| use crate::common::{ceil_log2_pow5, log2_pow5}; |
| use crate::f2s; |
| use crate::f2s_intrinsics::{ |
| mul_pow5_div_pow2, mul_pow5_inv_div_pow2, multiple_of_power_of_2_32, multiple_of_power_of_5_32, |
| }; |
| use crate::parse::Error; |
| #[cfg(feature = "no-panic")] |
| use no_panic::no_panic; |
| |
| const FLOAT_EXPONENT_BIAS: usize = 127; |
| |
| fn floor_log2(value: u32) -> u32 { |
| 31_u32.wrapping_sub(value.leading_zeros()) |
| } |
| |
| #[cfg_attr(feature = "no-panic", no_panic)] |
| pub fn s2f(buffer: &[u8]) -> Result<f32, Error> { |
| let len = buffer.len(); |
| if len == 0 { |
| return Err(Error::InputTooShort); |
| } |
| |
| let mut m10digits = 0; |
| let mut e10digits = 0; |
| let mut dot_index = len; |
| let mut e_index = len; |
| let mut m10 = 0u32; |
| let mut e10 = 0i32; |
| let mut signed_m = false; |
| let mut signed_e = false; |
| |
| let mut i = 0; |
| if unsafe { *buffer.get_unchecked(0) } == b'-' { |
| signed_m = true; |
| i += 1; |
| } |
| |
| while let Some(c) = buffer.get(i).copied() { |
| if c == b'.' { |
| if dot_index != len { |
| return Err(Error::MalformedInput); |
| } |
| dot_index = i; |
| i += 1; |
| continue; |
| } |
| if c < b'0' || c > b'9' { |
| break; |
| } |
| if m10digits >= 9 { |
| return Err(Error::InputTooLong); |
| } |
| m10 = 10 * m10 + (c - b'0') as u32; |
| if m10 != 0 { |
| m10digits += 1; |
| } |
| i += 1; |
| } |
| |
| if let Some(b'e') | Some(b'E') = buffer.get(i) { |
| e_index = i; |
| i += 1; |
| match buffer.get(i) { |
| Some(b'-') => { |
| signed_e = true; |
| i += 1; |
| } |
| Some(b'+') => i += 1, |
| _ => {} |
| } |
| while let Some(c) = buffer.get(i).copied() { |
| if c < b'0' || c > b'9' { |
| return Err(Error::MalformedInput); |
| } |
| if e10digits > 3 { |
| // TODO: Be more lenient. Return +/-Infinity or +/-0 instead. |
| return Err(Error::InputTooLong); |
| } |
| e10 = 10 * e10 + (c - b'0') as i32; |
| if e10 != 0 { |
| e10digits += 1; |
| } |
| i += 1; |
| } |
| } |
| |
| if i < len { |
| return Err(Error::MalformedInput); |
| } |
| if signed_e { |
| e10 = -e10; |
| } |
| e10 -= if dot_index < e_index { |
| (e_index - dot_index - 1) as i32 |
| } else { |
| 0 |
| }; |
| if m10 == 0 { |
| return Ok(if signed_m { -0.0 } else { 0.0 }); |
| } |
| |
| if m10digits + e10 <= -46 || m10 == 0 { |
| // Number is less than 1e-46, which should be rounded down to 0; return |
| // +/-0.0. |
| let ieee = (signed_m as u32) << (f2s::FLOAT_EXPONENT_BITS + f2s::FLOAT_MANTISSA_BITS); |
| return Ok(f32::from_bits(ieee)); |
| } |
| if m10digits + e10 >= 40 { |
| // Number is larger than 1e+39, which should be rounded to +/-Infinity. |
| let ieee = ((signed_m as u32) << (f2s::FLOAT_EXPONENT_BITS + f2s::FLOAT_MANTISSA_BITS)) |
| | (0xff_u32 << f2s::FLOAT_MANTISSA_BITS); |
| return Ok(f32::from_bits(ieee)); |
| } |
| |
| // Convert to binary float m2 * 2^e2, while retaining information about |
| // whether the conversion was exact (trailing_zeros). |
| let e2: i32; |
| let m2: u32; |
| let mut trailing_zeros: bool; |
| if e10 >= 0 { |
| // The length of m * 10^e in bits is: |
| // log2(m10 * 10^e10) = log2(m10) + e10 log2(10) = log2(m10) + e10 + e10 * log2(5) |
| // |
| // We want to compute the FLOAT_MANTISSA_BITS + 1 top-most bits (+1 for |
| // the implicit leading one in IEEE format). We therefore choose a |
| // binary output exponent of |
| // log2(m10 * 10^e10) - (FLOAT_MANTISSA_BITS + 1). |
| // |
| // We use floor(log2(5^e10)) so that we get at least this many bits; better to |
| // have an additional bit than to not have enough bits. |
| e2 = floor_log2(m10) |
| .wrapping_add(e10 as u32) |
| .wrapping_add(log2_pow5(e10) as u32) |
| .wrapping_sub(f2s::FLOAT_MANTISSA_BITS + 1) as i32; |
| |
| // We now compute [m10 * 10^e10 / 2^e2] = [m10 * 5^e10 / 2^(e2-e10)]. |
| // To that end, we use the FLOAT_POW5_SPLIT table. |
| let j = e2 |
| .wrapping_sub(e10) |
| .wrapping_sub(ceil_log2_pow5(e10)) |
