797 lines · c
1// REQUIRES: target-is-powerpc64le2// RUN: %clang_builtins %s %librt -o %t && %run %t3#include <stdio.h>4#include "DD.h"5 6long double __gcc_qmul(long double x, long double y);7int memcmp(const void *, const void *, __typeof__(sizeof(0)));8 9double testAccuracy();10int testEdgeCases();11 12int main(int argc, char *argv[]) {13 if (testEdgeCases())14 return 1;15 16 if (testAccuracy() > 2.0)17 return 1;18 19 return 0;20}21 22struct testVector {23 double xhi; double xlo;24 double yhi; double ylo;25 double rhi; double rlo;26};27 28#define INFINITY __builtin_inf()29#define HUGE 0x1.fffffffffffffp102330#define QNAN __builtin_nan("")31 32const struct testVector edgeCases[] = {33{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },34{ -0.0, 0.0, 0.0, 0.0, -0.0, 0.0 },35{ 0.0, 0.0, -0.0, 0.0, -0.0, 0.0 },36{ -0.0, 0.0, -0.0, 0.0, 0.0, 0.0 },37 38{ INFINITY, 0.0, 0.0, 0.0, QNAN, 0.0 },39{ -INFINITY, 0.0, 0.0, 0.0, QNAN, 0.0 },40{ INFINITY, 0.0, -0.0, 0.0, QNAN, 0.0 },41{ -INFINITY, 0.0, -0.0, 0.0, QNAN, 0.0 },42{ INFINITY, 0.0, 1.0, 0.0, INFINITY, 0.0 },43{ -INFINITY, 0.0, 1.0, 0.0, -INFINITY, 0.0 },44{ INFINITY, 0.0, -1.0, 0.0, -INFINITY, 0.0 },45{ -INFINITY, 0.0, -1.0, 0.0, INFINITY, 0.0 },46{ INFINITY, 0.0, HUGE, 0.0, INFINITY, 0.0 },47{ -INFINITY, 0.0, HUGE, 0.0, -INFINITY, 0.0 },48{ INFINITY, 0.0, -HUGE, 0.0, -INFINITY, 0.0 },49{ -INFINITY, 0.0, -HUGE, 0.0, INFINITY, 0.0 },50{ INFINITY, 0.0, INFINITY, 0.0, INFINITY, 0.0 },51{ -INFINITY, 0.0, INFINITY, 0.0, -INFINITY, 0.0 },52{ INFINITY, 0.0, -INFINITY, 0.0, -INFINITY, 0.0 },53{ -INFINITY, 0.0, -INFINITY, 0.0, INFINITY, 0.0 },54{ 0.0, 0.0, INFINITY, 0.0, QNAN, 0.0 },55{ 0.0, 0.0, -INFINITY, 0.0, QNAN, 0.0 },56{ -0.0, 0.0, INFINITY, 0.0, QNAN, 0.0 },57{ -0.0, 0.0, -INFINITY, 0.0, QNAN, 0.0 },58{ 1.0, 0.0, INFINITY, 0.0, INFINITY, 0.0 },59{ 1.0, 0.0, -INFINITY, 0.0, -INFINITY, 0.0 },60{ -1.0, 0.0, INFINITY, 0.0, -INFINITY, 0.0 },61{ -1.0, 0.0, -INFINITY, 0.0, INFINITY, 0.0 },62{ HUGE, 0.0, INFINITY, 0.0, INFINITY, 0.0 },63{ HUGE, 0.0, -INFINITY, 0.0, -INFINITY, 0.0 },64{ -HUGE, 0.0, INFINITY, 0.0, -INFINITY, 0.0 },65{ -HUGE, 0.0, -INFINITY, 0.0, INFINITY, 0.0 },66 67{ QNAN, 0.0, 0.0, 0.0, QNAN, 0.0 },68{ -QNAN, 0.0, 0.0, 0.0, QNAN, 0.0 },69{ QNAN, 0.0, -0.0, 0.0, QNAN, 0.0 },70{ -QNAN, 0.0, -0.0, 0.0, QNAN, 0.0 },71{ QNAN, 0.0, 1.0, 0.0, QNAN, 0.0 },72{ -QNAN, 0.0, 1.0, 0.0, QNAN, 0.0 },73{ QNAN, 0.0, -1.0, 0.0, QNAN, 