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Optimize remove_trailing_zeros
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Junekey Jeon
Victor Zverovich
parent
7b4323e1e0
commit
10642e6082
@ -1835,115 +1835,86 @@ bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept {
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// Remove trailing zeros from n and return the number of zeros removed (float)
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FMT_INLINE int remove_trailing_zeros(uint32_t& n) noexcept {
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#ifdef FMT_BUILTIN_CTZ
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int t = FMT_BUILTIN_CTZ(n);
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#else
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int t = ctz(n);
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#endif
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if (t > float_info<float>::max_trailing_zeros)
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t = float_info<float>::max_trailing_zeros;
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const uint32_t mod_inv1 = 0xcccccccd;
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const uint32_t max_quotient1 = 0x33333333;
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const uint32_t mod_inv2 = 0xc28f5c29;
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const uint32_t max_quotient2 = 0x0a3d70a3;
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FMT_ASSERT(n != 0, "");
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const uint32_t mod_inv_5 = 0xcccccccd;
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const uint32_t mod_inv_25 = mod_inv_5 * mod_inv_5;
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int s = 0;
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for (; s < t - 1; s += 2) {
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if (n * mod_inv2 > max_quotient2) break;
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n *= mod_inv2;
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while (true) {
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auto q = rotr(n * mod_inv_25, 2);
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if (q <= std::numeric_limits<uint32_t>::max() / 100) {
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n = q;
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s += 2;
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} else {
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break;
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}
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}
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if (s < t && n * mod_inv1 <= max_quotient1) {
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n *= mod_inv1;
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++s;
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auto q = rotr(n * mod_inv_5, 1);
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if (q <= std::numeric_limits<uint32_t>::max() / 10) {
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n = q;
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s |= 1;
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}
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n >>= s;
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return s;
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}
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// Removes trailing zeros and returns the number of zeros removed (double)
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FMT_INLINE int remove_trailing_zeros(uint64_t& n) noexcept {
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#ifdef FMT_BUILTIN_CTZLL
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int t = FMT_BUILTIN_CTZLL(n);
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#else
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int t = ctzll(n);
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#endif
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if (t > float_info<double>::max_trailing_zeros)
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t = float_info<double>::max_trailing_zeros;
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// Divide by 10^8 and reduce to 32-bits
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// Since ret_value.significand <= (2^64 - 1) / 1000 < 10^17,
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// both of the quotient and the r should fit in 32-bits
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FMT_ASSERT(n != 0, "");
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const uint32_t mod_inv1 = 0xcccccccd;
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const uint32_t max_quotient1 = 0x33333333;
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const uint64_t mod_inv8 = 0xc767074b22e90e21;
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const uint64_t max_quotient8 = 0x00002af31dc46118;
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// This magic number is ceil(2^90 / 10^8).
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constexpr auto magic_number = uint64_t(12379400392853802749ull);
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auto nm = umul128(n, magic_number);
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// If the number is divisible by 1'0000'0000, work with the quotient
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if (t >= 8) {
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auto quotient_candidate = n * mod_inv8;
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// Is n is divisible by 10^8?
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if ((nm.high() & ((1ull << (90 - 64)) - 1)) == 0 && nm.low() < magic_number) {
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// If yes, work with the quotient.
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auto n32 = static_cast<uint32_t>(nm.high() >> (90 - 64));
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if (quotient_candidate <= max_quotient8) {
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auto quotient = static_cast<uint32_t>(quotient_candidate >> 8);
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const uint32_t mod_inv_5 = 0xcccccccd;
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const uint32_t mod_inv_25 = mod_inv_5 * mod_inv_5;
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int s = 8;
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for (; s < t; ++s) {
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if (quotient * mod_inv1 > max_quotient1) break;
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quotient *= mod_inv1;
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int s = 8;
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while (true) {
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auto q = rotr(n32 * mod_inv_25, 2);
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if (q <= std::numeric_limits<uint32_t>::max() / 100) {
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n32 = q;
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s += 2;
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} else {
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break;
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}
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quotient >>= (s - 8);
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n = quotient;
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return s;
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}
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auto q = rotr(n32 * mod_inv_5, 1);
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if (q <= std::numeric_limits<uint32_t>::max() / 10) {
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n32 = q;
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s |= 1;
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}
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n = n32;
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return s;
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}
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// If n is not divisible by 10^8, work with n itself.
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const uint64_t mod_inv_5 = 0xcccccccc'cccccccd;
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const uint64_t mod_inv_25 = mod_inv_5 * mod_inv_5;
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int s = 0;
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while (true) {
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auto q = rotr(n * mod_inv_25, 2);
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if (q <= std::numeric_limits<uint64_t>::max() / 100) {
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n = q;
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s += 2;
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} else {
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break;
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}
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}
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// Otherwise, work with the remainder
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auto quotient = static_cast<uint32_t>(n / 100000000);
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auto remainder = static_cast<uint32_t>(n - 100000000 * quotient);
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if (t == 0 || remainder * mod_inv1 > max_quotient1) {
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return 0;
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auto q = rotr(n * mod_inv_5, 1);
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if (q <= std::numeric_limits<uint64_t>::max() / 10) {
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n = q;
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s |= 1;
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}
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remainder *= mod_inv1;
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if (t == 1 || remainder * mod_inv1 > max_quotient1) {
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n = (remainder >> 1) + quotient * 10000000ull;
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return 1;
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}
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remainder *= mod_inv1;
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if (t == 2 || remainder * mod_inv1 > max_quotient1) {
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n = (remainder >> 2) + quotient * 1000000ull;
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return 2;
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}
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remainder *= mod_inv1;
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if (t == 3 || remainder * mod_inv1 > max_quotient1) {
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n = (remainder >> 3) + quotient * 100000ull;
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return 3;
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}
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remainder *= mod_inv1;
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if (t == 4 || remainder * mod_inv1 > max_quotient1) {
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n = (remainder >> 4) + quotient * 10000ull;
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return 4;
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}
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remainder *= mod_inv1;
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if (t == 5 || remainder * mod_inv1 > max_quotient1) {
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n = (remainder >> 5) + quotient * 1000ull;
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return 5;
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}
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remainder *= mod_inv1;
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if (t == 6 || remainder * mod_inv1 > max_quotient1) {
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n = (remainder >> 6) + quotient * 100ull;
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return 6;
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}
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remainder *= mod_inv1;
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n = (remainder >> 7) + quotient * 10ull;
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return 7;
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return s;
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}
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// The main algorithm for shorter interval case
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