/* * dotest.c - actually generate mathlib test cases * * Copyright (c) 1999-2019, Arm Limited. * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception */ #include #include #include #include #include #include #include "semi.h" #include "intern.h" #include "random.h" #define MPFR_PREC 96 /* good enough for float or double + a few extra bits */ extern int lib_fo, lib_no_arith, ntests; /* * Prototypes. */ static void cases_biased(uint32 *, uint32, uint32); static void cases_biased_positive(uint32 *, uint32, uint32); static void cases_biased_float(uint32 *, uint32, uint32); static void cases_uniform(uint32 *, uint32, uint32); static void cases_uniform_positive(uint32 *, uint32, uint32); static void cases_uniform_float(uint32 *, uint32, uint32); static void cases_uniform_float_positive(uint32 *, uint32, uint32); static void log_cases(uint32 *, uint32, uint32); static void log_cases_float(uint32 *, uint32, uint32); static void log1p_cases(uint32 *, uint32, uint32); static void log1p_cases_float(uint32 *, uint32, uint32); static void minmax_cases(uint32 *, uint32, uint32); static void minmax_cases_float(uint32 *, uint32, uint32); static void atan2_cases(uint32 *, uint32, uint32); static void atan2_cases_float(uint32 *, uint32, uint32); static void pow_cases(uint32 *, uint32, uint32); static void pow_cases_float(uint32 *, uint32, uint32); static void rred_cases(uint32 *, uint32, uint32); static void rred_cases_float(uint32 *, uint32, uint32); static void cases_semi1(uint32 *, uint32, uint32); static void cases_semi1_float(uint32 *, uint32, uint32); static void cases_semi2(uint32 *, uint32, uint32); static void cases_semi2_float(uint32 *, uint32, uint32); static void cases_ldexp(uint32 *, uint32, uint32); static void cases_ldexp_float(uint32 *, uint32, uint32); static void complex_cases_uniform(uint32 *, uint32, uint32); static void complex_cases_uniform_float(uint32 *, uint32, uint32); static void complex_cases_biased(uint32 *, uint32, uint32); static void complex_cases_biased_float(uint32 *, uint32, uint32); static void complex_log_cases(uint32 *, uint32, uint32); static void complex_log_cases_float(uint32 *, uint32, uint32); static void complex_pow_cases(uint32 *, uint32, uint32); static void complex_pow_cases_float(uint32 *, uint32, uint32); static void complex_arithmetic_cases(uint32 *, uint32, uint32); static void complex_arithmetic_cases_float(uint32 *, uint32, uint32); static uint32 doubletop(int x, int scale); static uint32 floatval(int x, int scale); /* * Convert back and forth between IEEE bit patterns and the * mpfr_t/mpc_t types. */ static void set_mpfr_d(mpfr_t x, uint32 h, uint32 l) { uint64_t hl = ((uint64_t)h << 32) | l; uint32 exp = (hl >> 52) & 0x7ff; int64_t mantissa = hl & (((uint64_t)1 << 52) - 1); int sign = (hl >> 63) ? -1 : +1; if (exp == 0x7ff) { if (mantissa == 0) mpfr_set_inf(x, sign); else mpfr_set_nan(x); } else if (exp == 0 && mantissa == 0) { mpfr_set_ui(x, 0, GMP_RNDN); mpfr_setsign(x, x, sign < 0, GMP_RNDN); } else { if (exp != 0) mantissa |= ((uint64_t)1 << 52); else exp++; mpfr_set_sj_2exp(x, mantissa * sign, (int)exp - 0x3ff - 52, GMP_RNDN); } } static void set_mpfr_f(mpfr_t x, uint32 f) { uint32 exp = (f >> 23) & 0xff; int32 mantissa = f & ((1 << 23) - 1); int sign = (f >> 31) ? -1 : +1; if (exp == 0xff) { if (mantissa == 0) mpfr_set_inf(x, sign); else mpfr_set_nan(x); } else if (exp == 0 && mantissa == 0) { mpfr_set_ui(x, 0, GMP_RNDN); mpfr_setsign(x, x, sign < 0, GMP_RNDN); } else { if (exp != 0) mantissa |= (1 << 23); else exp++; mpfr_set_sj_2exp(x, mantissa * sign, (int)exp - 0x7f - 23, GMP_RNDN); } } static void set_mpc_d(mpc_t z, uint32 rh, uint32 rl, uint32 ih, uint32 il) { mpfr_t x, y; mpfr_init2(x, MPFR_PREC); mpfr_init2(y, MPFR_PREC); set_mpfr_d(x, rh, rl); set_mpfr_d(y, ih, il); mpc_set_fr_fr(z, x, y, MPC_RNDNN); mpfr_clear(x); mpfr_clear(y); } static void set_mpc_f(mpc_t z, uint32 r, uint32 i) { mpfr_t x, y; mpfr_init2(x, MPFR_PREC); mpfr_init2(y, MPFR_PREC); set_mpfr_f(x, r); set_mpfr_f(y, i); mpc_set_fr_fr(z, x, y, MPC_RNDNN); mpfr_clear(x); mpfr_clear(y); } static void get_mpfr_d(const mpfr_t x, uint32 *h, uint32 *l, uint32 *extra) { uint32_t sign, expfield, mantfield; mpfr_t significand; int exp; if (mpfr_nan_p(x)) { *h = 0x7ff80000; *l = 0; *extra = 0; return; } sign = mpfr_signbit(x) ? 0x80000000U : 0; if (mpfr_inf_p(x)) { *h = 0x7ff00000 | sign; *l = 0; *extra = 0; return; } if (mpfr_zero_p(x)) { *h = 0x00000000 | sign; *l = 0; *extra = 0; return; } mpfr_init2(significand, MPFR_PREC); mpfr_set(significand, x, GMP_RNDN); exp = mpfr_get_exp(significand); mpfr_set_exp(significand, 0); /* Now significand is in [1/2,1), and significand * 2^exp == x. * So the IEEE exponent corresponding to exp==0 is 0x3fe. */ if (exp > 0x400) { /* overflow to infinity anyway */ *h = 0x7ff00000 | sign; *l = 0; *extra = 0; mpfr_clear(significand); return; } if (exp <= -0x3fe || mpfr_zero_p(x)) exp = -0x3fd; /* denormalise */ expfield = exp + 0x3fd; /* offset to cancel leading mantissa bit */ mpfr_div_2si(significand, x, exp - 21, GMP_RNDN); mpfr_abs(significand, significand, GMP_RNDN); mantfield = mpfr_get_ui(significand, GMP_RNDZ); *h = sign + ((uint64_t)expfield << 20) + mantfield; mpfr_sub_ui(significand, significand, mantfield, GMP_RNDN); mpfr_mul_2ui(significand, significand, 32, GMP_RNDN); mantfield = mpfr_get_ui(significand, GMP_RNDZ); *l = mantfield; mpfr_sub_ui(significand, significand, mantfield, GMP_RNDN); mpfr_mul_2ui(significand, significand, 32, GMP_RNDN); mantfield = mpfr_get_ui(significand, GMP_RNDZ); *extra = mantfield; mpfr_clear(significand); } static void get_mpfr_f(const mpfr_t x, uint32 *f, uint32 *extra) { uint32_t sign, expfield, mantfield; mpfr_t significand; int exp; if (mpfr_nan_p(x)) { *f = 0x7fc00000; *extra = 0; return; } sign = mpfr_signbit(x) ? 