/* * ULP error checking tool for math functions. * * Copyright (c) 2019-2022, Arm Limited. * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception */ #include #include #include #include #include #include #include #include #include "mathlib.h" /* Don't depend on mpfr by default. */ #ifndef USE_MPFR # define USE_MPFR 0 #endif #if USE_MPFR # include #endif #ifndef WANT_VMATH /* Enable the build of vector math code. */ # define WANT_VMATH 1 #endif static inline uint64_t asuint64 (double f) { union { double f; uint64_t i; } u = {f}; return u.i; } static inline double asdouble (uint64_t i) { union { uint64_t i; double f; } u = {i}; return u.f; } static inline uint32_t asuint (float f) { union { float f; uint32_t i; } u = {f}; return u.i; } static inline float asfloat (uint32_t i) { union { uint32_t i; float f; } u = {i}; return u.f; } static uint64_t seed = 0x0123456789abcdef; static uint64_t rand64 (void) { seed = 6364136223846793005ull * seed + 1; return seed ^ (seed >> 32); } /* Uniform random in [0,n]. */ static uint64_t randn (uint64_t n) { uint64_t r, m; if (n == 0) return 0; n++; if (n == 0) return rand64 (); for (;;) { r = rand64 (); m = r % n; if (r - m <= -n) return m; } } struct gen { uint64_t start; uint64_t len; uint64_t start2; uint64_t len2; uint64_t off; uint64_t step; uint64_t cnt; }; struct args_f1 { float x; }; struct args_f2 { float x; float x2; }; struct args_d1 { double x; }; struct args_d2 { double x; double x2; }; /* result = y + tail*2^ulpexp. */ struct ret_f { float y; double tail; int ulpexp; int ex; int ex_may; }; struct ret_d { double y; double tail; int ulpexp; int ex; int ex_may; }; static inline uint64_t next1 (struct gen *g) { /* For single argument use randomized incremental steps, that produce dense sampling without collisions and allow testing all inputs in a range. */ uint64_t r = g->start + g->off; g->off += g->step + randn (g->step / 2); if (g->off > g->len) g->off -= g->len; /* hack. */ return r; } static inline uint64_t next2 (uint64_t *x2, struct gen *g) { /* For two arguments use uniform random sampling. */ uint64_t r = g->start + randn (g->len); *x2 = g->start2 + randn (g->len2); return r; } static struct args_f1 next_f1 (void *g) { return (struct args_f1){asfloat (next1 (g))}; } static struct args_f2 next_f2 (void *g) { uint64_t x2; uint64_t x = next2 (&x2, g); return (struct args_f2){asfloat (x), asfloat (x2)}; } static struct args_d1 next_d1 (void *g) { return (struct args_d1){asdouble (next1 (g))}; } static struct args_d2 next_d2 (void *g) { uint64_t x2; uint64_t x = next2 (&x2, g); return (struct args_d2){asdouble (x), asdouble (x2)}; } struct conf { int r; int rc; int quiet; int mpfr; int fenv; unsigned long long n; double softlim; double errlim; }; /* A bit of a hack: call vector functions twice with the same input in lane 0 but a different value in other lanes: once with an in-range value and then with a special case value. */ static int secondcall; /* Wrappers for vector functions. */ #if __aarch64__ && WANT_VMATH typedef __f32x4_t v_float; typedef __f64x2_t v_double; /* First element of fv and dv may be changed by -c argument. */ static float fv[2] = {1.0f, -INFINITY}; static double dv[2] = {1.0, -INFINITY}; static inline v_float argf(float x) { return (v_float){x,x,x,fv[secondcall]}; } static inline v_double argd(double x) { return (v_double){x,dv[secondcall]}; } #if WANT_SVE_MATH #include typedef __SVFloat32_t sv_float; typedef __SVFloat64_t sv_double; static inline sv_float svargf(float x) { int n = svcntw(); float base[n]; for (int i=0; i> 23 & 0xff; if (!e) e++; return e - 0x7f - 23; } static inline int ulpscale_d (double x) { int e = asuint64 (x) >> 52 & 0x7ff; if (!e) e++; return e - 0x3ff - 52; } static inline float call_f1 (const struct fun *f, struct args_f1 a) { return f->fun.f1 (a.x); } static inline float call_f2 (const struct fun *f, struct args_f2 a) { return f->fun.f2 (a.x, a.x2); } static inline double call_d1 (const struct fun *f, struct args_d1 a) { return f->fun.d1 (a.x); } static inline double call_d2 (const struct fun *f, struct args_d2 a) { return f->fun.d2 (a.x, a.x2); } static inline double call_long_f1 (const struct fun *f, struct args_f1 a) { return f->fun_long.f1 (a.x); } static inline double call_long_f2 (const struct fun *f, struct args_f2 a) { return f->fun_long.f2 (a.x, a.x2); } static inline long double call_long_d1 (const struct fun *f, struct args_d1 a) { return f->fun_long.d1 (a.x); } static inline long double call_long_d2 (const struct fun *f, struct args_d2 a) { return f->fun_long.d2 (a.x, a.x2); } static inline void printcall_f1 (const struct fun *f, struct args_f1 a) { printf ("%s(%a)", f->name, a.x); } static inline void printcall_f2 (const struct fun *f, struct args_f2 a) { printf ("%s(%a, %a)", f->name, a.x, a.x2); } static inline void printcall_d1 (const struct fun *f, struct args_d1 a) { printf ("%s(%a)", f->name, a.x); } static inline void printcall_d2 (const struct fun *f, struct args_d2 a) { printf ("%s(%a, %a)", f->name, a.x, a.x2); } static inline void printgen_f1 (const struct fun *f, struct gen *gen) { printf ("%s in [%a;%a]", f->name, asfloat (gen->start), asfloat (gen->start + gen->len)); } static inline void printgen_f2 (const struct fun *f, struct gen *gen) { printf ("%s in [%a;%a] x [%a;%a]", f->name, asfloat (gen->start), asfloat (gen->start + gen->len), asfloat (gen->start2), asfloat (gen->start2 + gen->len2)); } static inline void printgen_d1 (const struct fun *f, struct gen *gen) { printf ("%s in [%a;%a]", f->name, asdouble (gen->start), asdouble (gen->start + gen->len)); } static inline void printgen_d2 (const struct fun *f, struct gen *gen) { printf ("%s in [%a;%a] x [%a;%a]", f->name, asdouble (gen->start), asdouble (gen->start + gen->len), asdouble (gen->start2), asdouble (gen->start2 + gen->len2)); } #define reduce_f1(a, f, op) (f (a.x)) #define reduce_f2(a, f, op) (f (a.x) op f (a.x2)) #define reduce_d1(a, f, op) (f (a.x)) #define reduce_d2(a, f, op) (f (a.x) op f (a.x2)) #ifndef IEEE_754_2008_SNAN # define IEEE_754_2008_SNAN 1 #endif static inline int issignaling_f (float x) { uint32_t ix = asuint (x); if (!IEEE_754_2008_SNAN) return (ix & 0x7fc00000) == 0x7fc00000; return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000; } static inline int issignaling_d (double x) { uint64_t ix = asuint64 (x); if (!IEEE_754_2008_SNAN) return (ix & 0x7ff8000000000000) == 0x7ff8000000000000; return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL; } #if USE_MPFR static mpfr_rnd_t rmap (int r) { switch (r) { case FE_TONEAREST: return MPFR_RNDN; case FE_TOWARDZERO: return MPFR_RNDZ; case FE_UPWARD: return MPFR_RNDU; case FE_DOWNWARD: return MPFR_RNDD; } return -1; } #define prec_mpfr_f 50 #define prec_mpfr_d 80 #define prec_f 24 #define prec_d 53 #define emin_f -148 #define emin_d -1073 #define emax_f 128 #define emax_d 1024 static inline int call_mpfr_f1 (mpfr_t y, const struct fun *f, struct args_f1 a, mpfr_rnd_t r) { MPFR_DECL_INIT (x, prec_f); mpfr_set_flt (x, a.x, MPFR_RNDN); return f->fun_mpfr.f1 (y, x, r); } static inline int call_mpfr_f2 (mpfr_t y, const struct fun *f, struct args_f2 a, mpfr_rnd_t r) { MPFR_DECL_INIT (x, prec_f); MPFR_DECL_INIT (x2, prec_f); mpfr_set_flt (x, a.x, MPFR_RNDN); mpfr_set_flt (x2, a.x2, MPFR_RNDN); return f->fun_mpfr.f2 (y, x, x2, r); } static inline int call_mpfr_d1 (mpfr_t y, const struct fun *f, struct args_d1 a, mpfr_rnd_t r) { MPFR_DECL_INIT (x, prec_d); mpfr_set_d (x, a.x, MPFR_RNDN); return f->fun_mpfr.d1 (y, x, r); } static inline int call_mpfr_d2 (mpfr_t y, const struct fun *f, struct args_d2 a, mpfr_rnd_t r) { MPFR_DECL_INIT (x, prec_d); MPFR_DECL_INIT (x2, prec_d); mpfr_set_d (x, a.x, MPFR_RNDN); mpfr_set_d (x2, a.x2, MPFR_RNDN); return f->fun_mpfr.d2 (y, x, x2, r); } #endif #define float_f float #define double_f double #define copysign_f copysignf #define nextafter_f nextafterf #define fabs_f fabsf #define asuint_f asuint #define asfloat_f asfloat #define scalbn_f scalbnf #define lscalbn_f scalbn #define halfinf_f 0x1p127f #define min_normal_f 0x1p-126f #define float_d double #define double_d long double #define copysign_d copysign #define nextafter_d nextafter #define fabs_d fabs #define asuint_d asuint64 #define asfloat_d asdouble #define scalbn_d scalbn #define lscalbn_d scalbnl #define halfinf_d 0x1p1023 #define min_normal_d 0x1p-1022 #define NEW_RT #define RT(x) x##_f #define T(x) x##_f1 #include "ulp.h" #undef T #define T(x) x##_f2 #include "ulp.h" #undef T #undef RT #define NEW_RT #define RT(x) x##_d #define T(x) x##_d1 #include "ulp.h" #undef T #define T(x) x##_d2 #include "ulp.h" #undef T #undef RT static void usage (void) { puts ("./ulp [-q] [-m] [-f] [-r nudz] [-l soft-ulplimit] [-e ulplimit] func " "lo [hi [x lo2 hi2] [count]]"); puts ("Compares func against a higher precision implementation in [lo; hi]."); puts ("-q: quiet."); puts ("-m: use mpfr even if faster method is available."); puts ("-f: disable fenv testing (rounding modes and exceptions)."); #if __aarch64__ && WANT_VMATH puts ("-c: neutral 'control value' to test behaviour when one lane can affect another. \n" " This should be different from tested input in other lanes, and non-special \n" " (i.e. should not trigger fenv exceptions). Default is 1."); #endif puts ("Supported func:"); for (const struct fun *f = fun; f->name; f++) printf ("\t%s\n", f->name); exit (1); } static int cmp (const struct fun *f, struct gen *gen, const struct conf *conf) { int r = 1; if (f->arity == 1 && f->singleprec) r = cmp_f1 (f, gen, conf); else if (f->arity == 2 && f->singleprec) r = cmp_f2 (f, gen, conf); else if (f->arity == 1 && !f->singleprec) r = cmp_d1 (f, gen, conf); else if (f->arity == 2 && !f->singleprec) r = cmp_d2 (f, gen, conf); else usage (); return r; } static uint64_t getnum (const char *s, int singleprec) { // int i; uint64_t sign = 0; // char buf[12]; if (s[0] == '+') s++; else if (s[0] == '-') { sign = singleprec ? 