0.0 },74{ -QNAN, 0.0, -1.0, 0.0, QNAN, 0.0 },75{ QNAN, 0.0, HUGE, 0.0, QNAN, 0.0 },76{ -QNAN, 0.0, HUGE, 0.0, QNAN, 0.0 },77{ QNAN, 0.0, -HUGE, 0.0, QNAN, 0.0 },78{ -QNAN, 0.0, -HUGE, 0.0, QNAN, 0.0 },79{ QNAN, 0.0, INFINITY, 0.0, QNAN, 0.0 },80{ -QNAN, 0.0, INFINITY, 0.0, QNAN, 0.0 },81{ QNAN, 0.0, -INFINITY, 0.0, QNAN, 0.0 },82{ -QNAN, 0.0, -INFINITY, 0.0, QNAN, 0.0 },83{ QNAN, 0.0, QNAN, 0.0, QNAN, 0.0 },84{ -QNAN, 0.0, QNAN, 0.0, QNAN, 0.0 },85{ QNAN, 0.0, -QNAN, 0.0, QNAN, 0.0 },86{ -QNAN, 0.0, -QNAN, 0.0, QNAN, 0.0 },87{ 0.0, 0.0, QNAN, 0.0, QNAN, 0.0 },88{ 0.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },89{ -0.0, 0.0, QNAN, 0.0, QNAN, 0.0 },90{ -0.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },91{ 1.0, 0.0, QNAN, 0.0, QNAN, 0.0 },92{ 1.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },93{ -1.0, 0.0, QNAN, 0.0, QNAN, 0.0 },94{ -1.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },95{ HUGE, 0.0, QNAN, 0.0, QNAN, 0.0 },96{ HUGE, 0.0, -QNAN, 0.0, QNAN, 0.0 },97{ -HUGE, 0.0, QNAN, 0.0, QNAN, 0.0 },98{ -HUGE, 0.0, -QNAN, 0.0, QNAN, 0.0 },99{ INFINITY, 0.0, QNAN, 0.0, QNAN, 0.0 },100{ INFINITY, 0.0, -QNAN, 0.0, QNAN, 0.0 },101{ -INFINITY, 0.0, QNAN, 0.0, QNAN, 0.0 },102{ -INFINITY, 0.0, -QNAN, 0.0, QNAN, 0.0 },103};104 105const int numEdgeCases = sizeof(edgeCases) / sizeof(struct testVector);106 107 108int testEdgeCases() {109 int i;110 DD a, b, c, r;111 for (i=0; i<numEdgeCases; ++i) {112 a.hi = edgeCases[i].xhi;113 a.lo = edgeCases[i].xlo;114 b.hi = edgeCases[i].yhi;115 b.lo = edgeCases[i].ylo;116 r.hi = edgeCases[i].rhi;117 r.lo = edgeCases[i].rlo;118 119 int error;120 121 DD c = { .ld = __gcc_qmul(a.ld, b.ld) };122 123 if (r.hi != r.hi) {124 if (c.hi == c.hi)125 error = 1;126 else if (c.lo != 0.0)127 error = 1;128 else129 error = 0;130 }131 132 else if (r.hi == 0.0)133 error = memcmp(&c, &r, sizeof(DD));134 135 else136 error = ((c.hi != r.hi) || (c.lo != r.lo));137 138 if (error) {139 printf("Error on edge case %a x %a: expected (%a, %a), got (%a, %a).\n", a.hi, b.hi, r.hi, r.lo, c.hi, c.lo);140 return 1;141 }142 }143 144 return 0;145}146 147 148/*149 150 Code for generating the test cases, requires the mpfr package to run.151 152 #include <stdio.h>153 #include <stdlib.h>154 #include <mpfr.h>155 #include <math.h>156 157 #ifdef __x86_64__158 #define randlength 2159 #else160 #define randlength 4161 #endif162 163 void printTest(mpfr_t a, mpfr_t b, mpfr_t