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1//===-- funder.c - Handle single-precision floating-point underflow -------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8//9// This helper function is available for use by single-precision float10// arithmetic implementations to handle underflowed output values, if they were11// computed in the form of a normalized mantissa and an out-of-range exponent.12//13// On input: x should be a complete IEEE 754 floating-point value representing14// the desired output scaled up by 2^192 (the same value that would have been15// passed to an underflow trap handler in IEEE 754:1985).16//17// This isn't enough information to re-round to the correct output denormal18// without also knowing whether x itself has already been rounded, and which19// way. 'errsign' gives this information, by indicating the sign of the value20// (true result - x). That is, if errsign > 0 it means the true value was21// larger (x was rounded down); if errsign < 0 then x was rounded up; if22// errsign == 0 then x represents the _exact_ desired output value.23//24//===----------------------------------------------------------------------===//25 26#include <stdint.h>27 28#define SIGNBIT 0x8000000029#define MANTSIZE 2330#define BIAS 0xc031 32uint32_t __compiler_rt_funder(uint32_t x, uint32_t errsign) {33 uint32_t sign = x & SIGNBIT;34 uint32_t exponent = (x << 1) >> 24;35 36 // Rule out exponents so small (or large!) that no denormalisation37 // is needed.38 if (exponent > BIAS) {39 // Exponent 0xc1 or above means a normalised number got here by40 // mistake, so we just remove the 0xc0 exponent bias and go41 // straight home.42 return x - (BIAS << MANTSIZE);43 }44 uint32_t bits_lost = BIAS + 1 - exponent;45 if (bits_lost > MANTSIZE + 1) {46 // The implicit leading 1 of the intermediate value's mantissa is47 // below the lowest mantissa bit of a denormal by at least 2 bits.48 // Round down to 0 unconditionally.49 return sign;50 }51 52 // Make the full mantissa (with leading bit) at the top of the word.53 uint32_t mantissa = 0x80000000 | (x << 8);54 // Adjust by 1 depending on the sign of the error.55 mantissa -= errsign >> 31;56 mantissa += (-errsign) >> 31;57 58 // Shift down to the output position, keeping the bits shifted off.59 uint32_t outmant, shifted_off;60 if (bits_lost == MANTSIZE + 1) {61 // Special case for the exponent where we have to shift the whole62 // of 'mantissa' off the bottom of the word.63 outmant = 0;64 shifted_off = mantissa;65 } else {66 outmant = mantissa >> (8 + bits_lost);67 shifted_off = mantissa << (32 - (8 + bits_lost));68 }69 70 // Re-round.71 if (shifted_off >> 31) {72 outmant++;73 if (!(shifted_off << 1))74 outmant &= ~1; // halfway case: round to even75 }76 77 return sign | outmant;78}79