/* * mathtest.c - test rig for mathlib * * Copyright (c) 1998-2022, Arm Limited. * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception */ #include #include #include #include #include #include #include #include #include #include #include "mathlib.h" #ifndef math_errhandling # define math_errhandling 0 #endif #ifdef __cplusplus #define EXTERN_C extern "C" #else #define EXTERN_C extern #endif #ifndef TRUE #define TRUE 1 #endif #ifndef FALSE #define FALSE 0 #endif #ifdef IMPORT_SYMBOL #define STR2(x) #x #define STR(x) STR2(x) _Pragma(STR(import IMPORT_SYMBOL)) #endif int dmsd, dlsd; int quiet = 0; int doround = 0; unsigned statusmask = FE_ALL_EXCEPT; #define EXTRABITS (12) #define ULPUNIT (1<name, ((test_func*)b)->name); } int is_double_argtype(int argtype) { switch(argtype) { case at_d: case at_d2: case at_dc: case at_dc2: return 1; default: return 0; } } int is_single_argtype(int argtype) { switch(argtype) { case at_s: case at_s2: case at_sc: case at_sc2: return 1; default: return 0; } } int is_double_rettype(int rettype) { switch(rettype) { case rt_d: case rt_dc: case rt_d2: return 1; default: return 0; } } int is_single_rettype(int rettype) { switch(rettype) { case rt_s: case rt_sc: case rt_s2: return 1; default: return 0; } } int is_complex_argtype(int argtype) { switch(argtype) { case at_dc: case at_sc: case at_dc2: case at_sc2: return 1; default: return 0; } } int is_complex_rettype(int rettype) { switch(rettype) { case rt_dc: case rt_sc: return 1; default: return 0; } } /* * Special-case flags indicating that some functions' error * tolerance handling is more complicated than a fixed relative * error bound. */ #define ABSLOWERBOUND 0x4000000000000000LL #define PLUSMINUSPIO2 0x1000000000000000LL #define ARM_PREFIX(x) x #define TFUNC(arg,ret,name,tolerance) { t_func, arg, ret, (void*)&name, m_none, tolerance, #name } #define TFUNCARM(arg,ret,name,tolerance) { t_func, arg, ret, (void*)& ARM_PREFIX(name), m_none, tolerance, #name } #define MFUNC(arg,ret,name,tolerance) { t_macro, arg, ret, NULL, m_##name, tolerance, #name } #ifndef PL /* sincosf wrappers for easier testing. */ static float sincosf_sinf(float x) { float s,c; sincosf(x, &s, &c); return s; } static float sincosf_cosf(float x) { float s,c; sincosf(x, &s, &c); return c; } #endif test_func tfuncs[] = { /* trigonometric */ TFUNC(at_d,rt_d, acos, 4*ULPUNIT), TFUNC(at_d,rt_d, asin, 4*ULPUNIT), TFUNC(at_d,rt_d, atan, 4*ULPUNIT), TFUNC(at_d2,rt_d, atan2, 4*ULPUNIT), TFUNC(at_d,rt_d, tan, 2*ULPUNIT), TFUNC(at_d,rt_d, sin, 2*ULPUNIT), TFUNC(at_d,rt_d, cos, 2*ULPUNIT), TFUNC(at_s,rt_s, acosf, 4*ULPUNIT), TFUNC(at_s,rt_s, asinf, 4*ULPUNIT), TFUNC(at_s,rt_s, atanf, 4*ULPUNIT), TFUNC(at_s2,rt_s, atan2f, 4*ULPUNIT), TFUNCARM(at_s,rt_s, tanf, 4*ULPUNIT), TFUNCARM(at_s,rt_s, sinf, 3*ULPUNIT/4), TFUNCARM(at_s,rt_s, cosf, 3*ULPUNIT/4), #ifndef PL TFUNCARM(at_s,rt_s, sincosf_sinf, 3*ULPUNIT/4), TFUNCARM(at_s,rt_s, sincosf_cosf, 3*ULPUNIT/4), #endif /* hyperbolic */ TFUNC(at_d, rt_d, atanh, 4*ULPUNIT), TFUNC(at_d, rt_d, asinh, 4*ULPUNIT), TFUNC(at_d, rt_d, acosh, 4*ULPUNIT), TFUNC(at_d,rt_d, tanh, 4*ULPUNIT), TFUNC(at_d,rt_d, sinh, 4*ULPUNIT), TFUNC(at_d,rt_d, cosh, 4*ULPUNIT), TFUNC(at_s, rt_s, atanhf, 4*ULPUNIT), TFUNC(at_s, rt_s, asinhf, 4*ULPUNIT), TFUNC(at_s, rt_s, acoshf, 4*ULPUNIT), TFUNC(at_s,rt_s, tanhf, 4*ULPUNIT), TFUNC(at_s,rt_s, sinhf, 4*ULPUNIT), TFUNC(at_s,rt_s, coshf, 4*ULPUNIT), /* exponential and logarithmic */ TFUNC(at_d,rt_d, log, 3*ULPUNIT/4), TFUNC(at_d,rt_d, log10, 3*ULPUNIT), TFUNC(at_d,rt_d, log2, 3*ULPUNIT/4), TFUNC(at_d,rt_d, log1p, 2*ULPUNIT), TFUNC(at_d,rt_d, exp, 3*ULPUNIT/4), TFUNC(at_d,rt_d, exp2, 3*ULPUNIT/4), TFUNC(at_d,rt_d, expm1, ULPUNIT), TFUNCARM(at_s,rt_s, logf, ULPUNIT), TFUNC(at_s,rt_s, log10f, 3*ULPUNIT), TFUNCARM(at_s,rt_s, log2f, ULPUNIT), TFUNC(at_s,rt_s, log1pf, 2*ULPUNIT), TFUNCARM(at_s,rt_s, expf, 3*ULPUNIT/4), TFUNCARM(at_s,rt_s, exp2f, 3*ULPUNIT/4), TFUNC(at_s,rt_s, expm1f, ULPUNIT), /* power */ TFUNC(at_d2,rt_d, pow, 3*ULPUNIT/4), TFUNC(at_d,rt_d, sqrt, ULPUNIT/2), TFUNC(at_d,rt_d, cbrt, 2*ULPUNIT), TFUNC(at_d2, rt_d, hypot, 4*ULPUNIT), TFUNCARM(at_s2,rt_s, powf, ULPUNIT), TFUNC(at_s,rt_s, sqrtf, ULPUNIT/2), TFUNC(at_s,rt_s, cbrtf, 2*ULPUNIT), TFUNC(at_s2, rt_s, hypotf, 4*ULPUNIT), /* error function */ TFUNC(at_d,rt_d, erf, 16*ULPUNIT), TFUNC(at_s,rt_s, erff, 16*ULPUNIT), TFUNC(at_d,rt_d, erfc, 16*ULPUNIT), TFUNC(at_s,rt_s, erfcf, 16*ULPUNIT), /* gamma functions */ TFUNC(at_d,rt_d, tgamma, 16*ULPUNIT), TFUNC(at_s,rt_s, tgammaf, 16*ULPUNIT), TFUNC(at_d,rt_d, lgamma, 16*ULPUNIT | ABSLOWERBOUND), TFUNC(at_s,rt_s, lgammaf, 16*ULPUNIT | ABSLOWERBOUND), TFUNC(at_d,rt_d, ceil, 0), TFUNC(at_s,rt_s, ceilf, 0), TFUNC(at_d2,rt_d, copysign, 0), TFUNC(at_s2,rt_s, copysignf, 0), TFUNC(at_d,rt_d, floor, 0), TFUNC(at_s,rt_s, floorf, 0), TFUNC(at_d2,rt_d, fmax, 