// Copyright Naoki Shibata and contributors 2010 - 2024. // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) #include #include #include #include #include #include #include #include #include #include #ifdef ENABLE_SYS_getrandom #define _GNU_SOURCE #include #include #include #endif #include "sleef.h" #include "f128util.h" #define DORENAME #include "rename.h" #define POSITIVE_INFINITY INFINITY #define NEGATIVE_INFINITY (-INFINITY) int isnumberq(Sleef_quad x) { return !isinfq(x) && !isnanq(x); } int isPlusZeroq(Sleef_quad x) { return x == 0 && copysignq(1, x) == 1; } int isMinusZeroq(Sleef_quad x) { return x == 0 && copysignq(1, x) == -1; } mpfr_t fra, frb, frc, frd; double countULP(Sleef_quad d, mpfr_t c) { Sleef_quad c2 = mpfr_get_f128(c, GMP_RNDN); if (c2 == 0 && d != 0) return 10000; //if (isPlusZeroq(c2) && !isPlusZeroq(d)) return 10003; //if (isMinusZeroq(c2) && !isMinusZeroq(d)) return 10004; if (isnanq(c2) && isnanq(d)) return 0; if (isnanq(c2) || isnanq(d)) return 10001; if (c2 == POSITIVE_INFINITY && d == POSITIVE_INFINITY) return 0; if (c2 == NEGATIVE_INFINITY && d == NEGATIVE_INFINITY) return 0; if (!isnumberq(c2) && !isnumberq(d)) return 0; int e; frexpq(mpfr_get_f128(c, GMP_RNDN), &e); mpfr_set_f128(frb, fmaxq(ldexpq(1.0, e-113), FLT128_DENORM_MIN), GMP_RNDN); mpfr_set_f128(frd, d, GMP_RNDN); mpfr_sub(fra, frd, c, GMP_RNDN); mpfr_div(fra, fra, frb, GMP_RNDN); double u = fabs(mpfr_get_d(fra, GMP_RNDN)); return u; } double countULP2(Sleef_quad d, mpfr_t c) { Sleef_quad c2 = mpfr_get_f128(c, GMP_RNDN); if (c2 == 0 && d != 0) return 10000; //if (isPlusZeroq(c2) && !isPlusZeroq(d)) return 10003; //if (isMinusZeroq(c2) && !isMinusZeroq(d)) return 10004; if (isnanq(c2) && isnanq(d)) return 0; if (isnanq(c2) || isnanq(d)) return 10001; if (c2 == POSITIVE_INFINITY && d == POSITIVE_INFINITY) return 0; if (c2 == NEGATIVE_INFINITY && d == NEGATIVE_INFINITY) return 0; if (!isnumberq(c2) && !isnumberq(d)) return 0; int e; frexpq(mpfr_get_f128(c, GMP_RNDN), &e); mpfr_set_f128(frb, fmaxq(ldexpq(1.0, e-113), FLT128_MIN), GMP_RNDN); mpfr_set_f128(frd, d, GMP_RNDN); mpfr_sub(fra, frd, c, GMP_RNDN); mpfr_div(fra, fra, frb, GMP_RNDN); double u = fabs(mpfr_get_d(fra, GMP_RNDN)); return u; } typedef union { Sleef_quad d; __int128 u128; uint64_t u[2]; } conv_t; Sleef_quad rnd() { conv_t c; switch(random() & 15) { case 0: return INFINITY; case 1: return -INFINITY; } #ifdef ENABLE_SYS_getrandom syscall(SYS_getrandom, &c.u128, sizeof(c.u128), 0); #else c.u128 = random() | ((__int128)random() << 31) | ((__int128)random() << (31*2)) | ((__int128)random() << (31*3)) | ((__int128)random() << (31*4)); #endif return c.d; } Sleef_quad rnd_fr() { conv_t c; do { #ifdef ENABLE_SYS_getrandom syscall(SYS_getrandom, &c.u128, sizeof(c.u128), 0); #else c.u128 = random() | ((__int128)random() << 31) | ((__int128)random() << (31*2)) | ((__int128)random() << (31*3)) | ((__int128)random() << (31*4)); #endif } while(!isnumberq(c.d)); return c.d; } Sleef_quad rnd_zo() { conv_t c; do { #ifdef ENABLE_SYS_getrandom syscall(SYS_getrandom, &c.u128, sizeof(c.u128), 0); #else c.u128 = random() | ((__int128)random() << 