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Reindent decfloat

This commit is contained in:
bumbread 2022-08-05 19:16:49 +11:00
parent b349443f8a
commit 79f1449be3
2 changed files with 230 additions and 237 deletions
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458
src/decfloat/decfloat.c
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@ -1,16 +1,21 @@
#include "decfloat.h"
#include "decfloat_table.h" #include "decfloat_table.h"
typedef struct decfloat_t decfloat_t;
struct decfloat_t {
u64 exponent;
i64 mantissa;
};
#define DOUBLE_MANTISSA_BITS 52 #define DOUBLE_MANTISSA_BITS 52
#define DOUBLE_EXPONENT_BITS 11 #define DOUBLE_EXPONENT_BITS 11
#define DOUBLE_BIAS 1023 #define DOUBLE_BIAS 1023
static const char DIGIT_TABLE[200] = { static const char DIGIT_TABLE[200] = {
"00010203040506070809101112131415161718192021222324" "00010203040506070809101112131415161718192021222324"
"25262728293031323334353637383940414243444546474849" "25262728293031323334353637383940414243444546474849"
"50515253545556575859606162636465666768697071727374" "50515253545556575859606162636465666768697071727374"
"75767778798081828384858687888990919293949596979899" "75767778798081828384858687888990919293949596979899"
}; };
static inline uint32_t pow5Factor(uint64_t value) { static inline uint32_t pow5Factor(uint64_t value) {
@ -18,290 +23,287 @@ static inline uint32_t pow5Factor(uint64_t value) {
const uint64_t n_div_5 = 3689348814741910323u; // #{ n | n = 0 (mod 2^64) } = 2^64 / 5 const uint64_t n_div_5 = 3689348814741910323u; // #{ n | n = 0 (mod 2^64) } = 2^64 / 5
uint32_t count = 0; uint32_t count = 0;
for (;;) { for (;;) {
value *= m_inv_5; value *= m_inv_5;
if (value > n_div_5) if (value > n_div_5)
break; break;
++count; ++count;
} }
return count; return count;
} }
// Returns true if value is divisible by 5^p. // Returns true if value is divisible by 5^p.
static inline bool multipleOfPowerOf5(const uint64_t value, const uint32_t p) { static inline bool multipleOfPowerOf5(const uint64_t value, const uint32_t p) {
// I tried a case distinction on p, but there was no performance difference. // I tried a case distinction on p, but there was no performance difference.
return pow5Factor(value) >= p; return pow5Factor(value) >= p;
} }
// Returns true if value is divisible by 2^p. // Returns true if value is divisible by 2^p.
static inline bool multipleOfPowerOf2(const uint64_t value, const uint32_t p) { static inline bool multipleOfPowerOf2(const uint64_t value, const uint32_t p) {
// __builtin_ctzll doesn't appear to be faster here. // __builtin_ctzll doesn't appear to be faster here.
return (value & ((1ull << p) - 1)) == 0; return (value & ((1ull << p) - 1)) == 0;
} }
static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) { static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
return _umul128(a, b, productHi); return _umul128(a, b, productHi);
} }
static inline uint64_t umulh(const uint64_t a, const uint64_t b) { static inline uint64_t umulh(const uint64_t a, const uint64_t b) {
uint64_t hi; uint64_t hi;
umul128(a, b, &hi); umul128(a, b, &hi);
return hi; return hi;
} }
static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) { static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
return __shiftright128(lo, hi, (unsigned char) dist); return __shiftright128(lo, hi, (unsigned char) dist);
} }
static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) { static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
// m is maximum 55 bits // m is maximum 55 bits
uint64_t high1; // 128 uint64_t high1; // 128
const uint64_t low1 = umul128(m, mul[1], &high1); // 64 const uint64_t low1 = umul128(m, mul[1], &high1); // 64
uint64_t high0; // 64 uint64_t high0; // 64
umul128(m, mul[0], &high0); // 0 umul128(m, mul[0], &high0); // 0
const uint64_t sum = high0 + low1; const uint64_t sum = high0 + low1;
if (sum < high0) { if (sum < high0) {
++high1; // overflow into high1 ++high1; // overflow into high1
} }
return shiftright128(sum, high1, j - 64); return shiftright128(sum, high1, j - 64);
} }
static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j, static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) { uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
*vp = mulShift64(4 * m + 2, mul, j); *vp = mulShift64(4 * m + 2, mul, j);
*vm = mulShift64(4 * m - 1 - mmShift, mul, j); *vm = mulShift64(4 * m - 1 - mmShift, mul, j);
return mulShift64(4 * m, mul, j); return mulShift64(4 * m, mul, j);
} }
// Returns floor(log_10(2^e)); requires 0 <= e <= 1650. // Returns floor(log_10(2^e)); requires 0 <= e <= 1650.