0x80000000U : 0; if (mpfr_inf_p(x)) { *f = 0x7f800000 | sign; *extra = 0; return; } if (mpfr_zero_p(x)) { *f = 0x00000000 | sign; *extra = 0; return; } mpfr_init2(significand, MPFR_PREC); mpfr_set(significand, x, GMP_RNDN); exp = mpfr_get_exp(significand); mpfr_set_exp(significand, 0); /* Now significand is in [1/2,1), and significand * 2^exp == x. * So the IEEE exponent corresponding to exp==0 is 0x7e. */ if (exp > 0x80) { /* overflow to infinity anyway */ *f = 0x7f800000 | sign; *extra = 0; mpfr_clear(significand); return; } if (exp <= -0x7e || mpfr_zero_p(x)) exp = -0x7d; /* denormalise */ expfield = exp + 0x7d; /* offset to cancel leading mantissa bit */ mpfr_div_2si(significand, x, exp - 24, GMP_RNDN); mpfr_abs(significand, significand, GMP_RNDN); mantfield = mpfr_get_ui(significand, GMP_RNDZ); *f = sign + ((uint64_t)expfield << 23) + mantfield; mpfr_sub_ui(significand, significand, mantfield, GMP_RNDN); mpfr_mul_2ui(significand, significand, 32, GMP_RNDN); mantfield = mpfr_get_ui(significand, GMP_RNDZ); *extra = mantfield; mpfr_clear(significand); } static void get_mpc_d(const mpc_t z, uint32 *rh, uint32 *rl, uint32 *rextra, uint32 *ih, uint32 *il, uint32 *iextra) { mpfr_t x, y; mpfr_init2(x, MPFR_PREC); mpfr_init2(y, MPFR_PREC); mpc_real(x, z, GMP_RNDN); mpc_imag(y, z, GMP_RNDN); get_mpfr_d(x, rh, rl, rextra); get_mpfr_d(y, ih, il, iextra); mpfr_clear(x); mpfr_clear(y); } static void get_mpc_f(const mpc_t z, uint32 *r, uint32 *rextra, uint32 *i, uint32 *iextra) { mpfr_t x, y; mpfr_init2(x, MPFR_PREC); mpfr_init2(y, MPFR_PREC); mpc_real(x, z, GMP_RNDN); mpc_imag(y, z, GMP_RNDN); get_mpfr_f(x, r, rextra); get_mpfr_f(y, i, iextra); mpfr_clear(x); mpfr_clear(y); } /* * Implementation of mathlib functions that aren't trivially * implementable using an existing mpfr or mpc function. */ int test_rred(mpfr_t ret, const mpfr_t x, int *quadrant) { mpfr_t halfpi; long quo; int status; /* * In the worst case of range reduction, we get an input of size * around 2^1024, and must find its remainder mod pi, which means * we need 1024 bits of pi at least. Plus, the remainder might * happen to come out very very small if we're unlucky. How * unlucky can we be? Well, conveniently, I once went through and * actually worked that out using Paxson's modular minimisation * algorithm, and it turns out that the smallest exponent you can * get out of a nontrivial[1] double precision range reduction is * 0x3c2, i.e. of the order of 2^-61. So we need 1024 bits of pi * to get us down to the units digit, another 61 or so bits (say * 64) to get down to the highest set bit of the output, and then * some bits to make the actual mantissa big enough. * * [1] of course the output of range reduction can have an * arbitrarily small exponent in the trivial case, where the * input is so small that it's the identity function. That * doesn't count. */ mpfr_init2(halfpi, MPFR_PREC + 1024 + 64); mpfr_const_pi(halfpi, GMP_RNDN); mpfr_div_ui(halfpi, halfpi, 2, GMP_RNDN); status = mpfr_remquo(ret, &quo, x, halfpi, GMP_RNDN); *quadrant = quo & 3; mpfr_clear(halfpi); return status; } int test_lgamma(mpfr_t ret, const mpfr_t x, mpfr_rnd_t rnd) { /* * mpfr_lgamma takes an extra int * parameter to hold the output * sign. We don't bother testing that, so this wrapper throws away * the sign and hence fits into the same function prototype as all * the other real->real mpfr functions. * * There is also mpfr_lngamma which has no sign output and hence * has the right prototype already, but unfortunately it returns * NaN in cases where gamma(x) < 0, so it's no use to us. */ int sign; return mpfr_lgamma(ret, &sign, x, rnd); } int test_cpow(mpc_t ret, const mpc_t x, const mpc_t y, mpc_rnd_t rnd) { /* * For complex pow, we must bump up the precision by a huge amount * if we want it to get the really difficult cases right. (Not * that we expect the library under test to be getting those cases * right itself, but we'd at least like the test suite to report * them as wrong for the _right reason_.) * * This works around a bug in mpc_pow(), fixed by r1455 in the MPC * svn repository (2014-10-14) and expected to be in any MPC * release after 1.0.2 (which was the latest release already made * at the time of the fix). So as and when we update to an MPC * with the fix in it, we could remove this workaround. * * For the reasons for choosing this amount of extra precision, * see analysis in complex/cpownotes.txt for the rationale for the * amount. */ mpc_t xbig, ybig, retbig; int status; mpc_init2(xbig, 1034 + 53 + 60 + MPFR_PREC); mpc_init2(ybig, 1034 + 53 + 60 + MPFR_PREC); mpc_init2(retbig, 1034 + 53 + 60 + MPFR_PREC); mpc_set(xbig, x, MPC_RNDNN); mpc_set(ybig, y, MPC_RNDNN); status = mpc_pow(retbig, xbig, ybig, rnd); mpc_set(ret, retbig, rnd); mpc_clear(xbig); mpc_clear(ybig); mpc_clear(retbig); return status; } /* * Identify 'hard' values (NaN, Inf, nonzero denormal) for deciding * whether microlib will decline to run a test. */ #define is_shard(in) ( \ (((in)[0] & 0x7F800000) == 0x7F800000 || \ (((in)[0] & 0x7F800000) == 0 && ((in)[0]&0x7FFFFFFF) != 0))) #define is_dhard(in) ( \ (((in)[0] & 0x7FF00000) == 0x7FF00000 || \ (((in)[0] & 0x7FF00000) == 0 && (((in)[0] & 0xFFFFF) | (in)[1]) != 0))) /* * Identify integers. */ int is_dinteger(uint32 *in) { uint32 out[3]; if ((0x7FF00000 & ~in[0]) == 0) return 0; /* not finite, hence not integer */ test_ceil(in, out); return in[0] == out[0] && in[1] == out[1]; } int is_sinteger(uint32 *in) { uint32 out[3]; if ((0x7F800000 & ~in[0]) == 0) return 0; /* not finite, hence not integer */ test_ceilf(in, out); return in[0] == out[0]; } /* * Identify signalling NaNs. */ int is_dsnan(const uint32 *in) { if ((in[0] & 0x7FF00000) != 0x7FF00000) return 0; /* not the inf/nan exponent */ if ((in[0] << 12) == 0 && in[1] == 0) return 0; /* inf */ if (in[0] & 0x00080000) return 0; /* qnan */ return 1; } int is_ssnan(const uint32 *in) { if ((in[0] & 0x7F800000) != 0x7F800000) return 0; /* not the inf/nan exponent */ if ((in[0] << 9) == 0) return 0; /* inf */ if (in[0] & 0x00400000) return 0; /* qnan */ return 1; } int is_snan(const uint32 *in, int size) { return size == 2 ? is_dsnan(in) : is_ssnan(in); } /* * Wrapper functions called to fix up unusual results after the main * test function has run. */ void universal_wrapper(wrapperctx *ctx) { /* * Any SNaN input gives rise to a QNaN output. */ int op; for (op = 0; op < wrapper_get_nops(ctx); op++) { int size = wrapper_get_size(ctx, op); if (!wrapper_is_complex(ctx, op) && is_snan(wrapper_get_ieee(ctx, op), size)) { wrapper_set_nan(ctx); } } } Testable functions[] = { /* * Trig functions: sin, cos, tan. We test the core function * between -16 and +16: we assume that range reduction exists * and will be used for larger arguments, and we'll test that * separately. Also we only go down to 2^-27 in magnitude, * because below that sin(x)=tan(x)=x and cos(x)=1 as far as * double precision can tell, which is boring. */ {"sin", (funcptr)mpfr_sin, args1, {NULL}, cases_uniform, 0x3e400000, 0x40300000}, {"sinf", (funcptr)mpfr_sin, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x41800000}, {"cos", (funcptr)mpfr_cos, args1, {NULL}, cases_uniform, 0x3e400000, 0x40300000}, {"cosf", (funcptr)mpfr_cos, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x41800000}, {"tan", (funcptr)mpfr_tan, args1, {NULL}, cases_uniform, 0x3e400000, 