Floating-point to Integer Conversion Overview

IEEE 754 does not specify what results are obtained when converting a NaN or out-of-range floating-point value to integer, so different programming languages and ISAs have made different choices. The different conversion modes supported by the cffpr instruction are as follows:

  • P-Type:

    Used by most other PowerISA instructions, as well as commonly used floating-point to integer conversions on x86.

  • S-Type:

    Used for several notable programming languages:

    • Java's conversion from float/double to long/int1
    • Rust's as operator2
    • LLVM's llvm.fptosi.sat3 and llvm.fptoui.sat4 intrinsics
    • SPIR-V's OpenCL dialect's OpConvertFToU5 and OpConvertFToS6 instructions when decorated with the SaturatedConversion7 decorator.
    • Also WebAssembly's trunc_sat_u8 and trunc_sat_s9 instructions,

  • E-Type:

    Used for ECMAScript's ToInt32 abstract operation10. Also implemented in ARMv8.3A as the FJCVTZS instruction11.

Floating-point to Integer Conversion Semantics Summary

Let round be the result of bfp_ROUND_TO_INTEGER(rmode, input). Let w be the number of bits in the result's type. The result of Floating-point to Integer conversion is as follows:

+------+------+---------------------------------------------------------------+
|Type| Result | Category of rounding                                          |
|    | Sign   +----------+-----------+----------+-----------+---------+-------+
|    |        | NaN      | +Inf      | -Inf     | > Max     | < Min   | Else  |
|    |        |          |           |          | Possible  | Possible|       |
|    |        |          |           |          | Result    | Result  |       |
+----+--------+----------+-----------+----------+-----------+---------+-------+
|  P |Unsigned| 0        | 2^w - 1   | 0        | 2^w - 1   | 0       | round |
|    +--------+----------+-----------+----------+-----------+---------+-------+
|    | Signed | -2^(w-1) | 2^(w-1)-1 | -2^(w-1) | 2^(w-1)-1 | -2^(w-1)| round |
+----+--------+----------+-----------+----------+-----------+---------+-------+
|  S |Unsigned| 0        | 2^w - 1   | 0        | 2^w - 1   | 0       | round |
|    +--------+----------+-----------+----------+-----------+---------+-------+
|    | Signed | 0        | 2^(w-1)-1 | -2^(w-1) | 2^(w-1)-1 | -2^(w-1)| round |
+----+--------+----------+-----------+----------+-----------+---------+-------+
|  E | Either | 0                               | round & (2^w - 1)           |
+----+--------+---------------------------------+-----------------------------+
  1. Java float/double to long/int conversion: https://docs.oracle.com/javase/specs/jls/se16/html/jls-5.html#jls-5.1.3↩
  2. Rust's as operator: https://doc.rust-lang.org/1.70.0/reference/expressions/operator-expr.html#numeric-cast↩
  3. LLVM's llvm.fptosi.sat intrinsic: https://llvm.org/docs/LangRef.html#llvm-fptosi-sat-intrinsic↩
  4. LLVM's llvm.fptoui.sat intrinsic: https://llvm.org/docs/LangRef.html#llvm-fptoui-sat-intrinsic↩
  5. SPIR-V's OpConvertFToU instruction: https://www.khronos.org/registry/spir-v/specs/unified1/SPIRV.html#OpConvertFToU↩
  6. SPIR-V's OpConvertFToS instruction: https://www.khronos.org/registry/spir-v/specs/unified1/SPIRV.html#OpConvertFToS↩
  7. SPIR-V's SaturatedConversion decorator:
    https://www.khronos.org/registry/spir-v/specs/unified1/SPIRV.html#_a_id_decoration_a_decoration↩
  8. WASM's trunc_sat_u: https://webassembly.github.io/spec/core/exec/numerics.html#op-trunc-sat-u↩
  9. WASM's trunc_sat_s: https://webassembly.github.io/spec/core/exec/numerics.html#op-trunc-sat-s↩
  10. ECMAScript's ToInt32 abstract operation: https://262.ecma-international.org/14.0/#sec-toint32↩
  11. ARM's FJCVTZS instruction: https://developer.arm.com/documentation/dui0801/g/hko1477562192868↩