static inline uint32_t log10Pow2(const int32_t e) { static inline uint32_t log10Pow2(const int32_t e) {
// The first value this approximation fails for is 2^1651 which is just greater than 10^297. // The first value this approximation fails for is 2^1651 which is just greater than 10^297.
return (((uint32_t) e) * 78913) >> 18; return (((uint32_t) e) * 78913) >> 18;
} }
// Returns floor(log_10(5^e)); requires 0 <= e <= 2620. // Returns floor(log_10(5^e)); requires 0 <= e <= 2620.
static inline uint32_t log10Pow5(const int32_t e) { static inline uint32_t log10Pow5(const int32_t e) {
// The first value this approximation fails for is 5^2621 which is just greater than 10^1832. // The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
return (((uint32_t) e) * 732923) >> 20; return (((uint32_t) e) * 732923) >> 20;
} }
// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528. // Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
static inline int32_t pow5bits(const int32_t e) { static inline int32_t pow5bits(const int32_t e) {
// This approximation works up to the point that the multiplication overflows at e = 3529. // This approximation works up to the point that the multiplication overflows at e = 3529.
// If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
// than 2^9297. // than 2^9297.
return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1); return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1);
} }
static inline uint32_t decimalLength17(const uint64_t v) { static inline uint32_t decimalLength17(const uint64_t v) {
// This is slightly faster than a loop. // This is slightly faster than a loop.
// The average output length is 16.38 digits, so we check high-to-low. // The average output length is 16.38 digits, so we check high-to-low.
// Function precondition: v is not an 18, 19, or 20-digit number. // Function precondition: v is not an 18, 19, or 20-digit number.
// (17 digits are sufficient for round-tripping.) // (17 digits are sufficient for round-tripping.)
if (v >= 10000000000000000L) { return 17; } if (v >= 10000000000000000L) { return 17; }
if (v >= 1000000000000000L) { return 16; } if (v >= 1000000000000000L) { return 16; }
if (v >= 100000000000000L) { return 15; } if (v >= 100000000000000L) { return 15; }
if (v >= 10000000000000L) { return 14; } if (v >= 10000000000000L) { return 14; }
if (v >= 1000000000000L) { return 13; } if (v >= 1000000000000L) { return 13; }
if (v >= 100000000000L) { return 12; } if (v >= 100000000000L) { return 12; }
if (v >= 10000000000L) { return 11; } if (v >= 10000000000L) { return 11; }
if (v >= 1000000000L) { return 10; } if (v >= 1000000000L) { return 10; }
if (v >= 100000000L) { return 9; } if (v >= 100000000L) { return 9; }
if (v >= 10000000L) { return 8; } if (v >= 10000000L) { return 8; }
if (v >= 1000000L) { return 7; } if (v >= 1000000L) { return 7; }
if (v >= 100000L) { return 6; } if (v >= 100000L) { return 6; }
if (v >= 10000L) { return 5; } if (v >= 10000L) { return 5; }
if (v >= 1000L) { return 4; } if (v >= 1000L) { return 4; }
if (v >= 100L) { return 3; } if (v >= 100L) { return 3; }
if (v >= 10L) { return 2; } if (v >= 10L) { return 2; }
return 1; return 1;
} }
static inline uint64_t div5(const uint64_t x) { static inline uint64_t div5(const uint64_t x) {
return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2; return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
} }
static inline uint64_t div10(const uint64_t x) { static inline uint64_t div10(const uint64_t x) {
return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3; return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
} }
static inline uint64_t div100(const uint64_t x) { static inline uint64_t div100(const uint64_t x) {
return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2; return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
} }
static inline uint64_t div1e8(const uint64_t x) { static inline uint64_t div1e8(const uint64_t x) {
return umulh(x, 0xABCC77118461CEFDu) >> 26; return umulh(x, 0xABCC77118461CEFDu) >> 26;
} }
static decfloat_t dtodecfloat(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) { static decfloat_t dtodecfloat(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) {
int32_t e2; int32_t e2;
uint64_t m2; uint64_t m2;
if (ieeeExponent == 0) { if (ieeeExponent == 0) {
// We subtract 2 so that the bounds computation has 2 additional bits. // We subtract 2 so that the bounds computation has 2 additional bits.