0x40300000}, {"tanf", (funcptr)mpfr_tan, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x41800000}, {"sincosf_sinf", (funcptr)mpfr_sin, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x41800000}, {"sincosf_cosf", (funcptr)mpfr_cos, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x41800000}, /* * Inverse trig: asin, acos. Between 1 and -1, of course. acos * goes down to 2^-54, asin to 2^-27. */ {"asin", (funcptr)mpfr_asin, args1, {NULL}, cases_uniform, 0x3e400000, 0x3fefffff}, {"asinf", (funcptr)mpfr_asin, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x3f7fffff}, {"acos", (funcptr)mpfr_acos, args1, {NULL}, cases_uniform, 0x3c900000, 0x3fefffff}, {"acosf", (funcptr)mpfr_acos, args1f, {NULL}, cases_uniform_float, 0x33800000, 0x3f7fffff}, /* * Inverse trig: atan. atan is stable (in double prec) with * argument magnitude past 2^53, so we'll test up to there. * atan(x) is boringly just x below 2^-27. */ {"atan", (funcptr)mpfr_atan, args1, {NULL}, cases_uniform, 0x3e400000, 0x43400000}, {"atanf", (funcptr)mpfr_atan, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x4b800000}, /* * atan2. Interesting cases arise when the exponents of the * arguments differ by at most about 50. */ {"atan2", (funcptr)mpfr_atan2, args2, {NULL}, atan2_cases, 0}, {"atan2f", (funcptr)mpfr_atan2, args2f, {NULL}, atan2_cases_float, 0}, /* * The exponentials: exp, sinh, cosh. They overflow at around * 710. exp and sinh are boring below 2^-54, cosh below 2^-27. */ {"exp", (funcptr)mpfr_exp, args1, {NULL}, cases_uniform, 0x3c900000, 0x40878000}, {"expf", (funcptr)mpfr_exp, args1f, {NULL}, cases_uniform_float, 0x33800000, 0x42dc0000}, {"sinh", (funcptr)mpfr_sinh, args1, {NULL}, cases_uniform, 0x3c900000, 0x40878000}, {"sinhf", (funcptr)mpfr_sinh, args1f, {NULL}, cases_uniform_float, 0x33800000, 0x42dc0000}, {"cosh", (funcptr)mpfr_cosh, args1, {NULL}, cases_uniform, 0x3e400000, 0x40878000}, {"coshf", (funcptr)mpfr_cosh, args1f, {NULL}, cases_uniform_float, 0x39800000, 0x42dc0000}, /* * tanh is stable past around 20. It's boring below 2^-27. */ {"tanh", (funcptr)mpfr_tanh, args1, {NULL}, cases_uniform, 0x3e400000, 0x40340000}, {"tanhf", (funcptr)mpfr_tanh, args1f, {NULL}, cases_uniform, 0x39800000, 0x41100000}, /* * log must be tested only on positive numbers, but can cover * the whole range of positive nonzero finite numbers. It never * gets boring. */ {"log", (funcptr)mpfr_log, args1, {NULL}, log_cases, 0}, {"logf", (funcptr)mpfr_log, args1f, {NULL}, log_cases_float, 0}, {"log10", (funcptr)mpfr_log10, args1, {NULL}, log_cases, 0}, {"log10f", (funcptr)mpfr_log10, args1f, {NULL}, log_cases_float, 0}, /* * pow. */ {"pow", (funcptr)mpfr_pow, args2, {NULL}, pow_cases, 0}, {"powf", (funcptr)mpfr_pow, args2f, {NULL}, pow_cases_float, 0}, /* * Trig range reduction. We are able to test this for all * finite values, but will only bother for things between 2^-3 * and 2^+52. */ {"rred", (funcptr)test_rred, rred, {NULL}, rred_cases, 0}, {"rredf", (funcptr)test_rred, rredf, {NULL}, rred_cases_float, 0}, /* * Square and cube root. */ {"sqrt", (funcptr)mpfr_sqrt, args1, {NULL}, log_cases, 0}, {"sqrtf", (funcptr)mpfr_sqrt, args1f, {NULL}, log_cases_float, 0}, {"cbrt", (funcptr)mpfr_cbrt, args1, {NULL}, log_cases, 0}, {"cbrtf", (funcptr)mpfr_cbrt, args1f, {NULL}, log_cases_float, 0}, {"hypot", (funcptr)mpfr_hypot, args2, {NULL}, atan2_cases, 0}, {"hypotf", (funcptr)mpfr_hypot, args2f, {NULL}, atan2_cases_float, 0}, /* * Seminumerical functions. */ {"ceil", (funcptr)test_ceil, semi1, {NULL}, cases_semi1}, {"ceilf", (funcptr)test_ceilf, semi1f, {NULL}, cases_semi1_float}, {"floor", (funcptr)test_floor, semi1, {NULL}, cases_semi1}, {"floorf", (funcptr)test_floorf, semi1f, {NULL}, cases_semi1_float}, {"fmod", (funcptr)test_fmod, semi2, {NULL}, cases_semi2}, {"fmodf", (funcptr)test_fmodf, semi2f, {NULL}, cases_semi2_float}, {"ldexp", (funcptr)test_ldexp, t_ldexp, {NULL}, cases_ldexp}, {"ldexpf", (funcptr)test_ldexpf, t_ldexpf, {NULL}, cases_ldexp_float}, {"frexp", (funcptr)test_frexp, t_frexp, {NULL}, cases_semi1}, {"frexpf", (funcptr)test_frexpf, t_frexpf, {NULL}, cases_semi1_float}, {"modf", (funcptr)test_modf, t_modf, {NULL}, cases_semi1}, {"modff", (funcptr)test_modff, t_modff, {NULL}, cases_semi1_float}, /* * Classification and more semi-numericals */ {"copysign", (funcptr)test_copysign, semi2, {NULL}, cases_semi2}, {"copysignf", (funcptr)test_copysignf, semi2f, {NULL}, cases_semi2_float}, {"isfinite", (funcptr)test_isfinite, classify, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isfinitef", (funcptr)test_isfinitef, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"isinf", (funcptr)test_isinf, classify, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isinff", (funcptr)test_isinff, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"isnan", (funcptr)test_isnan, classify, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isnanf", (funcptr)test_isnanf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"isnormal", (funcptr)test_isnormal, classify, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isnormalf", (funcptr)test_isnormalf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"signbit", (funcptr)test_signbit, classify, {NULL}, cases_uniform, 0, 0x7fffffff}, {"signbitf", (funcptr)test_signbitf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"fpclassify", (funcptr)test_fpclassify, classify, {NULL}, cases_uniform, 0, 0x7fffffff}, {"fpclassifyf", (funcptr)test_fpclassifyf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff}, /* * Comparisons */ {"isgreater", (funcptr)test_isgreater, compare, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isgreaterequal", (funcptr)test_isgreaterequal, compare, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isless", (funcptr)test_isless, compare, {NULL}, cases_uniform, 0, 0x7fffffff}, {"islessequal", (funcptr)test_islessequal, compare, {NULL}, cases_uniform, 0, 0x7fffffff}, {"islessgreater", (funcptr)test_islessgreater, compare, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isunordered", (funcptr)test_isunordered, compare, {NULL}, cases_uniform, 0, 0x7fffffff}, {"isgreaterf", (funcptr)test_isgreaterf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"isgreaterequalf", (funcptr)test_isgreaterequalf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"islessf", (funcptr)test_islessf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"islessequalf", (funcptr)test_islessequalf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"islessgreaterf", (funcptr)test_islessgreaterf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff}, {"isunorderedf", (funcptr)test_isunorderedf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff}, /* * Inverse Hyperbolic functions */ {"atanh", (funcptr)mpfr_atanh, args1, {NULL}, cases_uniform, 