| .wrapping_add(f2s::FLOAT_POW5_BITCOUNT); |
| debug_assert!(j >= 0); |
| m2 = mul_pow5_div_pow2(m10, e10 as u32, j); |
| |
| // We also compute if the result is exact, i.e., |
| // [m10 * 10^e10 / 2^e2] == m10 * 10^e10 / 2^e2. |
| // This can only be the case if 2^e2 divides m10 * 10^e10, which in turn |
| // requires that the largest power of 2 that divides m10 + e10 is |
| // greater than e2. If e2 is less than e10, then the result must be |
| // exact. Otherwise we use the existing multiple_of_power_of_2 function. |
| trailing_zeros = |
| e2 < e10 || e2 - e10 < 32 && multiple_of_power_of_2_32(m10, (e2 - e10) as u32); |
| } else { |
| e2 = floor_log2(m10) |
| .wrapping_add(e10 as u32) |
| .wrapping_sub(ceil_log2_pow5(-e10) as u32) |
| .wrapping_sub(f2s::FLOAT_MANTISSA_BITS + 1) as i32; |
| |
| // We now compute [m10 * 10^e10 / 2^e2] = [m10 / (5^(-e10) 2^(e2-e10))]. |
| let j = e2 |
| .wrapping_sub(e10) |
| .wrapping_add(ceil_log2_pow5(-e10)) |
| .wrapping_sub(1) |
| .wrapping_add(f2s::FLOAT_POW5_INV_BITCOUNT); |
| m2 = mul_pow5_inv_div_pow2(m10, -e10 as u32, j); |
| |
| // We also compute if the result is exact, i.e., |
| // [m10 / (5^(-e10) 2^(e2-e10))] == m10 / (5^(-e10) 2^(e2-e10)) |
| // |
| // If e2-e10 >= 0, we need to check whether (5^(-e10) 2^(e2-e10)) |
| // divides m10, which is the case iff pow5(m10) >= -e10 AND pow2(m10) >= |
| // e2-e10. |
| // |
| // If e2-e10 < 0, we have actually computed [m10 * 2^(e10 e2) / |
| // 5^(-e10)] above, and we need to check whether 5^(-e10) divides (m10 * |
| // 2^(e10-e2)), which is the case iff pow5(m10 * 2^(e10-e2)) = pow5(m10) |
| // >= -e10. |
| trailing_zeros = (e2 < e10 |
| || (e2 - e10 < 32 && multiple_of_power_of_2_32(m10, (e2 - e10) as u32))) |
| && multiple_of_power_of_5_32(m10, -e10 as u32); |
| } |
| |
| // Compute the final IEEE exponent. |
| let mut ieee_e2 = i32::max(0, e2 + FLOAT_EXPONENT_BIAS as i32 + floor_log2(m2) as i32) as u32; |
| |
| if ieee_e2 > 0xfe { |
| // Final IEEE exponent is larger than the maximum representable; return |
| // +/-Infinity. |
| let ieee = ((signed_m as u32) << (f2s::FLOAT_EXPONENT_BITS + f2s::FLOAT_MANTISSA_BITS)) |
| | (0xff_u32 << f2s::FLOAT_MANTISSA_BITS); |
| return Ok(f32::from_bits(ieee)); |
| } |
| |
| // We need to figure out how much we need to shift m2. The tricky part is |
| // that we need to take the final IEEE exponent into account, so we need to |
| // reverse the bias and also special-case the value 0. |
| let shift = if ieee_e2 == 0 { 1 } else { ieee_e2 as i32 } |
| .wrapping_sub(e2) |
| .wrapping_sub(FLOAT_EXPONENT_BIAS as i32) |
| .wrapping_sub(f2s::FLOAT_MANTISSA_BITS as i32); |
| debug_assert!(shift >= 0); |
| |
| // We need to round up if the exact value is more than 0.5 above the value |
| // we computed. That's equivalent to checking if the last removed bit was 1 |
| // and either the value was not just trailing zeros or the result would |
| // otherwise be odd. |
| // |
| // We need to update trailing_zeros given that we have the exact output |
| // exponent ieee_e2 now. |
| trailing_zeros &= (m2 & ((1_u32 << (shift - 1)) - 1)) == 0; |
| let last_removed_bit = (m2 >> (shift - 1)) & 1; |
| let round_up = last_removed_bit != 0 && (!trailing_zeros || ((m2 >> shift) & 1) != 0); |
| |
| let mut ieee_m2 = (m2 >> shift).wrapping_add(round_up as u32); |
| debug_assert!(ieee_m2 <= 1_u32 << (f2s::FLOAT_MANTISSA_BITS + 1)); |
| ieee_m2 &= (1_u32 << f2s::FLOAT_MANTISSA_BITS) - 1; |
| if ieee_m2 == 0 && round_up { |
| // Rounding up may overflow the mantissa. |
| // In this case we move a trailing zero of the mantissa into the |
| // exponent. |
| // Due to how the IEEE represents +/-Infinity, we don't need to check |
| // for overflow here. |
| ieee_e2 += 1; |
| } |
| let ieee = ((((signed_m as u32) << f2s::FLOAT_EXPONENT_BITS) | ieee_e2) |
| << f2s::FLOAT_MANTISSA_BITS) |
| | ieee_m2; |
| Ok(f32::from_bits(ieee)) |
| } |