0), TFUNC(at_s2,rt_s, fmaxf, 0), TFUNC(at_d2,rt_d, fmin, 0), TFUNC(at_s2,rt_s, fminf, 0), TFUNC(at_d2,rt_d, fmod, 0), TFUNC(at_s2,rt_s, fmodf, 0), MFUNC(at_d, rt_i, fpclassify, 0), MFUNC(at_s, rt_i, fpclassifyf, 0), TFUNC(at_dip,rt_d, frexp, 0), TFUNC(at_sip,rt_s, frexpf, 0), MFUNC(at_d, rt_i, isfinite, 0), MFUNC(at_s, rt_i, isfinitef, 0), MFUNC(at_d, rt_i, isgreater, 0), MFUNC(at_d, rt_i, isgreaterequal, 0), MFUNC(at_s, rt_i, isgreaterequalf, 0), MFUNC(at_s, rt_i, isgreaterf, 0), MFUNC(at_d, rt_i, isinf, 0), MFUNC(at_s, rt_i, isinff, 0), MFUNC(at_d, rt_i, isless, 0), MFUNC(at_d, rt_i, islessequal, 0), MFUNC(at_s, rt_i, islessequalf, 0), MFUNC(at_s, rt_i, islessf, 0), MFUNC(at_d, rt_i, islessgreater, 0), MFUNC(at_s, rt_i, islessgreaterf, 0), MFUNC(at_d, rt_i, isnan, 0), MFUNC(at_s, rt_i, isnanf, 0), MFUNC(at_d, rt_i, isnormal, 0), MFUNC(at_s, rt_i, isnormalf, 0), MFUNC(at_d, rt_i, isunordered, 0), MFUNC(at_s, rt_i, isunorderedf, 0), TFUNC(at_di,rt_d, ldexp, 0), TFUNC(at_si,rt_s, ldexpf, 0), TFUNC(at_ddp,rt_d2, modf, 0), TFUNC(at_ssp,rt_s2, modff, 0), #ifndef BIGRANGERED MFUNC(at_d, rt_d, rred, 2*ULPUNIT), #else MFUNC(at_d, rt_d, m_rred, ULPUNIT), #endif MFUNC(at_d, rt_i, signbit, 0), MFUNC(at_s, rt_i, signbitf, 0), }; /* * keywords are: func size op1 op2 result res2 errno op1r op1i op2r op2i resultr resulti * also we ignore: wrongresult wrongres2 wrongerrno * op1 equivalent to op1r, same with op2 and result */ typedef struct { test_func *func; unsigned op1r[2]; /* real part, also used for non-complex numbers */ unsigned op1i[2]; /* imaginary part */ unsigned op2r[2]; unsigned op2i[2]; unsigned resultr[3]; unsigned resulti[3]; enum { rc_none, rc_zero, rc_infinity, rc_nan, rc_finite } resultc; /* special complex results, rc_none means use resultr and resulti as normal */ unsigned res2[2]; unsigned status; /* IEEE status return, if any */ unsigned maybestatus; /* for optional status, or allowance for spurious */ int nresult; /* number of result words */ int in_err, in_err_limit; int err; int maybeerr; int valid; int comment; int random; } testdetail; enum { /* keywords */ k_errno, k_errno_in, k_error, k_func, k_maybeerror, k_maybestatus, k_op1, k_op1i, k_op1r, k_op2, k_op2i, k_op2r, k_random, k_res2, k_result, k_resultc, k_resulti, k_resultr, k_status, k_wrongres2, k_wrongresult, k_wrongstatus, k_wrongerrno }; char *keywords[] = { "errno", "errno_in", "error", "func", "maybeerror", "maybestatus", "op1", "op1i", "op1r", "op2", "op2i", "op2r", "random", "res2", "result", "resultc", "resulti", "resultr", "status", "wrongres2", "wrongresult", "wrongstatus", "wrongerrno" }; enum { e_0, e_EDOM, e_ERANGE, /* * This enum makes sure that we have the right number of errnos in the * errno[] array */ e_number_of_errnos }; char *errnos[] = { "0", "EDOM", "ERANGE" }; enum { e_none, e_divbyzero, e_domain, e_overflow, e_underflow }; char *errors[] = { "0", "divbyzero", "domain", "overflow", "underflow" }; static int verbose, fo, strict; /* state toggled by random=on / random=off */ static int randomstate; /* Canonify a double NaN: SNaNs all become 7FF00000.00000001 and QNaNs * all become 7FF80000.00000001 */ void canon_dNaN(unsigned a[2]) { if ((a[0] & 0x7FF00000) != 0x7FF00000) return; /* not Inf or NaN */ if (!(a[0] & 0xFFFFF) && !a[1]) return; /* Inf */ a[0] &= 0x7FF80000; /* canonify top word */ a[1] = 0x00000001; /* canonify bottom word */ } /* Canonify a single NaN: SNaNs all become 7F800001 and QNaNs * all become 7FC00001. Returns classification of the NaN. */ void canon_sNaN(unsigned a[1]) { if ((a[0] & 0x7F800000) != 0x7F800000) return; /* not Inf or NaN */ if (!(a[0] & 0x7FFFFF)) return; /* Inf */ a[0] &= 0x7FC00000; /* canonify most bits */ a[0] |= 0x00000001; /* canonify bottom bit */ } /* * Detect difficult operands for FO mode. */ int is_dhard(unsigned a[2]) { if ((a[0] & 0x7FF00000) == 0x7FF00000) return TRUE; /* inf or NaN */ if ((a[0] & 0x7FF00000) == 0 && ((a[0] & 0x7FFFFFFF) | a[1]) != 0) return TRUE; /* denormal */ return FALSE; } int is_shard(unsigned a[1]) { if ((a[0] & 0x7F800000) == 0x7F800000) return TRUE; /* inf or NaN */ if ((a[0] & 0x7F800000) == 0 && (a[0] & 0x7FFFFFFF) != 0) return TRUE; /* denormal */ return FALSE; } /* * Normalise all zeroes into +0, for FO mode. */ void dnormzero(unsigned a[2]) { if (a[0] == 0x80000000 && a[1] == 0) a[0] = 0; } void snormzero(unsigned a[1]) { if (a[0] == 0x80000000) a[0] = 0; } static int find(char *word, char **array, int asize) { int i, j; asize /= sizeof(char *); i = -1; j = asize; /* strictly between i and j */ while (j-i > 1) { int k = (i+j) / 2; int c = strcmp(word, array[k]); if (c > 0) i = k; else if (c < 0) j = k; else /* found it! */ return k; } return -1; /* not found */ } static test_func* find_testfunc(char *word) { int i, j, asize; asize = sizeof(tfuncs)/sizeof(test_func); i = -1; j = asize; /* strictly between i and j */ while (j-i > 1) { int k = (i+j) / 2; int c = strcmp(word, tfuncs[k].name); if (c > 0) i = k; else if (c < 0) j = k; else /* found it! */ return tfuncs + k; } return NULL; /* not found */ } static long long calc_error(unsigned a[2], unsigned b[3], int shift, int rettype) { unsigned r0, r1, r2; int sign, carry; long long result; /* * If either number is infinite, require exact equality. If * either number is NaN, require that both are NaN. If either * of these requirements is broken, return INT_MAX. */ if (is_double_rettype(rettype)) { if ((a[0] & 0x7FF00000) == 0x7FF00000 || (b[0] & 0x7FF00000) == 0x7FF00000) { if (((a[0] & 0x800FFFFF) || a[1]) && ((b[0] & 0x800FFFFF) || b[1]) && (a[0] & 0x7FF00000) == 0x7FF00000 && (b[0] & 0x7FF00000) == 0x7FF00000) return 0; /* both NaN - OK */ if (!((a[0] & 0xFFFFF) || a[1]) && !((b[0] & 0xFFFFF) || b[1]) && a[0] == b[0]) return 0; /* both same sign of Inf - OK */ return LLONG_MAX; } } else { if ((a[0] & 0x7F800000) == 0x7F800000 || (b[0] & 0x7F800000) == 0x7F800000) { if ((a[0] & 0x807FFFFF) && (b[0] & 0x807FFFFF) && (a[0] & 0x7F800000) == 0x7F800000 && (b[0] & 0x7F800000) == 0x7F800000) return 0; /* both NaN - OK */ if (!(a[0] & 0x7FFFFF) && !(b[0] & 0x7FFFFF) && a[0] == b[0]) return 0; /* both same sign of Inf - OK */ return LLONG_MAX; } } /* * Both finite. Return INT_MAX if the signs differ. */ if ((a[0] ^ b[0]) & 0x80000000) return LLONG_MAX; /* * Now it's just straight multiple-word subtraction. */ if (is_double_rettype(rettype)) { r2 = -b[2]; carry = (r2 == 0); r1 = a[1] + ~b[1] + carry; carry = (r1 < a[1] || (carry && r1 == a[1])); r0 = a[0] + ~b[0] + carry; } else { r2 = -b[1]; carry = (r2 == 0); r1 = a[0] + ~b[0] + carry; carry = (r1 < a[0] || (carry && r1 == a[0])); r0 = ~0 + carry; } /* * Forgive larger errors in specialised cases. */ if (shift > 0) { if (shift > 32*3) return 0; /* all errors are forgiven! */ while (shift >= 32) { r2 = r1; r1 = r0; r0 = -(r0 >> 31); shift -= 32; } if (shift > 0) { r2 = (r2 >> shift) | (r1 << (32-shift)); r1 = (r1 >> shift) | (r0 << (32-shift)); r0 = (r0 >> shift) | ((-(r0 >> 31)) << (32-shift)); } } if (r0 & 0x80000000) { sign = 1; r2 = ~r2; carry = (r2 == 0); r1 = 0 + ~r1 + carry; carry = (carry && (r2 == 0)); r0 = 0 + ~r0 + carry; } else { sign = 0; } if (r0 >= (1LL<<(31-EXTRABITS))) return LLONG_MAX; /* many ulps out */ result = (r2 >> (32-EXTRABITS)) & (ULPUNIT-1); result |= r1 << EXTRABITS; result |= (long long)r0 << (32+EXTRABITS); if (sign) result = -result; return result; } /* special named operands */ typedef struct { unsigned op1, op2; char* name; } special_op; static special_op special_ops_double[] = { {0x00000000,0x00000000,"0"}, {0x3FF00000,0x00000000,"1"}, {0x7FF00000,0x00000000,"inf"}, {0x7FF80000,0x00000001,"qnan"}, {0x7FF00000,0x00000001,"snan"}, {0x3ff921fb,0x54442d18,"pi2"}, {0x400921fb,0x54442d18,"pi"}, {0x3fe921fb,0x54442d18,"pi4"}, {0x4002d97c,0x7f3321d2,"3pi4"}, }; static special_op special_ops_float[] = { {0x00000000,0,"0"}, {0x3f800000,0,"1"}, {0x7f800000,0,"inf"}, {0x7fc00000,0,"qnan"}, {0x7f800001,0,"snan"}, {0x3fc90fdb,0,"pi2"}, {0x40490fdb,0,"pi"}, {0x3f490fdb,0,"pi4"}, {0x4016cbe4,0,"3pi4"}, }; /* This is what is returned by the below functions. We need it to handle the sign of the number */ static special_op tmp_op = {0,0,0}; special_op* find_special_op_from_op(unsigned op1, unsigned op2, int is_double) { int i; special_op* sop; if(is_double) { sop = special_ops_double; } else { sop = special_ops_float; } for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) { if(sop->op1 == (op1&0x7fffffff) && sop->op2 == op2) { if(tmp_op.name) free(tmp_op.name); tmp_op.name = malloc(strlen(sop->name)+2); if(op1>>31) { sprintf(tmp_op.name,"-%s",sop->name); } else { strcpy(tmp_op.name,sop->name); } return &tmp_op; } sop++; } return NULL; } special_op* find_special_op_from_name(const char* name, int is_double) { int i, neg=0; special_op* sop; if(is_double) { sop = special_ops_double; } else { sop = special_ops_float; } if(*name=='-') { neg=1; name++; } else if(*name=='+') { name++; } for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) { if(0 == strcmp(name,sop->name)) { tmp_op.op1 = sop->op1; if(neg) { tmp_op.op1 |= 0x80000000; } tmp_op.op2 = sop->op2; return &tmp_op; } sop++; } return NULL; } /* helper function for the below type=0 for single, 1 for double, 2 for no sop */ int do_op(char* q, unsigned* op, const char* name, int num, int sop_type) { int i; int n=num; special_op* sop = NULL; for(i = 0; i < num; i++) { op[i] = 0; } if(sop_type<2) { sop = find_special_op_from_name(q,sop_type); } if(sop != NULL) { op[0] = sop->op1; op[1] = sop->op2; } else { switch(num) { case 1: n = sscanf(q, "%x", &op[0]); break; case 2: n = sscanf(q, "%x.%x", &op[0], &op[1]); break; case 3: n = sscanf(q, "%x.