31) | ((__int128)random() << (31*2)) | ((__int128)random() << (31*3)) | ((__int128)random() << (31*4)); #endif } while(!isnumberq(c.d) || c.d < -1 || 1 < c.d); return c.d; } void sinpifr(mpfr_t ret, Sleef_quad d) { mpfr_t frpi, frd; mpfr_inits(frpi, frd, NULL); mpfr_const_pi(frpi, GMP_RNDN); mpfr_set_d(frd, 1.0, GMP_RNDN); mpfr_mul(frpi, frpi, frd, GMP_RNDN); mpfr_set_f128(frd, d, GMP_RNDN); mpfr_mul(frd, frpi, frd, GMP_RNDN); mpfr_sin(ret, frd, GMP_RNDN); mpfr_clears(frpi, frd, NULL); } void cospifr(mpfr_t ret, Sleef_quad d) { mpfr_t frpi, frd; mpfr_inits(frpi, frd, NULL); mpfr_const_pi(frpi, GMP_RNDN); mpfr_set_d(frd, 1.0, GMP_RNDN); mpfr_mul(frpi, frpi, frd, GMP_RNDN); mpfr_set_f128(frd, d, GMP_RNDN); mpfr_mul(frd, frpi, frd, GMP_RNDN); mpfr_cos(ret, frd, GMP_RNDN); mpfr_clears(frpi, frd, NULL); } int main(int argc,char **argv) { mpfr_t frw, frx, fry, frz; mpfr_set_default_prec(2048); mpfr_inits(fra, frb, frc, frd, frw, frx, fry, frz, NULL); conv_t cd; Sleef_quad d, t, d2, zo; int cnt, ecnt = 0; srandom(time(NULL)); #if 0 cd.d = M_PIq; mpfr_set_f128(frx, cd.d, GMP_RNDN); cd.u128 += 3; printf("%g\n", countULP2(cd.d, frx)); #endif const Sleef_quad rangemax = 1e+9; for(cnt = 0;ecnt < 1000;cnt++) { switch(cnt & 7) { case 0: d = rnd(); d2 = rnd(); zo = rnd(); break; case 1: cd.d = rint((2 * (double)random() / RAND_MAX - 1) * 1e+10) * M_PI_4; cd.u128 += (random() & 0xff) - 0x7f; d = cd.d; d2 = rnd(); zo = rnd(); break; default: d = rnd_fr(); d2 = rnd_fr(); zo = rnd_zo(); break; } Sleef_quad2 sc = xsincospiq_u05(d); Sleef_quad2 sc2 = xsincospiq_u35(d); { const double rangemax2 = 1e+9; sinpifr(frx, d); double u0 = countULP2(t = sc.x, frx); if (u0 != 0 && ((fabs(d) <= rangemax2 && u0 > 0.505) || fabs(t) > 1 || !isnumberq(t))) { printf("Pure C sincospiq_u05 sin arg="); printf128(d); printf(" ulp=%.20g\n", u0); fflush(stdout); ecnt++; } double u1 = countULP2(t = sc2.x, frx); if (u1 != 0 && ((fabs(d) <= rangemax2 && u1 > 2.0) || fabs(t) > 1 || !isnumberq(t))) { printf("Pure C sincospiq_u35 sin arg=%.30Lg ulp=%.20g\n", (long double)d, u1); fflush(stdout); ecnt++; } } { const double rangemax2 = 1e+9; cospifr(frx, d); double u0 = countULP2(t = sc.y, frx); if (u0 != 0 && ((fabs(d) <= rangemax2 && u0 > 0.505) || fabs(t) > 1 || !isnumberq(t))) { printf("Pure C sincospiq_u05 cos arg=%.30Lg ulp=%.20g\n", (long double)d, u0); fflush(stdout); ecnt++; } double u1 = countULP2(t = sc.y, frx); if (u1 != 0 && ((fabs(d) <= rangemax2 && u1 > 2.0) || fabs(t) > 1 || !isnumberq(t))) { printf("Pure C sincospiq_u35 cos arg=%.30Lg ulp=%.20g\n", (long double)d, u1); fflush(stdout); ecnt++; } } #if 0 double2 sc = xsincos(d); double2 sc2 = xsincos_u1(d); { mpfr_set_d(frx, d, GMP_RNDN); mpfr_sin(frx, frx, GMP_RNDN); double u0 = countULP(t = xsin(d), frx); if ((fabs(d) <= rangemax && u0 > 3.5) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C sin arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(sc.x, frx); if ((fabs(d) <= rangemax && u1 > 3.5) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C sincos sin arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } double u2 = countULP(t = xsin_u1(d), frx); if ((fabs(d) <= rangemax && u2 > 1) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C sin_u1 arg=%.20g ulp=%.20g\n", d, u2); fflush(stdout); ecnt++; } double u3 = countULP(t = sc2.x, frx); if ((fabs(d) <= rangemax && u3 > 1) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C sincos_u1 sin arg=%.20g ulp=%.20g\n", d, u3); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_cos(frx, frx, GMP_RNDN); double u0 = countULP(t = xcos(d), frx); if ((fabs(d) <= rangemax && u0 > 3.5) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C cos arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(t = sc.y, frx); if ((fabs(d) <= rangemax && u1 > 3.5) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C sincos cos arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } double u2 = countULP(t = xcos_u1(d), frx); if ((fabs(d) <= rangemax && u2 > 1) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C cos_u1 arg=%.20g ulp=%.20g\n", d, u2); fflush(stdout); ecnt++; } double u3 = countULP(t = sc2.y, frx); if ((fabs(d) <= rangemax && u3 > 1) || fabs(t) > 1 || !isnumberq(t)) { printf("Pure C sincos_u1 cos arg=%.20g ulp=%.20g\n", d, u3); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_tan(frx, frx, GMP_RNDN); double u0 = countULP(t = xtan(d), frx); if ((fabs(d) < 1e+7 && u0 > 3.5) || (fabs(d) <= rangemax && u0 > 5) || isnan(t)) { printf("Pure C tan arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(t = xtan_u1(d), frx); if ((fabs(d) <= rangemax && u1 > 1) || isnan(t)) { printf("Pure C tan_u1 arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } } d = rnd_fr(); double d2 = rnd_fr(), zo = rnd_zo(); { mpfr_set_d(frx, fabs(d), GMP_RNDN); mpfr_log(frx, frx, GMP_RNDN); double u0 = countULP(t = xlog(fabs(d)), frx); if (u0 > 3.5) { printf("Pure C log arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(t = xlog_u1(fabs(d)), frx); if (u1 > 1) { printf("Pure C log_u1 arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, fabs(d), GMP_RNDN); mpfr_log10(frx, frx, GMP_RNDN); double u0 = countULP(t = xlog10(fabs(d)), frx); if (u0 > 1) { printf("Pure C log10 arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_log1p(frx, frx, GMP_RNDN); double u0 = countULP(t = xlog1p(d), frx); if ((-1 <= d && d <= 1e+307 && u0 > 1) || (d < -1 && !isnan(t)) || (d > 1e+307 && !(u0 <= 1 || isinf(t)))) { printf("Pure C log1p arg=%.20g ulp=%.20g\n", d, u0); printf("%g\n", t); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_exp(frx, frx, GMP_RNDN); double u0 = countULP(t = xexp(d), frx); if (u0 > 1) { printf("Pure C exp arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_exp2(frx, frx, GMP_RNDN); double u0 = countULP(t = xexp2(d), frx); if (u0 > 1) { printf("Pure C exp2 arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_exp10(frx, frx, GMP_RNDN); double u0 = countULP(t = xexp10(d), frx); if (u0 > 1) { printf("Pure C exp10 arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_expm1(frx, frx, GMP_RNDN); double u0 = countULP(t = xexpm1(d), frx); if (u0 > 1) { printf("Pure C expm1 arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_set_d(fry, d2, GMP_RNDN); mpfr_pow(frx, fry, frx, GMP_RNDN); double u0 = countULP(t = xpow(d2, d), frx); if (u0 > 1) { printf("Pure C pow