c) {164 static const double INFINITYD = __builtin_INFINITY();165 166 MPFR_DECL_INIT(tmp, 53);167 168 double ahi = mpfr_get_d(a, GMP_RNDN);169 mpfr_set_d(tmp, ahi, GMP_RNDN);170 mpfr_sub(tmp, a, tmp, GMP_RNDN);171 double alo = mpfr_get_d(tmp, GMP_RNDN);172 printf("{%0.13a, %0.13a, ", ahi, alo);173 174 double bhi = mpfr_get_d(b, GMP_RNDN);175 mpfr_set_d(tmp, bhi, GMP_RNDN);176 mpfr_sub(tmp, b, tmp, GMP_RNDN);177 double blo = mpfr_get_d(tmp, GMP_RNDN);178 printf("%0.13a, %0.13a, ", bhi, blo);179 180 double chi = mpfr_get_d(c, GMP_RNDN);181 mpfr_set_d(tmp, chi, GMP_RNDN);182 mpfr_sub(tmp, c, tmp, GMP_RNDN);183 double clo = isINFINITY(chi) ? 0.0 : mpfr_get_d(tmp, GMP_RNDN);184 printf("%0.13a, %0.13a},\n", chi, clo);185 }186 187 int main(int argc, char *argv[]) {188 189 MPFR_DECL_INIT(a, 106);190 MPFR_DECL_INIT(b, 106);191 MPFR_DECL_INIT(c, 106);192 193 int exponent_range = atoi(argv[1]);194 195 int i;196 for (i=0; i<128; ++i) {197 mpfr_random2(a, randlength, exponent_range);198 mpfr_random2(b, randlength, exponent_range);199 mpfr_mul(c, a, b, GMP_RNDN);200 printTest(a, b, c);201 202 mpfr_neg(b, b, GMP_RNDN);203 mpfr_mul(c, a, b, GMP_RNDN);204 printTest(a, b, c);205 206 mpfr_neg(a, a, GMP_RNDN);207 mpfr_neg(b, b, GMP_RNDN);208 mpfr_mul(c, a, b, GMP_RNDN);209 printTest(a, b, c);210 211 mpfr_neg(b, b, GMP_RNDN);212 mpfr_mul(c, a, b, GMP_RNDN);213 printTest(a, b, c);214 }215 return 0;216 }217 218 */219 220const struct testVector accuracyTests[] = {221{0x1.00001ffffff00p-784, 0x1.fffff83ff8000p-839, 0x1.00ffc00ffff00p-771, 0x1.fe0007fffff00p-827, 0x0.0000000000000p+0, 0x0.0000000000000p+0},222{0x1.00001ffffff00p-784, 0x1.fffff83ff8000p-839, -0x1.00ffc00ffff00p-771, -0x1.fe0007fffff00p-827, -0x0.0000000000000p+0, -0x0.0000000000000p+0},223{-0x1.00001ffffff00p-784, -0x1.fffff83ff8000p-839, 0x1.00ffc00ffff00p-771, 0x1.fe0007fffff00p-827, -0x0.0000000000000p+0, -0x0.0000000000000p+0},224{-0x1.00001ffffff00p-784, -0x1.fffff83ff8000p-839, -0x1.00ffc00ffff00p-771, -0x1.fe0007fffff00p-827, 0x0.0000000000000p+0, 0x0.0000000000000p+0},225{0x1.00001fffff800p-705, 0x1.fffffffe00000p-779, 0x1.3fffffff80000p+666, 0x1.ffffffff00000p+593, 0x1.400027ff7f5ffp-39, 0x1.e0001ffe80000p-111},226{0x1.00001fffff800p-705, 0x1.fffffffe00000p-779, -0x1.3fffffff80000p+666, -0x1.ffffffff00000p+593, -0x1.400027ff7f5ffp-39, -0x1.e0001ffe80000p-111},227{-0x1.00001fffff800p-705, -0x1.fffffffe00000p-779, 0x1.3fffffff80000p+666, 