amiga-bootcamp/11_libraries/mathffp.md
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← Home · Libraries

Math Libraries — Floating Point

Overview

AmigaOS provides multiple math libraries for floating-point operations. The 68000 has no FPU, so all math is done in software unless a 68881/68882/68040/68060 FPU is present.


Library Stack

Library Format Description
mathffp.library FFP (Motorola Fast Floating Point) Original Amiga format (32-bit)
mathieeesingbas.library IEEE 754 single (32-bit) IEEE single precision
mathieeedoubbas.library IEEE 754 double (64-bit) IEEE double precision
mathtrans.library FFP Transcendental functions (sin, cos, sqrt)
mathieeesingtrans.library IEEE single IEEE single transcendentals
mathieeedoubtrans.library IEEE double IEEE double transcendentals

FFP Format

Motorola FFP is NOT IEEE 754:

Bits 318: 24-bit mantissa (normalised, implicit 1.xxx)
Bits  71: 7-bit exponent (excess-64)
Bit     0: sign (0=positive, 1=negative)

Using IEEE Math

struct Library *MathIeeeSingBasBase =
    OpenLibrary("mathieeesingbas.library", 0);

float a = 3.14f;
float b = 2.0f;
float c = IEEESPMul(a, b);  /* 6.28 */
float d = IEEESPAdd(a, b);  /* 5.14 */
float e = IEEESPDiv(a, b);  /* 1.57 */

CloseLibrary(MathIeeeSingBasBase);

68881/68882 FPU

When an FPU is present, the math libraries are replaced with ROM patches that use native FPU instructions. The application code is identical — the library transparently switches to hardware.

if (SysBase->AttnFlags & AFF_68881) {
    /* 68881/68882 FPU present */
}
if (SysBase->AttnFlags & AFF_FPU40) {
    /* 68040 internal FPU */
}

References

  • NDK39: libraries/mathffp.h, libraries/mathieeesp.h