    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    241
    242
    243
    244
    245
    246
    247
    248
    249
    250
    251
    252
    253
    254
    255
    256
    257
    258
    259
    260
    261
    262
    263
    264
    265
    266
    267
    268
    269
    270
    271
    272
    273
    274
    275
    276
    277
    278
    279
    280
    281
    282
    283
    284
    285
    286
    287
    288
    289
    290
    291
    292
    293
    294
    295
    296
    297
    298
    299
    300
    301
    302
    303
    304
    305
    306
    307
    308

    //! Utilities for Rust numbers.

    #![doc(hidden)]

    #[cfg(all(not(feature = "std"), feature = "compact"))]
    use crate::libm::{powd, powf};
    #[cfg(not(feature = "compact"))]
    use crate::table::{SMALL_F32_POW10, SMALL_F64_POW10, SMALL_INT_POW10, SMALL_INT_POW5};
    #[cfg(not(feature = "compact"))]
    use core::hint;
    use core::ops;

    /// Generic floating-point type, to be used in generic code for parsing.
    ///
    /// Although the trait is part of the public API, the trait provides methods
    /// and constants that are effectively non-public: they may be removed
    /// at any time without any breaking changes.
    pub trait Float:
        Sized
        + Copy
        + PartialEq
        + PartialOrd
        + Send
        + Sync
        + ops::Add<Output = Self>
        + ops::AddAssign
        + ops::Div<Output = Self>
        + ops::DivAssign
        + ops::Mul<Output = Self>
        + ops::MulAssign
        + ops::Rem<Output = Self>
        + ops::RemAssign
        + ops::Sub<Output = Self>
        + ops::SubAssign
        + ops::Neg<Output = Self>
    {
        /// Maximum number of digits that can contribute in the mantissa.
        ///
        /// We can exactly represent a float in radix `b` from radix 2 if
        /// `b` is divisible by 2. This function calculates the exact number of
        /// digits required to exactly represent that float.
        ///
        /// According to the "Handbook of Floating Point Arithmetic",
        /// for IEEE754, with emin being the min exponent, p2 being the
        /// precision, and b being the radix, the number of digits follows as:
        ///
        /// `−emin + p2 + ⌊(emin + 1) log(2, b) − log(1 − 2^(−p2), b)⌋`
        ///
        /// For f32, this follows as:
        ///     emin = -126
        ///     p2 = 24
        ///
        /// For f64, this follows as:
        ///     emin = -1022
        ///     p2 = 53
        ///
        /// In Python:
        ///     `-emin + p2 + math.floor((emin+1)*math.log(2, b) - math.log(1-2**(-p2), b))`
        ///
        /// This was used to calculate the maximum number of digits for [2, 36].
        const MAX_DIGITS: usize;

        // MASKS

        /// Bitmask for the sign bit.
        const SIGN_MASK: u64;
        /// Bitmask for the exponent, including the hidden bit.
        const EXPONENT_MASK: u64;
        /// Bitmask for the hidden bit in exponent, which is an implicit 1 in the fraction.
        const HIDDEN_BIT_MASK: u64;
        /// Bitmask for the mantissa (fraction), excluding the hidden bit.
        const MANTISSA_MASK: u64;

        // PROPERTIES

        /// Size of the significand (mantissa) without hidden bit.
        const MANTISSA_SIZE: i32;
        /// Bias of the exponet
        const EXPONENT_BIAS: i32;
        /// Exponent portion of a denormal float.
        const DENORMAL_EXPONENT: i32;
        /// Maximum exponent value in float.
        const MAX_EXPONENT: i32;

        // ROUNDING

        /// Mask to determine if a full-carry occurred (1 in bit above hidden bit).
        const CARRY_MASK: u64;

        /// Bias for marking an invalid extended float.
        // Value is `i16::MIN`, using hard-coded constants for older Rustc versions.
        const INVALID_FP: i32 = -0x8000;

        // Maximum mantissa for the fast-path (`1 << 53` for f64).
        const MAX_MANTISSA_FAST_PATH: u64 = 2_u64 << Self::MANTISSA_SIZE;

        // Largest exponent value `(1 << EXP_BITS) - 1`.
        const INFINITE_POWER: i32 = Self::MAX_EXPONENT + Self::EXPONENT_BIAS;

