So decimal-to-float algorithms are following the track of float-to-decimal algorithms:
- Algorithm M (Clinger, 1990): A bignum-based baseline algorithm
- Bellerophon + Algorithm R (Clinger, 1990): An integer-based approximation algorithm; Bellerophon has ~1 ULP error which gets fixed by Algorithm R
- strtod (Gay, 1990): A hybrid integer/float/bignum-based algorithm using modified Bellerophon
- double-conversion (Loitsch et al., 2010): A complete algorithm which verifies an error-bound approximation with correct float-to-decimal algorithms; this "round-tripping" approach was, I believe, first described by Jaffer (2013)
- Eisel-Lemire (2020): An integer-based approximation algorithm with error tracking
By comparison float-to-decimal algorithms went like this:
- Dragon4 (Steele Jr. and White, 1990; improved by Burger and Dybvig, 1996): A bignum-based baseline algorithm, still used when the arbitrary precision is required
- dtoa (Gay, 1990): A hybrid integer/float/bignum-based algorithm using modified Dragon4
- Grisu3 (Loitsch, 2010): An integer-based approximation algorithm with error tracking, can be combined with Dragon4 to produce a complete algorithm
- double-conversion (Loitsch et al., 2010): A hybrid integer/bignum-based algorithm using Grisu3
- Errol3 (Andrysco et al., 2016): The first complete (no fallback) algorithm without bignum; relies on FP with a small number of precomputed exceptions and turned out to be slower than Grisu3
- SwiftDtoa (Swift authors, 2018): Improves upon Errol3 to eliminate any exceptions; later adapts Ryu as well
- Ryu (Adams, 2018): A complete integer-based algorithm with no error tracking required
- (I noticed that there were some more developments around 2018--2020, which I haven't yet fully reviewed.)
I find it surprising that the d-to-f algorithm comparable to Grisu3 only appeared 10 years later. Maybe the round-tripping approach was fast enough that the needs weren't great so far.
- Algorithm M (Clinger, 1990): A bignum-based baseline algorithm
- Bellerophon + Algorithm R (Clinger, 1990): An integer-based approximation algorithm; Bellerophon has ~1 ULP error which gets fixed by Algorithm R
- strtod (Gay, 1990): A hybrid integer/float/bignum-based algorithm using modified Bellerophon
- double-conversion (Loitsch et al., 2010): A complete algorithm which verifies an error-bound approximation with correct float-to-decimal algorithms; this "round-tripping" approach was, I believe, first described by Jaffer (2013)
- Eisel-Lemire (2020): An integer-based approximation algorithm with error tracking
By comparison float-to-decimal algorithms went like this:
- Dragon4 (Steele Jr. and White, 1990; improved by Burger and Dybvig, 1996): A bignum-based baseline algorithm, still used when the arbitrary precision is required
- dtoa (Gay, 1990): A hybrid integer/float/bignum-based algorithm using modified Dragon4
- Grisu3 (Loitsch, 2010): An integer-based approximation algorithm with error tracking, can be combined with Dragon4 to produce a complete algorithm
- double-conversion (Loitsch et al., 2010): A hybrid integer/bignum-based algorithm using Grisu3
- Errol3 (Andrysco et al., 2016): The first complete (no fallback) algorithm without bignum; relies on FP with a small number of precomputed exceptions and turned out to be slower than Grisu3
- SwiftDtoa (Swift authors, 2018): Improves upon Errol3 to eliminate any exceptions; later adapts Ryu as well
- Ryu (Adams, 2018): A complete integer-based algorithm with no error tracking required
- (I noticed that there were some more developments around 2018--2020, which I haven't yet fully reviewed.)
I find it surprising that the d-to-f algorithm comparable to Grisu3 only appeared 10 years later. Maybe the round-tripping approach was fast enough that the needs weren't great so far.