%x.%x", &op[0], &op[1], &op[2]); break; default: return -1; } } if (verbose) { printf("%s=",name); for (i = 0; (i < n); ++i) printf("%x.", op[i]); printf(" (n=%d)\n", n); } return n; } testdetail parsetest(char *testbuf, testdetail oldtest) { char *p; /* Current part of line: Option name */ char *q; /* Current part of line: Option value */ testdetail ret; /* What we return */ int k; /* Function enum from k_* */ int n; /* Used as returns for scanfs */ int argtype=2, rettype=2; /* for do_op */ /* clear ret */ memset(&ret, 0, sizeof(ret)); if (verbose) printf("Parsing line: %s\n", testbuf); while (*testbuf && isspace(*testbuf)) testbuf++; if (testbuf[0] == ';' || testbuf[0] == '#' || testbuf[0] == '!' || testbuf[0] == '>' || testbuf[0] == '\0') { ret.comment = 1; if (verbose) printf("Line is a comment\n"); return ret; } ret.comment = 0; if (*testbuf == '+') { if (oldtest.valid) { ret = oldtest; /* structure copy */ } else { fprintf(stderr, "copy from invalid: ignored\n"); } testbuf++; } ret.random = randomstate; ret.in_err = 0; ret.in_err_limit = e_number_of_errnos; p = strtok(testbuf, " \t"); while (p != NULL) { q = strchr(p, '='); if (!q) goto balderdash; *q++ = '\0'; k = find(p, keywords, sizeof(keywords)); switch (k) { case k_random: randomstate = (!strcmp(q, "on")); ret.comment = 1; return ret; /* otherwise ignore this line */ case k_func: if (verbose) printf("func=%s ", q); //ret.func = find(q, funcs, sizeof(funcs)); ret.func = find_testfunc(q); if (ret.func == NULL) { if (verbose) printf("(id=unknown)\n"); goto balderdash; } if(is_single_argtype(ret.func->argtype)) argtype = 0; else if(is_double_argtype(ret.func->argtype)) argtype = 1; if(is_single_rettype(ret.func->rettype)) rettype = 0; else if(is_double_rettype(ret.func->rettype)) rettype = 1; //ret.size = sizes[ret.func]; if (verbose) printf("(name=%s) (size=%d)\n", ret.func->name, ret.func->argtype); break; case k_op1: case k_op1r: n = do_op(q,ret.op1r,"op1r",2,argtype); if (n < 1) goto balderdash; break; case k_op1i: n = do_op(q,ret.op1i,"op1i",2,argtype); if (n < 1) goto balderdash; break; case k_op2: case k_op2r: n = do_op(q,ret.op2r,"op2r",2,argtype); if (n < 1) goto balderdash; break; case k_op2i: n = do_op(q,ret.op2i,"op2i",2,argtype); if (n < 1) goto balderdash; break; case k_resultc: puts(q); if(strncmp(q,"inf",3)==0) { ret.resultc = rc_infinity; } else if(strcmp(q,"zero")==0) { ret.resultc = rc_zero; } else if(strcmp(q,"nan")==0) { ret.resultc = rc_nan; } else if(strcmp(q,"finite")==0) { ret.resultc = rc_finite; } else { goto balderdash; } break; case k_result: case k_resultr: n = (do_op)(q,ret.resultr,"resultr",3,rettype); if (n < 1) goto balderdash; ret.nresult = n; /* assume real and imaginary have same no. words */ break; case k_resulti: n = do_op(q,ret.resulti,"resulti",3,rettype); if (n < 1) goto balderdash; break; case k_res2: n = do_op(q,ret.res2,"res2",2,rettype); if (n < 1) goto balderdash; break; case k_status: while (*q) { if (*q == 'i') ret.status |= FE_INVALID; if (*q == 'z') ret.status |= FE_DIVBYZERO; if (*q == 'o') ret.status |= FE_OVERFLOW; if (*q == 'u') ret.status |= FE_UNDERFLOW; q++; } break; case k_maybeerror: n = find(q, errors, sizeof(errors)); if (n < 0) goto balderdash; if(math_errhandling&MATH_ERREXCEPT) { switch(n) { case e_domain: ret.maybestatus |= FE_INVALID; break; case e_divbyzero: ret.maybestatus |= FE_DIVBYZERO; break; case e_overflow: ret.maybestatus |= FE_OVERFLOW; break; case e_underflow: ret.maybestatus |= FE_UNDERFLOW; break; } } { switch(n) { case e_domain: ret.maybeerr = e_EDOM; break; case e_divbyzero: case e_overflow: case e_underflow: ret.maybeerr = e_ERANGE; break; } } case k_maybestatus: while (*q) { if (*q == 'i') ret.maybestatus |= FE_INVALID; if (*q == 'z') ret.maybestatus |= FE_DIVBYZERO; if (*q == 'o') ret.maybestatus |= FE_OVERFLOW; if (*q == 'u') ret.maybestatus |= FE_UNDERFLOW; q++; } break; case k_error: n = find(q, errors, sizeof(errors)); if (n < 0) goto balderdash; if(math_errhandling&MATH_ERREXCEPT) { switch(n) { case e_domain: ret.status |= FE_INVALID; break; case e_divbyzero: ret.status |= FE_DIVBYZERO; break; case e_overflow: ret.status |= FE_OVERFLOW; break; case e_underflow: ret.status |= FE_UNDERFLOW; break; } } if(math_errhandling&MATH_ERRNO) { switch(n) { case e_domain: ret.err = e_EDOM; break; case e_divbyzero: case e_overflow: case e_underflow: ret.err = e_ERANGE; break; } } if(!