0x3e400000, 0x3fefffff}, {"asinh", (funcptr)mpfr_asinh, args1, {NULL}, cases_uniform, 0x3e400000, 0x3fefffff}, {"acosh", (funcptr)mpfr_acosh, args1, {NULL}, cases_uniform_positive, 0x3ff00000, 0x7fefffff}, {"atanhf", (funcptr)mpfr_atanh, args1f, {NULL}, cases_uniform_float, 0x32000000, 0x3f7fffff}, {"asinhf", (funcptr)mpfr_asinh, args1f, {NULL}, cases_uniform_float, 0x32000000, 0x3f7fffff}, {"acoshf", (funcptr)mpfr_acosh, args1f, {NULL}, cases_uniform_float_positive, 0x3f800000, 0x7f800000}, /* * Everything else (sitting in a section down here at the bottom * because historically they were not tested because we didn't * have reference implementations for them) */ {"csin", (funcptr)mpc_sin, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"csinf", (funcptr)mpc_sin, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"ccos", (funcptr)mpc_cos, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"ccosf", (funcptr)mpc_cos, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"ctan", (funcptr)mpc_tan, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"ctanf", (funcptr)mpc_tan, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"casin", (funcptr)mpc_asin, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"casinf", (funcptr)mpc_asin, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"cacos", (funcptr)mpc_acos, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"cacosf", (funcptr)mpc_acos, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"catan", (funcptr)mpc_atan, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"catanf", (funcptr)mpc_atan, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"csinh", (funcptr)mpc_sinh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"csinhf", (funcptr)mpc_sinh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"ccosh", (funcptr)mpc_cosh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"ccoshf", (funcptr)mpc_cosh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"ctanh", (funcptr)mpc_tanh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"ctanhf", (funcptr)mpc_tanh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"casinh", (funcptr)mpc_asinh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"casinhf", (funcptr)mpc_asinh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"cacosh", (funcptr)mpc_acosh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"cacoshf", (funcptr)mpc_acosh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"catanh", (funcptr)mpc_atanh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000}, {"catanhf", (funcptr)mpc_atanh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000}, {"cexp", (funcptr)mpc_exp, args1c, {NULL}, complex_cases_uniform, 0x3c900000, 0x40862000}, {"cpow", (funcptr)test_cpow, args2c, {NULL}, complex_pow_cases, 0x3fc00000, 0x40000000}, {"clog", (funcptr)mpc_log, args1c, {NULL}, complex_log_cases, 0, 0}, {"csqrt", (funcptr)mpc_sqrt, args1c, {NULL}, complex_log_cases, 0, 0}, {"cexpf", (funcptr)mpc_exp, args1fc, {NULL}, complex_cases_uniform_float, 0x24800000, 0x42b00000}, {"cpowf", (funcptr)test_cpow, args2fc, {NULL}, complex_pow_cases_float, 0x3e000000, 0x41000000}, {"clogf", (funcptr)mpc_log, args1fc, {NULL}, complex_log_cases_float, 0, 0}, {"csqrtf", (funcptr)mpc_sqrt, args1fc, {NULL}, complex_log_cases_float, 0, 0}, {"cdiv", (funcptr)mpc_div, args2c, {NULL}, complex_arithmetic_cases, 0, 0}, {"cmul", (funcptr)mpc_mul, args2c, {NULL}, complex_arithmetic_cases, 0, 0}, {"cadd", (funcptr)mpc_add, args2c, {NULL}, complex_arithmetic_cases, 0, 0}, {"csub", (funcptr)mpc_sub, args2c, {NULL}, complex_arithmetic_cases, 0, 0}, {"cdivf", (funcptr)mpc_div, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"cmulf", (funcptr)mpc_mul, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"caddf", (funcptr)mpc_add, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"csubf", (funcptr)mpc_sub, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"cabsf", (funcptr)mpc_abs, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"cabs", (funcptr)mpc_abs, args1cr, {NULL}, complex_arithmetic_cases, 0, 0}, {"cargf", (funcptr)mpc_arg, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"carg", (funcptr)mpc_arg, args1cr, {NULL}, complex_arithmetic_cases, 0, 0}, {"cimagf", (funcptr)mpc_imag, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"cimag", (funcptr)mpc_imag, args1cr, {NULL}, complex_arithmetic_cases, 0, 0}, {"conjf", (funcptr)mpc_conj, args1fc, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"conj", (funcptr)mpc_conj, args1c, {NULL}, complex_arithmetic_cases, 0, 0}, {"cprojf", (funcptr)mpc_proj, args1fc, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"cproj", (funcptr)mpc_proj, args1c, {NULL}, complex_arithmetic_cases, 0, 0}, {"crealf", (funcptr)mpc_real, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0}, {"creal", (funcptr)mpc_real, args1cr, {NULL}, complex_arithmetic_cases, 0, 0}, {"erfcf", (funcptr)mpfr_erfc, args1f, {NULL}, cases_biased_float, 0x1e800000, 0x41000000}, {"erfc", (funcptr)mpfr_erfc, args1, {NULL}, cases_biased, 0x3bd00000, 0x403c0000}, {"erff", (funcptr)mpfr_erf, args1f, {NULL}, cases_biased_float, 0x03800000, 0x40700000}, {"erf", (funcptr)mpfr_erf, args1, {NULL}, cases_biased, 0x00800000, 0x40200000}, {"exp2f", (funcptr)mpfr_exp2, args1f, {NULL}, cases_uniform_float, 0x33800000, 0x43c00000}, {"exp2", (funcptr)mpfr_exp2, args1, {NULL}, cases_uniform, 0x3ca00000, 0x40a00000}, {"expm1f", (funcptr)mpfr_expm1, args1f, {NULL}, cases_uniform_float, 0x33000000, 0x43800000}, {"expm1", (funcptr)mpfr_expm1, args1, {NULL}, cases_uniform, 0x3c900000, 0x409c0000}, {"fmaxf", (funcptr)mpfr_max, args2f, {NULL}, minmax_cases_float, 0, 0x7f7fffff}, {"fmax", (funcptr)mpfr_max, args2, {NULL}, minmax_cases, 0, 0x7fefffff}, {"fminf", (funcptr)mpfr_min, args2f, {NULL}, minmax_cases_float, 0, 0x7f7fffff}, {"fmin", (funcptr)mpfr_min, args2, {NULL}, minmax_cases, 0, 0x7fefffff}, {"lgammaf", (funcptr)test_lgamma, args1f, {NULL}, cases_uniform_float, 0x01800000, 0x7f800000}, {"lgamma", (funcptr)test_lgamma, args1, {NULL}, cases_uniform, 0x00100000, 0x7ff00000}, {"log1pf", (funcptr)mpfr_log1p, args1f, {NULL}, log1p_cases_float, 0, 0}, {"log1p", (funcptr)mpfr_log1p, args1, {NULL}, log1p_cases, 0, 0}, {"log2f", (funcptr)mpfr_log2, args1f, {NULL}, log_cases_float, 0, 0}, {"log2", (funcptr)mpfr_log2, args1, {NULL}, log_cases, 0, 0}, {"tgammaf", (funcptr)mpfr_gamma, args1f, {NULL}, cases_uniform_float, 0x2f800000, 0x43000000}, {"tgamma", (funcptr)mpfr_gamma, args1, {NULL}, cases_uniform, 0x3c000000, 0x40800000}, }; const int nfunctions = ( sizeof(functions)/sizeof(*functions) ); #define random_sign ( random_upto(1) ? 