0x1.ffffffff00000p+593, -0x1.400027ff7f5ffp-39, -0x1.e0001ffe80000p-111},228{-0x1.00001fffff800p-705, -0x1.fffffffe00000p-779, -0x1.3fffffff80000p+666, -0x1.ffffffff00000p+593, 0x1.400027ff7f5ffp-39, 0x1.e0001ffe80000p-111},229{0x1.0000000800000p-800, -0x1.0000000000000p-872, 0x1.000003fffc002p-916, -0x1.0000000000000p-1021, 0x0.0000000000000p+0, 0x0.0000000000000p+0},230{0x1.0000000800000p-800, -0x1.0000000000000p-872, -0x1.000003fffc002p-916, 0x1.0000000000000p-1021, -0x0.0000000000000p+0, -0x0.0000000000000p+0},231{-0x1.0000000800000p-800, 0x1.0000000000000p-872, 0x1.000003fffc002p-916, -0x1.0000000000000p-1021, -0x0.0000000000000p+0, -0x0.0000000000000p+0},232{-0x1.0000000800000p-800, 0x1.0000000000000p-872, -0x1.000003fffc002p-916, 0x1.0000000000000p-1021, 0x0.0000000000000p+0, 0x0.0000000000000p+0},233{0x1.000003ffffffep-19, -0x1.ffe0080000000p-103, 0x1.0800000000000p-211, -0x1.0000000000000p-307, 0x1.0800041fffffep-230, -0x1.00000020fef08p-286},234{0x1.000003ffffffep-19, -0x1.ffe0080000000p-103, -0x1.0800000000000p-211, 0x1.0000000000000p-307, -0x1.0800041fffffep-230, 0x1.00000020fef08p-286},235{-0x1.000003ffffffep-19, 0x1.ffe0080000000p-103, 0x1.0800000000000p-211, -0x1.0000000000000p-307, -0x1.0800041fffffep-230, 0x1.00000020fef08p-286},236{-0x1.000003ffffffep-19, 0x1.ffe0080000000p-103, -0x1.0800000000000p-211, 0x1.0000000000000p-307, 0x1.0800041fffffep-230, -0x1.00000020fef08p-286},237{0x1.0000007fffc00p-464, 0x1.efe0000000000p-558, 0x1.007fffffe0000p+756, 0x0.0000000000000p+0, 0x1.008000801fbfep+292, -0x1.fffeffff07900p+231},238{0x1.0000007fffc00p-464, 0x1.efe0000000000p-558, -0x1.007fffffe0000p+756, 0x0.0000000000000p+0, -0x1.008000801fbfep+292, 0x1.fffeffff07900p+231},239{-0x1.0000007fffc00p-464, -0x1.efe0000000000p-558, 0x1.007fffffe0000p+756, 0x0.0000000000000p+0, -0x1.008000801fbfep+292, 0x1.fffeffff07900p+231},240{-0x1.0000007fffc00p-464, -0x1.efe0000000000p-558, -0x1.007fffffe0000p+756, 0x0.0000000000000p+0, 0x1.008000801fbfep+292, -0x1.fffeffff07900p+231},241{0x1.3fe0000100000p-20, -0x1.0000000000000p-93, 0x1.3fffffffffe00p-397, 0x1.fe00040000000p-472, 0x1.8fd800013fd80p-417, 0x1.ffffc7d404500p-472},242{0x1.3fe0000100000p-20, -0x1.0000000000000p-93, -0x1.3fffffffffe00p-397, -0x1.fe00040000000p-472, -0x1.8fd800013fd80p-417, -0x1.ffffc7d404500p-472},243{-0x1.3fe0000100000p-20, 0x1.0000000000000p-93, 0x1.3fffffffffe00p-397, 