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More effisient formatting of numbers with small decimal mantissas #11

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More effisient formatting of numbers with small decimal mantissas #11

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55 changes: 22 additions & 33 deletions src/d2s.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -211,7 +211,7 @@ pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 {
let mut vr: u64;
let mut vp: u64 = unsafe { mem::uninitialized() };
let mut vm: u64 = unsafe { mem::uninitialized() };
let e10: i32;
let mut e10: i32;
let mut vm_is_trailing_zeros = false;
let mut vr_is_trailing_zeros = false;
if e2 >= 0 {
Expand Down Expand Up @@ -300,10 +300,9 @@ pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 {
}

// Step 4: Find the shortest decimal representation in the interval of valid representations.
let mut removed = 0i32;
let mut last_removed_digit = 0u8;
// On average, we remove ~2 digits.
let output = if vm_is_trailing_zeros || vr_is_trailing_zeros {
if vm_is_trailing_zeros || vr_is_trailing_zeros {
let mut last_removed_digit = 0u8;
// General case, which happens rarely (~0.7%).
loop {
let vp_div10 = div10(vp);
Expand All @@ -320,7 +319,7 @@ pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 {
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += 1;
e10 += 1;
}
if vm_is_trailing_zeros {
loop {
Expand All @@ -337,57 +336,47 @@ pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 {
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += 1;
e10 += 1;
}
}
if vr_is_trailing_zeros && last_removed_digit == 5 && vr % 2 == 0 {
// Round even if the exact number is .....50..0.
last_removed_digit = 4;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5)
as u64
vr += ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5) as u64
} else {
// Specialized for the common case (~99.3%). Percentages below are relative to this.
let mut round_up = false;
let vp_div100 = div100(vp);
let vm_div100 = div100(vm);
// Optimization: remove two digits at a time (~86.2%).
if vp_div100 > vm_div100 {
// Optimization: remove two digits at a time.
loop {
let vp_div100 = div100(vp);
let vm_div100 = div100(vm);
if vp_div100 <= vm_div100 {
break;
}
let vr_div100 = div100(vr);
let vr_mod100 = (vr - 100 * vr_div100) as u32;
round_up = vr_mod100 >= 50;
round_up = (vr - 100 * vr_div100) >= 50;
vr = vr_div100;
vp = vp_div100;
vm = vm_div100;
removed += 2;
e10 += 2;
}
// Loop iterations below (approximately), without optimization above:
// 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
// Loop iterations below (approximately), with optimization above:
// 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
loop {
let vp_div10 = div10(vp);
let vm_div10 = div10(vm);
if vp_div10 <= vm_div10 {
break;
}
let vm_div10 = div10(vm);
if div10(vp) > vm_div10 {
let vr_div10 = div10(vr);
let vr_mod10 = (vr - 10 * vr_div10) as u32;
round_up = vr_mod10 >= 5;
round_up = (vr - 10 * vr_div10) >= 5;
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += 1;
e10 += 1;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
vr + (vr == vm || round_up) as u64
vr += (round_up || vr == vm) as u64
};
let exp = e10 + removed;

FloatingDecimal64 {
exponent: exp,
mantissa: output,
exponent: e10,
mantissa: vr,
}
}

Expand Down
49 changes: 30 additions & 19 deletions src/f2s.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -240,7 +240,7 @@ pub fn f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal32 {
let mut vr: u32;
let mut vp: u32;
let mut vm: u32;
let e10: i32;
let mut e10: i32;
let mut vm_is_trailing_zeros = false;
let mut vr_is_trailing_zeros = false;
let mut last_removed_digit = 0u8;
Expand Down Expand Up @@ -302,8 +302,7 @@ pub fn f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal32 {
}

// Step 4: Find the shortest decimal representation in the interval of valid representations.
let mut removed = 0i32;
let output = if vm_is_trailing_zeros || vr_is_trailing_zeros {
if vm_is_trailing_zeros || vr_is_trailing_zeros {
// General case, which happens rarely (~4.0%).
while vp / 10 > vm / 10 {
vm_is_trailing_zeros &= vm - (vm / 10) * 10 == 0;
Expand All @@ -312,7 +311,7 @@ pub fn f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal32 {
vr /= 10;
vp /= 10;
vm /= 10;
removed += 1;
e10 += 1;
}
if vm_is_trailing_zeros {
while vm % 10 == 0 {
Expand All @@ -321,35 +320,47 @@ pub fn f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal32 {
vr /= 10;
vp /= 10;
vm /= 10;
removed += 1;
e10 += 1;
}
}
if vr_is_trailing_zeros && last_removed_digit == 5 && vr % 2 == 0 {
// Round even if the exact number is .....50..0.
last_removed_digit = 4;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5)
as u32
vr += ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5) as u32
} else {
// Specialized for the common case (~96.0%). Percentages below are relative to this.
// Loop iterations below (approximately):
// 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
while vp / 10 > vm / 10 {
last_removed_digit = (vr % 10) as u8;
vr /= 10;
vp /= 10;
vm /= 10;
removed += 1;
let mut round_up = last_removed_digit >= 5;
// Optimization: remove two digits at a time.
loop {
let vp_div100 = vp / 100;
let vm_div100 = vm / 100;
if vp_div100 <= vm_div100 {
break;
}
let vr_div100 = vr / 100;
round_up = (vr - 100 * vr_div100) >= 50;
vr = vr_div100;
vp = vp_div100;
vm = vm_div100;
e10 += 2;
}
let vm_div10 = vm / 10;
if vp / 10 > vm_div10 {
let vr_div10 = vr / 10;
round_up = (vr - 10 * vr_div10) >= 5;
vr = vr_div10;
vm = vm_div10;
e10 += 1;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
vr + (vr == vm || last_removed_digit >= 5) as u32
vr += (round_up || vr == vm) as u32
};
let exp = e10 + removed;

FloatingDecimal32 {
exponent: exp,
mantissa: output,
exponent: e10,
mantissa: vr,
}
}

Expand Down