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FATANHA

Operation

Approximates hyperbolic arctangent for finite source magnitudes at most one.

Assembler Syntax

FATANHA.{S|D}(z) Fn(s), Fn(d)

Privilege

Unprivileged

Required CPUID flags

FP

FPTRANSA

Repeat eligibility

REP eligible

Computes the \(\operatorname{atanh}(x)\) reference over finite \(x\) with \(|x| \le 1\) after DAZ and writes an implementation-bounded S- or D-format approximation under the selected FPTRANSA accuracy contract.

The required FPTRANSA_ACCURACY contract is 0x0024.

Special values

  • Zero source: the result is the source.

  • Source \(+1\) or \(-1\) generates DZ and returns infinity with the source sign.

  • A finite source with magnitude greater than one, or either infinity, generates NV and produces the architectural default quiet NaN.

Exact anchors

  • \(\operatorname{atanh}(+0) = +0\)

  • \(\operatorname{atanh}(-0) = -0\)

  • \(\operatorname{atanh}(\mathord{\pm}1) = \mathord{\pm}\infty\)

Required properties

  • odd

  • monotonically increasing on \((-1, 1)\)

2.75in

Encodings

FATANHA.{S|D}(z) Fn(s), Fn(d)

Format: Instruction format for FATANHA.{S|D}(z) Fn(s), Fn(d)

Format: Instruction format for FATANHA.{S|D}(z) Fn(s), Fn(d)