0x80000000 : 0 ) static int iszero(uint32 *x) { return !((x[0] & 0x7FFFFFFF) || x[1]); } static void complex_log_cases(uint32 *out, uint32 param1, uint32 param2) { cases_uniform(out,0x00100000,0x7fefffff); cases_uniform(out+2,0x00100000,0x7fefffff); } static void complex_log_cases_float(uint32 *out, uint32 param1, uint32 param2) { cases_uniform_float(out,0x00800000,0x7f7fffff); cases_uniform_float(out+2,0x00800000,0x7f7fffff); } static void complex_cases_biased(uint32 *out, uint32 lowbound, uint32 highbound) { cases_biased(out,lowbound,highbound); cases_biased(out+2,lowbound,highbound); } static void complex_cases_biased_float(uint32 *out, uint32 lowbound, uint32 highbound) { cases_biased_float(out,lowbound,highbound); cases_biased_float(out+2,lowbound,highbound); } static void complex_cases_uniform(uint32 *out, uint32 lowbound, uint32 highbound) { cases_uniform(out,lowbound,highbound); cases_uniform(out+2,lowbound,highbound); } static void complex_cases_uniform_float(uint32 *out, uint32 lowbound, uint32 highbound) { cases_uniform_float(out,lowbound,highbound); cases_uniform(out+2,lowbound,highbound); } static void complex_pow_cases(uint32 *out, uint32 lowbound, uint32 highbound) { /* * Generating non-overflowing cases for complex pow: * * Our base has both parts within the range [1/2,2], and hence * its magnitude is within [1/2,2*sqrt(2)]. The magnitude of its * logarithm in base 2 is therefore at most the magnitude of * (log2(2*sqrt(2)) + i*pi/log(2)), or in other words * hypot(3/2,pi/log(2)) = 4.77. So the magnitude of the exponent * input must be at most our output magnitude limit (as a power * of two) divided by that. * * I also set the output magnitude limit a bit low, because we * don't guarantee (and neither does glibc) to prevent internal * overflow in cases where the output _magnitude_ overflows but * scaling it back down by cos and sin of the argument brings it * back in range. */ cases_uniform(out,0x3fe00000, 0x40000000); cases_uniform(out+2,0x3fe00000, 0x40000000); cases_uniform(out+4,0x3f800000, 0x40600000); cases_uniform(out+6,0x3f800000, 0x40600000); } static void complex_pow_cases_float(uint32 *out, uint32 lowbound, uint32 highbound) { /* * Reasoning as above, though of course the detailed numbers are * all different. */ cases_uniform_float(out,0x3f000000, 0x40000000); cases_uniform_float(out+2,0x3f000000, 0x40000000); cases_uniform_float(out+4,0x3d600000, 0x41900000); cases_uniform_float(out+6,0x3d600000, 0x41900000); } static void complex_arithmetic_cases(uint32 *out, uint32 lowbound, uint32 highbound) { cases_uniform(out,0,0x7fefffff); cases_uniform(out+2,0,0x7fefffff); cases_uniform(out+4,0,0x7fefffff); cases_uniform(out+6,0,0x7fefffff); } static void complex_arithmetic_cases_float(uint32 *out, uint32 lowbound, uint32 highbound) { cases_uniform_float(out,0,0x7f7fffff); cases_uniform_float(out+2,0,0x7f7fffff); cases_uniform_float(out+4,0,0x7f7fffff); cases_uniform_float(out+6,0,0x7f7fffff); } /* * Included from fplib test suite, in a compact self-contained * form. */ void float32_case(uint32 *ret) { int n, bits; uint32 f; static int premax, preptr; static uint32 *specifics = NULL; if (!ret) { if (specifics) free(specifics); specifics = NULL; premax = preptr = 0; return; } if (!specifics) { int exps[] = { -127, -126, -125, -24, -4, -3, -2, -1, 0, 1, 2, 3, 4, 24, 29, 30, 31, 32, 61, 62, 63, 64, 126, 127, 128 }; int sign, eptr; uint32 se, j; /* * We want a cross product of: * - each of two sign bits (2) * - each of the above (unbiased) exponents (25) * - the following list of fraction parts: * * zero (1) * * all bits (1) * * one-bit-set (23) * * one-bit-clear (23) * * one-bit-and-above (20: 3 are duplicates) * * one-bit-and-below (20: 3 are duplicates) * (total 88) * (total 4400) */ specifics = malloc(4400 * sizeof(*specifics)); preptr = 0; for (sign = 0; sign <= 1; sign++) { for (eptr = 0; eptr < sizeof(exps)/sizeof(*exps); eptr++) { se = (sign ? 0x80000000 : 0) | ((exps[eptr]+127) << 23); /* * Zero. */ specifics[preptr++] = se | 0; /* * All bits. */ specifics[preptr++] = se | 0x7FFFFF; /* * One-bit-set. */ for (j = 1; j && j <= 0x400000; j <<= 1) specifics[preptr++] = se | j; /* * One-bit-clear. */ for (j = 1; j && j <= 0x400000; j <<= 1) specifics[preptr++] = se | (0x7FFFFF ^ j); /* * One-bit-and-everything-below. */ for (j = 2; j && j <= 0x100000; j <<= 1) specifics[preptr++] = se | (2*j-1); /* * One-bit-and-everything-above. */ for (j = 4; j && j <= 0x200000; j <<= 1) specifics[preptr++] = se | (0x7FFFFF ^ (j-1)); /* * Done. */ } } assert(preptr == 4400); premax = preptr; } /* * Decide whether to return a pre or a random case. */ n = random32() % (premax+1); if (n < preptr) { /* * Return pre[n]. */ uint32 t; t = specifics[n]; specifics[n] = specifics[preptr-1]; specifics[preptr-1] = t; /* (not really needed) */ preptr--; *ret = t; } else { /* * Random case. * Sign and exponent: * - FIXME * Significand: * - with prob 1/5, a totally random bit pattern * - with prob 1/5, all 1s down to some point and then random * - with prob 1/5, all 1s up to some point and then random * - with prob 1/5, all 0s down to some point and then random * - with prob 1/5, all 0s up to some point and then random */ n = random32() % 5; f = random32(); /* some random bits */ bits = random32() % 22 + 1; /* 1-22 */ switch (n) { case 0: break; /* leave f alone */ case 1: f |= (1< 0x3FF, the range is [-0x432/(e-0x3FF),+0x400/(e-0x3FF)] * * For e == 0x3FE or e == 0x3FF, the range gets infinite at one * end or the other, so we have to be cleverer: pick a number n * of useful bits in the mantissa (1 thru 52, so 1 must imply * 0x3ff00000.00000001 whereas 52 is anything at least as big * as 0x3ff80000.00000000; for e == 0x3fe, 1 necessarily means * 0x3fefffff.ffffffff and 52 is anything at most as big as * 0x3fe80000.00000000). Then, as it happens, a sensible * maximum power is 2^(63-n) for e == 0x3fe, and 2^(62-n) for * e == 0x3ff. * * We inevitably get some overflows in approximating the log * curves by these nasty step functions, but that's all right - * we do want _some_ overflows to be tested. * * Having got that, then, it's just a matter of inventing a * probability distribution for all of this. */ int e, n; uint32 dmin, dmax; const uint32 pmin = 0x3e100000; /* * Generate exponents in a slightly biased fashion. */ e = (random_upto(1) ? /* is exponent small or big? */ 0x3FE - random_upto_biased(0x431,2) : /* small */ 0x3FF + random_upto_biased(0x3FF,2)); /* big */ /* * Now split into cases. */ if (e < 0x3FE || e > 0x3FF) { uint32 imin, imax; if (e < 0x3FE) imin = 0x40000 / (0x3FE - e), imax = 0x43200 / (0x3FE - e); else imin = 0x43200 / (e - 0x3FF), imax = 0x40000 / (e - 0x3FF); /* Power range runs from -imin to imax. Now convert to doubles */ dmin = doubletop(imin, -8); dmax = doubletop(imax, -8); /* Compute the number of mantissa bits. */ n = (e > 0 ? 