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/* Copyright (C) 2006 Dave Nomura
dcnltc@us.ibm.com
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
This program 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
General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307, USA.
The GNU General Public License is contained in the file COPYING.
*/
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
typedef enum { FALSE=0, TRUE } bool_t;
typedef enum {
FADDS, FSUBS, FMULS, FDIVS,
FMADDS, FMSUBS, FNMADDS, FNMSUBS,
FADD, FSUB, FMUL, FDIV, FMADD,
FMSUB, FNMADD, FNMSUB, FSQRT
} flt_op_t;
typedef enum {
TO_NEAREST=0, TO_ZERO, TO_PLUS_INFINITY, TO_MINUS_INFINITY } round_mode_t;
char *round_mode_name[] = { "near", "zero", "+inf", "-inf" };
const char *flt_op_names[] = {
"fadds", "fsubs", "fmuls", "fdivs",
"fmadds", "fmsubs", "fnmadds", "fnmsubs",
"fadd", "fsub", "fmul", "fdiv", "fmadd", "fmsub", "fnmadd",
"fnmsub", "fsqrt"
};
typedef unsigned int fpscr_t;
typedef union {
float flt;
struct {
unsigned int sign:1;
unsigned int exp:8;
unsigned int frac:23;
} layout;
} flt_overlay;
typedef union {
double dbl;
struct {
unsigned int sign:1;
unsigned int exp:11;
unsigned int frac_hi:20;
unsigned int frac_lo:32;
} layout;
struct {
unsigned int hi;
unsigned int lo;
} dbl_pair;
} dbl_overlay;
void assert_fail(const char *msg,
const char* expr, const char* file, int line, const char*fn);
#define STRING(__str) #__str
#define assert(msg, expr) \
((void) ((expr) ? 0 : \
(assert_fail (msg, STRING(expr), \
__FILE__, __LINE__, \
__PRETTY_FUNCTION__), 0)))
float denorm_small;
double dbl_denorm_small;
float norm_small;
bool_t debug = FALSE;
bool_t long_is_64_bits = sizeof(long) == 8;
void assert_fail (msg, expr, file, line, fn)
const char* msg;
const char* expr;
const char* file;
int line;
const char*fn;
{
printf( "\n%s: %s:%d (%s): Assertion `%s' failed.\n",
msg, file, line, fn, expr );
exit( 1 );
}
void set_rounding_mode(round_mode_t mode)
{
switch(mode) {
case TO_NEAREST:
asm volatile("mtfsfi 7, 0");
break;
case TO_ZERO:
asm volatile("mtfsfi 7, 1");
break;
case TO_PLUS_INFINITY:
asm volatile("mtfsfi 7, 2");
break;
case TO_MINUS_INFINITY:
asm volatile("mtfsfi 7, 3");
break;
}
}
void print_double(char *msg, double dbl)
{
dbl_overlay D;
D.dbl = dbl;
printf("%15s : dbl %-20a = %c(%4d, %05x%08x)\n",
msg, D.dbl, (D.layout.sign == 0 ? '+' : '-'),
D.layout.exp, D.layout.frac_hi, D.layout.frac_lo);
}
void print_single(char *msg, float *flt)
{
flt_overlay F;
F.flt = *flt;
/* NOTE: for the purposes of comparing the fraction of a single with
** a double left shift the .frac so that hex digits are grouped
** from left to right. this is necessary because the size of a
** single mantissa (23) bits is not a multiple of 4
*/
printf("%15s : flt %-20a = %c(%4d, %06x)\n",
msg, F.flt, (F.layout.sign == 0 ? '+' : '-'), F.layout.exp, F.layout.frac << 1);
}
int check_dbl_to_flt_round(round_mode_t mode, double dbl, float *expected)
{
int status = 0;
flt_overlay R, E;
char *result;
char *eq_ne;
set_rounding_mode(mode);
E.flt = *expected;
R.flt = (float)dbl;
if ((R.layout.sign != E.layout.sign) ||
(R.layout.exp != E.layout.exp) ||
(R.layout.frac != E.layout.frac)) {
result = "FAILED";
eq_ne = "!=";
status = 1;
} else {
result = "PASSED";
eq_ne = "==";
status = 0;
}
printf("%s:%s:(double)(%-20a) = %20a",
round_mode_name[mode], result, R.flt, dbl);
if (status) {
print_single("\n\texpected", &E.flt);
print_single("\n\trounded ", &R.flt);
}
putchar('\n');
return status;
}
int test_dbl_to_float_convert(char *msg, float *base)
{
int status = 0;
double half = (double)denorm_small/2;
double qtr = half/2;
double D_hi = (double)*base + half + qtr;
double D_lo = (double)*base + half - qtr;
float F_lo = *base;
float F_hi = F_lo + denorm_small;
