/*
** fp_uscale.c - Unrounded Scaling float conversion
**
** Unified float formatting and parsing using the uscale algorithm.
** Based on Russ Cox's "Unrounded Scaling" approach.
** See https://research.swtch.com/fp
**
** Replaces fmt_fp.c (formatting) and readfloat.c (parsing).
*/

#include <mruby.h>

#ifndef MRB_NO_FLOAT

#include <string.h>
#include <math.h>
#include <stdint.h>

/* ======== Platform support ======== */

#if defined(__SIZEOF_INT128__)
static inline void mul64(uint64_t a, uint64_t b, uint64_t *hi, uint64_t *lo)
{
  __uint128_t r = (__uint128_t)a * b;
  *hi = (uint64_t)(r >> 64);
  *lo = (uint64_t)r;
}
#elif defined(_MSC_VER) && defined(_M_X64)
#include <intrin.h>
static inline void mul64(uint64_t a, uint64_t b, uint64_t *hi, uint64_t *lo)
{
  *lo = _umul128(a, b, hi);
}
#else
static inline void mul64(uint64_t a, uint64_t b, uint64_t *hi, uint64_t *lo)
{
  uint64_t a_lo = (uint32_t)a, a_hi = a >> 32;
  uint64_t b_lo = (uint32_t)b, b_hi = b >> 32;
  uint64_t p0 = a_lo * b_lo;
  uint64_t p1 = a_lo * b_hi;
  uint64_t p2 = a_hi * b_lo;
  uint64_t p3 = a_hi * b_hi;
  uint64_t mid = (p0 >> 32) + (uint32_t)p1 + (uint32_t)p2;
  *lo = (p0 & 0xFFFFFFFFULL) | (mid << 32);
  *hi = p3 + (p1 >> 32) + (p2 >> 32) + (mid >> 32);
}
#endif

#if defined(__GNUC__) || defined(__clang__)
#define clz64(x) __builtin_clzll(x)
#elif defined(_MSC_VER) && defined(_M_X64)
static inline int clz64(uint64_t x)
{
  unsigned long idx;
  _BitScanReverse64(&idx, x);
  return 63 - (int)idx;
}
#else
static inline int clz64(uint64_t x)
{
  int n = 0;
  if (x <= 0x00000000FFFFFFFFULL) { n += 32; x <<= 32; }
  if (x <= 0x0000FFFFFFFFFFFFULL) { n += 16; x <<= 16; }
  if (x <= 0x00FFFFFFFFFFFFFFULL) { n +=  8; x <<=  8; }
  if (x <= 0x0FFFFFFFFFFFFFFFULL) { n +=  4; x <<=  4; }
  if (x <= 0x3FFFFFFFFFFFFFFFULL) { n +=  2; x <<=  2; }
  if (x <= 0x7FFFFFFFFFFFFFFFULL) { n +=  1; }
  return n;
}
#endif

#define bits_len64(x) (64 - clz64(x))

/* ======== pow10 table ======== */

typedef struct {
  uint64_t hi;
  uint64_t lo;
} pow10_entry;

#define POW10_MIN (-343)
#define POW10_MAX 341
#define POW10_TAB_SIZE (POW10_MAX - POW10_MIN + 1)

