powers.h - tomo

(73 lines)
   1 // This file defines a function to get power-of-10 information about a floating
   2 // point number, used in fpconv.c
   3 // For license, see: fpconv_license.txt
   4 
   5 #include <stdint.h>
   6 
   7 #define npowers 87
   8 #define steppowers 8
   9 #define firstpower -348 /* 10 ^ -348 */
  10 
  11 #define expmax -32
  12 #define expmin -60
  13 
  14 typedef struct Fp {
  15     uint64_t frac;
  16     int exp;
  17 } Fp;
  18 
  19 static const Fp powers_ten[] = {
  20     {18054884314459144840U, -1220}, {13451937075301367670U, -1193}, {10022474136428063862U, -1166},
  21     {14934650266808366570U, -1140}, {11127181549972568877U, -1113}, {16580792590934885855U, -1087},
  22     {12353653155963782858U, -1060}, {18408377700990114895U, -1034}, {13715310171984221708U, -1007},
  23     {10218702384817765436U, -980},  {15227053142812498563U, -954},  {11345038669416679861U, -927},
  24     {16905424996341287883U, -901},  {12595523146049147757U, -874},  {9384396036005875287U, -847},
  25     {13983839803942852151U, -821},  {10418772551374772303U, -794},  {15525180923007089351U, -768},
  26     {11567161174868858868U, -741},  {17236413322193710309U, -715},  {12842128665889583758U, -688},
  27     {9568131466127621947U, -661},   {14257626930069360058U, -635},  {10622759856335341974U, -608},
  28     {15829145694278690180U, -582},  {11793632577567316726U, -555},  {17573882009934360870U, -529},
  29     {13093562431584567480U, -502},  {9755464219737475723U, -475},   {14536774485912137811U, -449},
  30     {10830740992659433045U, -422},  {16139061738043178685U, -396},  {12024538023802026127U, -369},
  31     {17917957937422433684U, -343},  {13349918974505688015U, -316},  {9946464728195732843U, -289},
  32     {14821387422376473014U, -263},  {11042794154864902060U, -236},  {16455045573212060422U, -210},
  33     {12259964326927110867U, -183},  {18268770466636286478U, -157},  {13611294676837538539U, -130},
  34     {10141204801825835212U, -103},  {15111572745182864684U, -77},   {11258999068426240000U, -50},
  35     {16777216000000000000U, -24},   {12500000000000000000U, 3},     {9313225746154785156U, 30},
  36     {13877787807814456755U, 56},    {10339757656912845936U, 83},    {15407439555097886824U, 109},
  37     {11479437019748901445U, 136},   {17105694144590052135U, 162},   {12744735289059618216U, 189},
  38     {9495567745759798747U, 216},    {14149498560666738074U, 242},   {10542197943230523224U, 269},
  39     {15709099088952724970U, 295},   {11704190886730495818U, 322},   {17440603504673385349U, 348},
  40     {12994262207056124023U, 375},   {9681479787123295682U, 402},    {14426529090290212157U, 428},
  41     {10748601772107342003U, 455},   {16016664761464807395U, 481},   {11933345169920330789U, 508},
  42     {17782069995880619868U, 534},   {13248674568444952270U, 561},   {9871031767461413346U, 588},
  43     {14708983551653345445U, 614},   {10959046745042015199U, 641},   {16330252207878254650U, 667},
  44     {12166986024289022870U, 694},   {18130221999122236476U, 720},   {13508068024458167312U, 747},
  45     {10064294952495520794U, 774},   {14996968138956309548U, 800},   {11173611982879273257U, 827},
  46     {16649979327439178909U, 853},   {12405201291620119593U, 880},   {9242595204427927429U, 907},
  47     {13772540099066387757U, 933},   {10261342003245940623U, 960},   {15290591125556738113U, 986},
  48     {11392378155556871081U, 1013},  {16975966327722178521U, 1039},  {12648080533535911531U, 1066}};
  49 
  50 static Fp find_cachedpow10(int exp, int *k) {
  51     const double one_log_ten = 0.30102999566398114;
  52 
  53     int approx = -(exp + npowers) * one_log_ten;
  54     int idx = (approx - firstpower) / steppowers;
  55 
  56     while (1) {
  57         int current = exp + powers_ten[idx].exp + 64;
  58 
  59         if (current < expmin) {
  60             idx++;
  61             continue;
  62         }
  63 
  64         if (current > expmax) {
  65             idx--;
  66             continue;
  67         }
  68 
  69         *k = (firstpower + idx * steppowers);
  70 
  71         return powers_ten[idx];
  72     }
  73 }