#include <stdint.h>

#define npowers 87
#define steppowers 8
#define firstpower -348 /* 10 ^ -348 */

#define expmax -32
#define expmin -60

typedef struct Fp {
  uint64_t frac;
  int exp;
} Fp;

static Fp powers_ten[] = {
    {18054884314459144840U, -1220}, {13451937075301367670U, -1193},
    {10022474136428063862U, -1166}, {14934650266808366570U, -1140},
    {11127181549972568877U, -1113}, {16580792590934885855U, -1087},
    {12353653155963782858U, -1060}, {18408377700990114895U, -1034},
    {13715310171984221708U, -1007}, {10218702384817765436U, -980},
    {15227053142812498563U, -954},  {11345038669416679861U, -927},
    {16905424996341287883U, -901},  {12595523146049147757U, -874},
    {9384396036005875287U, -847},   {13983839803942852151U, -821},
    {10418772551374772303U, -794},  {15525180923007089351U, -768},
    {11567161174868858868U, -741},  {17236413322193710309U, -715},
    {12842128665889583758U, -688},  {9568131466127621947U, -661},
    {14257626930069360058U, -635},  {10622759856335341974U, -608},
    {15829145694278690180U, -582},  {11793632577567316726U, -555},
    {17573882009934360870U, -529},  {13093562431584567480U, -502},
    {9755464219737475723U, -475},   {14536774485912137811U, -449},
    {10830740992659433045U, -422},  {16139061738043178685U, -396},
    {12024538023802026127U, -369},  {17917957937422433684U, -343},
    {13349918974505688015U, -316},  {9946464728195732843U, -289},
    {14821387422376473014U, -263},  {11042794154864902060U, -236},
    {16455045573212060422U, -210},  {12259964326927110867U, -183},
    {18268770466636286478U, -157},  {13611294676837538539U, -130},
    {10141204801825835212U, -103},  {15111572745182864684U, -77},
    {11258999068426240000U, -50},   {16777216000000000000U, -24},
    {12500000000000000000U, 3},     {9313225746154785156U, 30},
    {13877787807814456755U, 56},    {10339757656912845936U, 83},
    {15407439555097886824U, 109},   {11479437019748901445U, 136},
    {17105694144590052135U, 162},   {12744735289059618216U, 189},
    {9495567745759798747U, 216},    {14149498560666738074U, 242},
    {10542197943230523224U, 269},   {15709099088952724970U, 295},
    {11704190886730495818U, 322},   {17440603504673385349U, 348},
    {12994262207056124023U, 375},   {9681479787123295682U, 402},
    {14426529090290212157U, 428},   {10748601772107342003U, 455},
    {16016664761464807395U, 481},   {11933345169920330789U, 508},
    {17782069995880619868U, 534},   {13248674568444952270U, 561},
    {9871031767461413346U, 588},    {14708983551653345445U, 614},
    {10959046745042015199U, 641},   {16330252207878254650U, 667},
    {12166986024289022870U, 694},   {18130221999122236476U, 720},
    {13508068024458167312U, 747},   {10064294952495520794U, 774},
    {14996968138956309548U, 800},   {11173611982879273257U, 827},
    {16649979327439178909U, 853},   {12405201291620119593U, 880},
    {9242595204427927429U, 907},    {13772540099066387757U, 933},
    {10261342003245940623U, 960},   {15290591125556738113U, 986},
    {11392378155556871081U, 1013},  {16975966327722178521U, 1039},
    {12648080533535911531U, 1066}};

static Fp find_cachedpow10(int exp, int* k) {
  double const one_log_ten = 0.30102999566398114;

  int approx = static_cast<int>(-(exp + npowers) * one_log_ten);
  int idx = (approx - firstpower) / steppowers;

  while (1) {
    int current = exp + powers_ten[idx].exp + 64;

    if (current < expmin) {
      idx++;
      continue;
    }

    if (current > expmax) {
      idx--;
      continue;
    }

    *k = (firstpower + idx * steppowers);

    return powers_ten[idx];
  }
}