libm-test.c | 14 |
4 files changed, 480 insertions, 11 deletions
diff --git a/math/Makefile b/math/Makefile index 3b1ff4332b..62619111c9 100644 --- a/math/Makefile +++ b/math/Makefile @@ -77,14 +77,15 @@ 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 + test-ifloat test-idouble test-matherr test-fenv \ + atest-exp atest-sincos # We do the `long double' tests only if this data type is available and # distrinct from `double'. test-longdouble-yes = test-ldouble test-ildoubl -CFLAGS-test-float.c = -fno-inline -CFLAGS-test-double.c = -fno-inline -CFLAGS-test-ldouble.c = -fno-inline +CFLAGS-test-float.c = -fno-inline -ffloat-store +CFLAGS-test-double.c = -fno-inline -ffloat-store +CFLAGS-test-ldouble.c = -fno-inline -ffloat-store LDLIBS-test-ifloat = math/libm LDLIBS-test-idouble = math/libm LDLIBS-test-ildoubl = math/libm @@ -92,6 +93,8 @@ LDLIBS-test-float = math/libm LDLIBS-test-double = math/libm LDLIBS-test-ldouble = math/libm LDLIBS-test-matherr = math/libm +LDLIBS-atest-exp = math/libm +LDLIBS-atest-sincos = math/libm distribute += libm-test.c diff --git a/math/atest-exp.c b/math/atest-exp.c new file mode 100644 index 0000000000..28e572c444 --- /dev/null +++ b/math/atest-exp.c @@ -0,0 +1,191 @@ +/* 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 <stdlib/gmp.h> +#include <string.h> +#include <limits.h> +#include <assert.h> + +#define PRINT_ERRORS 0 + +#define TOL 80 +#define N2 17 +#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 hexdig[] = "0123456789abcdef"; + +void +print_mpn_hex (const mp_limb_t *x, unsigned size) +{ + char value[size + 1]; + unsigned i; + const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size; + + memset (value, '0', size); + + for (i = 0; i < final ; i++) + value[size - 1 - i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf]; + + value[size] = '\0'; + fputs (value, stdout); +} + +void +exp_mpn (mp1 ex, mp1 x) +{ + unsigned 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); +} + +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); + exp_mpn (ex, x); + de2 = exp (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_hex (ex, (FRAC / 4) + 1); + fputs ("\n ",stdout); + print_mpn_hex (e2, (FRAC / 4) + 1); + printf ("\n %c ", + e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P'); + print_mpn_hex (e3, (FRAC / 4) + 1); + 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); + + memset (e2, '\0', sizeof (mp1)); + for (i = -1; i < 100 && i < FRAC / 4; i++) + e2[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, exp1[i + 1]) - hexdig + << (FRAC - i * 4 - 4) % mpbpl); + + 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_hex (maxerror, (FRAC / 4) + 1); + fputs ("\nerror in exp(1): ", stdout); + print_mpn_hex (e3, (FRAC / 4) + 1); + putchar ('\n'); + + return failures == 0 ? 0 : 1; +} diff --git a/math/atest-sincos.c b/math/atest-sincos.c new file mode 100644 index 0000000000..98f1e719b1 --- /dev/null +++ b/math/atest-sincos.c @@ -0,0 +1,275 @@ +/* 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 <stdlib/gmp.h> +#include <string.h> +#include <limits.h> +#include <assert.h> + +#define PRINT_ERRORS 0 + +#define N 0 +#define N2 20 +#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]; + +/* These strings have exactly 100 hex digits in them. */ +static const char sin1[101] = +"d76aa47848677020c6e9e909c50f3c3289e511132f518b4def" +"b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264"; +static const char cos1[101] = +"8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2" +"300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934"; +static const char hexdig[] = "0123456789abcdef"; + +void +print_mpn_hex (const mp_limb_t *x, unsigned size) +{ + char value[size + 1]; + unsigned i; + const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size; + + memset (value, '0', size); + + for (i = 0; i < final ; i++) + value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf]; + + value[size] = '\0'; + fputs (value, stdout); +} + +void +sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix) +{ + int i; + mp2 s[4], c[4]; + mp1 tmp, x; + mp_limb_t chk, round; + + if (ix == NULL) + { + memset (si, 0, sizeof (mp1)); + memset (co, 0, sizeof (mp1)); + co[SZ-1] = 1; + memcpy (x, xx, sizeof (mp1)); + } + else + mpn_sub_n (x, xx, ix, SZ); + + for (i = 0; i < 1 << N; i++) + { +#define add_shift_mulh(d,x,s1,s2,sh,n) \ + /* d = (n ? -1 : 1) * (s1 + (s2>>sh)) * x / (1>>N); */ \ + do { \ + if (s2 != NULL) { \ + if (sh > 0) { \ + assert (sh < mpbpl); \ + mpn_lshift (tmp, s1, SZ, sh); \ + chk = (n ? mpn_sub_n : mpn_add_n)(tmp,tmp,s2+FRAC/mpbpl,SZ); \ + } else \ + chk = (n ? mpn_sub_n : mpn_add_n)(tmp,s1,s2+FRAC/mpbpl,SZ); \ + /* assert(chk == 0); */ \ + mpn_mul_n(d,tmp,x,SZ); \ + } else \ + mpn_mul_n(d,s1,x,SZ); \ + /* assert(d[SZ*2-1] == 0); */ \ + assert(N+sh < mpbpl); \ + if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh); \ + } while(0) +#define summ(d,ss,s,n) \ + /* d = ss +/- (s[0]+2*s[1]+2*s[2]+s[3])/6; */ \ + do { \ + chk = mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ); \ + mpn_lshift(tmp,tmp,SZ,1); \ + chk |= mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ); \ + chk |= mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ); \ + round = mpn_divmod_1(tmp,tmp,SZ,6); \ + /* chk |= mpn_add_1(tmp,tmp,SZ, (round > 3) ); */ \ + chk |= (n ? mpn_sub_n : mpn_add_n)(d,ss,tmp,SZ); \ + /* assert(chk == 0); */ \ + } while (0) + + add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */ + add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */ + add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */ + add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */ + add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */ + add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */ + add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */ + add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */ + summ (si, si, s, 0); /* s = s + (s0+2*s1+2*s2+s3)/6; */ + summ (co, co, c, 1); /* c = c - (c0+2*c1+2*c2+c3)/6; */ + } +#undef add_shift_mulh +#undef summ +} + +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 si, co, x, ox, xt, s2, c2, s3, c3; + int i; + int sin_errors = 0, cos_errors = 0; + int sin_failures = 0, cos_failures = 0; + mp1 sin_maxerror, cos_maxerror; + int sin_maxerror_s = 0, cos_maxerror_s = 0; + const double sf = pow (2, mpbpl); + + /* assert(mpbpl == mp_bits_per_limb); */ + assert(FRAC / mpbpl * mpbpl == FRAC); + + memset (sin_maxerror, 0, sizeof (mp1)); + memset (cos_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 s2s, s3s, c2s, c3s, j; + double ds2,dc2; + + mpn_mul_1 (x, xt, SZ, i); + sincosx_mpn (si, co, x, i == 0 ? NULL : ox); + memcpy (ox, x, sizeof (mp1)); + ds2 = sin (i / (double) (1 << N2)); + dc2 = cos (i / (double) (1 << N2)); + for (j = SZ-1; j >= 0; j--) + { + s2[j] = (mp_limb_t) ds2; + ds2 = (ds2 - s2[j]) * sf; + c2[j] = (mp_limb_t) dc2; + dc2 = (dc2 - c2[j]) * sf; + } + if (mpn_cmp (si, s2, SZ) >= 0) + mpn_sub_n (s3, si, s2, SZ); + else + mpn_sub_n (s3, s2, si, SZ); + if (mpn_cmp (co, c2, SZ) >= 0) + mpn_sub_n (c3, co, c2, SZ); + else + mpn_sub_n (c3, c2, co, SZ); + + s2s = mpn_bitsize (s2, SZ); + s3s = mpn_bitsize (s3, SZ); + c2s = mpn_bitsize (c2, SZ); + c3s = mpn_bitsize (c3, SZ); + if (s3s > 1 && s2s - s3s < 54 + || c3s > 1 && c2s - c3s < 54 + || 0) + { +#if PRINT_ERRORS + printf ("%06x ", i * (0x100000 / (1 << N2))); + print_mpn_hex(si, (FRAC / 4) + 1); + putchar (' '); + print_mpn_hex (co, (FRAC / 4) + 1); + putchar ('\n'); + fputs (" ", stdout); + print_mpn_hex (s2, (FRAC / 4) + 1); + putchar (' '); + print_mpn_hex (c2, (FRAC / 4) + 1); + putchar ('\n'); + printf (" %c%c ", + s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P', + c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P'); + print_mpn_hex (s3, (FRAC / 4) + 1); + putchar (' '); + print_mpn_hex (c3, (FRAC / 4) + 1); + putchar ('\n'); +#endif + sin_errors += s2s - s3s == 53; + cos_errors += c2s - c3s == 53; + sin_failures += s2s - s3s < 53; + cos_failures += c2s - c3s < 53; + } + if (s3s >= sin_maxerror_s + && mpn_cmp (s3, sin_maxerror, SZ) > 0) + { + memcpy (sin_maxerror, s3, sizeof (mp1)); + sin_maxerror_s = s3s; + } + if (c3s >= cos_maxerror_s + && mpn_cmp (c3, cos_maxerror, SZ) > 0) + { + memcpy (cos_maxerror, c3, sizeof (mp1)); + cos_maxerror_s = c3s; + } + } + + /* Check Range-Kutta against precomputed values of sin(1) and cos(1). */ + memset (x, 0, sizeof (mp1)); + x[FRAC / mpbpl] = 1 << FRAC % mpbpl; + sincosx_mpn (si, co, x, ox); + + memset (s2, 0, sizeof (mp1)); + memset (c2, 0, sizeof (mp1)); + for (i = 0; i < 100 && i < FRAC / 4; i++) + { + s2[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, sin1[i]) - hexdig + << (FRAC - i * 4 - 4) % mpbpl); + c2[(FRAC - i * 4 - 4) / mpbpl] |= (strchr (hexdig, cos1[i]) - hexdig + << (FRAC - i * 4 - 4) % mpbpl); + } + + if (mpn_cmp (si, s2, SZ) >= 0) + mpn_sub_n (s3, si, s2, SZ); + else + mpn_sub_n (s3, s2, si, SZ); + if (mpn_cmp (co, c2, SZ) >= 0) + mpn_sub_n (c3, co, c2, SZ); + else + mpn_sub_n (c3, c2, co, SZ); + + printf ("sin:\n"); + printf ("%d failures; %d errors; error rate %0.2f%%\n", + sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2)); + fputs ("maximum error: ", stdout); + print_mpn_hex (sin_maxerror, (FRAC / 4) + 1); + fputs ("\nerror in sin(1): ", stdout); + print_mpn_hex (s3, (FRAC / 4) + 1); + + fputs ("\n\ncos:\n", stdout); + printf ("%d failures; %d errors; error rate %0.2f%%\n", + cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2)); + fputs ("maximum error: ", stdout); + print_mpn_hex (cos_maxerror, (FRAC / 4) + 1); + fputs ("\nerror in cos(1): ", stdout); + print_mpn_hex (c3, (FRAC / 4) + 1); + putchar ('\n'); + + return (sin_failures == 0 && cos_failures == 0) ? 0 : 1; +} diff --git a/math/libm-test.c b/math/libm-test.c index a173a09631..da1de8385f 100644 --- a/math/libm-test.c +++ b/math/libm-test.c @@ -1003,7 +1003,7 @@ cbrt_test (void) CHOOSE (5e-18L, 0, 0)); check_eps ("cbrt (8) == 2", FUNC(cbrt) (8), 2, CHOOSE (5e-17L, 0, 0)); check_eps ("cbrt (-27) == -3", FUNC(cbrt) (-27.0), -3.0, - CHOOSE (3e-16L, 0, 0)); + CHOOSE (3e-16L, 5e-16, 0)); } @@ -1095,7 +1095,7 @@ exp_test (void) check_isinfp ("exp (+inf) == +inf", FUNC(exp) (plus_infty)); check ("exp (-inf) == 0", FUNC(exp) (minus_infty), 0); #endif - check_eps ("exp (1) == e", FUNC(exp) (1), M_E, CHOOSE (4e-18L, 0, 0)); + check_eps ("exp (1) == e", FUNC(exp) (1), M_E, CHOOSE (4e-18L, 5e-16, 0)); } @@ -1129,7 +1129,7 @@ expm1_test (void) #endif check_eps ("expm1 (1) == e-1", FUNC(expm1) (1), M_E - 1.0, - CHOOSE (4e-18L, 0, 0)); + CHOOSE (4e-18L, 0, 2e-7)); } @@ -4600,7 +4600,7 @@ static void inverse_functions (void) { inverse_func_pair_test ("asin(sin(x)) == x", - FUNC(sin), FUNC(asin), 1.0, CHOOSE (2e-18L, 0, 1e-7L)); + FUNC(sin), FUNC(asin), 1.0, CHOOSE (2e-18L, 0, 3e-7L)); inverse_func_pair_test ("sin(asin(x)) == x", FUNC(asin), FUNC(sin), 1.0, 0.0); @@ -4706,14 +4706,14 @@ identities (void) identities1_test (-1, CHOOSE (1e-18L, 0, 1e-7)); identities2_test (0.2L, CHOOSE (1e-19L, 1e-16, 0)); - identities2_test (0.9L, CHOOSE (0, 1e-15, 0)); + identities2_test (0.9L, CHOOSE (0, 1e-15, 2e-7)); identities2_test (0, 0); - identities2_test (-1, CHOOSE (1e-18L, 1e-15, 0)); + identities2_test (-1, CHOOSE (1e-18L, 1e-15, 2e-7)); identities3_test (0.2L, CHOOSE (1e-18L, 0, 1e-7)); identities3_test (0.9L, CHOOSE (1e-18L, 1e-15, 1e-6)); identities3_test (0, CHOOSE (0, 0, 1e-6)); - identities3_test (-1, CHOOSE (1e-18L, 0, 1e-6)); + identities3_test (-1, CHOOSE (1e-18L, 7e-16, 1e-6)); } |