/* generated by tools/gen_pow10_tab.rb */
static const pow10_entry pow10_tab[POW10_TAB_SIZE] = {
  {0xbf29dcaba82fdeafULL, 0x8bcd1178c77f03ccULL},
  {0xeef453d6923bd65bULL, 0xeec055d6f95ec4c0ULL},
  {0x9558b4661b6565f9ULL, 0xb53835a65bdb3af8ULL},
  {0xbaaee17fa23ebf77ULL, 0xa286430ff2d209b6ULL},
  {0xe95a99df8ace6f54ULL, 0x0b27d3d3ef868c23ULL},
  {0x91d8a02bb6c10595ULL, 0x86f8e46475b41796ULL},
  {0xb64ec836a47146faULL, 0x68b71d7d93211d7bULL},
  {0xe3e27a444d8d98b8ULL, 0x02e4e4dcf7e964daULL},
  {0x8e6d8c6ab0787f73ULL, 0x01cf0f0a1af1df08ULL},
  {0xb208ef855c969f50ULL, 0x4242d2cca1ae56caULL},
  {0xde8b2b66b3bc4724ULL, 0x52d3877fca19ec7dULL},
  {0x8b16fb203055ac77ULL, 0xb3c434afde5033ceULL},
  {0xaddcb9e83c6b1794ULL, 0x20b541dbd5e440c2ULL},
  {0xd953e8624b85dd79ULL, 0x28e29252cb5d50f2ULL},
  {0x87d4713d6f33aa6cULL, 0x798d9b73bf1a5297ULL},
  {0xa9c98d8ccb009507ULL, 0x97f10250aee0e73dULL},
  {0xd43bf0effdc0ba49ULL, 0xfded42e4da99210dULL},
  {0x84a57695fe98746eULL, 0xfeb449cf089fb4a8ULL},
  {0xa5ced43b7e3e9189ULL, 0xbe615c42cac7a1d2ULL},
  {0xcf42894a5dce35ebULL, 0xadf9b3537d798a46ULL},
  {0x818995ce7aa0e1b3ULL, 0x8cbc10142e6bf66cULL},
  {0xa1ebfb4219491a20ULL, 0xefeb14193a06f407ULL},
  {0xca66fa129f9b60a7ULL, 0x2be5d91f8888b109ULL},
  {0xfd00b897478238d1ULL, 0x76df4f676aaadd4bULL},
  {0x9e20735e8cb16383ULL, 0xaa4b91a0a2aaca4fULL},
  {0xc5a890362fddbc63ULL, 0x14de7608cb557ce2ULL},
  {0xf712b443bbd52b7cULL, 0x5a16138afe2adc1bULL},
  {0x9a6bb0aa55653b2eULL, 0xb84dcc36dedac991ULL},
  {0xc1069cd4eabe89f9ULL, 0x66613f4496917bf5ULL},
  {0xf148440a256e2c77ULL, 0x3ff98f15bc35daf2ULL},
  {0x96cd2a865764dbcbULL, 0xc7fbf96d95a1a8d7ULL},
  {0xbc807527ed3e12bdULL, 0x39faf7c8fb0a130dULL},
  {0xeba09271e88d976cULL, 0x0879b5bb39cc97d1ULL},
  {0x93445b8731587ea4ULL, 0x854c1195041fdee2ULL},
  {0xb8157268fdae9e4dULL, 0xa69f15fa4527d69bULL},
  {0xe61acf033d1a45e0ULL, 0x9046db78d671cc42ULL},
  {0x8fd0c16206306bacULL, 0x5a2c492b86071fa9ULL},
  {0xb3c4f1ba87bc8697ULL, 0x70b75b766788e793ULL},
  {0xe0b62e2929aba83dULL, 0xcce53254016b2178ULL},
  {0x8c71dcd9ba0b4926ULL, 0x600f3f7480e2f4ebULL},
  {0xaf8e5410288e1b70ULL, 0xf8130f51a11bb226ULL},
  {0xdb71e91432b1a24bULL, 0x3617d32609629eafULL},
  {0x892731ac9faf056fULL, 0x41cee3f7c5dda32dULL},
  {0xab70fe17c79ac6cbULL, 0x92429cf5b7550bf9ULL},
  {0xd64d3d9db981787eULL, 0xf6d34433252a4ef7ULL},
  {0x85f0468293f0eb4fULL, 0xda440a9ff73a715aULL},
  {0xa76c582338ed2622ULL, 0x50d50d47f5090db1ULL},
  {0xd1476e2c07286fabULL, 0xe50a5099f24b511eULL},
  {0x82cca4db847945cbULL, 0xaf267260376f12b2ULL},
  {0xa37fce126597973dULL, 0x1af00ef8454ad75fULL},
  {0xcc5fc196fefd7d0dULL, 0xe1ac12b6569d8d37ULL},
  {0xff77b1fcbebcdc50ULL, 0xda171763ec44f085ULL},
  {0x9faacf3df73609b2ULL, 0x884e6e9e73ab1653ULL},
  {0xc795830d75038c1eULL, 0x2a620a461095dbe8ULL},
  {0xf97ae3d0d2446f26ULL, 0xb4fa8cd794bb52e2ULL},
  {0x9becce62836ac578ULL, 0xb11c9806bcf513cdULL},
  {0xc2e801fb244576d6ULL, 0xdd63be086c3258c0ULL},
  {0xf3a20279ed56d48bULL, 0x94bcad8a873eeef0ULL},
  {0x9845418c345644d7ULL, 0x7cf5ec7694875556ULL},
  {0xbe5691ef416bd60dULL, 0xdc33679439a92aacULL},
  {0xedec366b11c6cb90ULL, 0xd340417948137557ULL},
  {0x94b3a202eb1c3f3aULL, 0x840828ebcd0c2956ULL},
  {0xb9e08a83a5e34f08ULL, 0x250a3326c04f33acULL},
  {0xe858ad248f5c22caULL, 0x2e4cbff070630097ULL},
  {0x91376c36d99995bfULL, 0xdceff7f6463de05eULL},
  {0xb58547448ffffb2eULL, 0x542bf5f3d7cd5875ULL},
  {0xe2e69915b3fff9faULL, 0xe936f370cdc0ae93ULL},
  {0x8dd01fad907ffc3cULL, 0x51c2582680986d1cULL},
  {0xb1442798f49ffb4bULL, 0x6632ee3020be8863ULL},
  {0xdd95317f31c7fa1eULL, 0xbfbfa9bc28ee2a7cULL},
  {0x8a7d3eef7f1cfc53ULL, 0xb7d7ca159994da8dULL},
  {0xad1c8eab5ee43b67ULL, 0x25cdbc9afffa1130ULL},
  {0xd863b256369d4a41ULL, 0x6f412bc1bff8957dULL},
  {0x873e4f75e2224e69ULL, 0xa588bb5917fb5d6eULL},
  {0xa90de3535aaae203ULL, 0x8eeaea2f5dfa34c9ULL},
  {0xd3515c2831559a84ULL, 0xf2a5a4bb3578c1fcULL},
  {0x8412d9991ed58092ULL, 0x17a786f5016b793dULL},