e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2; e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
m2 = ieeeMantissa; m2 = ieeeMantissa;
} else { } else {
e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2; e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa; m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
}
const bool even = (m2 & 1) == 0;
const bool acceptBounds = even;
// Step 2: Determine the interval of valid decimal representations.
const uint64_t mv = 4 * m2;
// Implicit bool -> int conversion. True is 1, false is 0.
const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
// We would compute mp and mm like this:
// uint64_t mp = 4 * m2 + 2;
// uint64_t mm = mv - 1 - mmShift;
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
uint64_t vr, vp, vm;
int32_t e10;
bool vmIsTrailingZeros = false;
bool vrIsTrailingZeros = false;
if (e2 >= 0) {
// I tried special-casing q == 0, but there was no effect on performance.
// This expression is slightly faster than max(0, log10Pow2(e2) - 1).
const uint32_t q = log10Pow2(e2) - (e2 > 3);
e10 = (int32_t) q;
const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
const int32_t i = -e2 + (int32_t) q + k;
vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
if (q <= 21) {
// This should use q <= 22, but I think 21 is also safe. Smaller values
// may still be safe, but it's more difficult to reason about them.
// Only one of mp, mv, and mm can be a multiple of 5, if any.
const uint32_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) div5(mv));
if (mvMod5 == 0) {
vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
} else if (acceptBounds) {
// Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
// <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
// <=> true && pow5Factor(mm) >= q, since e2 >= q.
vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
} else {
// Same as min(e2 + 1, pow5Factor(mp)) >= q.
vp -= multipleOfPowerOf5(mv + 2, q);
}
} }
} else { const bool even = (m2 & 1) == 0;
// This expression is slightly faster than max(0, log10Pow5(-e2) - 1). const bool acceptBounds = even;
const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
e10 = (int32_t) q + e2;
const int32_t i = -e2 - (int32_t) q;
const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
const int32_t j = (int32_t) q - k;
vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
if (q <= 1) {
// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
// mv = 4 * m2, so it always has at least two trailing 0 bits.
vrIsTrailingZeros = true;
if (acceptBounds) {
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
vmIsTrailingZeros = mmShift == 1;
} else {
// mp = mv + 2, so it always has at least one trailing 0 bit.
--vp;
}
} else if (q < 63) { // TODO(ulfjack): Use a tighter bound here.
// We want to know if the full product has at least q trailing zeros.
// We need to compute min(p2(mv), p5(mv) - e2) >= q
// <=> p2(mv) >= q && p5(mv) - e2 >= q
// <=> p2(mv) >= q (because -e2 >= q)
vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
}
}
// Step 4: Find the shortest decimal representation in the interval of valid representations. // Step 2: Determine the interval of valid decimal representations.
int32_t removed = 0; const uint64_t mv = 4 * m2;
uint8_t lastRemovedDigit = 0; // Implicit bool -> int conversion. True is 1, false is 0.
uint64_t output; const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
// On average, we remove ~2 digits. // We would compute mp and mm like this:
if (vmIsTrailingZeros || vrIsTrailingZeros) { // uint64_t mp = 4 * m2 + 2;
// General case, which happens rarely (~0.7%). // uint64_t mm = mv - 1 - mmShift;
for (;;) {
const uint64_t vpDiv10 = div10(vp); // Step 3: Convert to a decimal power base using 128-bit arithmetic.
const uint64_t vmDiv10 = div10(vm); uint64_t vr, vp, vm;
if (vpDiv10 <= vmDiv10) { int32_t e10;
break; bool vmIsTrailingZeros = false;
} bool vrIsTrailingZeros = false;
const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10); if (e2 >= 0) {
const uint64_t vrDiv10 = div10(vr); // I tried special-casing q == 0, but there was no effect on performance.
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10); // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
vmIsTrailingZeros &= vmMod10 == 0; const uint32_t q = log10Pow2(e2) - (e2 > 3);
vrIsTrailingZeros &= lastRemovedDigit == 0; e10 = (int32_t) q;
lastRemovedDigit = (uint8_t) vrMod10; const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
vr = vrDiv10; const int32_t i = -e2 + (int32_t) q + k;
vp = vpDiv10; vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
vm = vmDiv10; if (q <= 21) {
++removed; // This should use q <= 22, but I think 21 is also safe. Smaller values
} // may still be safe, but it's more difficult to reason about them.
if (vmIsTrailingZeros) { // Only one of mp, mv, and mm can be a multiple of 5, if any.