53 : 52+e); } else { /* Critical exponents. Generate a top bit index. */ n = 52 - random_upto_biased(51, 4); if (e == 0x3FE) dmax = 63 - n; else dmax = 62 - n; dmax = (dmax << 20) + 0x3FF00000; dmin = dmax; } /* Generate a mantissa. */ if (n <= 32) { out[0] = 0; out[1] = random_upto((1 << (n-1)) - 1) + (1 << (n-1)); } else if (n == 33) { out[0] = 1; out[1] = random_upto(0xFFFFFFFF); } else if (n > 33) { out[0] = random_upto((1 << (n-33)) - 1) + (1 << (n-33)); out[1] = random_upto(0xFFFFFFFF); } /* Negate the mantissa if e == 0x3FE. */ if (e == 0x3FE) { out[1] = -out[1]; out[0] = -out[0]; if (out[1]) out[0]--; } /* Put the exponent on. */ out[0] &= 0xFFFFF; out[0] |= ((e > 0 ? e : 0) << 20); /* Generate a power. Powers don't go below 2^-30. */ if (random_upto(1)) { /* Positive power */ out[2] = dmax - random_upto_biased(dmax-pmin, 10); } else { /* Negative power */ out[2] = (dmin - random_upto_biased(dmin-pmin, 10)) | 0x80000000; } out[3] = random_upto(0xFFFFFFFF); } static void pow_cases_float(uint32 *out, uint32 param1, uint32 param2) { /* * Pick an exponent e (-0x16 to +0xFE) for x, and here's the * range of numbers we can use as y: * * For e < 0x7E, the range is [-0x80/(0x7E-e),+0x95/(0x7E-e)] * For e > 0x7F, the range is [-0x95/(e-0x7F),+0x80/(e-0x7F)] * * For e == 0x7E or e == 0x7F, the range gets infinite at one * end or the other, so we have to be cleverer: pick a number n * of useful bits in the mantissa (1 thru 23, so 1 must imply * 0x3f800001 whereas 23 is anything at least as big as * 0x3fc00000; for e == 0x7e, 1 necessarily means 0x3f7fffff * and 23 is anything at most as big as 0x3f400000). Then, as * it happens, a sensible maximum power is 2^(31-n) for e == * 0x7e, and 2^(30-n) for e == 0x7f. * * We inevitably get some overflows in approximating the log * curves by these nasty step functions, but that's all right - * we do want _some_ overflows to be tested. * * Having got that, then, it's just a matter of inventing a * probability distribution for all of this. */ int e, n; uint32 dmin, dmax; const uint32 pmin = 0x38000000; /* * Generate exponents in a slightly biased fashion. */ e = (random_upto(1) ? /* is exponent small or big? */ 0x7E - random_upto_biased(0x94,2) : /* small */ 0x7F + random_upto_biased(0x7f,2)); /* big */ /* * Now split into cases. */ if (e < 0x7E || e > 0x7F) { uint32 imin, imax; if (e < 0x7E) imin = 0x8000 / (0x7e - e), imax = 0x9500 / (0x7e - e); else imin = 0x9500 / (e - 0x7f), imax = 0x8000 / (e - 0x7f); /* Power range runs from -imin to imax. Now convert to doubles */ dmin = floatval(imin, -8); dmax = floatval(imax, -8); /* Compute the number of mantissa bits. */ n = (e > 0 ? 24 : 23+e); } else { /* Critical exponents. Generate a top bit index. */ n = 23 - random_upto_biased(22, 4); if (e == 0x7E) dmax = 31 - n; else dmax = 30 - n; dmax = (dmax << 23) + 0x3F800000; dmin = dmax; } /* Generate a mantissa. */ out[0] = random_upto((1 << (n-1)) - 1) + (1 << (n-1)); out[1] = 0; /* Negate the mantissa if e == 0x7E. */ if (e == 0x7E) { out[0] = -out[0]; } /* Put the exponent on. */ out[0] &= 0x7FFFFF; out[0] |= ((e > 0 ? e : 0) << 23); /* Generate a power. Powers don't go below 2^-15. */ if (random_upto(1)) { /* Positive power */ out[2] = dmax - random_upto_biased(dmax-pmin, 10); } else { /* Negative power */ out[2] = (dmin - random_upto_biased(dmin-pmin, 10)) | 0x80000000; } out[3] = 0; } void vet_for_decline(Testable *fn, uint32 *args, uint32 *result, int got_errno_in) { int declined = 0; switch (fn->type) { case args1: case rred: case semi1: case t_frexp: case t_modf: case classify: case t_ldexp: declined |= lib_fo && is_dhard(args+0); break; case args1f: case rredf: case semi1f: case t_frexpf: case t_modff: case classifyf: declined |= lib_fo && is_shard(args+0); break; case args2: case semi2: case args1c: case args1cr: case compare: declined |= lib_fo && is_dhard(args+0); declined |= lib_fo && is_dhard(args+2); break; case args2f: case semi2f: case t_ldexpf: case comparef: case args1fc: case args1fcr: declined |= lib_fo && is_shard(args+0); declined |= lib_fo && is_shard(args+2); break; case args2c: declined |= lib_fo && is_dhard(args+0); declined |= lib_fo && is_dhard(args+2); declined |= lib_fo && is_dhard(args+4); declined |= lib_fo && is_dhard(args+6); break; case args2fc: declined |= lib_fo && is_shard(args+0); declined |= lib_fo && is_shard(args+2); declined |= lib_fo && is_shard(args+4); declined |= lib_fo && is_shard(args+6); break; } switch (fn->type) { case args1: /* return an extra-precise result */ case args2: case rred: case semi1: /* return a double result */ case semi2: case t_ldexp: case t_frexp: /* return double * int */ case args1cr: declined |= lib_fo && is_dhard(result); break; case args1f: case args2f: case rredf: case semi1f: case semi2f: case t_ldexpf: case args1fcr: declined |= lib_fo && is_shard(result); break; case t_modf: /* return double * double */ declined |= lib_fo && is_dhard(result+0); declined |= lib_fo && is_dhard(result+2); break; case t_modff: /* return float * float */ declined |= lib_fo && is_shard(result+2); /* fall through */ case t_frexpf: /* return float * int */ declined |= lib_fo && is_shard(result+0); break; case args1c: case args2c: declined |= lib_fo && is_dhard(result+0); declined |= lib_fo && is_dhard(result+4); break; case args1fc: case args2fc: declined |= lib_fo && is_shard(result+0); declined |= lib_fo && is_shard(result+4); break; } /* Expect basic arithmetic tests to be declined if the command * line said that would happen */ declined |= (lib_no_arith && (fn->func == (funcptr)mpc_add || fn->func == (funcptr)mpc_sub || fn->func == (funcptr)mpc_mul || fn->func == (funcptr)mpc_div)); if (!declined) { if (got_errno_in) ntests++; else ntests += 3; } } void docase(Testable *fn, uint32 *args) { uint32 result[8]; /* real part in first 4, imaginary part in last 4 */ char *errstr = NULL; mpfr_t a, b, r; mpc_t ac, bc, rc; int rejected, printextra; wrapperctx ctx; mpfr_init2(a, MPFR_PREC); mpfr_init2(b, MPFR_PREC); mpfr_init2(r, MPFR_PREC); mpc_init2(ac, MPFR_PREC); mpc_init2(bc, MPFR_PREC); mpc_init2(rc, MPFR_PREC); printf("func=%s", fn->name); rejected = 0; /* FIXME */ switch (fn->type) { case args1: case rred: case semi1: case t_frexp: case t_modf: case classify: printf(" op1=%08x.%08x", args[0], args[1]); break; case args1f: case rredf: case semi1f: case t_frexpf: case t_modff: case classifyf: printf(" op1=%08x", args[0]); break; case args2: case semi2: case compare: printf(" op1=%08x.