  {0xa5178fff668ae0b7ULL, 0x9d9168b241c6578dULL},
  {0xce5d73ff402d98e4ULL, 0x04f5c2ded237ed70ULL},
  {0x80fa687f881c7f8fULL, 0x831999cb4362f466ULL},
  {0xa139029f6a239f73ULL, 0xe3e0003e143bb17fULL},
  {0xc987434744ac874fULL, 0x5cd8004d994a9ddfULL},
  {0xfbe9141915d7a923ULL, 0xb40e0060ff9d4557ULL},
  {0x9d71ac8fada6c9b6ULL, 0x9088c03c9fc24b56ULL},
  {0xc4ce17b399107c23ULL, 0x34aaf04bc7b2de2cULL},
  {0xf6019da07f549b2cULL, 0x81d5ac5eb99f95b7ULL},
  {0x99c102844f94e0fcULL, 0xd1258bbb3403bd92ULL},
  {0xc0314325637a193aULL, 0x056eeeaa0104acf7ULL},
  {0xf03d93eebc589f89ULL, 0x86caaa548145d835ULL},
  {0x96267c7535b763b6ULL, 0xb43eaa74d0cba721ULL},
  {0xbbb01b9283253ca3ULL, 0x614e551204fe90e9ULL},
  {0xea9c227723ee8bccULL, 0xb9a1ea56863e3523ULL},
  {0x92a1958a76751760ULL, 0xf405327613e6e136ULL},
  {0xb749faed14125d37ULL, 0x31067f1398e09984ULL},
  {0xe51c79a85916f485ULL, 0x7d481ed87f18bfe5ULL},
  {0x8f31cc0937ae58d3ULL, 0x2e4d13474f6f77efULL},
  {0xb2fe3f0b8599ef08ULL, 0x79e05819234b55eaULL},
  {0xdfbdcece67006acaULL, 0x98586e1f6c1e2b65ULL},
  {0x8bd6a141006042beULL, 0x1f3744d3a392db1fULL},
  {0xaecc49914078536eULL, 0xa70516088c7791e7ULL},
  {0xda7f5bf590966849ULL, 0x50c65b8aaf957661ULL},
  {0x888f99797a5e012eULL, 0x927bf936adbd69fcULL},
  {0xaab37fd7d8f58179ULL, 0x371af784592cc47cULL},
  {0xd5605fcdcf32e1d7ULL, 0x04e1b5656f77f59bULL},
  {0x855c3be0a17fcd27ULL, 0xa30d115f65aaf980ULL},
  {0xa6b34ad8c9dfc070ULL, 0x0bd055b73f15b7e1ULL},
  {0xd0601d8efc57b08cULL, 0x0ec46b250edb25d9ULL},
  {0x823c12795db6ce58ULL, 0x893ac2f72948f7a7ULL},
  {0xa2cb1717b52481eeULL, 0xab8973b4f39b3591ULL},
  {0xcb7ddcdda26da269ULL, 0x566bd0a2308202f6ULL},
  {0xfe5d54150b090b03ULL, 0x2c06c4cabca283b3ULL},
  {0x9efa548d26e5a6e2ULL, 0x3b843afeb5e59250ULL},
  {0xc6b8e9b0709f109bULL, 0xca6549be635ef6e4ULL},
  {0xf867241c8cc6d4c1ULL, 0x3cfe9c2dfc36b49dULL},
  {0x9b407691d7fc44f9ULL, 0x861f219cbda230e2ULL},
  {0xc21094364dfb5637ULL, 0x67a6ea03ed0abd1bULL},
  {0xf294b943e17a2bc5ULL, 0xc190a484e84d6c62ULL},
  {0x979cf3ca6cec5b5bULL, 0x58fa66d3113063bdULL},
  {0xbd8430bd08277232ULL, 0xaf390087d57c7cacULL},
  {0xece53cec4a314ebeULL, 0x5b0740a9cadb9bd7ULL},
  {0x940f4613ae5ed137ULL, 0x78e4886a1ec94166ULL},
  {0xb913179899f68585ULL, 0xd71daa84a67b91c0ULL},
  {0xe757dd7ec07426e6ULL, 0xcce51525d01a7630ULL},
  {0x9096ea6f38489850ULL, 0xc00f2d37a21089deULL},
  {0xb4bca50b065abe64ULL, 0xf012f8858a94ac56ULL},
  {0xe1ebce4dc7f16dfcULL, 0x2c17b6a6ed39d76bULL},
  {0x8d3360f09cf6e4beULL, 0x9b8ed228544426a3ULL},
  {0xb080392cc4349dedULL, 0x427286b26955304cULL},
  {0xdca04777f541c568ULL, 0x130f285f03aa7c5fULL},
  {0x89e42caaf9491b61ULL, 0x0be9793b624a8dbbULL},
  {0xac5d37d5b79b623aULL, 0xcee3d78a3add312aULL},
  {0xd77485cb25823ac8ULL, 0x829ccd6cc9947d74ULL},
  {0x86a8d39ef77164bdULL, 0x51a20063fdfcce68ULL},
  {0xa8530886b54dbdecULL, 0x260a807cfd7c0203ULL},
  {0xd267caa862a12d67ULL, 0x2f8d209c3cdb0284ULL},
  {0x8380dea93da4bc61ULL, 0xbdb83461a608e192ULL},
  {0xa46116538d0deb79ULL, 0xad26417a0f8b19f7ULL},
  {0xcd795be870516657ULL, 0x986fd1d8936de074ULL},
  {0x806bd9714632dff7ULL, 0xff45e3275c24ac49ULL},
  {0xa086cfcd97bf97f4ULL, 0x7f175bf1332dd75bULL},
  {0xc8a883c0fdaf7df1ULL, 0x9edd32ed7ff94d32ULL},
  {0xfad2a4b13d1b5d6dULL, 0x86947fa8dff7a07eULL},
  {0x9cc3a6eec6311a64ULL, 0x341ccfc98bfac44fULL},
  {0xc3f490aa77bd60fdULL, 0x412403bbeef97563ULL},
  {0xf4f1b4d515acb93cULL, 0x116d04aaeab7d2bbULL},
  {0x991711052d8bf3c6ULL, 0x8ae422ead2b2e3b5ULL},
  {0xbf5cd54678eef0b7ULL, 0x2d9d2ba5875f9ca2ULL},
  {0xef340a98172aace5ULL, 0x7904768ee93783cbULL},
  {0x9580869f0e7aac0fULL, 0x2ba2ca1951c2b25fULL},
  {0xbae0a846d2195713ULL, 0x768b7c9fa6335ef6ULL},
  {0xe998d258869facd8ULL, 0xd42e5bc78fc036b4ULL},
  {0x91ff83775423cc07ULL, 0x849cf95cb9d82230ULL},
  {0xb67f6455292cbf09ULL, 0xe5c437b3e84e2abdULL},
  {0xe41f3d6a7377eecbULL, 0xdf3545a0e261b56cULL},
  {0x8e938662882af53fULL, 0xab814b848d7d1163ULL},
  {0xb23867fb2a35b28eULL, 0x16619e65b0dc55bcULL},