/*
** .....+-----+-----+-----+-----+---....
** ^F_lo ^ ^ ^
** D_lo
** D_hi
** F_hi
** F_lo and F_hi are two consecutive single float model numbers
** denorm_small distance apart. D_lo and D_hi are two numbers
** within that range that are not representable as single floats
** and will be rounded to either F_lo or F_hi.
*/
printf("-------------------------- %s --------------------------\n", msg);
if (debug) {
print_double("D_lo", D_lo);
print_double("D_hi", D_hi);
print_single("F_lo", &F_lo);
print_single("F_hi", &F_hi);
}
/* round to nearest */
status |= check_dbl_to_flt_round(TO_NEAREST, D_hi, &F_hi);
status |= check_dbl_to_flt_round(TO_NEAREST, D_lo, &F_lo);
/* round to zero */
status |= check_dbl_to_flt_round(TO_ZERO, D_hi, (D_hi > 0 ? &F_lo : &F_hi));
status |= check_dbl_to_flt_round(TO_ZERO, D_lo, (D_hi > 0 ? &F_lo : &F_hi));
/* round to +inf */
status |= check_dbl_to_flt_round(TO_PLUS_INFINITY, D_hi, &F_hi);
status |= check_dbl_to_flt_round(TO_PLUS_INFINITY, D_lo, &F_hi);
/* round to -inf */
status |= check_dbl_to_flt_round(TO_MINUS_INFINITY, D_hi, &F_lo);
status |= check_dbl_to_flt_round(TO_MINUS_INFINITY, D_lo, &F_lo);
return status;
}
void
init()
{
flt_overlay F;
dbl_overlay D;
/* small is the smallest denormalized single float number */
F.layout.sign = 0;
F.layout.exp = 0;
F.layout.frac = 1;
denorm_small = F.flt; /* == 2^(-149) */
if (debug) {
print_double("float small", F.flt);
}
D.layout.sign = 0;
D.layout.exp = 0;
D.layout.frac_hi = 0;
D.layout.frac_lo = 1;
dbl_denorm_small = D.dbl; /* == 2^(-1022) */
if (debug) {
print_double("double small", D.dbl);
}
/* n_small is the smallest normalized single precision float */
F.layout.exp = 1;
norm_small = F.flt;
}
int check_int_to_flt_round(round_mode_t mode, long L, float *expected)
{
int status = 0;
int I = L;
char *int_name = "int";
flt_overlay R, E;
char *result;
int iter;
set_rounding_mode(mode);
E.flt = *expected;
for (iter = 0; iter < 2; iter++) {
int stat = 0;
R.flt = (iter == 0 ? (float)I : (float)L);
if ((R.layout.sign != E.layout.sign) ||
(R.layout.exp != E.layout.exp) ||
(R.layout.frac != E.layout.frac)) {
result = "FAILED";
stat = 1;
} else {
result = "PASSED";
stat = 0;
}
printf("%s:%s:(float)(%4s)%9d = %11.1f",
round_mode_name[mode], result, int_name, I, R.flt);
if (stat) {
print_single("\n\texpected: %.1f ", &E.flt);
print_single("\n\trounded ", &R.flt);
}
putchar('\n');
status |= stat;
if (!long_is_64_bits) break;
int_name = "long";
}
return status;
}
int check_long_to_dbl_round(round_mode_t mode, long L, double *expected)
{
int status = 0;
dbl_overlay R, E;
char *result;
set_rounding_mode(mode);
E.dbl = *expected;
R.dbl = (double)L;
if ((R.layout.sign != E.layout.sign) ||
(R.layout.exp != E.layout.exp) ||
(R.layout.frac_lo != E.layout.frac_lo) ||
(R.layout.frac_hi != E.layout.frac_hi)) {
result = "FAILED";
status = 1;
} else {
result = "PASSED";
status = 0;
}
printf("%s:%s:(double)(%18ld) = %20.1f",
round_mode_name[mode], result, L, R.dbl);
if (status) {
printf("\n\texpected %.1f : ", E.dbl);
}
putchar('\n');
return status;
}
int test_int_to_float_convert(char *msg)
{
int status = 0;
int int24_hi = 0x03ff0fff;
int int24_lo = 0x03ff0ffd;
float pos_flt_lo = 67047420.0;
float pos_flt_hi = 67047424.0;
float neg_flt_lo = -67047420.0;
float neg_flt_hi = -67047424.0;
printf("-------------------------- %s --------------------------\n", msg);