(math_errhandling&MATH_ERRNO)) { switch(n) { case e_domain: ret.maybeerr = e_EDOM; break; case e_divbyzero: case e_overflow: case e_underflow: ret.maybeerr = e_ERANGE; break; } } break; case k_errno: ret.err = find(q, errnos, sizeof(errnos)); if (ret.err < 0) goto balderdash; break; case k_errno_in: ret.in_err = find(q, errnos, sizeof(errnos)); if (ret.err < 0) goto balderdash; ret.in_err_limit = ret.in_err + 1; break; case k_wrongresult: case k_wrongstatus: case k_wrongres2: case k_wrongerrno: /* quietly ignore these keys */ break; default: goto balderdash; } p = strtok(NULL, " \t"); } ret.valid = 1; return ret; /* come here from almost any error */ balderdash: ret.valid = 0; return ret; } typedef enum { test_comment, /* deliberately not a test */ test_invalid, /* accidentally not a test */ test_decline, /* was a test, and wasn't run */ test_fail, /* was a test, and failed */ test_pass /* was a test, and passed */ } testresult; char failtext[512]; typedef union { unsigned i[2]; double f; double da[2]; } dbl; typedef union { unsigned i; float f; float da[2]; } sgl; /* helper function for runtest */ void print_error(int rettype, unsigned *result, char* text, char** failp) { special_op *sop; char *str; if(result) { *failp += sprintf(*failp," %s=",text); sop = find_special_op_from_op(result[0],result[1],is_double_rettype(rettype)); if(sop) { *failp += sprintf(*failp,"%s",sop->name); } else { if(is_double_rettype(rettype)) { str="%08x.%08x"; } else { str="%08x"; } *failp += sprintf(*failp,str,result[0],result[1]); } } } void print_ulps_helper(const char *name, long long ulps, char** failp) { if(ulps == LLONG_MAX) { *failp += sprintf(*failp, " %s=HUGE", name); } else { *failp += sprintf(*failp, " %s=%.3f", name, (double)ulps / ULPUNIT); } } /* for complex args make ulpsr or ulpsri = 0 to not print */ void print_ulps(int rettype, long long ulpsr, long long ulpsi, char** failp) { if(is_complex_rettype(rettype)) { if (ulpsr) print_ulps_helper("ulpsr",ulpsr,failp); if (ulpsi) print_ulps_helper("ulpsi",ulpsi,failp); } else { if (ulpsr) print_ulps_helper("ulps",ulpsr,failp); } } int runtest(testdetail t) { int err, status; dbl d_arg1, d_arg2, d_res, d_res2; sgl s_arg1, s_arg2, s_res, s_res2; int deferred_decline = FALSE; char *failp = failtext; unsigned int intres=0; int res2_adjust = 0; if (t.comment) return test_comment; if (!t.valid) return test_invalid; /* Set IEEE status to mathlib-normal */ feclearexcept(FE_ALL_EXCEPT); /* Deal with operands */ #define DO_DOP(arg,op) arg.i[dmsd] = t.op[0]; arg.i[dlsd] = t.op[1] DO_DOP(d_arg1,op1r); DO_DOP(d_arg2,op2r); s_arg1.i = t.op1r[0]; s_arg2.i = t.op2r[0]; /* * Detect NaNs, infinities and denormals on input, and set a * deferred decline flag if we're in FO mode. * * (We defer the decline rather than doing it immediately * because even in FO mode the operation is not permitted to * crash or tight-loop; so we _run_ the test, and then ignore * all the results.) */ if (fo) { if (is_double_argtype(t.func->argtype) && is_dhard(t.op1r)) deferred_decline = TRUE; if (t.func->argtype==at_d2 && is_dhard(t.op2r)) deferred_decline = TRUE; if (is_single_argtype(t.func->argtype) && is_shard(t.op1r)) deferred_decline = TRUE; if (t.func->argtype==at_s2 && is_shard(t.op2r)) deferred_decline = TRUE; if (is_double_rettype(t.func->rettype) && is_dhard(t.resultr)) deferred_decline = TRUE; if (t.func->rettype==rt_d2 && is_dhard(t.res2)) deferred_decline = TRUE; if (is_single_argtype(t.func->rettype) && is_shard(t.resultr)) deferred_decline = TRUE; if (t.func->rettype==rt_s2 && is_shard(t.res2)) deferred_decline = TRUE; if (t.err == e_ERANGE) deferred_decline = TRUE; } /* * Perform the operation */ errno = t.in_err == e_EDOM ? EDOM : t.in_err == e_ERANGE ? ERANGE : 0; if (t.err == e_0) t.err = t.in_err; if (t.maybeerr == e_0) t.maybeerr = t.in_err; if(t.func->type == t_func) { switch(t.func->argtype) { case at_d: d_res.f = t.func->func.d_d_ptr(d_arg1.f); break; case at_s: s_res.f = t.func->func.s_s_ptr(s_arg1.f); break; case at_d2: d_res.f = t.func->func.d2_d_ptr(d_arg1.f, d_arg2.f); break; case at_s2: s_res.f = t.func->func.s2_s_ptr(s_arg1.f, s_arg2.f); break; case at_di: d_res.f = t.func->func.di_d_ptr(d_arg1.f, d_arg2.i[dmsd]); break; case at_si: s_res.f = t.func->func.si_s_ptr(s_arg1.f, s_arg2.i); break; case at_dip: d_res.f = t.func->func.dip_d_ptr(d_arg1.f, (int*)&intres); break; case at_sip: s_res.f = t.func->func.sip_s_ptr(s_arg1.f, (int*)&intres); break; case at_ddp: d_res.f = t.func->func.ddp_d_ptr(d_arg1.f, &d_res2.f); break; case at_ssp: s_res.f = t.func->func.ssp_s_ptr(s_arg1.f, &s_res2.f); break; default: printf("unhandled function: %s\n",t.func->name); return test_fail; } } else { /* printf("macro: name=%s, num=%i, s1.i=0x%08x s1.f=%f\n",t.func->name, t.func->macro_name, s_arg1.i, (double)s_arg1.f); */ switch(t.func->macro_name) { case m_isfinite: intres = isfinite(d_arg1.f); break; case m_isinf: intres = isinf(d_arg1.f); break; case m_isnan: intres = isnan(d_arg1.f); break; case m_isnormal: intres = isnormal(d_arg1.f); break; case m_signbit: intres = signbit(d_arg1.f); break; case m_fpclassify: intres = fpclassify(d_arg1.f); break; case m_isgreater: intres = isgreater(d_arg1.f, d_arg2.f); break; case