  {0xdec681f9f4c31f32ULL, 0x9bfa05ff1d136b2bULL},
  {0x8b3c113c38f9f37fULL, 0x217c43bf722c22fbULL},
  {0xae0b158b4738705fULL, 0x69db54af4eb72bbaULL},
  {0xd98ddaee19068c77ULL, 0xc45229db2264f6a8ULL},
  {0x87f8a8d4cfa417caULL, 0x1ab35a28f57f1a29ULL},
  {0xa9f6d30a038d1dbdULL, 0xa16030b332dee0b3ULL},
  {0xd47487cc8470652cULL, 0x89b83cdfff9698e0ULL},
  {0x84c8d4dfd2c63f3cULL, 0xd613260bffbe1f8cULL},
  {0xa5fb0a17c777cf0aULL, 0x0b97ef8effada76fULL},
  {0xcf79cc9db955c2cdULL, 0x8e7deb72bf99114bULL},
  {0x81ac1fe293d599c0ULL, 0x390eb327b7bfaacfULL},
  {0xa21727db38cb0030ULL, 0x47525ff1a5af9583ULL},
  {0xca9cf1d206fdc03cULL, 0x5926f7ee0f1b7ae3ULL},
  {0xfd442e4688bd304bULL, 0x6f70b5e992e2599cULL},
  {0x9e4a9cec15763e2fULL, 0x65a671b1fbcd7801ULL},
  {0xc5dd44271ad3cdbbULL, 0xbf100e1e7ac0d602ULL},
  {0xf7549530e188c129ULL, 0x2ed411a619710b83ULL},
  {0x9a94dd3e8cf578baULL, 0x7d448b07cfe6a731ULL},
  {0xc13a148e3032d6e8ULL, 0x1c95adc9c3e050feULL},
  {0xf18899b1bc3f8ca2ULL, 0x23bb193c34d8653eULL},
  {0x96f5600f15a7b7e6ULL, 0xd654efc5a1073f46ULL},
  {0xbcb2b812db11a5dfULL, 0x8bea2bb709490f18ULL},
  {0xebdf661791d60f57ULL, 0xeee4b6a4cb9b52deULL},
  {0x936b9fcebb25c996ULL, 0x354ef226ff4113cbULL},
  {0xb84687c269ef3bfcULL, 0xc2a2aeb0bf1158bdULL},
  {0xe65829b3046b0afbULL, 0xf34b5a5ceed5aeedULL},
  {0x8ff71a0fe2c2e6ddULL, 0xb80f187a15458d54ULL},
  {0xb3f4e093db73a094ULL, 0xa612de989a96f0a9ULL},
  {0xe0f218b8d25088b9ULL, 0xcf97963ec13cacd3ULL},
  {0x8c974f7383725574ULL, 0xe1bebde738c5ec04ULL},
  {0xafbd2350644eead0ULL, 0x1a2e6d6106f76705ULL},
  {0xdbac6c247d62a584ULL, 0x20ba08b948b540c6ULL},
  {0x894bc396ce5da773ULL, 0x94744573cd71487cULL},
  {0xab9eb47c81f51150ULL, 0xf99156d0c0cd9a9bULL},
  {0xd686619ba27255a3ULL, 0x37f5ac84f1010142ULL},
  {0x8613fd0145877586ULL, 0x42f98bd316a0a0c9ULL},
  {0xa798fc4196e952e8ULL, 0xd3b7eec7dc48c8fbULL},
  {0xd17f3b51fca3a7a1ULL, 0x08a5ea79d35afb3aULL},
  {0x82ef85133de648c5ULL, 0x6567b28c2418dd04ULL},
  {0xa3ab66580d5fdaf6ULL, 0x3ec19f2f2d1f1445ULL},
  {0xcc963fee10b7d1b4ULL, 0xce7206faf866d957ULL},
  {0xffbbcfe994e5c620ULL, 0x020e88b9b6808fadULL},
  {0x9fd561f1fd0f9bd4ULL, 0x01491574121059ccULL},
  {0xc7caba6e7c5382c9ULL, 0x019b5ad11694703fULL},
  {0xf9bd690a1b68637cULL, 0xc20231855c398c4fULL},
  {0x9c1661a651213e2eULL, 0xf9415ef359a3f7b1ULL},
  {0xc31bfa0fe5698db9ULL, 0xb791b6b0300cf59dULL},
  {0xf3e2f893dec3f127ULL, 0xa576245c3c103305ULL},
  {0x986ddb5c6b3a76b8ULL, 0x0769d6b9a58a1fe3ULL},
  {0xbe89523386091466ULL, 0x09444c680eeca7dcULL},
  {0xee2ba6c0678b5980ULL, 0x8b955f8212a7d1d3ULL},
  {0x94db483840b717f0ULL, 0x573d5bb14ba8e323ULL},
  {0xba121a4650e4ddecULL, 0x6d0cb29d9e931becULL},
  {0xe896a0d7e51e1567ULL, 0x884fdf450637e2e8ULL},
  {0x915e2486ef32cd61ULL, 0xf531eb8b23e2edd1ULL},
  {0xb5b5ada8aaff80b9ULL, 0xf27e666decdba945ULL},
  {0xe3231912d5bf60e7ULL, 0xef1e000968129396ULL},
  {0x8df5efabc5979c90ULL, 0x3572c005e10b9c3eULL},
  {0xb1736b96b6fd83b4ULL, 0x42cf7007594e834dULL},
  {0xddd0467c64bce4a1ULL, 0x53834c092fa22421ULL},
  {0x8aa22c0dbef60ee5ULL, 0x94320f85bdc55694ULL},
  {0xad4ab7112eb3929eULL, 0x793e93672d36ac39ULL},
  {0xd89d64d57a607745ULL, 0x178e3840f8845748ULL},
  {0x87625f056c7c4a8cULL, 0xeeb8e3289b52b68dULL},
  {0xa93af6c6c79b5d2eULL, 0x2a671bf2c2276430ULL},
  {0xd389b4787982347aULL, 0xb500e2ef72b13d3cULL},
  {0x843610cb4bf160ccULL, 0x31208dd5a7aec645ULL},
  {0xa54394fe1eedb8ffULL, 0x3d68b14b119a77d7ULL},
  {0xce947a3da6a9273fULL, 0x8cc2dd9dd60115cdULL},
  {0x811ccc668829b888ULL, 0xf7f9ca82a5c0ada0ULL},
  {0xa163ff802a3426a9ULL, 0x35f83d234f30d908ULL},
  {0xc9bcff6034c13053ULL, 0x03764c6c22fd0f4aULL},
  {0xfc2c3f3841f17c68ULL, 0x4453df872bbc531dULL},
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  {0x910ab1d4db9914a1ULL, 0xe263676dbff5dd5dULL},
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  {0x8c6c01c9498d8b89ULL, 0x438d0ecf99facc3cULL},
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  {0xdb68c2ca82ed2a06ULL, 0x598c67246097df1eULL},
};

