strtod and dtoa correct rounding FAST (only require 53 bits precision)
--> can go even FASTER with C-flag -D FAST_BF96
Both uses normalized 96-bits big float for calculations
If estimate is far from halfway, no need for arbitrary precision math
If estimate is guaranteed halfway, no need for arbitrary precision math
Remaining hard cases uses arbitrary precision math library to break ties.
| X | math libraries to use with -D USE_MAPM=X |
|---|---|
| 0 | use GMP for hard cases (note: GMP had GPL license) |
| 1 | link with MAPM v5.1 libmapm.a (DEFAULT setting) |
| 2 | same as 1, but use grade-school multiply only (no FFT) |
| 3 | same as 2, but #include as 1 BIG file (no need for libmapm.a) |
| 96-bit float nice properties | Eliminated bugs |
|---|---|
| no concept of normals/denormals | no boundary crossing bug |
| no need for correction loops | no infinite loops bug |
| no need to set precision mode | no double rounding bug |
| Files | Comments |
|---|---|
| dtoa-aux.c | common routine for dtoa-fast.c and dtoa-mode.c |
| dtoa-fast.c | double to string, use FE_TONEAREST mode |
| dtoa-fast.txt | algorithm used for dtoa-fast.c and dtoa-mode.c |
| dtoa-ifmt1.c | in-place format dtoa_fast() result, mode allowed = [regREG] |
| dtoa-ifmt2.c | same as above, but returned shortest string, e.g. "1e9" |
| dtoa-lite.c | dtoa-fast without bignum library, accurary 99.95% |
| dtoa-mode.c | double to string, honors rounding mode |
| dtoa.c | David Gay's dtoa.c |
| max_ulp.py | simulation shows max ulp error at most 95 ULP |
| max_ulp.txt | PROVED max ulp error is at most 95 ULP |
| strtod-aux.c | use MAPM to break ties for hard cases |
| strtod-fast.c | string to double, use FE_TONEAREST mode |
| strtod-fast.txt | algorithm used for strtod-fast.c and strtod-mode.c |
| strtod-lite.c | strtod-fast without bignum library, accuracy almost 100% |
| strtod-gmp.c | use GMP to break ties for hard cases |
| strtod-mode.c | string to double, honors rounding mode |
| strtod-mpfr.c | strtod implementation using MPFR |
| test.c | strtod, dtoa, and round-trip tests of my routines |