0x1.fe00040000000p-472, -0x1.8fd800013fd80p-417, -0x1.ffffc7d404500p-472},244{-0x1.3fe0000100000p-20, 0x1.0000000000000p-93, -0x1.3fffffffffe00p-397, -0x1.fe00040000000p-472, 0x1.8fd800013fd80p-417, 0x1.ffffc7d404500p-472},245{0x1.0001fff800000p-371, 0x1.ffffff0000ffep-425, 0x1.00ff000000800p-806, -0x1.0000000800000p-872, 0x0.0000000000000p+0, 0x0.0000000000000p+0},246{0x1.0001fff800000p-371, 0x1.ffffff0000ffep-425, -0x1.00ff000000800p-806, 0x1.0000000800000p-872, -0x0.0000000000000p+0, -0x0.0000000000000p+0},247{-0x1.0001fff800000p-371, -0x1.ffffff0000ffep-425, 0x1.00ff000000800p-806, -0x1.0000000800000p-872, -0x0.0000000000000p+0, -0x0.0000000000000p+0},248{-0x1.0001fff800000p-371, -0x1.ffffff0000ffep-425, -0x1.00ff000000800p-806, 0x1.0000000800000p-872, 0x0.0000000000000p+0, 0x0.0000000000000p+0},249{0x1.0000800000000p-723, -0x1.ffffffe400000p-786, 0x1.000001ffffffap-94, -0x1.ffe1f80400000p-169, 0x1.0000820000ffap-817, -0x1.0c100109bfa00p-879},250{0x1.0000800000000p-723, -0x1.ffffffe400000p-786, -0x1.000001ffffffap-94, 0x1.ffe1f80400000p-169, -0x1.0000820000ffap-817, 0x1.0c100109bfa00p-879},251{-0x1.0000800000000p-723, 0x1.ffffffe400000p-786, 0x1.000001ffffffap-94, -0x1.ffe1f80400000p-169, -0x1.0000820000ffap-817, 0x1.0c100109bfa00p-879},252{-0x1.0000800000000p-723, 0x1.ffffffe400000p-786, -0x1.000001ffffffap-94, 0x1.ffe1f80400000p-169, 0x1.0000820000ffap-817, -0x1.0c100109bfa00p-879},253{0x1.0000010000000p-343, -0x1.0000000000000p-448, 0x1.007fffffffc00p-425, 0x1.fffffc0000000p-496, 0x1.008001007fc00p-768, -0x1.e000002004000p-835},254{0x1.0000010000000p-343, -0x1.0000000000000p-448, -0x1.007fffffffc00p-425, -0x1.fffffc0000000p-496, -0x1.008001007fc00p-768, 0x1.e000002004000p-835},255{-0x1.0000010000000p-343, 0x1.0000000000000p-448, 0x1.007fffffffc00p-425, 0x1.fffffc0000000p-496, -0x1.008001007fc00p-768, 0x1.e000002004000p-835},256{-0x1.0000010000000p-343, 0x1.0000000000000p-448, -0x1.007fffffffc00p-425, -0x1.fffffc0000000p-496, 0x1.008001007fc00p-768, -0x1.e000002004000p-835},257{0x1.0080000000000p-417, -0x1.0000000000000p-490, 0x1.001ffffffc000p-985, 0x1.0000000000000p-1039, 0x0.0000000000000p+0, 0x0.0000000000000p+0},258{0x1.0080000000000p-417, -0x1.0000000000000p-490, -0x1.001ffffffc000p-985, -0x1.0000000000000p-1039, -0x0.0000000000000p+0, -0x0.0000000000000p+0},259{-0x1.0080000000000p-417, 0x1.0000000000000p-490, 0x1.001ffffffc000p-985, 0x1.0000000000000p-1039, -0x0.0000000000000p+0, -0x0.0000000000000p+0},260{-0x1.0080000000000p-417, 