/* ======== Uscale core ======== */

static inline int log10_pow2(int x)
{
  return (x * 78913) >> 18;
}

static inline int log2_pow10(int x)
{
  return (x * 108853) >> 15;
}

typedef struct {
  pow10_entry pm;
  int s;
} scaler;

static inline scaler prescale(int e, int p, int lp)
{
  scaler c;
  c.pm = pow10_tab[p - POW10_MIN];
  c.s = -(e + lp + 3);
  return c;
}

typedef uint64_t unrounded;

static inline uint64_t ur_floor(unrounded u) { return (u + 0) >> 2; }
static inline uint64_t ur_round(unrounded u) { return (u + 1 + ((u >> 2) & 1)) >> 2; }
static inline uint64_t ur_ceil(unrounded u) { return (u + 3) >> 2; }

static inline unrounded ur_div(unrounded u, uint64_t d)
{
  return (u / d) | (u & 1) | (u % d != 0 ? 1 : 0);
}

static inline unrounded ur_nudge(unrounded u, int delta)
{
  return u + delta;
}

static unrounded uscale(uint64_t x, scaler c)
{
  uint64_t hi, mid, mid2, lo_unused;
  mul64(x, c.pm.hi, &hi, &mid);

  uint64_t sticky = 1;

  if (c.s >= 64) {
    /* x * 10^p < 2^(c.s-64), i.e. < 1 in the unrounded "1.0 = 4" encoding;
       rounds to 0 with sticky=1 */
    return sticky;
  }

  uint64_t mask = (1ULL << c.s) - 1;

  if ((hi & mask) == 0) {
    mul64(x, c.pm.lo, &mid2, &lo_unused);
    sticky = (mid - mid2) > 1 ? 1 : 0;
    hi -= (mid < mid2) ? 1 : 0;
  }

  return (hi >> c.s) | sticky;
}

static void unpack64(double f, uint64_t *m, int *e)
{
  const int shift = 64 - 53;
  const int min_exp = -(1074 + shift);
  union { double d; uint64_t u; } u;
  u.d = f;
  uint64_t bits = u.u;
  int exp;

  *m = (1ULL << 63) | ((bits & ((1ULL << 52) - 1)) << shift);
  exp = (int)((bits >> 52) & ((1 << shift) - 1));

  if (exp == 0) {
    int s;
    *m &= ~(1ULL << 63);
    *e = min_exp;
    s = clz64(*m);
    *m <<= s;
    *e -= s;
  }
  else {
    *e = (exp - 1) + min_exp;
  }
}

static double pack64(uint64_t m, int e)
{
  union { double d; uint64_t u; } u;
  if ((m & (1ULL << 52)) == 0) {
    /* subnormal */
    u.u = m;
  }
  else {
    int biased = 1075 + e;
    if (biased >= 2047) {
      /* exponent overflow -> infinity */
      u.u = 0x7FF0000000000000ULL;
    }
    else {
      u.u = (m & ~(1ULL << 52)) | ((uint64_t)biased << 52);
    }
  }
  return u.d;
}

/* ======== Algorithm helpers ======== */

static const uint64_t uint64_pow10[20] = {
  1ULL, 10ULL, 100ULL, 1000ULL, 10000ULL,
  100000ULL, 1000000ULL, 10000000ULL, 100000000ULL, 1000000000ULL,
  10000000000ULL, 100000000000ULL, 1000000000000ULL, 10000000000000ULL,
  100000000000000ULL, 1000000000000000ULL, 10000000000000000ULL,
  100000000000000000ULL, 1000000000000000000ULL, 10000000000000000000ULL,
};

static int count_digits(uint64_t d)
{
  if (d == 0) return 1;  /* clz64(0) is UB; "0" is one digit */
  int nd = log10_pow2(bits_len64(d));
  return nd + (d >= uint64_pow10[nd] ? 1 : 0);
}

static void fixed_width(double f, int n, uint64_t *d, int *p)
{
  uint64_t m;
  int e;
  unrounded u;

  unpack64(f, &m, &e);
  *p = n - 1 - log10_pow2(e + 63);
  u = uscale(m, prescale(e, *p, log2_pow10(*p)));
  *d = ur_round(u);

  if (*d >= uint64_pow10[n]) {
    *d = ur_round(ur_div(u, 10));
    (*p)--;
  }
  *p = -(*p);
}

