Source File
	atofeisel.go

Belonging Package
	internal/strconv

// Copyright 2020 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package strconv

// This file implements the Eisel-Lemire ParseFloat algorithm, published in
// 2020 and discussed extensively at
// https://nigeltao.github.io/blog/2020/eisel-lemire.html
//
// The original C++ implementation is at
// https://github.com/lemire/fast_double_parser/blob/644bef4306059d3be01a04e77d3cc84b379c596f/include/fast_double_parser.h#L840
//
// This Go re-implementation closely follows the C re-implementation at
// https://github.com/google/wuffs/blob/ba3818cb6b473a2ed0b38ecfc07dbbd3a97e8ae7/internal/cgen/base/floatconv-submodule-code.c#L990
//
// Additional testing (on over several million test strings) is done by
// https://github.com/nigeltao/parse-number-fxx-test-data/blob/5280dcfccf6d0b02a65ae282dad0b6d9de50e039/script/test-go-strconv.go

import (
	"math/bits"
)

func eiselLemire64(man uint64, exp10 int, neg bool) (f float64, ok bool) {
	// The terse comments in this function body refer to sections of the
	// https://nigeltao.github.io/blog/2020/eisel-lemire.html blog post.

	// Exp10 Range.
	if man == 0 {
		if neg {
			f = float64frombits(0x8000000000000000) // Negative zero.
		}
		return f, true
	}
	pow, exp2, ok := pow10(exp10)
	if !ok {
		return 0, false
	}

	// Normalization.
	clz := bits.LeadingZeros64(man)
	man <<= uint(clz)
	retExp2 := uint64(exp2+63-float64Bias) - uint64(clz)

	// Multiplication.
	xHi, xLo := bits.Mul64(man, pow.Hi)

	// Wider Approximation.
	if xHi&0x1FF == 0x1FF && xLo+man < man {
		yHi, yLo := bits.Mul64(man, pow.Lo)
		mergedHi, mergedLo := xHi, xLo+yHi
		if mergedLo < xLo {
			mergedHi++
		}
		if mergedHi&0x1FF == 0x1FF && mergedLo+1 == 0 && yLo+man < man {
			return 0, false
		}
		xHi, xLo = mergedHi, mergedLo
	}

	// Shifting to 54 Bits.
	msb := xHi >> 63
	retMantissa := xHi >> (msb + 9)
	retExp2 -= 1 ^ msb

	// Half-way Ambiguity.
	if xLo == 0 && xHi&0x1FF == 0 && retMantissa&3 == 1 {
		return 0, false
	}

	// From 54 to 53 Bits.
	retMantissa += retMantissa & 1
	retMantissa >>= 1
	if retMantissa>>53 > 0 {
		retMantissa >>= 1
		retExp2 += 1
	}
	// retExp2 is a uint64. Zero or underflow means that we're in subnormal
	// float64 space. 0x7FF or above means that we're in Inf/NaN float64 space.
	//
	// The if block is equivalent to (but has fewer branches than):
	//   if retExp2 <= 0 || retExp2 >= 0x7FF { etc }
	if retExp2-1 >= 0x7FF-1 {
		return 0, false
	}
	retBits := retExp2<<float64MantBits | retMantissa&(1<<float64MantBits-1)
	if neg {
		retBits |= 0x8000000000000000
	}
	return float64frombits(retBits), true
}

func eiselLemire32(man uint64, exp10 int, neg bool) (f float32, ok bool) {
	// The terse comments in this function body refer to sections of the
	// https://nigeltao.github.io/blog/2020/eisel-lemire.html blog post.
	//
	// That blog post discusses the float64 flavor (11 exponent bits with a
	// -1023 bias, 52 mantissa bits) of the algorithm, but the same approach
	// applies to the float32 flavor (8 exponent bits with a -127 bias, 23
	// mantissa bits). The computation here happens with 64-bit values (e.g.
	// man, xHi, retMantissa) before finally converting to a 32-bit float.

	// Exp10 Range.
	if man == 0 {
		if neg {
			f = float32frombits(0x80000000) // Negative zero.
		}
		return f, true
	}
	pow, exp2, ok := pow10(exp10)
	if !ok {
		return 0, false
	}

	// Normalization.
	clz := bits.LeadingZeros64(man)
	man <<= uint(clz)
	retExp2 := uint64(exp2+63-float32Bias) - uint64(clz)

	// Multiplication.
	xHi, xLo := bits.Mul64(man, pow.Hi)

	// Wider Approximation.
	if xHi&0x3FFFFFFFFF == 0x3FFFFFFFFF && xLo+man < man {
		yHi, yLo := bits.Mul64(man, pow.Lo)
		mergedHi, mergedLo := xHi, xLo+yHi
		if mergedLo < xLo {
			mergedHi++
		}
		if mergedHi&0x3FFFFFFFFF == 0x3FFFFFFFFF && mergedLo+1 == 0 && yLo+man < man {
			return 0, false
		}
		xHi, xLo = mergedHi, mergedLo
	}

	// Shifting to 54 Bits (and for float32, it's shifting to 25 bits).
	msb := xHi >> 63
	retMantissa := xHi >> (msb + 38)
	retExp2 -= 1 ^ msb

	// Half-way Ambiguity.
	if xLo == 0 && xHi&0x3FFFFFFFFF == 0 && retMantissa&3 == 1 {
		return 0, false
	}

	// From 54 to 53 Bits (and for float32, it's from 25 to 24 bits).
	retMantissa += retMantissa & 1
	retMantissa >>= 1
	if retMantissa>>24 > 0 {
		retMantissa >>= 1
		retExp2 += 1
	}
	// retExp2 is a uint64. Zero or underflow means that we're in subnormal
	// float32 space. 0xFF or above means that we're in Inf/NaN float32 space.
	//
	// The if block is equivalent to (but has fewer branches than):
	//   if retExp2 <= 0 || retExp2 >= 0xFF { etc }
	if retExp2-1 >= 0xFF-1 {
		return 0, false
	}
	retBits := retExp2<<float32MantBits | retMantissa&(1<<float32MantBits-1)
	if neg {
		retBits |= 0x80000000
	}
	return float32frombits(uint32(retBits)), true
}

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