1ULL << 31 : 1ULL << 63; s++; } /* 0xXXXX is treated as bit representation, '-' flips the sign bit. */ if (s[0] == '0' && tolower (s[1]) == 'x' && strchr (s, 'p') == 0) return sign ^ strtoull (s, 0, 0); // /* SNaN, QNaN, NaN, Inf. */ // for (i=0; s[i] && i < sizeof buf; i++) // buf[i] = tolower(s[i]); // buf[i] = 0; // if (strcmp(buf, "snan") == 0) // return sign | (singleprec ? 0x7fa00000 : 0x7ff4000000000000); // if (strcmp(buf, "qnan") == 0 || strcmp(buf, "nan") == 0) // return sign | (singleprec ? 0x7fc00000 : 0x7ff8000000000000); // if (strcmp(buf, "inf") == 0 || strcmp(buf, "infinity") == 0) // return sign | (singleprec ? 0x7f800000 : 0x7ff0000000000000); /* Otherwise assume it's a floating-point literal. */ return sign | (singleprec ? asuint (strtof (s, 0)) : asuint64 (strtod (s, 0))); } static void parsegen (struct gen *g, int argc, char *argv[], const struct fun *f) { int singleprec = f->singleprec; int arity = f->arity; uint64_t a, b, a2, b2, n; if (argc < 1) usage (); b = a = getnum (argv[0], singleprec); n = 0; if (argc > 1 && strcmp (argv[1], "x") == 0) { argc -= 2; argv += 2; } else if (argc > 1) { b = getnum (argv[1], singleprec); if (argc > 2 && strcmp (argv[2], "x") == 0) { argc -= 3; argv += 3; } } b2 = a2 = getnum (argv[0], singleprec); if (argc > 1) b2 = getnum (argv[1], singleprec); if (argc > 2) n = strtoull (argv[2], 0, 0); if (argc > 3) usage (); //printf("ab %lx %lx ab2 %lx %lx n %lu\n", a, b, a2, b2, n); if (arity == 1) { g->start = a; g->len = b - a; if (n - 1 > b - a) n = b - a + 1; g->off = 0; g->step = n ? (g->len + 1) / n : 1; g->start2 = g->len2 = 0; g->cnt = n; } else if (arity == 2) { g->start = a; g->len = b - a; g->off = g->step = 0; g->start2 = a2; g->len2 = b2 - a2; g->cnt = n; } else usage (); } int main (int argc, char *argv[]) { const struct fun *f; struct gen gen; struct conf conf; conf.rc = 'n'; conf.quiet = 0; conf.mpfr = 0; conf.fenv = 1; conf.softlim = 0; conf.errlim = INFINITY; for (;;) { argc--; argv++; if (argc < 1) usage (); if (argv[0][0] != '-') break; switch (argv[0][1]) { case 'e': argc--; argv++; if (argc < 1) usage (); conf.errlim = strtod (argv[0], 0); break; case 'f': conf.fenv = 0; break; case 'l': argc--; argv++; if (argc < 1) usage (); conf.softlim = strtod (argv[0], 0); break; case 'm': conf.mpfr = 1; break; case 'q': conf.quiet = 1; break; case 'r': conf.rc = argv[0][2]; if (!conf.rc) { argc--; argv++; if (argc < 1) usage (); conf.rc = argv[0][0]; } break; #if __aarch64__ && WANT_VMATH case 'c': argc--; argv++; fv[0] = strtof(argv[0], 0); dv[0] = strtod(argv[0], 0); break; #endif default: usage (); } } switch (conf.rc) { case 'n': conf.r = FE_TONEAREST; break; case 'u': conf.r = FE_UPWARD; break; case 'd': conf.r = FE_DOWNWARD; break; case 'z': conf.r = FE_TOWARDZERO; break; default: usage (); } for (f = fun; f->name; f++) if (strcmp (argv[0], f->name) == 0) break; if (!f->name) usage (); if (!f->singleprec && LDBL_MANT_DIG == DBL_MANT_DIG) conf.mpfr = 1; /* Use mpfr if long double has no extra precision. */ if (!USE_MPFR && conf.mpfr) { puts ("mpfr is not available."); return 0; } argc--; argv++; parsegen (&gen, argc, argv, f); conf.n = gen.cnt; return cmp (f, &gen, &conf); }