/*
 * skewed returns floor(log10(3/4 * 2^e))
 * Used for shortest-width printing at powers of 2
 */
static inline int skewed(int e)
{
  return (e * 631305 - 261663) >> 21;
}

/*
 * trim_zeros removes trailing zeros from x * 10^p
 */
static void trim_zeros(uint64_t *x, int *p)
{
  const uint64_t inv5 = 0xcccccccccccccccdULL;
  const uint64_t inv5p2 = 0x8f5c28f5c28f5c29ULL;
  const uint64_t inv5p4 = 0xd288ce703afb7e91ULL;
  const uint64_t inv5p8 = 0xc767074b22e90e21ULL;
  uint64_t d;

  /* cut 1 zero, or else return */
  d = (*x * inv5);
  d = (d >> 1) | (d << 63);
  if (d <= UINT64_MAX / 10) {
    *x = d;
    (*p)++;
  }
  else {
    return;
  }

  /* cut 8 zeros */
  d = (*x * inv5p8);
  d = (d >> 8) | (d << 56);
  if (d <= UINT64_MAX / 100000000ULL) {
    *x = d;
    *p += 8;
  }

  /* cut 4 zeros */
  d = (*x * inv5p4);
  d = (d >> 4) | (d << 60);
  if (d <= UINT64_MAX / 10000) {
    *x = d;
    *p += 4;
  }

  /* cut 2 zeros */
  d = (*x * inv5p2);
  d = (d >> 2) | (d << 62);
  if (d <= UINT64_MAX / 100) {
    *x = d;
    *p += 2;
  }

  /* cut 1 zero */
  d = (*x * inv5);
  d = (d >> 1) | (d << 63);
  if (d <= UINT64_MAX / 10) {
    *x = d;
    (*p)++;
  }
}

/*
 * shortest computes the shortest formatting of f
 * Returns d and p such that d * 10^p equals f when parsed
 */
static void shortest(double f, uint64_t *d, int *p)
{
  const int min_exp = -1085;
  uint64_t m, min, max;
  int e, z, odd, lp;
  scaler pre;
  uint64_t dmin, dmax;

  unpack64(f, &m, &e);
  z = 11;

  if (m == (1ULL << 63) && e > min_exp) {
    *p = -skewed(e + z);
    min = m - (1ULL << (z - 2));
  }
  else {
    if (e < min_exp) {
      z = 11 + (min_exp - e);
    }
    *p = -log10_pow2(e + z);
    min = m - (1ULL << (z - 1));
  }
  max = m + (1ULL << (z - 1));
  odd = (int)((m >> z) & 1);

  lp = log2_pow10(*p);
  pre = prescale(e, *p, lp);

  dmin = ur_ceil(ur_nudge(uscale(min, pre), +odd));
  dmax = ur_floor(ur_nudge(uscale(max, pre), -odd));

  /* check if a multiple of 10 is in range */
  *d = dmax / 10;
  if (*d * 10 >= dmin) {
    int new_p = -(*p - 1);
    trim_zeros(d, &new_p);
    *p = new_p;
    return;
  }

  /* multiple valid values: pick the rounded one */
  if (dmin < dmax) {
    *d = ur_round(uscale(m, pre));
  }
  else {
    *d = dmin;
  }
  *p = -(*p);
}

static double parse_decimal(uint64_t d, int p)
{
  int b, lp, e;
  unrounded u;
  uint64_t m;

  if (d == 0) return 0.0;

  b = bits_len64(d);
  lp = log2_pow10(p);
  e = 53 - b - lp;
  if (e > 1074) e = 1074;

  u = uscale(d << (64 - b), prescale(e - (64 - b), p, lp));
  m = ur_round(u);

  if (m >= (1ULL << 53)) {
    u = (u >> 1) | (u & 1);
    m = ur_round(u);
    e--;
  }

  return pack64(m, -e);
}

/* ======== Formatting helpers ======== */

static const char i2a[] =
  "00010203040506070809"
  "10111213141516171819"
  "20212223242526272829"
  "30313233343536373839"
  "40414243444546474849"
  "50515253545556575859"
  "60616263646566676869"
  "70717273747576777879"
  "80818283848586878889"
  "90919293949596979899";

static void format_base10(char *buf, int nd, uint64_t u)
{
  int idx;
  while (nd >= 2) {
    nd -= 2;
    idx = (int)(u % 100) * 2;
    u /= 100;
    buf[nd] = i2a[idx];
    buf[nd + 1] = i2a[idx + 1];
  }
  if (nd > 0) {
    buf[0] = '0' + (char)u;
  }
}

static int
emit_exp(char *s, char e_char, int exp)
{
  char *p = s;
  *p++ = e_char;
  if (exp < 0) {
    *p++ = '-';
    exp = -exp;
  }
  else {
    *p++ = '+';
  }
  if (exp >= 100) {
    *p++ = '0' + exp / 100;
    exp %= 100;
  }
  *p++ = '0' + exp / 10;
  *p++ = '0' + exp % 10;
  return (int)(p - s);
}

/* ======== mrb_format_float ======== */

#ifdef MRB_USE_FLOAT32
#define FLT_MIN_BUF_SIZE 6
#else
#define FLT_MIN_BUF_SIZE 7
#endif

int
mrb_format_float(mrb_float f, char *buf, size_t buf_size, char fmt, int prec, char sign)
{
  char *s = buf;
  int buf_remaining = (int)buf_size - 1;
  int alt_form = 0;
  char e_char;

  if ((uint8_t)fmt & 0x80) {
    fmt &= 0x7f;
    alt_form = 1;
  }
  if (buf_size <= (size_t)FLT_MIN_BUF_SIZE) {
    if (buf_size >= 2) *s++ = '?';
    if (buf_size >= 1) *s = '\0';
    return buf_size >= 2;
  }
  if (signbit(f)) {
    *s++ = '-';
    f = -f;
  }
  else if (sign) {
    *s++ = sign;
  }
  buf_remaining -= (int)(s - buf);