0x1.0000000000000p-490, -0x1.001ffffffc000p-985, -0x1.0000000000000p-1039, 0x0.0000000000000p+0, 0x0.0000000000000p+0},261{0x1.000001fffff80p-758, 0x1.fffffc001fffcp-813, 0x1.00001ffff8000p+939, 0x1.00007f001e000p+884, 0x1.000021fff8380p+181, 0x1.7bc05e90173aep+127},262{0x1.000001fffff80p-758, 0x1.fffffc001fffcp-813, -0x1.00001ffff8000p+939, -0x1.00007f001e000p+884, -0x1.000021fff8380p+181, -0x1.7bc05e90173aep+127},263{-0x1.000001fffff80p-758, -0x1.fffffc001fffcp-813, 0x1.00001ffff8000p+939, 0x1.00007f001e000p+884, -0x1.000021fff8380p+181, -0x1.7bc05e90173aep+127},264{-0x1.000001fffff80p-758, -0x1.fffffc001fffcp-813, -0x1.00001ffff8000p+939, -0x1.00007f001e000p+884, 0x1.000021fff8380p+181, 0x1.7bc05e90173aep+127},265{0x1.00f3ffffff000p-189, 0x1.fff8000000000p-257, 0x1.3dfffffffc000p+294, 0x1.ff000003ffe00p+233, 0x1.3f2f17fffabe3p+105, 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-0x1.00701fdbe7000p+339},727{-0x1.fffffff000008p+565, 0x1.ffffff1000000p+488, 0x1.0001fffffff80p-162, 0x1.fffe000000000p-247, -0x1.0001fff7ffe84p+404, -0x1.00701fdbe7000p+339},728{-0x1.fffffff000008p+565, 0x1.ffffff1000000p+488, -0x1.0001fffffff80p-162, -0x1.fffe000000000p-247, 0x1.0001fff7ffe84p+404, 0x1.00701fdbe7000p+339},729};730 731const int numAccuracyTests = sizeof(accuracyTests) / sizeof(struct testVector);732 733#include <math.h>734 735double testAccuracy() {736 int i;737 DD a, b, c, r;738 739 double worstUlps = 0.5;740 741 for (i=0; i<numAccuracyTests; ++i) {742 a.hi = accuracyTests[i].xhi;743 a.lo = accuracyTests[i].xlo;744 b.hi = accuracyTests[i].yhi;745 b.lo = accuracyTests[i].ylo;746 r.hi = accuracyTests[i].rhi;747 r.lo = accuracyTests[i].rlo;748 749 DD c = { .ld = __gcc_qmul(a.ld, b.ld) };750 751 double error = __builtin_fabs(((r.hi - c.hi) + r.lo) - c.lo);752 753 if (error != 0.0) {754 755 int exponent = ilogb(r.hi);756 exponent = (exponent < -1022 ? -1022 : exponent);757 double ulpError = scalbn(error, 106 - exponent);758 759 if (ulpError > worstUlps) {760#ifdef PRINT_ACCURACY_INFORMATION761 printf("New worst rounding error for (%a,%a) x (%a,%a):\n", a.hi, a.lo, b.hi, b.lo);762 printf("\tExpected: (%a,%a)\n", r.hi, r.lo);763 printf("\tComputed: (%a,%a)\n", c.hi, c.lo);764 printf("\tError: %f ulps\n", ulpError);765#endif766 worstUlps = ulpError;767 }768 }769 }770 771 return worstUlps;772}773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797