API Reference

Function	Signature	Description
`simd_f128_from_double`	`simd_f128 simd_f128_from_double(double d)`	Promote a `double` to 128-bit. `lo` is initialised to `0.0`.
`simd_f128_extract`	`void simd_f128_extract(simd_f128 x, double* hi, double* lo)`	Extract the `hi` and `lo` components into separate doubles.
`simd_f128_add`	`simd_f128 simd_f128_add(simd_f128 a, simd_f128 b)`	Double-Double addition via Knuth's TwoSum.
`simd_f128_sub`	`simd_f128 simd_f128_sub(simd_f128 a, simd_f128 b)`	Double-Double subtraction (negates `b`, then adds).
`simd_f128_mul`	`simd_f128 simd_f128_mul(simd_f128 a, simd_f128 b)`	Double-Double multiplication via Dekker's TwoProd + FMA.
`simd_f128_div`	`simd_f128 simd_f128_div(simd_f128 a, simd_f128 b)`	Double-Double division via Newton-Raphson reciprocal refinement.
`simd_f128_sqrt`	`simd_f128 simd_f128_sqrt(simd_f128 x)`	Square root via inverse-sqrt Newton-Raphson + residual correction.

Function	Signature	Description
`simd_f128_print`	`void simd_f128_print(simd_f128 x)`	Print the value to `stdout` followed by a newline.
`simd_f128_to_string`	`void simd_f128_to_string(char* buf, size_t buf_size, simd_f128 x)`	Write up to 32 decimal digits into `buf`. `buf` must be at least 64 bytes. Handles `nan`, `inf`, and negative values.

Function	Signature	Description
`simd_f128_exp`	`simd_f128 simd_f128_exp(simd_f128 x)`	`e^x`. Returns `+Inf` for `x > 709.78`, `0` for `x < -745`.
`simd_f128_log`	`simd_f128 simd_f128_log(simd_f128 x)`	Natural logarithm. Returns `NaN` for `x ≤ 0`.
`simd_f128_pow`	`simd_f128 simd_f128_pow(simd_f128 base, simd_f128 exp)`	`base^exp`. Correctly handles base zero, infinity, and NaN according to IEEE-754.
`simd_f128_sin`	`simd_f128 simd_f128_sin(simd_f128 x)`	Sine (radians). Best accuracy for moderate arguments.
`simd_f128_cos`	`simd_f128 simd_f128_cos(simd_f128 x)`	Cosine (radians). Best accuracy for moderate arguments.
`simd_f128_sincos`	`void simd_f128_sincos(simd_f128 x, simd_f128* s, simd_f128* c)`	Computes sine and cosine simultaneously.

Function	Signature	Description
`simd_f128_cmp`	`int simd_f128_cmp(simd_f128 a, simd_f128 b)`	Returns `-1` if `a < b`, `1` if `a > b`, `0` if equal.
`simd_f128_eq`	`int simd_f128_eq(simd_f128 a, simd_f128 b)`	`1` if `a == b`.
`simd_f128_gt`	`int simd_f128_gt(simd_f128 a, simd_f128 b)`	`1` if `a > b`.
`simd_f128_lt`	`int simd_f128_lt(simd_f128 a, simd_f128 b)`	`1` if `a < b`.
`simd_f128_ge`	`int simd_f128_ge(simd_f128 a, simd_f128 b)`	`1` if `a >= b`.
`simd_f128_le`	`int simd_f128_le(simd_f128 a, simd_f128 b)`	`1` if `a <= b`.
`simd_f128_abs`	`simd_f128 simd_f128_abs(simd_f128 x)`	Absolute value. Correctly handles `-0.0` in the `lo` component.
`simd_f128_min`	`simd_f128 simd_f128_min(simd_f128 a, simd_f128 b)`	Returns the lesser of `a` and `b`.
`simd_f128_max`	`simd_f128 simd_f128_max(simd_f128 a, simd_f128 b)`	Returns the greater of `a` and `b`.