  {
    char uc = fmt & 0x20;
    if (isinf(f)) {
      *s++ = 'I' ^ uc;
      *s++ = 'N' ^ uc;
      *s++ = 'F' ^ uc;
      goto done;
    }
    if (isnan(f)) {
      *s++ = 'N' ^ uc;
      *s++ = 'A' ^ uc;
      *s++ = 'N' ^ uc;
      goto done;
    }
  }

  {
    int use_shortest = (prec == -2);
    if (prec < 0) prec = 6;
    e_char = 'E' | (fmt & 0x20);
    fmt |= 0x20;
    if (fmt == 'g') {
      if (use_shortest) fmt = 'S';   /* shortest mode */
      else if (prec == 0) prec = 1;
    }
  }

  if (f == 0.0) {
    /* zero */
    if (fmt == 'e') {
      *s++ = '0';
      if (prec > 0 || alt_form) {
        int i;
        if (prec > buf_remaining - 5) prec = buf_remaining - 5;
        *s++ = '.';
        for (i = 0; i < prec; i++) *s++ = '0';
      }
      s += emit_exp(s, e_char, 0);
    }
    else if (fmt == 'f') {
      int i;
      if (prec > buf_remaining - 2) prec = buf_remaining - 2;
      *s++ = '0';
      if (prec > 0 || alt_form) {
        *s++ = '.';
        for (i = 0; i < prec; i++) *s++ = '0';
      }
    }
    else { /* g */
      *s++ = '0';
      if (alt_form && prec > 1) {
        int i;
        *s++ = '.';
        for (i = 1; i < prec; i++) *s++ = '0';
      }
    }
  }
  else {
    /* nonzero finite */
    uint64_t d;
    int p, nd, exp;
    char digs[20] = {0};  /* gcc -Wmaybe-uninitialized false positive: count_digits() always returns >= 1 */

    if (fmt == 'S') {
      /* shortest representation for to_s */
      int i;
      shortest((double)f, &d, &p);
      nd = count_digits(d);
      exp = p + nd - 1;
      format_base10(digs, nd, d);

#ifdef MRB_USE_FLOAT32
      if (exp < -4 || exp >= 7) {
#else
      if (exp < -4 || exp >= 15) {
#endif
        /* e format */
        *s++ = digs[0];
        if (nd > 1) {
          *s++ = '.';
          for (i = 1; i < nd; i++) *s++ = digs[i];
        }
        s += emit_exp(s, e_char, exp);
      }
      else {
        /* f format */
        if (exp < 0) {
          *s++ = '0';
          *s++ = '.';
          for (i = 0; i < -(exp + 1); i++) *s++ = '0';
          for (i = 0; i < nd; i++) *s++ = digs[i];
        }
        else {
          for (i = 0; i <= exp && i < nd; i++) *s++ = digs[i];
          for (; i <= exp; i++) *s++ = '0';
          if (nd > exp + 1) {
            *s++ = '.';
            for (i = exp + 1; i < nd; i++) *s++ = digs[i];
          }
        }
      }
    }
    else if (fmt == 'g') {
      /* g/G format */
      int fprec, n = prec;
      if (n > 18) n = 18;
      if (n < 1) n = 1;
      fixed_width((double)f, n, &d, &p);
      nd = count_digits(d);
      exp = p + nd - 1;

      if (exp < -4 || exp >= prec) {
        /* use e format with prec-1 fractional digits */
        fprec = prec - 1;
        format_base10(digs, nd, d);
        *s++ = digs[0];
        if (fprec > 0 || alt_form) {
          int i, end = fprec < nd - 1 ? fprec : nd - 1;
          *s++ = '.';
          for (i = 0; i < end; i++) *s++ = digs[1 + i];
          for (; i < fprec; i++) *s++ = '0';
        }
        if (!alt_form) {
          /* strip trailing zeros */
          while (s > buf && s[-1] == '0') s--;
          if (s > buf && s[-1] == '.') s--;
        }
        s += emit_exp(s, e_char, exp);
      }
      else {
        /* use f format with prec-(exp+1) fractional digits */
        int i;
        fprec = prec - (exp + 1);
        format_base10(digs, nd, d);
        /* integer part */
        if (exp < 0) {
          *s++ = '0';
        }
        else {
          for (i = 0; i <= exp && i < nd; i++) *s++ = digs[i];
          for (; i <= exp; i++) *s++ = '0';
        }
        if (fprec > 0 || alt_form) {
          int frac_avail;
          *s++ = '.';
          if (exp < 0) {
            int zeros = -(exp + 1);
            for (i = 0; i < zeros && i < fprec; i++) *s++ = '0';
            frac_avail = fprec - zeros;
            for (i = 0; i < frac_avail && i < nd; i++) *s++ = digs[i];
            for (; i < frac_avail; i++) *s++ = '0';
          }
          else {
            frac_avail = nd - exp - 1;
            if (frac_avail < 0) frac_avail = 0;
            for (i = 0; i < frac_avail && i < fprec; i++) *s++ = digs[exp + 1 + i];
            for (; i < fprec; i++) *s++ = '0';
          }
        }
        if (!alt_form && fprec > 0) {
          while (s[-1] == '0') s--;
          if (s[-1] == '.') s--;
        }
      }
    }
    else if (fmt == 'e') {
      /* e/E format */
      int n = prec + 1;
      int i;
      if (n > 18) n = 18;
      if (n < 1) n = 1;
      fixed_width((double)f, n, &d, &p);
      nd = count_digits(d);
      exp = p + nd - 1;
      format_base10(digs, nd, d);
      *s++ = digs[0];
      if (prec > 0 || alt_form) {
        *s++ = '.';
        for (i = 1; i < nd; i++) *s++ = digs[i];
        for (i = nd - 1; i < prec; i++) *s++ = '0';
      }
      s += emit_exp(s, e_char, exp);
    }
    else {
      /* f/F format */
      int exp_est, i;
      union { double d; uint64_t u; } uf;
      uf.d = (double)f;
      exp_est = log10_pow2((int)((uf.u >> 52) & 0x7FF) - 1023);