status |= check_int_to_flt_round(TO_NEAREST, int24_lo, &pos_flt_lo);
status |= check_int_to_flt_round(TO_NEAREST, int24_hi, &pos_flt_hi);
status |= check_int_to_flt_round(TO_ZERO, int24_lo, &pos_flt_lo);
status |= check_int_to_flt_round(TO_ZERO, int24_hi, &pos_flt_lo);
status |= check_int_to_flt_round(TO_PLUS_INFINITY, int24_lo, &pos_flt_hi);
status |= check_int_to_flt_round(TO_PLUS_INFINITY, int24_hi, &pos_flt_hi);
status |= check_int_to_flt_round(TO_MINUS_INFINITY, int24_lo, &pos_flt_lo);
status |= check_int_to_flt_round(TO_MINUS_INFINITY, int24_hi, &pos_flt_lo);
status |= check_int_to_flt_round(TO_NEAREST, -int24_lo, &neg_flt_lo);
status |= check_int_to_flt_round(TO_NEAREST, -int24_hi, &neg_flt_hi);
status |= check_int_to_flt_round(TO_ZERO, -int24_lo, &neg_flt_lo);
status |= check_int_to_flt_round(TO_ZERO, -int24_hi, &neg_flt_lo);
status |= check_int_to_flt_round(TO_PLUS_INFINITY, -int24_lo, &neg_flt_lo);
status |= check_int_to_flt_round(TO_PLUS_INFINITY, -int24_hi, &neg_flt_lo);
status |= check_int_to_flt_round(TO_MINUS_INFINITY, -int24_lo, &neg_flt_hi);
status |= check_int_to_flt_round(TO_MINUS_INFINITY, -int24_hi, &neg_flt_hi);
return status;
}
#ifdef __powerpc64__
int test_long_to_double_convert(char *msg)
{
int status = 0;
long long55_hi = 0x07ff0ffffffffff;
long long55_lo = 0x07ff0fffffffffd;
double pos_dbl_lo = 36012304344547324.0;
double pos_dbl_hi = 36012304344547328.0;
double neg_dbl_lo = -36012304344547324.0;
double neg_dbl_hi = -36012304344547328.0;
printf("-------------------------- %s --------------------------\n", msg);
status |= check_long_to_dbl_round(TO_NEAREST, long55_lo, &pos_dbl_lo);
status |= check_long_to_dbl_round(TO_NEAREST, long55_hi, &pos_dbl_hi);
status |= check_long_to_dbl_round(TO_ZERO, long55_lo, &pos_dbl_lo);
status |= check_long_to_dbl_round(TO_ZERO, long55_hi, &pos_dbl_lo);
status |= check_long_to_dbl_round(TO_PLUS_INFINITY, long55_lo, &pos_dbl_hi);
status |= check_long_to_dbl_round(TO_PLUS_INFINITY, long55_hi, &pos_dbl_hi);
status |= check_long_to_dbl_round(TO_MINUS_INFINITY, long55_lo, &pos_dbl_lo);
status |= check_long_to_dbl_round(TO_MINUS_INFINITY, long55_hi, &pos_dbl_lo);
status |= check_long_to_dbl_round(TO_NEAREST, -long55_lo, &neg_dbl_lo);
status |= check_long_to_dbl_round(TO_NEAREST, -long55_hi, &neg_dbl_hi);
status |= check_long_to_dbl_round(TO_ZERO, -long55_lo, &neg_dbl_lo);
status |= check_long_to_dbl_round(TO_ZERO, -long55_hi, &neg_dbl_lo);
status |= check_long_to_dbl_round(TO_PLUS_INFINITY, -long55_lo, &neg_dbl_lo);
status |= check_long_to_dbl_round(TO_PLUS_INFINITY, -long55_hi, &neg_dbl_lo);
status |= check_long_to_dbl_round(TO_MINUS_INFINITY, -long55_lo, &neg_dbl_hi);
status |= check_long_to_dbl_round(TO_MINUS_INFINITY, -long55_hi, &neg_dbl_hi);
return status;
}
#endif
int check_single_arithmetic_op(flt_op_t op)
{
char *result;
int status = 0;
dbl_overlay R, E;
double qtr, half, fA, fB, fD;
round_mode_t mode;
int q, s;
bool_t two_args = TRUE;
float whole = denorm_small;
#define BINOP(op) \
__asm__ volatile( \
op" %0, %1, %2\n\t" \
: "=f"(fD) : "f"(fA) , "f"(fB));
#define UNOP(op) \
__asm__ volatile( \
op" %0, %1\n\t" \
: "=f"(fD) : "f"(fA));
half = (double)whole/2;
qtr = half/2;
if (debug) {
print_double("qtr", qtr);
print_double("whole", whole);
print_double("2*whole", 2*whole);
}