        // Round-to-even only happens for negative values of q
        // when q ≥ −4 in the 64-bit case and when q ≥ −17 in
        // the 32-bitcase.
        //
        // When q ≥ 0,we have that 5^q ≤ 2m+1. In the 64-bit case,we
        // have 5^q ≤ 2m+1 ≤ 2^54 or q ≤ 23. In the 32-bit case,we have
        // 5^q ≤ 2m+1 ≤ 2^25 or q ≤ 10.
        //
        // When q < 0, we have w ≥ (2m+1)×5^−q. We must have that w < 2^64
        // so (2m+1)×5^−q < 2^64. We have that 2m+1 > 2^53 (64-bit case)
        // or 2m+1 > 2^24 (32-bit case). Hence,we must have 2^53×5^−q < 2^64
        // (64-bit) and 2^24×5^−q < 2^64 (32-bit). Hence we have 5^−q < 2^11
        // or q ≥ −4 (64-bit case) and 5^−q < 2^40 or q ≥ −17 (32-bitcase).
        //
        // Thus we have that we only need to round ties to even when
        // we have that q ∈ [−4,23](in the 64-bit case) or q∈[−17,10]
        // (in the 32-bit case). In both cases,the power of five(5^|q|)
        // fits in a 64-bit word.
        const MIN_EXPONENT_ROUND_TO_EVEN: i32;
        const MAX_EXPONENT_ROUND_TO_EVEN: i32;

        /// Minimum normal exponent value `-(1 << (EXPONENT_SIZE - 1)) + 1`.
        const MINIMUM_EXPONENT: i32;

        /// Smallest decimal exponent for a non-zero value.
        const SMALLEST_POWER_OF_TEN: i32;

        /// Largest decimal exponent for a non-infinite value.
        const LARGEST_POWER_OF_TEN: i32;

        /// Minimum exponent that for a fast path case, or `-⌊(MANTISSA_SIZE+1)/log2(10)⌋`
        const MIN_EXPONENT_FAST_PATH: i32;

        /// Maximum exponent that for a fast path case, or `⌊(MANTISSA_SIZE+1)/log2(5)⌋`
        const MAX_EXPONENT_FAST_PATH: i32;

        /// Maximum exponent that can be represented for a disguised-fast path case.
        /// This is `MAX_EXPONENT_FAST_PATH + ⌊(MANTISSA_SIZE+1)/log2(10)⌋`
        const MAX_EXPONENT_DISGUISED_FAST_PATH: i32;

        /// Convert 64-bit integer to float.
        fn from_u64(u: u64) -> Self;

        // Re-exported methods from std.
        fn from_bits(u: u64) -> Self;
        fn to_bits(self) -> u64;

        /// Get a small power-of-radix for fast-path multiplication.
        ///
        /// # Safety
        ///
        /// Safe as long as the exponent is smaller than the table size.
        unsafe fn pow_fast_path(exponent: usize) -> Self;

        /// Get a small, integral power-of-radix for fast-path multiplication.
        ///
        /// # Safety
        ///
        /// Safe as long as the exponent is smaller than the table size.
        #[inline(always)]
        unsafe fn int_pow_fast_path(exponent: usize, radix: u32) -> u64 {
            // SAFETY: safe as long as the exponent is smaller than the radix table.
            #[cfg(not(feature = "compact"))]
            return match radix {
                5 => unsafe { *SMALL_INT_POW5.get_unchecked(exponent) },
                10 => unsafe { *SMALL_INT_POW10.get_unchecked(exponent) },
                _ => unsafe { hint::unreachable_unchecked() },
            };

            #[cfg(feature = "compact")]
            return (radix as u64).pow(exponent as u32);
        }

        /// Returns true if the float is a denormal.
        #[inline]
        fn is_denormal(self) -> bool {
            self.to_bits() & Self::EXPONENT_MASK == 0
        }

        /// Get exponent component from the float.
        #[inline]
        fn exponent(self) -> i32 {
            if self.is_denormal() {
                return Self::DENORMAL_EXPONENT;
            }

            let bits = self.to_bits();
            let biased_e: i32 = ((bits & Self::EXPONENT_MASK) >> Self::MANTISSA_SIZE) as i32;
            biased_e - Self::EXPONENT_BIAS
        }

