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0ceaaa27c4- a * b + c is two roundings on every processor and --cpu: the IR has no fast-math flags, and clang compiles it with -ffp-contract=on (checked in the assembly: never fused, also with FMA hardware) - fma(a, b, c) / v.fma(b, c): one rounding, always (llvm.fma) - muladd(a, b, c) / v.muladd(b, c): the fastest way here (llvm.fmuladd), what v.fma was before - f32_bits / f32_from_bits / f64_bits / f64_from_bits: bitcasts, also of vectors - f16_to_f32 / f32_to_f16 (LLVM half), bf16_to_f32 / f32_to_bf16 (integer ops, ties to even, NaN kept) - docs (en, pl): what is guaranteed about floats, the new built-ins Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Psc42moPLwP43Cmb9oZqSR
31 lines
1.4 KiB
Text
31 lines
1.4 KiB
Text
// a * b + c is never fused; fma rounds once; numbers as their bits; f16 and bf16
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fn plain(float a, float b, float c) -> float {
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return a * b + c
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}
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fn main() {
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// 0.1 * 10 is 1.0000000000000000555..., which rounds to 1 before the - 1 (two roundings), but not inside fma
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print(plain(0.1, 10.0, -1.0), fma(0.1, 10.0, -1.0))
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print(fma(f32(0.1), 10.0, -1.0), fma(2, 3, 4))
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m := muladd(1.5, 2.0, 0.25) // fused or not, exact here
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print(m, f32x4(1.5).muladd(2.0, 0.25), fma(f32x4(0.1), 10.0, f32x4(-1.0))[0])
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det := f32x4(0.1) * f32x4(10.0) - f32x4(1.0)
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print(det[0])
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// bits
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print(f32_bits(1.0), f64_bits(1.0), f32_bits(-0.0))
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print(f32_from_bits(0x40490fdb), f64_from_bits(f64_bits(2.5)), f32_from_bits(i32(-1082130432)))
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u32 inf = 0x7f800000
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print(f32_from_bits(inf), f32_bits(f32x4(1.0, 2.0, -2.0, 0.5)))
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// f16
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print(f16_to_f32(0x3c00), f16_to_f32(0xc000), f16_to_f32(0x7bff), f16_to_f32(0x0001))
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print(f32_to_f16(0.1), f32_to_f16(65504.0), f32_to_f16(1.0e6), f16_to_f32(f32_to_f16(0.333)))
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print(f16_to_f32(u16x8(0x3c00, 0x4000, 0x4200, 0x4400, 0, 0x8000, 0x3800, 0x3400)))
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// bf16
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print(bf16_to_f32(0x3f80), bf16_to_f32(0x4049), f32_to_bf16(3.14159))
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print(f32_to_bf16(f32_from_bits(0x3f808000)), f32_to_bf16(f32_from_bits(0x3f818000)), f32_to_bf16(f32_from_bits(0x7fc00001)))
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print(f32_to_bf16(f32x4(1.0, -2.0, 0.5, 3.14159)), bf16_to_f32(u16x4(0x3f80, 0xc000, 0x3f00, 0x4049)))
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}
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