for (mode = TO_NEAREST; mode <= TO_MINUS_INFINITY; mode++)
for (s = -1; s < 2; s += 2)
for (q = 1; q < 4; q += 2) {
double expected;
double lo = s*whole;
double hi = s*2*whole;
switch(op) {
case FADDS:
fA = s*whole;
fB = s*q*qtr;
break;
case FSUBS:
fA = s*2*whole;
fB = s*(q == 1 ? 3 : 1)*qtr;
break;
case FMULS:
fA = 0.5;
fB = s*(4+q)*half;
break;
case FDIVS:
fA = s*(4+q)*half;
fB = 2.0;
break;
default:
assert("check_single_arithmetic_op: unexpected op",
FALSE);
break;
}
switch(mode) {
case TO_NEAREST:
expected = (q == 1 ? lo : hi);
break;
case TO_ZERO:
expected = lo;
break;
case TO_PLUS_INFINITY:
expected = (s == 1 ? hi : lo);
break;
case TO_MINUS_INFINITY:
expected = (s == 1 ? lo : hi);
break;
}
set_rounding_mode(mode);
/*
** do the double precision dual operation just for comparison
** when debugging
*/
switch(op) {
case FADDS:
BINOP("fadds");
R.dbl = fD;
BINOP("fadd");
break;
case FSUBS:
BINOP("fsubs");
R.dbl = fD;
BINOP("fsub");
break;
case FMULS:
BINOP("fmuls");
R.dbl = fD;
BINOP("fmul");
break;
case FDIVS:
BINOP("fdivs");
R.dbl = fD;
BINOP("fdiv");
break;
default:
assert("check_single_arithmetic_op: unexpected op",
FALSE);
break;
}
#undef UNOP
#undef BINOP
E.dbl = expected;
if ((R.layout.sign != E.layout.sign) ||
(R.layout.exp != E.layout.exp) ||
(R.layout.frac_lo != E.layout.frac_lo) ||
(R.layout.frac_hi != E.layout.frac_hi)) {
result = "FAILED";
status = 1;
} else {
result = "PASSED";
status = 0;
}
printf("%s:%s:%s(%-13a",
round_mode_name[mode], result, flt_op_names[op], fA);
if (two_args) printf(", %-13a", fB);
printf(") = %-13a", R.dbl);
if (status) printf("\n\texpected %a", E.dbl);
putchar('\n');
if (debug) {
print_double("hi", hi);
print_double("lo", lo);
print_double("expected", expected);
print_double("got", R.dbl);
print_double("double result", fD);
}
}
return status;
}
int check_single_guarded_arithmetic_op(flt_op_t op)
{
typedef struct {
int num, den, frac;
} fdivs_t;
char *result;
int status = 0;
flt_overlay A, B, Z;
dbl_overlay Res, Exp;
double fA, fB, fC, fD;
round_mode_t mode;
int g, s;
int arg_count;
fdivs_t divs_guard_cases[16] = {
{ 105, 56, 0x700000 }, /* : 0 */
{ 100, 57, 0x608FB8 }, /* : 1 */
{ 000, 00, 0x000000 }, /* : X */
{ 100, 52, 0x762762 }, /* : 3 */
{ 000, 00, 0x000000 }, /* : X */
{ 100, 55, 0x68BA2E }, /* : 5 */
{ 000, 00, 0x000000 }, /* : X */
{ 100, 51, 0x7AFAFA }, /* : 7 */
{ 000, 00, 0x000000 }, /* : X */
{ 100, 56, 0x649249 }, /* : 9 */
{ 000, 00, 0x000000 }, /* : X */
{ 100, 54, 0x6D097B }, /* : B */
{ 000, 00, 0x000000 }, /* : X */
{ 100, 59, 0x58F2FB }, /* : D */
{ 000, 00, 0x000000 }, /* : X */
{ 101, 52, 0x789D89 } /* : F */
};
/* 0x1.00000 00000000p-3 */
/* set up the invariant fields of B, the arg to cause rounding */
B.flt = 0.0;
B.layout.exp = 124; /* -3 */
/* set up args so result is always Z = 1.200000000000<g>p+0 */
Z.flt = 1.0;
Z.layout.sign = 0;
#define TERNOP(op) \
arg_count = 3; \
__asm__ volatile( \
op" %0, %1, %2, %3\n\t" \
: "=f"(fD) : "f"(fA) , "f"(fB), "f"(fC));
#define BINOP(op) \
arg_count = 2; \
__asm__ volatile( \
op" %0, %1, %2\n\t" \
: "=f"(fD) : "f"(fA) , "f"(fB));
#define UNOP(op) \
arg_count = 1; \
__asm__ volatile( \
op" %0, %1\n\t" \
: "=f"(fD) : "f"(fA));
for (mode = TO_NEAREST; mode <= TO_MINUS_INFINITY; mode++)
for (s = -1; s < 2; s += 2)
for (g = 0; g < 16; g += 1) {
double lo, hi, expected;
int LSB;
int guard = 0;
int z_sign = s;