      if (exp_est >= buf_remaining) {
        /* too big for f, use e */
        int n = prec + 1;
        if (n > 18) n = 18;
        if (n < 1) n = 1;
        fixed_width((double)f, n, &d, &p);
        nd = count_digits(d);
        exp = p + nd - 1;
        format_base10(digs, nd, d);
        *s++ = digs[0];
        if (prec > 0 || alt_form) {
          *s++ = '.';
          for (i = 1; i < nd; i++) *s++ = digs[i];
          for (i = nd - 1; i < prec; i++) *s++ = '0';
        }
        s += emit_exp(s, e_char, exp);
      }
      else {
        if ((exp_est + prec + 2) > buf_remaining) {
          prec = buf_remaining - exp_est - 2;
          if (prec < 0) prec = 0;
        }

        if (exp_est + prec <= 17) {
          /* Direct uscale: compute round(f * 10^prec) */
          uint64_t m;
          int e, lp;
          unrounded u;
          unpack64((double)f, &m, &e);
          lp = log2_pow10(prec);
          u = uscale(m, prescale(e, prec, lp));
          d = ur_round(u);
          nd = count_digits(d);
          exp = nd - prec - 1;
        }
        else {
          /* Large number: use fixed_width, pad with zeros */
          int n = 18;
          fixed_width((double)f, n, &d, &p);
          nd = count_digits(d);
          exp = p + nd - 1;
        }
        format_base10(digs, nd, d);

        if (exp >= 0) {
          for (i = 0; i < nd && i <= exp; i++) *s++ = digs[i];
          for (; i <= exp; i++) *s++ = '0';
          if (prec > 0 || alt_form) {
            int frac_avail = nd - exp - 1;
            if (frac_avail < 0) frac_avail = 0;
            *s++ = '.';
            for (i = 0; i < frac_avail && i < prec; i++) *s++ = digs[exp + 1 + i];
            for (; i < prec; i++) *s++ = '0';
          }
        }
        else {
          int zeros, frac_avail;
          *s++ = '0';
          if (prec > 0 || alt_form) {
            *s++ = '.';
            zeros = -(exp + 1);
            for (i = 0; i < zeros && i < prec; i++) *s++ = '0';
            frac_avail = prec - zeros;
            for (i = 0; i < frac_avail && i < nd; i++) *s++ = digs[i];
            for (; i < frac_avail; i++) *s++ = '0';
          }
        }
      }
    }
  }

done:
  *s = '\0';
  return (int)(s - buf);
}

/* ======== mrb_read_float ======== */

MRB_API mrb_bool
mrb_read_float(const char *str, char **endp, double *fp)
{
  const char *p = str;
  const char *a = p;
  uint64_t d = 0;
  int nd = 0;
  int dp = 0;
  int trunc = 0;
  int sign = 1;
  int any_digits = 0;

  while (ISSPACE((unsigned char)*p)) p++;

  if (*p == '-') { sign = -1; p++; }
  else if (*p == '+') p++;

  /* skip leading zeros */
  while (*p == '0') { p++; any_digits = 1; }

  /* integer part */
  while (ISDIGIT(*p)) {
    if (nd < 19) {
      d = d * 10 + (*p - '0');
      nd++;
    }
    else {
      trunc++;
    }
    any_digits = 1;
    a = ++p;
  }

  /* fractional part */
  if (*p == '.') {
    p++;
    if (nd == 0) {
      while (*p == '0') { dp++; p++; any_digits = 1; }
    }
    while (ISDIGIT(*p)) {
      if (nd < 19) {
        d = d * 10 + (*p - '0');
        nd++;
        dp++;
      }
      any_digits = 1;
      p++;
    }
    a = p;
  }

  if (!any_digits) {
    if (endp) *endp = (char*)str;
    *fp = 0.0;
    return FALSE;
  }

  /* exponent (optional). On malformed exponent ("5e", "5e+"), keep `a`
     pointing at the 'e' so the caller's *endp reflects where parsing
     stopped, and fall through using the mantissa-only result. */
  int final_p = trunc - dp;
  if ((*p | 32) == 'e') {
    int e = 0;
    int exp_sign = 1;
    p++;
    if (*p == '-') { exp_sign = -1; p++; }
    else if (*p == '+') p++;

    if (ISDIGIT(*p)) {
      while (ISDIGIT(*p)) {
        if (e < 10000) e = e * 10 + (*p - '0');
        p++;
      }
      final_p += e * exp_sign;
      a = p;
    }
  }

  {
    double res;
    if (d == 0) {
      res = 0.0;
    }
    else if (final_p > 308) {
      res = HUGE_VAL;
    }
    else if (final_p < -342 - nd) {
      res = 0.0;
    }
    else {
      res = parse_decimal(d, final_p);
    }
    if (sign < 0) res = -res;
    *fp = res;
  }

  if (endp) *endp = (char*)a;
  return TRUE;
}

#endif /* MRB_NO_FLOAT */