%08x", args[0], args[1]); printf(" op2=%08x.%08x", args[2], args[3]); break; case args2f: case semi2f: case t_ldexpf: case comparef: printf(" op1=%08x", args[0]); printf(" op2=%08x", args[2]); break; case t_ldexp: printf(" op1=%08x.%08x", args[0], args[1]); printf(" op2=%08x", args[2]); break; case args1c: case args1cr: printf(" op1r=%08x.%08x", args[0], args[1]); printf(" op1i=%08x.%08x", args[2], args[3]); break; case args2c: printf(" op1r=%08x.%08x", args[0], args[1]); printf(" op1i=%08x.%08x", args[2], args[3]); printf(" op2r=%08x.%08x", args[4], args[5]); printf(" op2i=%08x.%08x", args[6], args[7]); break; case args1fc: case args1fcr: printf(" op1r=%08x", args[0]); printf(" op1i=%08x", args[2]); break; case args2fc: printf(" op1r=%08x", args[0]); printf(" op1i=%08x", args[2]); printf(" op2r=%08x", args[4]); printf(" op2i=%08x", args[6]); break; default: fprintf(stderr, "internal inconsistency?!\n"); abort(); } if (rejected == 2) { printf(" - test case rejected\n"); goto cleanup; } wrapper_init(&ctx); if (rejected == 0) { switch (fn->type) { case args1: set_mpfr_d(a, args[0], args[1]); wrapper_op_real(&ctx, a, 2, args); ((testfunc1)(fn->func))(r, a, GMP_RNDN); get_mpfr_d(r, &result[0], &result[1], &result[2]); wrapper_result_real(&ctx, r, 2, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_d(r, &result[0], &result[1], &result[2]); break; case args1cr: set_mpc_d(ac, args[0], args[1], args[2], args[3]); wrapper_op_complex(&ctx, ac, 2, args); ((testfunc1cr)(fn->func))(r, ac, GMP_RNDN); get_mpfr_d(r, &result[0], &result[1], &result[2]); wrapper_result_real(&ctx, r, 2, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_d(r, &result[0], &result[1], &result[2]); break; case args1f: set_mpfr_f(a, args[0]); wrapper_op_real(&ctx, a, 1, args); ((testfunc1)(fn->func))(r, a, GMP_RNDN); get_mpfr_f(r, &result[0], &result[1]); wrapper_result_real(&ctx, r, 1, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_f(r, &result[0], &result[1]); break; case args1fcr: set_mpc_f(ac, args[0], args[2]); wrapper_op_complex(&ctx, ac, 1, args); ((testfunc1cr)(fn->func))(r, ac, GMP_RNDN); get_mpfr_f(r, &result[0], &result[1]); wrapper_result_real(&ctx, r, 1, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_f(r, &result[0], &result[1]); break; case args2: set_mpfr_d(a, args[0], args[1]); wrapper_op_real(&ctx, a, 2, args); set_mpfr_d(b, args[2], args[3]); wrapper_op_real(&ctx, b, 2, args+2); ((testfunc2)(fn->func))(r, a, b, GMP_RNDN); get_mpfr_d(r, &result[0], &result[1], &result[2]); wrapper_result_real(&ctx, r, 2, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_d(r, &result[0], &result[1], &result[2]); break; case args2f: set_mpfr_f(a, args[0]); wrapper_op_real(&ctx, a, 1, args); set_mpfr_f(b, args[2]); wrapper_op_real(&ctx, b, 1, args+2); ((testfunc2)(fn->func))(r, a, b, GMP_RNDN); get_mpfr_f(r, &result[0], &result[1]); wrapper_result_real(&ctx, r, 1, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_f(r, &result[0], &result[1]); break; case rred: set_mpfr_d(a, args[0], args[1]); wrapper_op_real(&ctx, a, 2, args); ((testrred)(fn->func))(r, a, (int *)&result[3]); get_mpfr_d(r, &result[0], &result[1], &result[2]); wrapper_result_real(&ctx, r, 2, result); /* We never need to mess about with the integer auxiliary * output. */ if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_d(r, &result[0], &result[1], &result[2]); break; case rredf: set_mpfr_f(a, args[0]); wrapper_op_real(&ctx, a, 1, args); ((testrred)(fn->func))(r, a, (int *)&result[3]); get_mpfr_f(r, &result[0], &result[1]); wrapper_result_real(&ctx, r, 1, result); /* We never need to mess about with the integer auxiliary * output. */ if (wrapper_run(&ctx, fn->wrappers)) get_mpfr_f(r, &result[0], &result[1]); break; case semi1: case semi1f: errstr = ((testsemi1)(fn->func))(args, result); break; case semi2: case compare: errstr = ((testsemi2)(fn->func))(args, args+2, result); break; case semi2f: case comparef: case t_ldexpf: errstr = ((testsemi2f)(fn->func))(args, args+2, result); break; case t_ldexp: errstr = ((testldexp)(fn->func))(args, args+2, result); break; case t_frexp: errstr = ((testfrexp)(fn->func))(args, result, result+2); break; case t_frexpf: errstr = ((testfrexp)(fn->func))(args, result, result+2); break; case t_modf: errstr = ((testmodf)(fn->func))(args, result, result+2); break; case t_modff: errstr = ((testmodf)(fn->func))(args, result, result+2); break; case classify: errstr = ((testclassify)(fn->func))(args, &result[0]); break; case classifyf: errstr = ((testclassifyf)(fn->func))(args, &result[0]); break; case args1c: set_mpc_d(ac, args[0], args[1], args[2], args[3]); wrapper_op_complex(&ctx, ac, 2, args); ((testfunc1c)(fn->func))(rc, ac, MPC_RNDNN); get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]); wrapper_result_complex(&ctx, rc, 2, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]); break; case args2c: set_mpc_d(ac, args[0], args[1], args[2], args[3]); wrapper_op_complex(&ctx, ac, 2, args); set_mpc_d(bc, args[4], args[5], args[6], args[7]); wrapper_op_complex(&ctx, bc, 2, args+4); ((testfunc2c)(fn->func))(rc, ac, bc, MPC_RNDNN); get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]); wrapper_result_complex(&ctx, rc, 2, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]); break; case args1fc: set_mpc_f(ac, args[0], args[2]); wrapper_op_complex(&ctx, ac, 1, args); ((testfunc1c)(fn->func))(rc, ac, MPC_RNDNN); get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]); wrapper_result_complex(&ctx, rc, 1, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]); break; case args2fc: set_mpc_f(ac, args[0], args[2]); wrapper_op_complex(&ctx, ac, 1, args); set_mpc_f(bc, args[4], args[6]); wrapper_op_complex(&ctx, bc, 1, args+4); ((testfunc2c)(fn->func))(rc, ac, bc, MPC_RNDNN); get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]); wrapper_result_complex(&ctx, rc, 1, result); if (wrapper_run(&ctx, fn->wrappers)) get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]); break; default: fprintf(stderr, "internal inconsistency?!