/*
** one argument will have exponent = 0 as will the result (by
** design) so choose the other argument with exponent -3 to
** force a 3 bit shift for scaling leaving us with 3 guard bits
** and the LSB bit at the bottom of the manitssa.
*/
switch(op) {
case FADDS:
/* 1p+0 + 1.00000<g>p-3 */
B.layout.frac = g;
fB = s*B.flt;
fA = s*1.0;
/* set up Z to be truncated result */
/* mask off LSB from resulting guard bits */
guard = g & 7;
Z.layout.frac = 0x100000 | (g >> 3);
break;
case FSUBS:
/* 1.200002p+0 - 1.000000000000<g>p-3 */
A.flt = 1.125;
/* add enough to avoid scaling of the result */
A.layout.frac |= 0x2;
fA = s*A.flt;
B.layout.frac = g;
fB = s*B.flt;
/* set up Z to be truncated result */
guard = (0x10-g);
Z.layout.frac = guard>>3;
/* mask off LSB from resulting guard bits */
guard &= 7;
break;
case FMULS:
/* 1 + g*2^-23 */
A.flt = 1.0;
A.layout.frac = g;
fA = s*A.flt;
fB = 1.125;
/* set up Z to be truncated result */
Z.flt = 1.0;
Z.layout.frac = 0x100000;
Z.layout.frac |= g + (g>>3);
guard = g & 7;
break;
case FDIVS:
/* g >> 3 == LSB, g & 7 == guard bits */
guard = g & 7;
if ((guard & 1) == 0) {
/* special case: guard bit X = 0 */
A.flt = denorm_small;
A.layout.frac = g;
fA = A.flt;
fB = s*8.0;
Z.flt = 0.0;
Z.layout.frac |= (g >> 3);
} else {
fA = s*divs_guard_cases[g].num;
fB = divs_guard_cases[g].den;
Z.flt = 1.0;
Z.layout.frac = divs_guard_cases[g].frac;
}
break;
case FMADDS:
case FMSUBS:
case FNMADDS:
case FNMSUBS:
/* 1 + g*2^-23 */
A.flt = 1.0;
A.layout.frac = g;
fA = s*A.flt;
fB = 1.125;
/* 1.000001p-1 */
A.flt = 0.5;
A.layout.frac = 1;
fC = (op == FMADDS || op == FNMADDS ? s : -s)*A.flt;
/* set up Z to be truncated result */
z_sign = (op == FNMADDS || op == FNMSUBS ? -s : s);
guard = ((g & 7) + 0x4) & 7;
Z.flt = 1.0;
Z.layout.frac = 0x500000;
Z.layout.frac |= g + (g>>3) + ((g & 7)>> 2 ? 1 : 0);
break;
default:
assert("check_single_arithmetic_op: unexpected op",
FALSE);
break;
}
/* get LSB for tie breaking */
LSB = Z.layout.frac & 1;
/* set up hi and lo */
lo = z_sign*Z.flt;
Z.layout.frac += 1;
hi = z_sign*Z.flt;
switch(mode) {
case TO_NEAREST:
/* look at 3 guard bits to determine expected rounding */
switch(guard) {
case 0:
case 1: case 2: case 3:
expected = lo;
break;
case 4: /* tie: round to even */
if (debug) printf("tie: LSB = %d\n", LSB);
expected = (LSB == 0 ? lo : hi);
break;
case 5: case 6: case 7:
expected = hi;
break;
default:
assert("check_single_guarded_arithmetic_op: unexpected guard",
FALSE);
}
break;
case TO_ZERO:
expected = lo;
break;
case TO_PLUS_INFINITY:
if (guard == 0) {
/* no rounding */
expected = lo;
} else {
expected = (s == 1 ? hi : lo);
}
break;
case TO_MINUS_INFINITY:
if (guard == 0) {
/* no rounding */
expected = lo;
} else {
expected = (s == 1 ? lo : hi);
}
break;
}
set_rounding_mode(mode);
/*
** do the double precision dual operation just for comparison
** when debugging
*/
switch(op) {
case FADDS:
BINOP("fadds");
Res.dbl = fD;
break;
case FSUBS:
BINOP("fsubs");
Res.dbl = fD;
break;
case FMULS:
BINOP("fmuls");
Res.dbl = fD;
break;
case FDIVS:
BINOP("fdivs");
Res.dbl = fD;
break;
case FMADDS:
TERNOP("fmadds");
Res.dbl = fD;
break;
case FMSUBS:
TERNOP("fmsubs");
Res.dbl = fD;
break;