for (;;) { const uint32_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) div5(mv));
const uint64_t vmDiv10 = div10(vm); if (mvMod5 == 0) {
const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10); vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
if (vmMod10 != 0) { } else if (acceptBounds) {
break; // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
// <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
// <=> true && pow5Factor(mm) >= q, since e2 >= q.
vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
} else {
// Same as min(e2 + 1, pow5Factor(mp)) >= q.
vp -= multipleOfPowerOf5(mv + 2, q);
}
}
} else {
// This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
e10 = (int32_t) q + e2;
const int32_t i = -e2 - (int32_t) q;
const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
const int32_t j = (int32_t) q - k;
vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
if (q <= 1) {
// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
// mv = 4 * m2, so it always has at least two trailing 0 bits.
vrIsTrailingZeros = true;
if (acceptBounds) {
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
vmIsTrailingZeros = mmShift == 1;
} else {
// mp = mv + 2, so it always has at least one trailing 0 bit.
--vp;
}
} else if (q < 63) { // TODO(ulfjack): Use a tighter bound here.
// We want to know if the full product has at least q trailing zeros.
// We need to compute min(p2(mv), p5(mv) - e2) >= q
// <=> p2(mv) >= q && p5(mv) - e2 >= q
// <=> p2(mv) >= q (because -e2 >= q)
vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
} }
const uint64_t vpDiv10 = div10(vp);
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t) vrMod10;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
} }
if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) { // Step 4: Find the shortest decimal representation in the interval of valid representations.
// Round even if the exact number is .....50..0. int32_t removed = 0;
lastRemovedDigit = 4; uint8_t lastRemovedDigit = 0;
uint64_t output;
// On average, we remove ~2 digits.
if (vmIsTrailingZeros || vrIsTrailingZeros) {
// General case, which happens rarely (~0.7%).
for (;;) {
const uint64_t vpDiv10 = div10(vp);
const uint64_t vmDiv10 = div10(vm);
if (vpDiv10 <= vmDiv10) {
break;
}
const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
vmIsTrailingZeros &= vmMod10 == 0;
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t) vrMod10;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
if (vmIsTrailingZeros) {
for (;;) {
const uint64_t vmDiv10 = div10(vm);
const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
if (vmMod10 != 0) {
break;
}
const uint64_t vpDiv10 = div10(vp);
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t) vrMod10;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
}
if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
// Round even if the exact number is .....50..0.
lastRemovedDigit = 4;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
} else {
// Specialized for the common case (~99.3%). Percentages below are relative to this.
bool roundUp = false;
const uint64_t vpDiv100 = div100(vp);
const uint64_t vmDiv100 = div100(vm);
if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
const uint64_t vrDiv100 = div100(vr);
const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrDiv100);
roundUp = vrMod100 >= 50;
vr = vrDiv100;
vp = vpDiv100;
vm = vmDiv100;
removed += 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%
for (;;) {
const uint64_t vpDiv10 = div10(vp);
const uint64_t vmDiv10 = div10(vm);
if (vpDiv10 <= vmDiv10) {
break;
}
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
roundUp = vrMod10 >= 5;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr + (vr == vm || roundUp);
} }
// We need to take vr + 1 if vr is outside bounds or we need to round up. const int32_t exp = e10 + removed;
output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
} else {
// Specialized for the common case (~99.3%). Percentages below are relative to this.
bool roundUp = false;
const uint64_t vpDiv100 = div100(vp);
const uint64_t vmDiv100 = div100(vm);
if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
const uint64_t vrDiv100 = div100(vr);
const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrDiv100);
roundUp = vrMod100 >= 50;
vr = vrDiv100;
vp = vpDiv100;
vm = vmDiv100;
removed += 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%
for (;;) {
const uint64_t vpDiv10 = div10(vp);
const uint64_t vmDiv10 = div10(vm);
if (vpDiv10 <= vmDiv10) {
break;
}
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
roundUp = vrMod10 >= 5;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr + (vr == vm || roundUp);
}
const int32_t exp = e10 + removed;
decfloat_t fd; decfloat_t fd;
fd.exponent = exp; fd.exponent = exp;
fd.mantissa = output; fd.mantissa = output;
return fd; return fd;
} }

9
src/decfloat/decfloat.h
View File

@ -1,9 +0,0 @@
#pragma once
typedef struct {
uint64_t mantissa;
int32_t exponent;
} decfloat_t;
static decfloat_t todecfloat(const uint64_t ieeeMant, const uint32_t ieeeExp);