arg=%.20g, %.20g ulp=%.20g\n", d2, d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_cbrt(frx, frx, GMP_RNDN); double u0 = countULP(t = xcbrt(d), frx); if (u0 > 3.5) { printf("Pure C cbrt arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(t = xcbrt_u1(d), frx); if (u1 > 1) { printf("Pure C cbrt_u1 arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, zo, GMP_RNDN); mpfr_asin(frx, frx, GMP_RNDN); double u0 = countULP(t = xasin(zo), frx); if (u0 > 3.5) { printf("Pure C asin arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(t = xasin_u1(zo), frx); if (u1 > 1) { printf("Pure C asin_u1 arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, zo, GMP_RNDN); mpfr_acos(frx, frx, GMP_RNDN); double u0 = countULP(t = xacos(zo), frx); if (u0 > 3.5) { printf("Pure C acos arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(t = xacos_u1(zo), frx); if (u1 > 1) { printf("Pure C acos_u1 arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_atan(frx, frx, GMP_RNDN); double u0 = countULP(t = xatan(d), frx); if (u0 > 3.5) { printf("Pure C atan arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } double u1 = countULP(t = xatan_u1(d), frx); if (u1 > 1) { printf("Pure C atan_u1 arg=%.20g ulp=%.20g\n", d, u1); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_set_d(fry, d2, GMP_RNDN); mpfr_atan2(frx, fry, frx, GMP_RNDN); double u0 = countULP(t = xatan2(d2, d), frx); if (u0 > 3.5) { printf("Pure C atan2 arg=%.20g, %.20g ulp=%.20g\n", d2, d, u0); fflush(stdout); ecnt++; } double u1 = countULP2(t = xatan2_u1(d2, d), frx); if (u1 > 1) { printf("Pure C atan2_u1 arg=%.20g, %.20g ulp=%.20g\n", d2, d, u1); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_sinh(frx, frx, GMP_RNDN); double u0 = countULP(t = xsinh(d), frx); if ((fabs(d) <= 709 && u0 > 1) || (d > 709 && !(u0 <= 1 || (isinf(t) && t > 0))) || (d < -709 && !(u0 <= 1 || (isinf(t) && t < 0)))) { printf("Pure C sinh arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_cosh(frx, frx, GMP_RNDN); double u0 = countULP(t = xcosh(d), frx); if ((fabs(d) <= 709 && u0 > 1) || !(u0 <= 1 || (isinf(t) && t > 0))) { printf("Pure C cosh arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_tanh(frx, frx, GMP_RNDN); double u0 = countULP(t = xtanh(d), frx); if (u0 > 1) { printf("Pure C tanh arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_asinh(frx, frx, GMP_RNDN); double u0 = countULP(t = xasinh(d), frx); if ((fabs(d) < sqrt(DBL_MAX) && u0 > 1) || (d >= sqrt(DBL_MAX) && !(u0 <= 1 || (isinf(t) && t > 0))) || (d <= -sqrt(DBL_MAX) && !(u0 <= 1 || (isinf(t) && t < 0)))) { printf("Pure C asinh arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_acosh(frx, frx, GMP_RNDN); double u0 = countULP(t = xacosh(d), frx); if ((fabs(d) < sqrt(DBL_MAX) && u0 > 1) || (d >= sqrt(DBL_MAX) && !(u0 <= 1 || (isinf(t) && t > 0))) || (d <= -sqrt(DBL_MAX) && !isnan(t))) { printf("Pure C acosh arg=%.20g ulp=%.20g\n", d, u0); printf("%.20g\n", t); fflush(stdout); ecnt++; } } { mpfr_set_d(frx, d, GMP_RNDN); mpfr_atanh(frx, frx, GMP_RNDN); double u0 = countULP(t = xatanh(d), frx); if (u0 > 1) { printf("Pure C atanh arg=%.20g ulp=%.20g\n", d, u0); fflush(stdout); ecnt++; } } #endif } }