case FNMADDS:
TERNOP("fnmadds");
Res.dbl = fD;
break;
case FNMSUBS:
TERNOP("fnmsubs");
Res.dbl = fD;
break;
default:
assert("check_single_guarded_arithmetic_op: unexpected op",
FALSE);
break;
}
#undef UNOP
#undef BINOP
#undef TERNOP
Exp.dbl = expected;
if ((Res.layout.sign != Exp.layout.sign) ||
(Res.layout.exp != Exp.layout.exp) ||
(Res.layout.frac_lo != Exp.layout.frac_lo) ||
(Res.layout.frac_hi != Exp.layout.frac_hi)) {
result = "FAILED";
status = 1;
} else {
result = "PASSED";
status = 0;
}
printf("%s:%s:%s(%-13f",
round_mode_name[mode], result, flt_op_names[op], fA);
if (arg_count > 1) printf(", %-13a", fB);
if (arg_count > 2) printf(", %-13a", fC);
printf(") = %-13a", Res.dbl);
if (status) printf("\n\texpected %a", Exp.dbl);
putchar('\n');
if (debug) {
print_double("hi", hi);
print_double("lo", lo);
print_double("expected", expected);
print_double("got", Res.dbl);
}
}
return status;
}
int check_double_guarded_arithmetic_op(flt_op_t op)
{
typedef struct {
int num, den, hi, lo;
} fdiv_t;
typedef struct {
double arg;
int exp, hi, lo;
} fsqrt_t;
char *result;
int status = 0;
dbl_overlay A, B, Z;
dbl_overlay Res, Exp;
double fA, fB, fC, fD;
round_mode_t mode;
int g, s;
int arg_count;
fdiv_t div_guard_cases[16] = {
{ 62, 62, 0x00000, 0x00000000 }, /* 0 */
{ 64, 62, 0x08421, 0x08421084 }, /* 1 */
{ 66, 62, 0x10842, 0x10842108 }, /* 2 */
{ 100, 62, 0x9ce73, 0x9ce739ce }, /* 3 */
{ 100, 62, 0x9ce73, 0x9ce739ce }, /* X */
{ 102, 62, 0xa5294, 0xa5294a52 }, /* 5 */
{ 106, 62, 0xb5ad6, 0xb5ad6b5a }, /* 6 */
{ 108, 62, 0xbdef7, 0xbdef7bde }, /* 7 */
{ 108, 108, 0x00000, 0x00000000 }, /* 8 */
{ 112, 62, 0xce739, 0xce739ce7 }, /* 9 */
{ 114, 62, 0xd6b5a, 0xd6b5ad6b }, /* A */
{ 116, 62, 0xdef7b, 0xdef7bdef }, /* B */
{ 84, 62, 0x5ad6b, 0x5ad6b5ad }, /* X */
{ 118, 62, 0xe739c, 0xe739ce73 }, /* D */
{ 90, 62, 0x739ce, 0x739ce739 }, /* E */
{ 92, 62, 0x7bdef, 0x7bdef7bd } /* F */
};
fsqrt_t sqrt_guard_cases[16] = {
{ 0x1.08800p0, 0, 0x04371, 0xd9ab72fb}, /* :0 B8.8440 */
{ 0x0.D2200p0, -1, 0xcfdca, 0xf353049e}, /* :1 A4.6910 */
{ 0x1.A8220p0, 0, 0x49830, 0x2b49cd6d}, /* :2 E9.D411 */
{ 0x1.05A20p0, 0, 0x02cd1, 0x3b44f3bf}, /* :3 B7.82D1 */
{ 0x0.CA820p0, -1, 0xc7607, 0x3cec0937}, /* :4 A1.6541 */
{ 0x1.DCA20p0, 0, 0x5d4f8, 0xd4e4c2b2}, /* :5 F7.EE51 */
{ 0x1.02C80p0, 0, 0x01630, 0x9cde7483}, /* :6 B6.8164 */
{ 0x0.DC800p0, -1, 0xdb2cf, 0xe686fe7c}, /* :7 A8.6E40 */
{ 0x0.CF920p0, -1, 0xcd089, 0xb6860626}, /* :8 A3.67C9 */
{ 0x1.1D020p0, 0, 0x0e1d6, 0x2e78ed9d}, /* :9 BF.8E81 */
{ 0x0.E1C80p0, -1, 0xe0d52, 0x6020fb6b}, /* :A AA.70E4 */
{ 0x0.C8000p0, -1, 0xc48c6, 0x001f0abf}, /* :B A0.6400 */
{ 0x1.48520p0, 0, 0x21e9e, 0xd813e2e2}, /* :C CD.A429 */
{ 0x0.F4C20p0, -1, 0xf4a1b, 0x09bbf0b0}, /* :D B1.7A61 */
{ 0x0.CD080p0, -1, 0xca348, 0x79b907ae}, /* :E A2.6684 */
{ 0x1.76B20p0, 0, 0x35b67, 0x81aed827} /* :F DB.BB59 */
};
/* 0x1.00000 00000000p-3 */
/* set up the invariant fields of B, the arg to cause rounding */
B.dbl = 0.0;
B.layout.exp = 1020;
/* set up args so result is always Z = 1.200000000000<g>p+0 */
Z.dbl = 1.0;
Z.layout.sign = 0;
#define TERNOP(op) \
arg_count = 3; \
__asm__ volatile( \
op" %0, %1, %2, %3\n\t" \
: "=f"(fD) : "f"(fA) , "f"(fB), "f"(fC));