Function	Signature	Description
`simd_f128_complex_add`	`simd_f128_complex simd_f128_complex_add(a, b)`	Complex addition.
`simd_f128_complex_sub`	`simd_f128_complex simd_f128_complex_sub(a, b)`	Complex subtraction.
`simd_f128_complex_mul`	`simd_f128_complex simd_f128_complex_mul(a, b)`	Complex multiplication.
`simd_f128_complex_div`	`simd_f128_complex simd_f128_complex_div(a, b)`	Complex division.
`simd_f128_complex_abs_sqr`	`simd_f128 simd_f128_complex_abs_sqr(a)`	Absolute square magnitude (`real^2 + imag^2`).
`simd_f128_complex_abs`	`simd_f128 simd_f128_complex_abs(a)`	Magnitude (absolute value).
`simd_f128_complex_arg`	`simd_f128 simd_f128_complex_arg(a)`	Phase angle (argument).
`simd_f128_complex_conj`	`simd_f128_complex simd_f128_complex_conj(a)`	Complex conjugate.

Vectorized 4-lane operations (simd_f128x4) using pure AVX2 (fallback provided).

Function	Signature	Description
`simd_f128x4_from_doubles`	`simd_f128x4 simd_f128x4_from_doubles(d0, d1, d2, d3)`	Initialize parallel vector.
`simd_f128x4_add`	`simd_f128x4 simd_f128x4_add(a, b)`	Parallel addition.
`simd_f128x4_sub`	`simd_f128x4 simd_f128x4_sub(a, b)`	Parallel subtraction.
`simd_f128x4_mul`	`simd_f128x4 simd_f128x4_mul(a, b)`	Parallel multiplication.
`simd_f128x4_div`	`simd_f128x4 simd_f128x4_div(a, b)`	Parallel division.
`simd_f128x4_sqrt`	`simd_f128x4 simd_f128x4_sqrt(a)`	Parallel square root.

Function	Signature	Description
`simd_f128_array_add`	`void simd_f128_array_add(a, b, out, len)`	Batch add two arrays.
`simd_f128_array_sub`	`void simd_f128_array_sub(a, b, out, len)`	Batch subtract two arrays.
`simd_f128_array_mul`	`void simd_f128_array_mul(a, b, out, len)`	Batch multiply two arrays.
`simd_f128_array_div`	`void simd_f128_array_div(a, b, out, len)`	Batch divide two arrays.

Symbol	Kind	Description
`f128::float128`	Class	C++ wrapper around `simd_f128`.
`f128::float128(double)`	Constructor	Construct from a `double`.
`f128::float128(simd_f128)`	Constructor	Construct from a raw `simd_f128`.
`float128::extract(hi, lo)`	Method	Extract `hi` and `lo` components.
`+`, `-`, `*`, `/`	Operators	Arithmetic operators.
`+=`, `-=`, `*=`, `/=`	Operators	Compound assignment operators.
`==`, `!=`, `<`, `>`, `<=`, `>=`	Operators	Comparison operators.
`operator-()`	Unary	Negation.
`float128::to_string()`	Method	Returns `std::string` with 32-digit representation.
`operator<<`	Stream	`std::ostream` integration.
`f128::exp`, `f128::log`, `f128::pow`	Free functions	Transcendental math.
`f128::sin`, `f128::cos`, `f128::sqrt`, `f128::abs`	Free functions	Trigonometric and utility math.
`f128::pi`, `f128::e`, `f128::sqrt2`, `f128::ln2`	Constants	High-precision constants as `float128`.

Provides standard interoperability for complex numbers.

Symbol	Description
`std::complex<f128::float128>`	Fully supported via standard `std::complex` template.

Provides matrix traits for the Eigen linear algebra library.

Symbol	Description
`Eigen::NumTraits<f128::float128>`	Allows `float128` to be used directly in `Eigen::Matrix`.