        /// Get mantissa (significand) component from float.
        #[inline]
        fn mantissa(self) -> u64 {
            let bits = self.to_bits();
            let s = bits & Self::MANTISSA_MASK;
            if !self.is_denormal() {
                s + Self::HIDDEN_BIT_MASK
            } else {
                s
            }
        }
    }

    impl Float for f32 {
        const MAX_DIGITS: usize = 114;
        const SIGN_MASK: u64 = 0x80000000;
        const EXPONENT_MASK: u64 = 0x7F800000;
        const HIDDEN_BIT_MASK: u64 = 0x00800000;
        const MANTISSA_MASK: u64 = 0x007FFFFF;
        const MANTISSA_SIZE: i32 = 23;
        const EXPONENT_BIAS: i32 = 127 + Self::MANTISSA_SIZE;
        const DENORMAL_EXPONENT: i32 = 1 - Self::EXPONENT_BIAS;
        const MAX_EXPONENT: i32 = 0xFF - Self::EXPONENT_BIAS;
        const CARRY_MASK: u64 = 0x1000000;
        const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -17;
        const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 10;
        const MINIMUM_EXPONENT: i32 = -127;
        const SMALLEST_POWER_OF_TEN: i32 = -65;
        const LARGEST_POWER_OF_TEN: i32 = 38;
        const MIN_EXPONENT_FAST_PATH: i32 = -10;
        const MAX_EXPONENT_FAST_PATH: i32 = 10;
        const MAX_EXPONENT_DISGUISED_FAST_PATH: i32 = 17;

        #[inline(always)]
        unsafe fn pow_fast_path(exponent: usize) -> Self {
            // SAFETY: safe as long as the exponent is smaller than the radix table.
            #[cfg(not(feature = "compact"))]
            return unsafe { *SMALL_F32_POW10.get_unchecked(exponent) };

            #[cfg(feature = "compact")]
            return powf(10.0f32, exponent as f32);
        }

        #[inline]
        fn from_u64(u: u64) -> f32 {
            u as _
        }

        #[inline]
        fn from_bits(u: u64) -> f32 {
            // Constant is `u32::MAX` for older Rustc versions.
            debug_assert!(u <= 0xffff_ffff);
            f32::from_bits(u as u32)
        }

        #[inline]
        fn to_bits(self) -> u64 {
            f32::to_bits(self) as u64
        }
    }

    impl Float for f64 {
        const MAX_DIGITS: usize = 769;
        const SIGN_MASK: u64 = 0x8000000000000000;
        const EXPONENT_MASK: u64 = 0x7FF0000000000000;
        const HIDDEN_BIT_MASK: u64 = 0x0010000000000000;
        const MANTISSA_MASK: u64 = 0x000FFFFFFFFFFFFF;
        const MANTISSA_SIZE: i32 = 52;
        const EXPONENT_BIAS: i32 = 1023 + Self::MANTISSA_SIZE;
        const DENORMAL_EXPONENT: i32 = 1 - Self::EXPONENT_BIAS;
        const MAX_EXPONENT: i32 = 0x7FF - Self::EXPONENT_BIAS;
        const CARRY_MASK: u64 = 0x20000000000000;
        const MIN_EXPONENT_ROUND_TO_EVEN: i32 = -4;
        const MAX_EXPONENT_ROUND_TO_EVEN: i32 = 23;
        const MINIMUM_EXPONENT: i32 = -1023;
        const SMALLEST_POWER_OF_TEN: i32 = -342;
        const LARGEST_POWER_OF_TEN: i32 = 308;
        const MIN_EXPONENT_FAST_PATH: i32 = -22;
        const MAX_EXPONENT_FAST_PATH: i32 = 22;
        const MAX_EXPONENT_DISGUISED_FAST_PATH: i32 = 37;

        #[inline(always)]
        unsafe fn pow_fast_path(exponent: usize) -> Self {
            // SAFETY: safe as long as the exponent is smaller than the radix table.
            #[cfg(not(feature = "compact"))]
            return unsafe { *SMALL_F64_POW10.get_unchecked(exponent) };

            #[cfg(feature = "compact")]
            return powd(10.0f64, exponent as f64);
        }

        #[inline]
        fn from_u64(u: u64) -> f64 {
            u as _
        }

        #[inline]
        fn from_bits(u: u64) -> f64 {
            f64::from_bits(u)
        }

        #[inline]
        fn to_bits(self) -> u64 {
            f64::to_bits(self)
        }
    }

    #[inline(always)]
    #[cfg(all(feature = "std", feature = "compact"))]
    pub fn powf(x: f32, y: f32) -> f32 {
        x.powf(y)
    }

    #[inline(always)]
    #[cfg(all(feature = "std", feature = "compact"))]
    pub fn powd(x: f64, y: f64) -> f64 {
        x.powf(y)
    }