#define BINOP(op) \
arg_count = 2; \
__asm__ volatile( \
op" %0, %1, %2\n\t" \
: "=f"(fD) : "f"(fA) , "f"(fB));
#define UNOP(op) \
arg_count = 1; \
__asm__ volatile( \
op" %0, %1\n\t" \
: "=f"(fD) : "f"(fA));
for (mode = TO_NEAREST; mode <= TO_MINUS_INFINITY; mode++)
for (s = (op != FSQRT ? -1 : 1); s < 2; s += 2)
for (g = 0; g < 16; g += 1) {
double lo, hi, expected;
int LSB;
int guard;
int z_sign = s;
/*
** one argument will have exponent = 0 as will the result (by
** design) so choose the other argument with exponent -3 to
** force a 3 bit shift for scaling leaving us with 3 guard bits
** and the LSB bit at the bottom of the manitssa.
*/
switch(op) {
case FADD:
/* 1p+0 + 1.000000000000<g>p-3 */
B.layout.frac_lo = g;
fB = s*B.dbl;
fA = s*1.0;
/* set up Z to be truncated result */
/* mask off LSB from resulting guard bits */
guard = g & 7;
Z.layout.frac_hi = 0x20000;
Z.layout.frac_lo = g >> 3;
break;
case FSUB:
/* 1.2000000000002p+0 - 1.000000000000<g>p-3 */
A.dbl = 1.125;
/* add enough to avoid scaling of the result */
A.layout.frac_lo = 0x2;
fA = s*A.dbl;
B.layout.frac_lo = g;
fB = s*B.dbl;
/* set up Z to be truncated result */
guard = (0x10-g);
Z.layout.frac_hi = 0x0;
Z.layout.frac_lo = guard>>3;
/* mask off LSB from resulting guard bits */
guard &= 7;
break;
case FMUL:
/* 1 + g*2^-52 */
A.dbl = 1.0;
A.layout.frac_lo = g;
fA = s*A.dbl;
fB = 1.125;
/* set up Z to be truncated result */
Z.dbl = 1.0;
Z.layout.frac_hi = 0x20000;
Z.layout.frac_lo = g + (g>>3);
guard = g & 7;
break;
case FMADD:
case FMSUB:
case FNMADD:
case FNMSUB:
/* 1 + g*2^-52 */
A.dbl = 1.0;
A.layout.frac_lo = g;
fA = s*A.dbl;
fB = 1.125;
/* 1.0000000000001p-1 */
A.dbl = 0.5;
A.layout.frac_lo = 1;
fC = (op == FMADD || op == FNMADD ? s : -s)*A.dbl;
/* set up Z to be truncated result */
z_sign = (op == FNMADD || op == FNMSUB ? -s : s);
guard = ((g & 7) + 0x4) & 7;
Z.dbl = 1.0;
Z.layout.frac_hi = 0xa0000;
Z.layout.frac_lo = g + (g>>3) + ((g & 7)>> 2 ? 1 : 0);
break;
case FDIV:
/* g >> 3 == LSB, g & 7 == guard bits */
guard = g & 7;
if (guard == 0x4) {
/* special case guard bits == 4, inexact tie */
fB = s*2.0;
Z.dbl = 0.0;
if (g >> 3) {
fA = dbl_denorm_small + 2*dbl_denorm_small;
Z.layout.frac_lo = 0x1;
} else {
fA = dbl_denorm_small;
}
} else {
fA = s*div_guard_cases[g].num;
fB = div_guard_cases[g].den;
printf("%d/%d\n",
s*div_guard_cases[g].num,
div_guard_cases[g].den);
Z.dbl = 1.0;
Z.layout.frac_hi = div_guard_cases[g].hi;
Z.layout.frac_lo = div_guard_cases[g].lo;
}
break;
case FSQRT:
fA = s*sqrt_guard_cases[g].arg;
Z.dbl = 1.0;
Z.layout.exp = sqrt_guard_cases[g].exp + 1023;
Z.layout.frac_hi = sqrt_guard_cases[g].hi;
Z.layout.frac_lo = sqrt_guard_cases[g].lo;
guard = g >> 1;
if (g & 1) guard |= 1;
/* don't have test cases for when X bit = 0 */
if (guard == 0 || guard == 4) continue;
break;
default:
assert("check_double_guarded_arithmetic_op: unexpected op",
FALSE);
break;
}
/* get LSB for tie breaking */
LSB = Z.layout.frac_lo & 1;
/* set up hi and lo */
lo = z_sign*Z.dbl;
Z.layout.frac_lo += 1;
hi = z_sign*Z.dbl;
switch(mode) {
case TO_NEAREST:
/* look at 3 guard bits to determine expected rounding */
switch(guard) {
case 0:
case 1: case 2: case 3:
expected = lo;
break;
case 4: /* tie: round to even */
if (debug) printf("tie: LSB = %d\n", LSB);
expected = (LSB == 0 ? lo : hi);
break;
case 5: case 6: case 7:
expected = hi;
break;
default:
assert("check_double_guarded_arithmetic_op: unexpected guard",
FALSE);
}
break;
case TO_ZERO:
expected = lo;
break;
case TO_PLUS_INFINITY:
if (guard == 0) {
/* no rounding */
expected = lo;
} else {
expected = (s == 1 ? hi : lo);
}
break;
case TO_MINUS_INFINITY:
if (guard == 0) {
/* no rounding */
expected = lo;
} else {
expected = (s == 1 ? lo : hi);
}
break;
}
set_rounding_mode(mode);
/*
** do the double precision dual operation just for comparison
** when debugging
*/
switch(op) {
case FADD:
BINOP("fadd");
Res.dbl = fD;
break;
case FSUB:
BINOP("fsub");
Res.dbl = fD;
break;
case FMUL:
BINOP("fmul");
Res.dbl = fD;
break;
case FMADD:
TERNOP("fmadd");
Res.dbl = fD;
break;
case FMSUB:
TERNOP("fmsub");
Res.dbl = fD;
break;
case FNMADD:
TERNOP("fnmadd");
Res.dbl = fD;
break;
case FNMSUB:
TERNOP("fnmsub");
Res.dbl = fD;
break;
case FDIV:
BINOP("fdiv");
Res.dbl = fD;
break;
case FSQRT:
UNOP("fsqrt");
Res.dbl = fD;
break;
default:
assert("check_double_guarded_arithmetic_op: unexpected op",
FALSE);
break;
}
#undef UNOP
#undef BINOP
#undef TERNOP
Exp.dbl = expected;
if ((Res.layout.sign != Exp.layout.sign) ||
(Res.layout.exp != Exp.layout.exp) ||
(Res.layout.frac_lo != Exp.layout.frac_lo) ||
(Res.layout.frac_hi != Exp.layout.frac_hi)) {
result = "FAILED";
status = 1;
} else {
result = "PASSED";
status = 0;
}
printf("%s:%s:%s(%-13a",
round_mode_name[mode], result, flt_op_names[op], fA);
if (arg_count > 1) printf(", %-13a", fB);
if (arg_count > 2) printf(", %-13a", fC);
printf(") = %-13a", Res.dbl);
if (status) printf("\n\texpected %a", Exp.dbl);
putchar('\n');
if (debug) {
print_double("hi", hi);
print_double("lo", lo);
print_double("expected", expected);
print_double("got", Res.dbl);
}
}
return status;
}
int test_float_arithmetic_ops()
{
int status = 0;
flt_op_t op;
/*
** choose FP operands whose result should be rounded to either
** lo or hi.
*/
printf("-------------------------- %s --------------------------\n",
"test rounding of float operators without guard bits");
for (op = FADDS; op <= FDIVS; op++) {
status |= check_single_arithmetic_op(op);
}
printf("-------------------------- %s --------------------------\n",
"test rounding of float operators with guard bits");
for (op = FADDS; op <= FNMSUBS; op++) {
status |= check_single_guarded_arithmetic_op(op);
}
printf("-------------------------- %s --------------------------\n",
"test rounding of double operators with guard bits");
for (op = FADD; op <= FSQRT; op++) {
status |= check_double_guarded_arithmetic_op(op);
}
return status;
}
int
main()
{
int status = 0;
init();
status |= test_dbl_to_float_convert("test denormalized convert", &denorm_small);
status |= test_dbl_to_float_convert("test normalized convert", &norm_small);
status |= test_int_to_float_convert("test (float)int convert");
status |= test_int_to_float_convert("test (float)int convert");
#ifdef __powerpc64__
status |= test_long_to_double_convert("test (double)long convert");
#endif
status |= test_float_arithmetic_ops();
return status;
}