m_isgreaterequal: intres = isgreaterequal(d_arg1.f, d_arg2.f); break; case m_isless: intres = isless(d_arg1.f, d_arg2.f); break; case m_islessequal: intres = islessequal(d_arg1.f, d_arg2.f); break; case m_islessgreater: intres = islessgreater(d_arg1.f, d_arg2.f); break; case m_isunordered: intres = isunordered(d_arg1.f, d_arg2.f); break; case m_isfinitef: intres = isfinite(s_arg1.f); break; case m_isinff: intres = isinf(s_arg1.f); break; case m_isnanf: intres = isnan(s_arg1.f); break; case m_isnormalf: intres = isnormal(s_arg1.f); break; case m_signbitf: intres = signbit(s_arg1.f); break; case m_fpclassifyf: intres = fpclassify(s_arg1.f); break; case m_isgreaterf: intres = isgreater(s_arg1.f, s_arg2.f); break; case m_isgreaterequalf: intres = isgreaterequal(s_arg1.f, s_arg2.f); break; case m_islessf: intres = isless(s_arg1.f, s_arg2.f); break; case m_islessequalf: intres = islessequal(s_arg1.f, s_arg2.f); break; case m_islessgreaterf: intres = islessgreater(s_arg1.f, s_arg2.f); break; case m_isunorderedf: intres = isunordered(s_arg1.f, s_arg2.f); break; default: printf("unhandled macro: %s\n",t.func->name); return test_fail; } } /* * Decline the test if the deferred decline flag was set above. */ if (deferred_decline) return test_decline; /* printf("intres=%i\n",intres); */ /* Clear the fail text (indicating a pass unless we change it) */ failp[0] = '\0'; /* Check the IEEE status bits (except INX, which we disregard). * We don't bother with this for complex numbers, because the * complex functions are hard to get exactly right and we don't * have to anyway (C99 annex G is only informative). */ if (!(is_complex_argtype(t.func->argtype) || is_complex_rettype(t.func->rettype))) { status = fetestexcept(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW); if ((status|t.maybestatus|~statusmask) != (t.status|t.maybestatus|~statusmask)) { if (quiet) failtext[0]='x'; else { failp += sprintf(failp, " wrongstatus=%s%s%s%s%s", (status & FE_INVALID ? "i" : ""), (status & FE_DIVBYZERO ? "z" : ""), (status & FE_OVERFLOW ? "o" : ""), (status & FE_UNDERFLOW ? "u" : ""), (status ? "" : "OK")); } } } /* Check the result */ { unsigned resultr[2], resulti[2]; unsigned tresultr[3], tresulti[3], wres; switch(t.func->rettype) { case rt_d: case rt_d2: tresultr[0] = t.resultr[0]; tresultr[1] = t.resultr[1]; resultr[0] = d_res.i[dmsd]; resultr[1] = d_res.i[dlsd]; wres = 2; break; case rt_i: tresultr[0] = t.resultr[0]; resultr[0] = intres; wres = 1; break; case rt_s: case rt_s2: tresultr[0] = t.resultr[0]; resultr[0] = s_res.i; wres = 1; break; default: puts("unhandled rettype in runtest"); wres = 0; } if(t.resultc != rc_none) { int err = 0; switch(t.resultc) { case rc_zero: if(resultr[0] != 0 || resulti[0] != 0 || (wres==2 && (resultr[1] != 0 || resulti[1] != 0))) { err = 1; } break; case rc_infinity: if(wres==1) { if(!((resultr[0]&0x7fffffff)==0x7f800000 || (resulti[0]&0x7fffffff)==0x7f800000)) { err = 1; } } else { if(!(((resultr[0]&0x7fffffff)==0x7ff00000 && resultr[1]==0) || ((resulti[0]&0x7fffffff)==0x7ff00000 && resulti[1]==0))) { err = 1; } } break; case rc_nan: if(wres==1) { if(!((resultr[0]&0x7fffffff)>0x7f800000 || (resulti[0]&0x7fffffff)>0x7f800000)) { err = 1; } } else { canon_dNaN(resultr); canon_dNaN(resulti); if(!(((resultr[0]&0x7fffffff)>0x7ff00000 && resultr[1]==1) || ((resulti[0]&0x7fffffff)>0x7ff00000 && resulti[1]==1))) { err = 1; } } break; case rc_finite: if(wres==1) { if(!((resultr[0]&0x7fffffff)<0x7f800000 || (resulti[0]&0x7fffffff)<0x7f800000)) { err = 1; } } else { if(!((resultr[0]&0x7fffffff)<0x7ff00000 || (resulti[0]&0x7fffffff)<0x7ff00000)) { err = 1; } } break; default: break; } if(err) { print_error(t.func->rettype,resultr,"wrongresultr",&failp); print_error(t.func->rettype,resulti,"wrongresulti",&failp); } } else if (t.nresult > wres) { /* * The test case data has provided the result to more * than double precision. Instead of testing exact * equality, we test against our maximum error * tolerance. */ int rshift, ishift; long long ulpsr, ulpsi, ulptolerance; tresultr[wres] = t.resultr[wres] << (32-EXTRABITS); tresulti[wres] = t.resulti[wres] << (32-EXTRABITS); if(strict) { ulptolerance = 4096; /* one ulp */ } else { ulptolerance = t.func->tolerance; } rshift = ishift = 0; if (ulptolerance & ABSLOWERBOUND) { /* * Hack for the lgamma functions, which have an * error behaviour that can't conveniently be * characterised in pure ULPs. Really, we want to * say that the error in lgamma is "at most N ULPs, * or at most an absolute error of X, whichever is * larger", for appropriately chosen N,X. But since * these two functions are the only cases where it * arises, I haven't bothered to do it in a nice way * in the function table above. * * (The difficult cases arise with negative input * values such that |gamma(x)| is very near to 1; in * this situation implementations tend to separately * compute lgamma(|x|) and the log of the correction * term from the Euler reflection formula, and * subtract - which catastrophically loses * significance.) * * As far as I can tell, nobody cares about this: * GNU libm doesn't get those cases right either, * and OpenCL explicitly doesn't state a ULP error * limit for lgamma. So my guess is that this is * simply considered acceptable error behaviour for * this particular function, and hence I feel free * to allow for it here. */ ulptolerance &= ~ABSLOWERBOUND; if (t.op1r[0] & 0x80000000) { if (t.func->rettype == rt_d) rshift = 0x400 - ((tresultr[0] >> 20) & 0x7ff); else if (t.func->rettype == rt_s) rshift = 0x80 - ((tresultr[0] >> 23) & 0xff); if (rshift < 0) rshift = 0; } } if (ulptolerance & PLUSMINUSPIO2) { ulptolerance &= ~PLUSMINUSPIO2; /* * Hack for range reduction, which can reduce * borderline cases in the wrong direction, i.e. * return a value just outside one end of the interval * [-pi/4,+pi/4] when it could have returned a value * just inside the other end by subtracting an * adjacent multiple of pi/2. * * We tolerate this, up to a point, because the * trigonometric functions making use of the output of * rred can cope and because making the range reducer * do the exactly right thing in every case would be * more expensive. */ if (wres == 1) { /* Upper bound of overshoot derived in rredf.h */ if ((resultr[0]&0x7FFFFFFF) <= 0x3f494b02 && (resultr[0]&0x7FFFFFFF) > 0x3f490fda && (resultr[0]&0x80000000) != (tresultr[0]&0x80000000)) { unsigned long long val; val = tresultr[0]; val = (val << 32) | tresultr[1]; /* * Compute the alternative permitted result by * subtracting from the sum of the extended * single-precision bit patterns of +pi/4 and * -pi/4. This is a horrible hack which only * works because we can be confident that * numbers in this range all have the same * exponent! */ val = 0xfe921fb54442d184ULL - val; tresultr[0] = val >> 32; tresultr[1] = (val >> (32-EXTRABITS)) << (32-EXTRABITS); /* * Also, expect a correspondingly different * value of res2 as a result of this change. * The adjustment depends on whether we just * flipped the result from + to - or vice * versa. */ if (resultr[0] & 0x80000000) { res2_adjust = +1; } else { res2_adjust = -1; } } } } ulpsr = calc_error(resultr, tresultr, rshift, t.func->rettype); if(is_complex_rettype(t.func->rettype)) { ulpsi = calc_error(resulti, tresulti, ishift, t.func->rettype); } else { ulpsi = 0; } unsigned *rr = (ulpsr > ulptolerance || ulpsr < -ulptolerance) ? resultr : NULL; unsigned *ri = (ulpsi > ulptolerance || ulpsi < -ulptolerance) ? resulti : NULL; /* printf("tolerance=%i, ulpsr=%i, ulpsi=%i, rr=%p, ri=%p\n",ulptolerance,ulpsr,ulpsi,rr,ri); */ if (rr || ri) { if (quiet) failtext[0]='x'; else { print_error(t.func->rettype,rr,"wrongresultr",&failp); print_error(t.func->rettype,ri,"wrongresulti",&failp); print_ulps(t.func->rettype,rr ? ulpsr : 0, ri ? ulpsi : 0,&failp); } } } else { if(is_complex_rettype(t.func->rettype)) /* * Complex functions are not fully supported, * this is unreachable, but prevents warnings. */ abort(); /* * The test case data has provided the result in * exactly the output precision. Therefore we must * complain about _any_ violation. */ switch(t.func->rettype) { case rt_dc: canon_dNaN(tresulti); canon_dNaN(resulti); if (fo) { dnormzero(tresulti); dnormzero(resulti); } /* deliberate fall-through */ case rt_d: canon_dNaN(tresultr); canon_dNaN(resultr); if (fo) { dnormzero(tresultr); dnormzero(resultr); } break; case rt_sc: canon_sNaN(tresulti); canon_sNaN(resulti); if (fo) { snormzero(tresulti); snormzero(resulti); } /* deliberate fall-through */ case rt_s: canon_sNaN(tresultr); canon_sNaN(resultr); if (fo) { snormzero(tresultr); snormzero(resultr); } break; default: break; } if(is_complex_rettype(t.func->rettype)) { unsigned *rr, *ri; if(resultr[0] != tresultr[0] || (wres > 1 && resultr[1] != tresultr[1])) { rr = resultr; } else { rr = NULL; } if(resulti[0] != tresulti[0] || (wres > 1 && resulti[1] != tresulti[1])) { ri = resulti; } else { ri = NULL; } if(rr || ri) { if (quiet) failtext[0]='x'; print_error(t.func->rettype,rr,"wrongresultr",&failp); print_error(t.func->rettype,ri,"wrongresulti",&failp); } } else if (resultr[0] != tresultr[0] || (wres > 1 && resultr[1] != tresultr[1])) { if (quiet) failtext[0]='x'; print_error(t.func->rettype,resultr,"wrongresult",&failp); } } /* * Now test res2, for those functions (frexp, modf, rred) * which use it. */ if (t.func->func.ptr == &frexp || t.func->func.ptr == &frexpf || t.func->macro_name == m_rred || t.func->macro_name == m_rredf) { unsigned tres2 = t.res2[0]; if (res2_adjust) { /* Fix for range reduction, propagated from further up */ tres2 = (tres2 + res2_adjust) & 3; } if (tres2 != intres) { if (quiet) failtext[0]='x'; else { failp += sprintf(failp, " wrongres2=%08x", intres); } } } else if (t.func->func.ptr == &modf || t.func->func.ptr == &modff) { tresultr[0] = t.res2[0]; tresultr[1] = t.res2[1]; if (is_double_rettype(t.func->rettype)) { canon_dNaN(tresultr); resultr[0] = d_res2.i[dmsd]; resultr[1] = d_res2.i[dlsd]; canon_dNaN(resultr); if (fo) { dnormzero(tresultr); dnormzero(resultr); } } else { canon_sNaN(tresultr); resultr[0] = s_res2.i; resultr[1] = s_res2.i; canon_sNaN(resultr); if (fo) { snormzero(tresultr); snormzero(resultr); } } if (resultr[0] != tresultr[0] || (wres > 1 && resultr[1] != tresultr[1])) { if (quiet) failtext[0]='x'; else { if (is_double_rettype(t.func->rettype)) failp += sprintf(failp, " wrongres2=%08x.%08x", resultr[0], resultr[1]); else failp += sprintf(failp, " wrongres2=%08x", resultr[0]); } } } } /* Check errno */ err = (errno == EDOM ? e_EDOM : errno == ERANGE ? e_ERANGE : e_0); if (err != t.err && err != t.maybeerr) { if (quiet) failtext[0]='x'; else { failp += sprintf(failp, " wrongerrno=%s expecterrno=%s ", errnos[err], errnos[t.err]); } } return *failtext ? test_fail : test_pass; } int passed, failed, declined; void runtests(char *name, FILE *fp) { char testbuf[512], linebuf[512]; int lineno = 1; testdetail test; test.valid = 0; if (verbose) printf("runtests: %s\n", name); while (fgets(testbuf, sizeof(testbuf), fp)) { int res, print_errno; testbuf[strcspn(testbuf, "\r\n")] = '\0'; strcpy(linebuf, testbuf); test = parsetest(testbuf, test); print_errno = 0; while (test.in_err < test.in_err_limit) { res = runtest(test); if (res == test_pass) { if (verbose) printf("%s:%d: pass\n", name, lineno); ++passed; } else if (res == test_decline) { if (verbose) printf("%s:%d: declined\n", name, lineno); ++declined; } else if (res == test_fail) { if (!quiet) printf("%s:%d: FAIL%s: %s%s%s%s\n", name, lineno, test.random ? " (random)" : "", linebuf, print_errno ? " errno_in=" : "", print_errno ? errnos[test.in_err] : "", failtext); ++failed; } else if (res == test_invalid) { printf("%s:%d: malformed: %s\n", name, lineno, linebuf); ++failed; } test.in_err++; print_errno = 1; } lineno++; } } int main(int ac, char **av) { char **files; int i, nfiles = 0; dbl d; #ifdef MICROLIB /* * Invent argc and argv ourselves. */ char *argv[256]; char args[256]; { int sargs[2]; char *p; ac = 0; sargs[0]=(int)args; sargs[1]=(int)sizeof(args); if (!__semihost(0x15, sargs)) { args[sizeof(args)-1] = '\0'; /* just in case */ p = args; while (1) { while (*p == ' ' || *p == '\t') p++; if (!*p) break; argv[ac++] = p; while (*p && *p != ' ' && *p != '\t') p++; if (*p) *p++ = '\0'; } } av = argv; } #endif /* Sort tfuncs */ qsort(tfuncs, sizeof(tfuncs)/sizeof(test_func), sizeof(test_func), &compare_tfuncs); /* * Autodetect the `double' endianness. */ dmsd = 0; d.f = 1.0; /* 0x3ff00000 / 0x00000000 */ if (d.i[dmsd] == 0) { dmsd = 1; } /* * Now dmsd denotes what the compiler thinks we're at. Let's * check that it agrees with what the runtime thinks. */ d.i[0] = d.i[1] = 0x11111111;/* a random +ve number */ d.f /= d.f; /* must now be one */ if (d.i[dmsd] == 0) { fprintf(stderr, "YIKES! Compiler and runtime disagree on endianness" " of `double'. Bailing out\n"); return 1; } dlsd = !dmsd; /* default is terse */ verbose = 0; fo = 0; strict = 0; files = (char **)malloc((ac+1) * sizeof(char *)); if (!files) { fprintf(stderr, "initial malloc failed!\n"); return 1; } #ifdef NOCMDLINE files[nfiles++] = "testfile"; #endif while (--ac) { char *p = *++av; if (*p == '-') { static char *options[] = { "-fo", #if 0 "-noinexact", "-noround", #endif "-nostatus", "-quiet", "-strict", "-v", "-verbose", }; enum { op_fo, #if 0 op_noinexact, op_noround, #endif op_nostatus, op_quiet, op_strict, op_v, op_verbose, }; switch (find(p, options, sizeof(options))) { case op_quiet: quiet = 1; break; #if 0 case op_noinexact: statusmask &= 0x0F; /* remove bit 4 */ break; case op_noround: doround = 0; break; #endif case op_nostatus: /* no status word => noinx,noround */ statusmask = 0; doround = 0; break; case op_v: case op_verbose: verbose = 1; break; case op_fo: fo = 1; break; case op_strict: /* tolerance is 1 ulp */ strict = 1; break; default: fprintf(stderr, "unrecognised option: %s\n", p); break; } } else { files[nfiles++] = p; } } passed = failed = declined = 0; if (nfiles) { for (i = 0; i < nfiles; i++) { FILE *fp = fopen(files[i], "r"); if (!fp) { fprintf(stderr, "Couldn't open %s\n", files[i]); } else runtests(files[i], fp); } } else runtests("(stdin)", stdin); printf("Completed. Passed %d, failed %d (total %d", passed, failed, passed+failed); if (declined) printf(" plus %d declined", declined); printf(")\n"); if (failed || passed == 0) return 1; printf("** TEST PASSED OK **\n"); return 0; } void undef_func() { failed++; puts("ERROR: undefined function called"); }