\n"); abort(); } } switch (fn->type) { case args1: /* return an extra-precise result */ case args2: case args1cr: case rred: printextra = 1; if (rejected == 0) { errstr = NULL; if (!mpfr_zero_p(a)) { if ((result[0] & 0x7FFFFFFF) == 0 && result[1] == 0) { /* * If the output is +0 or -0 apart from the extra * precision in result[2], then there's a tricky * judgment call about what we require in the * output. If we output the extra bits and set * errstr="?underflow" then mathtest will tolerate * the function under test rounding down to zero * _or_ up to the minimum denormal; whereas if we * suppress the extra bits and set * errstr="underflow", then mathtest will enforce * that the function really does underflow to zero. * * But where to draw the line? It seems clear to * me that numbers along the lines of * 00000000.00000000.7ff should be treated * similarly to 00000000.00000000.801, but on the * other hand, we must surely be prepared to * enforce a genuine underflow-to-zero in _some_ * case where the true mathematical output is * nonzero but absurdly tiny. * * I think a reasonable place to draw the * distinction is at 00000000.00000000.400, i.e. * one quarter of the minimum positive denormal. * If a value less than that rounds up to the * minimum denormal, that must mean the function * under test has managed to make an error of an * entire factor of two, and that's something we * should fix. Above that, you can misround within * the limits of your accuracy bound if you have * to. */ if (result[2] < 0x40000000) { /* Total underflow (ERANGE + UFL) is required, * and we suppress the extra bits to make * mathtest enforce that the output is really * zero. */ errstr = "underflow"; printextra = 0; } else { /* Total underflow is not required, but if the * function rounds down to zero anyway, then * we should be prepared to tolerate it. */ errstr = "?underflow"; } } else if (!(result[0] & 0x7ff00000)) { /* * If the output is denormal, we usually expect a * UFL exception, warning the user of partial * underflow. The exception is if the denormal * being returned is just one of the input values, * unchanged even in principle. I bodgily handle * this by just special-casing the functions in * question below. */ if (!strcmp(fn->name, "fmax") || !strcmp(fn->name, "fmin") || !strcmp(fn->name, "creal") || !strcmp(fn->name, "cimag")) { /* no error expected */ } else { errstr = "u"; } } else if ((result[0] & 0x7FFFFFFF) > 0x7FEFFFFF) { /* * Infinite results are usually due to overflow, * but one exception is lgamma of a negative * integer. */ if (!strcmp(fn->name, "lgamma") && (args[0] & 0x80000000) != 0 && /* negative */ is_dinteger(args)) { errstr = "ERANGE status=z"; } else { errstr = "overflow"; } printextra = 0; } } else { /* lgamma(0) is also a pole. */ if (!strcmp(fn->name, "lgamma")) { errstr = "ERANGE status=z"; printextra = 0; } } } if (!printextra || (rejected && !(rejected==1 && result[2]!=0))) { printf(" result=%08x.%08x", result[0], result[1]); } else { printf(" result=%08x.%08x.%03x", result[0], result[1], (result[2] >> 20) & 0xFFF); } if (fn->type == rred) { printf(" res2=%08x", result[3]); } break; case args1f: case args2f: case args1fcr: case rredf: printextra = 1; if (rejected == 0) { errstr = NULL; if (!mpfr_zero_p(a)) { if ((result[0] & 0x7FFFFFFF) == 0) { /* * Decide whether to print the extra bits based on * just how close to zero the number is. See the * big comment in the double-precision case for * discussion. */ if (result[1] < 0x40000000) { errstr = "underflow"; printextra = 0; } else { errstr = "?underflow"; } } else if (!(result[0] & 0x7f800000)) { /* * Functions which do not report partial overflow * are listed here as special cases. (See the * corresponding double case above for a fuller * comment.) */ if (!strcmp(fn->name, "fmaxf") || !strcmp(fn->name, "fminf") || !strcmp(fn->name, "crealf") || !strcmp(fn->name, "cimagf")) { /* no error expected */ } else { errstr = "u"; } } else if ((result[0] & 0x7FFFFFFF) > 0x7F7FFFFF) { /* * Infinite results are usually due to overflow, * but one exception is lgamma of a negative * integer. */ if (!strcmp(fn->name, "lgammaf") && (args[0] & 0x80000000) != 0 && /* negative */ is_sinteger(args)) { errstr = "ERANGE status=z"; } else { errstr = "overflow"; } printextra = 0; } } else { /* lgamma(0) is also a pole. */ if (!strcmp(fn->name, "lgammaf")) { errstr = "ERANGE status=z"; printextra = 0; } } } if (!printextra || (rejected && !(rejected==1 && result[1]!=0))) { printf(" result=%08x", result[0]); } else { printf(" result=%08x.%03x", result[0], (result[1] >> 20) & 0xFFF); } if (fn->type == rredf) { printf(" res2=%08x", result[3]); } break; case semi1: /* return a double result */ case semi2: case t_ldexp: printf(" result=%08x.%08x", result[0], result[1]); break; case semi1f: case semi2f: case t_ldexpf: printf(" result=%08x", result[0]); break; case t_frexp: /* return double * int */ printf(" result=%08x.%08x res2=%08x", result[0], result[1], result[2]); break; case t_modf: /* return double * double */ printf(" result=%08x.%08x res2=%08x.%08x", result[0], result[1], result[2], result[3]); break; case t_modff: /* return float * float */ /* fall through */ case t_frexpf: /* return float * int */ printf(" result=%08x res2=%08x", result[0], result[2]); break; case classify: case classifyf: case compare: case comparef: printf(" result=%x", result[0]); break; case args1c: case args2c: if (0/* errstr */) { printf(" resultr=%08x.%08x", result[0], result[1]); printf(" resulti=%08x.%08x", result[4], result[5]); } else { printf(" resultr=%08x.%08x.%03x", result[0], result[1], (result[2] >> 20) & 0xFFF); printf(" resulti=%08x.%08x.%03x", result[4], result[5], (result[6] >> 20) & 0xFFF); } /* Underflow behaviour doesn't seem to be specified for complex arithmetic */ errstr = "?underflow"; break; case args1fc: case args2fc: if (0/* errstr */) { printf(" resultr=%08x", result[0]); printf(" resulti=%08x", result[4]); } else { printf(" resultr=%08x.%03x", result[0], (result[1] >> 20) & 0xFFF); printf(" resulti=%08x.%03x", result[4], (result[5] >> 20) & 0xFFF); } /* Underflow behaviour doesn't seem to be specified for complex arithmetic */ errstr = "?underflow"; break; } if (errstr && *(errstr+1) == '\0') { printf(" errno=0 status=%c",*errstr); } else if (errstr && *errstr == '?') { printf(" maybeerror=%s", errstr+1); } else if (errstr && errstr[0] == 'E') { printf(" errno=%s", errstr); } else { printf(" error=%s", errstr && *errstr ? errstr : "0"); } printf("\n"); vet_for_decline(fn, args, result, 0); cleanup: mpfr_clear(a); mpfr_clear(b); mpfr_clear(r); mpc_clear(ac); mpc_clear(bc); mpc_clear(rc); } void gencases(Testable *fn, int number) { int i; uint32 args[8]; float32_case(NULL); float64_case(NULL); printf("random=on\n"); /* signal to runtests.pl that the following tests are randomly generated */ for (i = 0; i < number; i++) { /* generate test point */ fn->cases(args, fn->caseparam1, fn->caseparam2); docase(fn, args); } printf("random=off\n"); } static uint32 doubletop(int x, int scale) { int e = 0x412 + scale; while (!(x & 0x100000)) x <<= 1, e--; return (e << 20) + x; } static uint32 floatval(int x, int scale) { int e = 0x95 + scale; while (!(x & 0x800000)) x <<= 1, e--; return (e << 23) + x; }